SOLAR ENERGY CONVERSION SYSTEMS
ENGINEERING AND ECONOMIC ANALYSIS
INPUT DEFINITION
Volume II
GILBERTO RUSSO*
prepared for the
UNITED
STATES
DEPARTMENT OF ENERGY
under contract
No. EX-76-A-01-2295
Task Order 37b
*on leave from the Polytechnic of Torino, Italy, Faculty of Engineering
TABLE OF CONTENTS
Page
INTRODUCTION
1
CHAPTER 6 IMPLEMENTATION CRITERIA OF THE MODEL:
CODE CIRR2
3
CHAPTER 7 CIRR2 OUTPUT ANALYSIS GLOBAL ENERGY FLUX
APPENDIX A7:
A_
CIRR2 PROGRAM DESCRIPTION
24
120
NOMENCLATURE
134
CONVERSION TABLE
139
REFERENCES
143
INTRODUCTION
The Solar Energy Conversion Systems transient operation mode
requires that the engineering and economic analysis of the system
be performed on the basis of an energy input to the system--solar
energy flux on the collector area--properly defined in relation
to the time constants of the components and the system itself.
Due to the worldwide dearth of solar energy data records, a
deterministic approach on the basis of a few "generally available"
meteorological parameters--that permit a day-to-day match of the
solar energy flux with the load--for the computation of the solar
data is performed in this work.
In Volume I, the solar radiative characteristics and radiation laws are presented in Chapter 1 and Appendix Al; the computation
of astronomical parameters is performed in Chapter 2; the interaction
of the electromagnetic flux with the atmosphere components is discussed in Chapter 3; the solar energy flux depletion analytical
model is presented in Chapter 4; and the correlation of the
depletion to the meteorological parameters, as well as an analysis
of the meteorological input data and presentation of alternative
ways of computing some of the meteorological parameters involved,
are discussed in Chapter 5 and Appendices A2, A3, A4, A5, and A6.
1
Model implementation criteria, the CIRR2 code for the
computation of the global energy flux, and a discussion of the
results are presented in this volume. Volume III will deal
with the direct (beam) component of the solar energy flux and
will contain an exhaustive statistical analysis of the results.
2
CHAPTER 6
IMPLEMENTATION CRITERIA OF THE MODEL:
CODE CIRR2
The astronomical parameters were defined in Chapters 1 and
2. The beam's depletion, due to the phenomena described in
Chapter 3, was studied in Chapter 4, and a physical parametric
model of the interaction was built.
In Chapter 5,
meteorological conditions were correlated with the depletion
parameters.
The last section of the previous chapter is a summary of
the mathematical algorithms and an analysis of the different
computation options, which are dependent on the meteorological
data available.
Independently of these computation options--or
type of input data-the "logic" block diagram of the noel
should be as reported in the block diagram below.
The general criteria of implementation will be:
i.
ii
iii.
economy of the model
minimization of memory locations employe
versatility of the input and output interfaces
3
CIRR 2
BLOCK DIAGRAM
GEOGRAPHIC INDIVIDUATION
ADDRESSES FOR
COMPUTATION
DATA
METEOROLOGICAL
j
I
-I
- I -
MEMORIZATION OF
METEOROLOGICAL DATA
.
COMPUTATION OF
DAILY VALUES OF
ASTRONOMICAL
PARAMETERS
-
ii
-~~~~~~
i
COMPUTATION OF
INSTANTANEOUS VALUES
OF ASTRONOMICAL
PARAMETERS
RANDOM EVALUATION OF
INSTANTANEOUS VALUES
OF METEOROLOGICAL
PARAMETERS
I_
,,
I
CORRELATION OF
ATMOSPHERIC ABSORBANCE
WITH ASTRO-METEO
PARAMETERS
I
_
I
COMPUTATION OF
ENERGY FLUX DENSITY
COMPUTATION OF
ENERGY FLUX
I
.I
_
t
ASTRONOMICAL AND
ESTIMATED METEOROLOGICAL
PARAMETERS
ENERGY FLUX DENSITY
AND ENERGY FLUX
SIRR'S
4
i
II
RESULTS ANALYSIS
SENSITIVITY ANALYSIS
PLOTTAGES
Therefore, the program will be "modular," with each
subroutine corresponding to a physical computation of the model
that may or may not be recalled following the running options
given.
The running options will depend on the meteorological
approximation option requested (see Section 5.4) and therefore
on the meteorological input data available and on the number of
oays in which the computation should be accomplished.
The meteorological data available may be in aifferent
formats, digitized or not.
Therefore, two types of input will
have to be previewed--from tape and batch--both allocating the
input data in storage files (arrays or matrices), from where
information will
e recalled, as needed, by the program.
The results of the computation of the meteorological aata
from the basic "state parameters," when performed, are stored in
the same storage files, in order to be recalled for printing.
Since the program is part of a set of codes aime
computing the solar input (direct,
at
iffuse, global) for the
simulation of the transient conditions of operation of solar
energy conversion systems, the output will have to be highly
diversified and elastic.
Printouts and plottages of the
significative functions and results of the model considered here
will be produced.
5
The main computation routine task is to perform the
computation of the density energy flux and its integral with
respect to time, i.e., the energy flux.
The progression of the
computation has already been described (see Section 5.4); the
logic sequence of the computation is as follows:
The first loop
performs the computation of the daily values of the astronomic
parameters-geographic inclination data sorted--and,
consequently, determines the limits of integration on the
horizontal surface. The second, nested loop calculates the
instantaneous values of the astronomic parameters, performs the
computation of KT-meteorological data stored--and A, following
the summing options.
If "instantaneous" values of
meteorological data are not available, a subroutine
ANDOM
elaborates the "instantaneous" values of these parameters, on
the basis of the integrated energy flux density values obtained
for the set of meteorological data available for the day.
Finally, the density energy flux is computed and the
"instantaneous" values are stored for the integral computation.
When necessary and significative, the meteorological data
have been linearly interpolated (mainly on the microclimatic
approximation).
A block diagram for the individuation of the single
subroutines and a diagram of the information flow between the
modules of the program are given below.
6
Finally, the flowcharts for each of the subroutines follow.
A detailed subroutine (and main program) description is
reported in Appendix A7.
A manual of operation instructions of the CIRR2 coae will
be available immediately after the conclusion of the CIRHR coae's
programming.
7
CIRR 2
BLOCK DIAGRAM
(SUBROUTINES)
/-
" \
SOLMETJ
I
I
I
I
CONVRT
I
I
L -I
METEOROLOGI CAL
T
yA
A
GEOGRAPHICAL
PARAMETERS
L1
-
RUNNING OPTIONS
COMPUTATION OPTIONS
PRINTING OPTIONS
METEOROLOGICAL
DATA
2
IC
F
t
-
I
I-
-m
MAIN PROGRAM
rEXPERIMENTAL
SUBROUTINE
I
_1
FLUX
o- --
JOUT
I
VALUES ENERGY
r
.
EXPERIMENTAL
VALUES ENERGY
\ LUX _
-
*UXILIARY
-PROGRAM
I
L. ..
SUBROUTINE
I
JWMFIT6
__.
WWEO
f
CEOC2
_J
I
t
ALB
_m
r
- .
HE 0
a
SUBROUTINE
PRIN
SUBROUTI NE
SUBROUTINE
C-RAND
IIIIII
I
I-
t.I
ASTRONOMICAL
AND ESTIMATED
METEOROLOGICAL
PARAMETERS
t
RESULTS ANALYSIS
SENSITIVITY
ANALYSIS
ENERGY FLUX
DENSITY AND
ENERGY FLUX
L_.--
I
SIRR'S
8
PLOTTAGES OF
OUTPUTS
I
CIRR 2
FLOW CHART
SYMBOLS KEY *
c
)
E- l
G
PROGRAM TERMINUS
INPUT TO PROGRAM
INPUT TO PROGRAM,
FROM TAPE
PROGRAM INSTRUCTION
DECISION; CONDITIONAL BRANCH
SUBROUTINE
OUTPUT
N
NO
Y
YES
Variables within boxes are defined on Nomenclature
9J
page.
CIRR 2
INFORMATION
KEY
FLOWS
A = COMPUTATION, RUNNING OPTIONS
B= PRINTING OPTIONS
C = GEOGRAPHICAL DATA
D= METEOROLOGICAL DATA
E ATTENUATION
"CONSTANT" COEFFICIENTS
F =ENERGY FLUX (computed values)
G =ASTRONOMICAL PARAMETERS
H= ENERGY FLUX DENSITY (computed values)
I = PRECIPITABLE WATER
(computed value)
J = EQUIVALENT HEIGHT OF THE ATMOSPHERE
(computed value)
K =ALBEDO OF CLOUD COVER (computed value)
L =RANDOM VALUE OF MINUTES OF SUNSHINE
M= ENERGY FLUX (non-digitized experimental values)
10
CIRR 2
I NFORMATI ON FLOW
B
A
( input )
C
D
MAIN PROGRAM
F (from CEOC2)
JOUT
A
B
C
D
E
(to CEOC2)
(from JOUT)
A
B
C
D
E
SUBROUTINE
<T- ( from WWEQ)
CEOC2
E
(from JWM FIT 6)
-c-j(from
HEQ)
K(from ALB)
L(from C-RAND)
B C wG H I F
D %;
(to ALB)(to WWEQ, (to PRIN) (to JOUT)
HEQ,
GRAND,
PRIN)
A
11
( see following page)
( Input)
( from CEOC2)
D
A
SUBROUTINE
ALB
K
(to CEOC2)
(input )
D
SUBROUTINE
C-RAND
( L
( to CEOC2)
(see following page )
12
(input)
A
C
B
D
E
M
I AUXILIARY PROGRAM
I
I
I
I
I
JWMFIT6
I
I
I
I
L
ID... C
A
B
A
B
D
(from CEOC 2 )
G
H
C
D
(to CEOC2)
E_
1
E
T
IUU
SUBROUTINE
PRIN
w
(output)
(see following page)
13
(from CEOC2)
D
SUBROUTINE
WWEQ
I
(to CEOC2)
(from CEOC2)
D
SUBROUTINE
HEQ
IU
(to CEOC2)
14
CIRR 2
FLOW CHARTS
CONVRT
15
CEOC2
COMPUTATI ON OPTIONS
RUNNING OPTIONS
OUTPUT OPTIONS
lb
(see following page )
C
COMPUTATION
ENERGY FLUX
DENSITY (idpal
I atmosphere )
i
i
COMPUTATION
ENERGY FLUX
DENSITY (real
atmosphere)
SUBROUTINE
HEQ
\
(COMPUTATION OF
EOUIVALENT HEIGT
OF THE ATMOSPHERE)/
/
COMPUTATION
HOURLY INTEGRAL
OF ENERGY FLUX
DENSITY (ideal
atmosphere)
COMPUTATION
HOURLY INTEGRAL
OF ENERGY FLUX
DENSITY (real
atmosphere)
/ SUBROUTINE
/
C-RAND
(RANDOM COMPUTATION OF
\ MINUTES-OF-SUNSHINEV/
17
LOCAL \N
3
HOUR
COMPLETED
Y
( see following page )
E
Irr
18
HEQ
l
l
w~~~
C
START
rz
INITIALIZATION
SATURATION TEMPERATURE,DRY AIR
CONSTANT, WATER
VAPOR CONSTANT
COMPUTATION
WATER VAPOR
PARTIAL
PRESSURE
COMPUTATION
WATER VAPOR
DENSITY
f
COMPUTATION
MIXING RATIO
COMPUTATION
MOIST AIR
CONSTANT
COMPUTATION
MOIST AIR
DENSITY
.. +
COMPUTATION
EQUIVALENT
HEIGHT OF THE
ATMOSPHERE
I
i
C
RETURN
-
~~~ ~
19
INPUT:
TEMPERATURE (dry
bulb, dew point )
PRESSURE
ALB
N
-
COMPUTATION
WEIGHTED AVERAGE OF ALBEDO
20
WWEQ
)START
)
INPUT
TEMPERATURE (dry
bulb, dew point)
PRESSURE
I
I INITIALIZATION
SATURATION TEM-
I DAY NUMBER
J
PERATURE,DRY AIR
CONSTANT, WATER
VAPOR CONSTANT
COMPUTATION
WATER VAPOR
PARTIAL PRESSURE
|
COMPUTATION
WATER VAPOR
DENSITY
'I.
RETRI EVE
OPTIMIZED
ATMOSPHERIC
'SCALE HEIGHT'
I
COMPUTATION
PRECIPITABLE
WATER
RETURN
.
21
I
JWMFIT6
INCREMENT
THE NDIG DIGIT
OF THE NPAR PARAMETER: PNPAR
(see following page)
SSO:=
( ERR )
22
SSQ
SUBROUTINE
CEOC2
(COMPUTATION OF
ENERGY FLUX)
23
Chapter 7
CIRR2 OUTPUT ANALYSIS
GLOBAL ENERGY FLUX
The availability of solar energy flux experimental data
has been extensively discussed in Chapter 5; the insolation
data furnished on SOLMET format using criteria presented in
references [64] and [65] are reported in Appendix A4.
For the purposes of analyzing results of the CIRR2 model,
the values of the global solar energy flux on the horizontal
have been furnished by the Solar Energy Meteorological Research
and Training Site of the Atmospheric Science Research Center,
State University of New York at Albany.
The months of February
and June 1979, being the only months for which solar data are
currently availabe, are used as the initial Dasis of discussion.
The Center will furnish other aata--months of July and
August 1979--and more data will be furnished soon by the
Lincoln Laboratories, M.I.T.
A statistical analysis of CIRR2 performance will be
performed as soon as the direct energy flux code, CIkk2, is
24
operative and as soon as all the data for different locations
of the U.S. are available in digitized form.
This chapter therefore will deal only with an analysis of
the results for the months of February and June 1979, Albany
N.Y., and will not attempt a statistical determination of the
computation error.
It should be pointed out, however, and in
order to build a general idea of the precision of computation
under different climatic approaches, the range of variation of
the monthly relative error, obtained for Southern-European
locations (for which all the data were available), is
restricted within a narrow band of approximately 5 percent [8j.
The global energy flux computation is performed as
summarized in Section 5.4. The albedo computation is performed
as indicated in Sections 5.2 and 5.3.
The .single steps of the
albedo computation, on a microclimatic approximation, are
reported below; computer outputs are self explanatory.
25
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The atmospheric density integral is performed on the basis
of the station pressure experimental values, recorded every
three hours.
These values may be linearly interpolated.
The
integral of the global energy flux, computed using the station
pressure or using the "Standaro Atmosphere" pressure values for
an artificial day with maximum difference between these two
pressures, is reported below, along with the corresponding
tabulation of global energy flux values of the two hypotheses.
33
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Finally, the global energy flux is computed (see Section
5.4) on a micro-climatic approximation, with linearly
interpolated values of amount of precipitable water and albeco
of the sky cover.
The surface meteorological data (described
in Appendix A5) have been furnished by the Weather Service
Forecast Office, N.O.A.A., Albany, N.Y..
The site of those
measurements is only a few miles from the site of the solar
energy flux measurements, at the Atmospheric Sciences Research
Center at the State University of New York at Albany.
As concerns the albedo computation, hourly values of the
albedo are computed as a function of the albedo of different
layers (as reported in the previous computer outputs).
The
corresponding global energy flux values and relative errors are
also computed.
In order to have an idea of the cloud alternation, the
global energy flux without clouds is also computed.
The meridian (local) time is computed through tne
following algorithm:*
T
=T
+a
meridian
solar
*Harold M. Wolfe, "On the Computation of Solar Elevation
Angles and the Determination of Sunrise and Sunset Times,"
National Meteorological Center, ESSA, Hillcrest Heights,
Maryland, NASA TM X-1645, 1968.
36
where:
= 0.123570 sin(D) -
.004289 cos(D) +
0.153809 sin(2D) + 0.060783 cos(2D) 4 (xtime
zone-
x)160
0 = (-1)360/365.242
In reference to the tabulations,
it should be noted that
for some hours, although S/D is reported equal to one, there is
an indication of clouds.
This means only that the clouds
present did not intercept the beam (which does not necessarily
mean they do not have an influence on the beam's depletion as
has been shown and taken into account through KT, which is a
function of KT and the cloud cover).
It also should be noted that sometimes, at the end or at
the beginning of the day, the S/U factor appears superior to
one.
This is physically impossible, as is evident from its
definition.
The reason for this is that the minutes of
sunshine are an experimental datum, which is divided exactly by
one hour (in order to obtain S/D) for all periods of the day,
except the sunrise and sunset hours.
In those periods, the S
factor has been divided by the appropriate computed fraction of
the hour:
this and the fact that the S measurement is rather
imprecise have caused, for those sunrise and sunset times for
which the fraction of the hour is particularly small, those
37
"over-computations," which have been reported without
correction.
The results of those computations, performed by CIRR2 on
the basis of the analytical model described here, are reported
below for the month of February 1979, at Albany, N.Y.
The monthly values of the computation and relative errors,
a synoptic table for the daily values, and a synoptic table for
the error distribution follow.
Finally, the same computations are reported for the month
of June 1979.
38
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of February and June 1979, Albany, N.Y.
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2. worldwide yearly average of minutes of sunshine per day
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pressure values
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i0
The results of the computation of the global energy flux
have been reported on the previous pages. As has already been
noted, no attempt to perform a statistical analysis of the
results will be attempted, either for daily or hourly
approaches, due to the reduced amount of data available.
Some
general considerations of the model performance, though, will
be presented, on the basis of the previous tabulations. A
deeper analysis of the results will be deferred until more data
are processed.
As expected, the monthly precision is higher than the
daily, which is higher than the hourly precision:
for the two
months considered, there is a one to three percent monthly
precision; at least three-quarters of the daily data are within
a 15 percent precision; and the hourly precision is lower. The
average of the relative error is extremely low, and the
standard deviation of the daily values for those two months is
also low.
The first simplified version of this program, run
for European locations, did not appear to have a sensible
statistical dependency on the month of the year (for the same
location) or, more generally, from location to location.
If days with no clouds during the entire insolation period
are considered, the daily match of experimental and computed
values is extremely satisfactory, as may be seen from the
previous tabulations.
In order to better visualize this, the
87
hourly global energy fluxes--the hourly interval is used
because experimental data were available only on an hourly
basis--both experimental and computed, are plotted versus
time.
All the days on which the factor S/D (minutes of
sunshine per hour) was equal to one during the entire day are
substantially represented by days such as February 3, February
6, February 11, February 28, June 14, June 20, and June 25.
Their plottages are reported below.
88
a)
T KIT
rr
D n I
C
lC D r Y
E'l
I IV
Un
SEO (EXPER. )
SEO (COMP.)
FEB. 3, 1979
CD
('"
DRY NUMBER 34
CD
in
cti
L¥
CD
r
-,
bI
n'-
CC
Ln
U(
rJ
'r
0
0
U,
0
12
TIME
89
16
(HRS.)
2
ok
T K -rE'(-
O nI
rK
Ln
M3
0
cv
o
c:
CD
0
uJ
0
0
Ln
CD
CI
0D
0
Ln
cr
Ln
·0
0
Ln
0o
0)
0
TIME
90
HRS.)
117 0r
,V
r
I
I I /
0)
O
u,
lrE'KIEY 'Y1
T klTCrDl
cr)
0
0
0
O
Ll
C
0
Cu
cr
cm
CD
--
0
0
Ln
mE
U)
ILLJ
F-
u
CC00
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o
u)
0
Li
0
TIME
91
HRS.)
lIV
C
C
U,
cT,
T
I
7 r77
O
I
r-
a)
cD
CD
0
0
0
Ln
CU
CI):
uli
0
C)
0
cmr
CT
CD
0
0
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cm
4=
CD
"r
I
CD
Ln
TIME
92
HRS.)
I r M -, V
r
I I I \/
CD
T
I -Tr
r
nD
I r_
1s
U,
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C:
CD
0
cr)
C)
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Ln
L.J
c-f
C)
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z
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I
C)
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cr
To
O
TO
TO
us
o
TIME
93
(HRS.)
r 'v
I I I \/
CD
Ln
cr)
INTEG
ENERGY FLUX
M JEO (EXPER.)
L
EO (COMP.)
JUNE 20, 1979
DRY NUMBER 171
a)
a)
CD
cn
CD
m
c,
0
L
CD
C%j
cm
r
LJ
a)
Lr
0
0
U,
z
I
0
0
CD
0
0
0
u>
0
1
TIME
94
HRS.)
CD
u)
INTEG
ENERGY FLUX
m EO
(EXPER.)
, EO (COMP.)
JUNE 25, 1979
DRY NUMBER 176
a
CM
0
0
(0
v,
cn
cu
0
rm
Lu
-
z
Ml
0
0
Ln
ru
0
LT
>I
0
0
0n
m
0
0
U,
0
TIME
95
HRS.)
The extensive presence of clouds intercepting the beam
tends to introduce an increase in the error. This error is
compounded by the fact that the albedo factors are interpolated
on an hourly basis, since the cloud coverage condition of the
sky-dome is observed at one instant during the hour (at the end
of the hour); this interpolation tends to affect the hourly
precision, when performed between zero and some albedo, but the
lack of data does not permit a deeper investigation.
Consequently, the interpolation has been left generalizea
during the whole day no matter what were the values between
which the interpolation was accomplished.
This fact is shown,
for instance, on the plottage of June 13 (the S/D value
different from one is that at 13.00 hours), and the plottage of
June 19 (the S/D values different from one are those at 16.00
ana 18.00 hours).
Both plottages are reported below.
96
T
I
r
r-
e-
r-,
e,,% i
r-
L
I
r-
r--
-
, ,
-
.
, . . .
C
CV7
C)
CD
cn
Ln
C?
0
0
U,
C.'
Co
CM
L:
cu
CL
L.J
0
Ln
I
Ln
0o
1,,
U,
c
4L
16
TIME
97
(HRS.I
20
2
CD
T
KI
r
-
-
I
Ln
CV
0
cD
m:
Ln
Cuj
LU
C
LU
C:
c:
03
rr
C
U.
I
=,
_.
r'r
"r"
u,
0
TIME
98
HRS.)
L i -- r-
-
, ,
Even on those days on which S/D equals one during the
whole day, the cloud's presence tends to affect the precision
of the model.
trend:
June 6 and June 21 are good examples of this
They both have S/D equal to one over the whole day, but
the former has cloud-cover fluctuations (n fluctuations)
ranging from 10 to 80 percent (even though the clouds never
intercept the beam) and the latter has a cloud cover
consistently less than 30 percent.
The precision of the latter
is lower than the precision of the former.
during the same day:
This happens also
On June 26, S/D equals one the entire
day, but the cloud cover is zero during the morning and
different from zero in the afternoon.
reported below.
99
The three plottages are
cm
a
Ln
Cr)
INTEGR
ENERGY FLUX
I
JEO (EXPER.)
A SEO (COMP.)
JUNE 6, 1979
C)
DRY NUMBER 157
.-
CD,
(,
N1.
Cu
LL
0
LJ
a)
c:
crI.
ul)
0
0
ct
a)
Jr
I
0
0
Ln
Ll
0o
0o
0o
0o
0o
U,
0
16
TIME
100
(HRS.)
t
0
0
U,
C,,
I NTEGR
ENERGY FLUX
a)
JUNE 21, 1979
\DRY NUMBER 172
C3
cn
C)
!-1
NC
w
LL
cu
Lf
LLJ
z
0=
I
0D
0
TIME
101
(HRS.)
0
0
U,
cV7
INTEG
ENERGY FLUX
SEO
\mSEO
(EXPER.)
(COMP.)
JUNE 26, 1979
DRY NUMBER 177
l=
0
I=
MU
0
Ln
0
>CT
0
cu
0
rn
o
(f)
C:
LuI
0
0
z
u,
-
--
0
0
U,
TIME
102
(HRS.)
It appears reasonable to state that, on a daily basis, the
analytical model represents well the interaction in the total
absence of clouds.
On an hourly basis, though, the model is
affected by the lack of information on meteorological
conditions (state parameters of the system).
Some
systematicity on the error introduced by the clouds, mainly at
high sky cover (S/D always being one), may be noticed (e.g.,
the influence of the clouds on the increase of humidity content
of the atmosphere).
Once more, nothing has been done to
decrease this "systeniatic" error, both for lack of relevant
amount of
ata in different climatological conditions and in
order to permit an analysis of the "physical" model.
reason is particularly relevant,
The first
ue to the fact that no real
information related to statistical fluctuations is available.
It is plausible to state that the amount of precipitable
water, though, is a critical measurement.
The limits of its
availability (twice a day) and reliability affect the precision
of the mooel, even though linear interpolation of its daily
values is performed.
This is evidenced by days such as
February 17, where both the cloud cover ana S/D equal one
during the entire day.
It may be seen from the plottage
reported below that the precision of computation tends to drop,
mainly around noon, which corresponds to the time between the
two precipitable water hours' measurements (performed at OO.UU
ano 12.00
MT).
103
CD
T kI T r
r) F
I
r-
Ln
cn
CD
0
CD
0
0
cm,
(I)
"I
1-1
0
0
L,
cu
C
i.I
CD
rLU
cr
a)
0
Cu
cU
-J
0
0
U,
F-
a)
e-
Z
0
U,)
To
To
us
0
TIME
104
HRS.)
KI r
-
I
"V I-
1
I
The sum of the two effects, i.e., the lack of information
on the humidity content and the effect that the clouds have on
the humidity content, is clearly shown by June 27.
The same
situation is represented by February 14, when cloud cover is
inferior to 30 percent in the morning, is superior to 30
percent in the afternoon, ana S/D equals one during the entire
oay.
Both plottages are reported below.
105
o
O
Ln
U,
T Kl T
r"
I1
'kI ED
r" Y
EI
C,,
CD
0
C,
Cr
en
-1
0
U,
CD
0
0
0
LL
cu
CD
C)
fm
Ul)
0
z
UC
0
- c:
C)
0
0
0
Ln
0
a)
1
TIME
106
(HRS.)
2
I
V
°-
,
T KI T ErDfI
r
I
dE'l~rYy
c
EnI
E
IV
U,
C3
'r
D EO
SEO (COMP.
FEB. 14, 1979
DRY NUMBER 45
C
CX
(c
(EXPER. )
O0
LnU
>-
_JC
Z
0
J
I
Ta
=O
16
TIME
107
(HRS.)
21
All discussion of the clouds thus far pertains only to
those days on which the S/U factor was consistently near one
during the entire day or on a portion of the day. The effect
of the clouds on the amount of precipitable water obviously
will be heightened on those days on which S/D equals zero the
entire day (or in those portions of the day on which S/D
consistently equals zero).
The stochastic presence of clouds
will therefore strongly affect the total humidity content of
the atmosphere, nullifying the effect of the interpolation
between those two available values of measured amount of
precipitable water.
Furthermore, as the cloud cover on those
days on which S/D is particularly low tends to be higher, the
visual information on the cloud types (used for the computation
of the albedo) will be more and more incomplete, lacking
information on the higher layers, which are shielded from
visual observation by the lower layers.
Tis will strongly
affect the precision of the computation of the global energy
flux, in which the albedo is an intensive factor that obviously
results from this "series" connection effect.
(Itis
worthwhile to note that this effect will be much less severe as
concerns the direct energy flux computation, as will
e seen.)
This lack of information on the higher layers will also
strongly affect the precision of the computation of the total
humidity content due to clouds, since the KT factor has only an
extensive factor (the total cloud cover) and does not
108
have an intensive factor, relative to the albedo of all the
layers.
Certain systematicities of the error also may be relevant
in this case, in which S/D is consistently low, but have not
been corrected, for the reasons previously stated.
Furthermore, those effects appear to be sensibly increased (and
this appears nieaningful) on those days on which S/D equals zero
during the entire day.
Typical days on which S/D equals zero the entire day and
the sky cover is 100 percent during the entire day are February
27 or June 11. These plottages are reported below.
109
cm°
T KTI
I
r
"
I
I
Ir
U
CD
cn
Xo
o
o
CD
I-n
a)
CN r
LLJ
LTo
LLJ o
o
-J
I
0a
1
TIME
110
[HRS.3
m rl- \/
I II\
r-
:)
'
"I
r
=,
r r
--
U,
(=)
CD
C
--CM
Uo
a
LI
O
-O
O
ET
U,
To
1O
TIME
111
(HRS.
i
-
,
,
,
For ays on which S/D equals substantially zero the whole
day and the cloud cover is 100 percent during the entire day
but with more transparent (lower albedo) clouds, the precision
is sensiDly increased, as may be seen from the plottage of June
28, reported below.
The lower albedo of the clouds on this day may be noticed
either from the tabulations or by comparing this day with the
two previously presented:
The former has an hourly maximum
value of global energy flux of approximately 3,000 kJ/m2; the
latter is less than 1,000 kJ/m2
112
a)
T
C' r '
1
an
cr)
CD
CD)
Cr
_
Ln
CU
L
CD
C)
Li
i-
:)
Ln
P-
I
a
rr
a
CD
CD
E:
a
'T
a
C)
u
0r
0
TIME
113
HRS.)
I r-
)
V
r-i
I I\/
Those days on which S/D equals zero only part of the day,
always with a high percent of cloud cover, are representted by
February 1 or June 18, on both of which S/D tends to be zero
from late morning until late afternoon.
reported below.
114
These plottages are
CD
T
lT'r'Dnl
IEklDr C
IY
El I
I IV
Ln
cr)
SEO
CEXPER.)
SEO (COMP.)
FEB. 1, 1979
DRY NUMBER 32
CD
cr)
O
-
4=
Co
ao
LLJ
I
C
C)
Z:
0
C:)
C)
IO
cr:
L,
O
TIME
115
(HRS.)
Ca
Ca
T kI T C r(-
N
CEKIECDrY
L)
M
a)
C,
I-
(:
'"3
n
Uc
lo
LL
Co
L1J
:3
ru
a:
r.z
U,
r
'1
U,
0
TIME
116
(HRS.)
I
I IV
Although rarely, the experimental global energy flux
behaves sometimes in a particularly unusual way.
This is
evident without reference to the computed values of the global
energy flux.
For instance, considering February 19, it may be seen that
all the weather and cloud conditions--although within the
limits of those measurements and observations,
respectively--are homogeneous from 09.00 to 14.00 hours:
he
experimental value of the global energy flux at 10.00, however,
peaks at a value that is 10 times the value it had at 09.U0,
and falls back to a consistent value at 11.00.
February 19 is reported below.
117
The plottage of
.0
T K1 7
r
r'
M n I
r- KI r
CD
cr
0
CD
CD
cn
N.
-
CD
Ln
0
0
CD,
C
4=
Cr)
U,
CU
-LLI
rr
Ln
CD
Cu
0
0
U,
cr
cE:
0
0
0
I _JCD
4-
0
0)
o
TIME
118
HRS.)
M (% '
-I
I /
No further attempt to interpret these results will be made.
It appears now that the analytical model permits an
extremely good approximation on a monthly basis (within the
limits of error of the energy flux measurements), ano is
slightly affected by a lack of frequency on the input data
(mainly precipitable water) on those days in which the global
flux equals the diffusion component of the radiation.
On those
days in which the diffuse component is particularly reduced (or
the coefficient S/D is equal to one), the precision of
computation is particularly satisfactory.
A general conclusion and error analysis of the work will
be made as soon as more data have been processed and after the
model for the computation of the direct component has been
implemented (Volume III).
119
APPENDIX A7
CIRR2 PROGRAM DESCRIPTIUN*
The subroutine CEOC2 is, in effect, the main program of
the model.
Meteorological input data are transmitted to the
subprogram via "common" arrays.
Geographical parameters are
written into the program, while running parameters (output
options, computing options, etc.) are transmitted at the time
of calling the subprogram.
Meteorological data are retrieved from data files by the
MAIN program, JUUT.
JOUT also interactively prompts the user
for output options ana sets the appropriate output-option
variables for transmission to CEUC2.
The outputs generated
within JUUT (i.e., the plots and tabulatea values) are only a
sample of what might be accomplished by the 1,vAIN program.
The
individual user coula put, in the place of (or in addition to)
the printing and plotting instructions, any further processing
of the energy flux values that he may wish to run.
Calculation of the values of precipitable water (if
experimental values are not available), equivalent atmospheric
*The description of this present, first version of the
program has been prepared by .I.T. student J. McCombie.
120
height, and the albedo of the cloud cover are computed via the
"function" subprograms WWEQ, HEQ, and ALB, respectively.
Appropriate input data are transmitted to these subroutines in
their "call" statements.
Using subroutines in this manner enhances the flexibility
of the program, as well as being an aid in the debugging
process.
The subroutine PRIN is used to generate an output file
with hourly values of energy flux density and meteorological
parameters.
Using a separate subroutine for printing gives the
user the flexibility to design the format of the final output,
printing only those values that are needed for a specific
implementation.
Fine tuning of the model is accomplished via the program
JWMFIT6. The parameters Pl, P2, and p3 (from the KT
computation) are varied in such a way that the error in
calculated values of energy flux density is minimized.
The
program requires the user to have in a data file both
meteorological data and experimental values of energy flux
density.
The program then prompts the user for initial
estimates of the parameters and the accuracy desired; the end
results are the optimized values for the parameters.
121
The technique used by JWMFIT6 to find the optimized values
is a variation on the "spider" technique of finding a local
minimum. Consider the system as a function in 4-space--the
three parameters and the sum-squared-errors (SSQ):
SSQ =
(EO I
-
exp
E i
)2
calc
Starting from the initial estimates of P1, P2 , and p3,
the program "crawls" around testing different values of the
three parameters, attempting to find a local minimum of SSQ.
When a location is reached at which SSQ increases with any
variation of Pl, P2, or p3 , a local minimum has been
reached:
values.
The program stops and reports the new parmeters'
The program JWMTEST calculates and prints SSQ for both
the initial and final estimates of the parameters for
comparison purposes.
In this implementation of the nmoel, there exists a clean,
application-independent set of programs for modeling solar
energy flux.
The user can use the entire set of programs as
written, producing his choice of various printouts and plots,
or use the calculating routine (CEUC2) with his own
main-program, and use the energy flux values for his own
purposes.
In either case, the user should have no problems in
the implementation of this model.
122
The worksheets of each of the subroutines and of the main
program are given below.
Refer to Chapter 6 for the logic of the programs.
123
NAME:
CONVRT
TYPE:
MAIN - auxiliary
UPDATE:
July 1, 1979
DESCRIPTION:
Reads records from a SOLMET tape and writes
desired data to an output file
SUBROUTINES:
No subroutines
COMMONS:
No commons
LOGIC:
1)
Position data tape (SOLMET) to beginning of
one year
2)
Read records from SOLMET tape and write to
output file until end of year
3)
Stop
ERRORS:
If SOLMET records end before 24.00 hours on
December 31, tape runs out of reel causing read
error
124
NAME:
JOUT
TYPE:
MAIN
UPDATE:
August 1, 1979
DESCRIPTION:
Determines and assigns run parameters; reads
appropriate meteorological data from files; calls
subroutine CEOC2
SUBROUTINES:
CEOC2 is called
COMMONS:
/BLK1/
LOGIC:
1) Prompt for running parameters
/PRSS/
/HBLK/
2) Prompt for output options
3) Write headers on output files
4) Call CEOC2
5) Write end-of-report data to main output file
6) Stop
125
NAME:
CEOC2
TYPE:
SUBROUTINE
UPDATING:
August 1, 1979
DESCRIPTION:
Computes and stores density of energy flux and energy
flux values; calls subroutine PRIN
SUBROUTINES:
PRIN
COMMONS:
/OUTBLK/
INPUT:
Values for parameters P1, P2, P3 ; number of days
for which program is to be run; number of integration
intervals per hour; value for albedo; flag determines
output options; eventually, computed values of
precipitable water, equivalent height of the
atmosphere, randomized c
OUTPUTS:
Density of energy flux; hourly, daily, monthly, or
yearly values of energy flux
LOGIC:
HEQ
/BLK1/
WWEQ
ALB
/PRSS/
C-RAND
are called
/HBLK/
1) Initialize all parameters
2) Initialize all output variables to zero
3) Compute daily parameters
4) Retrieve daily meteological parameters from
storage
5) Compute instantaneous astronomical parameters
6) Call ALB
7) Call C-RAND
8) Compute density of energy flux
9) Compute energy flux
ERRORS:
10)
Call PRIN
11)
Stop
1.
Overflow if P1 P2 P3 make KT unreasonably
small or large; program terminates
2.
Bad flag input (output-options); program
terminates
126
NAME:
PRIN
TYPE:
SUBROUTI NE
DESCRIPTION:
Prints astronomical parameters, meteorological parameters;
density of energy flux, and energy flux values, following
output options
SUBROUTINES:
None
COMMONS:
None
ARGUMENTS:
Name
Description
Type
I
TI
Time
R*8
I
H
Sun's altitude
R*8
I
MO
Month
1*4
1
IDY
Day
1*4
I
WW
Precipitable water
R*8
I
PO
Pressure
R*8
I
AO
Density integral
R*8
1
Al1
Relative atmospheric mass
K*8
1
KT
Atmospheric attenuation
constant
R*8
I
TAU
Atmospheric attenuation
R*8
I
EOORTI
Density of energy flux in
an ideal atmosphere
R*8
I
EURT
Density of energy flux in a *8
real atmosphere
I
EOHOR
Density of energy flux on
the horizontal
k*8
I
NCALL
Counter
1*4
I
ES
Extra terrestrial density
of energy flux
R*8
I
-
(see following page)
127
LOGIC:
1) If NCALL = 1 (first hour of printed data this day)
write column headers to main output file
2) Write hourly data to main output file
3) Increment NCALL
4) Return
128
NAME:
WWEQ
UPDATE:
August 3, 1979
TYPE:
FUNCTION - subprogram
DESCRIPTION:
WWEQ computes values of precipitable water (WW)
SUBROUTINES:
None
COMMONS:
None
INPUTS:
Values of dry-bulb temperature, dew-point, pressure
OUTPUT:
Computed WW value
LOGIC:
1) Compute WW value
2) Return
129
NAME:
HEQ
TYPE:
FUNCTION - subroutine
UPDATE:
August 3, 1979
DESCRIPTION:
Calculates the equivalent height, HH
SUBROUTINES:
None
COMMONS:
None
ARGUMENTS:
Dry-bulb temperature, dew-point, pressure (all input)
LOGIC:
1) Compute equivalent height (HH)
2) Return
130
NAME:
ALB
UPDATE:
August 1, 1979
TYPE:
FUNCTION - Subroutine and auxiliary
DESCRIPTION:
Computes the albeao of the cloud cover
ARGUMENTS:
NAME
DESCRIPTION
TYPE
I/0
IMO
Month number
I*4
I
IDY
Day number
1*4
I
HR
Hour
R*8
I
NOUT
Number of outputs desired
I*4
I
OUT1
(%
a )/n
R*8
U
OUT2
(%i
ai )/(%
R*8
0
OUT3
Undefined
R*8
U
OUT4
Maximum of albedos
R*8
0
OUT5
Minimum of albeaos
R*8
0
ALB
Linear average of albedos
R*
U
j)
SUBROUTINES:
None
COMMONS:
None
LOGIC:
1) Read in type of cloud, cloud layer, and percent of sky
dome covered (from meteorological data file)
2) n = total number of types of clouds
3) Compute albeuos for each type of clouo (= ai)
4) Compute total albedo for tnis hour, following tne
alternative methodologies defined as out: (see
argument aescription)
5) Return
131
NAME:
JWMFIT6
TYPE:
MAIN - Auxiliary
UPDATE:
August 1, 1979
DESCRIPTION:
Find values of P1 P2 P3 (from KT computation) such
ERR 2 is minimized (ERR = E/experimental that
Eo/computed)
SUBROUTINES:
CEOC2 is called
COMMONS:
/BLK1/
LOGIC:
1) Read meteological data and hourly experimental energy
flux values for clear days (days with no clouds or
obscuring phenomena)
/HBLK/
/PRSS/
2) Prompt for initial estimates of P1 P 2 P3
3) Prompt for accuracy desired
4) Vary parameters so as to minimize
5) Print the optimized parameters
6) Stop
132
(ERR) 2
NAME:
JWMTEST
TYPE:
MAIN - auxiliary
UPDATE:
August 1, 1979
DESCRIPTION:
Compares initial and final estimates of P1 P2 P3 and
prints (ERR)2 for both estimates
SUBROUTINES:
CEOC2 is called
COiMMONS:
/BLK1/
LOGIC:
1) Read meteological aata and hourly experimental energy
flux values for clear days (days with no clouas or
obscuring phenomena)
/HBLK/
/PRSS/
2) Prompt for initial and final estimates of P P2 P3
3) Compute (ERR) 2 for initial and final estimates of
P1 P2 P3
4) Print (ERR) 2 for initial and final estimates
5) Stop
133
NOMENCLATURE
A = parameter on the delination computation; in Appendix Al,
area
A0 = density integral of the atmosphere
A1 = relative atmospheric mass
b
= radiance in Appendix Al (Subsection 1.1) or brilliance
(Subsection 2.1)
D = geometrical day length
E - energy flux ensity; in Chapter 2, East; in Appendix Al
(Subsection 1.2), luminescence
ES = extraterrestrial solar energy flux density for average
Sun-Earth distance
ES
extraterrestrial solar energy flux
computed Sun-Earth distance
Eu = solar energy flux
ensity for daily
ensity on the ground
FO = irraoiance (integrated energy flux)
F0 = irradiance in the hypothesizeo absence of atmosphere
H
= equivalent height
I = energy as electromagnetic radiation
K = absorbance function of the atmosphere
KT = integral absorbance function of the atmosphere without
clouds
KT = integral absorbance function of the atmopshere with clouds
M = number of days in the month
M i = molecular weight of gas i
Mk = moist ratio
N
=
progressive number of the days of the year, first of
January N = 1
P
= pressure
134
R
= radius; in Appendix Al radiative energy intensity
(Subsection 1.1) or light intensity (Subsection 1.2);
Appendix A3 molar gas content
Ri
= gas constant of gas i
RD
= gas constant of dry air
RW
= gas constant of water vapor
S
= minutes of sunshine
S/D
=
T
= G.M.T. (Greenwhich Mean Time); in Chapter 1 and
Appenuixes absolute temperature
minutes of sunshine for interval time (hour or oay)
TDbK = dry-bulD temperature
TDp
= oew-point
V
= sensitivity factor (associated with the visibility curve)
w
= energy emission (electromagnetic waves) in Chapter 1;
otherwise, West
Wp
= light flux (photometric units)
W
= radiative tflux (radiometric units)
Z
= elevation Z
a
= albeoo
c
= 1 - S/D is the extensive factor of the cloud presence;
in Appendix Al, velocity of the electromagnetic radiation
e
= Earth orbit parameter
g
= acceleration of gravity
h
= altitude of the Sun; in Appendix A1, Planck's constant
h
r
= relative humidity
m
= mass
135
p =
local" factor of the KT expression; in eq. 2.1,
Earth orbit parameter and in eqs. 4.27, 4.28, and 4.29,
transparency coefficient of the atmosphere; in Appendix
A3, partial pressure
P1
=
intensive factor of depletion due to permanent components
of the atmosphere
P2
=
intensive factor of depletion due to precipitable water
P3 = intensive factor of depletion due to precipitable water
P4 = intensive factor of depletion due to "local" factors
r = number of rainy ays in a month
s
= generic beam direction abscissa
t
= solar time
tf = sunset time (solar time)
ti
sunrise time (solar time)
w - amount of precipitable water; in Appendix Al, radiative
tlux
zip
w,
a
x
= generic abscissa
total water vapor content in the atmosphere in the
vertical direction
z = zenith (vertical) axis abscissa
zo
elevation zo
Greek
a
v
angle of the "position triangle"; in Appendix Al,
absorpti vity
= angle of the "position triangle" (azimuth computation)
Y = angle of the "position triangle" (hourly angle)
y' = hourly angle value at sunrise (or sunset)
6
= aeclination
6o = daily averageu declination
c = emissivity coefficient
= angle between the Earth axis and the nor.?t to the plane
of the ecliptic; in Chapter 2 (Subsection 2.5) inclination
angle of an inclined surface
136
=
total cloud cover
n' = total opaque cloua cover
e = zenith angle
x = wavelength; in astronomical computations, longitude
= anomaly of the Earth in its orbit
w = 3.1415927
p = density; in Chapters 1 and 2, daily average value of the
Sun-Earth distance; in Appenaix Al, retlectivity
coefficient
p
= average between aphelion and perihelion of Sun-Earth
distance
a
= Stefan-Boltzmann's constant
T
= transmission coefficient
+ = latituae
+
= function symbol
= azimuth
A' = orientation angle of an inclined surface ("azimuth" of the
normal)
- = solid angle
Superscripts
= degrees
= minutes
Subscripts
U
= dry air
E
= Earth
i
= inciaent; in Appenoixes, i-th gas
137
1
= local
m
= meridian
M
= moist air
max
= maximum
S
= Sun
W
= water vapor
Z
= elevation Z
0
= zero
138
CONVERSION TABLE (in alphabetical order)
To convert from
Acceleration:
foot/sec 2
inch/sec 2
meter/sec 2
meter/sec 2
to
meter/sec 2
meter/sec 2
foot/sec 2
inch/sec 2
multiply by
(power
of 10)
3.048
2.540
3.281
-1
-1
0
3.937
1
9.290
6.452
2.590
8.361
1.550
1.076
1.196
3.861
-2
-4
1.056
4.185
4.185
3.600
9.470
3
0
3
6
-4
-1
-4
Area:
meter
sq. foot
sq. inch
sq. mile
sq. yard
sq. meter
sq.
sq.
sq.
sq.
sq.
sq. meter
sq. meter
sq. foot
sq. yard
sq. mile
sq. meter
meter
meter
meter
inch
6
-1
3
1
0
-7
Energy:
BTU
joule
calorie
kilocalorie
kilowatt hour
joule
joule
joule
joule
BTU
joule
joule
calorie
kilocalorie
Joule
Kilowatt hour
2.390
2.390
2.778
W/m2
W/m2
Wl/m 2
1.135
1.891
3.152
Energy/Area Time:
BTU/foot2 sec
BTU/foot 2 min
BTU/foot2 -hr
139
-7
4
2
0
CONVERSION TABLE (in alphabetical order) (continued)
To convert from
to
multiply by
(power
of 10)
Energy/Area Time: (continued)
BTU/inch 2 sec
W/m2
calories/cm 2 min
W/m2
W/cm 2
W/m2
W/m2
BTU/foot 2 sec
W/m2
BTU/foot 2 min
W/m2
BTU/foot 2 hr
W/m2
BTU/inch 2 sec
W/m2
calories/cm 2 min
W/m2
W/cm 2
Force:
dyne
kilogram force
pound force
1.634
6.973
6
2
1.000
8.811
5.288
3.1'73
4
-5
-3
-1
-7
-3
-4
6.120
1.434
1.000
Newton
Newton
Newton
1.000
9.807
4.448
Newton
Newton
dyne
1.000
0
5
kilogram force
1.020
-1
Newton
pound force
2.248
-1
centimeter
meter
meter
meter
mile
2.540
3.048
9.144
1.609
6.214
3.281
3.937
3.937
0
-1
-1
3
Length:
inch
foot
yard
mile
meter
meter
centimeter
millimeter
foot
inch
inch
140
-5
0
-4
0
-1
-2
CONVERSION TABLE (in alphabetical order) (continued)
To convert from
Power:
BTU/sec
BTU/min
calories/sec
calories/mi n
horsepower
watt
watt
watt
watt
Pressure:
atmosphere
bar
inch of mercury
(60-F)
inch of water
(60°F)
millibar
mm of mercury
(oC)
Pascal
torr (O°C)
N/sq. meter
N/sq. meter
N/sq. meter
N/sq. meter
N/sq. meter
N/sq. meter
N/sq. meter
to
multiply by
(power
of 10)
watt
watt
1.054
1.757
3
1
watt
watt
4.184
6.973
0
-2
watt
BTU/sec
7.460
9.488
2
-4
BTU/min
calories/sec
calories/min
5.692
2.390
1.434
-2
-1
N/sq. meter
N/sq. meter
N/sq. meter
1.013
1.000
3.377
5
5
3
N/sq. meter
2.488
2
N/sq. meter
N/sq. meter
1.000
1.333
2
2
N/sq. meter
N/sq. meter
atmospheres
1.000
1.333
9.872
0
2
-6
1.000
bar
inches of mercury (60'F) 2.961
4.019
inches of water (60°F)
millibars
1.000
°
7.502
mm of mercury (0 C)
7.502
torr (O°C)
-5
-4
141
1
-3
-2
-3
-3
CONVERSION TABLE (inalphabetical order) (continued)
To convert from
Temperature:
Fahrenheit
Fahrenheit
Celsius
Celsius
Rankine
Kelvin
to
Celsius
Kelvin
Fahrenheit
Kelvin
Kelvin
Rankine
142
multiply by
tc
=
(5/9)(tf - 32)
tk = (5/9)(tf + 459.67)
tf= (9/5)(tc) + 32
tk = tc + 273.15
tk = 5/9 tr
tr = 9/5 tk
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Solar