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Correlations between values of daily beam, diffuse and global radiation for Beer Sheva, Israel
0360-5442/92 $5.00+ 0.00 Copyright 0 1992Pergamon Press plc
Energy Vol. 17, No. 6, Pp. 523-533, 1992 Printed in Great Britain. All rights reserved
CORRELATIONS BETWEEN DIFFUSE AND GLOBAL SHEVA,
VALUES OF DAILY BEAM, RADIATION FOR BEER ISRAEL
A. IANETZ Israel Meteorological
Service, Research and Development Israel
Division, P.O. Box 25, Bet-Dagan 50205,
A. I. KUDlSHt Solar Energy Laboratory, Department of Chemical Engineering, Ben-Gurion University of the Negev, Beer Sheva 84105, Israel (Received 30 July 1991)
Abstract-Empirical correlations for predicting both beam and diffuse radiation at Beer Sheva, located in the semi-arid southern region of Israel, have been developed. These equations relate either the beam or the diffuse fraction of the global radiation to the clearness index. The available data, composed of normal incidence beam and global radiation measurements, have been analyzed on both a seasonal and a yearly basis. They have been compared to empirical equations previously reported in the literature for six sites in the Middle East region. In the case of Qidron, Israel, and three Greek sites, there was close agreement between the correlations, whereas in the remaining two sites (Gilat, Israel and Fudhaliyah, Iraq) the correlations were quite different. Reasons for the discrepancies in the latter two cases are presented in the text. The beam fraction of the global radiation was also correlated to the ratio of measured daily global to the corresponding clear sky daily global values, which were determined empirically in an attempt to reduce the degree of scatter observed in the correlations between beam fraction of global radiation and clearness index. This approach is intended to correct for the multiplicity of possible cloud conditions that can give the same value for the cloudiness index. It was not successful when applied to the Beer Sheva data, namely, it did not reduce the degree of scatter observed in the original correlations. This, in all likelihood, highlights the fact that the scatter is caused by local climatic conditions (such as turbidity and moisture content of the atmosphere).
INTRODUCTION
A prerequisite for designing solar energy conversion systems is the availability of solar radiation data for the site. The kind of data required depends upon the type of system under consideration, that is, whether it utilizes global or beam radiation. Most meteorological stations measure global radiation whereas the number of stations measuring beam radiation is much smaller. The reason for this is, in general, due to budgetary constrictions with regard to equipment and staff. Beam-radiation measurements require more expensive instrumentation and require maintenance for the daily adjustment of the declination angle of the tracking device (this is especially troublesome in remote automated stations). This problem has given impetus to the development of empirical correlations between beam and global radiation. These correlations usually take the form of beam or diffuse fraction of the global radiation as a function of some kind of normalized index of the global radiation and may be reported on either an hourly or daily basis. The most common format for reporting such correlations is as the diffuse fraction of global radiation on a daily basis as a function of the daily clearness index, i.e., the ratio of global to extraterrestrial radiation. It has been observed that such correlations are generally a function of the location of the meterological station, i.e., they are not universal. tTo whom all correspondence
should be addressed. 523
A. IANETZ and A. I. KUDISH
524
We have determined daily empirical correlations based upon data from Ben-Gurion University of the Negev’s Solar Energy Laboratory’s meteorological station, which is part of the national network. It is located in Beer Sheva (31”15’N, 34”48’E, 315 m MSL), in the semi-arid Negev region of southern Israel. This site is characterized by an abundance of global radiation, viz. an annual average daily global radiation of 18.43 MJ/m’.’ These correlations will also be compared to those previously reported in the literature for this region of the globe.
THEORY
The empirical correlations reported in the literature have described the beam or diffuse fraction of the global radiation as either a linear or polynomial function of the clearness index in the range of values corresponding to neither perfectly clear or cloudy days, viz. in the intermediate range. Thus, these correlations take the form of either Hi/H = a + bKT
(1)
or Hi/H = a,, + a,K,
+ a,Kt + a3K$ + a,K&
(2)
where (Hi/H) is either the daily beam or diffuse fraction and KT is the daily clearness index. Bugler* observed that the scatter of data points using the above type of correlations was due, in part, to the variety of possible cloudiness states corresponding to a particular value of KT. The amount of scatter that can be attributed to the multiplicity of cloudiness states is a function of the time interval under consideration, i.e., hourly or daily values, since as the time interval increases the cloudiness index is averaged over a longer time period and the contribution of individual cloudiness states is proportionally reduced. He corrected for this phenomena by normalizing the hourly global radiation values, I, to the corresponding clear sky hourly value, I,, and correlated his data for Melbourne by the following type of equation: f/I
=
a0
+
a,(Z/Z,) + a,(ZlZ,)* + a3(r/4)3 + a4(1/L)4.
(3)
Stauter and Klein3 have also used this type of analysis to correlate data for five U.S. cities. Lestrade et al4 have recently proposed the use of isonebs, lines of constant cloud cover, to correct for the multiplicity of possible cloudiness states corresponding to a singular value of K,.
MEASUREMENTS
The normal incidence beam radiation is measured using an Eppley Normal Incidence Pyrheliometer, Model NIP, which was connected to an Eppley Electronic Integrator Model 413-6140 (it includes a Digitec 6140 digital printer) and cumulative values were printed at hourly intervals. The global radiation is measured using Eppley Precision Spectral Pyranometers, Model PSP, which was connected to a Kipp & Zonen Printing Solarimeter Integrator CC 2 and the cumulative values were printed at 30 min intervals. The instruments are calibrated at regular intervals by the Israel Meteorological Service. The errors involved in the radiation measurements are assumed to be no less than f1.5% for the normal incidence beam radiation and f2.5% for the global radiation. Only days for which a complete set of hourly data existed for both radiation measuring devices were included in the analysis. The validity of the individual hourly values of global, beam and diffuse radiation were checked in accordance with WMO recommendations.’ Those
Empirical correlations for predicting beam and diffuse radiation
values which did not comply with the WMO recommendations rejected.? Extreme data were also omitted.
were considered
525
erroneous
and
RESULTS
We have presented the results of the analysis of our data in three different empirical formats. First, the daily beam fraction of global radiation as a function of the clearness index (H,,/H) = u f hK,. Second, the daily diffuse fraction of global radiation as a function of the clearness index
(H~/H) = c + dK,. Third, the daily beam fraction of global radiation global radiation to the clear day global radiation
as a function of the ratio of the measured
(HJH) = e +f(HIH,).
(6)
The clear day radiation was defined empirically for each individual month as the sum of the highest measured global radiation value for each hour of the day from the database for each month.h In each case we also analyzed the data using a second-order polynomial and observed that there was no significant improvement in the fit of the data to the polynomial empirical equation relative to that for the linear equation, i.e., the correlation coefficient was only marginally improved. Thus, we concluded that the use of the simpler linear equation was justified. The measured beam radiation data were converted to diffuse radiation values in order to facilitate comparison to those empirical correlations previously reported in the literature for sites in this region of the globe. The empirical correlation, suggested by Bugler,2 is based upon clear day giobal radiation ]see Eq. (6)] and was used to test whether it reduces the degree of scattering relative to that observed when correlating the data with the clearness index [Eq. (4)]. A priori, it is understood that in the case of daily radiation values its affect is limited, since the effect of a multiplicity of cloudiness states corresponding to a singular value of K7. is reduced as the time interval increases, viz. daily as opposed to hourly values. The measured hourly normal incidence beam radiation values, lb.“, were converted to beam radiation incident on a horizontal surface, jh, by applying the geometric conversion factor to individual hourly values, viz.
z,= It)*” cos
6,,
where 6, is the average hourly incidence angle. These hourly values were in turn summed to determine the daily beam radiation incident on a horizontal surface, Hi,. The daily diffuse radiation values were calculated from the daily global, H, and the daily beam radiation incident on a horizontal surface, Hi,, viz.
TThe major gaps in data acquisition were due, in general, to one of the following: (i) power failures, which caused the PSP integrator to reset to zero and froze the NIP integrator until reactivated manually. In addition, an error proportional to the length of the power failure was introduced into the integrator clocks and the NIP solar tracker; (ii) mechanical failure of the PSP integrator’s paper advance mechanism resulted in data being printed on top of each other and rendering them indecipherable. These probtems, except for the solar tracker, were eliminated in July 1988 when the NIP and PSP were connected to a (rechargeable) battery powered datalogger which utilizes a tape cassette to store the data.
A.
526
IANETZ
and A. I. KUDISH
Table 1. Empirical correlations, Season
i
Correlation
1 No. days1
1
RMSE
(a) HbiH = a + bKT Winter
261
Spring
331
925
Year
H,/H H,,/H Hi/H H,,lH H;fH
=-0.320 + 1.597 + 1.641 +2.051 + 1.433 + 1.520
=-0.410 =-0.673 =-0.225 =-0.304
KT Kr KT
0.924 0.933 0.867 0.901 0.930
KT‘I K;
0.093 0.070
I
0.035 0.068 0.077
(b) HJH = c + dKT
150
H&H HdtH HJH I H~/H
Autumn
I
Year
j 971 1Hi/H
= = = =
I .287 1.534 KT 1.372 - 1.577 KT 1.725 - 2.133 KT 1.215 - 1.436 K;
= 1.285 - 1.494 K;
0.091 0.072 0.034 0.065
I
0.928 0.933 0.878 0.912
I
]
0.932
1 L_ 0 078
0.941 0.921 0.740 0.908 0.923
0.083 0.076 0.042 0.058 0.081
(c) Hb/H = e + fH/H
The daily extraterrest~al radiation on a horizontal calculated using the following equation: H, = (24 x 36OOG,/rrt)[l+
surface from sunrise to sunset, I&,, was
0.033 cos(360n/365)] x [cos c) cos 6 cos co, + (2nwJ360)
sin Cpsin 61,
(9)
where Q, is the latitude, 6 the declination angle, o, the sunset hour angle, and G,, the solar constant (which was taken as 1367 W/m’). The data were analyzed both on a yearly and a seasonal basis and the results are presented in Table 1. We have also reported in Table 1 both the correlation coefficients (r) and the root 1
.o
08
06
I: \
+
Winter
x
spring
0
Summer
*
Autumn
1” 04
02
0.2
04
06
K(T)
Fig. 1. Relationship
between the daily beam fraction of global radiation and the clearness index.
08
527
Empirical correlations for predicting beam and diffuse radiation 10
08
06
I \
+
Winter
x
Sprmg
0
Summer
l
Autumn
+
.b
+ + +
<
‘3
+*+*
.* 04
+
.. +x + +
+
02
02
00
06
06
04
K(T)
Fig. 2. Relationship between the daily diffuse fraction of global radiation and the clearness index.
10
08
06
+ Winter 8 Spring 0
Summer
*
Autumn
? I”
04
” +
x t+
02
+
02
00
04
0.6
0.8
H/He
Fig. 3. Relationship
between the daily beam fraction of global radiation and the ratio between the measured global radiation to clear day global radiation.
IO
A. IANETZ and A. I. KUDISH
528
mean square error of the fit to the empirical equations (RMSE). The seasons were defined for Beer Sheva as follows: winter-December, January, and February; spring-March, April, and May; summer-June, July, and August; autumn-September, October, and November. The results are presented graphically in Figs. l-3.
DISCUSSION
It is apparent from the differences observed in Table 1 for the values of the coefficients of the empirical equations for the four seasons, irrespective of which correlation format is utilized, that the use of a single yearly empirical equation is not appropriate. In fact, in theory it would be more accurate to develop monthly as opposed to yearly or seasonal empirical equations. This is a consequence of the complicated functional dependence of solar radiation on cloudiness (conditions/types), moisture content of the atmosphere, and atmospheric turbidity, which, in general, vary from month to month. Also, the components of global radiation, viz. its distribution between beam and diffuse radiation components, are a function of air mass, which varies from month to month. Due to the limited size of our database, we have confined our analysis to yearly and seasonal correlations. There exists ample evidence that the empirical equations are not universal but a function of the location of the meteorological station (viz. latitude and local climatic conditions). In fact, Soler7 has recently attempted to correlate the empirical coefficients of the equation relating the diffuse fraction to the clearness index for 28 European sites located between 36 and 61”N lat and between 29”E and 11”W long. It is apparent from his analysis that there is a relatively large degree of scatter in the values for the empirical coefficients reported for these sites. We have therefore limited our comparative analysis of the present work with respect to previously published empirical correlations, to sites in the Middle East region (cf. Table 2). H,/H
us K,: yearly correlations
The coefficients of the empirical equations correlating the diffuse fraction as a function of the clearness index for six sites in our region, on a yearly basis, are listed in Table 3 for comparison purposes. All the correlations were derived from daily values, except for Qidron, Israel and Fudhaliyah, Iraq, which utilized average monthly values. It should also be emphasized that for all sites, except for Beer Sheva, the diffuse radiation was measured directly utilizing either a shadow band (Gilat, ’ Qidron,’ and Greek sites”) or shadow disk (Fudhaliyah”), whereas for Beer Sheva it was calculated from measured normal incidence beam radiation values as described above. It is important to emphasize, especially with regard to the following discussion, that the diffuse radiation measurements for Gilat were corrected for the anisotropy of sky radiation using the Drummond’* empirical correlation, whereas at Qidron the shadow band correction for anisotropy was calculated using a locally fitted factor. The latter procedure being the preferable one.13 In the case of both the Greek sites”’ and Fudhaliyah,” no definitive statement is made in their manuscripts concerning the application of a correction factor to the diffuse radiation measurements, though in the former a general statement is made that “all appropriate corrections have been made”. In a more recent manuscript describing the solar Table 2. Locations utilized in comparative analysis of empirical equations. Location
Reference
Beer Sheva. Israel Gilat. Israel Qidron, Israel Fudhaliyah, Iraq Athens, Greece Rodos, Greece Kythnos. Greece
this work : :2, 10 10
Empirical correlations for predicting beam and diffuse radiation Table 3. Correhtion
between f&/H
529
and K-,- iearly basis). -I_
site BeerSheva, israell-Gilat,Israel Qidron. Israel Fudhaliyah, Iraq Athens.Greece
Rodos, Greece Kythnos, Greece Greece -
(above 3 combined: --
3eriod(diyj C 971d 1.285 709d 1 539 1983-5 1.112 1985-6 1983 1984 1985 1982 1983 7981 1982 18196
1.102 1.37 1.38 1.35 138 1.35
1.31 1.35 136
1
d
r
-494 -1 755 -1.203 -1 299 -1.54 -165 -1.59 -1.64 -1.60 -1.52 -1.59 -160
0.932 0.84 0.917 0905 0.941 0.937 0.923 0.963 0.948 0.942 0.952 0.940
-I
Reference thiswork 8 9 11 t'El 10 10 ?O to 10 10
radiation climate of Fudhaliyah” it is clearly stated that no sky anisotropy correction was applied to the diffuse radiation measurements. It should be noted that in some cases the correction factor to diffuse radiation may be of the order of 20% (viz. the reported values can be significantly lower than the true values.) It is apparent from Table 3 that the correlation for Beer Sheva is most similar to those determined for the Greek sites. A comparison of values calculated from 12 empirical equations listed in Table 3 for the diffuse fraction in the range of 0.4 d Kr g 0.7 confirms this, viz. that the average relative di~eren~e between Beer Sheva and the Greek sites is the lowest, -5.8% (with the exception of Athens 1983, where the average relative difference is about 15%). The relative difference being defined as the difference in calculated diffuse fraction values relative to that value for Beer Sheva [i.e., A(&/H)/(H,IN)n,,, shcva1. The Greek site correlations predict somewhat greater diffuse fractions. There is also very good agreement between Beer Sheva and Qidron, the average retative difference being -7.7%. The correlation for Fudhaliyah predicts lower diffuse fractions (by about 16%) than that for Beer Sheva. The former is based upon monthly average values, whereas the latter is derived from daily values. Lalas et al” have reported both daily and monthly average correlations for all the Greek sites and the corresponding empiricat equations are significantly different in each case. This factor may contribute, somewhat, to the differences between Fudhahyah and Beer Sheva empirical correlations. Nevertheless, it is very likely that these discrepancies are the result of differences in data measurement and processing methods. If, indeed, no sky anisotropy correction was applied to the diffuse radiation measurements, as was stated with regard to a later manuscript,‘4 than the direction and magnitude of the discrepancy may be explained by this fact. The relatively large discrepancy between the correlations for Gilat and Beer Sheva is especially disturbing, since Gilat is located just about 20 km northwest of Beer Sheva and one would expect the two correlations to exhibit close agreement (cf. close agreement between Beer Sheva, the three Greek sites and Qidron). The former predicts much larger diffuse fractions as a function of clearness index than the latter (average relative difference being about 26%). We are of the opinion that either this region was characterized by an exceptionally high diEuse fraction during the time interval 1960-1964 when the data utilized in this analysis were collected or there may have been some systematic error in the data collection. It has been brought to our attention by Stanhillr3 that this was a p eriod of exceptionally high volcanic activity and hence atmospheric turbidity in the northern hemisphere,‘5 The diffuse fractions calculated using the Gifat equation appear to be abnormally high for this region (e.g., H,/N = 0.84 for Kr = 0.4 and E&/H = 0.49 for Kr = 0.6). Also, the correlation eoefEcient for Gilat is the lowest of all those reported in Table 3. We have no other suggestions for explaining this discrepancy, especially since the data in question were measured more than 26 yr ago. The close agreement between Beer Sheva and Qidron vis-a-vis the poor agreement between these two sites and Gilat may also reflect on the relative ability of the correction factor used to correct for the anisotropy of sky radiation to perform its function, i.e., a locally fitted factor as opposed to the empirical Drummond factor.
A.
530
IANETZ
and A. I. KUDISH
Table 4. Correlation between H,/H Site
C
1
and KT (seasonal basis). d
1
r
Reference
Winter
H,/H
Beer Sheva, Israel Fudhaliyah. Iraq Athens, Greece Rodos + Kythnos. Greece
1.207 1.199 1.38 1.33
-1.534 -1.494 -1.65 -1.56 Spring
0.928 0.902 0.922 0.938
this work
Beer Sheva. Israel Fudhaliyah. Iraq Athens. Greece Rodos + Kythnos. Greece
1.372 1.325 1.45 1.42
-1.577 -1.634 -1.67 -1.65 Summer
0.933 0.927 0.941 0.957
this work
Beer Sheva, Israel Fudhaliyah. Iraq Athens. Greece Rodos + Kythnos. Greece
1.725
-2.133 -1.480 -1.47 -1.61 Autumn
0.878 0.821 0.077 0.891
this work
1.202 1.29 1.35
Beer Sheva, Israel Fudhaliyah, Iraq Athens. Greece Rodos + Kythnos. Greece
1.215 1.127 1.40 1.35
-1.436 -1.390 -1.71 -1.65
0.912 0.903 0.941 0.958
this work
:; 10
::, 10
:: 10
:: 10
us K,: Seasonal correlations
The coefficients of the seasonal empirical correlations for four sites are listed in Table 4 (the data for Gilat and Qidron were not analyzed on a seasonal basis and the data for Rodos and Kythnos were combined). It should be noted that the seasons have not been defined alike for all sites. Al-Hamdani et al” defined them in the following manner: winter-January, February, and March; spring-April, May, and June; summer-July, August, and September; autumnOctober, November, and December, whereas Lalas et al” did not define them in their paper. In all cases, the coefficients are observed to vary from season-to-season, though the Rodos + Kythnos data exhibit the smallest seasonal dependence. It is important to note that the correlation coefficient is lowest, in all cases, for the summer data. Also, the empirical equations for summer for both Beer Sheva and Athens are distinctive in that their absolute values for both coefficients are a maximum for the former and minimum for the latter, relative to the other seasons. We believe that the relatively low correlation coefficients observed for the summer data can be attributed to the nature of the statistical analysis. The summer is characterized in this region by an abundance of relatively clear days, i.e., high KT values. The range of KT values on which the empirical correlations were derived is very narrow, as opposed to the other seasons. In the case of Beer Sheva the range is 0.59 < KT < 0.75 and for Fudhaliyah it was approximated to be 0.6 < KT < 0.7, as observed from Fig. 1 of Ref. 11. The range of values utilized for the Greek sites was not reported, but we believe that it is, in all likelihood, very similar. Thus, it is not surprising that attempting to fit a linear equation to such a narrow range of values for the independent parameter will result in a relatively low correlation coefficient. It may also be possible that atmospheric turbidity may contribute to the lower correlation coefficients that characterize the summer empirical equations in this region. Beer Sheva summers are characterized by hot dry weather and thus one would expect a higher turbidity caused by dust and sand in the atmosphere. Al-Hamdani et al” have proposed the same explanation with respect to his relatively low correlation coefficient for the summer. Lalas et al” have attempted to explain the relatively low correlation coefficients as being due to increased air pollution, caused by increased photochemical reactivity in the summer months. Since the clearness index does not account for turbidity, one would expect a greater degree of scatter in such correlations. We were unable to check this hypothesis for Beer Sheva, since such data are not available. The agreement between the seasonal empirical correlations is somewhat less than in the case of the yearly correlations (especially with regard to the summer). If we disregard the summer correlation the average differences, relative to Beer Sheva, are 17.6% for Fudhaliyah, 6.4% for
Empirical
correlations
for predicting
beam
and diffuse
radiation
531
Athens, and 4.9% for Rodos + Kythnos. This is as expected, since as the time interval is reduced (i.e., yearly to seasonal basis) the effect of local climatic conditions becomes more pronounced. H,/H us K,: seasonal and yearly correlations
The overwhelming majority of the correlations, between component fraction (either beam or diffuse) of the global radiation as a function of clearness index, reported in the literature are in terms of the diffuse fraction. The reasons for this are practical ones, as discussed in the Introduction section. This was the rationale for converting our measured beam data to diffuse radiation, as mentioned previously. Nevertheless, we believe that since normal incidence beam radiation has been measured for Beer Sheva, such correlations are more appropriate, cf. Table 1. Also, a prerequisite in the design of concentrating solar systems is the availability of beam radiation data or a means of calculating it, e.g., from such a correlation, which is preferable to basing it on diffuse radiation measurements. We did come across a few papers that reported correlations between beam and global radiation. Anderson,” referring to a manuscript that apparently was never published, suggested a linear logarithmic correlation between the beam and global radiation, viz. logH,,=g+hlogH,
(10)
and applied it to data for Madingley Wood (about 2 km from Cambridge), England. Becker” reported two correlations based upon average monthly values for Chiva-Chiva, Panama. In this case, the monthly mean daily beam radiation was calculated from the difference between measured global and diffuse (using a shadow band) radiation. He correlated his data both in a linear logarithmic format as suggested by Anderson and the usual format, i.e., beam fraction of global radiation as a function of clearness index. He observed that the former was slightly curvilinear, whereas the latter was linear and was described by the following equation: H,,/H = -0.14
+ 1.26KT,
(11)
with a correlation coefficient of 0.948. He also observed that the data for a number of months characterized by relatively clear skies were lower than expected (i.e., their values were below those predicted by the average yearly empirical equation) and hypothesized that it was due to increased turbidity. He was unable to validate his explanation, since no turbidity data have been recorded for Chiva-Chiva area. Kalma and Fleminglx normalized Anderson’s correlation by dividing both the daily beam and global radiation by the average monthly extraterrestrial radiation, Ho,_, in an attempt to remove the site dependence aspect of the correlation. They were successful in correlating average monthly data from 14 sites (from 28”35’N to 51”24’S, 12 of the sites being in the southern hemisphere) by a single correlation given by HJHo.svg = O.o032(H/H,,,,,,)‘-““,
(12)
but they did not report any indication of the data fit to the correlation. We have not attempted to compare our correlations to those reported for these sites, since these correlations were presented in a totally different format and the sites are very distant from our region and subject to different climatic conditions. H,,/H us H/H,.: seasonal and yearly correlations
We have applied the correlation equation in the form suggested by Bugler,’ which corrects for the multiplicity of possible cloud conditions that result in the same value of KT, to our data for Beer Sheva and the results are listed in Table 1. A comparison of the corresponding correlation coefficients and RMSE values for the empirical equations relating HJH to either K, or H/H, reveals that there is no improvement. In fact, the data for the summer season exhibits a significantly poorer fit. This is due to the fact that Bugler’s correlation is intended to
532
A. IANETZ and A. I. KUDISH
correct only for the effect of multiple cloud covers and does not attempt to consider the effect of either turbidity or moisture content of the atmosphere. This agrees with the abovementioned explanations regarding summer data for this region in general. Also, with regard to the other seasons it may be attributed to the fact that as the time interval of the analyses increases (i.e., from hourly to daily values), its ability to diminish the degree of scattering decreases.
CONCLUSIONS
Empirical correlations for predicting both beam and diffuse radigtion at Beer Sheva, located in the semi-arid southern region of Israel, have been developed. These equations relate either the beam or the diffuse fraction of the global radiation to the clearness index. The available data, composed of normal incidence beam and global radiation measurements, have been analyzed on both a seasonal and a yearly basis. They have been compared to empirical equations previously reported in the literature for six sites in the Middle East region. In the case of Qidron, Israel, and three Greek sites there was close agreement between the correlations, whereas in the remaining two sites (Gilat, Israel and Fudhaliyah, Iraq) the correlations were quite different. These discrepancies have been discussed in detail and explanations have been proposed in the text. The beam fraction of the global radiation was also correlated to the ratio of measured daily global to the corresponding clear sky daily global values (determined empirically), in an attempt to reduce the degree of scatter observed in the correlations between beam fraction of global radiation and clearness index. This approach is intended to correct for the multiplicity of possible cloud conditions that give the same value for the cloudiness index. It was not successful when applied to the Beer Sheva data, viz. it did not reduce the degree of scatter observed in the original correlations. This may be attributed, in part, to the fact that the effectiveness of the application of such a correction factor is, a priori, a function of the measurement time interval under consideration. As the measurement time interval increases, the affect of distinct but short-lived cloud formations on the average clearness index value during the time interval under consideration becomes of minor importance. Nevertheless, the major reason for the lack of improvement, especially with regard to the summer data, is due to the fact that the scatter is, in all likelihood, caused by local climatic conditions (viz. turbidity and moisture content of the atmosphere). Acknowledgements-We
are indebted to E. Berman for his partial support of this research by funding the purchase of the Normal Incidence Pyrheliometer system. We wish to thank G. Stanhill of the Volcani Institute for his remarks and suggestions during the preparation of this manuscript. We also wish to thank A. Manes and I. Seter of the Israel Meteorological Service for their encouragement of this joint research project.
REFERENCES 1. A. I. Kudish, D. Wolf, and Y. Machlav, Sol. Energy 30, 33 (1983). 2. J. W. Bugler, Sol. Energy 19, 477 (1977). 3. R. Stauter and S. A. Klein, private communication, cited in J. A. Duffie and W. A. Beckman, Engineering of Thermal Processes, p. 72, Wiley, New York, NY (1980). 4. J. P. Lestrade, B. Acock, and T. Trent, Sol. Energy 44, 115 (1990). 5. World Meteorological Organization, World Climate Program Report WCP-48 (1983). 6. S. I. Sivkov, Computation of Solar Radiation Characteristics (translated from the Russian), Program for Scientific Translations, Jerusalem (1971). 7. A. Soler, Sol. Energy 44, 297 (1990). 8. G. Stanhill, Sol. Energy lo,96 (1966). 9. G. Stanhill, J. Clim. 7, 247 (1987). 10. D. P. Lalas, M. Petrakis, and C. Papadopoulos, Sol. Energy 39, 455 (1987). 11. N. Al-Hamdani, M. Al-Riahi, and K. Tahir, Sol. Energy 42, 81 (1989).
Solar
Israel
Empirical
12. 13. 14. 15. 16. 17. 18.
correlations
for predicting
beam
and diffuse
radiation
A. J. Drummond, Arch. Met., Wein B. 7, 414 (1956). G. Stanhill, private communication (1991). M. Al-Riahi, N. Al-Hamdani, and K. Tahir, Sol. Energy 44, 7 (1990). P. Handler and K. Andsager, ht. J. Clim. 10,413 (1990). M. C. Anderson, Agric. Met. 3, 310 (1970). P. Becker, Sol. Energy 39, 445 (1987). J. D. Kalma and P. M. Fleming, Arch. Met. Geoph. Biokl, Ser. B. 20, 191 (1972).
533
Energy Vol. 17, No. 6, Pp. 523-533, 1992 Printed in Great Britain. All rights reserved
CORRELATIONS BETWEEN DIFFUSE AND GLOBAL SHEVA,
VALUES OF DAILY BEAM, RADIATION FOR BEER ISRAEL
A. IANETZ Israel Meteorological
Service, Research and Development Israel
Division, P.O. Box 25, Bet-Dagan 50205,
A. I. KUDlSHt Solar Energy Laboratory, Department of Chemical Engineering, Ben-Gurion University of the Negev, Beer Sheva 84105, Israel (Received 30 July 1991)
Abstract-Empirical correlations for predicting both beam and diffuse radiation at Beer Sheva, located in the semi-arid southern region of Israel, have been developed. These equations relate either the beam or the diffuse fraction of the global radiation to the clearness index. The available data, composed of normal incidence beam and global radiation measurements, have been analyzed on both a seasonal and a yearly basis. They have been compared to empirical equations previously reported in the literature for six sites in the Middle East region. In the case of Qidron, Israel, and three Greek sites, there was close agreement between the correlations, whereas in the remaining two sites (Gilat, Israel and Fudhaliyah, Iraq) the correlations were quite different. Reasons for the discrepancies in the latter two cases are presented in the text. The beam fraction of the global radiation was also correlated to the ratio of measured daily global to the corresponding clear sky daily global values, which were determined empirically in an attempt to reduce the degree of scatter observed in the correlations between beam fraction of global radiation and clearness index. This approach is intended to correct for the multiplicity of possible cloud conditions that can give the same value for the cloudiness index. It was not successful when applied to the Beer Sheva data, namely, it did not reduce the degree of scatter observed in the original correlations. This, in all likelihood, highlights the fact that the scatter is caused by local climatic conditions (such as turbidity and moisture content of the atmosphere).
INTRODUCTION
A prerequisite for designing solar energy conversion systems is the availability of solar radiation data for the site. The kind of data required depends upon the type of system under consideration, that is, whether it utilizes global or beam radiation. Most meteorological stations measure global radiation whereas the number of stations measuring beam radiation is much smaller. The reason for this is, in general, due to budgetary constrictions with regard to equipment and staff. Beam-radiation measurements require more expensive instrumentation and require maintenance for the daily adjustment of the declination angle of the tracking device (this is especially troublesome in remote automated stations). This problem has given impetus to the development of empirical correlations between beam and global radiation. These correlations usually take the form of beam or diffuse fraction of the global radiation as a function of some kind of normalized index of the global radiation and may be reported on either an hourly or daily basis. The most common format for reporting such correlations is as the diffuse fraction of global radiation on a daily basis as a function of the daily clearness index, i.e., the ratio of global to extraterrestrial radiation. It has been observed that such correlations are generally a function of the location of the meterological station, i.e., they are not universal. tTo whom all correspondence
should be addressed. 523
A. IANETZ and A. I. KUDISH
524
We have determined daily empirical correlations based upon data from Ben-Gurion University of the Negev’s Solar Energy Laboratory’s meteorological station, which is part of the national network. It is located in Beer Sheva (31”15’N, 34”48’E, 315 m MSL), in the semi-arid Negev region of southern Israel. This site is characterized by an abundance of global radiation, viz. an annual average daily global radiation of 18.43 MJ/m’.’ These correlations will also be compared to those previously reported in the literature for this region of the globe.
THEORY
The empirical correlations reported in the literature have described the beam or diffuse fraction of the global radiation as either a linear or polynomial function of the clearness index in the range of values corresponding to neither perfectly clear or cloudy days, viz. in the intermediate range. Thus, these correlations take the form of either Hi/H = a + bKT
(1)
or Hi/H = a,, + a,K,
+ a,Kt + a3K$ + a,K&
(2)
where (Hi/H) is either the daily beam or diffuse fraction and KT is the daily clearness index. Bugler* observed that the scatter of data points using the above type of correlations was due, in part, to the variety of possible cloudiness states corresponding to a particular value of KT. The amount of scatter that can be attributed to the multiplicity of cloudiness states is a function of the time interval under consideration, i.e., hourly or daily values, since as the time interval increases the cloudiness index is averaged over a longer time period and the contribution of individual cloudiness states is proportionally reduced. He corrected for this phenomena by normalizing the hourly global radiation values, I, to the corresponding clear sky hourly value, I,, and correlated his data for Melbourne by the following type of equation: f/I
=
a0
+
a,(Z/Z,) + a,(ZlZ,)* + a3(r/4)3 + a4(1/L)4.
(3)
Stauter and Klein3 have also used this type of analysis to correlate data for five U.S. cities. Lestrade et al4 have recently proposed the use of isonebs, lines of constant cloud cover, to correct for the multiplicity of possible cloudiness states corresponding to a singular value of K,.
MEASUREMENTS
The normal incidence beam radiation is measured using an Eppley Normal Incidence Pyrheliometer, Model NIP, which was connected to an Eppley Electronic Integrator Model 413-6140 (it includes a Digitec 6140 digital printer) and cumulative values were printed at hourly intervals. The global radiation is measured using Eppley Precision Spectral Pyranometers, Model PSP, which was connected to a Kipp & Zonen Printing Solarimeter Integrator CC 2 and the cumulative values were printed at 30 min intervals. The instruments are calibrated at regular intervals by the Israel Meteorological Service. The errors involved in the radiation measurements are assumed to be no less than f1.5% for the normal incidence beam radiation and f2.5% for the global radiation. Only days for which a complete set of hourly data existed for both radiation measuring devices were included in the analysis. The validity of the individual hourly values of global, beam and diffuse radiation were checked in accordance with WMO recommendations.’ Those
Empirical correlations for predicting beam and diffuse radiation
values which did not comply with the WMO recommendations rejected.? Extreme data were also omitted.
were considered
525
erroneous
and
RESULTS
We have presented the results of the analysis of our data in three different empirical formats. First, the daily beam fraction of global radiation as a function of the clearness index (H,,/H) = u f hK,. Second, the daily diffuse fraction of global radiation as a function of the clearness index
(H~/H) = c + dK,. Third, the daily beam fraction of global radiation global radiation to the clear day global radiation
as a function of the ratio of the measured
(HJH) = e +f(HIH,).
(6)
The clear day radiation was defined empirically for each individual month as the sum of the highest measured global radiation value for each hour of the day from the database for each month.h In each case we also analyzed the data using a second-order polynomial and observed that there was no significant improvement in the fit of the data to the polynomial empirical equation relative to that for the linear equation, i.e., the correlation coefficient was only marginally improved. Thus, we concluded that the use of the simpler linear equation was justified. The measured beam radiation data were converted to diffuse radiation values in order to facilitate comparison to those empirical correlations previously reported in the literature for sites in this region of the globe. The empirical correlation, suggested by Bugler,2 is based upon clear day giobal radiation ]see Eq. (6)] and was used to test whether it reduces the degree of scattering relative to that observed when correlating the data with the clearness index [Eq. (4)]. A priori, it is understood that in the case of daily radiation values its affect is limited, since the effect of a multiplicity of cloudiness states corresponding to a singular value of K7. is reduced as the time interval increases, viz. daily as opposed to hourly values. The measured hourly normal incidence beam radiation values, lb.“, were converted to beam radiation incident on a horizontal surface, jh, by applying the geometric conversion factor to individual hourly values, viz.
z,= It)*” cos
6,,
where 6, is the average hourly incidence angle. These hourly values were in turn summed to determine the daily beam radiation incident on a horizontal surface, Hi,. The daily diffuse radiation values were calculated from the daily global, H, and the daily beam radiation incident on a horizontal surface, Hi,, viz.
TThe major gaps in data acquisition were due, in general, to one of the following: (i) power failures, which caused the PSP integrator to reset to zero and froze the NIP integrator until reactivated manually. In addition, an error proportional to the length of the power failure was introduced into the integrator clocks and the NIP solar tracker; (ii) mechanical failure of the PSP integrator’s paper advance mechanism resulted in data being printed on top of each other and rendering them indecipherable. These probtems, except for the solar tracker, were eliminated in July 1988 when the NIP and PSP were connected to a (rechargeable) battery powered datalogger which utilizes a tape cassette to store the data.
A.
526
IANETZ
and A. I. KUDISH
Table 1. Empirical correlations, Season
i
Correlation
1 No. days1
1
RMSE
(a) HbiH = a + bKT Winter
261
Spring
331
925
Year
H,/H H,,/H Hi/H H,,lH H;fH
=-0.320 + 1.597 + 1.641 +2.051 + 1.433 + 1.520
=-0.410 =-0.673 =-0.225 =-0.304
KT Kr KT
0.924 0.933 0.867 0.901 0.930
KT‘I K;
0.093 0.070
I
0.035 0.068 0.077
(b) HJH = c + dKT
150
H&H HdtH HJH I H~/H
Autumn
I
Year
j 971 1Hi/H
= = = =
I .287 1.534 KT 1.372 - 1.577 KT 1.725 - 2.133 KT 1.215 - 1.436 K;
= 1.285 - 1.494 K;
0.091 0.072 0.034 0.065
I
0.928 0.933 0.878 0.912
I
]
0.932
1 L_ 0 078
0.941 0.921 0.740 0.908 0.923
0.083 0.076 0.042 0.058 0.081
(c) Hb/H = e + fH/H
The daily extraterrest~al radiation on a horizontal calculated using the following equation: H, = (24 x 36OOG,/rrt)[l+
surface from sunrise to sunset, I&,, was
0.033 cos(360n/365)] x [cos c) cos 6 cos co, + (2nwJ360)
sin Cpsin 61,
(9)
where Q, is the latitude, 6 the declination angle, o, the sunset hour angle, and G,, the solar constant (which was taken as 1367 W/m’). The data were analyzed both on a yearly and a seasonal basis and the results are presented in Table 1. We have also reported in Table 1 both the correlation coefficients (r) and the root 1
.o
08
06
I: \
+
Winter
x
spring
0
Summer
*
Autumn
1” 04
02
0.2
04
06
K(T)
Fig. 1. Relationship
between the daily beam fraction of global radiation and the clearness index.
08
527
Empirical correlations for predicting beam and diffuse radiation 10
08
06
I \
+
Winter
x
Sprmg
0
Summer
l
Autumn
+
.b
+ + +
<
‘3
+*+*
.* 04
+
.. +x + +
+
02
02
00
06
06
04
K(T)
Fig. 2. Relationship between the daily diffuse fraction of global radiation and the clearness index.
10
08
06
+ Winter 8 Spring 0
Summer
*
Autumn
? I”
04
” +
x t+
02
+
02
00
04
0.6
0.8
H/He
Fig. 3. Relationship
between the daily beam fraction of global radiation and the ratio between the measured global radiation to clear day global radiation.
IO
A. IANETZ and A. I. KUDISH
528
mean square error of the fit to the empirical equations (RMSE). The seasons were defined for Beer Sheva as follows: winter-December, January, and February; spring-March, April, and May; summer-June, July, and August; autumn-September, October, and November. The results are presented graphically in Figs. l-3.
DISCUSSION
It is apparent from the differences observed in Table 1 for the values of the coefficients of the empirical equations for the four seasons, irrespective of which correlation format is utilized, that the use of a single yearly empirical equation is not appropriate. In fact, in theory it would be more accurate to develop monthly as opposed to yearly or seasonal empirical equations. This is a consequence of the complicated functional dependence of solar radiation on cloudiness (conditions/types), moisture content of the atmosphere, and atmospheric turbidity, which, in general, vary from month to month. Also, the components of global radiation, viz. its distribution between beam and diffuse radiation components, are a function of air mass, which varies from month to month. Due to the limited size of our database, we have confined our analysis to yearly and seasonal correlations. There exists ample evidence that the empirical equations are not universal but a function of the location of the meteorological station (viz. latitude and local climatic conditions). In fact, Soler7 has recently attempted to correlate the empirical coefficients of the equation relating the diffuse fraction to the clearness index for 28 European sites located between 36 and 61”N lat and between 29”E and 11”W long. It is apparent from his analysis that there is a relatively large degree of scatter in the values for the empirical coefficients reported for these sites. We have therefore limited our comparative analysis of the present work with respect to previously published empirical correlations, to sites in the Middle East region (cf. Table 2). H,/H
us K,: yearly correlations
The coefficients of the empirical equations correlating the diffuse fraction as a function of the clearness index for six sites in our region, on a yearly basis, are listed in Table 3 for comparison purposes. All the correlations were derived from daily values, except for Qidron, Israel and Fudhaliyah, Iraq, which utilized average monthly values. It should also be emphasized that for all sites, except for Beer Sheva, the diffuse radiation was measured directly utilizing either a shadow band (Gilat, ’ Qidron,’ and Greek sites”) or shadow disk (Fudhaliyah”), whereas for Beer Sheva it was calculated from measured normal incidence beam radiation values as described above. It is important to emphasize, especially with regard to the following discussion, that the diffuse radiation measurements for Gilat were corrected for the anisotropy of sky radiation using the Drummond’* empirical correlation, whereas at Qidron the shadow band correction for anisotropy was calculated using a locally fitted factor. The latter procedure being the preferable one.13 In the case of both the Greek sites”’ and Fudhaliyah,” no definitive statement is made in their manuscripts concerning the application of a correction factor to the diffuse radiation measurements, though in the former a general statement is made that “all appropriate corrections have been made”. In a more recent manuscript describing the solar Table 2. Locations utilized in comparative analysis of empirical equations. Location
Reference
Beer Sheva. Israel Gilat. Israel Qidron, Israel Fudhaliyah, Iraq Athens, Greece Rodos, Greece Kythnos. Greece
this work : :2, 10 10
Empirical correlations for predicting beam and diffuse radiation Table 3. Correhtion
between f&/H
529
and K-,- iearly basis). -I_
site BeerSheva, israell-Gilat,Israel Qidron. Israel Fudhaliyah, Iraq Athens.Greece
Rodos, Greece Kythnos, Greece Greece -
(above 3 combined: --
3eriod(diyj C 971d 1.285 709d 1 539 1983-5 1.112 1985-6 1983 1984 1985 1982 1983 7981 1982 18196
1.102 1.37 1.38 1.35 138 1.35
1.31 1.35 136
1
d
r
-494 -1 755 -1.203 -1 299 -1.54 -165 -1.59 -1.64 -1.60 -1.52 -1.59 -160
0.932 0.84 0.917 0905 0.941 0.937 0.923 0.963 0.948 0.942 0.952 0.940
-I
Reference thiswork 8 9 11 t'El 10 10 ?O to 10 10
radiation climate of Fudhaliyah” it is clearly stated that no sky anisotropy correction was applied to the diffuse radiation measurements. It should be noted that in some cases the correction factor to diffuse radiation may be of the order of 20% (viz. the reported values can be significantly lower than the true values.) It is apparent from Table 3 that the correlation for Beer Sheva is most similar to those determined for the Greek sites. A comparison of values calculated from 12 empirical equations listed in Table 3 for the diffuse fraction in the range of 0.4 d Kr g 0.7 confirms this, viz. that the average relative di~eren~e between Beer Sheva and the Greek sites is the lowest, -5.8% (with the exception of Athens 1983, where the average relative difference is about 15%). The relative difference being defined as the difference in calculated diffuse fraction values relative to that value for Beer Sheva [i.e., A(&/H)/(H,IN)n,,, shcva1. The Greek site correlations predict somewhat greater diffuse fractions. There is also very good agreement between Beer Sheva and Qidron, the average retative difference being -7.7%. The correlation for Fudhaliyah predicts lower diffuse fractions (by about 16%) than that for Beer Sheva. The former is based upon monthly average values, whereas the latter is derived from daily values. Lalas et al” have reported both daily and monthly average correlations for all the Greek sites and the corresponding empiricat equations are significantly different in each case. This factor may contribute, somewhat, to the differences between Fudhahyah and Beer Sheva empirical correlations. Nevertheless, it is very likely that these discrepancies are the result of differences in data measurement and processing methods. If, indeed, no sky anisotropy correction was applied to the diffuse radiation measurements, as was stated with regard to a later manuscript,‘4 than the direction and magnitude of the discrepancy may be explained by this fact. The relatively large discrepancy between the correlations for Gilat and Beer Sheva is especially disturbing, since Gilat is located just about 20 km northwest of Beer Sheva and one would expect the two correlations to exhibit close agreement (cf. close agreement between Beer Sheva, the three Greek sites and Qidron). The former predicts much larger diffuse fractions as a function of clearness index than the latter (average relative difference being about 26%). We are of the opinion that either this region was characterized by an exceptionally high diEuse fraction during the time interval 1960-1964 when the data utilized in this analysis were collected or there may have been some systematic error in the data collection. It has been brought to our attention by Stanhillr3 that this was a p eriod of exceptionally high volcanic activity and hence atmospheric turbidity in the northern hemisphere,‘5 The diffuse fractions calculated using the Gifat equation appear to be abnormally high for this region (e.g., H,/N = 0.84 for Kr = 0.4 and E&/H = 0.49 for Kr = 0.6). Also, the correlation eoefEcient for Gilat is the lowest of all those reported in Table 3. We have no other suggestions for explaining this discrepancy, especially since the data in question were measured more than 26 yr ago. The close agreement between Beer Sheva and Qidron vis-a-vis the poor agreement between these two sites and Gilat may also reflect on the relative ability of the correction factor used to correct for the anisotropy of sky radiation to perform its function, i.e., a locally fitted factor as opposed to the empirical Drummond factor.
A.
530
IANETZ
and A. I. KUDISH
Table 4. Correlation between H,/H Site
C
1
and KT (seasonal basis). d
1
r
Reference
Winter
H,/H
Beer Sheva, Israel Fudhaliyah. Iraq Athens, Greece Rodos + Kythnos. Greece
1.207 1.199 1.38 1.33
-1.534 -1.494 -1.65 -1.56 Spring
0.928 0.902 0.922 0.938
this work
Beer Sheva. Israel Fudhaliyah. Iraq Athens. Greece Rodos + Kythnos. Greece
1.372 1.325 1.45 1.42
-1.577 -1.634 -1.67 -1.65 Summer
0.933 0.927 0.941 0.957
this work
Beer Sheva, Israel Fudhaliyah. Iraq Athens. Greece Rodos + Kythnos. Greece
1.725
-2.133 -1.480 -1.47 -1.61 Autumn
0.878 0.821 0.077 0.891
this work
1.202 1.29 1.35
Beer Sheva, Israel Fudhaliyah, Iraq Athens. Greece Rodos + Kythnos. Greece
1.215 1.127 1.40 1.35
-1.436 -1.390 -1.71 -1.65
0.912 0.903 0.941 0.958
this work
:; 10
::, 10
:: 10
:: 10
us K,: Seasonal correlations
The coefficients of the seasonal empirical correlations for four sites are listed in Table 4 (the data for Gilat and Qidron were not analyzed on a seasonal basis and the data for Rodos and Kythnos were combined). It should be noted that the seasons have not been defined alike for all sites. Al-Hamdani et al” defined them in the following manner: winter-January, February, and March; spring-April, May, and June; summer-July, August, and September; autumnOctober, November, and December, whereas Lalas et al” did not define them in their paper. In all cases, the coefficients are observed to vary from season-to-season, though the Rodos + Kythnos data exhibit the smallest seasonal dependence. It is important to note that the correlation coefficient is lowest, in all cases, for the summer data. Also, the empirical equations for summer for both Beer Sheva and Athens are distinctive in that their absolute values for both coefficients are a maximum for the former and minimum for the latter, relative to the other seasons. We believe that the relatively low correlation coefficients observed for the summer data can be attributed to the nature of the statistical analysis. The summer is characterized in this region by an abundance of relatively clear days, i.e., high KT values. The range of KT values on which the empirical correlations were derived is very narrow, as opposed to the other seasons. In the case of Beer Sheva the range is 0.59 < KT < 0.75 and for Fudhaliyah it was approximated to be 0.6 < KT < 0.7, as observed from Fig. 1 of Ref. 11. The range of values utilized for the Greek sites was not reported, but we believe that it is, in all likelihood, very similar. Thus, it is not surprising that attempting to fit a linear equation to such a narrow range of values for the independent parameter will result in a relatively low correlation coefficient. It may also be possible that atmospheric turbidity may contribute to the lower correlation coefficients that characterize the summer empirical equations in this region. Beer Sheva summers are characterized by hot dry weather and thus one would expect a higher turbidity caused by dust and sand in the atmosphere. Al-Hamdani et al” have proposed the same explanation with respect to his relatively low correlation coefficient for the summer. Lalas et al” have attempted to explain the relatively low correlation coefficients as being due to increased air pollution, caused by increased photochemical reactivity in the summer months. Since the clearness index does not account for turbidity, one would expect a greater degree of scatter in such correlations. We were unable to check this hypothesis for Beer Sheva, since such data are not available. The agreement between the seasonal empirical correlations is somewhat less than in the case of the yearly correlations (especially with regard to the summer). If we disregard the summer correlation the average differences, relative to Beer Sheva, are 17.6% for Fudhaliyah, 6.4% for
Empirical
correlations
for predicting
beam
and diffuse
radiation
531
Athens, and 4.9% for Rodos + Kythnos. This is as expected, since as the time interval is reduced (i.e., yearly to seasonal basis) the effect of local climatic conditions becomes more pronounced. H,/H us K,: seasonal and yearly correlations
The overwhelming majority of the correlations, between component fraction (either beam or diffuse) of the global radiation as a function of clearness index, reported in the literature are in terms of the diffuse fraction. The reasons for this are practical ones, as discussed in the Introduction section. This was the rationale for converting our measured beam data to diffuse radiation, as mentioned previously. Nevertheless, we believe that since normal incidence beam radiation has been measured for Beer Sheva, such correlations are more appropriate, cf. Table 1. Also, a prerequisite in the design of concentrating solar systems is the availability of beam radiation data or a means of calculating it, e.g., from such a correlation, which is preferable to basing it on diffuse radiation measurements. We did come across a few papers that reported correlations between beam and global radiation. Anderson,” referring to a manuscript that apparently was never published, suggested a linear logarithmic correlation between the beam and global radiation, viz. logH,,=g+hlogH,
(10)
and applied it to data for Madingley Wood (about 2 km from Cambridge), England. Becker” reported two correlations based upon average monthly values for Chiva-Chiva, Panama. In this case, the monthly mean daily beam radiation was calculated from the difference between measured global and diffuse (using a shadow band) radiation. He correlated his data both in a linear logarithmic format as suggested by Anderson and the usual format, i.e., beam fraction of global radiation as a function of clearness index. He observed that the former was slightly curvilinear, whereas the latter was linear and was described by the following equation: H,,/H = -0.14
+ 1.26KT,
(11)
with a correlation coefficient of 0.948. He also observed that the data for a number of months characterized by relatively clear skies were lower than expected (i.e., their values were below those predicted by the average yearly empirical equation) and hypothesized that it was due to increased turbidity. He was unable to validate his explanation, since no turbidity data have been recorded for Chiva-Chiva area. Kalma and Fleminglx normalized Anderson’s correlation by dividing both the daily beam and global radiation by the average monthly extraterrestrial radiation, Ho,_, in an attempt to remove the site dependence aspect of the correlation. They were successful in correlating average monthly data from 14 sites (from 28”35’N to 51”24’S, 12 of the sites being in the southern hemisphere) by a single correlation given by HJHo.svg = O.o032(H/H,,,,,,)‘-““,
(12)
but they did not report any indication of the data fit to the correlation. We have not attempted to compare our correlations to those reported for these sites, since these correlations were presented in a totally different format and the sites are very distant from our region and subject to different climatic conditions. H,,/H us H/H,.: seasonal and yearly correlations
We have applied the correlation equation in the form suggested by Bugler,’ which corrects for the multiplicity of possible cloud conditions that result in the same value of KT, to our data for Beer Sheva and the results are listed in Table 1. A comparison of the corresponding correlation coefficients and RMSE values for the empirical equations relating HJH to either K, or H/H, reveals that there is no improvement. In fact, the data for the summer season exhibits a significantly poorer fit. This is due to the fact that Bugler’s correlation is intended to
532
A. IANETZ and A. I. KUDISH
correct only for the effect of multiple cloud covers and does not attempt to consider the effect of either turbidity or moisture content of the atmosphere. This agrees with the abovementioned explanations regarding summer data for this region in general. Also, with regard to the other seasons it may be attributed to the fact that as the time interval of the analyses increases (i.e., from hourly to daily values), its ability to diminish the degree of scattering decreases.
CONCLUSIONS
Empirical correlations for predicting both beam and diffuse radigtion at Beer Sheva, located in the semi-arid southern region of Israel, have been developed. These equations relate either the beam or the diffuse fraction of the global radiation to the clearness index. The available data, composed of normal incidence beam and global radiation measurements, have been analyzed on both a seasonal and a yearly basis. They have been compared to empirical equations previously reported in the literature for six sites in the Middle East region. In the case of Qidron, Israel, and three Greek sites there was close agreement between the correlations, whereas in the remaining two sites (Gilat, Israel and Fudhaliyah, Iraq) the correlations were quite different. These discrepancies have been discussed in detail and explanations have been proposed in the text. The beam fraction of the global radiation was also correlated to the ratio of measured daily global to the corresponding clear sky daily global values (determined empirically), in an attempt to reduce the degree of scatter observed in the correlations between beam fraction of global radiation and clearness index. This approach is intended to correct for the multiplicity of possible cloud conditions that give the same value for the cloudiness index. It was not successful when applied to the Beer Sheva data, viz. it did not reduce the degree of scatter observed in the original correlations. This may be attributed, in part, to the fact that the effectiveness of the application of such a correction factor is, a priori, a function of the measurement time interval under consideration. As the measurement time interval increases, the affect of distinct but short-lived cloud formations on the average clearness index value during the time interval under consideration becomes of minor importance. Nevertheless, the major reason for the lack of improvement, especially with regard to the summer data, is due to the fact that the scatter is, in all likelihood, caused by local climatic conditions (viz. turbidity and moisture content of the atmosphere). Acknowledgements-We
are indebted to E. Berman for his partial support of this research by funding the purchase of the Normal Incidence Pyrheliometer system. We wish to thank G. Stanhill of the Volcani Institute for his remarks and suggestions during the preparation of this manuscript. We also wish to thank A. Manes and I. Seter of the Israel Meteorological Service for their encouragement of this joint research project.
REFERENCES 1. A. I. Kudish, D. Wolf, and Y. Machlav, Sol. Energy 30, 33 (1983). 2. J. W. Bugler, Sol. Energy 19, 477 (1977). 3. R. Stauter and S. A. Klein, private communication, cited in J. A. Duffie and W. A. Beckman, Engineering of Thermal Processes, p. 72, Wiley, New York, NY (1980). 4. J. P. Lestrade, B. Acock, and T. Trent, Sol. Energy 44, 115 (1990). 5. World Meteorological Organization, World Climate Program Report WCP-48 (1983). 6. S. I. Sivkov, Computation of Solar Radiation Characteristics (translated from the Russian), Program for Scientific Translations, Jerusalem (1971). 7. A. Soler, Sol. Energy 44, 297 (1990). 8. G. Stanhill, Sol. Energy lo,96 (1966). 9. G. Stanhill, J. Clim. 7, 247 (1987). 10. D. P. Lalas, M. Petrakis, and C. Papadopoulos, Sol. Energy 39, 455 (1987). 11. N. Al-Hamdani, M. Al-Riahi, and K. Tahir, Sol. Energy 42, 81 (1989).
Solar
Israel
Empirical
12. 13. 14. 15. 16. 17. 18.
correlations
for predicting
beam
and diffuse
radiation
A. J. Drummond, Arch. Met., Wein B. 7, 414 (1956). G. Stanhill, private communication (1991). M. Al-Riahi, N. Al-Hamdani, and K. Tahir, Sol. Energy 44, 7 (1990). P. Handler and K. Andsager, ht. J. Clim. 10,413 (1990). M. C. Anderson, Agric. Met. 3, 310 (1970). P. Becker, Sol. Energy 39, 445 (1987). J. D. Kalma and P. M. Fleming, Arch. Met. Geoph. Biokl, Ser. B. 20, 191 (1972).
533