(Received 17 June 1981; accepted 18 August 1981). AbarKt--Measured intensities of the solar direct radiation at normal incidence I~, have been correlated with ...
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CORRELATION BETWEEN NORMAL DIRECT RADIATION AND GLOBAL RADIATION DEPENDING ON CLOUDINESS CARLO CASTAGNOLI,CLAUDIOGIRAUD,ARNALDOLONGHETTOand OMBRETrAMORRA Istimto di Fisica Generale delrUniversit~ e C.N.R. Istituto di Cosmo-geoflsica, Corso Flume, 4--10133Torino, Italy and LUIGI CIVITANO Enel CRTN, Via Cesare Battisti, 69-56100 Pisa, Italy
(Received 17 June 1981; accepted 18 August 1981) AbarKt--Measured intensities of the solar direct radiation at normal incidence I~, have been correlated with the coefficients K,~ = I~//~, where I~ and Io~are respectivelythe intensity of the global solar radiation at ground level and the extraterrestrial radiation, both on a horizontal surface. Four correlation lines have been drawn, Ib, = F(Kta); each line is linked to a particular degree of cloudiness. The result shows that the relationship existing between It, and K~ is influenced by the degree of cloudiness, irrespective of the value of the air mass m. This allows a relationship to be found between Ibn and cloudiness degree, having K~ as parameter.
1. INTRODUCTION
If there were only molecules present in the atmosphere, with the help of Rayleigh's theory and knowing the absorption of the unitary air mass, we could, measuring the global radiation, determine the value of the diffuse radiation to a very close approximation. Unfortunately the atmosphere contains dust and sometimes drops of water, whose scattering indicatfix is considerably influenced by the dimensions of these particles and by their chemical composition. Besides, when clouds are present, the phenomenon of multiple scattering takes place; thus, it is impossible, with data supplied by an actinometric station, to find a mathematical model which allows us to determine, from an instantaneous measuring of the global radiation, its diffuse component. To this, we must add the effect of absorption which the solar radiation undergoes when crossing the atmosphere, and we see that problem becomes even more complicated. Notwithstanding these problems, many authors, among whom [1-4], in order to make up for the lack of a mathematical model, have looked for coarse relationships of the type Kd = G(Kh), existing between the coefficient Kh =/'/h//'/o (the so-called clearness index) a n d / G = Ha//'/o (transmission coefficient). In these accounts/'/h, Ho and/'/d are the averages (hourly or daily) respectively of the global terrestrial radiation on a horizontal surface, of the extraterrestrial radiation on a horizontal surface and of the diffuse radiation based on annual observations. This type of analysis has been dictated by the need to estimate the value of the diffused radiation (and therefore of the direct radiation) knowing the value of the global radiation only. Working on averages of long terms,
a better than real time correlation between Kh and /Ca could be obtained, but all the information qualified to explain the physics of the phenomenon which links these two quantities was lost. This paper intends to improve the understanding of the role played by clouds in this connection; to this end, series of experimental data from instantaneous observations of solar radiation, we performed during two different periods of the year, have been subdivided into four classes, each of them defined by its cloudiness degree. Class Class Class Class
I II III IV
from 1/8 to 2/8 cloudiness from3/8 to 4/8 cloudiness from S/8to6/8 cloudiness from7/8 to 8/8 cloudiness (cirrus)
For each of these groups the correlation existing between K~ =lh/Io and lbn has been found, where Ih[W/m2] is the intensity of the global solar radiation measured at ground level on a horizontal surface, Io[W/mz] is the extraterrestrial radiation on a horizontal surface (evalued with eqn (1) of Section 2) and lho [W/m z] is the intensity of the normal direct component of radiation measured within a solid angle of 5°. The aim of this work is to be able to find the instant value lbn knowing/(hi and the cloud cover index.
2. ANALYSIS OF TIEg DATA
The measurements were taken at Adrano, Sicily, latitude 37o 39~, altitude 214 m above sea level, where ENEL is building, in the frame of the CEC, a solar I MWe power station. The measurements of direct radiation Ibn were taken using an Eppley NIP pyreliometre. The glo289
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bal radiation Ib was measured with a Kipp and Zonen CM6 pyranometre. The outputs of these instruments were connected to a strip chart recorder, whose selected speed was 12 cms/hr. The sky was photographed with a Contax RST camera, with an automatic exposure time which was fitted with a fish-eye aperture giving 1800 on the diagonal. The data refers to a series of measurements carried out in June and December 1979. The direct radiation values are expressed in W/m 2, whereas those of global radiation Ih are expressed as a fraction of the extraterrestrial radiation Io through the adimensional coefficient Khj = Idlo where:
@
/(-,,,
direct
'~,\ \ /
L
"'
"" Iliffasiln
~
Fig. 1. Relative contribution of molecules, clouds and dust to rite
diffuse component of the solar radiation.
(sin , sin + cos 8 cos cos T" 15)]
(1)
and n = day of the year; 8 = elevation of the sun; ~b= latitude; and T, = solar time, expressed in min. (T, = 0 at the solar noon.) Each picture of the sky, belonging to one of the four groups of cloudiness degree, has then been linked to the corresponding pairs of values (Kh~; Ib,). 3. DISCUSSIONOF TIlE RESULTS
If we consider the cases in which on the terrestrial surface P (Fig. 1) both direct and diffuse radiation are present, the diffuse radiation (if dark (or low) clouds are excluded) has to be, in very close approximation, directly linked with the cloud cover of the sky, in that the clouds
give a scattering coefficient greater than that of the molecules and of the atmospheric dust. To investigate on the influence that the presence of the clouds plays on the relationships between lb. and Kh~ the best fitting line has been calculated of the points (lb,, K~) belonging to each of the above defined groups of cloudiness. In Fig. 2 the experimental points measured during the June and December field experiments and the best fitting lines are shown. It can be seen that as the cloudiness increases, the angular coefficient of the lines decreases passing from a clear sky to a cloudy sky condition. It is therefore possible to associate four straight lines (eqn 2) to the four groups of cloudiness. These lines are quite distinct from each other and the standard errors (-~ 50 W/m e) are such that, knowing Kh~ and the degree
Ibn (WIm2).
1000 + Eq.(2-1) ~/ • Eq.(2-2) +++~ + Eq.(2-3)
Eq.(2-lJ
500-
-
-
+
.2
Iz~
0
.4
OA
.6
.8
Kh i
Fig. 2. Experimental values of lb, measured during the June and December field experiments and their best fitting
lines as a function of the cloudiness index/(hi.
Correlation between normal direct radiation and global radiation depending on cloudiness of cloudiness, lb, can be determined with greater precision than that obtainable without bearing the fraction of cloudiness in mind. The equation of the best fitting line for the jth cloudiness class is: l~,j = a j K h i - bj
(j= 1,2,3,4)
(2)
where a~ and bj take on the values listed in Table 1. This relationship is valid in the range 0.2
