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P e r g a m o n

Solar Energy, Vol. 54, No. 3, pp. 1X3-191, 1995Copyright 0 1995 Elsevier Science LtdPrinted in the USA. All rights reserved

0038-092X195 $9.50 + .OO

0038-092X( 94)00116-2

SOLAR RADIATION RESOURCE ASSESSMENTBY MEANS OF SILICON CELLS

L. ALADOS-ARBOLEDAS, F. J. BATLLES,** and F. J. OLMO*Grupo de Fisica de la Atmbsfera; Dpto de Fisica Aplicada, Universidad de Granada, 1807 1, Granada.

Spain; * *Dpto de Fisica Aplicada, Universidad de Almeria, 04120, Almeria, Spain

Abstract-To provide an accurate solar resource assessment, radiometric stations measuring global, diffuse,and direct irradiance must be widespread. Nevertheless, the high capital costs of thermopile instruments,usually used in pyranometry, represent an important obstacle. Therefore, silicon photovoltaic sensors haveemerged as a more accessible alternative than standard thermopile sensors. However, their temperature andspectral responses must be taken into account in order to match silicon cells and thermopile responses.Global and diffuse u-radiance have been measured from early 1990 to the end of 1992 in Almeria, southeast-em Spain, by means of thermopile and photovoltaic sensor. Polar axis shadowbands were employed tomeasure the diffuse irradiance. These IO-minute coincident data sets, covering a complete range of atmo-spheric conditions, have been used to develop a correction procedure for the silicon detector measurements.Before the correction procedure was applied severe discrepancies were found, especially for the diffuseirradiance measurements performed under clear skies. Results of the correction method applied to anindependent data set show a remarkable improvement. After correction, the comparison of silicon cellmeasurements with those obtained by means of thermopile pyranometers leads to a root mean squaredeviation of about 4% and 5% over the mean value of global and diffuse horizontal irradiance, respectively.

1. INTRODUCTION

To find the value for different solar energy applica-tions an accurate solar radiation resource assessmentis necessary. This assessment would include informa-tion on the three components of solar radiation, thatis, global, diffuse, and direct solar irradiance. This isespecially true for applications that rely on the inter-ception of solar radiation by inclined surfaces.

A monitoring station typically measures only twoof the solar irradiance components and calculates thethird. However, the measurements of diffuse hori-zontal irradiance and direct normal irradiance are notwidespread due to the high cost of the instruments andthe necessity of periodical maintenance. The use of apyranometer with a polar axis shadowband to measurethe diffuse horizontal irradian ce, placed side-by-sidewith another pyranometer, to measure the global hori-zontal irradiance, provides the cheapest alternative formeasuring the three solar radiation components, ob-taining the third by means of the relationship:

Gd = G - G, cos 0, (1 )

where G is the global total horizontal irradiance, Gbis the direct normal irradiance, Gd is the diffuse hori-zontal irradiance, and 0, is the zenith angle of the sun.

Instruments measuring solar radiation may be clas-sified as thermal sensors and photovoltaic (PV) sen-sors. Photovoltaic radiation sensors provide the sim-plest and cheapest alternative. The photovoltaic detec-

* ISES members.

tors have time responses of about 10 /s. This factmakes these sensors appropriate for measuring rapidsolar radiation changes associated with intervals w henclouds move in front of the sun (Kerr et al., 1967;Licor, 1991 ; Michalsky et al., 1987; Pereira and Souza

Brito, 1990 ). Among other interesting features of pho-tovoltaic pyranometers are their stability, ruggedness,and tolerance to soiling. These combined featuresmake pyranometers suitable for use in severe environ-ments. Nevertheless, using PV cells as radiation sen-sors poses problems associated with the limited andnonun iform spectral response of silicon cells. A sec-ond-order problem with these sensors is their thermaldependence (about 0.15% per C) which could causea relevant change in sensitivity on mid-latitude regions(Michalsky et al., 1987).

Therm al sensors, on the other hand, are widely

used to measure solar radiation due to their nearlyconstant spectral sensitivity for the whole sola r spec-tral range. These devices have received a great dealof refinements and, thus, modem thermopile radiation

sensors are built with temperature compensating cir-cuits that reduce the error caused by changes in theambient temperature. However, the time constant ofthermopile is typically in the order of 1 to 10 s. and,therefore, are unable to follow rapid changes of radia-tion associated with clear/cloudy transitions duringpartly cloudy conditions. Consequently, significantmeasurement errors occur during the transition period.With integrated measurements, the errors associatedwith the slow response time tend to cancel, however,significant errors are introduced with instantaneousmeasurements (Suercke et al., 1990)

183

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184 L. ALADOS-ARBOLEDAS,F.J. BATLLES,~~ F.J.OLMO

3ca 400 yx) 1000 2cw xoo ac.l YYYJ

Wavelength (nanometers)

Fig. 1. Silicon pyranometer and thermopile pyranometer spectral responses. 1 = Spectral distribution ofsolar radiation at sea level for a 1 air mass. 2 = Relative spectral response for thermopile pyranometer

(Kipp & Zonen CM- 11) . 3 = Relative spectral response for photovoltaic sensor (Licor 200~SZ) .

A common problem for both kinds of sensors, sili-con cells pyranometers and thermoelectric pyranomet-ers, is associated with their cosine response at highangles of incidence, with wors e results for siliconcells. Neve rtheless, this difficulty is partially correcte dby placing a diffusing disk over the photodiode (Licor,1991).

As indicated, the spectral respons e of the siliconphotodiode does not extend uniformly over the fullsolar radiation range. A typical respons e c urve for theLicor silicon p yranom eter is presented in Fig. 1. Thesolar spectrum at surface level with a 1 air mass isincluded for reference purpose . Allowing for this Fig-

ure and the fact that the Licor silicon pyranometers arecalibrated outdoors against a thermopile pyranometer(Licor, 1991), it is found that the spectral responseproblems will be associated with a changing solarspectrum. The major change in the solar global spec-trum occurs in the infrared range where water vapourabsorption takes place. This change in the infraredrange is in opposition to the remarkab le constancy inthe spectral distribution of global irradiance for thevisible range. Nevertheless , spectral distributionchanges in the diffuse irradiance are more importantand especially affect the visible region o f the spec-

trum.This study discusses the limitations of silicon pho-

todiod es in performing irradiance measurem ents tradi-tionally mad e with thermo piles and correction proce-

dures that improve the level of accordance betweenthe two radiometric techniques. The goal is to suitsilicon cells for radiome tric observations by derivingempirical correctio ns to simulate thermopile sensors.The results o f a comparison between a set of photodi-odes are presented: one is equipped with a polar axisshadowband and a similar set of conventional thermo-pile instruments. A previous wor k( Alados-Arboledase t a l . , 1992) has addressed these questions using amore limited data set. The present study has beenenriched by the use of a more com plete data set andthe test performed over different integration periods.

2.DATA

Experimental data were recorded at Almeria,Spain, a seashore location (36 .83 N, 2.41W). Twophotovoltaic pyranom eters (Licor 200-SZ), one witha polar axis shadowband and another without it, wereused to do the silicon sensor measurements for diffuseand global com ponents, while an identical set of ther-mopile radiometers (Kipp & Zonen CM -l 1) wereused as a reference. According to the classification ofthe World Meteorological Organization ( 1983) the

CM- 11 pyranometer is a secondary standard. Othermeasurem ents included in the radiome tric station arethe air temperature at 1.5 m and the inner temperatureof an Eppley pyrgeometer.

Table 1. Licor versus CM-l 1 irradiances, lo-minute values

(W:-) b RMBD RMSD

(Wm-*) (Wm-)

Global uncorrectedLicor -7.2 1.006 0.999 -4.4 13.3

Global T,. corrected

Licor -6.1 1.009 0.999 -2.3 12.1Diffuse uncorrected

Licor -11.7 0.989 0.992 -13.8 16.8Diffuse T,. corrected

Licor -11.7 0.990 0.993 -13.1 16.3

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Solar radiation resource assessment 185

Table 2. Licor T,, corrected versus r. corrected.lo-minute values

tW:-) bMBD Rh4SD

R (Wm-*1 (Wm-7

Global 0.3 0.999 1.ooo -0.4 3.1

Diffuse 0.0 0.999 l.ooo -0.1 0.2

Data from all instruments were averaged and storedevery 10 minutes. Measurements used in this workbegan in early 199 0 and finished at the end of 1992.Thus, a complete range of temperatures and solarangles was included among the samples taken. Analyt-ical checks for measurement consistency were appliedto eliminate problems associated with shadowbandmisalignments and other questionable data. This studyonly used cases at a solar zenith angle of less than8.5. About 50 ,000 lo-minute values are available in

total. Measurements of solar global irradiance have anestimated experimental error of about 2-3%.

The whole data set has been divided into twogroups to develop the empirical correction procedure.The first group, including two-thirds of the total, hasbeen used for model development, whereas the re-maining one-third has been reserved for validationpurposes.

3. CORRECTION PROCEDURE AND RESULTS

The first problem that must be addressed is the

temperature dependence, Michalsky et al. ( 1987) pro-posed to normalize photodiode response at a standardtemperature of 30C using an empirically developedexpression:

R/Rx

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18 6 L. ALADOS-ARBOLEDAS,. J. BATLLES,nd F. J. OLMO

Table 3. Boundaries for the correction parameters

Parameter Boundaries

E 1.45 2.10 4.30 6.40A 0.090 0.135 0.185 0.2708, (decrees) 75 60 50 35

tions of the silicon pyranom eter, the scheme p roposedby Michalsky et al. ( 1991) has been followed. There-fore, a silicon efficacy has been derived, th at is,the ratio of thermopile pyranometer response to siliconpyranometer response. The silicon efficacy matchesthe silicon pyranometer with thermopile pyranometersmeasurem ents. This correction factor is influenced bythe sky conditions and, thus, the data is categorizedaccording to the clearness of the sky, the brightnessof skylight, and the solar zenith angle, as it is donein Perez et al . (1990). The sky clearness parameter,

denoted E, depends on cloud and aerosol amount, de-fined by:

E = ((G,, + G,,,)/G,, + 1.0416:)/(1 + 1.0418:)(3 )

where subindex u denotes uncorrected values mea-sured with the silicon pyranom eter, and Gbu is uncor-rected direct normal irradiance evaluated with diffuseand global uncorrected values. The skylight brightnessparameter, denoted A, depends on the aerosol burdenand the cloud thickness and is defined by the relation-

ship:

A = Gdu/(Gbacos 0,) (4 )

whe re Gbo is the extraterrestrial solar irradiance inWm-*. The third parameter in the model is the solarzenith angle, which defines the suns position in thesky hemisphere.

Table 3 contains the boundaries for the five binsof each parameter. T hese boundaries are chosen insuch way that real cases of each parameter were evenlydistributed. The boundaries in E and A are different

from those considered in the Michalsky et al. ( 1991)study where a rotating shadow band radiometer wasused due to the inherent differences between the twomeasuring techniques with respec t to diffuse irradi-ante. The rotating shadowband radiometer performsa real time correction for the amount of sky radianceblocked by the shadowband when making diffusemeasurement because shadowband measurements arenot corrected at this stage.

For each member of a bin, the ratio of the thermo-pile irradiance measurem ent to the correspond ing sili-con cell n-radiance measurem ent has been calculated.The mean of these ratios is used as a correction factorfor any subsequent silicon cell irradiance measure-ment with parameters falling within the bounds of theassocia ted bin. In this way two sets of correction fac-tors have been obtained: one for global and anothe r

for diffuse horizontal irradiance. Two -thirds of the lo-minute data has been used for this purpose, applyingthe correction model to the remaining one-third of thedata, with two different integration periods, 10 minand 1 hour.

Figure 3 shows the 3D diagram for the diffusecorrection factor in the E- A sp ace for a given valueof cos 8,, whic h is a visualization of a correctionmatrix, included in the Appen dix. The general behav-iour for the diffuse correction factor suggests the ne-cessity of increasing these measurements under E andA conditions associa ted w ith clear conditions. Thisfact is partially explained by the spectral ch aracteris-tics of diffuse irradiance under clear (blue) skiesand the calibration performed by Licor. On the otherhand, the performance of the global correction matrixshow s a more limited range and an inverse behaviour:The clear sky measurements must be reduced to matchthe thermopile measurements. Under cloudy and tur-

bid conditions, a slight increase in global silicon mea-surements is necessary, which is lesser for overcastconditions.

The non-ideal cosine response of the Licor pyrano-meter leads to an increase of the correction term forlow elevation angle as shown in the Appendix. Thisis specially evident for global correctio ns.

4. CORRECTIONPERFORMANCE

Figure 4 shows before and after correction plots ofthe diffuse and global irradian ce for a sequence of

days covering different sky conditions ranging fromclear to overcast conditions. According to the size ofthe correction factor that we found in the matrix in-cluded in the Appen dix, global horizontal irradianceneeds very little correction. The agreement for bothclear and cloudy conditions is good and the corrected

Fig. 3. Diffuse correction factor 3D diagram as a functionof E and A for 60 < 0, < 15.

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Solar radiation resource assessment 18 7

- THERMOPILE- - SILICON UNCORRECTED

------ S I L I C O N C O R R E C T E D

TIME

Fig. 4. Global and diffuse measurements during 3 different days

data overlap thermopile data, although they also arevery close to the uncorrected data (only temperaturecorrected).

The cloudy and clear behaviour is very differentfor the diffuse irradiance. Under cloudy conditions the

corrected and uncorrected data are very close, butthere is a considerable disagreement for clear condi-tions. There is a very close correspondence betweenthermopile and silicon cell diffuse irradiance data afterthe latter are corrected. The effect is especially im-portant taking into account the common scale usedboth for global and diffuse data which indicates a highrelative error in diffuse irradiance measurements in

1200, I / I1 I,, I,, I / I I, I, ,n

I I I1 I I I I1 I I ,a I I,, I,,,,

THERMOPILE (W/m) Ooo 1200

absence of spectral correction. Obviously, these re-sults take into account the previous comments on thepattern shown by the correction matrix and are directlyrelated w ith the spectral distribution of global anddiffuse irradiance under different sky conditions.

Figure 5 shows the scatter plots of the silicon ver-sus thermopile pyranometers after temperature correc-tion by means of eqn 2, using the inner pyrgeometertemperature. Global measurements show a goodagreement, while the diffuse measurements show amarked tendency to underestimation, specially in clearconditions, that is, for low values of diffuse irradiance.Table 2 shows the discrepancies between the two data

600,,,,,,,,,,,,,,,,,,,,,, /,I n

/N- TI CORRECTED DIFFUSE

EY -117 + 0989 x

\ 500 R 0992

Fig. 5. Silicon pyranometer versus thermopile global and diffuse irradiances after temperature correction(T, corrected), lo-minute values.

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188 L. ALADOS-ARBOLEDAS,. J. BATLLES,nd F. J. OLMO

Table 4. Licor versus CM-l 1 irradiances,lOminute values

(W:-, b RMBD Rh4SD

(Wm-) (Wm-*)

Global corrected Licor -0.8 1.003 0.999 0.3 10.8Diffuse Corrected Licor 0.1 0.999 0.997 0.0 5.7

sets. Especially relevant are the results of the meanbias deviations for diffuse irradiance whic h suggestan evident underestimation tendency according to thehigh frequency of cloudless sky conditions in ourstudy area.

The application of the correction procedure greatlyimproves the matching of the two kinds of sensorsmeasurem ents, particularly for the diffuse irradiance.Figure 6 also shows the improvement in the scatterplots: the experimental points lay close to the 1: 1 line

of perfect matching. Table 4 shows the statistical re-sults that we have obtained. After the correctionmethod was applied: the mean bias deviations wereclose to 0.0 Wm-, both for global and diffuse irradi-ante: the slope of the linear fitting of LIC OR irradi-antes versus CM-1 1 irradiances was close to 1, witha negligible intercept and high correlation coefficient.The RMSD shows a discrepancy between the twokinds of sensor measurements: about 4% for globalirradiance and about 5% for diffuse irradiance whichis a close value to the experimental errors associatedwith the thermopile measurements.

Figure 7 and Table 5 show the results obtained forthe hourly data base. The results are similar to thoseobtained for the lo-minutes data set. The size of thediffuse irradiance error is greatly redu ced. T he meanbias deviation final value is close to 0.0 Wm-. Theroot mean square deviation experience s a reductionof about 70% over the temperature corrected value.Therefore. it reaches a final value about 5% over the

mean diffuse irradiance. These results sh ow the feasi-bility o f using the correction term evaluated using thelo-minute data for wider integration period s.

5. CONCLUSIONS

The correction proced ure for silicon cells presentedin this pape r provides an interesting alternative to ther-mopile pyranometry by means of the combined useof silicon photovoltaic sensors for measuring global

and diffuse irradiance. The correction procedure usesthe uncorrected values of global horizontal and diffusehorizontal irradiance as input date obtained from thesilicon pyranometers. This method provides a goodmatching of silicon measurements (using the Licor200-SA pyranometer) with those provided by a setof thermopile pyranometers ( Kipp-Zonen, CM- 11) ofwhich one is equipped with a polar axis shadowband.The correction procedure has been developed usinglo-minute measurem ents and tested against an inde-pendent d ata set, including both lo-minute data andhourly d ata. The correction provides a uniform distri-

bution of the discrepancies between both kinds of sen-sors. The final values for the mean bias deviation andthe root mean square deviation are about 4% and 5%over the mean value fo r global ho rizontal and diffusehorizontal irradiance.

The goal of this study has been the matching ofphotovoltaic cells and thermopile m easurements forboth global and diffuse horizontal irradiance. This

Fig. 6. Silicon pyranometerversus thermopile global and diffuse irradiances after spectral correction, lo-minute values.

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THERMOPILE (W/m)0

v, /, I a I I I1 I I I, / I,, 1 I j00 20 0 400 600 800THERMOPILE (W/m) Ooo tzoo

CORRECTED DIFFUSE

cc- Y 0.0 + 1.003E

H:"RL?g%UESi

,500 J

by,,,,,,,,,,,,,,,,, ,00 10 0 20 0 300 400 500 I

THERMOPILE (W/m)

Fig. 7. Silicon pyranometer versus thermopile global and diffuse irradiances (a) after temperature correction(T, corrected) and, (b) after spectral correction. hourly values.

work has not addressed problems associated with the et al., in press) must be applied to the silicon photovol-undesirable shadowband obstructions. Obviously, the taic pyranometers, after their temperature and spectralnecessary correction for thermopile sensors (Bathes correction, to provide a corrected diffuse irradiance

Table 5. Licor versus CM-I 1 irradiances, hourly values

(VI:?) bMBD RMSD

R (Wrn-*) (Wm-*)

Global uncorrectedLicor -8.8 1.008 0.999 -5.0 13.5

Global T,, correctedLicor -7.7 1 Ol I 0.999 -2.8 12.1

Global correctedLicor -0.7 1.002 0.999 0.3 10.9

Diffuse uncorrected

Licor -13.6 0.995 0.993 - 14.4 16.9Diffuse T,, corrected

Licor -13.7 l.ooo 0.993 -13.7 16.4

Diffuse correctedLicor 0.0 1.003 0.997 0.2 5.6

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190 L. ALADOS-ARBOLEDAS,F.J. BATLLES, and F. .I. OLMO

measurements. One of the most exciting results of thiswork is the possibility of spreading the radiometricnetwork at a moderate cost and acceptable accuracy.

Acknow ledgments-This work was supported by the Direc-cidn General de Investigacidn en Ciencia y Tecnologia,

DGICYT, from the Research and Education Spanish Ministryunder grant PB91-0711. We appreciate receiving commentsand suggestions from the anonymous reviewers.

REFERENCES

L. Alados-Arboledas, Y. Castro-D&, F. J. Bathes, and J. I.Jimenez, Matching silicon cells and thermopile pyrano-meters responses, Proceedings of the II World Renew ableEnergy Congress, Reading, United Kingdom , 13- 18 Sep-tember, 19 92, 5,2736-2740 ( 1992).

F. J. Batlles, F. J. Olmo, and L. Alados-Arboledas, On shad-owband correction methods for diffuse irradiance mea-surements, Solar Energy (in press).

J. P. Kerr, G. W. Thurtell, and C. B. Tanner, An integratingpyranometer for climatological observer stations and me-&scale network, J. Appl. %fefeorol. 6, 688-690 (1967).

Licor, Inc, Terrestrial Radiat ion Sensors, Type SA. Instruc-tion Manual, No 8609-56 ( 1991).

J. J. Michalskv, L. Harrison. and B. A. LeBaron. Bmniricalradiometric correction of a silicon photodiode rotatingshadowband pyranometer, Solar Energy 39, 87-96(1987).

J. J. Michalsky, R. Perez, L . Harrison, and B. A. LeBaron,Spectral temperature correction of silicon photovoltaicsolar radiation detectors, Solar Energy 47, 299-305(1991).

A. C. Pereira and A. A. Souza Brito, A microprocessor-basedsemiconductor solar radiometer, Solar Energy 44, 137-141 (1990).

R. Perez, P. Ineichen, R. Seals, J. J. Michalsky, and R. Stew-art, Modelling daylight availability and irradiance compo-nents from direct and global irradiance,Solar Energy 44,271-289 ( 1990).

H. Suercke, C. P. Ling, and P. G. McCorm ick, The dynamicresponse of instruments m easuring instantaneous solar ra-diation, Sol ar Energy 44, 3, 14.51148 (1990).

World Meteorological Organization. Guide to meteorologicalinstrument and obser&g practices. W M08, 5th Ed&on,Geneve ( 1983).

APPENDIX I

This appendix includes correction tables for global hori- entered to imply that a correction for that particular conditionzontal (Table Al) and diffuse horizontal (Table A2) irradi- is not available. Although, it is not expected that many pointsante measurements performed with a pair of silicon photovol- fall in these bins. Following the proposal of Michalskyet al.taic cells, one equipped with a polar axis shadowband. Forthe model bins not covered by the range of geometry-sky

(1991 ), the correction procedure is presented in a tabular

conditions for our measurements location, 1 OOOhas beenform, more suitable for computer use.

(Appendix continues on next page)

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Table Al. Global horizontal irradiance corrections Table A2. Diffuse horizontal irradiance corrections

0,: O--35 degt cloudy ..__.......................... clear_IDark 1.068 1.053 1.219 1.159 1.049

1.070 1.078 1.101 1.065 0.9201.071 1.074 1.074 0.947 0.894

1.069 1.072 0.975 0.927 0.895Bright 1.045 1.000 0.946 0.918 1.0008,: 35550 deg; cloudy .._._. .._............_._............ clear

Dark 1.045 1.000 1.000 1.043 1.0301.049 1.081 1.057 1.025 0.9791.058 1.048 1.043 0.991 1.0001.053 1.046 0.997 0.972 1.000

Bright 1.036 1.009 0.973 1.000 1.0000,: 50-60 deg

;cloudy ..__....____................,. ......... clear

Dark 1.047 1.000 1.000 1.031 1.0161.035 1.000 1.043 1.021 1.005

1.030 1.050 1.028 1.006 1.0001.035 1.035 1.006 0.995 1.000

Bright 1.025 1.009 0.989 1.000 1.0000,: 60-75 deg; cloudy . . . . . . . . . . clear

Dark 1.041 1.000 1.000 1.000 1.0051.006 1.000 1.052 1.010 1.0011.006 1.048 1.016 1.000 1.0001.011 1.019 1.001 0.991 1.000

Bright I .012 1.003 0.992 1.000 1.0000,: 75--90 degh cloudy ..___.......................... clear

Dark 1.037 1.000 1.000 1.000 0.997

1 Ol I 1.000 1.000 0.998 0.9970.996 1.000 1.006 0.994 1.0000.997 1.010 0.993 0.989 1.000

Bright 0.995 0.995 0.988 1.000 1.000

0,: O-35 degt cloudy . . clearnDark

Bright0,: 35-50

ADark

Bright0,: 50-60

ADark 1.057 1.000 1.000 1.263 1.379

1.035 1.000 1.160 1.183 1.219

1.031 1.095 1.118 1.160 1.0001.033 1.059 1.094 1.143 1.000

Bright 1.017 1.033 1.074 1.000 1.0000,: 60-75 deg

cloudy ..__._..................... clearhDark

1.091 1.0971.094 1.0681.077 1.045

1.070 1.0471.053 1.056

dcg

1.330 1.271 1.3621.135 1.212 I.2851.106 1.182 1.219

1.116 1.125 1.1521.078 1.083 1.000

cloudy .._._.._ ..clear

1.066 1.0001.063 1.171I.069 1.1021.051 1.0581.033 1.044

deg

1.402.000 1.2691.163 1.1991.124 1.1771.1 10 1.1581.088 1.000

1.2751.0001.0001.000

cloudy .._.__._.._ ..clear

Bright0,: 75-90

nDark

Bright

1.0611.0081.0101.011I.004

deg

1.521 1.000 1.000 1.3581.000 1.179 1.161 1.2121.103 1.101 1.138 1.0001.060 1.082 1.119 1.0001.026 1.062 1.000 1.000

cloudy clear

1.047 1.000 1.000 1.000 1.356

1.016 1.000 1.000 1.150 1.1870.997 1.000 1.101 I.131 1.1340.998 1.049 1.073 1.102 1.0000.992 1.018 1.047 1.000 1.000

alados 1995

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