Solar & Wind Technoh)yy Vol. 4, No. I. pp. 81 93, 1987 0741 983X/87 $3,00+.00 Printed in Great Britain. Pergamon Journals Ltd,

S H O R T C O M M U N I C A T I O N

The dependence on turbidity and cloudiness of the distribution of the monthly average hourly diffuse, global and direct radiation

ALFONSO SOLER

Departamento de Fisica, Escuela Trcnica Superior de Arquitectura, Avda. Juan de Herrera s/n, 28040 Madrid, Spain

(Received 15 December 1985 ; accepted 25 February 1986)

Abstract--Monthly average hourly values of the direct, diffuse and global radiation are available for Uccle (Belgium) for the following sky conditions A, B, C and D. (A) Clear skies (fraction of possible sunshine = 1) and minimum turbidity, corresponding to the maximum values of radiation measured during the period considered ; (B) clear skies and average turbidity, corresponding to all the values of radiation measured when the fraction of possible sunshine is 1 during the period considered; (C) any sky conditions, cor- responding to all the solar radiation data collected during the period considered; (D) overcast skies, corresponding to the values of radiation measured when the fraction of possible sunshine is 0.

In this work we study the variations o f f t = [//J, t~d = [a/I~d, ~rt) = [t)//Jr) with ~qo for 0.5-7.5 h from solar noon, and conditions A, B, C and D; [being the monthly average hourly global radiat ion,/4 the monthly average daily global radiation, fd the monthly average hourly diffuse radiation,/qd the monthly average daily diffuse radiation, ft) the monthly average hourly direct radiation,/~D the monthly average daily direct radiation, all of them measured on a horizontal surface, and ~qo the monthly average number of hours from sunrise to sunset.

Results for the variation of ~t and ~d with ~qo for condition C are in rather good agreement with the 'universal plots" obtained by different authors for other locations. However, the f,, fd, t:D versus ~¢o plots are seen to vary with conditions A, B, C and D. A remarkable result is the similarity between cxperimental ?t values for condition A and the corresponding extraterrestrial values of ~:t.

INTRODUCTION

Whillier [I] and Liu and Jordan [2] presented plots of ft = [/171 and J:d = f~//Td versus ~qo for 0.5-7.5 h from solar noon and the different months of the year, where [ is the monthly average hourly global radiation, [d the monthly average hourly diffuse radiation, /7 the monthly average daily global radiation,/4a the monthly average daily diffuse radiation, all of them measured on a horizontal surface, and ~qo the monthly average number of hours from sunrise to sunset. Values of [, fd , /q and/Td were obtained using all the solar radiation data collected at a given location during a number of years (skies from clear to overcast and different degrees of atmospheric turbidity). The plots, as verified by other workers like Iqbal [3], seem to be site-independent. As a consequence they can be used, for example, to estimate [d and .?at any location, if 50,/4a a n d / 4 are known.

In this work, using radiation data for Uccle (Belgium) it is shown that the ft, ?d versus ,-¢o plots depend on atmospheric turbidity and the degree of cloudiness.

RESULTS

The data used have been supplied by Dogniaux [4, 5] and correspond to measurements undertaken at Uccle from 1951

81

to 1980. The data in refs [4, 5] include values for the monthly average hourly global radiation, the monthly average hourly diffuse radiation, both on a horizontal surface, and the monthly average hourly direct normal radiation (iDN), all of them for different degrees of cloudiness and atmospheric turbidity. Values of the monthly average hourly direct radi- ation To can be calculated by multiplying each value of IDN by sin ~, where ~ is the corresponding solar elevation anglc. The values o fg to be used for each hour are given in ref. [4],

day day day

and /qo = • [D. Also /)d = ~ [d and/4" = ~

Values of ~, fd and fD = lo//4o, calculated by using mean values of the hour pairs around solar noon, are given in Tables 1, 2 and 3 respectively.

The values of ft, ?d and ~o given in the tables correspond to data obtained for the following sky conditions A, B, C and D :

(A) Clear skies (fraction of possible sunshine = 1) and minimum turbidity, corresponding to the maximum values of radiation measured during the period considered ;

(B) Clear skies and average turbidity, corresponding to all the values of the radiation measured when the fraction of possible sunshine is 1 ;

(C) All the solar radiation data collected from 1951 to 1980, regardless of the state of the sky ;

X2 811OI t (Oll] l / / t l l l iC~l[l l l l !

Table I. \":duc~, o1"7 Ik~t ¢ondilions A. B, ( :lnd D. ats spccilicd in the text

7.5 6.5

Jan. A B C D

Hours from s o l a r n o o n

5.5 4.5 3.5 2.5

0.046 0.111 0.043 0.108 0.038 0.103 0.048 0.108

1.5 0.5

0.158 0.185 0.160 0.189 0.162 0.196 0.157 0.187

Feb. A B C D

0.025 0.068 0.109 0.140 0.156 0.017 0.066 0.109 0.145 0.163 0.017 0.059 0.107 0.147 0.170 0.023 0.065 0.108 0.143 0.163

Mar. A 0.015 0.044 0.076 0.105 0.125 0.135 B 0.012 0.041 0.073 0.106 0.128 0.140 C 0.011 0.037 0.072 0.106 0.131 0.144 D 0.014 0.042 0.075 0.102 0.128 0. 138

Apr. A 0.010 0.03 t 0.055 0.078 0.098 0.111 0.119 B 0.007 0.028 0.052 0.077 0.099 0.114 0.122 C 0.006 0.025 0.052 0.077 0.101 0. I 16 0.124 D 0.009 0.030 0.054 0.079 0.101 0.110 0. I 17

May A 0.004 B 0.003 C 0.003 D 0.005

0.018 0.038 0.058 0.077 0.092 0.103 0.109 0.016 0.035 0.056 0.077 0.094 0.106 0.112 0.014 0.034 0.055 0.078 0.095 0.108 0.114 0.019 0.037 0.057 0.077 0.093 0.103 0.110

Jun. A 0.006 B 0.006 C 0.005 D 0.009

0.022 0.040 0.059 0.076 0.091 0.100 0.106 0.020 0.038 0.058 0.076 0.092 0.102 0.108 0.019 0.037 0.057 0.076 0.092 0.103 0.109 0.023 0.040 0.058 0.075 0.091 0.101 0.105

Jul. A 0.005 B 0.004 C 0.004 D 0.007

0.020 0.039 0.062 0.077 0.092 0.101 0.107 0.018 0.037 0.058 0.077 0.093 0.104 0.109 0.017 0.036 0.057 0.077 0.094 0.104 0.110 0.020 0.038 0.059 0.075 0.092 0.102 0.108

Aug. A 0,014 0.035 0.057 0.078 0.096 0. t08 0.114 B 0.010 0.031 0.055 0.078 0.097 0. I 11 0.119 C 0.009 0.029 0.053 0.077 0.099 0. l 11 0.119 D 0.013 0.033 0.058 0.078 0.096 0.109 0.115

Sep. A 0.022 0.050 0.078 0.102 0.1 l 9 0.128 B 0.018 0.046 0.077 0.104 0.122 0.133 C 0.016 0.044 0.076 0.104 0.124 0.137 D 0.022 0.050 0.077 0.103 0.118 0. l 3 t

Oct. A B C D

0.035 0.074 0.109 0.135 0.147 0.027 0.070 0.109 0.140 0.155 0.025 0.066 0.108 0.142 0.151 0.031 0.070 0.109 0.140 0.150

Nov. A B C D

0.057 0.1 t I 0.155 0.178 0.053 0. I l l 0.157 0.184 0.046 0.106 0.159 0.189 0.055 0.110 0.155 0.182

Dec. A B C D

0.031 0.101 0.168 0.200 0.029 0.102 0.167 0.203 0.029 0.098 0.166 0.207 0.040 0.105 0.161 0.194

8

~4 Short (~7onlnlunicatit)ll

T;ible 3. Vzllues t*l" i:~ l'ov collctiti~)ns A. B and ¢. ;is specilied ill the text

Hours from solar noon 7.5 6.5 5.5 4.5 3.5 2.5 1.5 tt.5

Jan. A 0.024 0.102 0.169 0.204 B 0.026 0.100 0.168 0.205 C 0.016 0.091 0.169 0.223

Feb. A 0.008 0.056 0.I10 0.150 0.175 B 0.007 0.055 0.109 0.151 0.178 C 0.004 0.044 0.103 0.159 0.190

Mar. A 0.004 0.033 0.073 0.108 0.134 0.148 B 0.004 0.033 0.069 0.108 0.136 0.149 C 0.002 0.026 0.067 0.109 0.140 0.155

Apr. A 0.002 0.022 0.049 0.076 0.102 0.121 0,129 B 0.002 0.020 0.047 0.077 0.103 0.121 0.130 C 0.001 0.017 0.045 0.075 0. I04 0.123 0.136

May A 0.000 0.011 0.033 0.055 0.077 0.096 0.110 0.116 B 0.000 0.011 0.030 0.054 0.077 0.098 0.111 0.118 C 0.000 0.008 0.027 0.051 0.078 0.099 0.115 0,123

Jun. A 0.002 0.017 0.037 0.057 0.077 0.093 0.104 0,112 B 0.003 0.015 0.034 0.056 0.076 0.094 0.107 0.114 C 0.002 0.020 0.032 0.054 0.077 0.096 0.109 0.117

Jut. A 0.001 0.015 0.034 0.056 0.078 0.095 0.107 0. I 13 B 0.001 0.014 0.032 0.055 0.078 0.096 0.109 0.114 C 0.001 0.011 0.031 0.054 0.077 0.098 0.I10 0,117

Aug. A 0.006 0.026 0.053 0.078 0.100 0.114 0.122 B 0.005 0.025 0.051 0.078 0.106 0.115 0.125 C 0.003 0.021 0.047 0.076 0.103 0.120 0.129

Sep. A 0.012 0.039 0.076 0.106 0.127 0.137 B 0.011 0.040 0.075 0.106 0.128 0.140 C 0.007 0.035 0.072 0.106 0.132 0.148

Oct. A 0.019 0.063 0.110 0.144 0.164 B 0.017 0.061 0.109 0.146 0.166 C 0.012 0.056 0.108 0.151 0.173

Nov. A 0.035 0.106 0.163 0.196 B 0.035 0.105 0.164 0.195 C 0.026 0.096 0.166 0.211

Dec. A 0.011 0.090 0.177 0.222 B 0.011 0.094 0.174 0.219 C 0.008 0.080 0.175 0.240

(D) Overcast skies, corresponding to the values of the radiation measured when the fraction of possible sunshine is O.

For diffuse radiation, in the case of clear skies and mini- mum turbidity, no data are given in [4, 5], and for this reason the values given in Table 2 have been obtained as [d = [--[D. Ill Table 2 these values are those corresponding to A'. These values can be somewhat different from those obtained by measuring the diffuse radiation. Values of [~, as obtained from [d = [-[D for clear skies and average turbidity are

given in Table 2 (B') for the purpose of comparison with those corresponding to diffuse radiation measurements under the same conditions (B). It is seen that values of [d calculated by the two methods are not very different. Similar or even larger differences between values of Id calculated by the two methods in the case of clear skies and minimum turbidity (A' and A) do not affect the conclusions of this work.

In refs [1-3], only (t and (d are given for the conditions we have specified as C. It seems clear that F D is also a valuable source of information, and that the knowledge of ?,. ?~ and

Short Communicat ion

Table 4. Values of ~o (h) for the months of the year at Uccle

85

Jan. Feb. Mar. Apr. May Jun. Jul. Aug. Sep. Oct. Nov. Dec.

So (h) 8.3 9.8 11.7 13.6 15.3 16.2 15.8 14.3 12.5 10.6 8.8 7.8

fd in other conditions as A, B and D, will help to understand the physics concerning these coefficients.

In Table 4 we give the monthly average values of the number o f hours from sunrise to sunset (So) for Uccle, as obtained from the characteristic declinations at which the extraterrestrial irradiation is identical to its monthly average value.

To help the reader to visualize the evolution of it, fd and fD with turbidity and cloudiness, we have plotted in Figs 1-16 values for these coefficients versus the corresponding

values of g'o, for 0.5, 1.5, 4.5 and 5.5 h from solar noon (Figs 1~,; 5-8 ; 9-12 and 13-16 respectively).

We now refer to the two sets of figures for 0.5 and 1.5 h from solar noon. As the conclusions are identical for both sets, we refer specifically to the first one (Figs 1~,) for 0.5 h from solar noon.

As has been indicated, valucs of #,, ?~j have usually bccn given for conditions we have specified as C. Thus, the results in Fig. 3 are to be compared with those in refs [1, 2, 3]. In these papers it was shown that experimental fd values agree

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Short Communication

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Fig. 7. The distribution of the monthly average hourly diffuse, global and direct radiation for 1.5 h from solar noon, when all data for the period 1951 1980 are used.

89

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rather well with the corresponding values of #t, as calculated for the extraterrestrial radiation, and as seen in the figure, experimental results for Fd at Uccle, although somewhat higher, are in rather good agreement with extraterrestrial values of rt (continuous line).

On the other hand, in refs [1, 2, 3] experimental ft values are fitted by the dashed line of Fig. 3, and this line is also a good fit to the experimental values of ft obtained at Uccle.

The coincidence for different locations between exper-

imental values of #a and extraterrestrial values of ft, on one hand, and the experimental values of t=t and the dashed line, on the other hand, has led lqbal [6] to refer to the #~, ?d versus So correlations as "valid all over the world". Although this may be correct when all the radiation data are taken into account regardless of the state of the sky, consideration of Figs 1 4 indicates that the plots vary with cloudiness and turbidity.

In Fig. 1, we see that for clear skies and minimum turbidity,

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Fig. 10. The distribution of the monthly average hourly diffuse, direct and global radiation for 4.5 h from solar noon, clear skies and average turbidity.

Short Communicat ion 91

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Fig. 11. The distribution of the monthly average hourly diffuse, global and direct radiation for 4.5 h from solar noon when all data for the period 1951-1980 are used.

for each value of ~qo, r-D > ~ > ?d- The similarity between the experimental values of ft and the corresponding values of the extraterrestrial ?t is remarkable. In Fig. 2 (clear skies, average turbidity), fD values remain nearly the same as for Fig. 1 and values of ?d and ft are somewhat higher than those in Fig. 1. Figure 3, already described, shows values for ft, fd and fD higher than those in Fig. 2. For Figs 2 and 3, for each value of S0, fD > f~ > &. In Fig. 4, for overcast skies, values

offd are similar to those in Fig. 3, and ft = gd. The preceding comments are also valid for Figs 5-8.

Of course, we can imagine the case of no atmosphere, with fO values equal to the corresponding extraterrestrial values of ft.

Regarding the last two sets of figures (Figs 9 12 and 13 16) we refer to Figs 9-12 for 4.5 h from solar noon, as the same comments are valid for both sets.

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Fig. 12. The distribution o f the monthly average hourly diffuse and global radiation for 4.5 h from solar noon, overcast skies.

92 Short (Sore mtHiiczitit)tl

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Fig. 13. The distribution of the monthly average hourly diffuse, global and direct radiation for 5.5 h from solar noon, clear skies and minimum turbidity.

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i i i

× o ;o° / x o

/ ° 7 , , , II 12 1:5 14 I.'5 16 IT

HOURS FROM SUNRISE TO SUNSET

Fig. 14. The distribution of the monthly average hourly diffuse, global and direct radiation for 5.5 h from solar noon, clear skies and average turbidity.

O.06

F 0.0t5

0.04

0.0.3

0.02

0.01

O.O0 7

i i I I i i I I

ALL DATA (CLEAR TO OVERCAST SKIES)

55 HOURS FROM SOLAR NOON

- E × T R A ~ E S . ~ , A L G L . A L

- - ~ T F . G L O . ,REF , , ~ C _ ~ ; x - ~

GLOBAL .C_ % ' ' ' O O

0 DIRECT / ( I / / 0

~ / x / o

/ ' / O

I I I / 0 I I I I I

8 S 10 II 12 13 14. 15 16 17

HOURS FROM SUNRISE TO SUNSET

Fig. 15. The distribution of the monthly average hourly diffuse, global and direct radiation for 5.5 h from solar noon. when all data for the period 1951 1980 are used.

Short Communication

O . O B I i i = i i i # l

OVERCAST SKIES r ooo~ 5.5 HOURS FROM SOLAR NOON

- - EXTRATERRESTRIAL GLOBAL j . . . . . . . . . , - - "~_ 0.04 x GLOBAL /

0.0:3 • DIFFUSE ~ / ~

/ 0.02

0.01

0,00 I I I I I I I I I 8 9 I0 II 12 15 14 15 16 17

HOURS FROM SUNRISE TO SUNSET

Fig. 16. The distribution of the monthly average hourly diffuse and global radiation, for 5.5 h from solar noon, overcast skies.

93

In Fig. 9, for clear skies and minimum turbidity id > 6 > FD for each value of Oeo, and once again, as in Fig. I, 6 values fit rather well with the extraterrestrial ?t curve.

In Fig. 10, for clear skies, and average turbidity, ro values are similar to those in Fig. 9, but values of id and 6 are smaller than the corresponding ones in Fig. 9.

In Fig. 11, for all data, values of id, it and iD are smaller than the corresponding ones in Fig. 10. Again, as for Figs 3, 7 and 15, experimental values of 6 show good agreement with the fit of 'universal validity' [6] given by the dashed line. On the other hand, id values lie close to the corresponding values for the extraterrestrial 6, as in Figs 3, 7 and 15. In Figs 10 and 11 i d > 6 > fo.

Figure 12 shows values of 6 and i d for overcast skies. Values of it are somewhat higher than the corresponding ones in Fig. 11, but values of Fd remain nearly the same in both figures.

CONCLUSIONS

Summarizing the preceding comments we can state that results obtained at Uccle for the variation of Ft, Fd with So are in rather good agreement with the 'universal plots' obtained for other locations, when all the solar radiation data for the period 1951-1980 are taken into account.

However, the it, FD and Fd versus So plots are seen to vary with cloudiness degree and atmospheric turbidity, as shown for 0.5, 1.5, 4.5 and 5.5 h from solar noon in Figs 1 16. A remarkable result is the similarity between experimental i~

values and the corresponding extraterrestrial values of 6 for clear skies and minimum turbidity.

These results, if confirmed for other locations, can help in understanding the physics concerning the coefficients it, i d and iD.

REFERENCES

I. A. Whillier, The determination of total solar radiation from daily summations. Arch. Meterol. Geophys. Bin- klimatol. Ser B-7, 197-224 (1956).

2. B. Y. H. Liu and R. C. Jordan, The interrelationship and characteristic distribution of direct, diffuse and total solar radiation. Solar Energy 4, 1-19 (1960).

3. M. Iqbal, A study of Canadian diffuse and total solar radiation. II. Monthly average hourly horizontal radiation. Solar Energy 22, 87-90 (1979).

4. R. Dogniaux, l~clairement ~nerg~tique solaire direct, diffus et global des surfaces orientres el inclinres. I t partie. Miscellanea Srric B, No. 59. lnstitut Royal Mrtrorolo- gique de Bclgique, Bruxelles (1984).

5. R. Dogniaux, De l'influence de l'estimation du facteur total de trouble atmosphrrique sur l 'rvaluation du rayonnement solaire direct per cicl clair. Miscellanea S&ie C, No. 20. Institut Royal Mrtrorologiquc de Belgique, Bruxelles (1984).

6. M. lqbal, An Introduction to Solar Radiauom Chapter 8. Academic Press, New York (1983).