Thermal model of highway overpass bridge
by Tylar Paul Bunger
A thesis submitted in partial fulfillment of the requirements for the degree of Master of Science in
Mechanical Engineering
Montana State University
© Copyright by Tylar Paul Bunger (2003)
Abstract:
A model was developed to calculate the time varying temperature of a highway overpass bridge. This
model geometry was drawn using a three-dimensional CAD program, which was also used to discretize
the mode’s geometry into a mesh. This meshed geometry was then imported into RadThemVRT for
thermal analysis. RadThemVRT is a multi-mode finite differencing heat transfer code. Conduction,
wind convection, solar radiation which can account for shadowing and long wave radiation are the heat
transfer modes accounted for by the software. The meshed geometry had material properties assigned
to it, including; density, specific heat and thermal conductivity. In addition surface properties were
applied, including; emissivity and absorptivity. Emissivity is a measure of how well a body emits
thermal radiation and absorptivity is a measure of how well a body absorbs thermal radiation. In
addition an instrumentation and data acquisition system were developed for measuring model inputs.
Model inputs measured were; air temp (deg C), wind speed (m/s), wind direction (deg), barometric
pressure (mmhg), relative humidity (%), total global solar radiation flux (W/m2), diffuse solar radiation
(W/m2) and sky temperature (deg C). These values were measured over extended time periods, with
five minute time steps. These inputs were then formatted for input into RadThemVRT. In addition to
these parameters a single non-contact surface temperature was measured on the bridge deck (deg C) for
use in comparing to the computer solution. A convergence study was also performed to analyze how
mesh size and settings in RadThemVRT affect the accuracy of the solution. Two parameters were
varied; the size of the elements used in the bridge mesh and a setting used in the program for
calculation of view factors. Results of the convergence study reinforce the idea that the accuracy does
increase with increasing the number of elements and increasing the view factor settings. The overall
accuracy of the model was found to be adequate to justify further study and development of model. The
overall conclusion is that the model is accurate in modeling the time varying surface temperature
conditions that a bridge deck experiences. THERMAL MODEL OF HIGHWAY OVERPASS BRIDGE
by
Tylar Paul Bunger
A thesis submitted in partial fulfillment
of the requirements for the degree
of
Master of Science
in
Mechanical Engineering
MONTANA STATE UNIVERSITY - BOZEMAN
Bozeman, Montana
August, 2003
N3?<P
QPS3
ll
APPROVAL
of a thesis submitted by
Tylar Paul Bunger
This thesis has been read by each member of the thesis committee and has been
found to be satisfactory regarding content, English usage, format, citations,
bibliographic style, and consistency, and is ready for submission to the College of
Graduate Studies.
3-
Dr. Edward Adams
(Signature)
Date
Approved for the Department of Mechanical and Industrial
Engineering
Dr. Vic Cundy
Approved for the College of Graduate Studies
Dr. Bruce R Mcleod
(Signature)y
Date
~£OQ-3>
STATEMENT OF PERMISSION TO USE
In presenting this thesis in partial fulfillment of the requirements for a master’s
degree at Montana State University - Bozeman, I agree that the library shall make it
available to borrowers under rules of the Library.
If I have indicated my intention to copyright this thesis by including a copyright
notice page, copying is allowable only for scholarly purposes, consistent with “fair
use” as prescribed in the U.S. Copyright Law. Requests for permission for extended
quotation from or reproduction of this thesis (paper) in whole or in parts may be
granted only by the copyright holder.
Signature_
Date
____
hz./'t
?
© COPYRIGHT
by
Tylar Paul Hunger
2003
All Rights Reserved
ACKNOWLEDGEMENTS
I would like to thank my advisor Dr. Ed Adams for his guidance and advising. I
would also like to thank Ladean McKittrick whose help made this thesis possible.
V
TABLE OF CONTENTS
1. INTRODUCTION...........................................................................................................I
2. BACKGROUND........................................................................................................... 12
Current Thermal M apping ...................................................................................... 12
Rad Therm/R T .............................................................................................................. 13
Instrumentation ..................................................
15
Coastal Environmental WEATHERRAK............................................................. 16
Licor pyranometer....................................................................................................16
EpplyPIR..................................................................................................................19
Handheld Infrared Thermometer........................
20
M aterial Properties............................ '......... .......................................................... 21
Specific Heat............................................................................................................21
Thermal Conductivity............................................................................................ 23
Density..................................................................................................................... 24
Thermal diffusivity.................................................................................................24
Surface Properties...........................................................
24
Emissivity................................................................................................................ 25
Absorptivity............................................................................................................ 25
Governing Equations for Heat Transfer Problem ........................................ 26
Heat and M ass Transfer Principles........................
27
Conduction..........................................
27
Convection............................................................................................................ -2 8
Radiation Heat Transfer......................................................................................... 29
Radiation View Factors.......................................................................................... 31
Enclosure Theory.................................................................................................... 33
Solar Radiation.......... ........................................
36
3. METHODOLOGY.......................................................................................... - ......... 37
Rhino3D M odel ...........................................................................................................37
Bridge Models..........................................................................................................37
Terrain M esh............................................................................................................42
RADTHERM/RT Thermal Analysis S oftware ..................................................... 42
Governing Equations Rad Therm R T ....................................................................45
Standard Elements..................................................................................................45
Three Layer Elements...................................
50
Terrain Elements........................................
50
Concrete and Asphalt Models.................................
53
Foliage Models.........................................................................................................56
Background Elements and Sky Elements............................................................ 57
Element Definitions in RadThermRT...................................................................58
Vl
V iew.Factor Calculation in Rad Therm/R T .......................................................59
View Factor Setting................................................................................................ 59
View Factor Element Divison Setting..................................................................60
Apparent Area Resolution View Factor Setting................................................. 61
Solution to Temperature Distribution 1................................................................. 62
Experiment Method....................................................................................... ;...... 63
D ata formatting......................
66
Solar Data Formatting.....................................
67
70
Meteorological Data Formatting.............
Initialization..............................................
72
4. RESULTS AND FINDINGS....................................................................................... 75
Convergence Study Results..................
75
A dditional Results ................................................................................................... 86
Shadowing................................
88
Longwave d a t a .......................................
95
Instrumentation Issues..........................
97
5.
CONCLUSIONS AND RECOMMENDATIONS ......... ...............
99
REFERENCES...............................................................................................
104
APPENDICES..........................................
108
APPENDIX A: W eather File D a t a ........................:...........................................109
APPENDIX B : M easured Temperature D a t a ................................................. 118
APPENDIX C: D ata from Rad Therm/RT simulations ................................. 123
Vll
LIST OF TABLES
Table
Page
1. Typical specific heats of concrete (partially reproduced from Table
6, Rhodes [1978])......................................................................................................23
2. Thermal conductivities of carbonate aggregate concrete.
Reproduced from results [Rhodes1987],[Vodak et. Al,] [T.Z.
Harwathy] [H.Abe, et al 1970]................................................................................... 23
3. Shortwave radiation definitions (Touloukian and Dewitt[1972] and
Pliiss [1997])............................................................................................................... 36
4. !TYPE for concrete and asphalt.............
53
5. Surface condition of pavement concrete nodes (ISURF)......................................
53
6. Surface condition for asphalt nodes (ISURF)..................
53
7. Moisture state IWET........................
53
8. Thermal properties for material groups...............................................
54
9. Multiplying factor for capacitance and conductance. Adapted from
ThermoAnalytics Terrain Model Technical Manual.................................................. 55
10. Definition of Material Groups.................................................................................... 55
11. Thickness definition for ITHK.............................................................
56
12. View factor settings......................
61
13. Apparent area settings. Adapted from RadTherm manual...;...................................... 61
14. Variables for the .XWA, files adapted from RadTherm User manual..............
67
15. Correction factors supplied by Li-Cor for correcting diffuse
readings taken with a shadow band............................................................................ 69
16. View factor settings value.......................................................................................... 76
viii
LIST OF TABLES - CONTINUED
Table
Page
17. Calculation times for view factors(VFC) and solution calculation
(SC) times for twelve hour simulations run on Silicon Graphics
Origin 2100 Server..................................................................................................... 79
18. Nighttime simulation statistics for April 7, 9:00pm through April 8,
8:55am with low view factor settings and varying element size...................... ;........ 82
19. Nighttime simulation statistics for April I, 9:00pm through April 8,
8:55am with default view factor settings and varying element size........................... 82
20. Nighttime simulation statistics for April 7, 9:00pm through April 8,
8:55am with high view factor settings and varying element size............................... 82
21. Daytime simulation statistics for April 8, 9:01 am through April 8,
8:46 pm with low view factor settings and varying element size............................... 83
22. Daytime simulation statistics for April 8, 9:01 am through April 8,
8:46 pm with default view factor settings and varying element size.......................... 83
23. Daytime simulation statistics for April 8, 9:01 am through April 8,
8:46 pm with high view factor settings and varying element size.............................. 83
24. Summary of results for simulations; March 13, 6:50 am to March
13, 6:45pm, April 7, 9:00 pm to April 8 8:55 am, April 8, 9:01 am
to April ,8 8:46 pm, April 8, 9:01 pm to April 9, 1:36 am with
default view factors and 3000 elements bridge mesh.................................................86
LIST OF FIGURES
Figure
Page
1. Bozeman pass RadThemVRT thermal model............................................................. 8
2. Meridian surface temperature and wind forecast of 1-90 Corridor............................. 13
3.
Coastal Environmental meteorological station..........................
4. Radiation instruments including two Li-Cor pyranometer and one
EpplyPIR........... ......................................................................
16
17
5. LI-200SA spectral response curve. Copied from LI-COR Terrestrial
Radiation Sensors [1986] with permission.................................................................. 18
6. Omega IR thermometer............................................................................................... 20
7. Spectmm of electromagnetic radiation highlighting thermal region
(values from Incropera and Dewitt [1996]).................................................................30
8. Geometry for exchange between finite areas (adapted from Siegel
and Howell [1992])..................................................................................................... 32
9. Example enclosure with N surfaces............................................................................ 33
10. Radiative terms on surface area A ...............................................................................35
11. Perspective view of terrain mesh.......... ......................................................................38
12. Top view of bridge meshes, (A) is the 10 elements bridge mesh, (B)
is the 300 elements bridge mesh and (C) is the 3000 elements
bridge mesh.....................................
38
13. Example of a Rhino3D polyline with several vertices................................
39
14. Steps in creation of 3000 elements bridge m esh, (A) bridge outline
is drawn using polylines, (B) polylines are drawn where supports
will be, (C). polylines drawn around outline of supports and
barriers, (D). close up of mesh showing aligned vertices, (E)
perspective of 3000 elements bridge mesh..................................................................40
LIST OF FIGURES - CONTINUED
Figure
Page
15. Cross section view showing simplification made on supports and
barriers, (A) is from bridge blue prints and (B) is the cross section
of modeled bridge..................................... ................................ ................................ 41
16. Polygon mesh detailed optionsfrom RbinoSD............................................................ 42
17. Standard element................................ ........................................................................ 46
18. Heat transfer modes into standard element................................................................. 46
19. Three layer elements...... ...................................
50
20. Terrain elements......................................................................................................... 52
21. Schematic representing foliage nodes, (taken from
ThermoAnalytics website).......................................................................................... 57
22. Terrain element definitions, (A) elements defined as Interstate
Asphalt, (B) elements defined as county road asphalt, (C) elements
defined as heavy concrete pads, (D) elements defined as short grass
foliage.............................................................
58
23. View factor calculation. (I) two meshes view each other, (2) a
hemisphere is constructed in each element and rays are cast
intersecting other elements, (3) showing all of the rays cast from a
single element. Graphics from ThermoAnalytics website.........................................60
24. WTI mobile lab with WeatherPak meterologicalstation deployed..............................65
25. Example of a portion of an extended weather format file......................
68
26. Description of data formatting method steps 1-4........................................................ 73
27. Description of data formatting method steps 5-7...................................................... ..74
28. Temperature comparison between measured temperature and
calculated temperature for daytime simulations run on data from
April 8 9:01 am to April 8 8:46 pm with Default view factor
settings; (A) results from the 3000 elements bridge mesh, (B)
results from the 300 elements bridge mesh and (C) results from the
10 elements bridge mesh............................................................................................. 78
LIST OF FIGURES - CONTINUED
Figure
Page
29. Correlation graph for 300 elements bridge mesh with high view
factor settings April 8, 9:01 am through April 8, 8:46 pm..........................................84
30. Correlation graph for 3000 elements bridge mesh with high view
factors from April 8, 9:01 am through April 8, 8:46 pm data.....................................84
31. Histogram graph of 300 elements bridge mesh data with high view
factors from April 8, 9:01 am through April 8, 8:46 pm data and
associated normal curve distribution........................................................................... 85
32. Histogram graph of 3000 elements bridge mesh data with high view
factors from April 8, 9:01 am through April 8, 8:46 pm and
associated normal curve distribution..........................................
85
33. Temperature comparison between measured temperature and
calculated temperature for March 13, 2003 with standard view
factor settings...............................................................................................................87
34. Temperature comparison between measured temperature and
calculated temperature for March 8-9 with standard view factor
setting.......................................................................................................................... 87
35. Shadowing on terrain below bridge with bridge hiddenfrom view.............................91
36. Shadowing on section of large element number mesh bridge..................................... 92
37. Temperature values for three elements lying in pedestrian walkway
from east to west. For large number of bridge elements bridge mesh
from April 8 daytime simulation................................................................................. 93
38. Solar flux values from April 8 daytime simulation indicating times
when values undergo rapid change due to varible shadowing
conditions....... ......................................
93
39. Temperature values for element lying in pedestrian walkway for
300 elements bridge mesh from April 8 daytime simulation...................................... 94
40. Layout of bridge geometry showing element edges and area of
bridge measurement.................................................................................................... 94
41. March 13 simulation with offset bad longwave data...................................................97
xii
/_
Figure
LIST OF FIGURES - CONTINUED
Page
42. March 13 simulation with Bozeman Pass RWIS longwave data.............................. 97
xiii
NOMENCLATURE
A
Area (m2)
-AAk
Apparent area that the radiation sees (m2)
Au
C
c
Surface area exposed to convection (m2)
Correction factor from Table 15
Speed of light (m/s)
Cp
Specific heat (J/kg-K).
Cp
Specific heat of the body (J/kg-K).
C rc
Specific heat reinforced concrete (J/kg-K).
Dc
Corrected diffuse radiation (W/m2)
Dl
Measured value of diffuse solar radiation (W/m2)
Eb
Emitted radiation (Watts)
Er
Rate that the real surface emits radiant energy (Watts)
Fj-k
G
View factor of area Aj that arrives at area Ak
h
Convection heat transfer coefficient (WZm2-K)
hk
k
Convection coefficient (WZm2-K)
Thermal conductivity (WZm-K)
Thermal conductivity of the material between thermal nodes j and k
(WZm-K)
Length (m)
kkj
L
Lfcj
m
Measured global solar radiation value (W/m2)
Geometric distance between node k and node j (m)
Mass of the body (kg)
Q
Mass of element k (kg)
Total number of surfaces
Total number of conduction links between node k and all adjacent
nodes
Net heat transfer rate (Watts)
Q=
Heat transfer rate carbonate Concrete (Watts)
irik
N
Ncond
Qcon
■Conduction heat transfer rate (Watts)
Qconv
Convection heat transfer rate (Watts)
QDiffR
Global diffuse radiation (Watts)
QnirR
Direct solar radiation (Watts)
xiv
Q gr
qi,k
Qj
Qk
Total global radiation (Watts)
Incident radiant energy from other elements in the enclosure
(W/m2)
Outgoing radiation (Watts)
Heat transfer rate from the surface or as the net radiative loss from the
surface to the
enclosure (Watts)
Qiw
Longwave radiation flux of the sky in Watts
Qmass,k
QnetSk
Defined for each different terrain application type (Watts)
Explicit heat transfer rate imposed by the short wave solar energy
(Watts)
Explicit term involving the amount of solar radiation node k is
receiving (Watts)
qoj
Outgoing radiative terms from the other areas (W/m2)
q0;k
Emitted plus the reflected radiant energy (W/m2)
Qrad
Radiation heat transfer rate (Watts)
Qradk
Net radiative loss from surface k (Watts)
Qrc
Heat transfer rate reinforced concrete (Watts)
Amount of solar radiation reflected into element k from all other
elements and the default
background element (Watts)
QnetS
Qref_in,k
Qrefput, k
Amount of solar radiation reflected out from node k (Watts)
Qs
Qs .
Heat transfer rate reinforced steel (Watts)
Total amount of solar radiation received including direct and diffuse
solar radiation (Watts)
Qsolar,k
Amount of solar radiation into node k (Watts)
Qt
Net rate of radiation from the smaller surface (Watts)
Tf
Heat rate by conduction through a plane wall of area A (Watts)
Length (m)
Independent variable time (seconds)
Bulk temperature of the fluid (Kelvin)
The temperature of the fluid that is convecting heat to or away from
Ak (Kelvin)
Ts
Temperature of the surface (Kelvin)
Tsur
VFk
Surface that surrounds the smaller surface (Kelvin)
Qx
s
t
Too
w
Visibility factor used for shadowing
Rate of work done (Watts)
RadTherm modeled values (Kelvin)
Actual temperature data (Kelvin)
Dependent variable
Absorptivity
Absorptivity of node k
Thermal diffusivity (m2/s)
Change in temperature (Kelvin)
Kronecker delta defined
When k = j
When
j
Emissivity
Angle)
Spectrum of wavelengths pm
Mean value of all of the modeled temperature readings (Kelvin)
Mean of the measured temperature (Kelvin)
Frequency
Density of the material (kg/m3)
Density concrete (kg/m3)
Reflectance .
Ak density steel (kg/m3)
Stefan-Boltzmann constant 5.67 X 10-8 (W/m21K4)
XVl
ABSTRACT
A model was developed to calculate the time varying temperature of a highway
overpass bridge. This model geometry was drawn using a three-dimensional CAD
program, which was also used to discretize the mode’s geometry into a mesh. This
meshed geometry was then imported into RadThemVRT for thermal analysis.
RadThemVRT is a multi-mode finite differencing heat transfer code. Conduction,
wind convection, solar radiation which can account for shadowing and long wave
radiation are the heat transfer modes accounted for by the software. The meshed
geometry had material properties assigned to it, including; density, specific heat and
thermal conductivity. In addition surface properties were applied, including; emissivity
and absorptivity. Emissivity is a measure of how well a body emits thermal radiation
and absorptivity is a measure of how well a body absorbs thermal radiation. In
addition an instrumentation and data acquisition system were developed for measuring
model inputs. Model inputs measured were; air temp (deg C), wind speed (nVs), wind
direction (deg), barometric pressure (mmhg), relative humidity (%), total global solar
radiation flux (W/m2), diffuse solar radiation (W/m2) and sky temperature (deg C).
These values were measured over extended time periods, with five minute time steps.
These inputs were then formatted for input into RadThemVRT. In addition to these
parameters a single non-contact surface temperature was measured on the bridge deck
(deg C) for use in comparing to the computer solution. A convergence study was also
performed to analyze how mesh size and settings in RadThemVRT affect the accuracy
of the solution. Two parameters were varied; the size of the elements used in the
bridge mesh and a setting used in the program for calculation of view factors. Results
of the convergence study reinforce the idea that the accuracy does increase with
increasing the number of elements and increasing the view factor settings. The overall
accuracy of the model was found to be adequate to justify further study and
development of model. The overall conclusion is that the model is accurate in
modeling the time varying surface temperature conditions that a bridge deck
experiences.
I
INTRODUCTION
Winter highway travel impacts the lives of everyone who lives in an area that
experiences road icing events. Icing on roads can present dangerous driving conditions,
which increase the rate of accidents, and slow down the transport of goods. This has wide
reaching economic costs. During the past ten years there have been advances in winter
highway maintenance in ice prevention on roadways. These methods require advance
warning of roadway temperatures that are approaching the freezing point of water.
Maintenance managers need time to plan and prepare for icing events. A system that can
help to predict the surface temperature of roadway surfaces requires multi-mode heat
transfer analysis. This coupled system of conduction, convection, and radiation heat
transfer, requires a numerical method of solution. The radiative portion plays a major role
in the surface temperature of roadways.
A model that can predict surface temperatures while accounting for all forms of
radiation, would be an advance on current road temperature forecasting, which focus on
metrological factors, and often do not adequately account for radiation modes of heat
transfer [Ballard et al 2002]. In this thesis the thermal modeling software, RadThemVRT
(Radiation based Thermal model for Road Temperature), is used to calculate the surface
temperature of a highway overpass bridge, and the neighboring roadways and terrain. To
evaluate the performance of the software, this evaluation was carried out by measuring
the data inputs to the model and concurrently measuring the surface temperatures of the
bridge deck at a single point. Twelve to thirty six hour data collection periods were
carried out on, a highway overpass bridge. Input to the model includes meteorological
2
data and solar radiation parameters including; long-wave radiation, short-wave solar
radiation, and diffuse solar radiation.
Winter highway maintenance is primarily the responsibility of state and
municipality Departments of Transportation (DOT). Montana’s Maintenance provider is
the Montana Deptartment Of Transportation, MDT. Among their winter maintenance
tasks are plowing roads and applying chemicals and abrasives to roads. In order to
efficiently use resources, they maintain extensive information, communication, and
weather monitoring systems.
A common procedure of traditional snow and ice control practice is to wait until
an inch or more of snow accumulates on the pavement before beginning to plow and treat
the highway with chemicals or abrasives [Boselly 2001]. While this procedure is
straightforward, it frequently leads to a compacted snow layer (pack) that is tightly
bonded to the pavement surface. A subsequent “deicing” of the pavement is then
necessary, usually requiring a large quantity of deicing chemicals, and abrasives to work
their way through the pack to reach the snow/pavement interface and destroy or weaken
the bond [Ketcham et al 1996]. The abrasive is often mixed with a solution of deicing
chemicals. These chemicals help the sand to penetrate into the compressed snow or ice on
the roadbed. The most commonly used deicing chemical is sodium chloride [Gray- Fisher
2000] . One of the major problems of waiting until after precipitation has already fallen, is
the strong bond that can form between the road and the precipitation. Boselly [2001]
reports that after a bond has formed it takes five times more energy to remove the snow
or ice from the road surface. If the bond could be prevented from forming then the snow
3
or ice could be removed more efficiently and fewer chemicals would be required. Once
the bond has formed a large amount of chemical deicers must be used to break down this
bond. A standard application rate of salt for deicing is around 300 lbs per lane mile
[Ketcham et al 1996]. Among the environmental and economic impacts of highway salt
usage are, poisoning roadside vegetation, increasing concentrations in adjacent
waterways, and corrosion to vehicles [Ketcham et al 1996]. There are also some air
quality concerns with the use of abrasives; cities that struggle with EPA regulations on
clean air standards often ban the use of abrasives [Nixon 2001]. The abrasives are ground
up when driven over and increase the amount of particulates in the air. A method that
prevents the bonding of ice to pavement can reduce the amount of chemicals used and
remove the need for applications of abrasives, providing for a more efficient method for
removal of snow/ice.
Anti-icing is a strategy in winter highway maintenance that has been growing in
support for the last decade [Boselly 2001]. Anti-icing is the snow and ice control practice
of preventing the formation or development of bonds between precipitation and the road
surface, by timely application of chemical freezing-point depressants. It involves
maintenance crews getting out before or during the onset of a winter storm to apply liquid
brine to the surface of the roads that could have ice formation. The most common
chemical in use today in anti-icing is magnesium chloride [Gray-Fisher 2000]. This brine
mixes with the snow/ice at the surface of the road effectively lowering the freezing point
of the mixture, decreasing bond formation and strength. This method has been shown to
greatly reduce the amount of ice on roadways during and after a storm [Boselly 2001]. It
4
also makes removing the precipitation easier since it does not form a solid surface on the
roadbed. Anti-icing uses between 75 and 250 lbs per lane mile of chemicals depending on
the amount of precipitation expected [Ketcham et al 1996]. An effective anti icing
program requires the use of a systematic approach to snow and ice control. This approach
will maintain roads in the best conditions possible during a winter storm, while
minimizing chemical usage. As a consequence, antkicing has the potential to provide the
benefit of increased traffic safety at the lowest cost. However, to achieve this benefit the
maintenance manager must adopt a systematic approach to snow and ice control to ensure
that the performance of the operations is consistent with the objective of weakening the
formation or development of the bond between the precipitation and the road[Nixon,
2002]. To optimize efficiency this method also requires site-specific weather forecasting,
including some prediction of road surface temperatures. Consequently accurate thermal
mapping of road surfaces can be a huge benefit. The road surface temperature is
important for two reasons. If the road surface is not below freezing no ice will form, so
no chemicals need to be applied, and if the road is too cold, where the mixture of
chemicals and precipitation on the road would be below the eutectic temperature of the
mixture then anti-icing is ineffective.
Maintenance managers are responsible for the scheduling of maintenance tasks.
Thus they need to know that a storm is coming, when it is going to start, expected
precipitation amounts, and types of precipitation. They need to make sure that they have
all of the materials that will be needed in a storm. It is important to know when the storm
is starting so that the chemicals are not applied too early; this insures that there is an
5
adequate amount of chemicals on the road when the precipitation starts, and when the
road temperature is below the freezing point. The amount of precipitation is important in
deciding the rate of chemical application needed to insure that the freezing point of the
precipitation is depressed enough to prevent icing, it may also be necessary to reapply
chemicals during the storm.
A tool that has been identified as vital to a successful anti icing program is
Remote Weather Information System, (RWIS) stations. RWIS stations are strategically
located near critical road sections, such as mountain passes or bridge decks. RWIS
stations contain data collection and communication systems and data delivery systems.
Typical data collections system monitor; air temperature, relative humidity, wind speed,
wind direction and precipitation. They generally have embedded pavement sensors that
measure road surface and subsurface temperatures. These embedded sensors often also
monitor the freezing point and chemical concentrations. However these sensors only give
data at a single point on the road. Pavement temperature has high spatial variability.
These sites can also be outfitted with cameras and solar instruments, several state DOTs
have stated that they would like to have solar pyranometers included into their systems
[Ballard et al 2002].
RWIS sites are estimated to cost between $50,000 to $75,000 to purchase and
install, and up to $2,000 per year in maintenance costs [Nixon, Personal communication].
Location of each installation must be carefully analyzed. Also there are finite number of
sites that can be feasibly installed and maintained. Montana currently maintains 59 sites,
and has recently identified six potential new locations.
6
RWIS stations are also used in developing road weather forecasts. They are used
to help define the boundary conditions of the forecasts and can be a useful tool for
comparing what the forecast predicts and what is actually happening at a specific
location. These forecasts are generally for specific areas of interest and are called sitespecific forecasts. Data from the stations are also used to help create forecast surface
temperature maps.
This forecasting is necessary as the RWIS sites only provide weather information
at exact locations and a means of interpolating data between sites is necessary. A private
meteorology firm based in South Dakota provides road weather forecasts for MDT. Their
forecasts are based on national weather satellite data, weather models from the National
Center for Environmental Prediction (NCEP) and RWIS data. This data is collected and
used as input into meteorological forecast software called Advanced Regional Prediction
System, or ARPS. ARPS was developed at the University of Oklahoma’s Center for
Analysis and Prediction of Storms, CAPS. CAPS mission is to “demonstrate the
practicability of storm-scale numerical -weather prediction and to develop, test and
validate a regional forecast system”[Xue, et al, 2001]. The software that came out of this
program is ARPS, with the first version appearing in 1994 and the latest version
appearing in 2001. Using APRS weather forecasts are produced on refined grids with
adjustable time scales. ARPS can also produce surface temperature maps of the same
resolution as the meteorological forecasts. These refined forecast are then distributed to
the necessary divisions of MDT. Utah DOT decided to discontinue the purchasing of
surface temperature maps due to the fact that they generally only predicted the daily
7
freeze thaw cycle and were not useful for maintenance decisions [Ballard 2001]. Some of
the negative aspects associated with the surface temperature maps will be discussed in
greater detail in the next chapter. A software program has been developed that can more
accurately predict road surface temperatures using the same ARPS meteorological
forecast data. RadTherm/RT is a thermal modeling program derived from earlier codes
that were originally created for the military in identifying and modeling thermal
signatures of vehicles. RadTherm/RT has been developed to solve multi-mode heat
transfer utilizing advanced radiation solvers. The governing equations to the heat transfer
problem are solved using the Crank-Nicolson Method, this method utilizes a central
differencing scheme for both the time and space variable. This implicit method requires
the solving of a set of simultaneous equations at every time step. The software produces a
thermal map of calculated surface temperatures, with adjustable time steps between the
calculated temperatures. The temperatures of nodes that do not lie on the outer surfaces
are also calculated, and can be exported for use in spreadsheet programs.
A weather modeling chain culminating with a RadTherm/RT model of Bozeman
Pass between Bozeman and Livingston has been created, and is running in a forecast
mode that updates a website to display the road temperatures graphically. This model
uses a mesh with a 30 meter resolution, and is shown in Figure I. Presently there are no
structures or bridges incorporated into the model. It would be useful to incorporate
bridges into the model because the temperature on the bridge deck is often significantly
different than the neighboring roadway. As most drivers know highway bridges are more
likely to freeze and freeze more quickly than the rest of the highway. This is due to the
8
fact the roadway receives heat from the ground by conduction and only has convection
and radiation losses on one surface. Bridges have less thermal mass and have convection
and radiation losses on two surfaces. This surface freezing on bridge decks can be
dangerous to the driving public because the condition of the road surface may change
from wet on the roadway to black ice on the bridge. Thus maintenance crews may have to
apply anti-icing chemicals to the bridge deck earlier and possibly more often than to the
pavement in order to maintain a satisfactory level of service. The ability to predict
freezing on bridge decks could allow for more efficient use of anti-icing chemicals and
the ability to maintain the acceptable condition of the bridge deck.
9
In this thesis first principle thermal models are used to predict possible icing
condition on a highway bridge. RadThemVRT is used to analyze the model and the 19th
Street Bridge over 1-90 in Bozeman, MT is used as an example. The solution to the
surface temperatures is the simultaneous solution to multi-mode heat transfer equations.
It is very difficult to derive an analytical solution to these types of problems so a
numerical method is employed [Siegel Howell 1991]. RadThemVRT uses a spatially
implicit finite difference forward time stepping scheme to solve for the surface
temperatures. Each element in RadThemVRT requires a definition to be applied, the
Bozeman pass RadThemVRT model used terrain elements exclusively. Terrain elements
have thermal nodes that are coupled to a subsurface node that is below ground to a depth
where the temperature is diumally stable, and which is generally known. This subsurface
temperature is used as a boundary condition to help solve for the surface temperature.
The terrain elements allow the user to specify whether the terrain is a road surface, rocky
surface, vegetative surface, water or snow. Each of these types of terrain has some
adjustable parameters that can be set by the user. In the model used in this thesis only the
area around the bridge was modeled with terrain elements, The bridge structure was
represented with standard and three layer elements.
These elements are more general than the terrain elements and require more
parameter definitions than do the terrain elements. The bridge deck was modeled with an
exposed lower surface. Thus in the model there is convection on the top and lower
surfaces, conduction internally and between the support structures of the bridge and the
bridge deck itself, radiation between surfaces and imposed solar radiation loading. In
10
addition to the solar loading there are also shadowing effects on the bridge due to the
concrete barriers on the bridge deck and on the terrain under the bridge.
The conduction through the bridge deck and between the bridge deck and support
structures is dependent on the thermal conductivity. The thermal conductivity is
dependent on the materials used in constructing the bridge deck. Average values are
slightly higher than those of concrete due to the steel reinforcement. It is assumed in the
analysis that the material is homogenous and isotropic with respect to thermal
conductivity.
Convection takes place at the exposed surfaces of the bridge. RadTherm has three
options for calculating the convection coefficient for standard elements. The magnitude
of this mode of heat transfer is largely dependent on the wind velocity and the air
temperature compared to the bridge temp.
The radiation heat transfer is imposed in two major ways. There is the radiation
between two surfaces that “view” each other, and there is the solar radiation from the sun.
The magnitude of the first type of radiation is the difference between the two surface
temperatures taken to the fourth order. This mode also is dependent on some optical
surface properties, mainly surface emissivity. Emissivity is unity for a black body and for
real surfaces is a fraction that depends upon temperature and surface parameters:
roughness, texture, color, material, and coatings [White, 1991]. For this thesis it is
assumed that all radiation surface properties including emissivity, and absorptivity values
are averaged over temperature and angle. This is a gray body assumption, thus all bodies
in analysis are considered gray bodies. The other mode of radiation heat transfer is
11
explicitly solved for using measured or forecast data. This includes direct solar radiation,
diffuse solar radiation and reflected portions of solar radiation [Temps et al. 1977]. In
calculating the solar loading, RadThemVRT also accounts for shadowing effects.
It is desirable to have a model that can accurately predict the surface temperature
of the bridge deck, using weather and selected wavelengths of solar radiation data as the
input. The inputs for the model presented here were measured using a mobile weather
station and include; air temperature, wind speed, wind direction, relative humidity and
barometric pressure. In addition, three solar radiation instruments were used to measure
the total global solar radiation, global solar diffuse radiation, and long wave radiation. An
infrared handheld thermometer was used to measure the actual surface temperature of the
bridge. The data from this instrument was compared with output from the model. Once
established that the RadThemVRT bridge model can accurately calculate the surface
temperatures using measured weather data, this model may then be applied using
meteorological forecasts. A RadThemVRT model that can accurately forecast roadway
temperatures and bridge deck temperatures would be a great tool for DOT maintenance
managers. It would allow them to anticipate an icing event. In essence, these forecasts
could help to improve the level of service to roads and ensure safer driving conditions.
12
BACKGROUND
Current Thermal Mapping
Most DOTS use a private contractor for their meteorological forecasting. Although
these may include surface temperature forecasts they are not road specific forecasts.
MDT contracts with a North Dakota firm, Meridian. This company issues meteorological
forecast typically every twelve hours. They collect meteorological data from a variety of
sources, including the National Center for Environmental Prediction (NCEP). weather
data from RWIS sites, and from other sources such as airports that publish meteorological
data. NCEP runs a large scale weather forecast, ETA, that is broken up into geographical
regions in 20 km grids. The ETA data is distributed in three-hour time steps, thus any
atmospheric features that are small enough to traverse from outside the boundaries of the
domain to inside the domain in less than three hours would be ignored. Meridian
downloads the data for the Pacific Northwest Region and they run a nest model with 20
km resolution, using a meso scale meteorological forecast program called, Advanced
Regional Prediction System (ARPS). ARPS provides a run that has higher resolution in
time, and includes some atmospheric features that may have been ignored by the ETA
model. In addition ARPS utilizes Digital Elevation Maps to increase the accuracy of their
forecast. The forecasters at Meridian also consult the RWIS data for modifying the
boundary conditions. Then using data from the 20 km resolution ARPS model a finer
nested resolution (3km) model is run for areas of interest to the DOTs. This forecast is
then used to create thermal maps. All of this information is then passed to the DOTs for
13
maintenance planning [conversation with John Mewes, 2002]. These thermal maps are
meteorological based and often provide good forecasts for air temperature, relative
humidity and other meteorological data, but less satisfactory results for surface
temperature forecasts. They generally do not consider shadowing effects, have limited
knowledge of surface albedo and do not distinguish between a road surface and the
surrounding terrain. Thus in mountainous regions these maps can be highly inaccurate.
Figure 2 shows an example of a Meridian produced surface temperature forecast map of
Bozeman Pass using a 3km resolution grid.
Figure 2. Meridian surface temperature and wind forecast of 1-90 Corridor.
RadTherm/RT
The genesis of the RadTherm/RT software is based on two computational models
utilized by the U.S. military for prediction of vehicle infrared signatures. The first
principle heat transfer software from which the pavement model was derived is the TCM
(Thermal Contrast Model), developed for the U.S. Air Force [Johnson, K R, 1991,
14
Johnson, K.R., et al, 1996], also used is PRISM (Physically Reasonable Infrared
Signature Model) developed at Michigan Technological University’s Keweenaw
Research Center in partnership with the U.S Army Tank-automotive Command
(TACOM)[Prism 3.0 user’s Manual, 1991].
The purpose of these programs was to model the surface temperature of the vehicles
to be used in infrared imagery simulations. The surface temperatures of a vehicle subject
to a set of meteorological conditions gives a specific thermal signature. To simulate these
signatures, the 3-D geometry of the vehicles was defined by a series of flat plates or
facets. Originally the background was modeled as an isothermal flat plate. A
topographically varied terrain model was developed for snow by, Adams and
McDowell[1991], as background. This was extended to other backgrounds. Subsequent
availability of Geographic Information Systems (GIS) along with availability of Digital
Elevation Maps (DEM) offered digital sources for complex background models. GIS data
was used to obtain information about the properties of the terrain; this information along
with DEM data can now be readily input into a RadTherm model. This method of
utilizing DEMs and GIS was developed in the MPART program. Currently
RadThemVRT is being used in the Greater Yellowstone Regional Traveler and Weather
Information Systems Project (GYRTWIS). One of the tasks in this project is modeling
the Interstate highway, and surrounding terrain between Livingston Montana and
Lookout pass on the border of Montana and Idaho. The goal of the project is to generate
reasonably accurate forecasts of the road surface temperature. This knowledge could be
15
of great help in applying anti-icing principles, and increasing traveler awareness for this
stretch of highway.
By including detailed terrain features, RadTherm/RT is potentially much more
accurate for forecasting road surface temperatures than models that only utilize
meteorological data. The output is a three dimensional thermal map and clearly shows
regions that have temperatures of interest. Its ability to calculate shadowing along with its
advanced radiation solvers could make it a much more useful tool to maintenance
managers than previously available surface temperature maps
developed by
meteorologists. The GYRTWIS Bozeman pass project is using the weather forecast from
Meridian as the data input and computes road temperature forecasts twice daily and
automatically updates a website with graphical representations of the forecast road
temperatures.
Instrumentation
In addition to a standard meteorological package used from Coastal Environmental
Systems, three radiation sensors were utilized. Two Li-Cor pyranometers were utilized
and one Epply Precision Infrared Radiometer (PIR). The Li-Cor pyranometers measure
the solar spectrum between 0.4 toll .2 pm. The PIR is sensitive to the electromagnetic
spectrum between 3.5 to 50 pm. All of these instruments were specified and purchased
for use in model validations. A great deal of time went into developing this
instrumentation package and making all of the different instruments work properly. In
addition a data acquisition system had to be developed for these instruments.
16
Coastal Environmental WEATHERPAK.
The WEATHERPAK meteorological station instrument package measures; wind
speed and direction, air temperature, relative humidity and barometric pressure. All of the
instruments are sealed in the body of the instrument and all data is stored locally in the
system which communicates with proprietary software, INTERCEPT™, to collect,
display, archive and share data. The instrument is shown in Figure 3.
Figure 3. Coastal Environmental meteorological station.
Licor pyranometer.
The LI-COR 200SA pyranometor sensor is a field ready global solar radiation sensor. It
is used for measuring short wave solar radiation and is sensitive to wavelengths between
0.4 to 11.2 pm. It measures global solar radiation and if the direct solar beam is blocked
can be used to measure global diffuse radiation. For this project, it was used in a level
position to measure incoming solar radiation, this is shown in Figure 4. The current
17
output of the sensor is directly proportional to solar radiation. The response of the
photodiode used in this sensor is not ideal for the relative spectral response for this
sensor. An ideal response would be an equal reaction over the entire short-wave spectrum
of .280-2.80 pm. The typical response curve of the pyranometer is shown in Figure 5.
This response is very weak at 0.4 pm increasing almost linearly to a maximum sensitivity
at 0.95 pm and then linearly decreasing until a cutoff close to 1.2 pm. However the
absolute error when compared to the highest precision instrument is +5% maximum,
typically ±%3. [Licor Manual]. The LI-200 is factory calibrated against an Epply
Precision Spectral Pyranometer.
Figure 4. Radiation instruments including two Li-Cor pyranometer and one Epply PIR.
The Li-200SA can be converted to output millivolts with a 147-ohm adapter. This
adapter was used for both sensors to ease data acquisition. A mounting and leveling
18
fixture was also purchased for the sensors. This was used to mount to the plate that holds
all of the sensors.
Wavelength - pm
Figure 5. LI-200SA spectral response curve. Copied from LI-COR Terrestrial Radiation
Sensors [1986] with permission.
The second Pyranometer was used to measure diffuse solar radiation. Fitting a
shadow band to block the direct solar beam from the sun allows this measurement to be
taken, see Figure 4. A shadow ring that just blocked the direct solar beam and nothing
else would be beneficial, however it would have to be moved every few minutes to assure
that the sensor was still in the shade. This shadow band was manufactured for this project
using the specifications of a product that Li-Cor discontinued several years ago. The band
is six inches in diameter and a half inch thick. The shadow band, once aligned keeps the
sensor shaded for a day or two, requiring for minimal adjustment during the testing
periods. The amount of sky that is blocked, which does not include the direct solar beam,
is accounted for by using a calibration table supplied by LI-COR. It gives a correction
factor determined by the latitude and the month of the year, and is used to correct the
19
amount of diffuse radiation measured. In RadTherm the direct solar radiation can then
computed from the relation,
Q
Where
Q Gr
gr
= Q D iffR
(I)
Q o ir R
is the total global radiation and Q oiffR is the global diffuse radiation and QnirR
is the direct solar radiation. Thus the
Q Gr
and
Q oiffR
are measured and the
QnirR
can be
easily calculated.
Epplv PIR.
The long wave infrared sensor was purchased from The Epply Laboratory, Inc. (Fig
X.) It is a precision Infrared Radiometer. It is designed to measure global long-wave
radiation. The sensor has a filtered dome, this filter blocks the short-wave radiation and
allows the transmittance of long wave radiation. “Tests have demonstrated that this filter
does not exhibit significant transmission of short wavelength radiation” [Epply lab PIR
instruction sheet]. The transmission envelope has a sharp transition between 3 and 5 pm,
from complete opaqueness to maximum transmittance for the long wave radiation, and a
transmittance range of 3.5 to 50 pm. This dome also protects the sensor from the outside
elements. The actual sensor is a circular multi-junction wire-wound Eppley thermopile.
Its receiver is coated with Parson's black lacquer, a wavelength independent absorption
material. See Figure 4 for a picture of the sensor. A thermistor is installed inside of the
dome and measures, the temperature of the dome, which is used in a temperature
compensation circuit. A thermistor battery resistance circuit is used to accurately
compensate for emitted radiation. The instrument outputs a voltage that is proportional to
20
the received long wave radiation. To obtain the radiation measurements in units of W/m2,
the output voltage was divided by the sensitivity of the instrument. The sensitivity for the
instrument used in fieldwork was 4.31xl0"6 V/W-m"2. Calibration is traceable to the
International Practical Temperature Scale (IPTS). Some trouble was encountered in using
this specific device. Much of the data used was from a PIR mounted at the Bozeman pass
RWIS station. The reasons behind the use of the data from the pass is discussed in detail
in chapter four.
Handheld Infrared Thermometer.
The handheld infrared thermometer used is an Omega OS521 surface temperature
measurement device. (Fig 6.) This thermometer has adjustable emissivity from T t o l
with tenth increments. It has a response rate of 250 microseconds. A I milli-volt per
degree analog output that can be interfaced with data acquisition equipment. The field of
view ratio is 20:1 (e.g at a distance of 20 cm it will focus on an area that is I cm in
diameter). The thermometer is shown in Figure 6.
Figure 6. Omega IR thermometer.
21
Material Properties.
A large set of material properties may be assigned to elements in RadTherm. For
terrain elements, RadTherm uses internally defined values for each terrain type. New
terrain definitions may be added at the software programming level. In addition to the
terrain elements are more general elements which require material property definitions to
be assigned. The material properties that are assigned to standard and three layer
elements include; specific heat, thermal conductivity and density.
Specific Heat
Specific heat is defined as the amount of energy required to raise a unit mass of
material I degree. In SI units specific heat is expressed in J/kg K. The different types of
aggregates typically used in concrete have little effect on the specific heat of concrete
[Rhodes, 1978]. Some measured values of specific heat of concrete are listed in Table I.
The specific heat is however affected by the presence of steel reinforcement in the bridge
deck [Lie et ah, 1995], typically should resulting in a slightly higher value. An equation
proposed by Lie and Kodur [1995] for the calculation of specific heat, Crc (J/kg K) for
carbonate aggregate reinforced concrete is,
For 273.15< T < 673.15 degrees Kelvin
( 2 . 566 . 10^ 6)
^
"=
( 2)
A
This equation yields a value of around 1069 J/kg*K, if a density value of 2400 kg/m3 is
used. A value for the specific heat of reinforced concrete can also be derived from first
22
principle heat transfer equations. If the heat transfer is assumed to be an addition of a
concrete portion and a reinforced steel portion the equation is represented as,
( 3)
where Qt is the total rate of heat transfer (W), Qc is the rate of heat transfer in the
concrete (W) and Qs is the rate of heat transfer in the steel. If the following relationship
that holds for solid bodies is used,
(4)
dT
where m is the mass of the body and — is the time rate of change of temperature, and cp
dt
is the specific heat of the body. Substituting equation (4) into equation (3) and noting that
the time rate of change of temperature will be the same for the steel, the concrete and
subsequently for the whole body is.
,0.5^
c E +m,c^
( 5)
If this equation is solved for Crc and using the fact that 4% of the volume of the
reinforced concrete is steel results in the following equation for a one meter cubed section
of reinforced concrete.
(0.96m3p cCc) + (O M m 3p sCs)
0.96m3p c + 0.OAm3p s
( 6)
where pc is the density of concrete with a value of 2175 (kg/m3), ps is the density of steel
with a value of 7800 (kg/m3), Cc is the specific heat of concrete with a value of 1038
(J/kg K) and Cs is the specific heat of steel with a value of 440 (J/kg K). Using these
23
values obtained from Incropera and Dewitt [1996] the value for Crc is 960.3 J/kg. This is
around 10% less than the value given by the equation proposed by Lie and Kodur [1995].
The value used in the RadThermRT simulations was 1050 J/kg K.
Table !.Typical specific heats of concrete (partially reproduced from Table 6, Rhodes
[1978])___________________________________
Specific Heat J/kg K
Temperature, 0C
917
10
971
38
1038
66
Thermal Conductivity
Thermal conductivity is a measure of a material’s ability to conduct heat. It can be
defined as the ratio of heat flux to the temperature gradient. Customary SI units for
thermal conductivity are W/m-K [Rhodes, 1978]. Steel reinforcement will tend to
increase the thermal conductivity of the bridge deck, preformed beams, and the barriers
by a small amount. This is due to the fact that the thermal conductivity of steel is around
fifty times greater than that of concrete, though it only occupies about 4% of the volume.
Table 2. has some published values of thermal conductivities for carbonate aggregate
concretes. The thermal conductivity of specific heat used for this thesis was 2.5W/mK.
Table 2. Thermal conductivities of carbonate aggregate concrete. Reproduced from
results [Rhodes1987],[Vodak et. Al,] [T.Z. Harwathy][H.Abe, et al 1970]
Thermal Conductivity (W/m*K)
Source
2.3
Rhodes
2.2
Vodak
2.5
Harwathy
2.53
Abe et al.
24
Density
Density is a measure of how much mass occupies a unit of volume. Commonly used units
for density are kg/m3. Scott Keller[personal communication 2001], a MDT civil engineer
estimated that the density of the slab in the N 19th street Bridge is approximately 2400
kg/m3. This is the value used in this thesis for density of reinforced concrete.
Thermal diffusivity
An important property in heat transfer is the thermal diffusivity of a material
expressed as,
c c Id =
PCp
C7)
where atd is the thermal diffusivity which has units of m2 /s, k is the thermal conductivity,
Cp
is the specific heat and p is the density of the material. Incropera and Dewitt [1996]
state “The thermal diffusivity measures the ability of a material to conduct thermal
energy relative to its ability to store thermal energy. Materials of large Ottd will respond
quickly to changes in their thermal environment while materials of small atd will respond
more sluggishly.”
Surface Properties
Surface properties that may be assigned to the standard and three layer elements in
RadTherm will be considered next. These surface properties are used in the radiation heat
transfer relationships. For the terrain elements these values have been previously assigned
25
by the software programmers. These parameters include the absorptivity and emissiyity
of the surfaces.
Emissivity
Emissivity is a measure of how well the surface emits thermal radiation relative to a
black body. It is defined as the ratio of the radiation emitted by the surface to the
radiation emitted by a blackbody at the same temperature. Eicropera and Dewitt[1996]
list values for concrete as between 0.88 and 0.94. The value used for this project was
0.94. Higher emissivity values will increase the rate at which a body radiates heat away.
Absorptivity
For any material subjected to incident, radiation incident upon it there are three things
which can happen to the radiative energy. It can be absorbed, reflected, or transmitted.
For opaque materials no energy is transmitted. Using the conservation of energy it is
possible to say,
pr +a =\
(8)
where pr is the reflectance and a is the absorptivity. The absorptivity is the ratio of
absorbed radiation flux to incident flux. Reflectance or albedo is the ratio of reflected
radiation flux to the total incident flux. A mean value of absorptivity for gray Portland
cement concrete given by Levinson [2001] is .65, matching that given by Pomerantz et al.
[1999]. This was also the value used for this thesis
26
Governing Equations for Heat Transfer Problem
The governing equation that drives the problem is the first law of Thermodynamics.
The first law of thermodynamics or the conservation of energy for a control volume
states,
dt ’
where O is the net heat transfer rate, w is rate of work done, f
l a
(9)
the time rate of
change of the energy stored, and all terms are expressed in watts. For this case no work is
done so (9) simplifies to>
SE,
( 10)
Q = -
Expanding out the heat transfer rate into components for the different mechanisms yields.
Q com
+
Qcon
+
Qrad
+
6 netS
,
(H)
where Qconv is the convection heat transfer rate, Qcon is the conduction heat transfer rate,
Qrad is the radiation heat transfer rate, and Qnets is an explicit heat transfer rate that is
imposed by the short wave solar energy. Due to the fact that the body is a solid, the
following relation can be used [Incropera and DeWitt 1996],
a#,,
ck
ar
%
— P- = J n - C n -------
'
( 12)
27
where m is the mass of the body in kilograms and cp is the specific heat of the body and
dT
( ——) is the time rate of change of temperature in the body. Combining equation (11)
and (12) yields,
dT
m ' Cp ' ~ f t = Q onv +
+ Q ra d + Q m tS
C1 3 )
which is the governing equation RadTherm uses for its energy balance.
Heat and Mass Transfer Principles
Heat transfer is energy in transit due to a temperature difference [Incropia, 1996 pg2],
As implied above the important modes of heat transfer in the model are conduction,
convection, net longwave radiation heat exchange between surfaces and the solar
radiation.
Conduction
Conduction heat transfer is the transfer of energy front particles with more energy to ones
with less energy. In general, the conduction heat transfer follows Fourier’s law, which for
one dimension through a plane wall is,
(14)
where Qx (W) is the heat rate by conduction through a plane wall of area A (m2), this heat
'
dT
transfer rate is proportional to the temperature gradient (— ) in the wall, and k is the
dx
thermal conductivity (W/m-K) of the wall. This can be simplified if some assumptions
28
are made about the thermal conductivity and the area,A. If they the thermal conductivity
does not change with changing temperature and if the assumption is made that the area
does not change then the following equation can be used.
&
(15)
This is a linear relationship of Fourier’s law and is the equation that RadThemVRT uses
conduction. Conduction occurs in all of the elements in the RadThemVRT model. The
terrain elements have conduction in the direction normal to the surface and through their
depth between the thermal nodes. The standard elements have conduction between the
front thermal node and the back thermal node and between adjacent elements. This will
be discussed in more detail in the methods section.
Convection
Convection heat transfer can be broken up into two modes, energy transfer due to
diffusion (natural convection) and energy transfer carried by the motion of the bulk of a
fluid (forced convection) [kicropera and DeWitt 1996]. Generally, convection is the
transfer of energy between a surface and a flowing fluid that is in contact with the
surface. Transfer by diffusion is usually much smaller than the energy exchange due to
transfer by bulk motion. RadThemVRT therefore neglects diffusive energy transfer. The
governing equation of convection is Newton’s law of cooling which can be expressed as,
< 2 = jf-% -7 ;)
(16)
where the heat transfer Q is positive if it is into the surface of area A. The proportionality
constant h is the convection heat transfer coefficient (WZm2-K). Incropera and DeWitt
29
[1996] state that the coefficient depends on the conditions of the boundary layer, which
are influenced by surface geometry, the nature of the fluid motion, and an assortment of
fluid thermodynamic and transport properties. T00represents the bulk temperature of the
fluid and Ts is the temperature of the surface. RadTherm has three options for calculating
this coefficient for wind models in natural environments; low turbulent intensity, linear
convection, and power law convection. Each of these options will be described in more
detail in the methods section. It is up to the user to decide which option is the best to use
for the application.
Radiation Heat Transfer
Radiation heat transfer does not require a medium to carry the energy, in fact it is
most efficient in a vacuum [Incropera and DeWitt 1996]. The mechanism of energy
transport can be viewed as the propagation of electromagnetic waves, or as propagation
of quanta or photons [Siegel, et ah, 1992]. Both methods generally arrive at the same
formal equations and for this project the electromagnetic wave theory was used. Thermal
radiation is emitted from excited particles and differs only from other forms of
electromagnetic waves in that the particles are thermally excited. All electromagnetic
waves can be characterized by a spectrum of wavelengths X and frequencies v expressed
as [White,1991],
C-=X-V,
(17)
where c is the speed of light. The electromagnetic wavelength spectrum encompasses
a wide range of wavelengths from around IO"5 to IO4 pm [White 1991]. The thermal
radiation range of the spectrum is generally characterized in the range of IO"1to I O2 pm,
30
which contains a small portion of the ultraviolet, the entire visible region, and the infrared
spectrum, as shown in Figure 7.
Visible 0.4-0.7 |i m
4---------- ►
* p I T
IO"5
10"4
10"3
IO"2
10
10'
IO2
IO3
IO4
X(nm)
Figure 7. Spectrum of electromagnetic radiation highlighting thermal region (values from
Incropera and Dewitt [1996]).
All solid opaque bodies emit thermal radiation, in addition they can absorb incident
radiation or reflect incident radiation or any combination of absorbing and reflecting. A
perfect emitter is termed a “blackbody”. A perfect blackbody also absorbs all incident
radiation and is a diffuse emitter. If a black body has an area A and an absolute
temperature TSj its radiant emissive power is given by [White, 1991]
(18)
where Ey is the emitted radiation in watts, a is a fundamental constant called the StefanBoltzmann constant, equal to 5.67 X IO'8 (W/m2«K4), A is area in m2, and Ts is in Kelvin.
31
Real surfaces are not black bodies and emit thermal energy at some rate lower than a
black body which can be estimated [kicropera, et al. 1996] as,
Er =S-G-A-T*,
(19)
where Er is the rate that the real surface emits radiant energy, and £ is a radiative property
of the surface, called emissivity. Surface emissivities have a value between zero and one.
This property is a measure of how well the surface emits thermal radiation compared to a
black body. This property is strongly dependent on surface material and its finish.
According to Incropera and Dewitt [1996] for radiation exchange between a small
surface at Ts and a much larger isothermal surface at Tsur that surrounds the smaller
surface, the larger surface is assumed to have blackbody emission and the smaller surface
is assumed to be a gray body where the following equality holds for the small surface,
a =s .
(20)
Then the net rate of radiation, Qr (W), from the smaller surface is [fricropera, DeWitt
1996]
& = f. j - c r ^ - C )
(21)
This equation expresses the difference between the amount of thermal radiation released
by emission and that, which is gained through absorption.
Radiation View Factors
Radiation view factors are used to solve radiation heat transfer problems where
radiant exchange is occurring between two or more surfaces. They are used to express the
geometric relationship of how the surfaces “view” each other. If the following
32
assumptions are made about the surfaces, the problem can be greatly simplified; I)
emitted and reflected energy are uniform over the each surface, 2) reflected energy is
diffuse, 3) emissivity and absorptivity are equal and uniform over the surface and 4)
temperature is uniform over the surface [Siegel, Howell 1992]. If these assumptions are
made the equation for calculating the view factor between two finite areas reduces to,
( 22 )
where F , . 2 is the fraction of the energy leaving area At that arrives at area A2,
displayed graphically in Figure 8.
In a similar manner the fraction of energy that leaves area A2 and arrives at area Ai is.
(23)
This leads to a reciprocity relation for the view factors which is derived by the fact
that the integrals in the two equations are identical, thus
(24)
Figure 8. Geometry for exchange between finite areas (adapted from Siegel and Howell
[1992]).
33
Enclosure Theory
Enclosure theory considers a set of areas that are completely enclosed, such as in
Figure 9. Thus the radiation leaving one surface must be absorbed or reflected by another
surface. If the same assumptions are used as those in the view factor section, all radiation
contributions must be accounted for. The amount of energy that leaves one surface and
arrives at another is dependent on the view factors. In an enclosure with N surfaces, if
energy leaves one surface then fractions of that energy must eventually reach each of the
other surfaces that “view” it and the total of the fractions must be unity [Siegel, Howell
1992], that is
Fk-X+Fk^ + ... + Fk_k +... + Fk_N =1,
(25)
where Fk-k is a self view factor for concave surfaces. It is up to the modeler to decide
how to break up the surfaces, more surfaces increase accuracy but add complexity.
Figure 9. Example enclosure with N surfaces.
A typical heat balance for a single surface k, with area Ak inside the enclosure is
[Siegel, Howell 1992]
34
&
(26)
where Qk can be seen as either a heat transfer rate applied to the surface or as the net
radiative loss from the surface to the enclosure,
q 0;k
is the emitted plus the reflected
radiant energy, and q,_k is the incident radiant energy from other elements in the
enclosure, see Figure 10. The term q 0,k can be expressed as, [Siegel, Howell 1992]
9.^=
+
,
(2?)
where the first part of the equation on the right side of the equal sign is the emitted
portion and the second part is the reflected portion. The incident flux q^k is arrived at by
summing the portions of energy which are emitted from N number of surfaces in the
enclosure. This results in the following equation [Siegel, Howell 1992]
cIijc = Y j Fk- A ,
( 2 S)
M
where the F k-j are the view factors and q 0j are the outgoing radiative terms from the other
N
areas. Substituting (28) into (26) and noting that, ^ Fk_j = I ,results in,
M
Qk - Ak^ j Fk_j(qotk - cIoj) •
(29 )
In this equation all of the incoming (i) terms have been eliminated. By substituting
(27) into (26) a second simultaneous equation, where the incoming terms are eliminated
is,
A
Qk
I"**
(3 0 )
35
These two equations, (29) and (30), provide two simultaneous equations that can be
written for each N surfaces. This provides 2N equations with 2N unknowns, with either
the Qk or the Tk being unknown, which is dependent on the boundary conditions. If
however (30) is solved for q0_k and substituted into (29) the following equation results,
[Siegel, Howell 1992]
I
7=1
1 £J
*-y
(31)
y
Where Skj is the Kronecker delta defined as,
W h en k = j
0
(32)
W h en k ^ j
Expanding equation (31) and solving for Qk results in the governing equation for
enclosures used in this project and in RadTherm/RT, [Marttila, 1999]
Cradk
7=1
where
Q radk
(33)
k j’ 1 k - j
V
J
is the net radiative loss from surface k. This provides for N equations
with N unknowns where either the temperatures or the radiative losses must be known.
Figure 10. Radiative terms on surface area A.
36
Solar Radiation
The flux of solar radiation on an exposed surface consists of that due to the direct
solar beam, that due to diffuse skylight and portions of reflected radiation from other
surfaces [Temps et al 1977]. The portion of the electromagnetic spectrum that includes
solar radiation is; an infrared region, visible region and a portion of the ultraviolet, this is
shown in Table 3. As indicated in Table 3, the ultraviolet portion does not have a
significant influence on the energy balance at the surface of the earth and RadTherm does
not utilize data from this wavelength. Also no attempt was made to measure UV
radiation. The values for solar radiation are measured values and used as inputs into the
RadThemVRT model. The wavelengths between 0.4 to 1.2 pm represent the shortwave
region that is measured by the pyranometers. The instrument accounts for the
unmeasured regions if it has been calibrated to an instrument that can measure the whole
shortwave region [Licor Manual, 1986].
Table 3. Shortwave radiation definitions (Touloukian and Dewitt[1972] and Pluss
[1997]).
Wavelength (pm)
Region
Mean radiation energy at
the earth surface
0.2-0.4
0.4-0.75
0.75-5.0
Ultraviolet (UV)
Visible (VIS)
Near Infrared
9%
49%
42%
37
METHODOLOGY
The first section of this chapter describes the computer models developed. Experimental methods and data formatting are discussed in the second section.
RhinoSD Model
In this section the two geometry models are discussed. The bridge model had
three different meshes derived from the same geometry. There was only one terrain
model used throughout. Rhino is a surface-modeling program that is well suited to use in
conjunction with RadTherm. RadTherm requires the geometry of the problem to be
discretized into a mesh consisting of triangular and/or quadrilateral elements. Rhino has
meshing capabilities and the meshed geometry created by Rhino can be imported
seamlessly into RadTherm. The geometries of the bridge and the surrounding terrains
were done separately to ease in the drawing and to help give more control over mesh
development. Figure 11 shows the mesh created for the surrounding terrain, and Figure
12 shows the different bridge meshes. There were three different bridge meshes used in
the analysis of the RadThermRT software, they are named using the order of magnitude
of the number of elements in each bridge mesh, thus they are named; 10 element bridge
mesh, 300 element bridge mesh and the 3000 element bridge mesh.
Bridge Models
The geometry of the bridge was drawn in Rhino3D. There were no original computer
aided drawings (CAD) of the bridge available. Consequently the original blue print plans
38
were used to model the bridge. In future projects it would be highly beneficial to use
CAD drawings of the original structures. This would ensure that the geometry used in
RadTherm/RT accurately reflected the true environment.
Figure 11. Perspective view of terrain mesh.
X
X,
x
N
H... I.... E
X
A.
'
B.
C.
Figure 12. Top view of bridge meshes, (A) is the 10 elements bridge mesh, (B) is the 300
elements bridge mesh and (C) is the 3000 elements bridge mesh.
39
The bridge surface model was constructed in a deliberate and orderly fashion. First
the outline of the bridge deck was drawn using the polyline command. A polyline is a
line with vertexes connecting each straight section as shown in Figure 13. Polylines used
for the bridge are only two vertex lines, thus to draw a square four separate polylines
would be used. Next polylines were drawn, on the bridge surface along the centerlines of
the support structures and barriers. This served two purposes, one to help in drawing the
support structures and also to allow for individual areas to be created on the surface of the
bridge between the supports. These separate areas were necessary for proper meshing and
vertice alignment. After that the outline of the support structures and barriers were drawn,
also using polylines. Then areas were defined for each section of bridge deck between
supports and for each support and barrier using the “Create surface from curve network
command” This type of surface when meshed results in only quadrilateral elements.
Figure 13. Example of a Rhino3D polyline with several vertices.
40
0.
E.
Figure 14. Steps in creation of 3000 elements bridge mesh , (A) bridge outline is drawn
using polylines, (B) polylines are drawn where supports will be, (C). polylines
drawn around outline of supports and barriers, (D). close up of mesh showing
aligned vertices, (E) perspective of 3000 elements bridge mesh.
In order for the model to work more efficiently in RadTherm some simplifications
were made. The supports of the bridge are preformed concrete I beams, these I beams are
modeled as flat plates with the same volume. The model uses the same height as the
actual beam and then a uniform thickness was computed to make the support beams have
the same volume as the actual beams. The thickness was used in RadTherm to accurately
model the beam. Figure 15 shows how the simplification is represented. A similar
simplification was used for the support structures.
41
InrTnrhrTTaI
Figure 15. Cross section view showing simplification made on supports and barriers, (A)
is from bridge blue prints and (B) is the cross section of modeled bridge.
Finally the areas were meshed using Rhino’s Polygon Detailed Mesh Options, see
Figure 16 Rhino Polygon Detailed Mesh Options. By using the Min edge length and max
edge length options a clean looking mesh was created with quadrilaterals of relatively
constant area was created. The Max edge length value is approximately the maximum
edge length of the quads in the initial mesh grid. This option can be used for making sure
the polygons are approximately the same size. Thus this value was varied for each of the
three meshes. By creating a series of areas for the surface of the bridge deck the nodes on
the elements of the bridge deck were aligned with the nodes for the support and barrier
structures elements. This alignment is very important for the model to run correctly in
RadTherm/RT. If the mesh vertices do not line up then there is no conduction between
elements, since RadTherm/RT treats unaligned vertices as insulated. For the 10 element
bridge mesh all of the supports and barriers were deleted.
42
Xj
Polygon Mesh Detailed Options
Max angle:
|i
3
P Refine
Max aspect ratio:
[g
g
r Jagged seams
Min edge length:
3
Max edge length:
Max dist. edge to srf:
3
r
Simple planes
P Weld
Min initial grid quads:
OK
Cancel
I
Preview
I
Simple Controls..
Figure 16. Polygon mesh detailed options from Rhino3D.
Terrain Mesh
The area surrounding the bridge consists of built up embankments supporting the
bridge over 1-90 and ramps to allow access from the Interstate to N. 19th Ave. The
embankments were drawn as flat plates as were the bridge abutments. The mesh of the
surrounding areas was made to have elements that were around 10 m2. See Figure 11 for
a perspective view of the terrain mesh.
RadTherm/RT Thermal Analysis Software
RadTherm/RT is a thermal modeling package which uses a finite difference forward
time stepping spatially implicit code. It also has an embedded graphical user interface.
The version used in this thesis is RadTherm/RT where the RT stands for road
temperature. This version of RadTherm has built in “terrain” definitions. In addition to
modeling roads or terrain, it is also possible to model objects. This can include buildings,
vehicles or, as in this project, a highway bridge. RadTherm/RT has several different
43
element part types; standard, highly conductive, three layer, terrain, and transparent. Each
mesh polynomial is defined by using these element part types. Only the standard, three
layer, and terrain objects were used in this project, thus the discussion will be limited to
these three. Complex geometries must be imported into RadThemVRT from some other
program. In this project all geometries Were created and meshed in Rhino3D. Because the
model was built using two different geometry files, the imported geometries had to be
oriented and aligned with each other. Proper orientation is critical in RadThemVRT
because of the solar loading and shadowing. Near components that generate shadows, a
bridge running east to west may have very different solar loads than one running north to
south. The orientation adjustment is done by first selecting the parts that need to be
oriented. Then select the Geometry tab and the sub tab Edit and use the Translate and
Rotate operations. The mesh is given default part definitions, to modify the part
definitions first decide how the domain of the mesh should be divided into definitions. To
apply definitions to the mesh, first select all of the elements that will be in the part. For
example elements that correspond to the Interstate were chosen to be a separate part.
Then on the Editor Tab click the new part button. Next the selected elements are assigned
to a new part. After that the part is named Using the Parts tab. If the part type is a standard
or three layer type, then the user can define: material type, surface condition, and
convection model to be used. The material type defines the specific heat of the material,
the density of the material and the thermal conductivity. The surface definition includes
the absorptivity and emissivity of the surface. If the part type is a terrain then RadTherm
offers eight adjustable terrain types: Asphalt Model, Concrete Model, Foliage Model,
44
Layered Model, Snow Model, Soil Model, Swamp Model and Water Model. Each of
these categories has sub categories. Continue assigning part definitions until all of the
elements have the desired definition.
For the bridge model the surrounding terrain was imported first. All of the terrain
definitions were then assigned, including a grass portion, interstate asphalt portion and
highway asphalt portion. Next the Bridge geometry was imported. Using translate and
rotate commands the bridge was oriented and aligned with the terrain. Then part
definitions were assigned to the bridge deck sections, the support beams, and the concrete
barriers. In the Rhino section the alignment of the mesh vertices was discussed.
Unfortunately Rhino may not absolutely align all of the vertices; they may be separated
by a small amount. To see if there are unaligned elements vertices click on View and then
free edges. The free edges will be displayed in red and represent edges where no
conduction takes place. If there are edges that should be aligned but are showing up as
free edges, then the a condense operation can be used, this function is located in the
geometry tab under the edit sub tab. There is a blank box called Max Vertex Separation,
this condense command will align vertices that are closer than the Max Vertex
Separation. Thus using a small value for the Max Separation, around .1 mm, all vertices
should then be aligned properly. The previous red edges should now show up as yellow,
indicating that there is alignment between three or more vertices, and conduction is
enabled between adjacent nodes.
45
Governing Equations RadTherm RT
Standard Elements
Each standard element in the mesh has two surfaces, a front and a back surface with
one temperature node assigned to each surface, as shown in Figure 17. These surfaces are
separated by a user-defined thickness. Each thermal node is associated with a surface and
with one-half of the volume that is bounded by the two surfaces. A single temperature is
assumed for each thermal node and the volume that node occupies. Figure 18. shows all
of the heat transfer modes accounted for in a standard element. The governing equation
for the radiation heat transfer modes is Equation (13), restated here for convenience,
dT
m ‘ Cp
The
Q con,
and
Q conv
Ot
= Qconv + Q con + Q m d + Q netS '
(3 4 )
can be further expanded using the relationships shown in equations
(15) and (16) and for a specific thermal node k will result in,
PjrT
Ncond
- f kj
c x kj r ‘
O l
j= i
~
T j
Lkj y
+
Qrad,.
radk + ^Qn,e ts k >
(35)
where hk is the convection coefficient, Ak is the surface area exposed to convection, Akj is
the cross sectional area between elements k and j, Tf is the temperature of the fluid that is
convecting heat to or away from Ak, Ncond is the total number of conduction links
between node k and all adjacent nodes, ky is the thermal conductivity of the material
between thermal nodes j and k and L kj is the geometric distance between node k and
node j.
46
Thermal Nodes
Associated with
Standard Elements
Front Surface
Element Thickness
Back Surface
Figure 17. Standard element.
Q radiation
Q solar load
Q conduction
Q conduction
Q convection
iermal Node
op Surface
Q conduction
Q conduction
Q conduction
Figure 18. Heat transfer modes into standard element.
The
Qnetsk
term is an explicit term involving the amount of solar radiation node k is
receiving, expressed as,
^ nets,k
' solar,k
+ Qre/JnJ-Q,ref _o u t,k
>
(36)
47
where, Qs0Iar,k is the amount of solar radiation into node k, Qref_in,k is the amount of solar
radiation which is reflected into element k from all other elements and the default
background element and Qref_out, k is the amount of solar radiation which is reflected out
from node k. Qsoiar,kis defined as
(37)
where Oiic is the absorptivity of node k,
Qs
is the total amount of solar radiation received
including direct and diffuse solar radiation, AAk is the apparent area that the radiation
sees and VFk is a visibility factor used for shadowing. The reflected radiation is solved
using an iterative algorithm, first some initial guess is made for Q ref_out,k for each node k,
then QreMn,k is calculated for each node k.
better estimate for
Q reM u gc
repeated until some
Q reMn,k
depends on the guess for Q reM ut,k, and a
is calculated, it is just the reflected
Q reM n,k
minus
Q reMmt,k
Q reM n,k-
This process is
converges to some tolerance. [Personal
communication A. Curran]
The Qradk term in equation (35) is obtained from the net-radiation enclosure equation
(33). The term Qradk is equal to the negative of Qk in equation (33). Solving equation (35)
for Qradk and substituting in the value for Qk results in the following equation,
kj Jj- k-j
'k V
V
rsrp
=
x
^
Cl
\
Ncond
h
t Ak(Tf - T t ) * %
y=i
+ a■netsk
v
4/
/
J
(38)
48
This is the governing equation for the standard and three layer elements and is solved
simultaneously over the domain of the problem, where N is the total number of surfaces,
and Ncond is the total number of conduction links.
In order to solve the preceding equation some numerical iteration scheme must be
used. RadThemVRT uses a Crank-Nicholson implicit finite difference scheme. CrankNicholson is unconditionally stable and is second order accurate in time and space
[Tannehill et al 1997]. Applying this to equation (38) and linearizing the T4 terms by the
relationship in equation (39), yields equation (40)[Martilla 1999],
( ^ 4 - T ) 4) = ( 7 ^ - 7 } % + 7 } ) ,
-m c j
+E
1" 1 7pU h i Al
At
hkj,A kj T ' j +Tj
T y rP
'V 1 YT,
T \+ T k
(3 9 )
Q 'nets,.
nelsk + Z^netsk
Q,
+ -
y'=l ^kj
Ajc8k
^■-Fk-k
(l-W
Z ^ X ^ - 7 ) ') ( 7 ; + 7 ) )
>1
T ',-7 )
(4 0 )
/ 'h ii
V ^ J
The primed terms represent values from the current time step, the non primed terms
represent values from the previous time step. Equation (40) can be put in a more
convenient form by multiplying through by two,
49
-Zm1Cpl S t - S l + h i A i ( T ' f + Tf - T \ + T k )
Ncond fc
^4.
/
+ £ - r fc(r , y+ ry - r > :r) + e ,- , l + a ■nelsk
y=i Lkj
^
J
™r y,)(r* +Tj W '* +Ti‘ - T ' r T,'>
l l e
k -k
i}-~£k) y=i
4-.■2E
y=i 4
(41)
v
y
Solving (41) for T’k yields the final equation that is encoded in RadTherm for the
numerical solution [Martilla 1999],
l m k C Pk
At
Tt
+ , - Z tTf----- + T j ) ( T ' J + T J - T t )
1 fk-k I1
Ncond
+ A A tr v + r j- r .) + £ v y t ( r + + r , - ? ; ) + + a . ,
y=i Lkj
^-Acfk
1”
*
(l - 4
v gy y
) 7=1
J
-
~ g/
-V
Tt + — ^
N
//com/
NC
OM
---- ( Z F*-N(T* - tZ W 1 + T Z W t At + E
I - 11k-k v ~ £k) M
I-
A
(4 2 )
^kj^-kj
y=i
The outgoing radiation or Qj terms in equation (42) are evaluated each time Tk is
evaluated using equation (33). In order to solve for the temperature distribution over the
domain of the problem equation (42) is written for each thermal node. This system of
equations requires an iterative method The method that RadTherm/RT uses is Successive
Over Relaxation with an adjustable tolerance value , the matrix equation is solved using
Gauss Elimination with partial pivoting. The iterative method is used to converge the
governing equations on a solution at each time step.
50
Three Layer Elements
Three layer elements are similar to the standard elements, except that for each
element there are four temperature nodes and the ability to define the thickness for each
layer. The conductivities are also adjustable for each layer. This is shown in Figure 19.
The three layer elements have the same heat transfer modes as the standard elements and
also have the same governing equation. For the interior thermal node the only available
heat transfer mode is conduction. These elements were used to define the bridge deck.
Figure 19. Three layer elements.
Terrain Elements
There are several first principle terrain models built into RadThernVRT including
a soil model, foliage model, water model, snow model, swamp model and concrete or
asphalt model. These models are used to define the terrain elements. Terrain elements
used in this thesis are foliage elements and asphalt or concrete elements, thus details are
51
only given for these models. All of the terrain elements use multiple layers, where each
layer has a thermal node; these layers are perpendicular to the surface normal in the
direction of increasing ground depth. The foliage model uses a thermal node that is above
ground and represents the foliage. For the interior nodes the only available mode of heat
transfer is conduction between nodes above and below. The core temperature, is defined
at the bottom node, and must be defined as an input into the model, as shown in Figure
20. The terrain elements take into account the physical processes of; convection between
the air and ground, convection between the air and foliage, and radiation between the
ground and sky, radiation between the ground and foliage, radiation between foliage and
sky,
conduction through
ground layers,
solar loading including
shadowing,
evaporation/condensation, and precipitation. Unlike the standard and three layer elements
there is no conduction between the elements. This is reasonable as the thermal
conductivity of most terrain nodes is relatively small, and the temperature is relatively
constant at similar depths, thus virtually no conduction would take place in a direction
perpendicular to the surface. Each first principle model uses the same governing equation
as is used for the standard and three layer elements with the addition of a mass transport
coefficient to track the precipitation, evaporation and condensation rates. Adding these
terms yields Equation(43),
52
2m*C,*
Tk + —
^ a f T k1 - T / XTk +Tj X T ' j + Tj - Tk)
1~ At-* l 1-£,AJ y=i
Ncond
Ic,. A1
+ ^4(r%+7;-7;)+ ^ - ^ ( r ',+ 7 ; -7 ;)+ 8 ^ + 8 ^ + G '_ „ + 8massk
>i
2A g*
y
(l-^ )A _ y ' lZ f l
v f V y A;
l _ A - * ( 1 _ g * ) 7=1
T\
2m*C^
Lkj
A
C
^
7V
r, +1—^ --- { L
1 - A -*V - g U >i
/VCOAU
F ^ T ? - T A ^ +T M h kAk + X
y=1
AA
(43)
where the Qmas8ik term is defined for each different terrain application type. For further
information on how each of the Qmassk terms are calculated see ThermoAnalytics Terrain
Model Technical Manual [2000].
Q Solar
Surface Thermal Node
Q
radiation
convection
iduction
Multiple Layers
iduction
Core
Temp .
Thermal
Node
Figure 20. Terrain elements.
Ground Layer
Associated with
Core
Temperature
53
Concrete and Asphalt Models
The concrete and asphalt models have capabilities to change material properties and
layer thickness based on different applications. The concrete and asphalt models have six
different application types (!TYPE). They are listed in Table 4.
Table 4. !TYPE for concrete and asphalt
Name of ITYPE
!TYPE# Concrete
I
2
3
4
5
6
Interstate Road
Sidewalk Country Road
Runway
Parking Lot
Highway Bridge
Heavy Pad
ITYPE # Asphalt
I
2
3
4
5
X
Each application type then has three different surface conditions or colors (!SURE)
and three different moisture states (IWET).
Table 5. Surface condition of pavement concrete nodes (!SURE)
Emissivity
Name
ISURE Concrete
.94
Uncolored
I
.94
Black
2
.94
Brown
' 3
Table 6. Surface condition for asphalt nodes
Name
ISURF Asphalt
Aged
I
New
2
Table 7. Moisture state IWET
IWET #
I
2
3
(!SURE)
Emissivity
.94
.94
State
Covered (Dry)
Exposed (Normal)
Wet
Solar Absortivity
.64
.91
.87
Solar Absortivity
.85
.93
54
The moisture parameter is used for pre-adjusting the thermal properties, capacitance and
conductivity, based on moisture activity that occurred before the simulation. Precipitation
occurring during the simulation will affect the convective and mass transfer cooling as
expected during the simulation. The concrete and asphalt models use a 17 thermal node
model, these nodes are connected through the depth of the material. Each terrain element
has three types of material groups through its depth. The separate material groups are
divided as; nodes 1-8, nodes 9-16 and node 17 and are defined as material groups (I).
These material groups can be concrete, gravel, sand, asphalt or external air. For example
a typical highway asphalt road section will have the asphalt, then a sub grade of gravel,
below that a bed of sand. Thus each different application type, !TYPE, has predefined
thickness for each type of sub grade used. The thermal properties for each group are
listed in Table 8. Each of the three material groups is given a representative thickness for
the application type [TA terrain model tech manual].
Table 8. Thermal properties for material groups.
Concrete
I
IP
2245.0
Mass Density (kg/m3)
9 2 2 .0
Specific Heat (J/kg K)
1.903
Thermal Conductivity (W/m K)
Gravel
2
2050.0
1840.0
0.52
Sand
3
1520.0
800.0
0.33
Asphalt
4
2243.0
920.0
1.211
Air
5
1.177
1005.7
1000.0
The values from Table 8 are the default values for the dry condition, IWET=2. If the
condition is not dry then a multiplying factor is applied to the capacitance, CAP, and
conductance, CON for the first material group defined in Table 9.
55
Table 9. Multiplying factor for capacitance and conductance. Adapted from
ThermoAnalytics Terrain Model Technical Manual
Asphalt
Concrete
IWET CAP Factor CON Factor CAP Factor CON Factor
0.95
0.91
0.95
I
0.89
1.00
1.00
1.00
1.00
2
1.05
1.05
1.27
1.33
3
The first group of nodes ,1-8, is divided evenly into 7 layers, node I and 8 are at one
half of the layer thickness. This was also done for the second material group. Layer 17 is
a single full layer that is 1/7 of the full group thickness. The three material groups, (I),
have a type, (IP) and a thickness, (ITHCK), defined for each application type, (!TYPE).
These are defined in Table 10. Where the thickness (ITHCK) is in meters, and is defined
in Table 11.
Table 10. Definition of Material Groups
Asphalt
Concrete
ITYPE I IP ITHCK IP ITHCK
4 5
I I 5
I
2 7
2 2 7
3 I
3 3 3
3
4
I I 3
2
2 7
2 3 7
3 I
I
3
3
4 5
I I 5
3
4 5
2 I 5
2 7
3 2 7
4 3
I I 4
4
2 7
2 2 7
3 I
3 3 I
4 2
I I 5
5
I 5
2 5 4
4
5
3 I 5
I I 5
6
2 I 6
3 2 7
56
Table 11. Tliickness definition for ITH <
ITHCK
I
2
3
4
5
6
7
THCK (m) 0.0254 0.0508 0 .0 8 8 9 0.1270 0.2032 0.4064 1.0
RadThemVRT uses the values in the preceding tables for solving the governing
equations. “The above data provides a matrix of options for adjusting the model to the
appropriate situation based on material, concrete or asphalt, and application. As well as
surface and moisture variations.’’[ThermoAnalytics Technical Manual 2000]
Foliage Models
Foliage elements are used for partial to full coverage, dormant to growing and dry to
moist conditions. A single layer represents the foliage, then the ground below is divided
into thirteen layers. The heat transfer modes include: convection with the air, foliage and
ground, radiation between the foliage and sky and between ground and sky, and
conduction through the soil layers, hi addition mass transfer involving evapotranspiration
within the foliage, evaporation from the ground and precipitation to the foliage and
ground are represented in the model. Figure 21 shows an example of the nodal layout of
foliage elements. The following types of foliage can be chosen by the user; short grass,
tall grass, coniferous trees, deciduous trees and mixed trees. The following parameters
are adjustable by the user; foliage pover factor, growing state, dew state, surface moisture
state, and bulk depth moisture state. For more information on the mathematical models
used for the foliage models see ThermoAnalytics Terrain Model Technical
Manual[2000].
57
AIR NODE
FOLIAGE
SURFACE
SOIL
SUB-SURFACE
SOIL
CORE
Figure 21. Schematic representing foliage nodes, (taken from ThermoAnalytics website).
Background Elements and Sky Elements
For the enclosure theory to work a body being modeled must be fully enclosed.
RadTherm/RT accomplishes this enclosure with the use of a background element and a
sky element. The background element serves as a boundary on the periphery of the
geometric model on the horizontal. The sky element is an envelope that arches above the
horizontal in a hemispherical fashion and joins with the background elements on the
horizon. These elements provide a means for accounting for all multi-bounce radiation.
Thus when calculating the view factors, if a ray doesn’t intersect another geometry
element, then it must either hit the background element or the sky element. The
background element can be defined with the same terrain definitions available for terrain
elements. For this Project the background node was defined as short grass with a core
temp equal to that of the rest of the terrain nodes.
The Sky element is considered to be a black body at the temperature given by the
long wave radiation measurement. Any energy that reaches it from the ground is
considered to be perfectly absorbed, with no reflection.
58
Element Definitions in RadThermRT
For the RadTherm/RT model used in this Project the elements representing the
Interstate were defined as Interstate Highway asphalt terrain elements, the landscape is
defined as foliage short grass, N 19th is defined as a county highway asphalt, and the
bridge abutments as heavy concrete pads. The terrain element parts are displayed in
Figure 22.
A.
Figure 22. Terrain element definitions, (A) elements defined as Interstate Asphalt, (B)
elements defined as county road asphalt, (C) elements defined as heavy
concrete pads, (D) elements defined as short grass foliage.
Each part of the bridge model was imported as a separate part, that is each section
of bridge deck, each support I beam, and each barrier. Correct properties could be input
for each part namely; thickness(mm), density(kg/mA3), thermal conductivity(W/m-K),
59
specific heat(J/kg-K),emissivity values and absorptivity values. For this project a new
material property was defined in RadTherm/RT called “reinforced concrete” with the
following properties; density of 2400 kg/m3, specific heat of 1050 J/kg-K and
conductivity of 2.5W/m-K. In addition a new surface property definition was created with
the following values; absorptivity of 0.65 and emissivity of .94. These definitions were
applied to all of the bridge elements and the thickness was defined for each part
individually.
View Factor Calculation in RadTherm/RT
View Factor Setting
RadTherm/RT utilizes a ray-tracing scheme to calculate the view factors,(22).
Conceptually a hemisphere is constructed at the centroid of each element and on each
side of the element, see Figure 23. Then rays are cast out from this hemisphere into the
enclosure and intersections with other elements are determined and tabulated. Thus each
time a ray reaches another element equation (22) is calculated. If multiple rays hit an
element the view factor calculation is performed multiple times and an average value is
reached. Figure 23 shows a single ray being cast into space and intersecting another
element [RadTherm manual Determining Radiation View Factors], The more rays that
are cast from each element, the more accurate the view factor calculation is. Table 12
shows how the amount of rays cast can be adjusted. There is a computation time cost for
an increase in the number of rays cast.
60
Figure 23. View factor calculation. (I) two meshes view each other, (2) a hemisphere is
constructed in each element and rays are cast intersecting other elements, (3)
showing all of the rays cast from a single element. Graphics from
ThermoAnalytics website.
View Factor Element Divison Setting
In addition to being able to adjust the number of rays to be sent out from each
element, there is also the ability to subdivide each element and cast rays from each
section of the divided element. Thus a setting of one means that the element is not
subdivided, a setting of two will divide the element in half. Care must be used when
increasing the number of subdivisions; each increase in subdivisions can lead to greatly
increased computation time. Although increasing the subdivisions also increases the
accuracy. Thus the user can decide on a balance between a speed optimized solution or an
accuracy optimized solution.
61
Table 12. View factor settings
Element Division setting
I
View Factor Settings
I
2
3
4
5
512
(Fastest)
1152
(default)
2048
3200
4608
2
3
4
5
Rays Cast from Each Element
1024 1536
2048
2560
2248
3456
4608
5760
4096
6400
9216
6144
9600
13824
8192
10240
16000
23040(most
accurate)
12800
18432
Apparent Area Resolution View Factor
Setting
In addition to the view factors between elements, it is also necessary to know how the
elements view the sun. RadThermRT uses its ray-tracing scheme to make an apparent
area calculation. This approach is very similar to the view factor calculation, essentially a
view factor is calculated between for each element to the sun, at each time step, where the
area of the sun is known and the distance to the sun is known. The rays are cast from the
centroid of the element to the sun at each time step to make the apparent area calculation.
The number of rays that are cast from the centroid of each element to the sun can be
adjusted for desired accuracy.
Table 13. Apparent area settings. Adapted from RadTherm manual
Rays Cast from Each Element
Apparent Area Setting
512 (Fastest)
1
1152(default)
2
2048
3
3200
4
4608 (most accurate)
5
62
The apparent area calculation is how RadTherm accounts for shadowing. If the rays are
blocked by another element, then the body is in shadow. If only some of the rays are
blocked, then the body is only partially shadowed.
Solution to Temperature Distribution
RadTherm allows for several different ways of specifying initial temperatures of
parts. These temperatures are set as boundary conditions during model setup. If no
previous runs have been carried out then the initial part temperatures can be specified or
RadThemVRT can assign temps from a previous run, or from a different model using the
same geometry. The methods used for temperature initialization in this project are
discussed in the Initialization section.
If the model parameters and meteorological data have been entered correctly then
solving the system of governing equations, which are written for each thermal node,
should result in a physically reasonable temperature distribution. This system of
equations is solved using a semi direct solution method. RadThemVRT uses Successive
Over-Relaxation, SOR for its iterative solution. SOR uses a relaxation parameter that is
adjusted to speed convergence. RadThemVRT automatically adjusts this parameter based
on how the solution is converging. To solve the matrix solution, or the direct method,
RadThemVRT uses Gauss elimination with partial pivoting. The Gauss elimination is
done at the beginning of each iteration of the SOR solution as a preconditioner for nodes
that are known to be strongly dependent upon one another. The direct solution solves the
governing equations of these nodes simultaneously, which allows the node temperatures
to converge quickly from the initial values to the temperatures that satisfy the governing
63
equations. After the direct solution is complete the solution proceeds with an SOR
iteration in which the governing equations are evaluated for each node. The iterations
continue until all node temperatures have converged. Then the solution advances to the
next time step and repeats [Martilla 1999].
Two different methods are available for determining when the iterative solution has
converged; a tolerance method and a tolerance slope method. Both methods use the
solution tolerance, which is the maximum change in any node temperature between two
iterations. The tolerance method specifies convergence when the solution tolerance is less
than the specified tolerance value. The tolerance slope method keeps a record of the
solution tolerance for each iteration. A line is fit to the last portion of the tolerance data
using a linear lest squares curve fit. The tolerance slope method specifies convergence
when the absolute value of the slope of the fit line is less than the specified tolerance
slope value for 2 consecutive iterations.
Experiment Method.
Western Transportation Institute’s (WTI) mobile laboratory was utilized in the data
collection for this thesis. The mobile lab is a versatile vehicle with many systems to aid in
the collection of data at sites away from the university, without having to build a
permanent site for housing of instruments and computers. The mobile lab has an
advanced electrical system, which has deep cell batteries, a dc generator, a true sine
power inverter, and the necessary circuitry for clean AC power delivery.
The mobile lab is equipped with a National Instruments (NI) Data Acquisition
computer. Which is a standard Windows based PC processor with a built in data
64
acquisition board ,DAQ. LabView is software, which is installed on the PC, isdeveloped
to work with NI DAQ boards. LabView is a graphical programming language and is
considered one of the standards for data acquisition software. LabView programming
language is used to develop Virtual Instruments (VI). For this project a VI was developed
that will read data from the three solar radiation instruments and the road surface
temperature sensor, this VI also converts the voltage readings to a flux value for the solar
radiation sensors and a temperature value for the IR thermometer, using the sensitivity
values of the sensors. The data along with a time stamp for each data reading is stored in
a space delimited ASCII text file that can be read by spreadsheet software.
The mobile lab is equipped with a telescoping pneumatic mast which can go to
around 50’ in height and which a WeatherPak meteorological weather system can be
attached. There is also a coiled cable that is attached to the mast at the top and bottom,
and carries the data signal from the WeatherPak to the DAQ computer. Figure 24 shows
the van with the weather station deployed.
The NI DAQ computer is used to acquire and store all of the meteorological data
using proprietary software from WeatherPak, called Intercept. The data cable is attached
via the serial port on the computer. Intercept creates an archive spreadsheet file with the
time stamped meteorological data.
65
Figure 24. WTI mobile lab with WeatherPak meterological station deployed.
The mobile lab was parked on the south east side of the bridge, on the shoulder of the
road. The van was leveled using the hydraulic leveling system. The meteorological
system was then attached to the mast, and raised to its maximum height. The solar
instruments were placed on the top of the van. The array of sensors was then aligned so
that it pointed south and the shadow band for the diffuse sensor was adjusted to correct
angle so that it remained in shade for the entire test period. The IR thermometer was
placed on the walkway of the bridge at the center of the bridge. The thermometer was
then aimed at the area of interest. A cable with two conducting wires was used to transmit
the temperature data to the DAQ board in the van. The power systems in the van were
turned on. The NI DAQ computer was turned on and the LabView Virtual Instrument,
66
and the Intercept software, was then started in the van and continued to collect data for
the length of the experiment.
Data formatting
The data was then formatted for input into RadTherm/RT. RadTherm/RT requires
that the data be in the format called Extended Weather File Format(.XWA), the XWA file
format structure is a Space-character delimited ASCII Text File. The first line of the
weather file identifies the file as an extended format weather file. In this file each data
record is stored as 2 lines. Thus, following the file type identifier, there are two header
groups. The header for the first group starts with
The header for the second group
starts with "#A". The variables for this format are shown and are in the order they need to
be input. An example of what this data file looks like is presented in Figure 25.
The data was formatted in Excel and then using a script [Mckittrick, unpublished],
was formatted into the correct .XWA format. The data was acquired using two different
DAQ systems, Lab View and Intercept. Unfortunately the Intercept software was unable
to acquire data on a regular time interval and some interpolation of data was required for
the data to be in a regular time step of five minutes. Because the LabView solar VI was
able to acquire data on a consistent time interval the meteorological data was interpolated
to the.solar data times.
67
Table 14. Variables for the .XWA, files adapted from RadTherm User manual
Variable
DATE
TIME
WINDSPD
w in d d ir
TAIR
RHUM
PAIR
HELIUM*
PYRANOM* =
DIF SOLAR* =
Sk y t * =
IRSKYT* =
CLOUD=
RAIN =
RAINT =
ZENITH** =
AZIMUTH**
Description
DDMMYY (Day, Month, Year)
Seconds
Wind Speed in Knots
Wind Direction (from North to East) in Degrees
Air Temperature in degrees C
Relative Humidity in %
Barometric Pressure in Millibars
Pyrheliometer Reading (Direct Solar Beam) in W/m2
Pyranometer Reading (Total Solar on Horizontal) in W/m2
Diffuse Solar Component in W/m2
Broadband Effective Sky Temperamre in degrees C
Sensor Band Effective Sky Temperature in degrees C
Cloud cover in tenths (0 = clear, 10 = total overcast)
Rain Rate in mm/hr
Rain TemperaWre in degrees C (dew point will override this value)
Solar Zenith Angle (from Vertical to Horizontal) in Degrees
= Solar Azimuth Angle (from North to East) in Degrees
* : The value -999 can be substituted for solar parameters and a
model will provide the desired value. Also by checking the
"Modeled" checkbox for solar or sky, these values will be
overwritten. IRSKYT will always be overwritten by modeled
values.
Note ** : Any value can be used since thermal solver will
automatically re-compute.
Solar Data Formatting
Three values are measured for the radiation data; global solar radiation, diffuse solar
radiation, and longwave radiation. Each of these values is measured as a flux in watts per
meter squared. The diffuse measurement has to be modified to account for the amount of
sky blocked by the shadow band. This was done using correction factors supplied by the
manufacturer of the instrument.
68
XFOOOl
#W E A T H E R , L O C A L E # L A T , L O N , S T D _ L O N , E L E V ,R H O , 4 5 . 6 0 , 1 1 1 . 0 5 , 1 0 5 . 0 0 , 1 5 2 4 . 0 0 , 0. 0 0
#DATE TIME WINDSPD WINDDIR TAIR RHUM PAIR HELIOM PYRAN
#D D M M Y Y SECNDS KNOTS DEGREES DEG C PERC E N T M B A R W/M 2 W/M 2
# aD I F S O L A R SKY T IRSKYT CLOUD RAIN RAINT ZENITH A Z I M U T H
#A W/m2 C C
mm/hr C
1 3 0 3 0 3 2 4 6 3 2 1.4 0 2 . 5 0 1 0 . 9 0 3 6 . 0 0 8 5 2 . 0 0 - 9 9 9 . 0 0 0.0 0
A 0. 0 0 - 1 1 . 1 1 - 9 9 9 . 0 0 0.0 0 0.0 0 0. 0 0 - 9 9 9 . 0 0 - 9 9 9 . 0 0
1 3 0 3 0 3 2 4 9 3 2 1.4 1 2.7 4 1 0 .98 3 6 . 0 0 8 5 2 . 0 0 - 9 9 9 . 0 0 4.31
A 3.48 - 1 2 . 1 3 - 9 9 9 . 0 0 0.0 0 0 . 0 0 0 . 0 0 - 9 9 9 . 0 0 - 9 9 9 . 0 0
1 3 0 3 0 3 2 5 2 3 2 1 . 0 9 2.1 2 1 0 . 9 1 3 5 . 8 9 8 5 2 . 0 0 - 9 9 9 . 0 0 2 2 . 1 0
A 1 8 . 7 9 - 1 3 . 1 1 - 9 9 9 . 0 0 0.0 0 0.00 0.0 0 - 9 9 9 . 0 0 - 9 9 9 . 0 0
1 3 0 3 0 3 2 5 5 3 2 1. 3 1 2 . 5 5 1 1 . 4 8 3 4 .08 8 5 2 . 0 0 - 9 9 9 . 0 0 3 8 . 3 1
A 3 3 . 4 9 - 1 0 . 6 0 - 9 9 9 . 0 0 0.0 0 0.00 0.0 0 - 9 9 9 . 0 0 - 9 9 9 . 0 0
1 3 0 3 0 3 2 5 8 3 2 2.1 4 4.17 1 1 . 7 5 3 3 . 5 1 8 5 1 . 0 0 - 9 9 9 . 0 0 6 4 . 5 9
A 5 6 . 9 9 - 9 . 3 1 - 9 9 9 . 0 0 0. 0 0 0.00 0.0 0 - 9 9 9 . 0 0 - 9 9 9 . 0 0
130303 26132 2 . 6 0 5 . 0 5 1 2 .1 0 3 3 .0 2 8 5 1 .0 0
-
999.00 70.10
A 4 3 .78 - 8 . 1 8 - 9 9 9 . 0 0 0. 0 0 0.00 0.0 0 - 9 9 9 . 0 0 - 9 9 9 . 0 0
1 3 0 3 0 3 2 6 4 32 3 . 1 9 6.20 1 1 . 3 2 3 6 . 0 0 8 5 1 . 0 0 - 9 9 9 . 0 0 1 1 7 . 6 1
A 4 9 . 8 2 - 7 . 7 5 - 9 9 9 . 0 0 0. 0 0 0.00 0.00 - 9 9 9 . 0 0 - 9 9 9 . 0 0
1 3 0 3 0 3 2 6 7 3 2 1.87 3 . 6 3 1 1 .67 3 5 . 2 5 8 5 1 . 0 0 - 9 9 9 . 0 0 9 4 . 7 6
A 3 6 . 9 3 - 4 . 5 5 - 9 9 9 . 0 0 0.0 0 0. 0 0 0. 0 0 - 9 9 9 . 0 0 - 9 9 9 . 0 0
Figure 25. Example of a portion of an extended weather format file.
Using the following equations and reading the right correction factor off of Table 15,
from the LTCOR LI-200SB pyranometer user manual, the corrected diffuse radiation
value can be obtained,
D =
Dl C
1
1.171.2+11.8(x)
D
G
(44)
(4 5 )
69
where Dc is the corrected diffuse radiation, Dl is the measured value of diffuse solar
radiation, C is the correction factor from Table 15, G is the measured global solar
radiation value. The Dc values were calculated after the data was acquired and were
calculated in an Excel spreadsheet. These values were then used as the data for input into
the extended weather file format.
Table 15. Correction factors supplied
with a shadow band.
Mar Apr May
Lat. Jan Feb
°N
Jul Aug Sep Oct Nov
1.12 1.15 1.17 1.15 1.14
0°
10° 1.11 1.14 1.16 1.16 1.14
1.10 1.12 1.15 1.16 1.15
20°
1.09 1.11 1.14 1.15 1.15
30°
1.07 1.09 1.12 1.14 1.15
40°
1.06 1.08 1.11 1.13 1.14
50°
1.05 1.06 1.09 1.11 1.14
60°
1.05 1.07 1.10 1.13
70°
1.05 1.09 1.14
80°
1.09 1.14
90°
by Li-Cor for correcting diffuse readings taken
Jun
Dec
1.12
1.13
1.14
1.14
1.14
1.14
1.14
1.15
1.15
1.16
Jul
Jan
1.12
1.14
1.14
1.15
1.15
1.14
1.14
1.14
1.14
1.15
Aug
Feb
1.14
1.15
1.15
1.15
1.15
1.14
1.12
1.11
1.11
1.11
Sep
Mar
1.16
1.16
1.15
1.14
1.13
1.11
1.10
1.09
1.07
1.06
Oct
Apr
1.15
1.14
1.13
1.11
1.10
1.09
1.07
1.05
1.04
Nov
May
1.14
1.12
1.11
1.09
1.08
1.07
1.05
1.04
Dec
Jun
1.12
1.11
1.09
1.08
1.07
1.05
1.04
The longwave radiation flux data had to be converted to a sky temperature. This is
done using the Stefan-Boltzmann law for a black body stated here [Incrope et al 1996],
(4 6 )
where here Qiw is the longwave radiation flux of the sky in Watts/m2 , where the sky is
assumed to be a blackbody, a is the Stefan-Boltzmann constant. Thus the measured
longwave radiation data is Qiw. Thesky temp is calculated using,
(47)
70
This was also done in Excel at the same time as the calculation for the corrected diffuse
radiation measurement. The solar data was then ready to be combined with the
meteorological data for input into RadTherm/RT.
Meteorological Data Formatting
This was all done in Excel using sort functions and interpolation functions. The
method used for this project is discussed next. The time values for the .XWA file are in
seconds. Excel stores dates and times as serial numbers. If the format of a time or date
column is changed to a general number format, a long string of numbers is viewed. The
numbers preceding the decimal are the date. Where January,! 1900 has a value of I and
December,31 9999 has a value of 2958465. The numbers after the decimal are the time of
day, and represent the fraction of day that has passed thus 12:00:00 pm is .5. So
December,31 9999 at noon would be represented as 2958465.5. This method allows the
dates to be manipulated. Intercept’s time stamp included the date and time. So it was
necessary to convert this time stamp to a column of dates and a column of seconds
passed. First two new columns were inserted next to the time stamp column. Then in the
second column a function was used to first subtract the date part of the serial number and
then multiply the time portion by the number of seconds in a day, 86400. The resultant
value is the number of seconds that have passed that day, then the date was manually
input into the first column in the DDMMYY format. Next the columns were moved to
match the order required by the extended weather file format. And columns were inserted
next to each data type. These new columns were for the interpolated data. The time stamp
was similarly manipulated for the solar data. In addition, a new column of ascending
71
numbers (l,2,3...n) was added in the solar data spreadsheet. This column of ascending
numbers was used to sort the data after the interpolation calculations were completed.
The solar data spreadsheet was then copied and pasted below the meteorological data
with the time columns lined up. The global, diffuse, and resort data was then moved to
the empty columns to the right of the meteorological data. After selecting all of the data,
the sort ascending function, was applied to all of the data with the time passed in seconds
column as the criteria of the sort. This step was used to show where the meteorological
data needed to be interpolated. An interpolation formula was then input into the first
space where interpolation needed to be done. The interpolation function used is a time
weighted linear interpolation formula. The formula used was.
•t +
J
I
XO
/
+
\
V (t +
1) - (7 - 1)
■(f + 1)
(4 8 )
This formula can be easily input into Excel. For example if the data from which the
interpolation is for is in column C and the time data is in column B then the formula for
the first row would be.
= IF (C 2 = " " ,((C 3 -C 1 )/($ B 3 -$ B 1 )* $ B 2 )+ (((C 3 X C 3 -C 1 )/($ B 3 -$ B 1 )* $ B 3 ))," " )
Where the double apostrophe,
(4 9 )
means “nothing”. Thus the function reads If cell C2
was equal to nothing then use the interpolation function, else do nothing. Then using the
fill command this function was then filled down the first column and then across. Then it
can be filled down each of the interpolation columns. The data was the copied and a new
sheet was opened. The data was then input using a special paste function that only inputs
the values of the cells and not the formulas. Then a sort function was again used, this
72
time on the column of ascending numbers. Now the data was in a uniform time step
format. See Figure 26 and 27 for a visual description of this method.
Initialization
RadTherm/RT requires that some of the temperatures be specified at the beginning of
the analysis. These values are used as the first values in the solution routine. The terrain
elements require the core temperature to be specified. The standard and three layer
elements require the initial surface temperature. If simulations are run on a continuous
basis then results from previous runs can be used to initialize the subsequent runs. An
attempt was made to measure surface temperatures on several regions of the bridge at the
beginning of each data collection period. These measured values were used as the initial
temperatures for three of the simulations; The April 7 9:00 pm to April 8 8:55 am
simulation, April 8 9:01 pm to April 9 1:36 am simulation, and the March 13 simulation.
The April 8 9:01am to April 8 8:46pm simulation was initialized using results from the
April 7 9:00 pm to April 8 8:55 am simulation. The core temperatures were calculated
using an equation developed by Bristow [2002] which gives the core temperature, Tgis in
degrees Celsius based on the day of the year. The data that this equation is based on was
measured in Montana and should give a reasonable approximation to the actual core
temperature.
+10.3,
(5 0 )
73
(1 IThis is a porti on o f the ori gi nal data Aa u ir ed from the W e a t h e r P a k via Intercept.
Station
# 1 2 5 7 ( R W IS s t a t i o n
for R a d T h e r m
),M o n t a n a
Avg.W ind
L o c a l D ate
(
2
)
and
3 /1 3
3 /1 3
3 /1 3
3 /1 3
3 /1 3
3 /1 3
3 /1 3
3 /1 3
3 /1 3
3 /1 3
Tim
/2 0 0
/2 0 0
/2 0 0
/2 0 0
/2 0 0
/2 0 0
/2 0 0
/2 0 0
/2 0 0
/2 0 0
e
3
3
3
3
3
3
3
3
3
3
Speed
0
1
I
I
6:5 9
7:0 3
7:0 5
7:0 7
7:0 8
7:0 9
7:11
7:12
7:13
7:17
I
2
3
2
2
State
University
Avg.W ind
D i r e c Ii o n
.7
.6
.3
.6
1
.5
.8
.5
.8
.6
I
2
I
1
1
1
1
I
I
I
9
I
7
8
5
5
6
7
5
9
8
0
5
6
5
8
5
5
9
I
Barometric
P re s s u re
8 5
8 5
8 5
8 5
8 5
8 5
8 5
8 5
8 5
8 5
A ir T e m p
10.8
1 I .1
1 1 .5
I 1 .5
I 1 .7
I 1 .6
I 1 .9
I 2 .3
I 2 .5
I 1 .9
Relative
H u m i d i ty
2
2
2
I
I
I
I
1
I
1
3
3
3
3
3
3
3
3
3
3
7
6
4
4
4
4
3
I
1
4
The ti me s t a m p s are m o d i f i e d to s h o w the d at e in DDIVIMYY format and
ti me in s e c o n d s
A v g W
D A T E
D D M M Y Y
T i m e
S
S p e e d
In d
A v g W
B a r o m
in d
Di r e c t i o n
Ai r
T e m
p
R e Ia l i v e
elric
H u m
P r e s s u r e
id i t y
3 7
8 5 2
0 .7
19 8
0 .8
2 5 2 8 7
I .4
2 0 7
I I
2 5 5 3 7
I .3
17
1 3 0 3 0 3
2 5 6 3 0
I .6
18 6
I .5
8 5 I
3 4
1 3 0 3 0 3
2 5 7 2 4
I
15 5
I .7
8 5 I
3 4
1 3 0 3 0 3
2 5 16 3
1 3 0 3 0 3
1 3 0 3 0 3
5
I .5
8 5 2
3 5
8 5 2
3 4
1 3 0 3 0 3
2 5 7 8 6
I .5
15 8
I .6
8 5 I
3 4
1 3 0 3 0 3
2 5 8 7 9
2 .8
16 5
1 .9
8 5 I
3 3
1 3 0 3 0 3
2 5 9 4 2
3 .5
17
5
2 .3
8 5 I
3 I
1 3 0 3 0 3
2 6 0 0 5
2 .8
15 9
2 .5
8 5 I
3 I
1 3 0 3 0 3
2 6 2 5 5
2 .6
19
I .9
8 5 I
3 4
1
131 The s o l a r data s c o o i e d to the r e a i o n b e l o w the m e t e r o l o a i c a l data with the
Avg.
Avg. Interp
Interp Air Barometric
Interp
Wind
Wind Wind
DATE DDMMYY Time S Speed Sp eed Direction Wind Dir Air Temp
Tem p
P ressu re P ressu re
852
10.8
198
0.7
25163
130303
852
11
207
1.4
25287
130303
852
11.5
175
1.3
25537
130303
851
11.5
186
1.6
25630
130303
851
11.7
155
25724
I
130303
851
11.6
158
1.5
25786
130303
851
11.9
165
2.8
25879
130303
851
12.3
175
3.5
25942
130303
851
12.5
159
2.8
130303
26005
851
11.9
191
2.6
26255
130303
25232
25532
25832
26132
Relative
Humidity
37
35
34
34
34
34
33
31
31
34
Interp
Humidity Global Diffuse IR SKY T RESORT
22.10
38.31
64.59
70.10
18.79
33.49
56.99
43.78
-13.11
-10.60
-9.31
-8.18
3.00
4.00
5.00
6.00
141 S o r t F u n c t i o n u s e d with Ti me S c o l u m n u s e d to d e f i n e w h a t
to s o r t
Avg.
Interp
Avg.
Interp
R elative
Interp
Interp Air B arom etric
Interp
Wind
Wind W ind
DATE
T em p
P re ss u re P re ss u re Humidity Humidity Global Diffuse IR SKY T RESO R T
DDMMYY
Time S S p e e d S p e e d Direction Wind Dir Air Tem p
37.00
852.00
10.80
198.00
130303.00 25 163.00 0.70
-13.11
22.10 18.79
25 232.00
35.00
852.00
11.00
207.00
130303.00 25287.00 1.40
-10.60
33.49
38.31
25532.00
34.00
852.00
11.50
175.00
1.30
130303.00 25537.00
34.00
851.00
11.50
186.00
130303.00 25 630.00 1.60
34.00
851.00
11.70
155.00
130303.00 25724.00 1.00
34.00
851.00
11.60
158.00
130303.00 25786.00 1.50
64.59 56.99
-9.31
25832.00
33.00
851.00
11.90
165.00
130303.00 25879.00 2.80
31.00
851.00
12.30
175.00
130303.00 25 942.00 3.50
31.00
851.00
12.50
159.00
130303.00 26 005.00 2.80
70.10 43.78
-8.18
26 132.00
34.00
851.00
11.90
191.00
130303.00 26255.00 2.60
Figure 26. Description of data formatting method steps 1-4.
74
(S)Insert the interpolation fo rm ia and fill it across and dcwwi each interpolation
Irlerp
AyWrd Wnd Ay Whd Intap
CATE
CCfVTvtyY TimeS Sfceed Sfceed Drecbcn WndDr
19800
130303 25163
QTO
1.09
20301
25232
207.00
1.40
130303 25287
1.30
17564
25532
1.30
17500
130308 25537
18600
1.83
130303 25630
15500
130803 25724
1.00
15800
1.53
130303 25786
214
161.46
25832
16500
280
130803 25879
17500
350
130303 25942
19900
280
130303 26005
270
17526
26132
191.00
263
130308 26255
CdUTTI
IrterpAr Baomgthc Irterp
ArTenp Terrp Ressue FTessue
85200
1Q80
1Q91
85200
85200
11.00
11.49
85200
85200
11.50
851.00
11.50
851.00
11.70
851.00
11.60
11.75
851.00
861.00
11.90
851.00
1230
851.00
1250
1220
851.00
851.00
11.90
tiarve Irtop
Krridty Fimdty
37.00
3589
3500
34.02
34.00
34.00
34.00
34.00
3351
3300
31.00
31.00
3252
34.00
Qctd
Dffvse IRSCTT FtiSCRT
2210
1879
-1311
3
3831
3349
-1Q60
4
61.59
5699
-931
5
7Q10
4378
-818
6
(6) Do another sort function, this time on the Resort C d u m
IrterpAr c
Irterp
Ftiarve rtep
Ay Wnd Wnd
Ay Wnd Intap
CATE
Dffuse IRSKVT FtiSCRT
FTeesue FTessue Firridty Hrridty Qdti
DCMVTyY TimeS Sbeed §Deed Drecbcn WndDr ArTerrp Terrp
2210
1879 -1311
3
3589
1Q91
85200
1.09
20301
130303 25232
4
34.02
3831
3349 -1Q60
11.49
85200
1.30
17564
130303 25632
5
61.59
5899
-931
3351
11.75
851.00
214
161.46
130303 25832
6
TQ10
4378
-818
3252
1220
851.00
270
17526
130303 26132
37.00
85200
19800
1Q80
130303 25163
QTO
3500
85200
11.00
207.00
1.40
130303 25287
34.00
85200
11.50
17500
1.30
130333 25537
34.00
11.50
851.00
18600
1.60
133303 25630
34.00
851.00
11.70
15500
25724
1.00
130303
34.00
851.00
11.60
15800
1.50
130303 25786
3300
851.00
11.90
16500
130303 25879
280
31.00
851.00
1230
17500
350
130303 25942
31.00
851.00
1250
15900
280
130303 26005
34.00
861.00
11.90
191.00
260
130303 26256
(T)DeletecxiiiTTBWithorignaIrnetdata, n c w d a ta is o n a irifo rm tim e s te p a n d
ready to be iir th r a j^ T the Pearl script for input into RadTherm
Irterp
InterpAr Irterp
Irterp
Interp
Dffuse IRSKTT
R e s s u b Hrridty Ocbel
DME CCMWY EmsS Wnd
WndDr Terrp
2210
1879 -1311
35.89
10.91 85200
1.09 203.01
130308 25232
38.31
33.49 -10.60
34.02
11.49 85200
1.30 175.64
130308 25532
-9.31
64.59
56.99
3351
11.75 851.00
214 161.46
130303 25832
-818
70.10
4378
3252
1220
851.00
175.26
26132
270
130803
Figure 27. Description of data formatting method steps 5-7.
75
RESULTS AND FINDINGS
In this chapter, the modeled data is compared with measured data. In the first
section results from a convergence study are presented. In the next section results from a
total of four RadTherm/RT simulations are presented. Also presented to the data are some
interesting results from RadTherm/RT.
Convergence Study Results
This section presents comparisons between model results and actual data. The
temperature was collected on the pedestrian walkway to isolate the measurement point
from vehicle influences. Data presented is from two simulations. One simulation occurs
mainly during the night and the other during daylight hours. Results are shown for each
of the simulation periods with different bridge mesh densities and different view factor
settings. These data sets are used to show trends between computation time and model
accuracy. This comparison study is for drawing some general conclusions on the
convergence of the solution due to variations in two different parameters. The parameters
that were varied are the number of elements used in the bridge mesh and the view factor
settings in the software. There were three different bridge models used, a bridge mesh
with around 3000 elements, a bridge mesh with around 300 elements and one with
around 10 elements. In addition to varying the number of elements in each bridge model,
the view factor settings were modified. There are three different view factor adjustments;
view factor, apparent area, and number of divisions per element. They were varied
76
according to Table 16. The minimum value for each setting is one and the maximum
value is five. The physical meaning of these view factor settings was discussed in
Chapter 3,(section 3, View Factor Calculations). There is a computation time cost
associated with increasing either the number of elements or increasing the view factor
settings. Table 17 is a presentation of the relationship between the computation time and
the mesh and view factor parameters. RadThermTRT first computes the view factors for
all of the geometry, that is how each element views the other elements. Next,
RadThemVRT calculates the time varying temperature solution. Figure 28 shows some of
the differences between the results of the different bridge meshes. This figure shows
results from the April 8 9:01 am to April '8 8:4.6 pm simulation with default view factor
settings.
Table.16. View factor settings value
Low setting
View Factor Setting
I.
View Factor
I
Apparent Area
I
Element Division
Default setting
I
2
I
High setting
4
4
4
Some observations that can be made from Figure 28are that the 3000 elements bridge
mesh tracks the shadowing that occurs on the pedestrian walkway in the afternoon very
well. The 300 elements bridge mesh simulation takes more time to cool in the late
afternoon. This can be attributed to the fact that there is only one horizontal element
between the vertical pedestrian barriers on each side of the walkway. The 3000 elements
bridge mesh has three elements between the vertical pedestrian barriers. This leads to the
large numbers of elements bridge mesh simulation ability to track the shadowing that
77
occurs in the center of the walkway more accurately. This behavioris discussed in greater
detail in the shadowing section of this Chapter. The 10 elements bridge mesh, as
discussed previously does not have any barriers or support beams, this results in no
shadowing on the bridge deck. This lack of shadowing causes the temperature to rise
earlier in the morning, compared to the other two bridge mesh results. The measured and
the actual temperatures do intersect near the middle of the day, so this bridge simulation
does model the behavior of the bridge deck in an overall sense, however this model can
not predict shadowing events on small regions of the bridge deck.
Statistical results are presented in tables 18 through 23. These were calculated by
comparing the results file from the RadThemVRT simulations with the measured
temperature data. The error values are computed in degrees Kelvin by subtracting the
measured value from the calculated value. The mean of the error values and the standard
deviation values are shown in the tables. The coefficient of determination (R2 mod) is a
statistic used to measure how well the modeled data matches the measured data. If
multiplied by a hundred, R2 mod can be viewed as the probability that the modeled result
will match the measured data for the given scenario, R2mocI is calculated using the
following equations.
( 51)
mod
Sxx
(52)
^xx
(x i
/T l)
•
(53)
78
30
25
20
15
I
i
7:12A M
9:36A M
12:00PM
224 PM
♦ Bridge Walkway Measured Temperature
4:48PM
7:12PM
9:36PM
•- BridgeWalkway PredictedTemperature
Figure 28. Temperature comparison between measured temperature and calculated
temperature for daytime simulations run on data from April 8 9:01 am to April
8 8:46 pm with Default view factor settings; (A) results from the 3000
elements bridge mesh, (B) results from the 300 elements bridge mesh and (C)
results from the 10 elements bridge mesh.
79
Table 17. Calculation times for view factors(VFC) and solution calculation (SC) times
for twelve hour simulations run on Silicon Graphics Origin 2100 Server
300
element
3000
element
10
. element
mesh
mesh
mesh
HH:MM:SS
HH:MM:SS
HH:MM:SS
Low View Factor
00:00:55
00:00:20
200:00:15
VFC
00:19:56
00:12:18
00:11:50
SC
Default View Factor
00:30:50
00:01:15
00:00:30
VFC
00:14:13
00:29:48
00:12:30
SC
High View Factor
1:00:50
00:20:00
00:14:55
VFC
SC
00:18:50
00:14:30
00:34:30
Where the x values refer to the RadThemVRT modeled values and the y values refer to
the measured temperature data. The n values are the number of time steps in the
simulations, px is the mean value of all of the modeled temperature readings. Rmod is the
correlation coefficient and provides a measure of the how well the modeled results data
correlate with the measured data, and is the square root of R2mod- Rfit is a statistic that
gives an indication of how well the relationship between the modeled and measured data
temperatures can be represented with a linear relationship.
All of the R values lie
between one and zero. The closer the values are to one the better fit or correlation. Rfit is
the square root OfR2At, which is calculated using the following equations,
Sxy2
R f * = - Syy ■Sxx
(54)
Xl(A
(55)
Ryy
Rxy~
~~
(xi
Ay) >
MxXyl
My)’
(56)
80
where Jiy is the mean of the measured temperature. The AT and 8T values in tables 18
through 23 are the error values at the maximum and minimum actual temperature
measurements. The “percentage high” measurements are the percentage of modeled
temperatures that are above the measured temperature values and the “percentage low”
values are the percentage of modeled temperatures that are below the measured values.
The results from the convergence study are mixed. There is a clear indication that the
3000 and 300 element bridge mesh models do a better job than the 10 elements bridge
mesh model. This is reflected in lower values of the mean error and higher values of for
the correlation coefficients for the denser meshes. However the results between the 3000
elements bridge mesh and the 300 elements bridge mesh do not indicate greater accuracy
with greater number of elements. There is also indication that the accuracy of the results
increases as the view factor settings are increased. The values for the AT and ST are
smaller from the simulations with the highest view factor settings as is the mean of the
error. In addition the correlation coefficients are higher which would indicate a better
correlation with the measured data. Generally the results from the 300 and 3000 number
of elements are very close. This may lead to the conclusion that the medium mesh is a
better model choice on which to continue study than the 3000 elements model. In the next
section a discussion on the shadowing calculations in RadThemVRT is presented. This
focuses on how some error may have been introduced in the analysis of the 3000
elements bridge mesh simulations.
81
Figures 29 and 30 show the correlation graphs of the data from the 300 elements
bridge mesh and the 3000 elements bridge mesh with high view factor settings. These
figures demonstrate the correlation between the calculated and the actual temperatures.
Where the abscissa is the actual data and the ordinate is the data calculated by
RadTherm/RT. A perfect correlation would lie on the dotted line in the graph, this would
occur if there was no error. Both of these figures show that most the data is above the
perfect correlation line.
Figures 31and 32 show a normalized histogram against a normal curve of the error
data from the 300 elements bridge mesh and the 3000 elements bridge mesh, with both
having high view factor settings. Because the data in the histogram diverge from the bell
curve the data is not perfectly described by statistics based upon a normal distribution.
The figures do show that the error is largely centered on the mean, value of the error. The
3000 elements bridge mesh results fall more closely within the normalized curve. This
would indicate that this model may actually be more accurate than the results in the
previous tables show. Figure 32 for the 3000 elements bridge mesh would indicate that
the model is consistently off and not randomly inaccurate. The shadowing section
discusses a possible reason for this error.
82
Table 18. Nighttime simulation statistics for April 7, 9:00pm through April 8, 8:55am
with low view factor settings and varying element size.
10 elem ent
Mean o f Error
1.20
300 elem ent
3000 e lem ent
0.68
0.68
S tandard D eviation o f Error
0.82
0.73
0.73
R2 m od
0.19
0.18
0.62
Rmod
0.43
0.43
0.79
R2 fit
0.75
0.80
0.80
Rfit
0.86
0.89
0.89
AT
1.24
1.59
1.60
5t
1.63
0.92
-1.32
percentage low
94.44%
81.25%
82.64%
percentage high
5.56%
18.75%
17.36%
Table 19. Nighttime simulation statistics for April 7, 9:00pm through April 8, 8:55am
with default view factor settings and varying element size.
10 elem ent
300 elem ent
3000 e lem ent
1.20
0.68
0.57
0.82
0.72
0.75
R2 mod
0.19
0.18
0.66
Rm od
0.43.
0.43
0.81
R2 fit
0.75
0.80
0.79
Rfit
0.86
0.89
0.89
AT
2.02
1.59
1.60
0.74
Mean o f Error
S tandard D eviation o f Error
5t
percentage low
1.63
0.92
94.44%
81.25%
75.69%
percentage high
5.56%
18.75%
24.31%
Table 20 Nighttime simulation statistics for April I, 9:00pm through April 8, 8:55am
with high view factor settings and varying element size.
10 elem ent
300 elem ent
3000 e lem ent
0.66
Mean o f Error
1.21
0.48
Standard D eviation o f Error
0.81
0.73
0.73
R2 mod
0.18
0.27
0.64
Rmod
0.43
0.52
0.80
R2 fit
0.75
0.80
0.80
Rfit
0.86
0.89
0.89
AT
2.02
1.48
1.58
6t
percentage low
1.64
0.71
0.86
94.44%
72.22%
84.03%
percentage high
5.56%
27.78%
15.97%
83
Table 21. Daytime simulation statistics for April 8, 9:01 am through April 8, 8:46 pm
with low view factor settings and varying element size.
10 elem ent
Mean o f Error
-4.90
300 elem ent
3000 elem ent
-3.60
-3.85
3.07
S tandard D eviation o f Error
3.90
3.08 '
R2 m od
0.31
0.61
0.58
Rm od
0.56
0.78
0.76
R2 fit
0.78
0.84
0.84
Rfit
0.88
0.92
0.92
AT
2.69
1.34
1.32
5t
percentage low
-11.71
3.18
-8.29
13.38%
14.08%
8.45%
percentage high
86.62%
85.92%
91.55%
Table 22. Daytime simulation statistics for April 8, 9:01 am through April 8, 8:46 pm
with default view :?actor settings and varying element size.
10 elem ent
300 elem ent
3000 elem ent
Mean o f Error
-4.90
-3.17
-3.76
S tandard D eviation o f Error
3.90
2.93
3.08
R2 mod
0.31
0.67
0.59
Rm od
0.56
0.82
0.77
R2 fit
0.78
0.85
0.84
Rfit
0.88
0.92
0.92
AT
2.97
2.05
2.13
5t
-11.72
-4.54
-7.68
percentage low
13.38%
19.01%
11.97%
percentage high
86.62%
80.99%
88.03%
Table 23. Daytime simulation statistics for April 8, 9:01 am through April 8, 8:46 pm
with high view factor settings and varying element size. .
10 elem ent
Mean o f Error
-5.22
300 elem ent
-3.17
3000 elem ent
-3.85
S tandard D eviation o f Error
3.70
2.93
3.07
R2 mod
0.28
0.64
0.58
Rm od
0.53
0.80
0.76
R2 fit
0.76
0.84
0.84
Rfit
0.87
0.92
0.91
AT
2.11
1.52
1.85
5t
-9.43
-5.32
-7.56
percentage low
11.97%
19.01%
8.45%
percentage high
88.03%
80.99%
91.55%
84
Measured Temperature (deg C)
Figure 29. Correlation graph for 300 elements bridge mesh with high view factor settings
April 8, 9:01 am through April 8, 8:46 pm.
H 10
Measured Temneratnre (deg CO
Figure 30. Correlation graph for 3000 elements bridge mesh with high view factors from
April 8, 9:01 am through April 8, 8:46 pm data.
85
-15.41 -12.39 -9.38 -6.37 -3.35 -0.34
2.68
5.69
8.71
11.72
Figure 3 1. Histogram graph of 300 elements bridge mesh data with high view factors
from April 8, 9:01 am through April 8, 8:46 pm data and associated normal
curve distribution.
0.25 I
0.25
' ' ‘
p=-3.78
0.2
Densit
0.15
0.1
0.05
0
-16.18 -13.08 -9.98 -6.88 -3.78 -0.69
2.41
5.51
8.61
Figure 32. Histogram graph of 3000 elements bridge mesh data with high view factors
from April 8, 9:01 am through April 8, 8:46 pm and associated normal curve
distribution.
86
Additional Results
In addition to the simulations run for April 7, 9:00 pm through April 8, 8:55 am
and April 8, 9:01 am through April 8, 8:46 pm there is also data from March 13, 6:50 am
6:45 pm, and for April 8, 8:51 pm through April 9, 1:36 am. These two other simulations
were run with the default view factor setting and the 3000 elements bridge mesh was
used. In total there are two daytime periods and two nighttime periods. The results from
these simulations are presented in Table 24, which includes data shown in the previous
section. The comparison graphs for the two new data sets are shown in Figure 33 and 34.
The results compare very closely to the results discussed in the previous section. This
would indicates that performance is repeatable and that the bridge model is stable and is
capable of calculating reasonable results for different situations.
Table 24. Summary of results for simulations; March 13, 6:50 am to March 13, 6:45pm,
April 7, 9:00 pm to April 8 8:55 am, April 8, 9:01 am to April ,8 8:46 pm,
April 8, 9:01 pm to April 9, 1:36 am with default view factors and 3000
elements bridge mesh
April 8
A pril 8-9
March 13
A pril 7-8
0.31
0.57
S tandard D eviation o f Error
0.67
0.75
3.08
3.07
R2 m od
0.61
0.66
0.59
0.77
Rmod
0.78
0.81
0.77
.88
R2 fit
0.81
0.79
0.84
0.81
Rfit
0.90
0.89
0.92
0.91
Mean o f Error
-3.76
-3.85
.17
1.60
2.13
1.32
5t
percentage low
-1.74
0.74
-7.68
-1.20
22.92%
75.69%
11.97%
75.59%
percentage high
77.08%
24.31%
88.03%
22.41%
AT
87
u,
6:43 AM 9:07 AM 11:31 AM 1:55 PM
♦ Bridge Walkway Measured Temperature —
4:19 PM
6:43 PM
Bridge Walkway Predicted Temperature
Figure 33. Temperature comparison between measured temperature and calculated
temperature for March 13, 2003 with standard view factor settings.
U 20
^ 15
I 10
<D
CL
E 5
H
-5
8:24 PM
9:36 PM
10:48 PM
•Bridge Walkway Measured Temperature —
12:00 AM
1:12 AM
2:24 AM
Bridge Walkway Predicted Temperature
Figure 34. Temperature comparison between measured temperature and calculated
temperature for March 8-9 with standard view factor setting.
88
Shadowing
The ability of RadTheraVRT to account for shadowing is a major advantage, since it
has the ability to predict freezing events in areas where shadowing plays a critical role.
The two places where the shadowing can be easily observed in these models are the area
under the bridge and the pedestrian walkway. Figure 35 depicts the region surrounding
the bridge during a daytime simulation in forty minute time steps from the March 13
simulation. In this figure the bridge has been hidden from view to facilitate the viewing
of the shadowing, resulting primarily from the bridge. From these pictures it is evident
how the region that is in shadow from the bridge moves from west to east. This is the
dark stripe that runs north south over the interstate elements. It also shows how this
shadowing significantly cools the surface of the interstate, in some cases over 25 (deg C)
cooler. This is reasonable because the surface in the shadow is receiving significantly less
direct solar radiation than the areas not in shadow. For the figure shown, at noon the
shadow areas according to the RadThemVRT results are receiving on the order of 40
W/m2 of direct solar radiation which has been reflected from elements which are not in
shadow. And the regions not in shadow are receiving over 700 W/m2 of direct solar
radiation. Where the terrain facets are around 10 m2in area.
Figure 36 shows a section of the 3000 elements bridge mesh, results of a daytime
simulation in forty minute time steps from the March 13 simulation. The pedestrian
walkway is three elements wide on the eastern edge of the bridge (the right side). Figure
37 shows how the temperature of these three elements varies over time in a graphical
format.
This figure shows how the western elements in the walkway warm up more
89
quickly than the other elements to the east of it. The middle elements begin to warm up
more quickly than the eastern element. After the sun reaches its apex and begins to
dropping to the west the western elements begin to cool as they fall into shadow, next the
middle element fall into shadow and begin to cool followed by the eastern element. This
result is the expected result and demonstrates how RadThemVRT accounts for
shadowing.
Figure 28A and Figure 33, shows how the late afternoon shadowing on the walkway
by the western barrier correlates very well with actual temperature measurements. Due to
the way the bridge was drawn so that vertices on the bridge deck elements line up with
the element of the support beams and the barrier beams, the three elements across the
pedestrian walkway do not have equal width, that is the dimension across the bridge. This
is because a support beam that is under the walkway does not sit in the middle of the
walkway. This may help to explain why the large mesh simulations show that the sun
strikes the middle element sooner than the measured temperature data shows. Because the
eastern element has a smaller width than the other two elements, the middle element is
shifted east, and does not lie in the dimensional middle of the walkway, however the
temperature measurement was taken in the middle of the pedestrian walkway. From
Figure 37 and Figure 38 it can be seen how the direct solar first hits the western element
at 9:15am and the middle element at 10:00am and the eastern element at around
12:00pm. This is evident from the rapid increase in the slope of the temperature on Figure
36 and the rapid change in solar flux values for Figure 37. These, values of solar flux are
from RadThemVRT results. From these figures it is also evident that the western element
90
begins to fall into shadow first at around 2:00pm followed by the middle element at
4:00pm and finally the eastern element at around 5:20pm. Again this can be seen by the
rapid change in slope of the temperature, and the rapid drop off in amount of direct solar
radiation. If the elements were equally spaced then the time spacing of the direct solar
hitting the elements would have been more consistent. The results show that the
measured area of the walkway begins receiving direct sunlight around 10:51, almost an
hour later than the simulation predicts. This negatively affected the comparison of the
statistic results by increasing the amount of error at each time step. As can be seen from
Figure 32 the slopes of the results and the simulations are similar in the region where the
bridge deck is warming up, with the measured results shifted about an hour later than the
simulations. Results from the 3000 elements bridge mesh simulations would have been
improved if the measured area had matched better the area to which they were compared.
The reason that the results do compare with the simulation after shadowing begins again
in the late afternoon is because the eastern edge of the middle element is much closer to
the eastern edge of the measured area than the western edge of the middle element is to
the western edge of the measured area. This can be seen in Figure 40 where the
measurements show where the edge of the elements lie compared to the measurement
area. Thus the shadowing results for the late afternoon are very good.
The statistics of the previous section seem to show that the 300 elements bridge mesh
is more accurate. That may be misleading. The 300 elements bridge mesh, due to the
larger area of elements and the subsequent averaging of the apparent area calculations
results in a comparison graph, Figure 28 B, that does not show the rapid drop in
91
temperature that the measured temperature show. Figure 37 when compared to Figure 39
shows how this averaging affects the temperature output and how the resulting data is
smoothed, without any rapid change in slope except in the late afternoon when over half
of the area has fallen into shadow.
11:06 AM
-
4,0
11:46 AM
12:26 PM
12:46 PM
1:26 PM
2:06 PM
4:46 PM
5:26 PM
6:06 PM
0.9
5,8
10,7
15,6
20.5
25,4
30,3
40,1
45,0
Figure 35. Shadowing on terrain below bridge with bridge hidden from view.
92
i
f .
U-
V
• Y .:
I
I
I
#
12:46 PM
12:06 PM
x
I
;
I
F
I
If
HdMfeiB
x'
xX
4
r;
I
E
Si 3
#3
#
I
#
4.0
-
0.6
n
4:46 PM
4:06 PM
X
-*
.!
3
ri
%
r
6:06 PM
5:26 PM
-
I
3:26 PM
I
2:06 PM
111
I
2:46 PM
$
I
x<
I
#1.
I
Ii
XX
11
#
L iW tkH
10:46 AM
10:06 AM
9:26 AM
2.8
6.2
9.6
13.0
16.4
19.8
23 2
Figure 36. Shadowing on section of large element number mesh bridge.
26 6
30 0
93
7:12 AM
2:24 PM
12:00 PM
9:36 AM
7:12 PM
4:48 PM
9:36 PM
-------West .........Middle “ ““ East
Figure 37. Temperature values for three elements lying in pedestrian walkway from east
to west. For large number of bridge elements bridge mesh from April 8
daytime simulation.
600.0
2:11 PM
12:01 PM
500.0
3:56 P M
lux (W/m2)
400.0
10:06 A M
200.0
5:26 P M
9:16 A m /
300.0
-
100.0
0.0 4----------------1---------------- T
7:12 A M
9:36 A M
12:00 PM
West
2:24 PM
4:48 PM
7:12 PM
9:36 PM
1Middle “ ““ East
Figure 38. Solar flux values from April 8 daytime simulation indicating times when
values undergo rapid change due to varible shadowing conditions.
94
7:12 A M
9:36 A M
12:00 PM
2:24 PM
4:48 PM
7:12 PM
9:36 PM
■^■Bridge Walkway Predicted Temperature
Figure 39. Temperature values for element lying in pedestrian walkway for 300 elements
bridge mesh from April 8 daytime simulation.
EAST
Pedestrian
,Walkway
Figure 40. Layout of bridge geometry showing element edges and area of bridge
measurement.
95
Longwave data
When the computer model was completed the meteological data that had been
collected was used to “drive the model. The output data was significantly and
consistently offset in a positive direction from the measured surface temperature data,
with a magnitude of around 6 (deg C). Investigation into this offset led to a thorough
examination of the instruments used to collect data, with a focus on the radiation sensors.
It was felt that the error was probably due to the readings from one of the sensors. The
RadThemVRT simulations appeared to track the actual temperature trends on the bridge.
That is the slope of the lines appeared to be similar. If the longwave radiation reading
were consistently off then the surface temperature would also be consistently off. It was
discovered that the readings from the Epply PIR sensor were offset by 140W/m2 in the
positive direction, indicating that incoming longwave radiation was more significant that
it really was. This was discovered by comparing readings from a PIR located about thirty
miles away on an RWIS station at the top of Bozeman Pass. The instrument on the Pass
uploads its readings to a central computer server every hour and the data is archived. This
archived longwave data was compared to the data collected at the bridge site and this
comparison showed the offset. Archived data from the RWIS PIR was then substituted
for the data collected at the site in one of the input weather files. Using this new
longwave data improved the accuracy of the temperature correlations with the
RadThemVRT outputs. This led to further questions as to whether the PIR used at the site
was faulty. A comparison of the readings from the two instruments was then carried out
at the pass, the van was driven to the RWIS site on Bozeman Pass and the solar
96
instruments were set up. Again the data collected by the PER. in the van had a large
positive offset when compared to the data from the RWIS station. Epply Labs was
contacted and a more complete users manual was delivered, this manual discussed the
temperature compensation circuit and how to test it. A test of the temperature
compensation circuit showed that it was not properly calibrated. After calibration it
correlated with the readings from the Bozeman Pass RWIS PER. It was then concluded
that the data from the PIR on the pass would be used instead of the readings taken at the
bridge site. Figure 41 shows the March 13 daytime simulation with the erronous long
wave data in it. As can be seen the temperature is about six degrees higher than would be
expected. This potential problem was not evident during the data collection periods and
was only understood much later. Figure 42 shows the March 13 daytime simulation with
the RWIS PIR data. Unfortunately, the archived longwave data was not complete and
several days of data that were collected at the bridge site were not able to be included
because no accurate longwave data existed. This eliminated 6 of ten test periods leaving
only four remaining.
Unfortunately the longwave data from the pass may not absolutely reflect the
longwave conditions that took place at the bridge site. The substituted values are most
accurate when there was no cloud cover at either site. Any differences in cloud cover
would introduce errors in the readings. However this substitution was deemed as the most
appropriate solution to the problem.
97
30
-5 T---- ----- 1
--------- 1
--------- 1
--------- 1
--------- 1
-6:00 A M
8:24 A M
10:48 A M
1:12 P M
3:36 P M
6:00 PM
— Bridge Walkway Measured Temperature
■
Bridge Walkway Predicted Temperature
Figure 41. March 13 simulation with offset bad longwave data.
6:00AM
8:24AM
10:48AM
♦ Bridge Walkway Measured Temperature
1:12PM
3:36PM
6:00PM
Ridge Walkway Predicted Tenperature
Figure 42. March 13 simulation with Bozeman Pass RWIS longwave data.
Instrumentation Issues
The PIR was not the only instrument that caused some collected data to be discarded.
One of the Licor pyranometers had to be replaced, after it was found to have bad
readings. This problem was very unfortunate in that it was not recognized until the data
98
was being formatted to be input into RadThermRT. The first version of the data
acquisition program stored the voltage readings directly with the intent that the flux
values would be calculated in an Excel spreadsheet. This made it difficult to notice an
aberrant reading. This bad pyranometor affected over ten days of data collection and all
of that data was discarded. Subsequently a new LiCor pyranometer was purchased and
installed onto the radiation instrument array. The LabView data aquistion program was
also updated, so that it would graph the radiation flux readings, making it easier to notice
any deviation of the instrument readings.
99
CONCLUSIONS AND RECOMMENDATIONS
For this Project a thermal model was developed for use in calculating road surface
temperatures on a highway overpass bridge, The bridge model calculates the temperature
that occurs on a highway overpass bridge deck with some accuracy. The model does
show promise as it tracks the temperature well. The results from the model developed in
this Project were compared to values measured in a real environment.
The outcome of this Project depended on the development of an instrumentation and
data acquisitions systems for providing data to the model, and for providing validation
data to the model. These instruments are now fully operational and can be used in further
research. Upward of twenty data collection periods were completed, due to various
instrumentation problems only four data collection periods were used for validation.
For the input data there was no outside control on any of the six weather parameters
or the three solar parameters required to run this model. All of the data was measured by
instruments in the field. The model’s ability to track the sun and accurately use solar data
to impose surface heating, in addition to the multi mode heat transfer energy balance
calculations, provides for an accurate calculation of the surface temperature. This
conclusion is based on the fact that the mean error over twelve hour periods was between
4.9C and 0.68C. As discussed in the shadowing section it is also believed that the results
would be more accurate if the measured area would have lined up with the element used
for data comparison. The model presented in this Project was run on a SGI Unix server
computer. Run times for simulating 12 hours of data with five minute time steps took
100
between 12 and 35 minutes to process. The run time depended on the view factor settings
and the size of the bridge mesh used.
It was unfortunate that the longwave solar data had to come from a device located
on Bozeman pass instead of the instrument purchased for this experiment. The results
may have been more accurate had the measurement been taken at the bridge. This would
have allowed for more accurate modeling of cloud conditions and their influence on the
incoming long wave radiation. It was interesting to see how strong an influence this
parameter has. An error of an extra 140 W/mA2 resulted in calculated bridge surface
temperature increase of 6 (degrees C) on average. The effect of longwave radiation has
not been adequately calculated or used in many previous systems. I believe that these
instruments should be installed in all RWIS stations. In addition I believe that an
instrument, from a competitor to the Epply Lab manufactured PIR be tested against the
PER. Another instrument that is commercially available does not require a temperature
compensation circuit, this would have simplified the data collection.
The ability of the model to accurately model shadowing is clearly shown in
Figures 28 A and 33 where the RadThermRT temperature accurately tracks the actual
temperature drop as the center of the pedestrian walkway falls into shadow. The models
with fewer elements could not accurately follow the temperature drop. The results for the
3000 element mesh bridge would be more accurate if the measured area had been in the
same location as the element whose data was used to compare to the measured data. This
was an unforeseen result and there was no time for additional data collection. It is also
believed that the accuracy for the 300 element mesh bridge would have been better if the
101
thermometer was set up to read the temperature of the whole pedestrian walkway. In this
way the temperature would have been averaged over the whole area. This is similar to
what RadThemVRT does in its calculations. There is also value in accurately modeling
the temperature of the Interstate that lies in shadow under the bridge. The shadowed
section of roadway was always at a lower temperature than the rest of the Interstate.
Overall the ability of RadThemVRT ability to calculate shadowing can provide a much
more accurate surface temperature forecast than models based only on meteorological
parameters.
A good way to better ensure the long-term accuracy of the model would be to run
one in a continuous state. This would require a permanent RWIS site located on or near a
bridge. A bridge deck could be instrumented with a variety of surface temperature
sensing devices. It would be beneficial to have these surface temperature sensors in
several locations, including the roadway under the bridge. This will help to verify the
code and facilitate knowledge of correct settings to optimal output. RWIS sites are often
placed near bridges due to the greater number of freeze events that they incur in a winter.
Many of them already have at least one sensor embedded in the bridge deck. It may be
possible to add additional sensors to an RWIS station. In addition to the standard RWIS
sensors it is my recommendation to install a ground moisture sensor and a depth
temperature sensor. This data could be used to define more accurate boundary conditions
and help the modelers to develop better understanding of fluctuations of these readings.
These instruments are available from many of the RWIS manufacturers. The
RadThemVRT models developed here should provide good results provided the location
102
of the temperature sensors are located such that it would be the center of an element in
the models
This model run in forecast mode will perform well if the meterological models
work well. The ability to generate accurate surface temperatures is dependent on the
accuracy of the forecast. This can be tested by the addition of a highway bridge model to
current Bozeman pass model. There are several overpasses on the section of 1-90 in this
model. This bridge model could be periodically checked using the Mobile Laboratory’s
capabilities to perform spot temperature analysis. In addition the mobile lab
meteorological station can be used to better model the weather at the bridge.
A brief convergence study on the necessary size of the model was completed. The
results of this convergence study indicate that the accuracy does increase as the view
factor settings are increased. An increase in the number of elements used in the bridge
also shows some increased accuracy in tracking the temperature. However the 3000
element model had a greater error reading than did the 300 elements bridge mesh.
Increasing the number of elements or increasing the view factor settings does increase the
computation time. The larger mesh did predict the temperature drop in the afternoon as
the center of the walkway fell into shadow. However the exact relationship between size
of mesh and accuracy was not determined. The small time penalty paid by using the
larger model is compensated by more accurate shadowing results. Thus if a forecast is
given for twelve hours then after the forecast data is input into the RadTherm/RT there
will still be eleven and a half hours of road temperature forecast.
103
In Conclusion RadThermRT can accurately calculate road surface temperature
and can accurately take into account complex shadowing. This bridge model can be run
in a continuous state and a bridge model can confidently be added to current
RadThermRT models running on long stretches of Interstate highway that previously did
not take bridges into account. This should help to make RadThermRT models more
accurately reflect critical road temperatures, and can provide advanced warning to
maintenance personal of possible icing events.
104
REFERENCES
105
REFERENCES
I. HiAbe5 T. Kawahara5 I. Ito5 A. Haraguchi5 Concrete fo r Nuclear Reactors, ACI
Special Publ. No 34, Vol.2, Paper SP34-40, pg 847. American Concrete Institute5
Detroit 1970
2. Adams5 E. E., P ro o f o f concept fo r prediction o f pavement temperature: a tactical
decision aid fo r highway safety. Prepared for MDT with US DOT FHA5 Montana
State University5MT. 1999.
3. Adams5 E. E5 Scott A. McDowell, Thermal M odel fo r Snow on Three Dimensional
Terrain. Proc. Juwsldpc. 1991.
4. Adams5 E. E., S. McDowell. Thermal model fo r snow on three dimensional terrain.
Proc. Japan-U.S. Workshop on Snow Avalanche, Landslide, Debris Flow Prediction
and Control. 1991.
5. Ballard, Lisa5Andy Beddoe5Jason Ball, Erik Eidswick5Kagan Rutz. Assess Caltrans
Road Weather Information Systems (RWIS) Devices and Related Sensors. Prepared
for Caltrans New Technology and Research Program. July 17, 2002.
6. Beddoe5 A. G. A spectrally integrated temporal albedo model fo r thin composite
layers o f snow and ice on roads. Master’s Thesis5 Montana State University5
Bozeman5MT. 2001.
7. Boselly5 Edward S. Benefit/Cost Study o f RWIS and Anti-Icing Technologies.
National Cooperative Highway Research Program5 Transportation Research Board5
National Research Council. March 2001.
8. Bristow5 Jeffrey
R.
THE DEVELOPMENT AND VALIDATION OF A
SNOW/ICEPACK PAVEMENT TEMPERATURE THERMODYNAMIC MODEL.
Master’s Thesis5Montana State University5Bozeman5MT. 2002
9. Gray-Fisher5 Dena M. 1999-2000 Technology Transfer and Usage Survey Results
Anti-Icing Techniques and Road Weather Information Systems Technologies.
Strategic Highway Research Program Anti-Icing/RWIS Lead States Team5May 2000
106
10. Johnson, Keith R., Bobbi S. Wood, Peter L. Rynes, Ban K. Yee, Frank C. Burroughs
Tim Byrd. A Methodology fo r Rapid Calculation o f Computational Thermal Models,
Final Manuscript for presentation at 1995 SAE International Congress &Exposition,
Underhood Thermal Management Session, Paper Number 951012, March 2, 1995,
Detroit Michigan.
11. T.Z. Harwathy, ASTM journal o f Materials 5, pg 47, 1970
12. Incropera, Frank P, David P. DeWitt, Introduction to Heat Transfer, John Wiley and
Sons, NY, 1996
13. Ketcham, Stephen A. David L. Minsk, Robert R. Blackburn, Edward J. Fleege,
Manual o f Practice fo r and Effective Anti-Icing Program, US Army Cold Regions
Research and Engineering Laboratory, February 1996
14. Kondratyev,K. YA. Radiation in the atmosphere. Academic Press, NY. 1969
15. Levinson, Ronnen, Hashem Akbari. Effects o f Composition and Exposure on the
' Solar Reflectance o f Portland Cement Concrete. Heat Island Group, Environmental
Energy Technologies Division, Lawrence Berkeley National Laboratory,2001
16. LI-COR. LI-COR Terrestrial Radiation Sensors. Type SA Instruction Manual, LICOR, Inc.: 28pp. 1986.
17. LI-COR. LI-COR LI-200SB, Instruction Manual, LI-COR, inc. 1985
18. Nixon, W. Winter Highway Maintenance: Class lectures. University of Iowa, Class#
53:164. 2001.
19. Pluss, C. The energy balance over an alpine snowcover. Zurcher Geographicshe
Schrifterri, Heft 65, 1997
20. Pomerantx, M., H. Akbari, P. Berdahl, S i. Konopacki, A.H. Rosenfeld. Reflective
surfaces fo r cooler buildings and cities. PhilisophicaI Magazie B, 79(9) :14571476pp. 1999.
107
21. White, F.M. H eat and mass transfer. Addison-Wesley Publishing Co. 675pp. 1991.
22. Tannehill, John C, Dale A. Anderson, Richard H. Fletcher. Computational Fluid
Mechanics and Heat Transfer, 2nd Ed. Hemisphere Publishing Corporation, 1997
23. Tan, S.A., T.F. Fwa, C.T. Chuaichip, B.H. Low. Determination of thermal properties
of pavements materials and unbound aggregates by transient heat conduction. Journal
of Testing and Evaluation, 25(1): 15-22. 1997
24. Temps, Ralph C., K. L. Coulson, Solar Radiation IncidentUpon Slopes O f Different
Orientations. Solar Energy, Vol. 19, 1977 pgl79-184
25. ThermoAnalytics, Inc. WinTherm 6.0 Manual Calumet, ML 2000.
26. Touloukian, Y.S., D.P. Dewitt, Thermal Radiative Properties Nonmettallic Solids,
Thermophysical Properties o f Matter, TPRC Data Series, Volume 8, Plenum
Publishing Corp, New York, 1972.
27. Touloukian Y.S., R.W. Powell, C.Y. Ho, P.G. Klemens, Thermal Conductivity Non
Metallic Solids, Thermophysical Properties o f matter, TPRC Data Series, Volume 2,
Plenum Publishing Corp, New York, 1970.
28. US Department of Transportation, Federal Highway Administration, Manual of
practice for an effective anti-icing program. Publication No FHWA-RD-95-202,
Washington DC. 1996.
108
APPENDICES
109
APPENDIX A:
WEATHER FILES
no
XFOOO1
1524
111.05 90
45.6
STD LON ELEV RHO
SWEAT HE R LOCALE-LAT LON
RHUM
PAIR HELIOM PYRAN Sa DlFSOLAR SKYT
WINDSPD w in d d ir TAIR
TIME
SDATE
W/M2 Sa W/m2
C
DEGREES DEG C PERCENT MBAR W/M2
SDDMMYY SECNDS
KNOTS
70403
70403
70403
70403
70403
70403
70403
70403
70403
70403
70403
70403
70403
70403
70403
70403
70403
70403
70403
70403
70403
70403
70403
70403
70403
70403
70403
70403
70403
70403
70403
70403
70403
70403
70403
70403
70403
80403
80403
80403
80403
80403
80403
80403
80403
80403
80403
80403
80403
80403
80403
80403
80403
80403
80403
80403
80403
80403
80403
80403
80403
80403
80403
80403
80403
80403
80403
80403
80403
80403
80403
75601
75707
76007
76307
76607
76907
77207
77507
77807
78107
78407
78707
79007
79307
79607
79907
80207
80507
80807
81107
81407
81707
82007
82307
82607
82907
83207
83507
83807
84107
84407
84707
85007
85307
85607
85907
86207
107
407
707
1007
1307
1607
1907
2207
2507
2807
3107
3407
3707
4007
4307
4607
4907
5207
5507
5807
6107
6407
6707
7007
7307
7607
7907
8207
8507
8807
9107
9407
9707
10007
3.72
4.76
3.89
2.53
2.14
1.84
2.35
3.53
1.55
2.85
0
2.06
2.45
1.59
1.79
0.42
0.14
1.01
3.24
2.07
0.12
2.14
2.88
1.51
1.96
1.36
0.56
2.39
1.67
1.64
0.8
4.07
2.44
4.67
4.91
5.71
4.33
7.22
5.18
3.8
4.28
4.21
2.84
3.18
2.06
1.75
2.24
2.23
2.38
0
1.83
2.72
0.58
0.87
0.6
0
0.98
2.47
0.13
2.14
2.92
2.1
1.9
1.1
1.36
2.04
1.69
1.63
0.77
4
2.56
103.44
90.34
84.08
124.02
123.9
136.97
108.48
89
90.74
99.18
0
26.98
344.64
222.4
329.56
11.7
25.5
293.1
348.34
9.57
199.09
315.23
320.41
249.67
120.64
27.89
35.13
7.56
33.61
75.45
29.73
349.19
338.1
350
344.73
344.68
342.65
232.33
206.95
104.96
97.32
74.1
121.24
112.1
129.08
136.3
115.84
110.45
93.41
0
45.35
357.79
136.39
26.41
16.68
0
346.39
205.27
220
315.2
322.09
331.24
135.73
21.54
46.95
273.95
34.45
75.53
23.15
350.31
338.86
4.65
4.84
5.2
5.16
5.23
5.2
5.03
4.78
4.54
4.42
4.45
4.64
4.8
4.9
4.9
3.71
3.43
3.42
3.86
3.89
3.58
3.82
3.8
3.4
3.3
2.98
2.53
2.63
2.9
2.7
2.7
2.81
3.1
3.26
3.7
4.1
4.43
6.46
5.87
4.94
4.73
5.2
5.12
5.13
5.2
5.1
5
4.58
4.47
4.58
4.52
4.8
4.9
4.17
3.68
3.5
3.4
3.9
3.57
3.82
3.8
3.55
3.3
3.09
2.92
2.6
2.9
2.7
2.69
2.89
3.1
40.2
37.74
36.67
37
36.68
35
37
37.84
38.74
39.57
39
35
34
33
33.74
43.43
42.71
40
37.68
39
40.4
38
39
42.75
43
43.38
47
44.85
44
45.09
45
44
43.74
42.61
41
38.37
37
31.44
34
41
39.12
36 12
37
37.02
36.83
36.02
36.27
39.62
39.65
39
35.78
34
33
40
43.62
42
40
39
40.33
38
39
41.49
43
44
44.61
45
44
45.11
45
44
43.64
863
863
863
863
863
863
863
863
863
863
863
863
863
863
863
863
863
864
864
864
864
864
864
864
864
864
864
864
864
864
864
864
864
864
864
864
864
862
863
863
863
863
863
863
863
863
863
863
863
863
863
863
863
863
863
863
864
864
864
864
864
864
864
864
864
864
864
864
864
864
864
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
IRSKYT CLOUD RAIN RAINT ZENITH AZIMUTH
mm/hr C
C
0
0
0
-999
-999
- 23.45 -999
- 23.45
-23 42
- 23.38
- 22.61
- 22.99
- 23.39
- 23.73
- 23.73
- 23.59
- 23.59
- 23.59
- 23.38
- 24.05
- 24.08
- 24.22
- 24.39
- 24.29
- 24.24
- 24.58
- 24.22
- 24.22
- 24.15
- 24.34
- 23.41
- 23.87
- 23.45
- 22.94
- 23.16
- 23.88
- 22.41
- 23.42
- 24.31
- 24.37
- 24.46
- 24.51
- 24.47
- 24.33
- 24.31
- 24.15
- 24.35
- 24.66
- 24.88
- 24.62
- 33.8
- 24.89
- 24.82
- 24.77
- 24.91
- 25.13
- 25.77
- 25.83
- 25.66
- 25.38
- 24.5
- 24.67
- 24.31
- 24.02
- 24.4
- 24.57
- 24.89
- 24.89
- 25.18
- 25.4
- 25.62
- 25.38
- 25.1
- 24.79
- 25.18
- 25.1
- 25.1
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
Ill
80403
80403
80403
80403
80403
80403
80403
80403
80403
80403
80403
80403
80403
80403
80403
80403
80403
80403
80403
80403
80403
80403
80403
80403
80403
80403
80403
80403
80403
80403
80403
80403
80403
80403
80403
80403
80403
80403
80403
80403
80403
80403
80403
80403
80403
80403
80403
80403
80403
80403
80403
80403
80403
80403
80403
80403
80403
80403
80403
80403
80403
80403
80403
80403
80403
80403
80403
80403
80403
80403
80403
80403
80403
80403
10307
10607
10907
11207
11507
11807
12107
12407
12707
13007
13307
13607
13907
14207
14507
14807
15107
15407
15707
16007
16307
16607
16907
17207
17507
17807
18107
18407
18707
19007
19307
19607
19907
20207
20507
20807
21107
21407
21707
22007
22307
22607
22907
23207
23507
23807
24107
24407
24707
25007
25307
25607
25907
26207
26507
26807
27107
27407
27707
28007
28307
28607
28907
29207
29507
29807
30107
30407
30707
31007
31307
31607
31907
32207
4.67
4 96
5.51
4.39
6.58
5.87
4.91
5.25
6.88
5.69
4.86
5.11
4.73
5.58
5.67
5.83
5.91
6.06
5.84
6.42
642
7.86
7.77
7.52
7.69
8.74
9.06
7.96
7.23
7.37
6.72
5.95
5.82
5.12
4.35
5.77
5.58
3.84
4.08
4.2
4.44
5.36
5.34
5.64
5.9
6.14
5.69
5.39
6.4
6.42
6.53
7.39
7.33
6.64
7.44
7.48
7.58
7.04
7.91
7.47
6.19
6.12
6.06
6.24
5.48
5.79
5.64
5.19
4.67
4.72
3.89
3.3
2.83
3.74
350
344.5
344.53
342.79
125.78
120.98
104.61
112.08
115.79
128.48
121.38
129.31
126.79
127
128.2
119.74
112.58
104.22
104.02
109.01
113.86
117.43
123.17
110.99
114.4
111.1
96.7
107.44
116.84
115.18
117.18
129.97
128.89
122.32
101.95
95.96
98.86
120.19
126.58
121.1
114.36
109.79
121.56
111.44
109.91
105.42
105.13
97.68
97.09
98.83
100.53
99
107.82
112
108.32
105.17
105.37
105.67
102.32
100.41
92.42
94.07
99.82
102.5
97.29
101.32
104.11
96
93.51
78.87
77.49
80.9
78.62
82.74
3.23
3.7
4.32
4.44
0
0.14
0
0
0.36
0.45
- 0.08
0.3
0.41
0.57
0.9
0.93
0.76
0.38
- 0.1
- 0.23
- 0.3
0.24
- 0.36
- 0.07
- 0.39
- 0.19
0.52
0.29
0.08
0.2
0.28
0.1
0.3
0.03
- 0.61
- 0.63
- 0.63
- 0.72
- 0.82
- 0.94
- 0.88
- 0.86
- 0.76
- 0.6
- 0.7
- 0.43
- 0.29
- 0.16
- 0.18
0.2
0.19
- 0.05
0.01
0
- 0.1
- 0.3
- 0.4
- 0.33
0.06
0.5
0.33
0.15
0.04
0.36
0.41
0.5
0.54
0.7
0.91
1.21
1.43
1.75
2.02
2.26
42.83
41
37
37
61.04
58.6
60.88
59.08
56.58
57.48
61.38
58
56.9
56
54
54
55.21
57.62
60
60.67
61
57.57
61.72
60
61.87
59.94
54
56
57
56
55.18
57.6
56
59.68
63.88
61.34
62.14
64.16
66.19
67.42
65.79
66
64
63
63.82
62
60.87
60.63
60.81
58
58.12
60.47
60
61
61.42
63
65
64.27
60.68
58.59
59.72
62.46
63.46
61.63
63.8
64
65
65.33
63
61.43
60
60.55
59.82
58.37
864
864
864
864
864
864
864
864
864
864
864
864
864
864
864
864
864
864
864
864
864
864
864
864
864
864
864
864
864
864
864
864
864
864
864
864
864
864
864
864
864
864
864
864
864
864
864
864
864
864
864
864
864
864
864
864
864
864
864
864
864
864
864
864
864
864
864
864
864
864
864
864
864
864
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1.39
6.71
12.81
20.21
26.43
29.49
34.82
41.75
49.94
58.9
68.94
80.83
95.46
105.4
114.3
132
150.2
157.7
181.8
195.6
224.5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0.74
5.92
11.48
17.95
23.24
26.57
31.25
37.92
45.22
53.42
61.99
73.02
86.55
96.12
103.46
119.96
136.64
144.38
146
148.21
148.65
24.83
24.86
- 25.27
- 25.63
- 25.48
- 25.67
- 25.16
- 25.47
- 24.89
- 25.22
- 24.89
- 24.89
- 24.83
- 24.47
- 24.1
- 24.02
- 23.79
- 23.86
- 24.08
- 24.85
- 24.46
- 24.46
- 24.86
- 24.47
- 24.19
- 24.66
- 24.66
- 24.02
- 23.74
- 23.46
- 23.16
- 23.06
- 22.82
- 22.88
- 22.95
- 23.16
- 23.04
- 22.39
- 21.75
- 21.47
- 21.3
- 21.12
- 20.52
- 20.44
- 19.86
- 19.81
- 19.81
- 19.78
- 19.81
- 19.87
- 19.78
- 19.53
- 18.65
- 18.53
- 18.2
- 18.3
- 18.04
- 18.72
- 17.62
- 17.03
- 17.08
- 16.95
- 17.2
- 17.11
- 16.56
- 15.99
- 14.92
- 13.9
- 13.77
- 13.64
- 13.33
- 14.03
- 14.65
- 14.77
-
-
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
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-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
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-999
-999
-999
-999
-999
-999
-999
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-999
-999
-999
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0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
112
XFOOO1
45.6
111.05 90
STDJ.ON ELEV RHO
#WEATHER LOCALE-LAT LON
PAIR
HELIOM PYRAN
WINDSPC WINDDIR TAIR RHUM
TIME
#DATE
KNOTS DEGREES DEG C PERCENT MBAR W/M2
W/M2
#DDMMYY SECNDS
80403
80403
80403
80403
80403
80403
80403
80403
80403
80403
80403
80403
80403
80403
80403
80403
80403
80403
80403
80403
80403
80403
80403
80403
80403
80403
80403
80403
80403
80403
80403
80403
80403
80403
80403
80403
80403
80403
80403
80403
80403
80403
80403
80403
80403
80403
80403
80403
80403
80403
80403
80403
80403
80403
80403
80403
80403
80403
80403
80403
80403
80403
80403
80403
80403
80403
80403
80403
80403
80403
32507
32807
33107
33407
33707
34007
34307
34607
34907
35207
35507
35507
35807
36107
36407
36707
37007
37307
37607
37907
38207
38507
38807
39107
39407
39707
40007
40307
40607
40907
41207
41507
41807
42107
42407
42707
43007
43307
43607
43907
44207
44507
44807
45107
45407
45707
46007
46307
46607
46907
47207
47507
47807
48107
48407
48707
49007
49307
49607
49907
50207
50507
50807
51107
51407
51707
52007
52307
52607
52907
3.39
2.98
3.78
3.27
2.99
2.4
1.34
1.4
0.26
1.94
4.29
4.29
5.12
6.64
5.93
4.84
4.65
4.8
4.36
3.76
4.56
4.34
2.6
1.87
3.92
3.39
2.23
3.05
2.49
2.38
2.87
2.29
0.63
3.54
4.48
2.76
1.54
0.54
2.34
3.7
3.24
3.81
3.56
3.74
5.29
5.25
6.7
5.55
6.76
7.25
3.13
4.96
5.01
5.59
6.32
3.1
3.83
4.83
5.54
7.26
7.23
7.35
4.03
5.9
1.15
5.66
3.8
5.48
4.44
6.61
84.82
95.77
92.3
93.02
102.8
93.37
86.74
64.17
0.09
270.9
332.43
332.43
333.21
330.86
324.76
339.24
336.49
348.05
347.9
351.56
321.58
316.19
346.45
326.87
292.08
285.38
349.9
347.57
14.19
105.63
303.43
115.61
35.78
53.32
34.03
4.73
11.9
3.35
206.44
347.26
351.65
332.07
278.32
295.32
335.45
332.78
322.73
336.4
320.71
342.44
316.7
337.29
333.89
336.81
321.72
329.47
341.29
78.94
302.06
348.89
311.9
340.74
331.04
318.02
34.73
306.31
303.23
307.71
349.28
280.73
2.52
3.1
3.25
3.57
3.92
4 .4
4.83
5.22
5.82
5.82
5.57
5.57
5.4
5.29
5.36
5.6
5.7
6.1
6.47
6.62
6.75
7.22
7.53
7.81
7.48
7.5
8.36
8.41
8.84
9.28
9.02
9.52
9.87
11.1
10.1
10.6
11.6
11.6
11.5
11.8
11.6
11.9
11.4
11.4
12.3
12.2
12.3
11.9
12.1
12.5
12.2
12.6
12.6
12.7
12.8
13.3
13.7
13.7
13.2
13.7
13.6
13.9
14.1
14.3
14.6
14.5
14.9
14.7
15.2
15
56.82
54.77
53.73
52.73
51
48.66
47.74
47
44.27
45.59
48
48
48
45.14
46
42.78
41.95
37.46
37.98
38.51
37.48
38
35
34
35.16
35.43
33.34
33
32.32
32
32
31.24
31
28.13
31.92
30
28.66
28.28
30
29.81
29.39
29.28
29.41
30
27.94
27
28
26.95
28.19
25.12
26.94
24.81
25
24
24
24.12
25
25
24.77
24.24
24.66
24.1
24.26
24.87
23
23.83
23
23.81
22.48
22
864
864
864
864
864
864
864
864
864
864
864
864
864
864
864
864
864
864
864
864
864
864
864
864
864
864
863.3
863
863
863
863
863
863
863
863
863
863
863
862
862
862
862
862
862
862
862
862
862
862
862
862
862
862
862
861
861
861
861
861
861
861
861
861
861
861
861
861
861
861
861
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
222.37
213.46
233.49
216.08
241.22
236.08
238.99
242.25
267.74
293.14
266.17
266.17
330.83
428.5
514.54
173.14
468.38
430.04
456.66
542.6
678.43
676.04
385.96
283.02
239.54
729.08
770.73
501 89
782.08
718.15
803.05
790.33
836.81
826.42
644.61
701.41
790.76
799.66
802.67
807.36
615.4
821.82
825.95
825.14
855.97
811.35
801.18
751.99
767.56
833.02
850.35
844.82
849.88
848.26
846.96
844.88
842.27
840.87
838.85
835.24
827.25
821.16
821.72
820.41
816.76
812.22
808.35
802.03
794.42
789.64
1524
#A DIFSOLAR SKY T
#AW/m2
C
C
CLOUD RAIN RAINT ZENITH AZIMUTH
mm/hr C
148.7
150.4
149.97
151.96
152.22
152.95
153.69
155.69
157.67
156.72
160.88
160.88
166.73
171.82
153.63
167.21
194
180.02
172.94
169.31
168.42
189.34
179.57
166.7
190.78
180.86
161.55
150.01
127.59
118.72
111.3
141.84
142.15
134.5
124.56
104.36
99.17
82.39
63.61
58.88
57
60.57
64.2
73.71
84.33
89.64
93.24
94.79
97.86
82.16
68.58
63.36
58.96
57.91
55.15
54.08
53.65
52.95
52.59
53.25
53.72
55.12
54.67
51.85
56.02
55.38
54.32
53.22
52.18
51.1
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
14.47
14.47
- 13.92
- 13.49
- 13.16
- 12.73
- 12.42
- 13.11
- 12.95
- 12.73
- 11.63
- 10.54
- 10.27
- 11.21
- 11.48
- 12.48
- 13.44
- 12.92
- 11.72
- 10.54
- 9.92
- 10.25
- 10.58
- 10.32
- 9.68
- 9.72
- 10.96
- 11.08
- 8.38
- 12.81
- 13.06
- 12.11
- 10.49
- 12.59
- 12.27
- 12.39
- 11.12
- 10.15
- 11.26
- 10.95
- 10.93
- 10.79
- 10.74
- 10.45
- 7.84
- 10.23
- 10.14
- 10.81
- 9.78
- 8.71
- 7.98
- 9.47
- 8.85
- 8.19
- 7.91
- 8.69
- 7.32
- 8.43
- 8.01
- 6.76
- 7.31
- 7.34
- 7.96
- 6.68
- 5.84
- 8.9
- 8.99
- 7.3
- 7.39
- 7.62
-
-
IRSKYT
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
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-999
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-999
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-999
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-999
-999
-999
-999
-999
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-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
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-999
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-999
-999
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-999
-999
-999
-999
-999
-999
-999
-999
113
80403
80403
80403
80403
80403
80403
80403
80403
80403
80403
80403
80403
80403
80403
80403
80403
80403
80403
80403
80403
80403
80403
80403
80403
80403
80403
80403
80403
80403
80403
80403
80403
80403
80403
80403
80403
80403
80403
80403
80403
80403
80403
80403
80403
80403
80403
80403
80403
80403
80403
80403
80403
80403
80403
80403
80403
80403
80403
80403
80403
80403
80403
80403
80403
80403
80403
80403
80403
80403
80403
80403
80403
80403
53207
53507
53807
54107
54407
54707
55007
55307
55607
55907
56207
56507
56807
57107
57407
57707
58007
58307
58607
58907
59207
59507
59807
60107
60407
60707
61007
61307
61607
61907
62207
62507
62807
63107
63407
63707
64007
64307
64607
64907
65207
65507
65807
66107
66407
66707
67007
67307
67607
67907
68207
68507
68807
69107
69407
69707
70007
70307
70607
70907
71207
71507
71807
72107
72407
72707
73007
73307
73607
73907
74207
74507
74807
7.96
5.17
3.88
5.27
6
6.06
4.99
1.77
7.44
7.1
5.69
4.46
8.45
3.3
7.56
5.42
3.95
4.66
6.63
1.68
5.29
4.67
2.72
7.77
2.63
3.82
3.78
5.75
1.83
1.72
0.77
2.53
6.26
6.08
4.45
3.53
1.91
3.61
1.41
8
9.33
7.04
6.85
6.43
4.6
4.63
2.88
5.54
2.59
6.92
6.39
7.73
5.72
6.01
6
6.18
5.78
6.49
5.73
4.43
2.61
3.3
1.3
4.7
3.1
3.87
3.79
3.21
4.2
5.63
6.35
4.11
3.11
261.41
330.86
297.18
301.39
205.24
302.54
315
231.09
335.89
306.6
292.3
322.72
250.96
313.29
283.23
328.04
321.79
307.52
309.36
267.5
50.1
288.6
190.2
283.7
342.51
343.11
285.14
310.88
248.74
234.73
132.86
45.6
285.43
299.15
308.7
284.62
188.2
337
316.46
283.5
288.69
278.78
273.87
266.16
277.81
292.95
300.48
292
293.51
271.1
277.63
278.02
283.9
303.98
301.59
294.34
306.28
310.52
325.8
335
346.19
351.43
142.59
270.22
318.79
291.65
260.46
236.48
207.26
208.52
165.45
115.71
76.09
15.4
15
15.2
15.8
15.7
15.9
15.9
15.8
16.2
16.2
15.8
16.3
16.7
16.8
16.3
16.6
17.1
17
17
17.3
17.3
16.9
16.7
17
17.1
17.6
17.9
17.6
17.8
18.2
18.5
18.6
18
17.5
17.6
17.8
18.6
18
18.6
18
17.5
17.5
17.7
17.5
17.6
17.6
17.8
18
17.7
17.7
17.5
17.2
17.1
17
16.8
16.7
16.4
16.3
16.1
16
15.8
15.5
14.9
14.2
14.2
14.3
14.1
13.5
13
12.8
12.3
12.3
11.8
22.22
22.86
22
21
21.37
22.03
21.67
21
21
22
21.77
21.84
20.74
21
21
21
21.33
20.1
20.27
20.86
20.19
21.2
21.4
21.25
20.7
21
20.43
21
20.95
20
20.34
20
21
22
21.72
21
20
20.59
20
20.17
20.76
20.56
21.38
20.28
20.31
21
20.74
21
20
20.82
20.41
21
21
21
22.71
22.11
23.32
24
24.73
24
25
26
27.66
29
28
26.88
27.26
30.32
32.77
34
34.34
33.15
34.04
861
860
860
860
860
860
860
860
860
860
860
860
860
860
860
860
860
859
859
859
859
859
859
859
859
859
859
859
859
859
859
859
859
859
859
859
859
859
858
858
858
858
858
858
858
858
858
858
858
858
858
858
858
858
858
858
858
858
858
858
858
858
858
858
858
858
858
858
858
858
858
858
859
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
783.1
775.51
766.84
758.77
753.71
745.64
736.37
727.9
716.31
707.26
697.36
685.91
674.64
663.32
650.88
639.17
626.57
612.2
600.71
584.51
569.88
565.58
548.21
533.35
519.38
504.32
491.08
473.65
456.68
439.56
423.78
410.29
393.22
375.18
359.46
343.15
354.87
336.38
319.1
302.82
281.45
261.56
245.67
228.52
213.09
197.73
182.53
167.58
152.03
137.75
123.21
108.27
90.05
70.51
55.09
39.79
25.97
14.75
4.05
0
0
0
0
0
0
0
0
0
0
0
0
0
0
49.99
48.86
47.74
46.78
44.54
45.34
45.28
46.16
44.78
42.92
46.35
43.7
42.99
43.61
42.58
42.64
41.91
41.89
40.01
40.49
37.06
57
40.84
39.41
38.94
38.13
35.57
35.76
34.25
34.15
34.48
33.62
32.39
30.58
30.31
29.31
30.85
28.55
26.89
25
22.86
20.48
20
19.69
18.05
17.1
15.76
14.67
12.22
10.94
7.79
11.69
17.15
19.74
20.91
19.33
15.21
10.34
11.41
0
0
0
0
0
0
0
0
0
0
0
0
0
0
7.48
7.98
- 5.96
- 7.38
- 6.34
- 7.61
- 7.34
- 8.2
- 7.43
- 8.23
- 7.74
- 7.46
-7
- 7.4
- 7.8
- 8.86
- 8.25
- 8.2
- 8.11
- 7.78
- 7.54
- 8.76
- 7.32
- 7.74
- 8.2
- 8.43
- 8.42
- 7.38
- 6.92
- 7.63
- 9.15
- 7.51
- 8.42
- 8.52
- 8.27
- 9.46
- 8.74
- 9.31
- 8.74
- 10.09
- 9.53
- 9.68
- 9.91
- 10.19
- 9.81
- 10.09
- 10.33
-10
-10
- 9.88
- 10.5
- 11.38
- 11.49
- 11.6
- 11.48
- 11.64
- 12.45
- 12.56
- 13.3
- 13.7
- 13.8
- 14.61
- 15.33
- 15.22
- 15.37
- 15.25
- 15.48
- 15.76
- 16.39
- 16.05
- 16.34
- 16.74
- 16.74
-
-
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
114
XFOOOI
45.6
STD_LON ELEV RHO
#WEATHER LOCALE-LAT LON
RHUM
PAIR
WINDSPD WINDDIR TAIR
#DATE
TIME
DEGREES DEGC PERCENT MBAR
#DDMMYY SECNDS
KNOTS
80403
80403
80403
80403
80403
80403
80403
80403
80403
80403
80403
80403
80403
80403
80403
80403
80403
80403
80403
80403
80403
80403
80403
80403
80403
80403
80403
80403
80403
80403
80403
80403
80403
80403
80403
80403
80403
80403
90403
90403
90403
90403
90403
90403
90403
90403
90403
90403
90403
90403
90403
90403
90403
90403
90403
90403
90403
90403
90403
90403
90403
90403
90403
90403
90403
90403
90403
90403
90403
90403
90403
75108
75408
75708
76008
76308
76608
76908
77208
77508
77808
78108
78408
78708
79008
79308
79609
79909
80209
80509
80809
81109
81409
81709
82009
82309
82609
82909
83209
83509
83809
84109
84409
84709
85009
85307
85607
85907
86207
107
407
707
1007
1307
1607
1907
2207
2507
2807
3107
3407
3707
4007
4307
4607
4907
5207
5507
5807
6107
6407
6707
7007
7307
7607
7907
8207
8507
8807
9107
9407
9707
1.91
1.37
2.03
3.14
2.3
2.27
2.51
2.4
2.54
4.59
4.92
4.9
4.78
4.47
4.71
3.83
3.98
4.34
5.02
5.53
5.5
5.3
5.23
4.06
3.18
3.1
2.66
3.43
3.61
3.83
4.23
2.83
3.9
4.34
4.7
3.91
5.5
4.65
5.86
6.19
5.02
6.39
6.36
4.02
4.38
4.38
4.43
4.31
4.93
5.38
5.57
5.5
5.69
5.23
5.28
4.86
4.48
5.13
4.54
4.48
5.08
3.72
3.86
5.04
6.37
5.15
5.64
5.46
4.8
6.32
4.02
172.87
123.61
126.78
123.9
131.87
96.06
96.71
100.55
108
116.19
107.74
104.22
109.94
112.05
124.23
106.11
102.98
104.44
99.73
95.96
107.75
100.58
106.93
111.85
105.82
100.38
105.54
97.33
102.63
96.28
92.58
92.35
100.78
94.14
93.89
120.82
103.83
105.31
103
103.6
101.34
96.73
91.43
111.31
104.16
102.5
96.43
97.24
104.7
102.93
98
108.02
108
104.53
105.59
97.64
102.74
100.1
120.73
120.24
108.93
110.9
108.36
108.38
111.28
109.93
104.8
110.16
114.05
111.18
116.8
12
12.55
12.16
12
11.99
11.73
11.39
10.85
10.16
9.4
9.82
9.52
9.25
8.83
8.61
9
8.66
8.21
8.32
8.5
7.95
8.5
8.51
8.01
7.6
7.54
7.22
6.7
6.7
6.97
7.19
6.22
6.73
6.84
6.8
6.44
7.6
6.72
6.75
6.67
6.52
6.63
6.19
6.05
6.08
6
6.8
6.93
7.23
6.86
6.34
7.02
6.8
6.69
6.62
6.16
6.01
5.71
5.39
4.94
4.79
4.92
5.2
4.67
4.79
4.36
4.45
5.42
4.85
4.96
5.44
33.15
31.74
34
34
33.04
33
36
38.45
40.13
41.06
39
40.59
42.26
44
44
42
44
44.63
44.41
42.52
46.18
42.84
41
45.43
46
47.25
49
50
49.79
47.66
45.21
51.84
47.75
46.57
47
50
41.09
48.38
46
46.6
47.83
45.73
48.47
49
49.08
49
43.43
43.68
41.59
43.61
45.75
42.8
43.98
43.06
45.41
47.39
47
48.24
50.09
51.81
53.03
50.02
50
52.67
51.14
54.21
53.6
45.92
51.26
48.82
47.2
858.15
859
859
859
859
859
859
859
859
859
858.18
859
859
859
859
859
859
859
859
859
859
859
859
859
859
859
859
859
859
859
859
859
859
859
858
858
858
858
858
858
858
858
858
858
858
858
858
858
858
858
858
858
858
858
858
858
858
858
858
858
858
858
858
858
858
858
858
858
858
858
858
111.05
90
1524
0
HELlOM PYRAN
W/ M2
W/ M2
#ADIFSOLAR SKY T
#AW/ m2
C
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
16.74
15.79
16.82
- 17.08
- 16.95
- 17.18
- 17.69
- 17.49
- 17.19
- 17.48
- 17.28
- 17.17
- 17.8
- 17.9
- 18.05
- 27.66
- 18.16
- 18.1
- 18.38
- 18.5
- 19.61
- 19.86
- 19.73
- 19.7
- 19.2
- 19.29
- 19.1
- 19.5
- 19.5
- 19.39
- 19.37
- 19.12
- 19.53
- 19.04
- 19.08
- 18.58
- 17.99
-17
- 17.53
- 17.03
- 16.56
- 17.72
- 17.49
- 17.84
- 18.45
- 18.8
- 18.92
- 20.08
- 19.93
- 20.24
- 19.86
- 19.91
- 19.87
- 19.53
- 19.76
- 19.86
- 20.05
- 20.05
- 20.05
- 19.72
- 19.93
- 20.44
- 21.24
- 20.89
- 20.66
- 20.64
- 20.24
- 19.86
- 20.23
-21
- 20.69
-
-
-
IRSKYT CLOUD RAIN RAINT ZENITH AZIMUTH
mm/hr C
C
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
115
90403
90403
90403
90403
90403
90403
90403
90403
90403
90403
90403
90403
90403
90403
90403
90403
90403
90403
90403
90403
90403
90403
90403
90403
90403
90403
90403
90403
90403
90403
90403
90403
90403
90403
90403
90403
90403
90403
90403
90403
90403
90403
90403
90403
90403
90403
90403
90403
90403
90403
90403
90403
90403
90403
90403
90403
90403
90403
90403
90403
90403
90403
90403
90403
10007
10307
10607
10907
11207
11507
11807
12107
12407
12707
13007
13307
13607
13907
14207
14507
14807
15107
15407
15707
16007
16307
16607
16907
17207
17507
17807
18107
18407
18707
19007
19307
19607
19907
20207
20507
20807
21107
21407
21707
22007
22307
22607
22907
23207
23507
23807
24107
24407
24707
25007
25307
25607
25907
26207
26507
26807
27107
27407
27707
28007
28307
28607
28907
3.3
3.63
5.67
5.7
4.98
4.67
4.52
5.18
4.7
4.54
3.92
3.14
3.87
3.57
3.8
4.67
5.29
4.81
5.09
4.9
5.1
4.99
3.57
4.17
4.72
3.68
3.01
3.18
1.23
1.93
3.35
3.43
4.29
5.43
5.49
4.82
4.56
4.37
4.05
5.8
4.69
5.22
5.09
3.49
4.53
3.41
4.38
3.35
3.69
3.2
3.03
2.82
3.34
3.09
2.98
3.47
3.23
2.94
3.37
2.52
2.86
2.4
3.23
3.01
117
102
107.85
96.93
101.75
111.25
113.51
104.68
109.62
124.51
123.95
125.78
116.52
92.21
109
96.66
92.64
94.69
106.38
107.65
116.24
105.3
100.64
111.59
120.81
120.8
128.05
131.24
135.24
110.33
94.11
106.98
112.32
123.73
127.46
123.25
115.47
104.46
98.18
102.91
110.36
105.62
108.43
88.82
117.15
126.08
105.41
120.53
121.61
120.48
109.2
115.89
121.39
101.26
110.56
115.34
127.72
118.3
114.38
112.36
121.26
110.39
116.31
119.79
4.9
4.67
4.58
4.83
4.4
4.15
4.7
3.92
4.2
4.52
4.54
4.12
3.67
3.37
3.8
3.5
3.59
4.41
4.3
4.6
4.25
3.91
3.4
3.54
4.06
3.7
3.61
3.93
3.15
3.12
3.13
2.91
3.34
3.5
3.63
3.36
3.13
2.88
2.58
2.57
2.93
2.84
3.74
4.24
3.72
2.98
3.22
3.12
3.06
2.97
2.57
2.41
2.58
2.9
2.34
2.8
3.13
3.32
3.24
3.3
3.65
4.1
4.23
4.71
49.67
51.28
50.79
49.68
52.92
52.75
49.72
55.62
52
49.88
49.59
52.81
54.61
55.51
53
55
53.73
49
50
48
50.25
52.43
54.32
52.74
50
52
51.95
51.24
55.4
55
54.37
55.9
53.19
52
52.46
53.19
54.69
56.11
57.58
56.04
54.68
55.08
49.93
47.44
50.61
55.1
53.84
53.75
54
54.17
57.28
57.9
56.2
54.05
58.56
55.18
53.36
52.9
55.81
56.97
55.26
53
53.34
51
858
858
858
858
858
858
858
858
858
858
858
858
858
858
858
858
858
858
858
858
858
858
858
858
858
858
858
858
858
858
858
858
858
857
857
857
857
857
857
857
857
857
857
857
857
857
857
857
857
857
857
857
857
857
857
857
857
857
857
857
857
857
857
857
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1.85
27.4
77.92
101.15
123.43
119.94
141.97
164.32
183.16
138.79
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1.31
26.99
78.45
99.93
122.59
117.96
139.2
159.3
292.97
27
20.91
20.47
- 20.66
- 20.16
- 20.83
- 20.87
- 21.47
- 21.45
- 20.48
- 21.1
-21
- 20.69
- 21.06
- 21.83
- 21.91
- 21.54
- 20.99
- 21.08
- 20.94
- 20.99
- 21.51
- 21.68
- 21.94
- 22.34
- 22.28
- 21.88
- 21.72
- 21.16
- 21.3
- 21.51
- 21.29
- 21.61
- 22.61
-23
- 23.16
- 23.16
- 23.23
- 22.84
- 22.7
- 22.5
- 21.98
- 21.13
- 21.16
- 21.41
- 22.32
- 22.11
- 21.38
- 20.79
- 20.66
- 22.09
- 21.34
- 20.15
- 29.97
- 23.26
- 21.04
- 20.77
- 20.47
- 20.11
- 20.08
- 20.3
- 19.57
- 20.03
- 20.88
- 20.39
-
-
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-999
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-999
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-999
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-999
-999
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-999
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116
XFOOO1
45.6
STDJ-ON ELEV RHO
#WEATHER LOCALE LAT LON
RHUM
PAIR
WlNDSPD WINDDIR TAlR
TIME
#DATE
#DDMMYY SECNDS
KNOTS
DEGREES DEGC PERCENT MBAR
130303
130303
130303
130303
130303
130303
130303
130303
130303
130303
130303
130303
130303
130303
130303
130303
130303
130303
130303
130303
130303
130303
130303
130303
130303
130303
130303
130303
130303
130303
130303
130303
130303
130303
130303
130303
130303
130303
130303
130303
130303
130303
130303
130303
130303
130303
130303
130303
130303
130303
130303
130303
130303
130303
130303
130303
130303
130303
130303
130303
130303
130303
130303
130303
130303
130303
130303
130303
130303
130303
130303
24632
24932
25232
25532
25832
26132
26432
26732
27032
27332
27632
27932
28232
28532
28832
29132
29432
29732
30032
30332
30632
30932
31232
31532
31832
32132
32432
32732
33032
33332
33632
33932
34232
34532
34832
35132
35432
35732
36032
36332
36632
36932
37232
37532
37832
38132
38432
38732
39032
39332
39632
39932
40232
40532
40832
41132
41432
41732
42032
42332
42632
42932
43232
43532
43832
44132
44432
44732
45032
45332
45632
1.4
1.41
1.09
1.31
2.14
2.6
3.19
1.87
3.2
1.13
2
1.35
1.15
0.1
0.25
1.88
2.1
2.1
2.4
2.51
2.54
0.8
1.04
0.66
0.53
2.32
2.46
2.93
2.02
1.91
3.95
2.1
1.29
1.51
1.22
0.52
1.25
2.07
1.99
1.37
2.77
3.12
3.05
3.69
3.2
2.99
2.69
2.73
4.21
5.09
3.77
3.5
2.49
2.59
1.75
2.8
3.1
4.46
3.2
2.72
1.31
0.92
0.78
1.49
0.3
2.2
2.4
0.78
1.79
2.4
2.55
2.5
2.74
2.12
2.55
4.17
5.05
6.2
3.63
6.23
2.2
3.88
2.62
2.24
0.19
0.49
3.66
4.08
4.08
4.66
4.88
4.94
1.56
2.03
1.29
1.03
4.5
4.79
5.69
3.92
3.71
7.68
4.07
2.5
2.94
2.37
1.01
2.44
4.03
3.87
2.67
5.39
6.07
5.93
7.16
6.22
5.81
5.23
5.3
8.18
9.89
7.33
6.8
4.83
5.03
3.4
5.45
6.03
8.66
6.22
5.28
2.54
1.79
1.52
2.9
0.59
4.28
4.66
1.51
3.48
4.66
4.95
10.9
10.98
10.91
11.48
11.75
12.1
11.32
11.67
9.79
10.29
10.55
10.98
10.82
10.7
11.35
10.74
11.23
11.9
12.35
12.2
12.36
11.44
11.1
11.54
12.2
12.7
13.49
13.68
13.08
13.79
14.1
14.39
14.14
15.02
14.85
15.68
16.2
16.5
16.43
16.62
16.47
16.28
16.15
15.7
15.75
16.02
16.15
15.34
15.46
15.5
15.9
15.8
16.45
17.3
16.45
16.39
16.3
16.21
16.04
16.04
16.45
17.55
17.12
17.7
17.93
17.95
17.15
17.34
18.52
17.9
17.85
36
36
35.89
34.08
33.51
33.02
36
35.25
45.77
38.48
39.5
36.35
38
38.93
34
39.94
35
33.02
31.49
32
32
40
38.95
38.8
38.35
31
29
32.29
32
28.13
29
28.15
29
29.44
30.09
28
26
24.97
25
24
24.94
24
26
27
27.47
26
26
27.86
26.87
26
26.65
25.06
24
24.01
26
25.02
26
25
27.39
25.79
25.51
23.23
25.4
22.02
24.66
23.09
24.49
26
24
23
24
852
852
852
852
851
851
851
851
851.41
852
852
852
852
852
852
852
852
852
851.51
852
852
852
852
851
851
851
851
851
851
851
851
851
851
851
851
851
851
851
851
851
851
851
851
851
851
850.16
850
850
850
850
850
850
850
850
850
850
850
850
850
850
850
850
850
850
850
850
850
850
850
850
849
111.05
105
HELIOM PYRAN
W/M2
W/M2
1524
0
#ADIFSOLAR SKYT
#AW/m2
C
IRSKYT CLOUD RAIN RAINT ZENITH AZIMUTH
mm/hr C
C
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
0
3.48
18.79
33.49
56.99
43.78
49.82
36.93
35.32
39.18
49.64
63.02
72.85
89.27
87.79
90.23
89.1
87.75
87.24
87.62
88.08
89.32
102.42
110.95
118.02
119.51
118.2
99.87
113.64
107.92
98.87
86.44
79.29
83.18
89.5
102.84
102.79
92.48
94.45
100.45
102.67
103.83
97.88
105.18
99.28
99.71
95.92
100.98
111.64
93.59
80.84
111.61
114.71
113
110.76
110.17
110.11
124.64
127.15
125.41
123.28
128.45
127.98
124.98
124.15
126.85
125.24
132.7
111.91
114.06
118.97
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
0
4.31
22.1
38.31
64.59
70.1
117.61
94.76
48.54
46.01
56.84
80.99
85.27
103.81
129.71
129.22
172.37
152.21
128.42
119.67
126.24
134.26
156.21
456.94
371.16
515.18
546.9
518.96
167.13
378.43
311.76
482.65
450.99
294.15
503.13
538
452.95
580.71
356.47
397.13
527.01
577.75
604.87
470.19
636.97
500.97
510.51
428.07
542.88
645.57
666.65
559.99
753.11
749.2
706.95
653.14
665.15
621.95
695.89
694.86
655.48
608.01
724.88
714.11
645.89
627.29
688.08
651.7
743.27
568.51
616.77
11.11
12.13
13.11
- 10.6
- 9.31
- 8.18
- 7.75
- 4.55
- 3.67
- 4.09
- 6.16
- 5.86
- 6.12
- 7.46
- 9.29
- 9.15
- 9.78
- 10.27
- 10.26
- 8.15
- 6.63
- 5.24
- 4.99
- 7.66
- 12.39
- 12.72
- 10.48
- 8.87
- 9.32
- 8.39
- 9.87
- 9.23
- 10.25
- 10.76
-10
- 9.1
- 8.97
- 6.99
- 8.28
- 8.74
- 9.05
- 8.31
- 6.88
- 6.6
- 7.14
- 6.71
- 6.59
- 4.24
- 6.07
- 7.74
- 6.31
- 5.9
- 5.94
- 12.83
- 11.69
- 6.41
- 6.11
- 6.46
- 5.02
- 4.96
- 6.36
- 5.22
- 11.2
- 10.07
- 5.3
- 11.87
- 11.69
- 4.02
- 4.38
- 4.66
- 3.87
-
-
-
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
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0
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-999
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-999
-999
-999
-999
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-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
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-999
-999
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-999
-999
-999
-999
-999
-999
-999
-999
-999
117
130303
130303
130303
130303
130303
130303
130303
130303
130303
130303
130303
130303
130303
130303
130303
130303
130303
130303
130303
130303
130303
130303
130303
130303
130303
130303
130303
130303
130303
130303
130303
130303
130303
130303
130303
130303
130303
130303
130303
130303
130303
130303
130303
130303
130303
130303
130303
130303
130303
130303
130303
130303
130303
130303
130303
130303
130303
130303
130303
130303
130303
130303
130303
130303
130303
130303
130303
130303
130303
130303
130303
130303
130303
130303
45932
46232
46532
46832
47132
47432
47732
48032
48332
48632
48932
49232
49531
49831
50131
50431
50731
51031
51331
51631
51931
52231
52531
52831
53131
53431
53731
54031
54331
54631
54931
55231
55531
55831
56131
56431
56731
57031
57331
57631
57931
58231
58531
58831
59131
59431
59731
60031
60331
60631
60931
61231
61531
61831
62131
62431
62731
63031
63331
63631
63931
64231
64531
64831
65131
65431
65731
66031
66331
66631
66931
67231
67531
67831
2.88
2.13
1.75
2.31
2.24
0.99
1.91
5.94
8.29
8.53
6.77
6.88
9.18
7.26
6.54
6.04
8.33
8.44
8.6
9.66
9.75
7.92
10.19
7.84
9.38
6.97
8.93
8.12
7.5
8.33
6.67
7.78
5.74
6.2
7.47
7.1
5.22
8.96
6.3
5.65
6.73
7.34
5.93
6.82
7.24
5.87
5.25
6.79
7.01
7.81
6.67
6.48
6.5
6.52
6.08
5.45
4.51
5.7
4.44
5.65
6.34
4.88
4.72
3.6
4.7
4.94
4.22
5.11
4.94
5.06
5.19
5
5.58
5.17
5.59
4.13
3.41
4.49
4.35
1.93
3.71
11.54
16.11
16.58
13.16
13.37
17.84
14.11
12.72
11.74
16.2
16.41
16.71
18.77
18.96
15.4
19.8
15.24
18.23
13.54
17.35
15.78
14.58
16.19
12.96
15.13
11.16
12.05
14.52
13.8
10.15
17.41
12.25
10.98
13.09
14.27
11.53
13.26
14.08
11.41
10.2
13.21
13.62
15.17
12.96
12.59
12.63
12.67
11.81
10.59
8.78
11.08
8.63
10.98
12.33
9.49
9.17
6.99
9.13
9.61
8.21
9.94
9.61
9.84
10.09
9.72
10.85
10.06
18.3
18.39
18.84
18.75
18.88
19.22
19.31
19.18
19.2
18.9
19.01
18.87
18.54
18.35
18.3
18.51
18.31
18.49
18.6
18.76
18.5
18.5
18.7
18.7
18.78
18.64
18.5
18.34
18.5
18.33
18.4
18.25
18.11
18.25
17.97
17.81
17.51
17.9
17.9
18.16
18.09
17.95
18.36
17.8
17.66
17.09
16.91
16.8
16.7
16.37
16.1
16.34
16.82
16.9
17.21
17.35
16.9
17.65
17.68
17.8
17.7
17.6
17.3
17.35
17.2
16.87
16.49
16.3
16.08
15.79
15.7
15.74
15.8
15.74
24
25.75
24
22.48
22.21
19.76
22.02
21.25
19
21
20.76
21.63
19
22.5
22
23.1
22.95
21.54
20.99
18.71
22.95
23
18.31
20.01
18.46
21.56
20.1
22
22
21.62
21
21.54
22.77
23.52
23.83
25.86
28.94
23
24
24
24
23.46
22.34
22.95
22.22
24
23.97
23.78
24
24
25
24
22
23
23
23.02
25.87
21
22
22
22
22
23.95
22.49
23.01
23.66
25
25
25.06
26.38
26
26
26
25.54
849
849
849
849
849
849
849
849
849
849
849
849
849
849
849
849
849
849
849
849
849
849
849
849
849
849
849
849
849
849
849
849
849
849
849
849
849.97
849
850
850
850
849
850
849
849
849
849
849
849
849
849
849
849
849
849
849
849
849
849
849
849
849
849
849
849
849
849
849
849
849
849
849
849
849
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
732.26
731.64
687.58
573.06
600.47
572.23
660.59
618.44
679.93
675.53
673.2
507.9
633.53
459.24
643.9
643.64
631.82
648.52
614.33
613.7
609.02
598.3
583.27
578.03
556.57
549.27
530.79
526.52
509.59
506.82
490.6
468.83
473.88
453.54
440.64
429.2
406.78
398.9
388.66
370.8
354.57
357.58
356.04
194.81
87.27
59.98
57.66
58.37
47.84
46.44
47.5
59.78
148.66
160.31
164.72
93.78
115.2
122.76
154.02
112.59
73.43
61.68
40.86
28.86
15.42
2.54
0
0
0
0
0
0
0
0
118.95
117.1
112.12
113.34
112.08
115.96
121.66
101.47
85.34
81.72
84.04
90.55
84.54
88.66
92.17
85.45
105.39
119.68
97.33
95.74
88.01
81.29
80.62
74.99
72.93
70.76
71.59
67.23
67.86
79.28
87.22
88.45
87.55
86.97
86.46
85.43
85.07
84.59
83.76
82.99
83.13
81.56
78.39
99.75
80.34
54.73
53.55
54.67
44.27
43.12
44.03
47.04
53.52
61.37
65.57
60.98
68.27
70.87
68.86
63.62
62.97
52.95
35.42
25.25
12.94
3.37
0
0
0
0
0
0
0
0
11.2
9.22
- 4.54
- 5.69
- 5.27
- 5.47
- 4.91
- 5.29
- 4.05
- 4.88
- 5.17
- 4.64
- 6.33
- 6.33
- 6.16
- 6.13
- 6.55
- 6.96
- 6.15
- 6.15
- 6.06
- 13.32
- 12.42
- 7.12
- 12.97
- 12.07
- 5.89
- 6.04
- 7.21
- 6.67
- 13.32
- 12.92
- 6.94
- 6.59
- 7.19
- 8.02
- 8.66
- 8.51
- 8.14
- 8.42
- 8.42
- 8.51
- 8.18
- 9.85
- 11.72
- 9.44
-9
- 11.13
- 17.28
- 16.89
- 9.88
- 8.42
- 6.99
- 6.32
- 3.64
- 3.5
- 1.56
0.94
1.45
2.28
1.27
1.13
- 0.67
- 3.01
- 6.95
- 8.42
- 8.36
- 7.76
- 6.86
- 6.91
- 7.21
- 7.31
- 13.16
- 13.47
-
-
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
-999
APPENDIX B:
MEASURED TEMPERATURE DATA
119
Measured Temperature April 7, 9:00pm through April 8, 8:55am
T im e
A ctual tem p
9:00:01 PM -1
9:01:47 PM -1
9:06:47 PM -1
9:11:47 PM 1
1
9:16:47 PM
9:21:47 PM 2
9:26:47 PM 3
9:31:47 PM 3
9:36:47 PM 3
9:41:47 PM 3
9:46:47 PM 3
9:51:47 PM 3
9:56:47 PM 3
10:01:47 PM 3
10:06:47 PM 3
10:11:47 PM 3
10:16:47 PM 3
10:21:47 PM 3
10:26:47 PM 3
10:31:47 PM 3
10:36:47 PM 3
10:41:47 PM 3
10:46:47 PM 3
10:51:47 PM 3
10:56:47 PM 3
11:01:47 PM 3
11:06:47 PM 3
11:11:47 PM 3
11:16:47 PM 3
11:21:47 PM 3
11:26:47 PM 3
11:31:47 PM 3
11:36:47 PM 3
11:41:47 PM 3
11:46:47 PM 3
11:51:47 PM 3
11:56:47 PM 3
12:01:47 AM 2
12:06:47 AM 2
12:11:47 AM 2
12:16:47 AM 2
12:21:47 AM 2
12:26:47 AM 2
12:31:47 AM 2
12:36:47 AM 2
12:41:47 AM 2
12:46:47 AM
12:51:47 AM
12:56:47 AM
1:01:47 AM
1:06:47 AM
1:11:47 AM
1:16:47 AM
1:21:47 AM
1:26:47 AM
1:31:47 AM
1:36:47 AM
1:41:47 AM
1:46:47 AM
1:51:47 AM
1:56:47 AM
2:01:47 AM
2:06:47 AM
2:11:47 AM
2:16:47 AM
2:21:47 AM
2:26:47 AM
2:31:47 AM
2:36:47 AM
2:41:47 AM
2:46:47 AM
2:51:47 AM
2:56:47 AM
3:01:47 AM
3:06:47 AM
3:11:47 AM
3:16:47 AM
3:21:47 AM
3:26:47 AM
3:31:47 AM
3:36:47 AM
3:41:47 AM
3:46:47 AM
3:51:47 AM
3:56:47 AM
4:01:47 AM
4:06:47 AM
4:11:47 AM
4:16:47 AM
4:21:47 AM
4:26:47 AM
4:31:47 AM
1
1
1
1
1
0
1
1
0
0
-1
-1
-1
-1
-1 .
0
0
-1
0
0
0
-1
0
-1
-I
-1
-1
-1
0
-1
0
0
-1
-1
-1
-1
-1
-1
0
-1
-1
-1
-1
-1
-1
-1
4:36:47 AM
4:41:47 AM
4:46:47 AM
4:51:47 AM
4:56:47 AM
5:01:47 AM
5:06:47 AM
5:11:47 AM
5:16:47 AM
5:21:47 AM
5:26:47 AM
5:31:47 AM
5:36:47 AM
5:41:47 AM
5:46:47 AM
5:51:47 AM
5:56:47 AM
6:01:47 AM
6:06:47 AM
6:11:47 AM
6:16:47 AM
6:21:47 AM
6:26:47 AM
6:31:47 AM
6:36:47 AM
6:41:47 AM
6:46:47 AM
6:51:47 AM
6:56:47 AM
7:01:47 AM
7:06:47 AM
7:11:47 AM
7:16:47 AM
7:21:47 AM
7:26:47 AM
7:31:47 AM
7:36:47 AM
7:41:47 AM
7:46:47 AM
7:51:47 AM
7:56:47 AM
8:01:47 AM
8:06:47 AM
8:11:47 AM
8:16:47 AM
8:21:47 AM
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
8:26:47 AM
8:31:47 AM
8:36:47 AM
8:41:47 AM
8:46:47 AM
8:51:47 AM
8:56:47 AM
'
-1
-I
-1
-1
-1
-1
-1
120
Measured Temperature April 8,9:01am April,8, 8:46 pm
T im e
A ctual tem p (rounded up)
12:46:47 PM
9
9:01:47 AM
-1
12:51:47 PM
9
9:06:47 AM
-1
12:56:47 PM 11
9:11:47 AM
-1
1:01:47 PM 12
-1
9:16:47 AM
1:06:47
PM 14
-1
9:21:47 AM
1:11:47
PM 14
-1
9:26:47 AM
1:16:47 PM 15
-1
9:31:47 AM
1:21:47 PM 16
9:36:47 AM
-1
1:26:47 PM 17
-1
9:41:47 AM
1:31:47 PM 18
-1
9:46:47 AM
1:36:47 PM 18
-1
9:51:47 AM
1:41:47 PM 19
-1
9:56:47 AM
1:46:47 PM 19
-1
10:01:47 AM
1:51:47 PM 19
10:06:47 AM
-1
1:56:47 PM 16
10:11:47 AM
-1
2:01:47 PM 16
-2
10:16:47 AM
2:06:47 PM 15
-1
10:21:47 AM
2:11:47 PM 16
-1
10:26:47 AM
2:16:47 PM 17
-1
10:31:47 AM
2:21:47 PM 19
-2
10:36:47 AM
2:26:47 PM 21
0
10:41:47 AM
2:31:47 PM 21
-1
10:46:47 AM
2:36:47 PM 22
0
10:51:47 AM
2:41:47 PM 22
-1
10:56:47 AM
2:46:47 PM 22
1
11:01:47 AM
2 :5 1 :47 PM 23
2
11:06:47 AM
2:56:47 PM 23
2
11:11:47 AM
3:01:47 PM 23
4
11:16:47 AM
3:06:47 PM 23
5
11:21:47 AM
3:11:47 PM 24
7
11:26:47 AM
3:16:47 PM 23
7
11:31:47 AM
3:21:47 PM 24
9
11:36:47 AM
3:26:47 PM 24
9
11:41:47 AM
3:31:47 PM 24
8
11:46:47 AM
3:36:47 PM 23
6
11:51:47 AM
3:41:47 PM 23
6
11:56:47 AM
3:46:47 PM 23
6
12:01:47 PM
3:51:47 PM 24
6
12:06:47 PM
3:56:47 PM 22
7
12:11:47 PM
4:01:47 PM 18
8
12:16:47 PM
4:06:47 PM 15
6
12:21:47 PM
4:11:47 PM 18
7
12:26:47 PM
4:16:47 PM 18
8
12:31:47 PM
4:21:47 PM 19
7
12:36:47 PM
4:26:47 PM 18
8
12:41:47 PM
4:31:47
4:36:47
4:41:47
4:46:47
4:51:47
4:56:47
5:01:47
5:06:47
5:11:47
5:16:47
5:21:47
5:26:47
5:31:47
5:36:47
5:41:47
5:46:47
5:51:47
5:56:47
6:01:47
6:06:47
6:11:47
6:16:47
6:21:47
6:26:47
6:31:47
6:36:47
6:41:47
6:46:47
6:51:47
6:56:47
7:01:47
7:06:47
7:11:47
7:16:47
7:21:47
7:26:47
7:31:47
7:36:47
7:41:47
7:46:‘4 7
7:51:47
7:56:47
8:01:47
8:06:47
8:11:47
PM
PM
PM
PM
PM
PM
PM
PM
PM
PM
PM
PM
PM
PM
PM
PM
PM
PM
PM
PM
PM
PM
PM
PM
PM
PM
PM
PM
PM
PM
PM
PM
PM
PM
PM
PM
PM
PM
PM
PM
PM
PM
PM
PM
PM
17
17
17
17
16
16
16
16
16
15
14
14
12
12
12
13
12
11
11
9
8
5
4
7
8
9
9
10
10
9
10
11
11
11
11
11 .
11
12
11
11
11
11
11
11
11
8:16:47
8:21:47
8:26:47
8:31:47
8:36:47
8:41:47
8:46:47
PM
PM
PM
PM
PM
PM
PM
11
11
11
10
10
10
10
121
Measured temperature for April, 8 9:01 pm through April, 9 1:36 pm
T im e
9:01:47
9:06:47
9:11:47
9:16:47
9:21:47
9:26:47
9:31:47
9:36:47
9:41:47
9:46:47
9:51:47
9:56:47
10:01:47
10:06:47
10:11:47
10:16:47
10:21:47
10:26:47
10:31:47
10:36:47
10:41:47
10:46:47
10:51:47
10:56:47
11:01:47
11:06:47
11:11:47
11:16:47
11:21:47
11:26:47
11:31:47
11:36:47
PM
PM
PM
PM
PM
PM
PM
PM
PM
PM
PM
PM
PM
PM
PM
PM
PM
PM
PM
PM
PM
PM
PM
PM
PM
PM
PM
PM
PM
PM
PM
PM
A ctual tem p
10
9
9
9
9
9
8
8
8
8
8
7
8
7
8
8
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
11:41:47
11:46:47
11:51:47
11:56:47
12:01:47
12:06:47
12:11:47
12:16:47
12:21:47
12:26:47
12:31:47
12:36:47
12:41:47
12:46:47
12:51:47
12:56:47
1:01:47
1:06:47
1:11:47
1:16:47
1:21:47
1:26:47
1:31:47
1:36:47
PM
PM
PM
PM
AM
AM
AM
AM
AM
AM
AM
AM
AM
AM
AM
AM
AM
AM
AM
AM
AM
AM
AM
AM
7
7
7
7
7
7
7
6
5
5
5
5
5
6
5
5
4
4
4
4
4
4
.4
4
122
Measured Temperature March 13, 6:50 am through March 13, 6:45pm
Tem p
T im e
1
6:50:32 AM
1
6:55:32 AM
7:00:32 AM
1
1
7:05:32 AM
1
7:10:32 AM
1
7:15:32 AM
-1
7:20:32 AM
-1
7:25:32 AM
-1
7:30:32 AM
-1
7:35:32 AM
0
7:40:32 AM
1
7:45:32 AM
1
7:50:32 AM
1
7:55:32 AM
8:00:32 AM
2
8:05:32 AM
1
2
8:10:32 AM
1
8:15:32 AM
0
8:20:32 AM
0
8:25:32 AM
1
8:30:32 AM
1
8:35:32 AM
2
8:40:32 AM
3
8:45:32 AM
3
8:50:32 AM
3
8:55:32 AM
4
9:00:32 AM
3
9:05:32 AM
3
9:10:32 AM
3
9:15:32 AM
9:20:32 AM
3
3
9:25:32 AM
3
9:30:32 AM
4
9:35:32 AM
3
9:40:32 AM
2
9:45:32 AM
1
9:50:32 AM
1
9:55:32 AM
2
10:00:32 AM
10:05:32 AM
10:10:32 AM
10:15:32 AM
10:20:32 AM
10:25:32 AM
10:30:32 AM
10:35:32 AM
10:40:32 AM
10:45:32 AM
10:50:32 AM
10:55:32 AM
11:00:32 AM
11:05:32 AM
11:10:32 AM
11:15:32 AM
11:20:32 AM
11:25:32 AM
1 1 :3 0 :3 2 A M
11:35:32 AM
11:40:32 AM
11:45:32 AM
11:50:32 AM
11:55:32 AM
12:00:32 PM
12:05:32 PM
12:10:32 PM
12:15:32 PM
12:20:32 PM
12:25:32 PM
12:30:32 PM
12:35:32 PM
12:40:32 PM
12:45:32 PM
12:50:32 PM
12:55:32 PM
1:00:32 PM
1:05:32 PM
1:10:32 PM
1:15:32 PM
2
3
3
3
3
4
4
4
4
5
4
4
5
6
8
8
9
9
9
11
9
9
10
10
12
10
11
12
14
13
10
11
13
14
15
16
16
17
15
1:20:32
1:25:32
1:30:32
1:35:32
1:40:32
1:45:31
1:50:31
1:55:31
2:00:31
2:05:31
2:10:31
2:15:31
2:20:31
2:25:31
2:30:31
2:35:31
2:40:31
2:45:31
2:50:31
2:55:31
3:00:31
3:05:31
3:10:31
3:15:31
3:20:31
3:25:31
3:30:31
3:35:31
3:40:31
3:45:31
3:50:31
3:55:31
4:00:31
4:05:31
4:10:31
4:15:31
4:20:31
4:25:31
4:30:31
PM
PM
PM
PM
PM
PM
PM
PM
PM
PM
PM
PM
PM
PM
PM
PM
PM
PM
PM
PM
PM
PM
PM
PM
PM
PM
PM
PM
PM
PM
PM
PM
PM
PM
PM
PM
PM
PM
PM
17
18
19
20
18
17
18
20
21
22
22
22
22
21
21
22
20
19
18
18
17
17
17
16
18
18
18
21
19
18
21
23
17
15
15
15
14
13
13
4:35:31
4:40:31
4:45:31
4:50:31
4:55:31
5:00:31
5:05:31
5:10:31
5:15:31
5:20:31
5:25:31
5:30:31
5:35:31
5:40:31
5:45:31
5:50:31
5:55:31
6:00:31
6:05:31
6:10:31
6:15:31
6:20:31
6:25:31
6:30:31
6:35:31
6:40:31
6:45:31
PM
PM
PM
PM
PM
PM
PM
PM
PM
PM
PM
PM
PM
PM
PM
PM
PM
PM
PM
PM
PM
PM
PM
PM
PM
PM
PM
14
14
15
14
12
11
11
11
11
11
12
13
12
11
11
10
9
9
10
11
11
11
11
10
11
11
11
123
APPENDIX C
DATA FROM RADTHERM/RT SIMULATIONS
J
124
Results from nighttime simulation for 3000 element mesh with high view factor settings
Time
9:01:47 PM
9:06:47 PM
9:11:47 PM
9:16:47 PM
9:21:47 PM
9:26:47 PM
9:31:47 PM
9:36:47 PM
9:41:47 PM
9:46:47 PM
9:51:47 PM
9:56:47 PM
10:01:47 PM
10:06:47 PM
10:11:47 PM
10:16:47 PM
10:21:47 PM
10:26:47 PM
10:31:47 PM
10:36:47 PM
10:41:47 PM
10:46:47 PM
10:51:47 PM
10:56:47 PM
11:01:47 PM
11:06:47 PM
11:11:47 PM
11:16:47 PM
11:21:47 PM
11:26:47 PM
11:31:47 PM
11:36:47 PM
11:41:47 PM
11:46:47 PM
11:51:47 PM
11:56:47 PM
12:01:47 AM
12:06:47 AM
12:11:47 AM
12:16:47 AM
12:21:47 AM
12:26:47 AM
12:31:47 AM
12:36:47 AM
12:41:47 AM
12:46:47 AM
12:51:47 AM
12:56:47 AM
Temp
3.00
3.00
3.00
3.00
3.00
3.00
3.00
3.00
3.00
3.00
3.00
3.00
3.00
3.00
3.00
3.00
3,00
3.00
3.00
3.00
3.00
3.00
3.00
3.00
3.00
3.00
3.00
3.00
3.00
3.00
3.00
3.00
3.00
3.00
3.00
3.00
2.00
2.00
2.00
2.00
2.00
2.00
2.00
2.00
2.00
TOO
1.00
1.00
1:01:47 AM
1:06:47 AM
1:11:47 AM
1:16:47 AM
1:21:47 AM
1:26:47 AM
1:31:47 AM
1:36:47 AM
1:41:47 AM
1:46:47 AM
1:51:47 AM
1:56:47 AM
2:01:47 AM
2:06:47 AM
2:11:47 AM
2:16:47 AM
2:21:47 AM
2:26:47 AM
2:31:47 AM
2:36:47 AM
2:41:47 AM
2:46:47 AM
2:51:47 AM
2:56:47 AM
3:01:47 AM
3:06:47 AM
3:11:47 AM
3:16:47 AM
3:21:47 AM
3:26:47 AM
3:31:47 AM
3:36:47 AM
3:41:47 AM
3:46:47 AM
3:51:47 AM
3:56:47 AM
4:01:47 AM
4:06:47 AM
4:11:47 AM
4:16:47 AM
4:21:47 AM
4:26:47 AM
4:31:47 AM
4:36:47 AM
4:41:47 AM
4:46:47 AM
4:51:47 AM
4:56:47 AM
1.00
1.00
0.00
1.00
1.00
0.00
0.00
-1.00
-1.00
-1.00
-1.00
-1.00
0.00
0.00
-1.00
0.00
0.00
0.00
-1.00
0.00
-1.00
-1.00
-1.00
-1.00
-1.00
0.00
-1.00
0.00
0.00
-1.00
-1.00
-1.00
-1.00
-1.00
-1.00
0.00
-1.00
-1.00
-1.00
-1.00
-1.00
-1.00
-1.00
-1.00
-1.00
-1.00
-1.00
-1.00
5:01:47 AM
5:06:47 AM
5:11:47 AM
5:16:47 AM
5:21:47 AM
5:26:47 AM
5:31:48 AM
5:36:48 AM
5:41:48 AM
5:46:48 AM
5:51:48 AM
5:56:48 AM
6:01:48 AM
6:06:48 AM
6:11:48 AM
6:16:48 AM
6:21:48 AM
6:26:48 AM
6:31:48 AM
6:36:48 AM
6:41:48 AM
6:46:48 AM
6:51:48 AM
6:56:48 AM
7:01:48 AM
7:06:48 AM
7:11:48 AM
7:16:48 AM
7:21:48 AM
7:26:48 AM
7:31:48 AM
7:36:48 AM
7:41:48 AM
7:46:48 AM
7:51:48 AM
7:56:48 AM
8:01:48 AM
8:06:48 AM
8:11:48 AM
8:16:48 AM
8:21:48 AM
8:26:48 AM
8:31:48 AM
8:36:48 AM
8:41:48 AM '
8:46:48 AM
8:51:48 AM
8:56:48 AM
-1.00
-1.00
-1.00
-1.00
-1.00
-1.00
-1.00
-1.00
-1.00
-1.00
-1.00
-1.00
-1.00
-1.00
-1.00
-1.00
-1.00
-1.00
-1.00
-1.00
-1.00
-1.00
-1.00
-1.00
-1.00
-1.00
-1.00
-1.00
-1.00
-1.00
-1.00
-1.00
-1.00
-1.00
-1.00
-1.00
-1.00
-1.00
-1.00
-1.00
-1.00
-1.00
-1.00
-1.00
-1.00
-1.00
-1.00
-1.00
125
Results from daytime simulation for 3000 element mesh with high view factor settings
Tim e
9:01:47 AM
9:06:47 AM
9:11:47 AM
9:16:47 AM
9:21:47 AM
9:26:47 AM
9:31:47 AM
9:36:47 AM
9:41:47 AM
9:46:47 AM
9:51:47 AM
9:56:47 AM
10:01:47 AM
10:06:47 AM
10:11:47 AM
10:16:47 AM
10:21:47 AM
10:26:47 AM
10:31:47 AM
10:36:47 AM
10:41:47 AM
10:46:47 AM
10:51:47 AM
10:56:47 AM
11:01:47 AM
11:06:47 AM
11:11:47 AM
11:16:47 AM
11:21:47 AM
11:26:47 AM
11:31:47 AM
11:36:47 AM
11:41:47 AM
11:46:47 AM
11:51:47 AM
11:56:47 AM
12:01:47 PM
12:06:47 PM
12:11:47 PM
12:16:47 PM
12:21:47 PM
12:26:47 PM
12:31:47 PM
12:36:47 PM
12:41:47 PM
12:46:47 PM
12:51:47 PM
12:56:47 PM
Tem p
-0.94
-0.82
-0.68
-0.55
-0.43
-0.32
-0.22
-0.06
0.14
0.48
0.95
1.40
1.82
2.30
2.84
3.33
3.82
4.39
4.98
5.56
6.22
6.91
7.54
8.13
8.67
9.19
9.71
10.20
10.69
11.16
11.61
12.08
12.53
12.94
13.35
13.79
14.25
14.65
15.01
15.37
15.70
16.02
16.32
16.58
16.86
17.08
17.33
17.52
1:01:47 PM
17.72
1:06:47 PM
18.06
18.30
1:11:47 PM
1:16:47 PM
18.55
18.76
1:21:47 PM
1:26:47 PM
18.94
19.25
1:31:47 PM
19.55
1:36:47 PM
1:41:47 PM
19.79
1:46:47 PM
19.98
20.08
1:51:47 PM
20.21
1:56:47 PM
2:01:47 PM
20.34
20.62
2:06:47 PM
20.81
2:11:47 PM
2:16:47 PM
21.19
2:21:47 PM
21.35
21.58
2:26:47 PM
21.73
2:31:47 PM
21.91
2:36:47 PM
22.00
2:41:47 PM
22.03
2:46:47 PM
22.19
2:51:47 PM
2:56:47 PM
22.39
22.52
3:01:47 PM
3:06:47 PM . 22.52
22.45
3:11:47 PM
22.45
3:16:47 PM
22.54
3:21:47 PM
22.36
3:26:47 PM
22.15
3:31:47 PM
21.94
3:36:47 PM
21.78
3:41:47 PM
21.49
3:46:47 PM
21.44
3:51:47 PM
21.25
3:56:47 PM
21.00
4:01:47 PM
20.68
4:06:47 PM
20.42
4:11:47 PM
20.15
4:16:47 PM
20.00
4:21:47 PM
19.70
4:26:47 PM
19.37
4:31:47 PM
19.08
4:36:47 PM
18.73
4:41:47 PM
18.45
4:46:47 PM
18.15
4 :5 1 :47 PM
17.91
4:56:47 PM
5:01:47 PM
5:06:47 PM
5:11:47 PM
5:16:47 PM
5:21:47 PM
5:26:47 PM
5:31:47 PM
5:36:47 PM
5:41:47 PM
5:46:47 PM
5:51:47 PM
5:56:47 PM
6:01:47 PM
6:06:47 PM
6:11:47 PM
6:16:47 PM
6:21:47 PM
6:26:47 PM
6:31:47 PM
6:36:47 PM
6:41:47 PM,
6:46:47 PM
6:51:47 PM
6:56:47 PM
7:01:47 PM
7:06:47 PM
7:11:47 PM
7:16:47 PM
7:21:47 PM
7:26:47 PM
7:31:47 PM
7:36:47 PM
7:41:47 PM
7:46:47 PM
7 :5 1 :47 PM
7:56:47 PM
8:01:47 PM
8:06:47 PM
8:11:47 PM
8:16:47 PM
8:21:47 PM
8:26:47 PM
8:31:47 PM
8:36:47 PM
8:41:47 PM
8:46:47 PM
17.71
17.54
17.40
17.28
17.19
17.13
17.04
16.93
16.84
16.77
16.72
16.65
16.66
16.61
16.53
16.47
16.40
16.32
16.25
16.17
16.13
16.06
16.02
15.96
15.90
15.81
15.71
15.62
15.52
15.42
15.31
15.20
15.07
14.94
14.80
14.65
14.48
14.32
14.19
14.06
13.93
13.78
13.62
13.46
13.32
13.19
126
Results from nighttime simulation for 300 element bridge mesh with high view factor
settings
Tim e
9:00:01 PM
9:05:01 PM
9:10:01 PM
9:15:01 PM
9:20:01 PM
9:25:01 PM
9:30:01 PM
9:35:01 PM
9:40:01 PM
9:45:01 PM
9:50:01 PM
9:55:01 PM
10:00:01 PM
10:05:01 PM
10:10:01 PM
10:15:01 PM
10:20:01 PM
10:25:01 PM
10:30:01 PM
10:35:01 PM
10:40:01 PM
10:45:01 PM
10:50:01 PM
10:55:01 PM
11:00:01 PM
11:05:01 PM
11:10:01 PM
11:15:01 PM
11:20:01 PM
11:25:01 PM
11:30:01 PM
11:35:01 PM
11:40:01 PM
11:45:01 PM
11:50:01 PM
11:55:01 PM
12:00:01 AM
12:05:01 AM
12:10:01 AM
12:15:01 AM
12:20:01 AM
12:25:01 AM
12:30:01 AM
12:35:01 AM
12:40:01 AM
12:45:01 AM
12:50:01 AM
12:55:01 AM
Tem p
1:00:01 AM
3.00
1:05:01 AM
2.83
2.69
1:10:01 AM
2.56
1:15:01 AM
1:20:01 AM
2.45
2.35
1:25:01 AM
2.27
1:30:01 AM
1:35:01 AM
2.18
1:40:01 AM
2.09
1.98
1:45:01 AM
1:50:01 AM
1.90
1.84
1:55:01 AM
2:00:01 AM
1.78
1.72
2:05:01 AM
2:10:01 AM
1.65
2:15:01 AM
1.55
1.45
2:20:01 AM
2:25:01 AM
1.39
1.34
2:30:01 AM
2:35:01 AM
1.27
2:40:01 AM
1.22
1.18
2:45:01 AM
1.13 ■ 2:50:01 AM
1.08
2:55:01 AM
1.02
3:00:01 AM
3:05:01 AM
0.94
3:10:01 AM
0.87
3:15:01 AM
0.81
3:20:01 AM
0.75
3:25:01 AM
0.69
3:30:01
AM
0.66
3:35:01
AM
0.63
3:40:01 AM
0.63
3:45:01 AM
0.65
3:50:01 AM
0.69
3:55:01 AM
0.74
4:00:01 AM
0.85
4:05:01 AM
0.99
4:10:01 AM
1.04
4:15:01 AM
1.05
4:20:01 AM
1.04
4:25:01 AM
1.02
4:30:01 AM
1.00
4:35:01 AM
0.97
4:40:01 AM
0.92
4:45:01 AM
0.88
4:50:01 AM
0.85
4:55:01 AM
0.80
0.73
0.67
0.65
0.60
0.54
0.48
0.39
0.32
0.29
0.23
0.20
0.19
0.18
0.14
0.09
0.03
-0.02
-0.07
-0.12
-0.17
-0.19
-0.20
-0.18
-0.14
-0.07
-0.01
-0.01
-0.14
-0.30
-0.44
-0.54
-0.62
-0.70
-0.77
-0.83
-0.88
-0.90
-0.91
-0.93
-0.95
-1.00
-1.07
-1.13
-1.18
-1.21
-1.25
-1.29
-1.33
5:00:01
5:05:01
5:10:01
5:15:01
5:20:01
5:25:01
5:30:01
5:35:01
5:40:01
5:45:01
5:50:01
5:55:01
6:00:01
6:05:01
6:10:01
6:15:01
6:20:01
6:25:01
6:30:01
6:35:01
6:40:01
6:45:01
6:50:01
6:55:01
7:00:01
7:05:01
7:10:01
7:15:01
7:20:01
7:25:01
7:30:01
7:35:01
7:40:01
7:45:01
7:50:01
7:55:01
8:00:01
8:05:01
8:10:01
8:15:01
8:20:01
8:25:01
8:30:01
8:35:01
8:40:01
8:45:01
8:50:01
8:55:01
AM
AM
AM
AM
AM
AM
AM
AM
AM
AM
AM
AM
AM
AM
AM
AM
AM
AM
AM
AM
AM
AM
AM
AM
AM
AM
AM
AM
AM
AM
AM
AM
AM
AM
AM
AM
AM
AM
AM
AM
AM
AM
AM
AM
AM
AM
AM
AM
-1.34
-1.33
-1.34
-1.37
-1.39
-1.42
-1.45
-1.48
-1.54
-1.61
-1.67
-1.74
-1.80
-1.86
-1.92
-1.97
-2.00
-2.03
-2.06
-2.07
-2.08
-2.09
-2.09
-2.08
-2.06
-2.03
-2.00
-1.99
-1.96
-1.94
-1.93
-1.92
-1.89
-1.84
-1.78
-1.74
-1.71
-1.68
-1.63
-1.58
-1.52
-1.47
-1.42
-1.35
-1.29
-1.22
-1.15
-1.06
127
Results from daytime simulation for 300 element bridge mesh with high view factor
settings
Tim e
9:01:47 AM
9:06:47 AM
9:11:47 AM
9:16:47 AM
9:21:47 AM
9:26:47 AM
9:31:47 AM
9:36:47 AM
9:41:47 AM
9:46:47 AM
9:51:47 AM
9:56:47 AM
10:01:47 AM
10:06:47 AM
10:11:47 AM
10:16:47 AM
10:21:47 AM
10:26:47 AM
10:31:47 AM
10:36:47 AM
10:41:47 AM
10:46:47 AM
10:51:47 AM
10:56:47 AM
11:01:47 AM
11:06:47 AM
11:11:47 AM
11:16:47 AM
11:21:47 AM
11:26:47 AM
11:31:47 AM
11:36:47 AM
11:41:47 AM
11:46:47 AM
11:51:47 AM
11:56:47 AM
12:01:47 PM
12:06:47 PM
12:11:47 PM
12:16:47 PM
12:21:47 PM
12:26:47 PM
12:31:47 PM
12:36:47 PM
12:41:47 PM
12:46:47 PM
12:51:47 PM
12:56:47 PM
Tem p
-0.96
-0.86
-0.73
-0.62
-0.51
-0.41
-0.33
-0.24
-0.12
0.12
0.44
0.77
1.09
1.41
1.74
2.04
2.36
2.70
3.01
3.32
3.61
3.87
4.10
4.54
5.08
5.56
6.04
6.47
6.89
7.29
7.67
8.06
8.54
9.00
9.39
9.78
10.25
10.80
11.31
11.77
12.20
12.59
12.99
13.43
13.85
14.21
14.55
14.84
1:01:47 PM
1:06:47 PM
1:11:47 PM
1:16:47 PM
1:21:47 PM
1:26:47 PM
1:31:47 PM
1:36:47 PM
1:41:47 PM
1:46:47 PM
1:51:47 PM
1:56:47 PM
2:01:47 PM
2:06:47 PM
2:11:47 PM
2:16:47 PM
2:21:47 PM
2:26:47 PM
2:31:47 PM
2:36:47 PM
2:41:47 PM
2:46:47 PM
2:51:47 PM
2:56:47 PM
3:01:47 PM
3:06:47 PM
3:11:47 PM
3:16:47 PM
3:21:47 PM
3:26:47 PM
3:31:47 PM
3:36:47 PM
3:41:47 PM
3:46:47 PM
3:51:47 PM
3:56:47 PM
4:01:47 PM
4:06:47 PM
4:11:47 PM
4 :1 6 :4 7 P M
4:21:47 PM
4:26:47 PM
4:31:47 PM
4:36:47 PM
4:41:47 PM
4:46:47 PM
4:51:47 PM
4:56:47 PM
15.23
15.76
16.20
16.60
16.95
17.26
17.66
18.03
18.36
18.63
18.82
19.02
19.22
19.54
19.78
20.19
20.39
20.66
20.85
21.08
21.21
21.29
21.49
21.71
21.87
22.01
22.13
22.30
22.48
22.33
22.25
22.23
22.23
22.07
22.14
22.04
21.94
21.86
21.77
21.64
21.64
21.50
21.39
21.33
21.13
21.11
20.94
20.69
5:01:47 PM
5:06:47 PM
5:11:47 PM
5:16:47 PM
5:21:47 PM
5:26:47 PM
5:31:47 PM
5:36:47 PM
5:41:47 PM
5:46:47 PM
5:51:47 PM
5:56:47 PM
6:01:47 PM
6:06:47 PM
6:11:47 PM
6:16:47 PM
6:21:47 PM
6:26:47 PM
6:31:47 PM
6:36:47 PM
6:41:47 PM
6:46:47 PM
6:51:47 PM
6:56:47 PM
7:01:47 PM
7:06:47 PM
7:11:47 PM
7:16:47 PM
7:21:47 PM
7:26:47 PM
7:31:47 PM
7:36:47 PM
7:41:47 PM
7:46:47 PM
7:51:47 PM
7:56:47 PM
8:01:47 PM
8:06:47 PM
8:11:47 PM
8:16:47 PM
8:21:47 PM
8:26:47 PM
8:31:47 PM
8:36:47 PM
8:41:47 PM
8:46:47 PM
20.44
20.29
20.17
20.06
19.92
19.70
19.43
19.19
18.97
18.78
18.57
18.39
18.23
18.03
17.86
17.71
17.58
17.45
17.33
17.22
17.15
17.05
16.96
16.86
16.76
16.64
16.52
16.40
16.28
16.16
16.03
15.90
15.76
15.62
15.48
15.33
15.15
14.99
14.84
14.71
14.57
14.41
14.24
14.07
13.92
13.79
128
Results from nighttime simulation for 10 element bridge mesh with high view factor,
settings
Tim e
9:00:01 PM
9:05:01 PM
9:10:01 PM
9:15:01 PM
9:20:01 PM
9:25:01 PM
9:30:01 PM
9:35:01 PM
9:40:01 PM
9:45:01 PM
9:50:01 PM
9:55:01 PM
10:00:01 PM
10:05:01 PM
10:10:01 PM
10:15:01 PM
10:20:01 PM
10:25:01 PM
10:30:01 PM
10:35:01 PM
10:40:01 PM
10:45:01 PM
10:50:01 PM
10:55:01 PM
11:00:01 PM
11:05:01 PM
11:10:01 PM
11:15:01 PM
11:20:01 PM
11:25:01 PM
11:30:01 PM
11:35:01 PM
11:40:01 PM
11:45:01 PM
11:50:01 PM
11:55:01 PM
12:00:01 AM
12:05:01 AM
12:10:01 AM
12:15:01 AM
12:20:01 AM
12:25:01 AM
12:30:01 AM
12:35:01 AM
12:40:01 AM
12:45:01 AM
12:50:01 AM
12:55:01 AM
Temp
3.00
2.74
2.51
2.31
2.14
1.99
1.87
1.73
1.61
1.47
1.35
1.27
1.18
1.11
1.01
0.88
0.76
0.69
0.63
0.54
0.47
0.42
0.37
0.30
0.22
0.13
0.05
-0.02
-0.09
-0.16
-0.20
-0.23
-0.23
-0.20
-0.15
-0.10
0.03
0.18
0.23
0.23
0.22
0.20
0.17
0.12
0.06
0.02
-0.03
-0.08
1:00:01 AM
1:05:01 AM
1:10:01 AM
1:15:01 AM
1:20:01 AM
1:25:01 AM
1:30:01 A M '
1:35:01 AM
1:40:01 AM
1:45:01 AM
1:50:01 AM
1:55:01 AM
2:00:01 AM
2:05:01 AM
2:10:01 AM
2:15:01 AM
2:20:01 AM
2:25:01 AM
2:30:01 AM
2:35:01 AM
2:40:01 AM
2:45:01 AM
2:50:01 AM
2:55:01 AM
3:00:01 AM
3:05:01 AM
3:10:01 AM
3:15:01 AM
3:20:01 AM
3:25:01 AM
3:30:01 AM
3:35:01 AM
3:40:01 AM
3:45:01 AM
3:50:01 AM
3:55:01 AM
4:00:01 AM
4:05:01 AM
4:10:01 AM
4:15:01 AM
4:20:01 AM
4;25:01 AM
4:30:01 AM
4:35:01 AM
4:40:01 AM
4:45:01 AM
4:50:01 AM
4:55:01 AM
-0.17
-0.24
-0.27
-0.32
-0.39
-0.47
-0.57
-0.65
-0.69
-0.75
-0.79
-0.80
-0.81
-0.85
-0.91
-0.98
-1.03
-1.08
-1.14
-1.20
-1.22
-1.22
-1.20
-1.14
-1.06
-0.99
-0.97
-1.10
-1.26
-1.40
-1.50
-1.57
-1.65
-1.73
-1.79
-1.84
-1.86
-1.87
-1.88
-1.90
-1.95
-2.01
-2.08
-2.11
-2.14
-2.17
-2.21
-2.24
5:00:01 AM
5:05:01 AM
5:10:01 AM
5:15:01 AM
5:20:01 AM
5:25:01 AM
5:30:01 AM
5:35:01 AM
5:40:01 AM
5:45:01 AM
5:50:01 AM
5:55:01 AM
6:00:01 AM
6:05:01 AM
6:10:01 AM
6:15:01 AM
6:20:01 AM
6:25:01 AM
6:30:01 AM
6:35:01 AM
6:40:01 AM
6:45:01 AM
6:50:01 AM
6:55:01 AM
7:00:01 AM
7:05:01 AM
7:10:01 AM
7:15:01 AM
7:20:01 AM
7:25:01 AM
7:30:01 AM
7:35:01 AM
7:40:01 AM
7:45:01 AM
7:50:01 AM
7:55:01 AM
8:00:01 AM
8:05:01 AM
8:10:01 AM
8:15:01 AM
8:20:01 AM
8:25:01 AM
8:30:01 AM
8:35:01 AM
8:40:01 AM
8:45:01 AM
8:50:01 AM
8:55:01 AM
-2.24
-2.23
-2.24
-2.26
-2.29
-2.32
-2.36
-2.41
-2.47
-2.55
-2.61
-2.69
-2.77
-2.84
-2.90
-2.95
-2.99
-3.01
-3.03
-3.05
-3.05
-3.06
-3.06
-3.04
-3.01
-2.96
-2.91
-2.86
-2.80
-2.73
-2.65
-2.58
-2.48
-2.35
-2.21
-2.07
-1.94
-1.80
-1.65
-1.48
-1.29
-1.10
-0.90
-0.68
-0.45
-0.21
0.04
0.31
129
Results from daytime simulation for 10 element bridge mesh with high view factor
settings
Tim e
9:01:47 AM
9:06:47 AM
9:11:47 AM
9:16:47 AM
9:21:47 AM
9:26:47 AM
9:31:47 AM
9:36:47 AM
9:41:47 AM
9:46:47 AM
9:51:47 AM
9:56:47 AM
10:01:47 AM
10:06:47 AM
10:11:47 AM
10:16:47 AM
10:21:47 AM
10:26:47 AM
10:31:47 AM
10:36:47 AM
10:41:47 AM
10:46:47 AM
10:51:47 AM
10:56:47 AM
11:01:47 AM
11:06:47 AM
11:11:47 AM
11:16:47 AM
11:21:47 AM
11:26:47 AM
11:31:47 AM
11:36:47 AM
11:41:47 AM
11:46:47 AM
11:51:47 AM
11:56:47 AM
12:01:47 PM
12:06:47 PM
12:11:47 PM
12:16:47 PM
12:21:47 PM
12:26:47 PM
12:31:47 PM
12:36:47 PM
12:41:47 PM
12:46:47 PM
12:51:47 PM
12:56:47 PM
Temp
0.61
0.93
1.27
1.60
1.94
2.29
2.64
3.00
3.36
3.76
4.17
4.55
4.92
5.27
5.61
5.96
6.32
6.69
7.06
7.43
7.81
8.20
8.59
8.96
9.32
9.70
10.08
10.47
10.86
11.24
11.62
12.03
12.42
12.79
13.15
13.55
13.97
14.34
14.68
15.01
15.32
15.62
15.90
16.15
16.42
16.63
16.87
17.05
1:01:47 PM
1:06:47 PM
1:11:47 PM
1:16:47 PM
1:21:47 PM
1:26:47 PM
1:31:47 PM
1:36:47 PM
1:41:47 PM
1:46:47 PM
1:51:47 PM
1:56:47 PM
2:01:47 PM
2:06:47 PM
2:11:47 PM
2:16:47 PM
2:21:47 PM
2:26:47 PM
2:31:47 PM
2:36:47 PM
2:41:47 PM
2:46:47 PM
2:51:47 PM
2:56:47 PM
3:01:47 PM
3:06:47 PM
3:11:47 PM
3:16:47 PM
3:21:47 PM
3:26:47 PM
3:31:47 PM
3:36:47 PM
3:41:47 PM
3:46:47 PM
3:51:47 PM
3:56:47 PM
4:01:47 PM
4:06:47 PM
4:11:47 PM
4:16:47 PM
4:21:47 PM
4:26:47 PM
4:31:47 PM
4:36:47 PM
4:41:47 PM
4:46:47 PM
4:51:47 PM
4:56:47 PM
17.25
17.57
17.81
18.04
18.25
18.42
18.73
19.01
19.24
19.42
19.52
19.64
19.76
20.02
20.19
20.54
20.69
20.90
21.03
21.20
21.27
21.30
21.44
21.61
21.73
21.81
21.89
22.00
22.22
22.19
22.20
22.24
22.32
22.26
22.41
22.36
22.38
22.46
22.51
22.46
22.59
22.57
22.54
22.56
22.37
22.39
22.37
22.35
5:01:47 PM
5:06:47 PM
5:11:47 PM
5:16:47 PM
5:21:47 PM
5:26:47 PM
5:31:47 PM
5:36:47 PM
5:41:47 PM
5:46:47 PM
5:51:47 PM
5:56:47 PM
6:01:47 PM
6:06:47 PM
6:11:47 PM
6:16:47 PM
6:21:47 PM
6:26:47 PM
6:31:47 PM
6:36:47 PM
6:41:47 PM
6:46:47 PM
6:51:47 PM
6:56:47 PM
7:01:47 PM
7:06:47 PM
7:11:47 PM
7:16:47 PM
7:21:47 PM
7:26:47 PM
7:31:47 PM
7:36:47 PM
7:41:47 PM
7:46:47 PM
7:51:47 PM
7:56:47 PM
8:01:47 PM
8:06:47 PM
8:11:47 PM
8:16:47 PM
8:21:47 PM
8:26:47 PM
8:31:47 PM
8:36:47 PM
8:41:47 PM
8:46:47 PM
22.25
22.26
22.25
22.27
22.21
22.04
21.84
21.68
21.55
21.47
21.34
21.24
20.99
20.69
20.44
20.22
20.00
19.82
19.63
19.47
19.28
19.11
18.89
18.67
18.43
18.20
17.97
17.74
17.51
17.27
17.04
16.80
16.58
16.36
16.13
15.90
15.64
15.41
15.20
15.01
14.82
14.62
14.40
14.18
14.00
13.83
130
Results from nighttime simulation for 3000 element bridge mesh with default view factor
settings.
Tim e
9:00:00 PM
9:05:00 PM
9:10:00 PM
9:15:00 PM
9:20:00 PM
9:25:00 PM
9:30:00 PM
9:35:00 PM
9:40:00 PM
9:45:00 PM
9:50:00 PM
9:55:00 PM
10:00:00 PM
10:05:00 PM
10:10:00 PM
10:15:00 PM
10:20:00 PM
10:25:00 PM
10:30:00 PM
10:35:00 PM
10:40:00 PM
10:45:00 PM
10:50:00 PM
10:55:00 PM
11:00:00 PM
11:05:00 PM
11:10:00 PM
11:15:00 PM
11:20:00 PM
11:25:00 PM
11:30:00 PM
11:35:00 PM
11:40:00 PM
11:45:00 PM
11:50:00 PM
11:55:00 PM
12:00:00 AM
12:05:00 AM
12:10:00 AM
12:15:00 AM
12:20:00 AM
12:25:00 AM
12:30:00 AM
12:35:00 AM
12:40:00 AM
12:45:00 AM
12:50:00 AM
12:55:00 AM
Temp
3.00
2.82
2.66
2.52
2.39
2.28
2.19
2.09
1.99
1.87
1.77
1.71
1.64
1.58
1.49
1.39
1.29
1.22
1.17
1.09
1.03
1.00
0.95
0.89
0.82
0.74
0.67
0.61
0.55
0.49
0.46
0.43
0.43
0.46
0.51
0.55
0.67
0.82
0.87
0.88
0.88
0.86
0.84
0.81
0.76
0.72
0.69
0.65
1:00:00 AM
0.57
1:05:00 AM
0.51
1:10:00 AM
0.49
1:15:00 AM
0.45
1:20:00 AM
0.39
1:25:00 AM
0.33
1:30:00AM
0.25
0.17
1:35:00 AM
0.14
1:40:00 AM
■ 0.09
1:45:00 AM
1:50:00 AM
0.06
0.05
1:55:00 AM
0.04
2:00:00 AM
2:05:00 AM
0.01
-0.04
2:10:00 AM
-0.10
2:15:00 AM
-0.14
2:20:00 AM
-0.19
2:25:00 AM
-0.24
2:30:00 AM
2:35:00 A M , -0.29
2:40:00 AM
-0.31
-0.31
2:45:00 AM
-0.29
2:50:00 AM
-0.24
2:55:00 AM
-0.17
3:00:00 AM
-0.11
3:05:00 AM
-0.1 Q
3:10:00 AM
-0.23
3:15:00 AM
-0.39
3:20:00 AM
-0.52
3:25:00 AM
-0.62
3:30:00 AM
-0.70
3:35:00 AM
-0.77
3:40:00 AM
-0.85
3:45:00 AM,
-0.91
3:50:00 AM
-0.95
3:55:00 AM
-0.97
4:00:00 AM
-0.98
4:05:00 AM
-0.99
4:10:00 AM
-1.02
4:15:00 AM
-1.07
4:20:00 AM
-1.13
4:25:00 AM
-1.19
4:30:00 AM
-1.24
4:35:00 AM
-1.27
4:40:00 AM
-1.31
4:45:00 AM
-1.35
4:50:00 AM
-1.38
4:55:00 AM
5:00:00 AM
5:05:00 AM
5:10:00 AM
5:15:00 AM
5:20:00 AM
5:25:00 AM
5:30:00 AM
5:35:00 AM
5:40:00 AM
5:45:00 AM
5:50:00 AM
5:55:00 AM
6:00:00 AM
6:05:00 AM
6:10:00 AM
6;15:00 AM
6:20:00 AM
6:25:00 AM
6:30:00 AM
6:35:00 AM
6:40:00 AM
6:45:00 AM
6:50:00 AM
6:55:00 AM
7:00:00 AM
7:05:00 AM
7:10:00 AM
7:15:00 AM
7:20:00 AM
7:25:00 AM
7:30:00 AM
7:35:00 AM
7:40:00 AM
7:45:00 AM
7:50:00 AM
7:55:00 AM
8:00:00 AM
8:05:00 AM
8:10:00 AM
8:15:00 AM
8:20:00 AM
8:25:00 AM
8:30:00 AM
8:35:00 AM
8:40:00 AM
8:45:00 AM
8:50:00 AM
8:55:00 AM
-1.39
-1.38
-1.39
-1.41
-1.44
-1.46
-1.50
-1.53
-1.59
-1.65
-1.72
-1.78
-1.85
-1.91
-1.97
-2.01
-2.05
-2.08
-2.10
-2.11
-2.12
-2.13
-2.13
-2.12
-2.09
-2.07
-2.04
-2.03
-2.00
-1.97
-1.95
-1.94
-1.91
-1.85
-1.80
-1.76
-1.73
-1.68
-1.61
-1.54
-1.47
-1.41
-1.34
-1.27
-1.20
-1.12
-1.03
-0.93
131
Results from daytime simulation for 3000 element bridge mesh with default view factor
settings.
Tim e
9:01:00 AM
9:06:00 AM
9:11:00 AM
9:16:00 AM
9:21:00 AM
9:26:00 AM
9:31:00 AM,
9:36:00 AM
9:41:00 AM
9:46:00 AM
9:51:00 AM
9:56:00 AM
10:01:00 AM
10:06:00 AM
10:11:00 AM
10:16:00 AM
10:21:00 AM
10:26:00 AM
10:31:00 AM
10:36:00 AM
10:41:00 AM
10:46:00 AM
10:51:00 AM
10:56:00 AM
11:01:00 AM
11:06:00 AM
11:11:00 AM
11:16:00 AM
11:21:00 AM
11:26:00 AM
11:31:00 AM
11:36:00 AM
11:41:00 AM
11:46:00 AM
11:51:00 AM
11:56:00 AM
12:01:00 PM
12:06:00 PM
12:11:00 PM
12:16:00 PM
12:21:00 PM
12:26:00 PM
12:31:00 PM
12:36:00 PM
12:41:00 PM
12:46:00 PM
12:51:00 PM
12:56:00 PM
Temp
-0.82
-0.71
-0.57
-0.44
-0.32
-0.21
-0.12
-0.02
0.17
0.52
0.90
1.25
1.59
2.13
2.84
3.47
4.04
4.57
5.06
5.68
6.41
7.07
7.69
8.26
8.78
9.30
9.81
10.30
10.78
11.24
11.69
12.16
12.60
13.01
13.42
13.86
14.32
14.72
15.08
15.43
15.77
16.08
16.37
16.63
16.91
17.13
17.37
17.56
1:01:00 PM
1:06:00 PM
1:11:00 PM
1:16:00 PM
1:21:00 PM
1:26:00 PM
1:31:00 PM
1:36:00 PM
1:41:00 PM
1:46:00 PM
1:51:00 PM
1:56:00 PM
2:01:00 PM
2:06:00 PM
2:11:00 PM
2:16:00 PM
2:21:00 PM
2:26:00 PM
2:31:00 PM
2:36:00 PM
2:41:00 PM
2:46:00 PM
2:51:00 PM
2:56:00 PM
3:01:00 PM
3:06:00 PM
3:11:00 PM
3:16:00 PM
3:21:00 PM
3:26:00 PM
3:31:00 PM
3:36:00 PM
3:41:00 PM
3:46:00 PM
3:51:00 PM
3:56:00 PM
4:01:00 PM
4:06:00 PM
4:11:00 PM
4:16:00 PM
4:21:00 PM
4:26:00 PM
4:31:00 PM
4:36:00 PM
4:41:00 PM
4:46:00 PM
4:51:00 PM
4:56:00 PM
17.75
18.09
18.34
18.57
18.78
18.96
19.27
19.56
19.80
19.98
20.08
20.21
20.33
20.61
20.79
21.17
21.32
21.55
21.69
21.87
21.95
21.98
22.13
22.33
22.45
22.54
22.63
22.76
22.83
22.48
22.24
22.08
22.01
21.83
21.87
21.75
21.39
20.84
20.38
19.97
19.72
19.46
19.23
18.91
18.44
18.12
17.86
17.65
5:01:00 PM
5:06:00 PM
5:11:00 PM
5:16:00 PM
5:21:00 PM
5:26:00 PM
5:31:00 PM
5:36:00 PM
5:41:00 PM '
5:46:00 PM
5:51:00 PM
5:56:00 PM
6:01:00 PM
6:06:00 PM
6:11:00 PM
6:16:00 PM
6:21:00P M
6:26:00 PM
6:31:00 PM
6:36:00 PM
6:41:00 PM
6:46:00 PM
6:51:00 PM
6:56:00 PM
7:01:00 PM
7:06:00 PM
7:11:00 PM
7:16:00 PM
7:21:00 PM
7:26:00 PM
7:31:00 PM
7:36:00 PM
7:41:00 PM
7:46:00 PM
7:51:00 PM
7:56:00 PM
8:01:00 PM
8:06:00 PM
8;11:00 PM
8:16:00 PM
8:21:00 PM
8:26:00 PM
8:31:00 PM
8:36:00 PM
8:41:00 PM
8:46:00 PM
17.48
17.31
17.18
17.07
16.99
16.94
16.85
16.75
16.66
16.59
16.54
16.47
16.48
16.45
16.38
16.31
16.25
16.17
16.10
16.02
15.99
15.92
15.88
15.81
15.75
15.65
15.56
15.47
15.38
15.27
15.17
15.06
14.93
14.79
14.65
14.50
14.34
14.18
14.04
13.92
13.78
13.64
13.48
13.32
13.18
13.05
132
Results from nighttime simulation for 300 element bridge mesh with default view factor
settings.
Time
9:00:00 PM
9:05:00 PM
9:10:00 PM
9:15:00 PM
9:20:00 PM
9:25:00 PM
9:30:00 PM
9:35:00 PM
9:40:00 PM
9:45:00 PM
9:50:00 PM
9:55:00 PM
10:00:00 PM
10:05:00 PM
10:10:00 PM
10:15:00 PM
10:20:00 PM
10:25:00 PM
10:30:00 PM
10:35:00 PM
10:40:00 PM
10:45:00 PM
10:50:00 PM
10:55:00 PM
11:00:00 PM
11:05:00 PM
11:10:00 PM
11:15:00 PM
11:20:00 PM
11:25:00 PM
11:30:00 PM
11:35:00 PM
11:40:00 PM
11:45:00 PM
11:50:00 PM
11:55:00 PM
12:00:00 AM
12:05:00 AM
12:10:00 AM
12:15:00 AM
12:20:00 AM
12:25:00 AM
12:30:00 AM
12:35:00 AM
12:40:00 AM
12:45:00 AM
12:50:00 AM
12:55:00 AM
Temp
3.00
2.81
2.66
2.51
2.38
2.27
2.19
2.08
1.99
1.88
1.78
1.72
1.66
1.60
1.51
1.41
1.31
1.24
1.20
1.12
1.06
1.02
0.97
0.91
0.85
0.77
0.69
0.63
0.57
0.51
0.47
0.45
0.44
0.47
0.51
0.56
0.68
0.82 .
0.87
0.87
0.87
0.85
0.82
0.79
0.74
0.69
0.65
0.61
1:00:00 AM
1:05:00 AM
1:10:00 AM
1:15:00 AM
1:20:00 AM
1:25:00 AM
1:30:00 AM
1:35:00 AM
1:40:00 AM
1:45:00 AM
1:50:00 AM
1:55:00 AM
2:00:00 AM
2:05:00 AM
2:10:00 AM
2:15:00 AM
2:20:00 AM
2:25:00 AM
2:30:00 AM
2:35:00 AM
2:40:00 AM
2:45:00 AM
2:50:00 AM
2:55:00 AM
3:00:00 AM
3:05:00 AM
3:10:00 AM
3:15:00 AM
3:20:00 AM
3:25:00 AM
3:30:00 AM
3:35:00 AM
3:40:00 AM
3:45:00 AM
3:50:00 AM
3:55:00 AM
4:00:00 AM
4:05:00 AM
4:10:00 AM
4:15:00 AM
4:20:00 AM
4:25:00 AM
4:30:00 AM
4:35:00 AM
4:40:00 AM
4:45:00 AM
4:50:00 AM
4:55:00 AM
0.53
0.47
0.45
0.40
0.34
0.27
0.18
0.11
0.07
0.02
-0.02
-0.03
-0.04
-0.08
-0.13
-0.19
-0.24
-0.29
-0.34
-0.40
-0.42
-0.43
-0.41
-0.36
-0.29
-0.23
-0.23
-0.36
-0.51
-0.65
-0.76
-0.83
-0.91
-0.99
-1.05
-1.09
-1.12
-1.13
-1.14
-1.17
-1,22
-1.28
-1.35
-1.39
-1.42
-1.46
-1.50
-1.54
5:00:00 AM
5:05:00 AM
5:10:00 AM
5:15:00 AM
5:20:00 AM
5:25:00 AM
5:30:00 AM
5:35:00 AM
5:40:00 AM
5:45:00 AM
5:50:00 AM
5:55:00 AM
6:00:00 AM
6:05:00 AM
6:10:00 AM
6:15:00 AM
6:20:00 AM
6:25:00 AM
6:30:00 AM
6:35:00 AM
6:40:00 AM
6:45:00 AM
6:50:00 AM
6:55:00 AM
7:00:00 AM
7:05:00 AM
7:10:00 AM
7:15:00 AM
7:20:00 AM
7:25:00 AM
7:30:00 AM
7:35:00 AM
7:40:00 AM
7:45:00 AM
7:50:00 AM
7:55:00 AM
8:00:00 AM
8:05:00 AM
8:10:00 AM
8:15:00 AM'
8:20:00 AM
8:25:00 AM
8:30:00 AM
8:35:00 AM
8:40:00 AM
8:45:00 AM
8:50:00 AM
8:55:00 AM
-1.54
-1.53
-1.55
-1.57
-1.59
-1.62
-1.66
-1.69
-1.75
-1.82
-1.88
-1.95
-2.02
-2.08
-2.14
-2.19
-2.23
-2.26
-2.28
-2.29
-2.30
-2.31
-2.31
-2.30
-2.27
-2.25
-2.22
-2.20
-2.18
-2.15
-2.14
-2.13
-2.10
-2.05
-1.99
-1.96
-1.93
-1.89
-1.84
-1.79
-1.73
-1.68
-1.63
-1.57
-1.51
-1.45
-1.38
-1.29
133
Results from daytime simulation for 10 element mesh with default view factor settings
Time
9:01:47 AM
9:06:47 AM
9:11:47 AM
9:16:47 AM
9:21:47 AM
9:26:47 AM
9:31:47 AM
9:36:47 AM
9:41:47 AM
9:46:47 AM
9:51:47 AM
9:56:47 AM
10:01:47 AM
10:06:47 AM
10:11:47 AM
10:16:47 AM
10:21:47 AM
10:26:47 AM
10:31:47 AM
10:36:47 AM
10:41:47 AM
10:46:47 AM
10:51:47 AM
10:56:47 AM
11:01:47 AM
11:06:47 AM
11:11:47 AM
11:16:47 AM
11:21:47 AM
11:26:47 AM
11:31:47 AM
11:36:47 AM
11:41:47 AM
11:46:47 AM
11:51:47 AM
11:56:47 AM
Temp
0.83
1.52
2.17
2.76
3.32
3.86
4.37
4.88
5.37
5.86
6.32
6.73
7.10
7.46
7.83
8.21
8.57
8.95
9.35
9.72
10.09
10.50
10.92
11.27
11.62
12.00
12.37
12.74
13.13
13.48
13.84
14.24
14.58
14.88
15.21
15.59
12:01:47 PM
12:06:47 PM
12:11:47 PM
12:16:47 PM
12:21:47 PM
12:26:47 PM
12:31:47 PM
12:36:47 PM
12:41:47 PM
12:46:47 PM
12:51:47 PM
12:56:47 PM
1:01:47 PM
1:06:47 PM
1:11:47 PM
1:16:47 PM
1:21:47 PM
1:26:47 PM
1:31:47 PM
1:36:47 PM
1:41:47 PM
1:46:47 PM
1:51:47 PM
1:56:47 PM
2:01:47 PM
2:06:47 PM
2:11:47 PM
2:16:47 PM
2:21:47 PM
2:26:47 PM
2:31:47 PM
2:36:47 PM
2:41:47 PM
2:46:47 PM
2:51:47 PM
2:56:47 PM
15.99
16.32
16.58
16.86
17.11
17.35
17.56
17.73
17.92
18.05
18.22
18.32
18.43
18.71
18.88
19.05
19.18
19.28
19.53
19.75
19.91
20.01
20.03
20.07
20.11
20.30
20.40
20.69
20.75
20.89
20.94
21.03
21.03
20.98
21.04
21.13
3:01:47 PM
3:06:47 PM
3:11:47 PM
3:16:47 PM
3:21:47 PM
3:26:47 PM
3:31:47 PM
3:36:47 PM
3:41:47 PM
3:46:47 PM
3:51:47 PM
3:56:47 PM
4:01:47 PM
4:06:47 PM
4:11:47 PM
4:16:47 PM
4:21:47 PM
4:26:47 PM
4:31:47 PM
4:36:47 PM
4:41:47 PM
4:46:47 PM
4:51:47 PM
4:56:47 PM
5:01:47 PM
5:06:47 PM
5:11:47 PM
5:16:47 PM
5:21:47 PM
5:26:47 PM
5:31:47 PM
5:36:47 PM
5:41:47 PM
5:46:47 PM
5:51:47 PM
5:56:47 PM
21.16
21.17
21.16
21.20
21.32
21.22
21.15
21.11
21.10
20.98
21.03
20.92
20.86
20.84
20.80
20.69
20.70
20.60
20.50
20.41
20.20
20.12
20.01
19.91
19.77
19.66
19.55
19.45
19.33
19.16
18.95
18.75
18.57
18.41
18.25
18.07
6:01:47
6:06:47
6:11:47
6:16:47
6:21:47
6:26:47
■6:31:47
6:36:47
6:41:47
6:46:47
6:51:47
6:56:47
7:01:47
7:06:47
7:11:47
7:16:47
7:21:47
7:26:47
7:31:47
7:36:47
7:41:47
7:46:47
7:51:47
7:56:47
8:01:47
8:06:47
8:11:47
8:16:47
8:21:47
8:26:47
8:31:47
8:36:47
8:41:47
8:46:47
PM
PM
PM
PM
PM
PM
PM
PM
PM '
PM
PM
PM
PM
PM
PM
PM
PM
PM
PM
PM
PM
PM
PM
PM
PM
PM
PM
PM
PM
PM
PM
PM
PM
PM
17.91
17.70
17.48
17.28
17.08
16.88
16.69
16.49
16.34
16.15
16.00
15.84
15.69
15.53
15.38
15.25
15.12
14.99
14.87
14.75
14.62
14.47
14.34
14.18
14.03
13.86
13.72
13.59
13.45
13.29
13.13
12.97
12.81
12.66
134
Results from nighttime simulation for 10 elements mesh with default view factor settings
Tim e
9:00:00 PM
9:05:00 PM
9:10:00 PM
9:15:00 PM
9:20:00 PM
9:25:00 PM
9:30:00 PM
9:35:00 PM
9:40:00 PM
9:45:00 PM
9:50:00 PM
9:55:00 PM
10:00:00 PM
10:05:00 PM
10:10:00 PM
10:15:00 PM
10:20:00 PM
10:25:00 PM
10:30:00 PM
10:35:00 PM
10:40:00 PM
10:45:00 PM
10:50:00 PM
10:55:00 PM
11:00:00 PM
11:05:00 PM
11:10:00 PM
11:15:00 PM
11:20:00 PM
11:25:00 PM
11:30:00 PM
11:35:00 PM
11:40:00 PM
11:45:00 PM
11:50:00 PM
11:55:00 PM
12:00:00 AM
12:05:00 AM
12:10:00 AM
12:15:00 AM
12:20:00 AM
12:25:00 AM
12:30:00 AM
12:35:00 AM
12:40:00 AM
12:45:00 AM
12:50:00 AM
12:55:00 AM
'
Tem p
3.00
2.74
2.51
2.31
2.14
1.99
1.87
1.73
1.61
1.47
1.35
1.27
1.19
1.11
1.01
0.88
0.76
0.69
0.63
0.54
0.47
0.43
0.37
0.30
0.22
0.13
0.05
-0.02
-0.09
-0.16
-0.20
-0.23
-0.23
-0.20
-0.14
-0.10
0.03
0.18
0.23
0.23
0.23
0.20
0.17
0.13
0.07
0.02
-0.02
-0.07
1:00:00 AM
1:05:00 AM
1:10:00 AM
1:15:00 AM
1:20:00 AM
1:25:00 AM
1:30:00 AM
1:35:00 AM
1:40:00 AM
1:45:00 AM
1:50:00 AM
1:55:00 AM
2:00:00 AM
2:05:00 AM
2:10:00 AM
2:15:00 AM
2:20:00 AM
2:25:00 AM
2:30:00 AM
2:35:00 AM
2:40:00 AM
2:45:00 AM
2:50:00 AM
2:55:00 AM
3:00:00 AM
3:05:00 AM
3:10:00 AM
3:15:00 AM
3:20:00 AM
3:25:00 AM
3:30:00 AM
3:35:00 AM
3:40:00 AM
3:45:00 AM
3:50:00 AM
3:55:00 AM
4:00:00 AM
4:05:00 AM
4:10:00 AM
4:15:00 AM
4:20:00 AM
4:25:00 AM
4:30:00 AM
4:35:00 AM
4:40:00 AM
4:45:00 AM
4:50:00 AM
4:55:00 AM
-0.16
-0.24
-0.26
-0.31
-0.39
-0.47
-0.56
-0.65
-0.68
-0.74
-0.79
-0.79
-0.81
-0.84
-0.90
-0.97
-1.02
-1.08
-1.13
-1.20
-1.21
-1.21
-1.19
-1.13
-1.05
-0.98
-0.97
-1.09
-1.25
-1.39
-1.49
-1,56
-1.64
-1.72
-1.79
-1.83
-1.85
-1.86
-1.87
-1.89
-1.94
-2.01
-2.07
-2.11
-2.13
-2.17
-2.20
-2.23
5:00:00 AM
5:05:00 AM
5:10:00 AM
5:15:00 AM
5:20:00 AM
5:25:00 AM
5:30:00 AM
5:35:00 AM
5:40:00 AM
5:45:00 AM
5:50:00 AM
5:55:00 AM
6:00:00 AM
6:05:00 AM
6:10:00 AM
6:15:00 AM
6:20:00 AM
6:25:00 AM
6:30:00 AM
6:35:00 AM
6:40:00 AM
6:45:00 AM
6:50:00 AM
6:55:00 AM
7:00:00 AM
7:05:00 AM
7:10:00 AM
7:15:00 AM
7:20:00 AM
7:25:00 AM
7:30:00 AM
7:35:00 AM
7:40:00 AM
7:45:00 AM
7:50:00 AM
7:55:00 AM
8:00:00 AM
8:05:00 AM
8:10:00 AM
8:15:00 AM
8:20:00 AM
8:25:00 AM
8:30:00 AM
8:35:00 AM
8:40:00 AM
8:45:00 AM
8:50:00 AM
8:55:00 AM
-2.23
-2.22
-2.23
-2.25
-2.28
-2.31
-2.35
-2.40
-2.46
-2.54
-2.60
-2.68
-2.76
-2.83
-2.89
-2.94
-2.98
-3.00
-3.02
-3.04
-3.04
-3.05
-3.05
-3.03
-3.00
-2.95
-2.90
-2.85
-2.79
-2.71
-2.64
-2.57
-2.47
-2.33
-2.20
-2.06
-1.93
-1.79
-1,64
-1.46
-1.28
-1.09
-0.89
-0.67
-0.44
-0.20
0.05
0.32
135
Results from 3000 elements mesh bridge daytime simulation with low view factor
settings
Time
9:01:47 AM
9:06:47 AM
9:11:47 AM
9:16:47 AM
9:21:47 AM
9:26:47 AM
9:31:47 AM
9:36:47 AM
9:41:47 AM
9:46:47 AM
9:51:47 AM
9:56:47 AM
10:01:47 AM
10:06:47 AM
10:11:47 AM
10:16:47 AM
10:21:47 AM
10:26:47 AM
10:31:47 AM
10:36:47 AM
10:41:47 AM
10:46:47 AM
10:51:47 AM
10:56:47 AM
11:01:47 AM
11:06:47 AM
11:11:47 AM
11:16:47 AM
11:21:47 AM
11:26:47 AM
11:31:47 AM
11:36:47 AM
11:41:47 AM
11:46:47 AM
11:51:47 AM
11:56:47 AM
12:01:47 PM
12:06:47 PM
12:11:47 PM
12:16:47 PM
12:21:47 PM
12:26:47 PM
12:31:47 PM
12:36:47 PM
12:41:47 PM
12:46:47 PM
12:51:47 PM
12:56:47 PM
Temp
-0.94
1:01:47 PM
-0.83
1:06:47 PM
-0.69
1:11:47 PM
-0.56
1:16:47 PM
-0.44
1:21:47 PM
-0.32
1:26:47 PM
-0.23
1:31:47 PM
-0.12 ■ 1:36:47 PM
-0.05
1:41:47 PM
0.10
1:46:47 PM
1:51:47 PM
0.31
0.51
1:56:47 PM
0.72
2:01:47 PM
2:06:47 PM
1.40
2:11:47 PM
2.47
2:16:47 PM
3.40
2:21:47 PM
4.23
2:26:47 PM
4.98
2:31:47 PM
5.66
2:36:47 PM
6.29
2:41:47 PM
6.89
7.45
2:46:47 PM
2:51:47 PM
7.99
2:56:47 PM
8.50
3:01:47 PM
8.97
9.45
3:06:47 PM
3:11:47 PM
9.92
3:16:47 PM
10.38
10.84
3:21:47 PM
3:26:47 PM
11.28
3:31:47 PM
11.71
3:36:47 PM
12.17
3:41:47 PM
12.59
3:46:47 PM
12.99
3:51:47 PM
13.39
13.82
3:56:47 PM
4:01:47 PM
14.27
4:06:47 PM
14.67
15.03
4:11:47 PM
4:16:47 PM
15.38
4:21:47 PM
15.71
4:26:47 PM
16.03
4:31:47 PM
16.32
4:36:47 PM
16.58
4:41:47 PM
16.86
4:46:47 PM
17.08
4:51:47 PM
17.33
4:56:47 PM
17.52
17.71
18.05
18.29
18.53
18.74
18.92
19.24
19.53
19.77
19.96
20.07
20.20
20.33
20.61
20.79
21.18
21.33
21.56
21.70
21.89
21.97
22.00
22.16
22.36
22.49
22.59
22.68
22.81
23.07
23.04
23.05
23.11
23.21
23.15
23.33
23.28
22.69
21.66
20.81
20.08
19.58
19.11
18.72
18.40
18.08
17.85
17.67
17.53
5:01:47 PM
5:06:47 PM
5:11:47 PM
5:16:47 PM
5:21:47 PM
5:26:47 PM
5:31:47 PM
5:36:47 PM
5:41:47 PM
5:46:47 PM
5:51:47 PM
5:56:47 PM
6:01:47 PM
6:06:47 PM
6:11:47 PM
6:16:47 PM
6:21:47 PM
6:26:47 PM
6:31:47 PM
6:36:47 PM
6:41:47 PM
6:46:47 PM
6:51:47 PM
6:56:47 PM
7:01:47 PM
7:06:47 PM
7:11:47 PM
7:16:47 PM
7:21:47 PM
7:26:47 PM
7:31:47 PM
7:36:47 PM
7:41:47 PM
7:46:47 PM
7:51:47 PM
7:56:47 PM
8:01:47 PM
8:06:47 PM
8:11:47 PM
8:16:47 PM
8:21:47 PM
8:26:47 PM
8:31:47 PM
8:36:47 PM
8:41:47 PM
8:46:47 PM
17.40
17.28
17.18
17.10
17.04
17.00
16.93
16.84
16.76
16.70
16.66
16.60
16.61
16.58
16.51
16.46
16.40
16.33
16.27
16.21
16.18
16.11
16.06
15.98
15.90
15.80
15.70
15.60
15.50
15.39
15.28
15.17
15.05
14.91
14.78
14.62
14.47
14.31
14.17
14.05
13.91
13.77
13.61
13.45
13.31
13.18
136
Results for nighttime simulation of 3000 elements bridge mesh with low view factor
settings
Time
9:00:01 PM
9:05:01 PM
9:10:01 PM
9:15:01 PM
9:20:01 PM
9:25:01 PM
9:30:01 PM
9:35:01 PM
9:40:01 PM
9:45:01 PM
9:50:01 PM
9:55:01 PM
10:00:01 PM
10:05:01 PM
10:10:01 PM
10:15:01 PM
10:20:01 PM
10:25:01 PM
10:30:01 PM
10:35:01 PM
10:40:01 PM
10:45:01 PM
10:50:01 PM
10:55:01 PM
11:00:01 PM
11:05:01 PM
11:10:01 PM
11:15:01 PM
11:20:01 PM
11:25:01 PM
11:30:01 PM
11:35:01 PM
11:40:01 PM
11:45:01 PM
11:50:01 PM
11:55:01 PM
12:00:01 AM
Temp
3.00
2.82
2.66
2.52
2.39
2.28
2.19
2.08
1.98
1.87
1.77
1.70
1.64
1.57
1.49
1.38
1.28
1,21
1.16
1.08
1.02
0.98
0.93
0.87
0.80
0.72
0.64
0.58
0.52
0.46
0.42
0.40
0.39
0.42
0.47
0.51
0.63
12:05:01 AM
12:10:01 AM
12:15:01 AM
12:20:01 AM
12:25:01 AM
12:30:01 AM
12:35:01 AM
12:40:01 AM
12:45:01 AM
12:50:01 AM
12:55:01 AM
1:00:01 AM
1:05:01 AM
1:10:01 AM
1:15:01 AM
1:20:01 AM
1:25:01 AM
1:30:01 AM
1:35:01 AM
1:40:01 AM
1:45:01 AM
1:50:01 AM
1:55:01 AM
2:00:01 AM
2:05:01 AM
2:10:01 AM
2:15:01 AM
2:20:01 AM
2:25:01 AM
2:30:01 AM
2:35:01 AM
2:40:01 AM
2:45:01 AM
2:50:01 AM
2:55:01 AM
3:00:01 AM
3:05:01 AM
0.77
0.82
0.82
0.82
0.80
0.78
0.74
0.69
0.65
0.61
0.57
0.49
0.43
0.41
0.36
0.30
0.23
0.15
0.07
0.04
-0.02
-0.05
-0.06
-0.07
-0.11
-0.16
-0.22
-0.27
-0.32
-0.37
-0.43
-0.44
-0.45
-0.43
-0.38
-0.31
-0.25
3:10:01
3:15:01
3:20:01
3:25:01
3:30:01
3:35:01
3:40:01
3:45:01
3:50:01
3:55:01
4:00:01
4:05:01
4:10:01
4:15:01
4:20:01
4:25:01
4:30:01
4:35:01
4:40:01
4:45:01
4:50:01
4:55:01
5:00:01
5:05:01
5:10:01
5:15:01
5:20:01
5:25:01
5:30:01
5:35:01
5:40:01
5:45:01
5:50:01
5:55:01
6:00:01
6:05:01
6:10:01
AM
AM
AM
AM
AM
AM
AM
AM
AM
AM
AM
AM
AM
AM
AM
AM
AM
AM
AM
AM
AM
AM
AM
AM
AM
AM
AM
AM
AM
AM
AM
AM
AM
AM
AM
AM
AM
-0.24
-0.37
-0.53
-0.66
-0.77
-0.84
-0.92
-1.00
-1.06
-1.10
-1.12
-1.13
-1.15
-1.17
-1.22
-1.28
-1.35
-1.39
-1.42
-1.46
-1.50
-1,53
-1.54
-1.53
-1.54
-1.56
-1.59
-1.62
-1.65
-1.69
-1.74
-1.81
-1.88
-1.94
-2.01
-2.07
-2.13
6:15:01 AM
6:20:01 AM
6:25:01 AM
6:30:01'AM
6:35:01 AM
6:40:01 AM
6:45:01 AM
6:50:01 AM
6:55:01 AM
7:00:01 AM
7:05:01 AM
7:10:01 AM
7:15:01 AM
7:20:01 AM
7:25:01 AM
7:30:01 AM
7:35:01 AM
7:40:01 AM
7:45:01 AM
7:50:01 AM
7:55:01 AM
8:00:01 AM
8:05:01 AM
8:10:01 AM
8:15:01 AM
8:20:01 AM
8:25:01 AM
8:30:01 AM
8:35:01 AM
8:40:01 AM
8:45:01 AM
8:50:01 AM
8:55:01 AM
-2.18
-2.21
-2.24
-2.26
-2.28
-2.29
-2.29
-2.29
-2.28
-2.26
-2.23
-2.20
-2.18
-2.16
-2.14
-2.13
-2.13
-2.10
-2.05
-2.00
-1.97
-1.95
-1.89
-1.80
-1.71
-1.62
-1.54
-1.47
-1.38
-1.30
-1.22
-1.14
-1.05
137
Results from daytime simulation with 300 element mesh bridge with low view factor
settings
Time
9:01:47 AM
9:06:47 AM
9:11:47 AM
9:16:47 AM
9:21:47 AM
9:26:47 AM
9:31:47 AM
9:36:47 AM
9:41:47 AM
9:46:47 AM
9:51:47 AM
9:56:47 AM
10:01:47 AM
10:06:47 AM
10:11:47 AM
10:16:47 AM
10:21:47 AM
10:26:47 AM
10:31:47 AM
10:36:47 AM
10:41:47 AM
10:46:47 AM
10:51:47 AM
10:56:47 AM
11:01:47 AM
11:06:47 AM
11:11:47 AM
11:16:47 AM
11:21:47 AM
11:26:47 AM
11:31:47 AM
11:36:47 AM
11:41:47 AM
11:46:47 AM
11:51:47 AM
11:56:47 AM
Temp
-1.16
-1.07
-0.95
-0.84
-0.73
-0.63
-0.56
-0.47
-0.41
-0.28
-0.07
0.12
0.34
0.49
.0.61
0.72
0.83
0.95
1.05 .
1.18
1.31
1.38
1.43
2.22
3.53
4.64
5.65
6.55
7.36
8.10
8.78
9.42
10.05
10.64
11.18
11.72
12:01:47 PM
12:06:47 PM
12:11:47 PM
12:16:47 PM
12:21:47 PM
12:26:47 PM
12:31:47 PM
12:36:47 PM
12:41:47 PM
12:46:47 PM
12:51:47 PM
12:56:47 PM
1:01:47 PM
1:06:47 PM
1:11:47 PM
1:16:47 PM
1:21:47 PM
1:26:47 PM
1:31:47 PM
1:36:47 PM
1:41:47 PM
1:46:47 PM
1:51:47 PM
1:56:47 PM
2:01:47 PM
2:06:47 PM
2:11:47 PM
2:16:47 PM
2:21:47 PM
2:26:47 PM
2:31:47 PM
2:36:47 PM
2:41:47 PM
2:46:47 PM
2:51:47 PM
2:56:47 PM
12.25
12.74
13.20
13.64
14.05
14.44
14.80
15.14
15.48
15.77
16.07
16.32
16.58
16.93
17.22
17.49
17.74
17.95
18.29
18.60
18.88
19.09
19.24
19.40
19.57
19.86
20.07
20.46
20.64
20.89
21.06
21.26
21.38
21.44
21.62
21.83
3:01:47 PM
3:06:47 PM
3:11:47 PM
3:16:47 PM
3:21:47 PM
3:26:47 PM
3:31:47 PM
3:36:47 PM
3:41:47 PM
3:46:47 PM
3:51:47 PM
3:56:47 PM
4:01:47 PM
4:06:47 PM
4:11:47 PM
4:16:47 PM
4:21:47 PM
4:26:47 PM
4:31:47 PM
4:36:47 PM
4:41:47 PM
4:46:47 PM
4:51:47 PM
4:56:47 PM
5:01:47 PM
5:06:47 PM
5:11:47 PM
5:16:47 PM
5:21:47 PM
5:26:47 PM
5:31:47 PM
5:36:47 PM
5:41:47 PM
5:46:47 PM
5:51:47 PM
5:56:47 PM
21.98
22.10
22.21
22.36
22.63
22.63
22.66
22.73
22.85
22.81
23.00
22.98
23.03
23.16
23.23
23.21
23.38
23.38
23.39
23.44
23.26
23.33
22.83
21.94
21.16
20.61
20.17
19.81
19.50
19.20
18.91
18.66
18.46
18.32
18.18
18.06
6:01:47
6:06:47
6:11:47
6:16:47
6:21:47
6:26:47
6:31:47
6:36:47
6:41:47
6:46:47
6:51:47
6:56:47
7:01:47
7:06:47
7:11:47
7:16:47
7:21:47
7:26:47
7:31:47
7:36:47
7:41:47
7:46:47
7:51:47
7:56:47
8:01:47
8:06:47
8:11:47
8:16:47
8:21:47
8:26:47
8:31:47
8:36:47
8:41:47
8:46:47
PM
PM
PM
PM
PM
PM
PM
PM
PM
PM
PM
PM
PM
PM
PM
PM
PM
PM
PM
PM
PM
PM
PM
PM
PM
PM
PM
PM
PM
PM
PM
PM
PM
PM
17.96
17.82
17.69
17.57
17.47
17.37
17.28
17.19
17.13
17.06
16.96
16.83
16.70
16.56
16.43
16.30
16.18
16.05
15.92
15.79
15.66
15.52
15.38
15.22
15.05
14.88
14.73
14.60
14.46
14.30
14.13
13.96
13.81
13.67
138
Results nighttime simulation for 300 elements bridge mesh with low view factor settings
Time
9:00:01 PM
9:05:01 PM
9:10:01 PM
9:15:01 PM
9:20:01 PM
9:25:01 PM
9:30:01 PM
9:35:01 PM
9:40:01 PM
9:45:01 PM
9:50:01 PM
9:55:01 PM
10:00:01 PM
10:05:01 PM
10:10:01 PM
10:15:01 PM
10:20:01 PM
10:25:01 PM
10:30:01 PM
10:35:01 PM
10:40:01 PM
10:45:01 PM
10:50:01 PM
10:55:01 PM
11:00:01 PM
11:05:01 PM
11:10:01 PM
11:15:01 PM
11:20:01 PM
11:25:01 PM
11:30:01 PM
11:35:01 PM
11:40:01 PM
11:45:01 PM
11:50:01 PM
11:55:01 PM
12:00:01 AM
12:05:01 AM
12:10:01 AM
12:15:01 AM
12:20:01 AM
12:25:01 AM
12:30:01 AM
12:35:01 AM
12:40:01 AM
12:45:01 AM
12:50:01 AM
12:55:01 AM
Temp
3.00
2.81
2.66
2.51
2.38
2.27
2.19
2.09
1.99
1.88
1.78
1.72
1.66
1.60
1.51
1.41
1.31
1.25
1.20
1.12
1.06
1.02
0.97
0.92
0.85
0.77
0.69
0.63
0.57
0.51
■ 0.47
0.45
0.45
0.47
0:52
0.56
0.68
0.82
0.87
0.87
0.87
0.85
0.82
0.79
0.74
0.69
0.66
0.61
1:00:01
1:05:01
1:10:01
1:15:01
1:20:01
1:25:01
1:30:01
1:35:01
1:40:01
1:45:01
1:50:01
1:55:01
2:00:01
2:05:01
2:10:01
2:15:01
2:20:01
2:25:01
2:30:01
2:35:01
2:40:01
2:45:01
2:50:01
2:55:01
3:00:01
3:05:01
3:10:01
3:15:01
3:20:01
3:25:01
3:30:01
3:35:01
3:40:01
3:45:01
3:50:01
3:55:01
4:00:01
4:05:01
4:10:01
4:15:01
4:20:01
4:25:01
4:30:01
4:35:01
4:40:01
4:45:01
4:50:01
4:55:01
AM
AM
AM
AM
AM
AM
AM
AM
AM
AM
AM
AM
AM
AM
AM
AM
AM
AM
AM
AM
AM
AM
AM
AM
AM
AM
AM
AM
AM
AM
AM
AM
AM
AM
AM
AM
AM
AM
AM
AM
AM
AM
AM
AM
AM
AM
AM
AM
0.53
0.47
0.45
0.40
0.34
0.27
0.18
0.11
0.07
0.02
-0.02
-0.03
-0.04
-0.08
-0.13
-0.19
-0.24
-0.29
-0.34
-0.40
-0.42
-0.43
-0.41
-0.36
-0.29
-0.23
-0.23
-0.36
-0.52
-0.65
-0.76
-0.83
-0.91
-0.99
-1.05
-1.09
-1.12
-1.13
-1.14
-1.17
-1.22
-1.28
-1.35
-1.39
-1.42
-1.46
-1.50
-1.54
5:00:01
5:05:01
5:10:01
5:15:01
5:20:01
5:25:01
5:30:01
5:35:01
5:40:01
5:45:01
5:50:01
5:55:01
6:00:01
6:05:01
6:10:01
6:15:01
6:20:01
6:25:01
6:30:01
6:35:01
6:40:01
6:45:01
6:50:01
6:55:01
7:00:01
7:05:01
7:10:01
7:15:01
7:20:01
7:25:01
7:30:01
7:35:01
7:40:01
7:45:01
7:50:01
7:55:01
8:00:01
8:05:01
8:10:01
8:15:01
8:20:01
8:25:01
8:30:01
8:35:01
8:40:01
8:45:01
8:50:01
8:55:01
AM
AM
AM
AM
AM
AM
AM
AM
AM
AM
AM
AM
AM
AM
AM
AM
AM
AM
AM
AM
AM
AM
AM
AM
AM
AM
AM
AM
AM
AM
AM
AM
AM
AM
AM
AM
AM
AM
AM
AM
AM
AM
AM
AM
AM
AM
AM
AM
-1.54
-1.54
-1.55
-1.57
-1.59
-1.62
-1.66
-1,69
-1.75
-1.82
-1.89
-1.95
-2.02
-2.08
-2.14
-2.19
-2.23
-2.26
-2.28
-2.29
-2.30
-2.31
-2.31
-2.30
-2.27
-2.25
-2.22
-2.20
-2.18
-2.16
-2.15
-2.15
-2.12
-2.07
-2.03
-2.00
-1.97
-1.93
-1.86
-1.79
-1.73
-1.66
-1.60
-1.53
-1.47
-1,40
-1.34
-1.25
139
Results from daytime simulation small mesh low view factor settings
Time
9:01:47 AM
9:06:47 AM
9:11:47 AM
9:16:47 AM
9:21:47 AM
9:26:47 AM
9:31:47 AM
9:36:47 AM
9:41:47 AM
9:46:47 AM
9:51:47 AM
9:56:47 AM
10:01:47 AM
10:06:47 AM
10:11:47 AM
10:16:47 AM
10:21:47 AM
10:26:47 AM
10:31:47 AM
10:36:47 AM
10:41:47 AM
10:46:47 AM
10:51:47 AM
10:56:47 AM
11:01:47 AM
11:06:47 AM
11:11:47 AM
11:16:47 AM
11:21:47 AM
11:26:47 AM
11:31:47 AM
11:36:47 AM
11:41:47 AM
11:46:47 AM
11:51:47 AM
11:56:47 AM
12:01:47 PM
12:06:47 PM
12:11:47 PM
12:16:47 PM
12:21:47 PM
12:26:47 PM
12:31:47 PM
12:36:47 PM
12:41:47 PM
12:46:47 PM
12:51:47 PM
12:56:47 PM
Temp
0.83
1.52
2.17
2.76
3.32
3.85
4.37
4.87
5.37
5.86
6.31
6.73
7.10
7.46
7.83
8.20
8.57
8.95
9.34
9.71
10.09
10.50
10.92
11.27
11.62
12.00
12.37
12.74
13.12
13.47
13.83
14.24
14.58
14.88
15.21
15.58
15.99
16.31
16.58
16.86
17.10
17.34
17.55
17.72
17.92
18.05
18.21
18.32
1:01:47 PM
1:06:47 PM
1:11:47 PM
1:16:47 PM
1:21:47 PM
1:26:47 PM
1:31:47 PM
1:36:47 PM
1:41:47 PM
1:46:47 PM
1:51:47 PM
1:56:47 PM
2:01:47 PM
2:06:47 PM
2:11:47 PM
2:16:47 PM
2:21:47 PM
2:26:47 PM
2:31:47 PM
2:36:47 PM
2:41:47 PM
2:46:47 PM
2:51:47 PM
2:56:47 PM
3:01:47 PM
3:06:47 PM
3:11:47 PM
3:16:47 PM
3:21:47 PM
3:26:47 PM
3:31:47 PM
3:36:47 PM
3:41:47 PM
3:46:47 PM
3:51:47 PM
3:56:47 PM
4:01:47 PM
4:06:47 PM
4:11:47 PM
4:16:47 PM
4:21:47 PM
4:26:47 PM
4:31:47 PM
4:36:47 PM
4:41:47 PM
4:46:47 PM
4:51:47 PM
4:56:47 PM
18.43
18.70
18.88
19.04
19.18
19.28
19.53
19.74
19.91
20.01
20.02
20.07
20.11
20.30
20.40
20.68
20.74
20.88
20.93
21.02
21.02
20.97
21.04
21.12
21.15
21.16
21.16
21.19
21.31
21.21
21.14
21.10
21.09
20.97
21.02
20.91
20.85
20.83
20.79
20.68
20.69
20.60
20.49
20.41
20.19
20.11
20.00
19.91
5:01:47 PM
5:06:47 PM
5:11:47 PM
5:16:47 PM
5:21:47 PM
5:26:47 PM
5:31:47 PM
5:36:47 PM
5:41:47 PM
5:46:47 PM
5:51:47 PM
5:56:47 PM
6:01:47 PM
6:06:47 PM
6:11:47 PM
6:16:47 PM
6:21:47 PM
6:26:47 PM
6:31:47 PM
6:36:47 PM
6:41:47 PM
6:46:47 PM
6:51:47 PM
6:56:47 PM
7:01:47 PM
7:06:47 PM
7:11:47 PM
7:16:47 PM
7:21:47 PM
7:26:47 PM
7:31:47 PM
7:36:47 PM
7:41:47 PM
7:46:47 PM
7:51:47 PM
7:56:47 PM
8:01:47 PM
8:06:47 PM
8:11:47 PM
8:16:47 PM
8:21:47 PM
8:26:47 PM
8:31:47 PM
8:36:47 PM
8:41:47 PM
8:46:47 PM
19.76
19.65
19.54
19.44
19.32
19.15
18.95
18.74
18.56
18.40
18.24
18.06
17.90
17.69
17.47
17.27
17.07
16.87
16.68
16.48
16.33
16.14
15.99
15.83
15.68
15.52
15.37
15.24
15.11
14.98
14.86
14.74
14.61
14.47
14.33
14.18
14.02
13.86
13.72
13.59
13.44
13.29
13.13
12.96
12.81
12.66
140
Results from nightime 10 elements bridge mesh with low view factor settings
Time
9:00:01 PM
9:05:01 PM
9:10:01 PM
9:15:01 PM
9:20:01 PM
9:25:01 PM
9:30:01 PM
9:35:01 PM
9:40:01 PM
9:45:01 PM
9:50:01 PM
9:55:01 PM
10:00:01 PM
10:05:01 PM
10:10:01 PM
10:15:01 PM
10:20:01 PM
10:25:01 PM
10:30:01 PM
10:35:01 PM
10:40:01 PM
10:45:01 PM
10:50:01 PM
10:55:01 PM
11:00:01 PM
11:05:01 PM
11:10:01 PM
11:15:01 PM
11:20:01 PM
11:25:01 PM
11:30:01 PM
11:35:01 PM
11:40:01 PM
11:45:01 PM
11:50:01 PM
11:55:01 PM
12:00:01 AM
12:05:01 AM
12:10:01 AM
12:15:01 AM
12:20:01 AM
12:25:01 AM
12:30:01 AM
12:35:01 AM
12:40:01 AM
Temp (deg
3.00
2.74
2.51
2.31
2.14
1.99
1.87
1.73
1.61
1.47
1.35
1.27
1.19
1.11
1.01
0.88
0.76
0.69
0.63
0.54
0.47
0.43
0.37
0.30
0.22
0.13
0.05
-0.02
-0.09
-0.16
-0.20
-0.23
-0.23
-0.20
-0.14
-0.10
0.03
0.18
0.23
0.23
0.23
0.20
0.17
0.13
0.07
C)
12:45:01 AM
12:50:01 AM
12:55:01 AM
1:00:01 AM
1:05:01 AM
1:10:01 AM
1:15:01 AM
1:20:01 AM
1:25:01 AM
1:30:01 AM
1:35:01 AM
1:40:01 AM
1:45:01 AM
1:50:01 AM
1:55:01 AM
2:00:01 AM
2:05:01 AM
2:10:01 AM
2:15:01 AM
2:20:01 AM
2:25:01 AM
2:30:01 AM
2:35:01 AM
2:40:01 AM
2:45:01 AM
2:50:01 AM
2:55:01 AM
3:00:01 AM
3:05:01 AM
3:10:01 AM
3:15:01 AM
3:20:01 AM
3:25:01 AM
3:30:01 AM
3:35:01 AM
3:40:01 AM
3:45:01 AM
3:50:01 AM
3:55:01 AM
4:00:01 AM
4:05:01 AM
4:10:01 AM
4:15:01 AM
4:20:01 AM
4:25:01 AM
0.02
-0.02
-0.07
-0.16
-0.24
-0.26
-0.31
-0.39
-0.47
-0.56
-0.65
-0.68
-0.74
-0.79
-0.79
-0.81
-0.84
-0.90
-0.97
-1.02
-1,08
-1.13
-1.20
-1.21
-1.21
-1.19
-1.13
-1.05
-0.98
-0.97
-1.09
-1.25
-1.39
-1.49
-1.56
-1.64
-1.72
-1.79
-1.83
-1.85
-1.86
-1.87
-1.89
-1.94
-2.01
4:30:01
4:35:01
4:40:01
4:45:01
4:50:01
4:55:01
5:00:01
5:05:01
5:10:01
5:15:01
5:20:01
5:25:01
5:30:01
5:35:01
5:40:01
5:45:01
5:50:01
5:55:01
6:00:01
6:05:01
6:10:01
6:15:01
6:20:01
6:25:01
6:30:01
6:35:01
6:40:01
6:45:01
6:50:01
6:55:01
7:00:01
7:05:01
7:10:01
7:15:01
7:20:01
7:25:01
7:30:01
7:35:01
7:40:01
7:45:01
7:50:01
7:55:01
8:00:01
8:05:01
8:10:01
AM
AM
AM
AM
AM
AM
AM
AM
AM
AM
AM
AM
AM
AM
AM
AM
AM
AM
AM
AM
AM
AM
AM
AM
AM
AM
AM
AM
AM
AM
AM
AM
AM
AM
AM
AM
AM
AM
AM
AM
AM
AM
AM
AM
AM
-2.07
-2.11
-2.13
-2.17
-2.20
-2.23
-2.23
-2.22
-2.23
-2.25
-2.28
-2.31
-2.35
-2.40
-2.47
-2.54
-2.61
-2.68
-2.76
-2.83
-2.89
-2.94
-2.98
-3.00
-3.02
-3.04
-3.04
-3.05
-3.05
-3.03
-3.00
-2.95
-2.90
-2.85
-2.79
-2.71
-2.64
-2.57
-2.47
-2.33
-2.20
-2.06
-1.93
-1.79
-1.64
8:15:01
8:20:01
8:25:01
8:30:01
8:35:01
8:40:01
8:45:01
8:50:01
8:55:01
AM
AM
AM
AM
AM
AM
AM
AM
AM
-1.47
-1.28
-1.09
-0.89
-0.67
-0.45
-0.20
0.05
0.32
141
Results from April 8, 9:01 pm to April 9, 1:36 am simulation
Time
.
Temp
13.34
8:51:47 PM
8:56:47 PM
13.25
9:01:47 PM
13.16
9:06:47 PM
13.05
9:11:47 PM
12.95
9:16:47 PM
12.86
9:21:47 PM
12.75
12.63
9:26:47 PM
9:31:47 PM
12.50
12.31
9:36:47 PM
12.13
9:41:47 PM
9:46:47 PM
11.97
11.82
9:51:47 PM
9:56:47 PM
11.67
10:01:47 PM
11.51
10:06:47 PM
11.38
10:11:47 PM
11.27
10:16:47 PM
11.13
10:21:47 PM
10.99
10.86
10:26:47 PM
10.72
10:31:47 PM
10.61
10:36:47 PM
10.52
10:41:47 PM
10.43
10:46:47 PM
10.34
10:51:47 PM
10.24
10:56:47 PM
10.15
11:01:47 PM
10.03
11:06:47 PM
9.90
11:11:47 PM
11:16:47 PM
9.78
11:21:47 PM
9.68
11:26:47 PM
9.58
9.46
11:31:47 PM
9.36
11:36:47 PM
9.26
11:41:47 PM
11:46:47 PM
9.17
9.08
11:51:47 PM
9.01
11:56:47 PM
8.90
12:01:47 AM
8.80
12:06:47 AM
8.71
12:11:47 AM
8.61
12:16:47 AM
8.50
12:21:47 AM
8.42
12:26:47 AM
8.34
12:31:47 AM
12:36:47 AM
8.25
8.19
12:41:47 AM
8.15
12:46:47 AM
8.12
12:51:47 AM
8.07
12:56:47 AM
8.00
1:01:47 AM
7.93
1:06:47 AM
7.88
1:11:47 AM
7.83
1:16:47 AM
7.76
1:21:47 AM
7.69
.1:26:47 AM
7.61
1:31:47 AM
7.51
1:36:47 AM
142
Results for March 13 simulation
Tim e
6:50:32 AM
6:55:32 AM
7:00:32 AM
7:05:32 AM
7:10:32 AM
7:15:32 AM
7:20:32 AM
7:25:32 AM
7:30:32 AM
7:35:32 AM
7:40:32 AM
7:45:32 AM
7:50:32 AM
7:55:32 AM
8:00:32 AM
8:05:32 AM
8:10:32 AM
8:15:32 AM
8:20:32 AM
8:25:32 AM
8:30:32 AM
8:35:32 AM
8:40:32 AM
8:45:32 AM
8:50:32 AM
8:55:32 AM
9:00:32 AM
9:05:32 AM
9:10:32 AM
9:15:32 AM
9:20:32 AM
9:25:32 AM
9:30:32 AM
9:35:32 AM
9:40:32 AM
9:45:32 AM
9:50:32 AM
9:55:32 AM
10:00:32 AM
10:05:32 AM
10:10:32 AM
10:15:32 AM
10:20:32 AM
10:25:32 AM
10:30:32 AM
10:35:32 AM
10:40:32 AM
Tem p
-1.00
-0.82
-0.69
-0.54
-0.32
-0.07
0.18
0.30
0.48
0.48
0.56
0.62
0.67
0.67
0.71
0.87
1.03
1.20
1.40
1.59
1.78
1.83
1.89
1.93
1.99
2.19
2.40
2.65
2.80
2.94
3.32
3.64
3.88
4.14
4.59
5.19
5.81
6.44
7.01
7.49
8.16
8.90
9.56
10.18
10.72
11.22
11.69
10:45:32 AM
10:50:32 AM
10:55:32 AM
11:00:32 AM
11:05:32 AM
11:10:32 AM
11:15:32 AM
11:20:32 AM
11:25:32 AM
11:30:32 AM
11:35:32 AM
11:40:32 AM
11:45:32 AM
11:50:32 AM
11:55:32 AM
12:00:32 PM
12:05:32 PM
12:10:32 PM
12:15:32 PM
12:20:32 PM
12:25:32 PM
12:30:32 PM.
12:35:32 PM
12:40:32 PM
12:45:32 PM
12:50:32 PM
12:55:32 PM
1:00:32 PM
1:05:32 PM
1:10:32 PM
1:15:32 PM
1:20:32 PM
1:25:32 PM
1:30:32 PM
1:35:32 PM
1:40:32 PM
1:45:32 PM
1:50:32 PM
1:55:32 PM
2:00:32 PM
2:05:32 PM
2:10:32 PM
2:15:32 PM
2:20:32 PM
2:25:32 PM
2:30:32 PM
2:35:32 PM
12.13
12.57
12.99
13.39
13.77
14.13
14.52
14.88
15.23
15.56
15.88
16.17
16.46
16.75
17.06
17.37
17.67
17.98
18.27
18.54
18.79
19.06
19.31
19.54
19.77
20.01
20.26
20.49
20.71
20.95
21.16
21.31
21,42
21.51
21.62
21.72
21.75
21.81
21.88
21.96
21.98
21.85
21.61
21.41
21.26
21.16
21.04
2:40:32 PM
2:45:32 PM
2:50:32 PM
2:55:32 PM
3:00:32 PM
3:05:32 PM
3:10:32 PM
3:15:32 PM
3:20:32 PM
3:25:32 PM
3:30:32 PM
3:35:32 PM
3:40:32 PM
3:45:32 PM
3:50:32 PM
3:55:32 PM
4:00:32 PM
4:05:32 PM
4:10:32 PM
4:15:32 PM
4:20:32 PM
4:25:32 PM
4:30:32 PM
4:35:32 PM
4:40:32 PM
4:45:32 PM
4:50:32 PM
4:55:32 PM
5:00:32 PM
5:05:32 PM
5:10:32 PM
5:15:32 PM
5:20:32 PM
5:25:32 PM
5:30:32 PM
5:35:32 PM
5:40:32 PM
5:45:32 PM
5:50:32 PM
5:55:32 PM
6:00:32 PM
6:05:32 PM
6:10:32 PM
6:15:32 PM
6:20:32 PM
6:25:32 PM
6:30:32 PM
20.99
20.66
20.15
19.72
19.37
19.10
18.86
18.55
18.18
17.86
17.60
17.39
17.20
17.01
16.88
16.75
16.65
16.58
16.51
16.44
16.38
16.30
16.20
16.09
15.98
15.87
15.76
15.64
15.53
15.46
15.41
15.37
15.32
15.24
15.20
15.15
15.12
15.10
15.04
14.97
14.88
14.79
14.71
14.59
14.48
14.36
14.25
6:35:32 PM
6:40:32 PM
6:45:32 PM
14.14
14.04
13.96
97
U
I
20
15
& 10
I o;
-5
6:00 A M
8:24 A M
10:48 A M
1:12 P M
-$— Bridge Walkway Measured Temperature
■
3:36 P M
6:00 PM
Bridge Walkway Predicted Temperature
Figure 41. March 13 simulation with offset bad longwave data.
6:00 AM
8:24 AM
10:48 AM
♦ Bridge Walkway Measured Temperature
1:12 PM
3:36 PM
6:00 PM
Bridge Walkway Predicted Tenperature
Figure 42. March 13 simulation with Bozeman Pass RWIS longwave data.
Instrumentation Issues
The PIR was not the only instrument that caused some collected data to be discarded.
One of the Licor pyranometers had to be replaced, after it was found to have bad
readings. This problem was very unfortunate in that it was not recognized until the data