Theor. Appl. Climatol. 43, 211- 215 (1991) Theoretical and AEplied

Climatology © Springer-Verlag 1991 Printed in Austria

Notes 551.521.1(495)

School of Geology, Department of Meteorology and Climatology Aristotelian University of Thessaloniki, Greece

Empirical Estimation of Daily Clear Sky Solar Radiation in Thessaloniki, Greece

H. S. Sahsamanoglou and T. J. Makrogiannis

With 2 Figures

Received March 1, 1990

Summary

In the present study a mathematical model is proposed for estimating daily clear sky solar radiation in Thessaloniki. The relation I = A.sin (h) + B was used for calculating the inten- sity I of solar radiation. The coefficients A and B depend on the quantities of water vapour and aerosols in the atmosphere and the sunheight (h). A and B have been estimated separately for each month. The application of the proposed model is only possible when the values of A and B and two other astronomical parameters (sun's declination c~ and hour angle /7) are known. A good agreement has been found between observed and computed values, a fact significantly reinforcing the accuracy of the proposed model.

1. Introduction

Many different formulae have been proposed for estimating total solar radiation in Greece. These are based on the sunshine duration values (Flocas, 1980; Flocas et al., 1990; Katsoulis and Papach- ristopoulos, 1978; Sahsamanoglou and Makro- giannis, 1988) and other meteorological data (Karalis et al., 1982; Haradonis , 1985).

Other empirical models have been proposed for the estimation of solar radiation on the basis of actual, oberserved solar radiation data (Koure- menos et al., 1987; Flocas et al., 1988).

In the present work we have used actual daiIy values of total solar radiation in order to estimate the daily clear sky solar radiation in Thessaloniki.

2. Data and Method Used

The main source of data used in this study are the measurements made at the meteorological station of the Aristotelian University in Thessaloniki, lo- cated very near the city centre. These measure- ments cover the period between January 1, 1983 and August 31, 1989 and were made using an Ep- pley Precision Pyranometer , model PSP. F rom the

3 O O4

2 5

2 0 ~

8 I

[E 10

-6 a i G9

I I

5 0 1OO 1 5 0 2 0 0 2 5 0 3 0 0

D A Y S O F T H E Y E A R

3 5 0

Fig. 1. Daily total solar radiation values, during clear sky days in Thessaloniki

212 H.S. Sahsamanoglou and T. J. Makrogiannis

total of 2435 days of this period we have only selected the values of 513 days on which the sky was clear or negligibly cloudy. The daily values of clear sky solar radiadion, vary from 5.38 M J/ m 2 to 25.94 MJ/m 2.

Figure 1 shows that there are different values for the same calendar days of the year. This is due to the different amount of water vapour and aero- sols in the atmosphere during these days. These quantities obviously depend upon the human ac- tivities and weather conditions (Sahsamanoglou and Bloutsos, 1989). The attenuation of solar ra- diation (which is) due to aerosols can indirectly be estimated after having estimated the absorption due to water vapour.

In the present study, in order to have an esti- mate of these quantities, we have estimated them for two characteristic, almost continuous clear sky days (June 19, 1985 and June22, 1985) according to the following logic. The estimation of the at- tenuation AI of solar radiation due to water va- pour and for a specific moment can be made by using the well known relationship of Moller- Miigge (Kondratyev, 1969):

AI = 120" [m*Pw] °3 (Watt/m 2) (1)

where m is the optical mass and Pw the precipitable water in cm.

Considering that during a day the amount of water vapour in the atmosphere over a specific area does not vary significantly it is possible to integrate the Eq. (1) over the period between sun- rise and sunset, thus giving the total daily ab- sorption due to water vapour. Thus, for the above two characteristic days, during which the real daily values of total solar radiation were 21.67 MJ/m 2 and 21.95 MJ/m 2 respectively, we have a total absorption of due to water vapour 8.5 MJ/m z for the first day (Pw = 16.4ram) and 9.0 MJ/m 2 for the second day (Pw = 20.0 mm).

According to these results and despite the fact that during the first day the absorption due to water vapour was smaller, total solar radiation was also smaller in relation to the corresponding values of the second day. This means that the difference of 0.78 MJ/m 2 is due to the quantity of aerosols, which was obviously bigger during the first day. In other words, the above gives an in- dication that the attenuation of total solar radia- tion in Thessaloniki during clear sky days is due both to the quantity of water vapour and the quan- tity of aerosols existing in the atmosphere.

3. M o d e l - R e s u l t s

As already known, the intensity (I) of total solar radiation reaching the surface of the earth under clear sky conditions can be estimated by using a relation of the form:

I = A,sin (h) + B (2)

where A and B are coefficients depending upon the turbidity of the atmosphere and h the height of the sun. Relation (2) was used in the past by Holtslag and Van Ulden (1983), Van Ulden and Holtslag (1985). This is also similar to other re- lations proposed by other research such as Lumb (1964), Kasten and Czeplak (1980), Collier and Lockwood (1974), to estimate the intensity (I) as a function of sunheight (h). It is obvious that the coefficients A and B indirectly describe the quan- tity of water vapour and aerosols existing in the atmosphere.

Therefore, the daily solar radiation value R will be given by the relation:

s

R= ' rdt (3) r

where r and s indicate the time of sunrise and sunset respectively.

According to the above relation (2) will become the following:

w s

R = A S sin(h) dt + B ~ dt (4) r r

sin (h) is estimated as:

sin (h) -- sin (~0)*sin (fi) + cos (~0)*cos (fi)*cos(H)

(5) where, ~0 is the latitude of the location/_

is the declination of the sun H is the hour angle of the sun

The estimation of 6 and H can be made by using the empirical relations:

c~ = 23.45°*sin [0.01745* (262-d] (6) cos (/4) = tan (~0)*tan (6) (7)

where d is the number of day. Hence the equation (4) is reduced to

R = 0.02752.A* [H's in ((0)*sin (fi) + cos (~0)*cos (fi)*sin (H)] + 0.02752*B*H

The above equation is the proposed model for estimating clear sky total solar radiation values in

Empi r i ca l E s t i m a t i o n o f Dai ly Clear Sky Solar R a d i a t i o n in Thessa lonik i , Greece

Table I. Monthly Values of Coefficients d and B (W/m 2) for Three Categories of Turbidity in Thessaloniki

213

H i g h tu rb id i ty M e a n tu rb id i ty L o w tu rb id i ty

A B A B A B

J a n u a r y 995 - 48 1,102 - 47 1,156 - 12 F e b r u a r y 913 - 37 1,061 - 43 1,177 - 15 M a r c h 880 - 41 1,050 - 39 1,184 - 11 Apr i l 872 - 41 1,045 - 37 1,158 - 10 M a y 875 - 4 3 1,051 - 35 1,170 - 15 June 878 - 42 1,056 - 34 1, i 71 - 13 July 878 - 42 1,062 - 36 1,144 - 12 A u g u s t 871 - 38 1,064 - 35 1,180 - 15 S e p t e m b e r 906 - 45 1,083 - 42 1,194 - 19 O c t o b e r 983 - 44 1,106 - 40 1,256 - 14 N o v e m b e r 932 - 47 1,163 - 42 1,244 - 15 D e c e m b e r 886 - 50 1,094 - 46 1,253 - 16

Table 2. Values of Coefficients A and B (W/m 2) for Different Areas (Holstlag- Van Ulden 1983)

A r e a A B Refe rence

B o s t o n 1,098 - 65 (42o13 ' N/71°07 ' W)

N. A t l an t i c 1,100 - 50 (52°30 ' N /20 ° W)

H a r r o g a t e 990 - 30 (54°00 'N/ l °30 ' W)

H a m b u r g 910 - 30 (53°38 ' N/9°50 ' E)

D e Bilt 1,041 - 69 (52o06 , N /5° l 1' E)

H a u r w i t z (1945)

L u m b (1964)

Coll ier and L o c k w o o d (1975)

K a s t e n and Czep lak (1980)

Hols t lag and Van U l d e n (1983)

3 O

W 2 5 -3 z

"J 2 0

_8 < > 1 5

~ ~a pr

0 oo

0

0 5 10 15 ~0 25 3 0

0 E~ S. V A L U E S

Fig. 2. O b s e r v e d a n d c o m p u t e d dai ly values o f to ta l so lar r ad i a t i on in Thessa lonik i , du r ing clear sky days

MJ/m 2 according to corresponding monthly val- ues for A and B. Regarding the values of A and B the following are valid. Because the quantities of water vapour and aerosols in the atmosphere

vary from month to month it is calculated that the pair of the values of coefficients A and B throughout the year would not satisfactorily de- scribe the cause for which these coefficients come into the above equation. For this reason we have estimated for each month a different pair of values of A and B believing that the proposed model provides more accuracy. This estimation was made on the basis of hourly values of total solar radiation and the application of the least squares method for Eq. (2). Results are shown in Table 1.

The criterion for dividing into different cate- gories of turbidity has been: The largest daily val- ues of total solar radiation during the second 10 day period of each month concerning days of "low turbidity" and the smallest corresponding value concerning days of "high turbidity".

214 H.S. Sahsamanoglou and T. J. Makrogiannis

Table 3. Mean Monthly Computed (~') and Observed (X) Values (M Jim 2) of Total Solar Radiation in Thessaloniki (Period." January 1, 1983- August 31, 1989)

Y X SD N Y-X o cr/Y (%)

January 7.27 7.37 0.89 (23) -0 .10 0.76 10 February 9.68 9.44 1.61 (16) 0.24 1.03 11 March 13.67 13.45 1.98 (23) 0.21 1.92 14 April 17.98 18.68 1.84 (32) - 0.70 1.96 11 May 21.45 22.26 1.82 (29) -0.81 1.83 9 June 23.07 23.23 1.67 (59) - 0.16 1.65 7 July 21.22 21.45 1.80 (97) - 0.23 1.71 8 August 19.69 19.70 1.70 (92) -0.01 1.43 7 September 15.64 15.54 1.48 (59) 0.10 1.30 8 October 11.44 11.34 1.39 (34) 0.10 0.82 7 November 8.42 8.15 1.00 (22) 0.27 0.62 7 December 6.50 6.49 0.50 (26) 0.01 0.48 7

N Number of clear sky days, ~ root mean square error, SD standard deviation

Based on Eq. (2) and values of A and B (Table 1) it comes out that during the summer, under con- ditions of mean turbidity, the limiting height of the sun over which solar radiation reaches the ground is about 2 ° , while during the winter it is about 2.5 ° .

We can see (Table 1) that the values of A and B show a big difference between days with "low turbidity" and days with "high turbidity" for all months.

Further, as it is shown by Table 2, the pair of A and B values seems to differ from place to place, a fact which has also been reported in other re- search.

To check the accuracy of the proposed model we have estimated the daily values of total solar radiation for the 365 days of the year, taking them, of course, as clear sky days. To do this we used the values of A and B from Table 1 for "mean turbidity". Figure 2 shows the result of the com- parison of the 513 observed daily clear sky values of total solar radiation with the corresponding computed values. The shape of Fig. 2 shows that the above proposed model is accurate enough for Thessaloniki on the clear sky days. In addition, Table 3 indicates that the values of the differences [ ITcomputed)- Jf(observed)] are relatively small, varying between 0.27 and -0.81 MJ/m 2. The ac- curacy of the proposed model is also reinforced by the value of the o-/Y parameter (o- is the root mean square error). We can see (Table 3) that for all months the ~ represent only 7%-14% of the

mean monthly value. Finally, the values of the coefficient of correlation between the observed and computed values are >~ 0.96, as expected.

4. Conclusions

For the same calendar days of the year with clear sky we have observed differences between values of total solar radiation. These differences are mainly due to the varying quantities of water va- pour and aerosols in the atmosphere.

When having values of mean turbidity in the atmosphere of Thessaloniki the height of the sun has to be about 2 ° and 2.5 ° in summer and winter respectively for solar radiator to reach the ground.

The monthly values of A and B coefficients of the proposed model vary and depend both on the turbidity and on the geographical site.

The proposed model can be used with great accuracy (7%-14%) for estimating daily clear sky solar radiation in Thessaloniki.

References

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Flocas, A., Bloutsos, A., Pennas, P., 1988: Estimation of mean monthly hourly values of total solar radiation over Greece. Proc. 3 rd National Congr. Mild Energy Sources, VolA, 57-67 (in Greek).

Flocas, A., Giles, B., Bloutsos, A., 1990: On estimation of monthly mean values of global irradiation over Greece, Z. Meteor., 40, 55-59.

Empirical Estimation of Daily Clear Sky Solar Radiation in Thessaloniki, Greece 215

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Authors' address: H. S. Sahsamanoglou, T. J. Makrogiannis, School of Geology, Department of Meteorology and Cli- matology, University of Thessaloniki, GR-54006 Thessalo- niki, Greece.