Solar Energy. Vol. 23, pp. 61-67 0038-092X/79107(11-00611502.0010 © Pergamon Press Ltd., 1979. Printedin Great Britain CONTRIBUTION TO THE STUDY OF THE SOLAR RADIATION CLIMATE OF LISBON A. J. BIoA and Rut ROSA Ministerio da Industria e Technologia, Laboratrrio de Fisica e Engenharia Nucleares, Sacav~m, Portugal (Received 5 January 1979; accepted 29 January 1979) Abstrad--Based upon a statistical analysis of available data, this paper offers relationships permitting the determination of the direct, diffuse and global radiation intensities, on a horizontal surface and on clear days, and it establishes linear correlations between those three components. Daily sums of diffuse and global radiation, on a horizontal surface and on cloudy days, are found to be correlated with one another and they both can be determined from the knowledge of the insolation fraction. This paper also analyses the contribution of the direct and diffuse components to the daily sum of global radiation on the ground, with emphasis to the contribution of diffuse radiation from the cloudy regions of the sky, and infers some global characteristics of the clouds. Finally, it is shown that four regression parameters alone are enough to make fair predictions of all the statistical relationships involvingdally sums of solar radiation. I. INTRODUCTION The present study was carried out to provide detailed information for the design of solar energy equipment and for predicting their performance under the actual con- ditions in Lisbon. It is based on radiation measurements at Instituto Geofisico da Universidade (the geophysical observatory next to Lisbon University), namely hourly and daily sums of global and diffuse solar radiation, direct solar radiation intensity and duration of sunshine, and on radio-soundings of the atmosphere made by In- stituto Nacional de Meteorologia e Geofisica (the national meteorological office). Solar radiation measurements have been carried out in Lisbon for many years. Global and diffuse radiation sums are obtained by means of a Kipp pyranometer and direct radiation intensity with Eppley and Kipp pyr- heliometers; sunshine records are obtained with a Campbell-Stokes type heliograph. Much of this work is based on the statistical analysis of the data available for the 5 yr 1968, 1972 and 1974-76 which were casually selected from the records. But the precipitable water and turbidity coefficient determinations were done over a period of 11 yr (1966-76) and the variation of the direct radiation with air-mass was determined on the basis of the records of a 9 yr period (1962-70). The present paper studies, in the first place, solar radiation with a clear sky. It establishes the correlation between diffuse and direct radiation intensities as well as the variation of radiation intensity (direct, diffuse and global) with air-mass. Next, the daily sums of solar radiation with cloudy skies are studied. Correlations between diffuse and global radiation sums, as well as of these with insolation fraction, were established. Finally, direct and diffuse contributions to global radiation were analysed, with emphasis to the diffuse radiation con- tribution due to the presence of clouds. 2. THE CORRELATION BETWEEN DIFFUSE AND DIRECT RADIATION INTENSITIES UNDER CLOUDLESS CONDITIONS As solar radiation penetrates the atmosphere, it is depleted by absorption (due to molecular gases, mainly Rayleigh scattering produced by air molecules and Mie scattering by atmospheric dust). The short wavelength radiation finally arriving at ground level has two com- ponents, one direct and the other diffuse, which in- tensities reflect the influence of solar altitude, atmos- pheric water vapor and dust contents as well as other minor extinction factors. The whole picture is even more involved because ground albedo rein-forces the intensity of the diffuse radiation. We shall now define the atmospheric transmission coefficients for the solar direct radiation rs and for the diffuse solar radiation ~'o, for a horizontal surface at ground level. These quantities are given by the ratio between those intensities falling on such a surface and the intensity arriving on a horizontal surface on top of the atmosphere: rs = S*/H* and ro = D*/H*. According to the analysis carried out by Liu and Jordan[l] with the data for clear skies from three sta- tions in the U.S.A., there exists a statistical linear rela- tionship between zo and rs of the form: ro = c~- c2rs (1) which should be applicable to different localities having not very different atmospheric contamination by dust and ground albedo and which was found to be not sensitive to solar altitude (or air-mass). The variation of both quantities is then basically determined by atmos- pheric water vapor content. 61 SE Vol. 23, No. I--E