Prediction of global solar radiation from bright sunshine hours and other meteorological data

Energy Convers. Mgmt Vol. 23, No. 2, pp. 113-118, 1983 Printed in Great Britain. All rights reserved

0196-8904/8353.00+0.00 Copyright © 1983 Pergamon Press Ltd

PREDICTION OF GLOBAL SOLAR RADIATION FROM BRIGHT SUNSHINE HOURS A N D OTHER METEOROLOGICAL DATA H. P. G A R G and S. N. G A R G Centre of Energy Studies, Indian Institute of Technology, Hauz Khas, New Delhi 110 016, India

(Received 24 April 1982) Abstract Three existing empirical relations which predict global radiation from bright sunshine hours and meteorological parameters, were tried for 14 Indian stations where all relevant data was available. A large amount of error ( + 50%0)was found. So a new empirical relation was established between global radiation and meteorological parameters. The new relation predicted the insolation within a + 10% error limit in most cases. Global radiation dependence on ambient temperature and relative humidity was introduced through atmosperic water content per unit volume. The relation is

WAT = RH (4.7923 + 0.3647 x T + 0.0055 x T 2 + 0.0003 x T ~) G = G~xt (0.414 + 0.400 × S S - 0.0055 × WAT) SS=

S . Z

Global radiation Bright sunshine hours radiation prediction

Relative humidity

NOMENCLATURE

daily global radiation on a horizontal surface L = latitude of the place S = measured bright sunshine hours Z = maximum possible bright sunshine hours Tmax = maximum temperature of the day CC) R H = monthly mean relative humidity 6 = sun declination F/ - - No. of day of the year Gex I := extraterrestrial daily global radiation on a horizontal surface G o b := daily global solar radiation on a horizontal surface observed on earth W~ := sunrise hour angle WAT := atmospheric water content per unit volume near the earth surface (kg/m 3) SS:- fraction of maximum possible bright sunshine hours G=

!. INTRODUCTION In a given region, solar energy conversion devices should be installed only in those places where one gets sufficient insolation. This necessitates knowledge of the distribution of insolation over the region. The best way of knowing it is to install pyranometers at many locations in the given region and look after their day-to-day maintenance and recording, which is a very costly exercise. The alternative approach is to correlate insolation with the meteorological parameters such as sunshine hours, relative humidity, ambient temperature, etc. Daily recordings of these parameters are available from a lot of stations covering many years. So, for a few stations, if global radiation as well as meteorological parameters are

Ambient temperature

Solar

available, and if such a correlation is established, then one can know global radiation for those stations where only meteorological parameters are available, provided these stations also have similar atmospheric conditions. A basic point, helpful in this correlation study is that, outside the atmosphere, global radiation on a horizontal surface can be determined very precisely. Radiation reaching a station depends upon the atmospheric conditions of that station. The most important atmospheric condition is the water content in the atmosphere. F r o m relative humidity and ambie n t temperature, water content per unit volume near the station can be determined. Water content is important because it highly absorbs solar radiation in the infrared region. The other meteorological parameter is sunshine hours, which is used as a fraction of the maximum possible bright sunshine hours. Different authors [1-3] have tried to establish this correlation. Angstrom [4] has tried to establish a linear relationship between global radiation and bright sunshine hours. Page [5] includes extraterrestrial radiation also in the computation of global radiation. In the present study, we have tried to predict insolation using three commonly used formulas, Sayigh formula [1], Reddy's formula [2] and Swartman's formula [3], and found that, in each case, there was a large amount of error. Hence, a new empirical relation was developed which predicted the global radiation within a + 10% error limit in most of the cases. Radiation data, as well as meteorological data, for 14 stations was available from the book compiled by Mani [6]. The data conforms to the international 113

114

GARG and GARG: PREDICTION OF GLOBAL SOLAR RADIATION Table 1. Indian stations used in this study, with daily records of meteorological parameters

Station

Latitude (N) (deg)

Longitude (E) (deg)

Global radiation

Period of record Sunshine Ambient hours temperature

Relative humidity

28.63 26.30 23.07 22.65 21.75 21.10 19.12 18.53 17.72 15.48 13.00 12.97 10.23 8.48

77.20 73.02 72.63 88.45 72.18 79.50 72.85 73.85 83.23 73.82 80.18 77.58 77.47 76.95

1957 78 1960-78 1962-78 1957-78 1967-78 1960-78 1969-78 1957-78 1961-78 1963-78 1957-78 1978-80 1962-78 1959-78

1954-63 1954-63 1954-63 1954-63 1954-63 1954-63 1954-63 1954-63 1962 67 1954-67 1954-63 1977-80 1954-63 1954-63

1958-67 1958-65 1958-67 1958-67 1976-78 1958-67 1958-67 1958-67 1958-67 1958-66 1958-67 1977-80 1958-67 !958-67

New Delhi Jodhpur Ahmedabad Calcutta Bhavnagar Nagpur Bombay Poona Vizagapatanam Goa Madras Bangalore Kodai Kanal Trivandrum

meteorological standards as specified by WMO. Table 1 shows the list of stations as well as periods of data used. Although data periods for different meteorological parameters, including global radiation parameter, do not coincide, these periods are so long that one can use them with sufficient accuracy. Computer programmes were drawn at various stages of the present study.

2. PREDICTIONS BY THE EXISTING EMPIRICAL RELATIONS

2.1. Sayigh "s formula This formula takes into consideration parameters like latitude, mean sun declination for the month, and maximum possible bright sunshine hours in addition to the main meteorological parameters like measured bright sunshine hours, relative humidity and maximum temperature for the mean day of the month. The entire range of relative humidity (RH) is divided into three subranges, viz. RH ~<65~, RH/> 70% and 65~ < RH < 70~, and corresponding to each subrange, a graph has been drawn between humidity factor, ~k and 12 months of the year. One has to know the annual mean daily relative humidity for a given station, and depending upon this annual mean value, one chooses a particular graph out of the three graphs and determines the values of qJ for different months of the year. The complete formula is

G = N K exp L

15

Tm,

(1)

1958 67 1958-66 1958-67 1958-67 1976-78 1958-67 1958-67 1958-67 1958-67 1964-67 1958-69 1977 80 1958-67 1958-67

K = 100(2Z + ~qcos L)

(5)

2 = \l-~d~.lL]'

(6)

is in degrees.

In ~0, i corresponds to the subrange of relative humidity, and j corresponds to the number of the month of the year. Using all these equations, global radiation has been computed for 14 Indian stations, and the results are shown only for one station (chosen randomly), Poona, in Fig. 1. From Fig. 1, it is clear that this empirical relation does not fit at all during the rainy months of July and August. During these months, the error is as high as + 40}/o. The formula over-estimates the radiation during rainy months. During the clear months of December, January and February, this relation under-estimates the insolation, the error being as low as -28.2~o (December). A similar trend is also seen in the other 13 stations. The maximum under-estimation is - 5 2 . 8 ~ (Kodai Kanal, December), and the maximum over-estimation is +60.7~o (Bangalore, July).

2.2. Reddy's formula This formula does not consider maximum ambient temperature, rather it considers the number of rainy days in a month. The formula is G

K(1 + 0.8s)(1 - 0.2/)

where K = 100(£Z + ~/cos L)

where N = 1 . 7 - 0.458 L, L is in radians

(2)

Z = ~5cos -~ [ - tan L tan fi]

(3)

(7)

0.2 where L is in degrees 1 +0.1L

2- -

(8) (9)

i=1,2 J = 1 , 2 , 3 . . . 12

= 23.45 sin [(284 + n)360] 3~ J

(4)

t=

no. of rainy days in a month total no. of days in the month"

(lO)

GARG and GARG: PREDICTION OF GLOBAL SOLAR RADIATION A

trend is observed for other stations also, except for the two stations, Kodai Kanal and Trivandrum. For these stations, the formula always under-estimates the insolation but the common feature is still there, i.e. under-estimation is high during rainy months and low during clear months. Partly, it is due to the fact that Kodai Kanal is a high altitude station. For all the 14 stations, the maximum over-estimation is + 53.1~o (New Delhi, December), and the maximum under-estimation is -25.8'~o (Kodai Kanal, June).

$6 ,\

32

E

~x

/

28 24 ~

20

~

16

..-

© ~

g E >, E ©

,,,,W/,.,

"--

- - Meosured o - - - --,3 (S J Reddy) E}. . . . . -4a (A A M Soyigh) --~ (RK Swartman)

12

8

\A---~ | I

-~

Predicted

3. PRESENT ¢

O[

I

i

]

d

F

M

! __L A

[ M

L

d d Months

115

I S

L 0

i D

Fig. 1. Monthly variation of daily average global radiation for Poona.

METHODOLOGY

From geometrical considerations, one can determine the extraterrestrial daily global radiation on a horizontal surface for a given latitude. The equations used are 24.0 x F Ge,t- - x (cos L cos 3 sin W,

Two values ot" i designate whether the station considered is an inland station or coastal station, and values of ~',I can be read from the tables for the particular station. Figure 1 shows the comparison of the predicted insolation by this formula with the measured values for Poona. Figure 1 shows that this formula is good fitting during the rainy months of July and August. During the clear months of January to April, the formula over-estimates the radiation, and this over-estimation is as high as +35% (April). During rainy months, the over-estimation is as low as +4.0% (July). The graph shows that this relation overestimates the radiation during all months of the year. The same trend is observed for other stations also.

2.3. Swartman's jbrmula This formula predicts global radiation on a horizontal surface from bright sunshine hours and relative humidity only. Swartman and others have evolved two empirical equations which are as follows G, = 4 9 0 . 0 ( S )

0.357 (RH)o.26:

(ll)

Instead of using the sunshine hours parameter as a fraction of maximum possible bright sunshine hours, the author uses sunshine hours here as a fraction of 12 only, i.e. mean possible bright sunshine hours, which is a simplification. For the same values of S and RH, both these equations give approximately the same value of G. Again, we have tried these two equations for 14 stations, and results are compared in Fig. 1, for Poona only. The figure shows that these equations over-estimate the insolation during clear months and under-estimate it during rainy months. For Poona, the maximum under-estimation is - 18.5Y',,~(July), and the maximum over-estimation is + 30.1'),;;in the month of December. A similar type of ~ , 4 23/2

z~

7~

+ W~sin L sin3) (W~ is in radians)

(13)

F = 1.95 × 60.0 x

1 +0.033cos

3-65

W , = c o s ' [ - t a n L tan6]

(14) (15)

The factor, K takes into account the variation of earth-sun center-to-center distance from day-to-day. This formula gives the extraterrestrial radiation in Cal/cm 2day, which can be converted to MJ/m 2day by multiplying with a factor 0.04183. On the earth surface, measured values of global radiation on a horizontal surface are available, and so by dividing this measured value by G.... one determines the transmission of the atmosphere for global radiation (in contrast to the direct radiation). For a given location, hourly values of ambient temperature and relative humidity are known. From relative humidity and ambient temperature, one can determine the atmospheric water content per unit volume. From Fig. 2, at any ambient temperature, the saturated water amount is known, and as relative humidity is the ratio of actual water content to the saturated water content at a given temperature, actual water content per unit volume is determined. The analytical way of determining this quantity is by using the following equation WAT = RH(4.7923 + 0.3647 x T + 0.0055 X T 2 + 0.0003 x T3). (16) This expression has been determined from Fig. 2 using a least square method. Instead of making atmospheric transmission (Go~/Gex,)dependent upon two quantities, relative humidity and ambient temperature, we have made it dependent upon one

116

GARG and GARG: PREDICTION OF GLOBAL SOLAR RADIATION 16x 10-3kg/M 3 to 2 2 x 10-3kg/M 3, and transmission varies from 0.45 to 0.35. The scattering of these points does not show clearly whether the dependence of Gob/Gex t upon water content and fraction of sunshine hours is linear, exponential or of any other type. For simplicity, we have assumed linear dependence. Using a least square technique, the following equation was obtained.

48

4.2 x

36

3o

u

G = Ge,,[0.414 + 0.400 x SS - 0.0055 x WAT].

o9 0

i

[

i

I

4.

8

12

16

L 20

1

I

i

[

I

24

28

32

36

40

Temperature

(°C)

Fig. 2. Variation of saturated water amount with ambient temperature for air.

07) Using this equation, global radiation has been computed for each month for each of the 14 stations, and the values have been compared with measured values as shown in Table 2.

4. DISCUSSION OF RESULTS

quantity, water content. It has many advantageous points, like firstly it is easier to deal with a few number of variables, and secondly, from morning until evening, the relative humidity goes on decreasing, and ambient temperature goes on increasing for a clear day, the water content per unit volume changes very slowly during this period. For each station, we have calculated hourly values of water content from 9 a.m. to 5 p.m. and taken the average of these. These calculations show that, even if one tries to know water content at 12.00 (L.A.T.), one gets nearly the same value as the average one. The time period 9 a.m. to 5 p.m. has been chosen because most of the radiation is received during this period. Figure 3 shows the variation of Gob/Ge,,t with water content. The fraction of maximum possible sunshine hours, SS, runs as a parameter. Figure 3 shows that, for low values of SS, water content varies from

0.8

0.7 - -

~

o°

o 8

o

SS=0-80+0'05

o~""~,.,,~.~.~~ 8o oo

_

°OoO vo-o~

o

Table 2 shows the observed insolation, predicted insolation and the corresponding error for all the stations. It is seen that, in most of the predictions, the error remains within a + 10% limit. Out of a total of 14 x 12 predictions, only 12 predictions have gone beyond this limit. The maximum over-estimation is +12.67o, and the maximum under-estimation is -19.67o. So, as far as over-estimation is concerned, it is also very close to the + 10% limit. In the case of Poona, just for comparison purposes with other formulas, results are shown graphically also in Fig. 4. Figure 4 shows that, during rainy months, the formula under-estimates the insolation, but during the clear months, the formula may under-estimate as well as over-estimate the insolation. The maximum overestimation for Poona is 2.870 (May), and the maximum under-estimation is - 6.470 (October). After scanning through Table 2, one sees that the trend of under-estimation during rainy months is observed in the present study also, but this underestimation is not so high as in other studies. Errors

~

o o o

0.6

o>.

32 - -

13

28

x

0.5

x

Xx 24

g

~" 0 4 m

×

,,7 2 0 o_

× x x

16

SS = 0 . 3 0 - + 0 . 0 5

0.3

3 _o

12

-

Q2--

-

Measured

......

Predicted (present study )

E _>,

0.I --

g I

I

I

I

I

I

4 8 12 16 20 24 Surface water amount ( k g / m 3) x 10 -3

Fig. 3. Variation of

Gob/Gcx t

I 28

with surface water amount.

I I I I I I I I I I I I

J

F

M

A

M

J

J

A

S

O

N

D

Months

Fig. 4. Monthly variation of daily global radiation for Poona (calculated from the proposed method).

~

Trivandrum

Kodai Kanal

Bangalore

Madras

Goa

Vizagapalnam

Poona

Bombay

Nagpur

Bhavnagar

Calcutla

Ahmedabad

Jodhpur

New Delhi

Stations

Months

Obs. Pred. O~, er. Obs. Pred. ~ er. Obs. Pred. °'o er. Obs. Pred. ".,~, er. Obs. Pred. ",, er. Obs. Pred. 'll, er. Obs. Pred. ",, er. Obs. Pred. "o er. Obs. Pred. '~,, er. Obs. Pred. "~i er. Obs. Pred. °/o er. Obs. Pred. o¢,, / er. Obs. Pred. '7o er. Obs. Pred. o; '0 er.

14.36 14.62 1.8 17.00 16.94 -0.2 17.64 18.42 4.4 15.21 16.21 6.5 18.52 18.91 2.0 17.70 18.57 4.8 18.19 19.10 4.9 19.10 19.40 1.4 19.35 19.01 1.7 20.48 19.54 4.6 18.85 18.78 0.3 21.78 21.85 0.3 22.61 19.6 -13.2 21.36 19.98 6.4

ja n . 18.01 18.59 3.1 20.04 20.27 1.1 20.84 21.62 3.7 18.12 19.14 5.6 21.47 21.82 1.6 20.44 21.88 7.0 20.73 21.56 3.9 22.23 22.50 1.2 21.91 21.93 0.0 22.97 22.00 4.2 22.66 22.13 -2.3 21.00 22.30 6.1 24.16 22.05 -8.7 22.90 21.45 6.3

Feb. 22.11 20.55 7.0 23.59 22.19 -5.9 24.26 23.10 -4.7 20.87 20.70 0.8 24.73 23.97 3.1 22.73 23.28 2.4 23.23 22.90 1.3 24.54 24.20 - 1.2 23.44 22.67 3.2 24.34 22.88 5.9 24.81 23.07 -6.9 24.28 24.83 2.2 24.75 22.91 -7.4 24.07 22.03 8.4

March 24.98 23.54 -6.3 26.05 25.63 1.6 26.42 25.39 -3.8 22.77 21.93 3.6 26.17 25.44 2.8 24.43 25.04 2.4 25.18 23.66 -6.0 25.80 25.20 2.0 23.99 22.78 4.7 24.95 23.70 5.0 24.93 23.19 -6.9 23.75 24.35 2.5 23.16 21.97 -5.1 22.21 19.94 -10.2

April 26.25 28.33 7.9 27.18 31.44 15.6 27.41 30.08 9.7 23.50 23.87 1.5 27.38 29.35 7.2 24.90 28.04 12.6 26.16 25.36 -3.0 26.30 27.00 2.8 24.05 24.72 2.8 24.26 24.26 0.0 23.53 23.28 - 1.0 22.93 23.18 1.0 21.04 20.04 -4.7 19.78 17.61 10.9

May 23.57 20.46 13.1 25.46 24.42 -4.0 23.01 22.86 0.6 17.89 16.26 -9.0 21.73 20.00 - 7.9 20.32 21.35 5.0 18.65 18.30 - 1.8 21.20 20.00 -5.8 18.64 17.51 - 6.0 17.24 16.97 1.5 20.98 19.51 -6.9 22.05 18.03 -18.2 19.01 17.12 9.9 18.91 15.20 -19.6

June 19.21 18.99 1.1 21.54 20.22 -6.1 17.45 16.95 -2.8 16.72 15.96 -4.5 16.64 15.59 - 6.3 15.79 15.96 1.0 14.63 14.33 2.0 16.30 15.80 3.5 16.81 16.91 0.5 14.38 14.44 0.4 19.46 17.38 10.6 15.73 16.33 3.8 16.36 16.36 0.0 18.11 15.72 -13.1

July 18.20 17.79 -2.2 18.97 18.91 -0.2 16.28 16.63 2.1 16.08 15.39 -4.2 15.51 15.34 - 1.0 14.86 16.33 9.8 14.32 13.97 -2.4 16.50 16.00 2.9 17.82 18.08 1.4 17.14 16.36 4.5 20.09 18.33 -8.7 15.94 17.63 10.5 16.92 17.43 3.0 20.02 17.68 -ll.7

Aug. 20.18 18.29 -9.3 21.98 19.37 -11.8 19.97 17.52 -12.2 16.12 15.08 6.4 19.67 18.73 -4.8 18.42 16.64 9.6 17.57 16.69 -5.0 19.10 17.90 -6.3 18.60 18.01 - 3.1 19.11 17.85 - 6.5 20.57 19.37 -5.8 16.99 17.27 1.6 17.31 17.30 0.0 21.40 18.56 -13.2

Sept.

Oct. 19.28 18.46 -4.3 20.99 20.14 4.0 20.79 20.29 -2.3 16.41 16.10 - 1.9 21.27 20.52 - 3.5 20.22 19.39 -4.0 19.60 19.22 - 1.9 20.40 19.10 -6.4 19.03 19.07 0.2 20.22 19.56 - 3.2 17.46 17.77 1.7 18.81 19.58 4.0 15.99 16.64 4.0 18.85 17.27 -8.3

Table 2. Comparison of predicted global radiation with observed values for fourteen Indian stations (MJ/m 2 day)

16.29 16.39 0.5 17.66 17.87 1.1 18.01 18.65 3.5 15.76 17.13 8.6 18.80 17.77 5.4 18.48 18.78 1.6 18.27 18.66 2.0 18.90 18.60 - 1.5 18.60 18.59 0.0 20.22 19.29 - 4.6 15.64 16.65 6.4 16.17 16.48 1.9 17.08 16.40 -3.9 17.79 16.58 -6.8

Nov. DEC.

18.13 -1.8

18.48

13.84 14.07 1.6 15.96 16.08 0.7 16.53 17.34 4.8 14.76 15.69 6.3 17.23 17.49 1.4 16.80 17.71 5.3 17.27 17.74 2.7 17.80 18.10 2.1 18.25 17.94 1.6 19.41 18.03 -7.1 15.39 16.80 9.1 16.07 16.81 4.6 18.81 17.83 -5.1

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118

GARG and GARG:

PREDICTION OF GLOBAL SOLAR RADIATION

are due to several factors. Altitude varies from sealevel for Bombay, Madras, Calcutta etc. to 921 m for Bangalore and 2400 m for Kodai Kanal. Atmospheric turbidity also varies highly from station to station. Jodhpur is a very clear station while Calcutta has maximum turbidity due to its heavy industrialization. Also, some stations are inland stations while others are coastal stations. Atmosphere, which attenuates the solar radiation reaching a station, is much different for these two types of stations. Also on a particular day for different stations, the zenith angle at solar noon is different, and so radiation will travel different depths of the atmosphere for different stations. Thus the radiation will suffer different amounts of attenuation. This fact also has not been taken into consideration in order to make the formula as useable as possible. If one takes into consideration all these facts, errors can be further minimised. 5. CONCLUSIONS F r o m this study, the following conclusions can be drawn: 1. The three methods discussed in this study are not able to predict monthly mean global radiation for

these 14 Indian stations within the prescribed error limits of 4- 10%. The error goes beyond 4-500/0 limits even in some cases. 2. The present study predicts global radiation within __+_10% limits in most of the cases. The maximum over-estimation is _+ 12.6'~Jo, and the maximum under-estimation is - 19.6%. 3. Dependence on relative humidity and ambient temperature can be better shown through water content per unit volume on the earth surface. It is more effective and easier to deal with, as it reduces the number of parameters also.

REFERENCES

I. A. A. M. Sayigh, 1V Course on Solar Energy Conversion, Vol. II, p. 51. International Centre for Theoretical Physics, Trieste, Italy (1977). 2. S. J. Reddy, Solar Energy 13, 289 (1971). 3. R. K. Swartman and O. Ogunlade, Solar Energy I1, 170 (1967). 4. A. K. Angstrom, Q. Jl R. met. Soc. 20, 121 (1924). 5. J. K. Page, Proe. UN Conf. in New Sources of Energy, Vol. 4, Paper 5/98, pp. 378 387 (1964). 6. Handbook of Solar Radiation Data .]or India, 1980

(Compiled by Anna Mani). Allied Publishers Pvt, New Delhi ( 1981 ).