Dependence on wavelength of the diurnal variation of the monthly mean hourly values of global radiation on horizontal surfaces

Solar Energy, Vol. 52, No. 3, pp. 227-232, 1994

Pergamon Copyriglrt 0 1994 Elsevier Science Ltd Printed in the USA. All rights reserved

0038-092X/94 $6.00 + .OO

DEPENDENCE ON WAVELENGTH OF THE DIURNAL VARIATION OF THE MONTHLY MEAN HOURLY VALUES

OF GLOBAL RADIATION ON HORIZONTAL SURFACES

ALF~NSO SOLER Departamento de Fisica e Instalaciones, Escuela Tecnica Superior de Arquitectura,

Avda. Juan de Herrera, 4,28040 Madrid, Spain

Abstract-We studied the dependence on wavelength X of the r; = I;/I?x versus so plots, & and Rx, respectively being the monthly mean hourly and daily values of global radiation for each wavelength considered, and so being the monthly mean daily number of maximum possible sunshine hours. Values of IA correspond to Uccle (50”48’N, 4”2I’E) and were obtained in 1980 for X = 315, 400, 446, 545, 646, 730, 816, and 914 nm. The & versus&plots clearly depend on wavelength. For X = 400 nm, the ix versus So plots are practically identical to the usual ?versus & plots, as obtained when all wavelengths for which global radiation is received are considered. The & versus So plots for X = 3 15 nm lie far apart from those for other wavelengths. When individual values before and after the solar noon are studied instead of mean values of global radiation, asymmetries are clearly observed for all the months, only for X = 3 15 nm.

1. INTRODUCHON

Many authors have studied the r= !fI?versus & plots for “average skies” (for example [ l-9]), that is, when all the hourly values of global radiation are taken into account independently of cloudiness and atmospheric conditions. In this relation, fand fl are, respectively, the monthly mean hourly and daily values of global radiation, and & is the maximum possible number of daily sunshine hours. Values of F in the r versus so plots are mean values of the hour pairs around solar noon. True solar noon is considered through the present work. The dependence on turbidity [ lo], cloudiness [ 1 0, 1 1] and latitude [ 12 ] of these plots has also been studied. Similar plots have been obtained for global illuminances [ 13 1.

In the present work, we studied the dependence on wavelength X of the rx versus so plots for “average skies.” We also studied for different wavelengths the possible asymmetries about solar noon of the ratio of monthly mean hourly to daily values of global radiation. This research is of interest, not only in the context of solar radiation (as atmospheric components and clouds present different absorption coefficients de- pending on wavelength ) , but also for daylighting stud- ies, where a specific range of wavelengths in the visible range of the solar spectrum (380-760 nm) is considered.

2. DATA USED

The data used in the present work were obtained at Uccle (50”48’N, 4”2 1 ‘E) in 1980, from January 1st to December 3 1st [ 14,15 1. Half hourly values of global radiation are given in[ 14,151 for h = 3 15, 400, 446, 545, 646, 730, 816, and 914 nm, and also for “total global” radiation, that is when, as usual, radiation received for all wavelengths is considered. A detailed de-

scription of the instruments used has been given in [ 16 1. The relation between instantaneous values of “total global” radiation, and radiation measured for different wavelengths has been studied in 1171.

3. RESULTS

3. I. Dependence on wavelength of the f, versus so plots

Using mean values of the hour pairs around solar noon, values of 7; have been obtained for the different wavelengths, the months of the year, and the hours centered at 0.5, 1.5, . . , 6.5 h from solar noon. For 0.5, 1.5,. . . , 6.5 h from solar noon, best fits for the & versus &, plots were obtained with second-degree polynomials for the different wavelengths involved. Best fits were also obtained for the ! versus s,, plots. Cor- relation coefficients were always higher than 0.97. In- terpolated values for & = 8, 9, . . . , 15, 16 h were obtained in all cases. In Table 1 (a-i) we give, respectively, the values of r 315, r;tlH, 646, ‘7545, 646, 630, 616.

Fg14, and F, for 0.5 h, 1.5 h, . . . ,6.5 h from solar noon, and $, = 8 h, 9 h, . . , 15 h, 16 h. In Fig. I(a-d) we have plotted the best fits obtained for 0.5 h, 2.5 h, 4.5 h, and 6.5 h, from solar noon,

From Table 1 and Fig. 1 we observe that the ,=A versus & plots clearly depend on wavelength. The 7 versus & plots are practically coincident with the r; plots for X = 400 nm. The plots for X = 3 15 nm lie clearly aside from the rest. In Fig. 2, the best fits of r; versus $0 for X = 3 15 nm are compared to the usual r versus & plots for all the hours for which data are available.

3.2. The asymmetry about solar noon ofthe ratio of the monthly mean hour1.v to daily values of solar radiation

As already mentioned, values of rx and fgiven in Figs. 1 and 2 and Table 1 correspond to mean values of corresponding hour pairs about solar noon.

227

228 A. SOLER

Table I (a-i). Values of & for different values of &, and 0.5 to 6.5 hours from solar noon, as obtained from best fits of the experimental & versus & plots

I 9 10 I1 12 13 14 15 16

0.5 h 0.194 0.183 0.172 0.161 0.151 0.140 0.130 0.120 0.1 IO 1.5 h 0,162 0.154 0.147 0.140 0.133 0.126 0.119 0.112 0.105 2.5 h 0.102 0.103 0.103 0.103 0.102 0.100 0.097 0.094 0.090 3.5 h 0.040 0.049 0.056 0.062 0.066 0.070 0.072 0.072 0.07 I 4.5 h 0.002 0.011 0.020 0.028 0.033 0.039 0.044 0.048 0.05 I 5.5 h 0.000 0.000 0.002 0.007 0.012 0.018 0.023 0.029 0.035 6.5 h 0.000 0.000 0.000 0.000 0.001 0.006 0.011 0.016 0.02 1

b

0.5 h 0.200 0.182 0.166 0.151 0.139 0.129 0.120 0.114 0.110 1.5 h 0.163 0.153 0.144 0.136 0.128 0.121 0.115 0.110 0.106 2.5 h 0.102 0.104 0.106 0.106 0.105 0.104 0.101 0.098 0.093 3.5 h 0.036 0.049 0.060 0.068 0.074 0.078 0.079 0.078 0.075 4.5 h 0.000 0.012 0.023 0.032 0.040 0.046 0.05 1 0.054 0.055 5.5 h 0.000 0.000 0.001 0.007 0.013 0.020 0.025 0.03 I 0.036 6.5 h 0.000 0.000 0.000 0.000 0.000 0.003 0.008 0.013 0.019

C

0.5 h 0.203 0.185 0.169 0.155 0.142 0.132 0.123 0.116 0.111 1.5 h 0.164 0.154 0.145 0.137 0.129 0.123 0.117 0.112 0.109 2.5 h 0.100 0.103 0.104 0.105 0.105 0.103 0.101 0.098 0.094 3.5 h 0.035 0.048 0.058 0.066 0.072 0.076 0.078 0.077 0.075 4.5 h 0.000 0.010 0.02 I 0.03 I 0.039 0.045 0.049 0.052 0.053 5.5 h 0.000 0.000 0.001 0.007 0.013 0.019 0.024 0.029 0.034 6.5 h 0.000 0.000 0.000 0.000 0.000 0.003 0.008 0.012 0.017

d

0.5 h 0.208 0.189 0.172 0.157 0.144 0.133 0.124 0.117 0.112 1.5 h 0.166 0.156 0.147 0.138 0.130 0.124 0.118 0.113 0.109 2.5 h 0.098 0.101 0.104 0.105 0.106 0.105 0.102 0.099 0.094 3.5 h 0.030 0.044 0.056 0.065 0.072 0.076 0.078 0.078 0.075 4.5 h 0.000 0.009 0.019 0.029 0.037 0.043 0.048 0.052 0.055 5.5 h 0.000 0.000 0.000 0.006 0.011 0.017 0.022 0.028 0.034 6.5 h 0.000 0.000 0.000 0.000 0.000 0.001 0.006 0.011 0.016

e

0.5 h 0.209 0.190 0.173 0.157 0.144 0.133 0.124 0.116 0.111 1.5 h 0.167 0.156 0.146 0.137 0.130 0.123 0.117 0.112 0.109 2.5 h 0.097 0.100 0.103 0.104 0.104 0.104 0.102 0.099 0.095 3.5 h 0.029 0.044 0.056 0.065 0.072 0.077 0.079 0.078 0.075 4.5 h 0.000 0.009 0.020 0.030 0.038 0.045 0.049 0.052 0.054 5.5 h 0.000 0.000 0.000 0.004 0.011 0.018 0.024 0.029 0.034 6.5 h 0.000 0.000 0.000 0.000 0.000 0.002 0.007 0.011 0.016

f

0.5 h 0.206 0.187 0.170 0.155 0.143 0.132 0.123 0.116 0.117 1.5 h 0.167 0.156 0.146 0.177 0.129 0.122 0.117 0.112 0.109 2.5 h 0.099 0.102 0.105 0.106 0.106 0.104 0.102 0.099 0.094 3.5 h 0.003 0.044 0.056 0.065 0.072 0.077 0.079 0.078 0.075 4.5 h 0.000 0.010 0.020 0.030 0.038 0.044 0.049 0.052 0.054 5.5 h 0.000 0.000 0.001 0.006 0.012 0.018 0.023 0.029 0.034 6.5 h 0.000 0.000 0.000 0.000 0.000 0.003 0.007 0.01 I 0.016

0.5 h 0.207 0.288 0.170 0.156 0.143 0.131 0.123 0.116 0.111 1.5 h 0.167 0.156 0.146 0.137 0.129 0.122 0.117 0.112 0.108 2.5 h 0.099 0.102 0.105 0.106 0.106 0.105 0.102 0.099 0.094 3.5 h 0.029 0.044 0.056 0.065 0.072 0.077 0.078 0.078 0.075 4.5 h 0.000 0.008 0.020 0.030 0.038 0.045 0.050 0.053 0.054

a

Wavelength and diurnal variation on global radiation

Table I (a-i). (Co&)

s’o

229

7 9 10 II 12 13 14 15 16

5.5 h 0.000 6.5 h 0.000

0.5 h 0.209 1.5 h 0.167 2.5 h 0.097 3.5 h 0.030 4.5 h 0.006 5.5 h 0.000 6.5 h 0.000

0.5 h 0.202 1.5 h 0.164 2.5 h 0.102 3.5 h 0.035 4.5 h 0.000 5.5 h 0.000 6.5 h 0.000

0.000 0.000

0.190 0.157 0.101 0.043 0.007 0.000 0.000

0.183 0. I54 0.104 0.049 0.009 0.000 0.000

0.001 0.006 0.000 0.000

g (Contd.)

0.012 0.000

0.018 0.023 0.029 0.035 0.003 0.007 0.011 0.016

h

0.173 0.158 0.145 0.134 0.125 0.117 0.112 0.148 0.140 0.132 0.125 0.119 0.114 0.110 0.105 0.104 0.105 0.106 0.105 0.103 0.100 0.055 0.064 0.070 0.075 0.077 0.078 0.076 0.002 0.029 0.037 0.043 0.048 0.05 1 0.053 0.000 0.005 0.010 0.016 0.022 0.028 0.034 0.000 0.000 0.002 0.006 0.010 0.015 0.02 I

i

0.167 0.152 0.140 0.129 0.121 0.114 0.110 0.144 0.135 0.127 0.120 0.115 0.110 0.106 0.105 0.106 0.105 0.103 0.101 0.098 0.094 0.060 0.068 0.075 0.078 0.080 0.079 0.075 0.02 1 0.032 0.040 0.047 0.05 I 0.054 0.055 0.000 0.007 0.013 0.019 0.025 0.03 1 0.036 0.000 0.000 0.000 0.003 0.007 0.011 0.017

a)X=315nm;b)X=400nm;c)X=446nm;d)X=545nm;e)X=646nm;f)h=73Onm;g)X=8]6nm;h)X=914 nm; i) total spectrum.

Table 2 (a-c). Values of &/Fand &,/Ffor different values of the hour angle w

w

A (nm) +7.5 +22.5 +37.5 +52.5 +67.5 +82.5 97.5

315 1.014 I.010 1.105 1.122 1.190 1.230 400 1.009 0.987 1.062 1.046 0.988 0.950 446 1.010 0.987 1.064 1.048 0.988 0.942 545 1.006 0.982 I .062 1.043 0.985 0.935 646 1.000 0.973 1.049 1.027 0.965 0.878 730 1.004 0.98 I 1.056 1.035 0.982 0.943 816 1.004 0.98 I 1.058 1.035 0.992 0.956 914 1.008 1.009 1.074 1.068 1.077 1.025

Global Total 1.002 0.985 0.941 1.033 0.941 0.947

315 1.041 0.978 0.933 0.894 0.812 0.692 0.633 400 0.994 1.056 1.064 I .085 1.076 1.019 0.930 446 1 .oso 1.007 1.011 1.030 1.019 0.966 0.890 545 1.050 I .005 1.007 1.027 1.013 0.962 0.98 I 646 1.050 1.005 1.007 1.027 1.012 0.963 0.979 730 1.051 1.006 1.006 1.027 1.010 0.960 0.984 816 1.051 1.005 I .006 1.024 I.006 0.958 0.994 914 1.053 1.004 1.001 1.022 1.003 0.955 0.994

Global Total I .050 1.004 1.005 1.026 1.009 0.957 0.968

315 0.983 0.978 0.877 0.643 0.416 400 1.007 1.038 0.988 0.998 1.035 446 0.960 0.978 1.015 1.022 1.099 545 0.953 0.973 1.017 0.997 1.167 646 0.949 0.964 1 .OO5 0.926 1.106 816 0.95 I 0.970 1.016 0.919 1.178 914 0.954 0.963 1.005 0.955 1.125

Global Total 0.944 0.964 1.010 1.010 1.083

a

b

c

a) March; b) July; c) November.

230 A.%LER

(a)

020,

039 lid 91L nm

5L5nm&L6nm 038

,_,730nm=816nm

017

IX 5L5nm= 6L6 nm 016 ’

i

6% n

015 /

, SlLnm

OKI t

TOTAL - GLOBAL

011 t 0,5h

(b)

6&m=73730nm=816nm _I

(d)

Fig. 1. (a-d): Best fits for the f, ?A versus & plots. (a) 0.5 hours from solar noon; (b) 2.5 hours from solar noon; (c) 4.5 hours from solar noon; (d) 6.5 hours from solar noon.

When individual mean hourly values are considered, asymmetries about solar noon may occasionally be observed [ 18,191. These asymmetries can be char- acterized by studying the dependence of i&/F or T;r,,, / ran w for the different months of the year, where L,, and i&, respectively, are the ratios of the monthly mean hourly to daily values of global radiation for hours before or after the solar noon, ?corresponds to mean values of the hour pairs, and w is the hour angle[19]. In[l9], the Tarn/T; &,/Fversus o plots are fitted by straight lines.

We have searched for possible asymmetries of values of “total global” radiation and for all the wavelengths for which data are available. In Table 2( a-c) we give the Ttirn/ rA and Tp,,, / r values for, respectively, March, July, and November. For March and July, asymmetries are important for X = 3 15 nm, but not for “total global” radiation or for other wavelengths. For November, asymmetries are very important for X = 3 15 nm and much less for “total global” radiation and for the other wavelengths.

In Fig. 3 we give the best fits obtained with second degree polynomials for the r;, 5am / F3, 5 versus w values. Correlation coefficients higher than 0.97 were obtained for all months. The T;ISam/T;IJ values are close. to 1 for (J = $7.5” and decrease with increasing values of w for all the months of the year, with the exception of March (the darkest month March ever recorded in Uccle), as for this particular month an increase of &rSa,,, r315 with w is obtained. Values of ?315am/r315 for w - ‘Lo - O, obtained from Fig. 3 are plotted in Fig. 4.

4. CONCLUSIONS

Relating the dependence on & of the 7 versus & plots, from Figs. I and 2 and Table I, it is clear that, in general, they are not identical for all wavelengths, although plots for X = 545,646,730, and 816 nm are practically coincident for some of the houts about solar noon. The most surprising results are: (a) the TX versus so plots are practically coincident with the fversus so

Wavelength and diurnal variation on global radiation

12

231

Fig. 2.

- 315 nm ---TOTAL GLOBAL _

~o(hours)

Best fits for the r, & versus & plots for 0.5 h, . . , 6.5 h from solar noon.

c 1 , , 1 I

75+&25+675+52.5+375+22.5 +75 wbagrd

Fig. 3. Best fits for the T;,~,&T;rJ versus o plots, as obtained for the different months of the year.

1.1 -

1.0 -

03-

a6 -

a7 -

0.6 -

0.5 w= t50’

0.4 ; I I ’ 8 ’ I ’ ’ ’ ’ ( FMAHJ JA S 0 N Cl

MONTH

_i

Fig. 4. Dependence of &,,, for w /$;,“,ijh the month of the year

plots for X = 400 nrn, and (b) the 7i versus $0 plots for X = 3 15 nm clearly lie aside from those obtained for other wavelengths.

The rversus so plots are used for the estimation of f values when I? values are either measured or calcu- lated. The present results for the fi versus so plots are not very encouraging regarding this application because of their clear dependence on A.

When not the mean values of global radiation but individual values before or after solar noon are studied, asymmetries are clearly observed for all months, only for h = 315 nm. From Table 2 and Fig. 3, the hourly asymmetry factor can be as low as 0.4 for w = +70°. This is a very low value when compared to usual values for global radiation, although it is somewhat closer to some of the available values for direct radiation [ IS,19 1. In our opinion, results for other locations and for a longer period must be obtained before any explanation relating the dependence on X of the hourly asymmetry factor is advanced. Also, detailed analysis of possible asymmetries detected for ultraviolet radiation [ 201 should be undertaken,

I.

2.

3.

4.

5.

6.

7.

8.

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Documents

Dependence on wavelength of the diurnal variation of the monthly mean hourly values of global radiation on horizontal surfaces