MODELING CLEAR WEATHER DAY SOLAR IRRADIANCE

IN BAGHDAD, IRAQ

M. AL-RIAHI,$ K. J. AL-JUMAILY% and H. Z. ALI}$Solar Energy Research Center, Jadiriayh, P.O. Box 13026, Baghdad, Iraq

%Meteorological Department, College of Science, Al-Mustansiriyah University, Baghdad, Iraq

}Space Research Center, Jadiriyah, Baghdad, Iraq

(Received 3 April 1997)

AbstractÐA clear day model for the beam transmittance of the atmosphere is presented. The clear skyis modeled because this condition generally produces the maximum energy available. This maximumestablished the criteria from which engineers can design solar cells, space and process water heatingequipment and estimate the thermal loading on buildings, etc. The model is based on ®ve-years of dailyglobal radiation data assembled from measurements at the Solar Energy Research Center at Baghdad,Iraq. The model o�ers the prediction of clear day hourly values of direct normal and global solar radi-ation for any day of the year at a given location with no required meteorological inputs. Modeled dataare compared with observations, demonstrating good agreement for several days from di�erent seasons.This model provides a baseline for solar energy researchers and is utilized for quality control of solarradiation parameters. # 1998 Elsevier Science Ltd. All rights reserved

Global radiation Clearness index Beam transmittance Clear day irradiance model

INTRODUCTION

A reasonable estimate of the hourly values for beam normal solar irradiation is required for thedesign of many solar conversion devices. Because the consistently adequate operation of a track-ing pyrheliometer is demanding on time and other resources, accurate and reliable beam normalirradiation data is not so readily available as global solar irradiation. This situation has madethe development of models for the estimation of beam irradiation from global irradiation of ahigh priority among solar energy researchers.

Several attempts have been made in order to give a theoretical basis to the various formulasused in computation of the solar irradiation. Hence, di�erent categories of atmospheric modelshave been proposed. Prominent among these are the models of Fowle [1], Moon [2], Allen [3],Gates [4] and Boer [5], which require spectral integrations over all wavelengths and dwell mainlyon the direct component for a clear sky. Moon, Allen and Gates give tabular data for the directbeam solar irradiation as a function of the intervening atmosphere, typically for ®ve air massvalues corresponding to ®ve solar elevations. The clean air model given by Allen includes thetotal precipitable water overhead, w, as a variable. The data presented by Moon and by Gatesdeveloped only the standard relative air mass and were easily ®t by a sum of three exponentials.In order to avoid the di�culties of applicability of Moon's relations, Cole [6] has determinedthe attenuation e�ect of the precipitable water depth w for an assumed dust content C= 400particles/cm3 and performed a ®tting for air mass range m= 1±5.

McClatchey et al. [7] presented a complete analysis in terms of fundamental concepts and ex-pressions for speci®c climates; and Hottel [8] next established a model based on these climates.A rather more general and universal model for the direct component on a cloudless day hasbeen given by King and Buckius [9]. However, in general, there are currently three levels ofparameterization models to estimate direct and di�use irradiation on clear days. The highestlevel is presented by elaborate computer simulation models (such as SOLTRAN andLOWTRAN 2) which require a considerable amount of input parameters and long compu-tational times. The middle level is presented by less complex models. Bird and Hulstrom [10]belong to the middle level. The ASHRAE algorithm [11] for the determination of clear sky

Energy Convers. Mgmt Vol. 39, No. 12, pp. 1289±1294, 1998# 1998 Elsevier Science Ltd. All rights reserved

Printed in Great Britain0196-8904/98 $19.00+0.00PII: S0196-8904(97)10053-X

1289

beam transmittance is a model of the lowest level. Algorithms on this level do not attempt tomodel the in¯uence of changing atmospheric parameters; instead only one equation is used totake into account the variation of the air mass and of constants which are unique for a particu-lar month of the year. The ASHRAE algorithm is usually in the form of an exponential attenu-ation such as the simple Bouguer's Law formula [12].

The purpose of the present work is to apply the methodology proposed by Jeter and Phan [13]for evaluating the direct solar transmittance using ®ve-years of daily global radiation data on ahorizontal surface, beginning in 1991, collected at the site of the Solar Energy Research Centerat Baghdad, Iraq (338 14' N, 458 14' E). the results are compared with observations and withthe performance of the generalized ASHRAE algorithm.

RADIATION MEASUREMENTS

The basic data set assembled at the Solar Energy Research Center (SERC) consists of radi-ation values integrated over one-hour periods and recorded at the end of each period during theday. For this recent data base, the pertinent instruments were an Epply PSP pyranometer tomeasure global radiation and an NIP pyrheliometer on a common polar mount to measurebeam normal radiation. All instruments have been periodically calibrated. No signi®cant cali-bration adjustments have been necessary for any of the PSP and NIP data developed in thisstation since operations began in 1991. The site is situated in the ®eld experiments of the SERC,the location is essentially free from obstruction of the solar path and the building to the northdoes not signi®cantly reduce the ®eld of view of the instruments. A daily validation test wasinstituted to eliminate certain data from further consideration. Periods with solar altitudes lowerthan 68 were rejected to avoid the consequent refraction e�ects on tracking accuracy. A routinecheck procedure has been implemented for the data since its inception. Only a very few isolatederrors caused by intermittent radiometer or tracker problems were discovered. An e�ective dataquality control procedure and elimination of questionable data are essential to produce a re-liable model.

DATA BASE PREPARATION

Daily global radiation measurements were collected by the Automatic Weather ObservationStation at SERC from 1991 to 1995. A convenient compressed format for the presentation andanalysis of daily global radiation is the daily clearness index de®ned as:

KT � H=H0 �1�where H = measured daily global radiation and H0=calculated daily extraterrestrial radiationon a horizontal surface. H0 is obtained using an equation given by Iqbal [14].

The KT values could be considered as a good estimate of the irradiance absorbed by aerosols,clouds, etc. plus the irradiance scattered upward by clouds and gaseous and solid aerosols. Thisfrequency gives an opinion about the transmission phenomena in locations which do not havemeasurements of such atmospheric constituents.

For the computation of KT all data of daily global radiation have been archived in a data ®le,since it provides great ¯exibility in data handling. The data for each year in the record of dailyglobal radiation are scanned each ®ve days at a time. The clearest one of these ®ve days isselected, yielding 73 data per year. The criterion for selecting the clearest day is based on the% KT. Dividing the year into 18 intervals (each 20 days long), the entire record is scanned andthe clearest day in each interval is found. A smooth curve is drawn by least Root Mean Square®t (RMS) to the selected extreme values of KT as illustrated in Fig. 1.

The resulting curve may now be utilized in the development of the clear sky model. Thiscurve of maximum expected daily clearness, KTc, gives, for any date the limiting ratio:

KTc � Hc=H0 �2�where Hc=maximum expected daily global irradiance, the % KTc is expressed as a function ofday of the year (x) using a least square polynomial of ®fth degree.

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%KTc � 6:15 Eÿ11:x5ÿ5:581Eÿ8:x4 � 1:841 Eÿ5:x3

ÿ2:694 Eÿ3:x2 � 2:108Eÿ1:x� 0:0057533 �3�

METHODOLOGY

The solar irradiance received at any locality comprises both direct and di�use components.The direct component is equal to the beam normal irradiance, Gb, from the apparent solar disktimes the sine of the solar altitude angle h; h may be calculated as shown in standard texts [15].The global irradiance, symbolized as G, may then be simpli®ed to

G � Gb sin h� Gd �4�The balance Gd is the di�use radiation ¯ux (scattered irradiance). On a clear day, the magnitudeof the di�use ¯ux is quite small compared with the direct radiation ¯ux (5±14% of Gb). It ismost convenient to assume that the ratio between the beam and di�use irradiance is constantthroughout a particular clear day without producing signi®cant error [11]. Let this fraction bedenoted as C. The global irradiance may be re-written as follows:

G � Gb�sin h� C� �5�The values of C for the twenty-®rst day of each month are presented in Ref. [11]. A Fourierharmonic curve ®t for these values yields the following equation:

C�x� � 0:0936� 0:041 sin��xÿ 104:5�p=167� � 0:004773 sin��x� 24:4�p=83:5� �6�where x is the number of days after 1 January.

The beam normal transmittance may be expected to follow a Bouguer's Law dependence onatmospheric extinction (due to absorption and scattering) and air mass m such that:

Gb � Gb0 exp�ÿkm� � Gb0 exp�ÿk�1=sin h�0:678� �7�where Gb0 is the extraterrestrial beam normal irradiance. The value of Gb0 can be calculatedaccurately by celestial mechanic equations for any given day [14]. Here, k is the overall atmos-pheric coe�cient of extinction which varies over the year, and the exponent, 0.678, compensatesfor the actual curvature of the atmosphere. The extinction coe�cient, k, can be expressed as thezero of the following function:

F�k� � KTc ÿHc=H0 �8�

Fig. 1. Maximum expected daily clearness index (KTc) curve for Baghdad, Iraq.

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where

Hc � Gbo

�t2t1

exp�ÿkm��sin h� C� dt �9�

H0 � Gb0

�t2t1

sin h dt �10�

where t1, t2=sunrise, sunset times

Substituting equations (9) and (10) into equation (8) yields the result:

F�k� �%KTc

100ÿ� t2t1

exp�ÿkm��sin h� C�dt� t2t1

sin hdt�11�

In developing equation (11), it was assumed that the % KTc for a given day is known from theempirical curve or tabulation de®ned in equation (2). A FORTRAN program was developed toevaluate the value for k for each day of the year by solving equation (11). The Romberg inte-gration technique was used to evaluate the right hand side of equation (11) and the RegulaFalsi method was used to ®nd the root of F(k). Due to its physical limit, k should lie in therange from 0.1 to 0.50.

The value of k that yields a zero of equation (8) was obtained for each day of the year. Forthis value, the irradiance predicted by the model equals that actually observed. A Fourier curve®t for these values yields the result:

Fig. 2. Comparison of model and observed global radiation for Baghdad, Iraq.

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k�x� �0:3917397ÿ5:596 Eÿ2:sin�2p=365:x� � 5:293 Eÿ3:cos�2p=365:x�� 1:3594 Eÿ2:sin�4p=365:x� � 4:0383 Eÿ3:cos�4p=365:x� �12�

MODEL APPLICATION AND DISCUSSION

To evaluate the clear day irradiance model presented in this report, the results obtained mustbe compared with observations. By using equations (5)±(7) and (12), the calculated clear dayhourly direct normal and global radiation values were plotted against selected clear daymeasured data for di�erent days (Figs 2 and 3) from the Automatic Weather ObservationStation at Baghdad SERC. Two statistical tests, the Root Mean Square Error (RMSE) andMean Bias Error (MBE), were used to evaluate the accuracy of the predicted direct normal andglobal values. The results showed, in all cases, the di�erence between modeled and measuredclear day values never exceeds 5%, which is well within the error bands of pyrheliometers andpyranometers. However, the di�erences arise from the fact that the data for the scattered irradi-ance fraction, C, in equation (6) are not speci®c to the particular site.

The atmospheric extinction coe�cient over the year for Baghdad, Iraq, is shown in Fig. 4, inwhich the values from ASHRAE [11] and Atlanta, Georgia (33.408 N, 84.758 W) [13] are alsoshown. A notable point of this ®gure is that the three curves are nearly similar in pattern, withthe present work giving generally slightly higher values than those of ASHRAE's and Atlanta'svalues. It should further be noted that the values referring to ASHRAE generally fall betweenthe curves of Baghdad kbag and Atlanta kAtl, approaching the curve kAtl especially during the

Fig. 3. Comparison of model and observed direct-normal radiation for Baghdad, Iraq.

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period (August±November). This implies that any model of the beam irradiance will be mostconstrained by clear day data.

The major advantage of the foregoing model is its easily input parameter. The calculationsneed only long term daily global irradiance data which is available for many sites in Iraq.

REFERENCES

1. Fowle, F. E., Astrophys. J, 1913, 38, 392.2. Moon, P., J. Franklin Inst., 1940, 230, 583.3. Allen, C. W., Astrophysical Quantities, Article 58, 2nd Edn, University of London, The Athlone Press, 1964.4. Gates, D. M., Science, 1966, 151, .5. Boer, K. W., Solar Energy, 1977, 19, 525.6. Cole, R. J., Building and Environment, Vol. II. Pergamon Press, Oxford, 1976, pp. 173±179, 181±186.7. McClatchey, R. A., Fenn, K. W., Selby, J. A., Voltz, F. E. and Garing, J. S., Envir. Res., Paper 411, 1972.8. Hottel, H., Solar Energy, 1976, 18, 129.9. King, R. and Bucklius, R. O., Solar Energy, 1979, 22, 297.

10. Bird, R. E. and Hulstrom, R. L., Solar Energy Research Institute, TR-642-761, 1981.11. 1977 Handbook of Fundamentals, ASHRAE, New York, 1977, pp. 26.2±26.9.12. Bouguer, P., L'Academic Royales des Sciences, Paris, 1760, trans. W.E.K. Middleton, University of Toronto, 1961,

pp. 154±158.13. Jeter, S. M. and Phan, C. N., J. Energy, 1982, 6, 115.14. Iqbal, M., An Introduction to Solar Radiation, Academic Press, Toronto, Canada, 1983.15. Spencer, J. W., Search, 1971, 2(5), 172.

Fig. 4. Regression curves of the atmospheric extinction coe�cient from ASHRAE's (kASH) andAtlanta's (kAtl) values. Comparison with the calculated values from the model at Baghdad location

(kBag).

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