Renewable Energy, Vol.5, Part I1, pp. 1517-1519, 1994 a-©a t g n - u a m o n Elsevier Science Lid

Printed in Great Britain 0960--1481/94 $7.004-0.00

A SEARCH FOR THE BEST RELATION TO BE USED TO ESTIMATE MONTHLY MEAN DAILY DIFFUSE SOLAR RADIATION ON A HORIZONTAL SURFACE FOR EUROPE

A. Soler and P. Oteiza

Radiation and Daylighting Research Unit, Departamento de Fisica, ETS de Arquitectura, Universidad Polit6cnica, Avda. Juan de Herrera, 4. 28040 Madrid (Spain).

Fax: (91) 336 65 34

ABSTRACT

A number of relations are availm~ole to estimate monthly mean diffuse solar radiation on an horizontal surface (D) when the monthly mean daily global radiation (G) and/or the monthly mean daily number of sunshine hours (S) are known. In the present work, taking as a reference 264 values of D computed for the period 1966-1975 with the European Community solar radiation model, it is shown that many new types of relations can be found, which perform statistically better than those available. Mean monthly solar declination is a new, easy to use, variable to be taken into account when D has to be predicted over large areas with the highest possible accuracy.

KEYWORDS

Mean Monthly Diffuse Radiation, Estimation of Radiation for Europe.

INTRODUCTION

Relating monthly mean daily values of diffuse radiation (D), correlations available have been classified in four groups, as correlations for estimating: 1) diffuse radiation from clearness index (Page, 1961; Soler, 1990); 2) diffuse radiation fi'om global radiation before striking the ground (Hay, 1976); 3) diffuse radiation from relative sunshine duration (Iqbal, 1979); 4) diffuse radiation from both, clearness index and sun.~hine data (Gopinathan and Soler, 1994). Statistical analysis shows that when both, clearness index and relative sunshine duration are combined together in multiple linear correlation analysis, it is observed that the accuracy of the estimated values of D is better than when they are used separately (Gopinathan and Soler, 1994). In the present work, taking as a reference values of D computed for 22 European locations with the European Community (E.U.) solar radiation model (Page, 1986, European Solar Passive Handbook, 1986), it is found that many new types of correlations perform statistically better than those available.

DATA USED

We have used values of D computed with the E.U model for the period 1966-75 for 22 European locations (Page, 1986, European Solar Passive Handbook, 1986), with latitudes in the range 380-60%/. Values of the monthly clearness index G/Go (Go being the monthly mean extraterrestrial radiation), S/So (So being the monthly mean daily number of sunshine hours), and (a+b), this being the sum of the coefficients a and b in the Angstron regression equation for each month, are empirical (Commission of the European Communities,

1517

1518

1984). Values of the mean solar declination for each month 8 are available (Page, 1986).

DIFFUSE RADIATION CORRELATIONS DEVELOPED FOg THE 264 VALUES OF D

A p~limlntry analysis of all the data showed that correlations of the following general type could be used to predict values of D.

D ~ ~ ~ ~ 3 K 3 ! - - = a + b ' Y ' .b(S / So)+'~" . ~(G /Go)+~"~, .dg+'~" g(a+b)+fO (1) G ~--J i I i ~ ~ -d ] = l j - - a . l V* &,-dl-14[

Up to 43 correlations were tested. An example of the adopted procedure follows. Let us suppose that we establish the following correlation for the 264 sets ofmontldy values:

D = a +b(S / So)+c(G / Go)+d~ (2) G

Then, in equation (1) i=l, j=l, k=l, and no dependence on (a+b), (1= -), or ~ (n= -), is assumed. Using the values of the coefficients in equation (2), obtained by the least squares method, values of D/G are predicted, and values of D are computed. The~, we calculate the MBE, RMSE, % MBE and % RMSE (the last two ones using the mean value of D, obtained from the 264 values given by the E.U. model). The 43 correlations tested have been ordered taking into account the % RMSE, and some of them are given in Table 1. Correlations number 29 (Gopinathan and Soler, 1994), 36 (Page, 1961, Soler, 1990) and 39 (Iqbal, 1979) are those used up to now.

Tabla 1. % RMSE, and % MBE for some of the 43 correlation studied.

l~anking fi'om % RMSE i j k 1 n %RMSE %MBE

1 st 1,2 1,2 1,2 1 2 nd 1,2 1,2 1,2 - 3rd 1 1 1 1 1 4 th 1,2 1 1,2 1 - 5th 1 1 1 1 - lOth 1,2 1 1,2 1 - 13th 1 1 1 - 15 th 1 1,2 1 - 20 th 1 1 - 25 th 1,2 1 - 29 th 1 1 - 36th 1 - 39 th 1

86 ,88 ,96 ,98 ,06

3 3 3 3 4 4,20 4,58 4,80 5.16 5,34 5,93 6,83 6,97

-0,04 0,30

-0,10 0,11

-0,04 0,39

-0,04 0,02 0,02

-0,96 1,04

-1,10 -0,29

The ratios of file differences between the values given by the E.U. model, and tile values pledicted by conelations have been obtained and the % dcvialion computed. For the first equation in Table 1, for 11% of

1519

the 264 values o lD the % deviation is larger than 5 % and only 5 % of the predicted values of D show a % deviation higher than 7 %. For equations 29, 36 and 39 in Table 1 however, 33 %, 35% y 39 % of the values of D are predicted with a % deviation higher than 5 %.

CONCLUSIONS

As a part of a larger work, the E.U. solar radiation model has been used in a search for the best relation to estimate monthly mean daily diffuse solar radiation a horizontal surface for Europe. The importance of taking into account a dependence on ~ and (a+b) has been investigated, see Table 1, and is stressed apparently for the first time.

REFERENCES

Commission of the European Communities. (1984). European solar radiation atlas, Vol l, 2nd edition, Global radiation on horizontal surfaces, TUV Verlag.

European Solar Passive Handbook. (1986). Basic principles and concepts for passive solar architecture. Preliminary Edition, Appendix D.

Gopinathan, K.I~ and A. Soler. (1994). A multiple linear correlation for diffuse radiation from global and sunshine data. Int. Jour. of Solar Energy, in press.

Hay, J.E. (1976). A revised method for determining the direct and diffuse components of total short wave radiation. Atmosphere, 14, 278-287.

Iqbal, M. (1979). Correlation of average diffuse and beam radiation with hours of bright sunghine. Solar Energy, 23, 169-173.

Page, J.IL (1961). The estimation of monthly mean values of daily short wawe radiation on vertical and inclined surfaces from sunshine records for latitudes 40°N-40°S. Proc. U.N. Conference on new sources of energy. Paper S. 98, Vol 4, 378-390.

Page, J .g , editor. (1986). Solar radiation on inclined surfaces. D. Reidel Publ. Co. Soler, A. (1990). Dependence on latitude of the relation between the diffuse fraction of so-

lar radiation and the ratio of global to extraterrestrial radiation for monthly average daily values. Solar Energy, 44, 297-302.

RE 5:8-YY