1

DOE/NASA/1022-78/28 NASA TM-78842

EVALUATION OF MODELS TO PREDICT INSOLATION ON TILTED SURFACES

Thomas M. Klucher National Aeronautics and Space Administration Lewis Research Center Cleveland, Ohio 44135

March 1978

Prepared for

U.S. DEPARTMENT OF ENERGY Div is ion of Solar Energy Under lnteragency Agreement E(49-26)-1022

NOTICE

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the United States Government. Neither the United States

nor its agent, the United States Department of Energy,

nor any Federal employees , nor any of their contractors,

subcontractors or their employees, makes any warranty ,

express or implied, or assumes any legal liability or

responsibility for the accuracy , completeness, or useful­

ness of any information, apparatus, product or process

disclosed, or represents that its use would not infringe

p r ivately owned rights.

1. Report No.

NASA TM-78842 I 2. Government Accession No. 3. Recipient's Catalog No.

4. Title and Subtitle

EVALUATION OF MODELS TO PREDICT INSOLATION ON TILTED SURFACES

5. Report Date March 1978

6. Performing Organization Code

7. Author(s) 8. Performing Organization Report No.

Thomas M. Klucher E-9556

~-------------------------------. 10. Work Unit No. 9. Performing Organization Name and Address

National Aeronautics and Space Administration 11. Contract or Grant No.

Lewis Research Center Cleveland, Ohio 44135

12. Sponsoring Agency Name and Address U. S. Department of Energy Division of Solar Energy Washington, D. C. 20545

15. Supplementary Notes

13. Type of Report and Period Covered

14. Sponsoring Agency Code

DOE/NASA/1022-78/2 8

Prepared wider Interagency Agreement E(49-26)-1022.

16. Abstract

An empirical study was performed to evaluate the validity of various insolation models which employ either an isotropic or an anisotropic distribution approximation for sky light when predicting insolation on tilted surfaces. Data sets of measured hourly insolation values were obtained over a six-month period using pyranometers which received diffuse and total solar radiation on a horizontal plane and total radiati~n on surf aces tilted toward the equator at 3 7° and 60° angles above the horizon. Data on the horizontal surfaces were used in the insolation models to predict insolation on the tilted surface; comparisons of measured versus calculated insolation on the tilted surf ace were examined to test the validity of the sky light approxima­tions. It was found that the Liu-Jordan isotropic distribution model provides a good fit to em­pirical data under overcast skies but underestimates the amount of solar radiation incident on tilted surface under clear and partly cloudy conditions. The anisotropic-clear-sky distribu­tion model by Temps and Coulson provides a good prediction for clear skies but overestimates the solar radiation when used for cloudy days. An anisotropic-all-sky model was formulated in this effort which provided excellent agreement between measured and predicted insolation throughout the six-month period.

17. Key Words (Suggested by Author(sl I

Solar radiation Insolation models

19. Security Classif. (of this report)

Unclassified

18. Distribution Statement

Unclassified - unlimited STAR Category 92 DOE Category UC -63d

20. Security Classif. (of this page)

Unclassified 21. No. of Pages

"For saie by the National Technical Information Service. Springfield. Virginia 22161

22. Price·

EVALUATION OF MODELS TO PREDICT INSOLATION

ON TILTED SURFACES

by Thomas M. Klucher

National Aeronautics and Space Administration

Lewis Research Center

Cleveland, Ohio 44135

SUMMARY

An empirical study was performed to evaluate the validity of various insola­

tion models which employ either an isotropic or an anisotropic distribution ap­

proximation for sky light when predicting insolation on tilted surfaces. Data sets

of measured hourly insolation values were obtained over a six-month period using

pyranometers which received diffuse and total solar radiation on a horizontal

plane and total radiation on surfaces tilted toward the equator at 37° and 60° angles

above the horizon. Data on the horizontal surfaces were used in the insolation

models to predict insolation on the tilted surface; comparisons of measured versus

calculated insolation on the tilted surface were examined to test the validity of the

sky light approximations. It was found that the Liu-Jordan isotropic distribution

model provides a good fit to empirical data under overcast skies but underestimates

the amount of solar radiation incident on tilted surface under clear and partly cloudy

conditions. The anisotropic-clear-sky distribution model by Temps and Coulson

provides a good prediction for clear skies but overestimates the solar radiation

when used for cloudy days. An anisotropic-all-sky model was formulated in this

effort which provided excellent agreement between measured and predicted insola­

tion throughout the six-month period.

INTRODUCTION

Flat plate solar heating/cooling or solar electric arrays in field applications are

usually oriented at a fixed tilt angle to maximize the solar radiation falling on the

array for the period of use. Occasionally, angle adjustments are provided to opti­

mize the insolation for shorter periods (i.e. , monthly or seasonally). Accurate

prediction of the tilt angle for best array performance is complicated, however,

by insufficient knowledge of the exact magnitude of solar radiation falling on

2

tilted surfaces. Estimates of insolation for a given array orientation and loca­

tion usually cannot be based on radiation data on tilted surfaces because such

data are generally not available. Instead, the historical data bases of climatic

variables, which include cloud cover, percentage of sunshine, and solar radia­

tion on horizontal surfaces, are generally used in combination with some inso­

lation model to estimate insolation on tilted surfaces. Selection of the tilt angle is then dependent on the procedures and approximations employed in the insola-

tion model. A number of insolation models have been developed which predict the amount

of solar radiation incident on tilted arrays from historical data of solar radia­

tion falling on a horizontal surface. Because of the variety and complexity of sky radiation, a common assumption made is that the diffuse component of solar

radiation (sky light) has an isotropic distribution (refs. 1 and 2) over the hemi­

spherical sky. This assumption conveniently allows the direct and diffuse com­

ponents on the horizontal plane to be corrected to total radiation on the inclined

plane by simple geometric relationships. However, it has been shown that sky

light is anisotropic in many instances and that the assumption of an isotropic

distribution may introduce significant error in modelling calculations for tilted

surfaces (refs. 3 and 4). Recently, a model for improving the diffuse radiation

approximation for clear skies was introduced by Temps and Coulson (reL 5);

simple correction terms were developed to account for the anisotropy of the

diffuse radiation field. Although the model gave good results for clear sky con­

ditions, it was not extended to the cases for partly cloudy and overcast skies.

The objective of th~ present effort (a part of the National Photovoltaic Con­

version Program established by the Department of Energy) was to test the

validity of certain insolation models which use either an isotropic or ani.so­

tropic sky light distribution approximation to predict insolation on tilted sur­

faces under cloudy as well as clear sky conditions. The approach taken to

achieve this objective was to establish a data set over a six-month period (January-June 1977) in Cleveland, Ohio, consisting of hourly average insola­

tion measured by pyranometers on horizontal and inclined planes. Total and

diffuse radiation data i.n the horizontal plane were utilized in the Liu-Jordan

insolation model (reL 2) to predict insolation falling on tilted surfaces under

the assumptionof isotropic sky light. The,isotropic model was then modified by

the Temps-Coulson clear-sky (ref. 5) c:orrection terms to evaluate that aniso­tropic model under all sky conditions O Finally, th~ anisotropio-clear-sky model

was modified when it was found inadequate to account for cloudy sky conditions.

3

Evaluation of the validity of the three models was made by comparing the solar

radiation measured on the tilted surfaces with the radiation predicted by each in­

solation model.

APPARATUS AND MEASUREMENTS

The test facility used to measure, catalog, and process the hourly solar

irradiance data has been previously described in reference 6. Figure 1 shows

the details of sensor orientation. Three precision pyranometers measure total insolation received at o0

, 37°, and 60° tilt angles facing due south. The diffuse component is measured by a fourth pyranometer horizontally mounted (0° tilt)

and equipped with a black shadow band to block out the direct radiation compo­nent. The amount of diffuse radiation which is screened by the shadow band

was added to the measured values by application of a correction factor recom­mended by Drummond (ref. 7). The pyranometers tilted at 37° and 60° were

equipped with black metal artificial horizon bands, which prevented any radia­

tion reflected from below the horizon from reaching the sensors. Each pyranometer was corrected to a voltage-controlled oscillator and a

counter which integrated the data continuously. The integrated data were moni­tored every hour and time averages of the hourly data were obtained for evalua­

tion.

METHOD OF ANALYSIS

The starting point for the evaluation of insolation models was the isotropic

sky model described by Liu and Jordan in reference 2. In this model, the inso­

lation on a surface tilted toward the equator at an angle e to the horizontal is

given by:

(I - I ) ~ ~ I = H D cos l/J + I 1 + cos e T sin a D 2

\. I\ I

"""""" """"" Direct radiation

Diffuse

radiation

(1)

4

where

IT total insolation received by tilted surface

IH total insolation received by horizontal surface

In diffuse insolation received by horizontal surface

a solar elevation angle

¢ angle between sun direction and normal direction

e tilt angle above horizon of tilted surface

In this effort the insolation terms inserted into equation (1) were hourly average

values of insolation obtained from sunrise to sunset during each day. The geometric terms, cos ¢ and sin a, were hourly average values cal­

culated from well established geophysical and astronomical equations (refs. 2 and 8). The insolation IH and In were measured by the pyranometers and used in equation (1) to calculate the total insolation received on the surfaces tilted at 37° and 60°. These calculated insolation values were then compared with the in-

o O '• solation IT measured at 37 and 60 to determine how well the Liu-Jordan model

predicted the insolation on each tilted surface. The data were also compared with the anisotropic-clear-sky model developed

by Temps and Coulson. In their model Temps and Coulson combined three cor­

rection factors with the isotropic diffuse radiation term to account for each of three regions of anisotropy in the diffuse radiation field. They determined that a factor, 1 + sin 3(£/2), accounts for the increase in sky light observed near the

horizon during q\ear days; similarly, sky brightening near the sun could be ap­proximated by the factor 1 + cos2

l/J sin 3 (90 - a). A third factor which accounts

for surface reflection enhancement is not included in this report because this effect was eliminated by the· horizon shades previously described. Applying the Temps and Coulson correction terms to the Liu-Jordan model, then, the aniso­tropio-clear-sky model has the form:

Here again, measured values for radiation on tilted surfaces were compared to those calculated from measured values of total and diffuse radiation on horizontal surfaces to determine the fit of the model.

5

The final model evaluated was an anisotropic model developed in this effort

based upon preliminary results found with the previous two models. This last

model involves an adjustment to the Temps-Coulson factors by a simple function

containing the ratio of diffuse to total insolation on the horizontal plane. As will

be shown in the RESULTS AND DISCUSSION, the Liu-Jordan model worked well

for overcast days and the Temps-Coulson model worked well for clear days. The purpose of the new function was to modulate the Temps-Coulson factors as the skies varied from clear to overcast. This anisotropic, "all sky" model thus takes the form:

where F is the modulating function described above. Two slightly different

functions, F = 1 - ID/IH, and F = 1 - (ID/IH)2, were studied in the all-sky model.

Under overcast conditions, when the ratio of diffuse to total insolation, ID/IH' is unity, the all-sky model, using either "F", reduces to the Liu-Jordan isotropic model. Under clear sky, when the ratio of diffuse to total is observed to be small, the all-sky model approximates the Temps-Coulson anisotropic-clear-sky

model.

RESULTS AND DISCUSSION

Comparison plots of hourly measured versus calculated solar irradiance at 37° and 60° tilt angles were made for each month and each model to determine

how well each model predicts insolation on a tilted surface. A total of 48 plots

were examined for the six-month period from January to June 1977. In the inter­est of clarity, selected plots of the monthly data were chosen from this group for

discussion of the major results of this effort. A complete set of monthly plots for the three models are shown for comparative purposes at the end of the report

(figs. 16 to 27) • Figures 2 to 7 illustrate the results of the application of the Liu-Jordan model

to the prediction of solar radiation falling on the tilted sensor for the months of January, March, and June for 37° and 60°. Inspection of e~ch plot indicates that

the model provides a good fit to the empirical data at the low intensity conditions (<20 to 30 mw /cm 2); this might be expected, since the low intensities are primar-

6

ily associated with the occurrence of overcast sky conditions, little direct inso­

lation, and uniform diffuse sky radiation. In additton, each of the plots also demonstrate a nearly linear correlation between computed and measured insola­

tion. At the higher intensities (>50 mw /cm 2), however, figures 2 to 7 illus­

trate that the Liu-Jordan model underestimates the amount of solar radiation

falling on tilted surfaces. This error is greatest in January - about 5 mw /cm2

at 37° and 8 mw /cm 2 at 60° tilt angles - and decreases to about 3 mw /cm2 in

June. These results clearly demonstrate that the isotropic sky model is defi­

cient in predicting insolation on tilted surfaces for nonuniform (clear and partly

cloudy) sky conditions. Figures 8 and 9 illustrate typical results obtained when comparisons of mea­

sured and calculated insolations are made using the anisotropic-clear- sky model of Temps and Coulson under partly cloudy and overcast, as well as clear-sky conditions. Data for days on which the sky was observed and recorded as clear and basically cloudless were inspected as an initial check of the Temps-Coulson

regression model for clear days. The comparison for clear days in MaTch (figs. s. and 9) were very good; the hourly data were found to fall along the 1:1

correlation line in the figures, indicating a good fit between measured and pre­

dicted clear-sky insolation. Such good comparisons for clear-sky data were

found to be true throughout the six-month period of this eff<~rt and confirm the results of Temps and Coulson. On the other hand, during no.nclear days, the

comparison plots demonstrate that application of the Temps-Coulson corrective

terms to overcast and cloudy conditions often result in an overestimate of the

solar radiation falling on a tilted surface. Figures 8 and 9 show predicted val­ues exceeding measured by as much as 10 mw /cm2; such overestimates are greater than 10 mw /cm 2 in winter and smallest in summer. In their report,

Temps and Coulson speculated that their sky model might improve modeling

predictions for scattered cloud conditions, but would not give good results for heavily clouded and overcast skies. The'. results in .thi's six-month study are con­

sistent with their expectations. Comparison plots of the anisotropic-all-sky insolation model are shown in

figures 10 to 15. The model using parameter F = 1 - (In/IH>2 in equation (3) was chosen because it provides a slightly better fit to the empirical data than

does the linear parameter F = 1 - In/IH.

The primary effect of correction terms in the all-sky model was a reduction

in the systematic error previously observed in the January and March plots of the Liu-Jordan model. For example, the systematic error in January is reduced to

7

less than 2. 5 mw /cm2; similar reductions also occur in the March plots. In

June, when the Liu-Jordan model has a good fit to the measured data, the two

models appear to fit equally well. Comparisons between the Temps-Coulson clear­

sky model and the all-sky model also demonstrate the effect of the correction

terms used in the all-sky model. While the error in January to June plots are

less than 2. 5 mw /cm2 in the all-sky model, the errors in the Temps-Coulson

model results range from about 12 mw /c~2 in January to 3 to 5 mw /cm2 in June during nonclear days. Since the accuracy of first-class pyranometer mea­surements is, at best, ,::2 mw /cm2

, the all-sky model is considered to fit well for the six months studied. Thus the anisotropic-all-sky model formulated in

this effort provides a better prediction of solar radiation on tilted surfaces than either the isotropic or anisotropic-clear-sky models.

CONCLUSIONS

As a result of the study of three insolation models which predict the solar

radiation incident on tilted surfaces from measured values of total and diffuse

radiation on a horizontal surface, the following conclusions were formed: (1) The commonly used Liu-Jordan isotropic-sky insolation model provides

a good fit to empirical data at low intensity conditions found during overcast

skies; however, the model underestimates the amount of solar radiation falling

on tilted surfaces at intensity levels above about 5gmw /cm 2

. In this effort the error is about 3 mw /cm2 in June and rises to 5 to 8 mw Lm2 in January. e, ..... 1,..

(2) The anisotropic-clear-sky model of Temps and Coulson provides a good

correlation between measured and predicted insolation on tilted surfaces for the case of clear skies. However, this model overestimates the insolation for

mostly cloudy and overcast conditions by as much as 12 mw /cm 2 in January and from 3 to 5 mw/cm2 in June.

(3) The anisotropic-all-sky model formulated in this effort provides a better

prediction of solar radiation on tilted surfaces than either the isotropic or

anisotropic-clear-sky models. The systematic error between measured and

predicted insolation resulting from the application of the anisotropic-all-sky

model is less than 2. 5 mw /cm2

.

8

REFERENCES

1. Liu, Benjamin Y. H.; and Jordan, Richard C.: Daily In.solation on Surfaces

Tilted Toward the Equator. ASHRAE J., vol. 3, no. 10, Oct. 1961,

pp. 53-59.

2. Liu, Benjamin Y. H.; and Jordan, Richard C.: The Long Term Average

Performance of Flat-Plate Solar-Energy Collectors. Sol. Energy, vol. 7,

no. 2, 1963, pp. 53-74.

3. Kondratyev, K. J.; and Manolova, M. P.: The Radiation Balance of Slopes.

Sol. Energy, vol. 4, no. 1, Jan. 1960, pp. 14-19.

4. Dave, J. V.: Validity of the Isotropic-D~stribution Approximation in Solar

Energy Estimations. Sol. Energy, vol. 19, no. 4, 1977, pp. 331-333.

5. Temps, Ralph C.; and Coulson, K. L.: Solar Radiation Incident Upon Slopes of Different Orientations. Sol. Energy, vol. 19, no. 2, 1977,

pp. 179-184.

6. Klucher, Thomas M.: Test Facility for Solar-Cell Reference Conditions.

Terrestrial Photovoltaic Measurements - II. NASA CP-2010, 1976,

pp. 67-77.

7. Drummond, A. J.: Comments on "Sky Radiation Measurement and Cor­

rections". J. Appl. Meteorol., vol. 3, Dec. 1964, pp. 810-811.

8. IGY fustruction Manual, Pt. VI, Radiation Instruments and Measurements.

Ann. Int. Geophys. Year, vol. V, 1958, pp. 371-466.

·11

South

Artificial horizon bands

Artificial horizon bands

6rP Tilt pyranometer

37° Tilt pyranometer

Horizontal pyranometer

Figure 1. - Sensor orientation.

Horizontal pyranometer with shadow band

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CALCULATED INSDLATIDN.11 HW/50 C/1

Figure 2. - Comparison between measured and calculated insolation on a tilted surface using the liu-Joroon isotropic-sky model.

JAN 't JAN 31 1977

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¢ ¢

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Figure 3. - Comparison between measured and calculated insolatlon on a tilted surface using the Llu-Joroon Isotropic-sky model.

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Figure 4. - Comparison between measured and calculated insolation on a tilted surface using the Liu-Jordon isotropic-sky model.

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Figure 5. - Comparison between measured and calculated in solation on a tilted surface using the Liu-Jordon isotropic-sky model.

12.9

11.9 JUN JUN 3.0' 197?

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Figure 6. • Comparison between measured and calculated insolation on a tilted surface using the Liu·Jordon isotropic·sky model.

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Figure 9. - Comparison between measured and calculated insolation on a tilted surface using the Temps-Cou Ison anisotropic-clear-sky method.

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Figure 10. - Comparison between measured and calculated lnsolatlon on a tilted surface using the anisotropic-all-sky model.

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Figure ll. - Comparison between measured and calculated insolation on a tilted surface using the anisotropic-all-sky model.

1·

12.11'

II.II' MAR MAR 31 1977

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I

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Figure 13. - Comparison between measured and calculated insolation on a tilted surface using the anisotropic-all-sky model.

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Figure 14. - Comparison between measured and calculated insolation on a tilled surface using the anisotropic-all-sky model.

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Figure 15. - Comparison between measured and calculated insolation on a tilted surface using the anisotropic-all-sky model.

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.. 5,1

t•

.. u

, . .

"' .... .. .. IU' IU'

CALCULATED JNSDLAT!ON1 MN/SO CH

lei Anisotropic • all•sky model.

Figure 16. - Comparison between measured and calculated lnsolatlon on a tllled surface for each sky model,

,,.

"' :a:: .. , l)

c:, Vl

~ ,.

:a:: u

:;; Cl .... '-s,: -.J Cl Vl <: .. Cl l;J

"' :::, Vl s,: l;J

,. 'IC:

..

JAN. 4 JAN ll 1977 lilDEG. TILT

. . ~ .. JI> . •.

I!,·· ,1 'l>O

'

\al lsotrc~:llc - sky model.

'IC: l)

c:, c,

~ :a::

:;; Cl .... ..... '<

c3 Vl <: .... c::, l..J

"' :::, Vl

' l..J :a:

Q • . ... !'

.

... ... '"

JAN. 4 JAN )l 1977 lilOEG. TILT

'l,Q

'* Q .

. Q •

oo\ 'I, t>

0 • "' ··;··~ ~ ti,• ~

(#' 0 .. "

,. .. ..

..

.. ,. .. bl Anisotropic - clt..1r·sky model.

JAN. 4 JAN Jl 1977 6Cl DEG. IILT

Q . ' . .s Q

CII LCULIITEO INSOL ll {!ON , N/./ /50 C /1

tel Anisotropic • all·sky model.

figure 17. - COnparison betwt«I mtiasuredand calculated ln~ation on a tilted surtac.e tor e.xh sky model.

. i.

" Q ..

" ... ...

ll•

11•

::t: IR (.)

Q

:('. =l: ::t:

~ c:i ,. ..... ._ <t: -.J c:i V)

~ ..... c:::i l.u .. Cl:: ::::i V)

st .. l,J ::t:

u

1•

l

\:;,J,

FEB FEB 28 1'117

37 DEG. TILT

<>~ o.V;oo <>·

o/ ~/

f/!,·'<>"o ~~

.J ~/$ <>

:,'1 <>

' ~ <> ..

la) Isotropic· sky model.

~ ID (.)

Q

:('. =l: ::t: ..

<: c:i ..... ._ st

~ ..

V)

~ s.o ..... Cl l.u .. Cl:: ::::i V)

st lJJ ::t:

FEB FEB 28 I'll?

37 DEii. TILT

9t,9 ($0

,<>

lb) Anisotropic· clear-sky moclel.

CALCULATED /NSOLAT/ON• HU/SQ CH

!Cl Anisotropic • all-sky model.

Figure 18. • Comparison between measured and calculated insolatlon on a tilted surface for each sky model.

1n

111 lsotrq,lc • sky model.

~ (.)

~

\ ~ ~

~ C) ..... ..._ <c .... C) I.I') ~ ......

C) llJ ~ ::::i I.I')

<c u \oJ ~

zir

l'fB l'EB is 1971

6S DfG. TJI.T

•• .. ..

CALCULATED JNSOLATION, H~/SO CH

ICI Anlsotfqllc • all-$1cy modal,

Figure 19. ~ COmparlson betwHn mrasured and calculated lnSOlallon on I tllled surface for each ~ model.

,. ..• ..• . ..

._)

0' I

f;r)

,a

MAR l MAR 31 1977

JI DEG. Tlll

(a I Isotropic - sky model, !bl Anisotropic - clear-sky model,

MAR I MAR 31 1'117

~ ·~~ (.J

C) U)

\ ::i: ~ .. -

~ C:) "'-.

'-<,:

~ .a

U)

~ c::: l..J ~ :::, U)

' LJ ::;,:

C-1LCUL4TtD l~SDL''IT!DNi M;,//50 C"1

tel Anisotropic - all-sky model.

Figure 20. - comparison between measured and calculated insolation on a tilted surface for e.1ch sky model.

IU

11• ltAR NAR NM! 31 1977

t,.J :JE,;. blil DEG. TILT )::;: 1.a c..,

~

\ ,.

~ ~ .. .. < C) ,. ..... "-sq:; ..... .. C) Vi < s, ..... c:i ll.i .. Cl:: :::i V') sq:; ,. l..aJ ~

u

..

. ,. .. ,. .. ... '" 121 ,... ... ,,.

lal lsotrq>lc - slcy model. t>I Anisotropic - clear--sty model. ,u

11, NAR NAR 31 19;;,

6/J DEG. TILT ~ lff c..,

~

\ ,. ~ ~ .. < c:i ,. ..... "-sq:; ..... .. C) V'J < u ..... c:i ll.i Cl:: :::i V'J sq:; ,. l..aJ ~

u

.. .. 211 u .. u .. .. ... •i•

CALCULATED !NSOLA T IONP HJ.I/SQ CH

!cl Anisotropic • all-sty model.

Figure 21. • Comparison between mmured and calculated lnsolatlon on a tilted surrac:e for each sky 1111del.

,u

/ ... APR APR 3.IJ ,,n APR Al'R 3.0' 1'71

31 om. TI l T 37 OfG, TILT

lff

tal Isotropic· sky model. lbl Anisotropic • c11111r-sky model.

APR APR 38 I '117

3? DEG, TILT

CAL CUL/! TEO IN.,DL/i T JON• !11.//SQ CH

tel Anisotropic • all-sky model.

Figure 22. - Comparison between measured and calculated insolation on a Ii tied surface for each sky model.

APR APR '3B 1'1?7

6B OEG, TILT

(al lsotrcplc - sky model.

,.

APR APR 3.0 1'177

6B DEG, Tl LT

CALCULATED JNSOLATIDN9 HW/50 CH

lcl Anisolropic - all-sky model.

Ill Anisotropic - clear-sky model.

Figure 23. - Comparison between measured and calcu laled insolatlon on a ti fled surface for each sky model.

,()

LJ ;_ l

tal Isotropic - sky model. lb) Anisotropic - clear-sky model.

MAY MAY 31 1977

U JU

CALCULATED JN5DLATIDN9 NW/SQ CN

lc) Aniwtropic - all-sky model.

Figure 24. - Comparison between measured and calculated insolation on a tilted surface for each sky model.

~ (.,)

Qi

\ ::.: ~ .. "' <':

C) , . ..... '-"C -.J C) I.I)

<: SIJ .... t:) l.lJ ct :::i I.I)

"C .. ll.i ~

u

..

Cal Isotropic· sky model. Ill AnlsolJ'oplc - clear-sty IIIOdll.

~ (.,)

Qi

\ ::.: ~

~ C) ..... '-"C ...... C) I.I) <: ..... t:) lU ct :::i vi "C lU ~

in

... , . .. ,.

n

CALCULATED JNSOLAT!ON• HW/50 CH

tel Anisotropic - all-sty model.

Figure 2S. • Comparison bttween measured and ca!eulaled lnsclallon on a Hlled surface for each sty model.

,() :...l L) (}'

I

f.r~

~ C.)

Cl

~ ::i: ~

< C) .... "-

" c5 V)

< .... c:i ,.._, Cle ::::i V)

" l.t.r ~

,.

.. .• ..

JUN JUN 3.3 I "li7

3? DEG. TILT

u .. 1a1 Isotropic - sky model. lbl Anisotropic - clear-sky model.

...

... .JUN JmJ 3.3 1<Jn / 3? OfG, TILT

~ C.)

Cl V)

~ ~

~ ~ .... "-

" ~ V)

< .... Cl lJ.J t• Cl,,: ::::i V)

<C ,.

,.._, ~ ..

CALCULATED /NSOLATIONP HW/50 CH

(cl Anisotropic - all-skv model.

Figure 26. - Comparison between me.1sured and calculated irisolatlon on a tilted surface lor each sky model.

:t:. C..)

la) Isotropic - sky model. Gl> Anisotropic - dear-sky model.

IU

JUN ,JUtl 3H 1'177

6H orr,, f!LT

CALCULATED !NSOLATJONP NN/SQ CH

IC) Anisotropic - all-sky model.

Figure l1. - Comparison between measured and calculated insolatlon on a tilted surface lor each sky model.