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. 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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 -999 -999 -999 -999 -999 -999 -999 -999 -999 -999 -999 -999 -999 -999 -999 -999 -999 -999 -999 -999 -999 -999 -999 -999 -999 -999 -999 -999 -999 -999 -999 -999 -999 -999 -999 -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 -999 112 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 -999 -999 -999 -999 -999 -999 -999 -999 -999 -999 -999 -999 -999 -999 -999 -999 -999 -999 -999 -999 -999 -999 -999 -999 -999 -999 -999 -999 -999 -999 -999 -999 -999 -999 -999 -999 -999 -999 -999 -999 -999 -999 -999 -999 -999 -999 -999 -999 -999 -999 -999 -999 -999 -999 -999 -999 -999 -999 -999 -999 -999 -999 -999 -999 -999 -999 -999 -999 -999 -999 -999 -999 -999 -999 -999 -999 -999 -999 -999 -999 -999 -999 -999 -999 -999 -999 -999 -999 -999 -999 -999 -999 -999 -999 -999 -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 - - -999 -999 -999 -999 -999 -999 -999 -999 -999 -999 -999 -999 -999 -999 -999 -999 -999 -999 -999 -999 -999 -999 -999 -999 -999 -999 -999 -999 -999 -999 -999 -999 -999 -999 -999 -999 -999 -999 -999 -999 -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 -999 -999 -999 -999 -999 -999 -999 -999 -999 -999 -999 -999 -999 -999 -999 -999 -999 -999 -999 -999 -999 -999 -999 -999 -999 -999 -999 -999 -999 -999 -999 -999 -999 -999 -999 -999 -999 -999 -999 -999 -999 -999 -999 -999 -999 -999 -999 -999 -999 -999 -999 -999 -999 -999 -999 -999 -999 -999 -999 -999 -999 -999 -999 -999 -999 -999 -999 -999 -999 -999 -999 -999 -999 -999 -999 -999 -999 -999 -999 -999 -999 -999 -999 -999 -999 -999 -999 -999 -999 -999 -999 -999 -999 -999 -999 -999 -999 -999 -999 -999 -999 -999 -999 -999 -999 -999 -999 -999 -999 -999 -999 -999 -999 -999 -999 -999 -999 -999 -999 -999 -999 -999 -999 -999 -999 -999 -999 -999 116 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 -999 117 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