Monthly average daily global beam and diffuse solar radiation and its correlation with hours of bright sunshine for Karachi, Pakistan

Renewable Ener,qy Vol. 1. No. I,pp. 115 118, 1991 Printed in Great Britain.

0960-1481/91 $3.00+.00 Pergamon Press pie

DATA BANK Monthly average daily global beam and diffuse solar radiation and its correlation with hours of bright sunshine for Karachi, Pakistan FIROZ A H M A D , * S. M . AQtL BURNEY~" a n d S. A . HUSAIN* *Solar Energy Research Group, Institute of Pure and Applied Physics, Department of Physics, University of Karachi, Karachi, Pakistan tDepartment of Statistics, University of Karachi, Karachi, Pakistan

(Received 25 September 1989 ; accepted 30 October 1989) Correlation equations have been developed to obtain the monthly average of daily global, beam and diffuse solar radiation at Karachi, Pakistan from the fraction of maximum possible sunshine hours. The global, beam and diffuse solar radiation estimated via these equations are then compared with the measured values with excellent agreement. Diffuse and beam radiation can be estimated even in the absence of global radiation. Abstract

1. INTRODUCTION Adequate information regarding the availability of global solar radiation and its components at a particular location is essential to predict the efficiency and performance of many solar thermal devices. The total solar radiation (direct plus diffuse) is the important factor in applications such as climatology and agriculture. Direct radiation is important in some industrial applications such as solar furnaces and other solar energy concentrating devices. Whereas diffuse radiation data is required for energy related problems associated with building research, and for information regarding solar radiation on inclined surfaces. The solar radiation measuring network usually records global solar radiation on horizontal surface. This data is mostly available on a daily and hourly basis. Values on horizontal surface are then used to compute the insolation on an inclined surface. In developing countries, the situation regarding solar radiation recording stations is not encouraging at all. In Pakistan only five stations : Karachi, Lahore, Quetta, MuRan and Peshawar record global solar radiation on a horizontal surface. Therefore for other locations in Pakistan, one has to depend on the different empirical relationships which have been suggested so far for estimation purposes, employing different climatological parameters. The measured data of global solar radiation is available, but the data on diffuse solar radiation is not available at all, since no station in the country records it. To assess the availability and variation of diffuse and beam radiation, one relies and depends on the estimated values, for a particular location. Under these circumstances, the need was to develop correlation of global, beam and diffuse radiation with the most commonly available hours of bright sunshine for Karachi. The idea of employing sunshine hours for estimation purpose is based on the quick availability of this parameter for about 100 stations for a period of more than 60 years. Successful correlation obtained for Karachi, will therefore be extended for other stations where global, beam and diffuse radiation data is not available at all. Iqbal [I] has carried out similar studies for Montreal, Toronto and Goose Bay in Canada while Barbaro et al. [2]

have developed the relationships for Italian stations Palermo, Macerata and Genova.

2. M E T H O D O L O G Y Following the methodology adopted by lqbal [1], we proceed as follows. We have ~=

al+a2 ~

(l)

where I4a/H is the fraction of diffuse to total radiation and ri//V is the percentage of possible sunshine hours, ri is the monthly mean daily number of hours of observed bright sunshine (hr day '), / t is the monthly mean daily global solar radiation falling on a horizontal surface at a particular location (MJ m - 2 d- ~). The percentage of possible sunshine hours may be considered as a correlation procedure where /4 should be known, experimentally or estimated. W h e n / 4 is not known experimentally, it can be estimated from the well known equation suggested by Angstrom [3]. This is of the form

Ho

a3+a4 ~

(2)

where n o is the monthly mean daily radiation on a horizontal surface in the absence of any atmosphere at a particular location (MJ m 2 d ~). This famous equation has been widely used to estimate the total insolation for various places, with remarkable success. Furthermore, we multiply eq. (1) and eq. (2) to get the following quadratic equation [210 = as-~-a6

IV + a 7

P~

"

(3)

From this equation, one can estimate the diffuse solar radiation directly from the extraterrestrial radiation,/~0, without knowing the global solar radiation,/~. Therefore eq. (1) and eq. (3) are the two different approaches to estimate/ta. The empirical relationship for the beam radiation with the 115

Data Bank

116

Table 1. Relative sunshine hours for Karachi Months

Jan.

Feb.

Mar.

Apr,

May

Jun.

Jul.

Aug.

Sep.

Oct.

Nov.

Dec.

Average ti/N

0.805

0,776

0.762

0.738

0.743

0.595

0.381

0.390

0.602

0.818

0.837

0.830

hours of bright sunshine is developed as follows. The monthly average daily beam radiation/~b on a horizontal surface can be written as /Th = / ? - - Ha.

(4)

evident that the coefficients obtained through regression equation are very closely predicting the global, beam and diffuse radiation for Karachi. The analysis and the comparison of the computed data with the available data is

Dividing the right hand side of the eq. (4) by/70, we get nb

It--nd

H0

H0

Table 2(a). Regression coefficient and standard error of estimate from eq. (1)

/7

/7,,

H0

H0

(5)

substituting (2) and (3) in the right hand side of eq. (5), the ratio of beam to extraterrestrial radiation is obtained as ql, = a8+a9

H0

Coefficient a~ a2

Station

+alo

Karachi Standard error of estimate

Table 2(b). Regression coefficient and standard error of estimate from eq. (2) Coefficient a3 a4

Station Karachi Standard error of estimate

0.323 0.015

0.405 0.022

Table 2(c). Regression coefficient and standard error of estimate from eq. (3)

3. RESULTS AND DISCUSSIONS Regression analysis were carried out to compute the coefficients ai used in eqs (l), (2), (3) and (6). The results obtained through this technique are given in Table 2(ad) whereas Table 1 shows the monthly average of relative sunshine hours for Karachi. The sunshine hours and the monthly average daily global radiation for Karachi were obtained from Pakistan Meteorological Department, Quetta [4]. Table 2(a~t) also gives us the standard error of estimates in the determination of these coefficients. All these standard errors of estimates are compiled and tabulated in Table 3. From the examination of these values, it is quite evident that a good correlation is obtained. Shown in Table 4(a-c) are the values of global, beam and diffuse radiation obtained from the regression analysis along with the measured global radiation and/~a and Hb obtained via different methods [5]. A good correlation is found. These are shown in Fig. 1(a-c) as well, from where it is very much

Station

a5

Karachi Standard error of estimate

0.181 0.013

Coefficient a6 0.145 0.047

a7

-0.179 0.036

Table 2(d). Regression coefficient and standard error of estimate from eq. (6) Coefficient Station Karachi Standard error of estimate

Table 3. Compilation o f standard error of estimate for coefficient ae (i = 1, 2 , . . . ,

Standard error o f estimate

-0.378 0.0173

(6)

.

All these correlations (1), (2), (3) and (6) are related with the relative sunshine hours ri/57, where ti is the actual number o f observed sunshine hours and ~r is the monthly mean daily number o f hours o f sunshine in a given month between sunrise and sunset (hr day J). From these equations /4, /~a and fih can be estimated without any complications, especially/Ta and/Tb are so correlated that these could be estimated, even in the absence of global solar radiation data.

Coefficient

0.584 0.012

a8

a9

a 10

0.171 0.078

0.162 0.273

0.261 0.223

10) in eqs (1), (2), (3) and (6)

a ~

az

a3

a4

a5

a6

a7

a8

a9

a t0

0.012

0.017

0.015

0.022

0.013

0.047

0.036

0.078

0.273

0.223

Data Bank

117

3o - (a)

? E

c*-o-o Measured e-e-o Estimated

•

8 k~

I " e,

from eq.(8} •

._o 20

~

~

tm

o

I

I

I

I

I

I

I

I

I

I

I

I

J

F

M

A

M

J

J

A

S

0

N

D

Month

15

v-"

30 "o ? E

(b)

E

~ (cl

Averoge /~ ×-x-× from Poget Liu ond dordon

8

,,,,~.. x~

o-o-o H-Hd fromRef.15l x-x-x Estimated from

.9

~ zc

v-v-~' Average H~ from eqs (-/)and (9)

eq.(10)

E

8

~,,,,

g g o

.,%x

~ " ~v,,

X

~X

o

t~

5 i

i

J

F

I M

i A

I

I

i

M

J

J

I A

I

I

i

I

i

I

I

I

S

0

N

D

J

F

M

A

I M

Month

I

i

I

I

i

I

I

J

J

A

S

0

N

D

Month

Fig. l(a). Comparison of measured monthly average daily global radiation and estimated global solar radiation from eq. (8). (b) Comparison of/4a estimated via Page and Liu and Jordan method and that obtained from eqs (7) and (9). (c) Comparison of/4~ (E¢-/4,/) and that estimated from eq. (10).

important from the application point of view for locations where/4, /la and Jq~ are not available at all. Knowledge of either of these parameters along with the observed sunshine hours and extraterrestrial radiation will give us a lot of information regarding the availability and variation of these components for usual solar energy design procedure. Therefore for Karachi, to obtain monthly average daily diffuse radiation, when/4 is known, use /4" fi-

0.584-0.3 8 ( ~ ) . 7 '~

ation, we obtain :

(-)

(8)

~ = 0 323+0.405 N ~t 0

'

,

Also the monthly average daily diffuse radiation /4,~can be estimated, even in the absence of measured or estimated monthly average daily global radiation /4, provided extraterrestrial radiation no is known, then

(7)

For the estimation of monthly average of global solar radi-

"'

(1

(1

H- =0.181+0.145 ~ -0.1"79 ~ .

(9)

118

Data Bank

Table 4(a). Comparison of measured and estimated data from eq. (8)

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

Global measured

Radiation estimated

Percent error

15.89 18.09 21.16 22.57 23.56 22.73 19.21 17.91 19.84 19.35 16.68 15.04

15.64 18.04 20.91 23.16 24.63 22.64 18.96 18.28 19.56 19.39 16.57 15.05

1.57 0.27 1.18 - 2.61 -4.54 0.39 1.30 -2.06 1.40 -0.20 0.66 - 0.05

(All radiation are in MJ m - 2 d

1)

Table 4(c). Comparison of the values of beam radiation obtained from eq. (10) and that obtained f r o m / q - / t d , i.e. from measured global and estimated diffuse from Page and Liu and Jordan [5]

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

Beam /1-/~d

Radiation estimated

Percent error

11.71 13.04 15.21 15.70 16.28 14.83 11.01 10.13 13.06 14.23 12.45 11.13

I 1.27 12.80 14.66 16.01 17.09 14.33 10.66 10.35 12.42 14.07 12.19 11.02

3.75 1.84 3.61 - 1.97 - 4.97 3.37 3.18 -2.17 4.90 1.12 2.08 0.98

(All radiation is in MJ m - 2 d - ~.)

Table 4(b). Comparison of diffuse radiation values from eqs (7) and (9) and that obtained from Page and Liu and Jordan

[5]

~= H0

Monthly average diffuse radiation

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

Average from Page and Liu and Jordan

Average from (7) and (9)

Percent error

3.97 4.85 5.68 6.77 7.26 7.65 8.00 7.68 6.51 4.94 4.03 3.76

4.40 5.25 6.22 6.97 7.31 8.14 8,34 7,88 7,04 5,31 4.46 4.05

- 10.83 -8.24 - 9.50 -- 2.95 -0.68 - 6.40 - 4.62 --2.60 -8.14 - 7.49 - 10.74 - 7.70

(All radiation values are in MJ m -2 d ~.)

To obtain monthly average daily beam (direct) radiation the use of the following equation is recommended for Karachi 1

ff

1 ~

The above eqs (7-10) are developed for Karachi, and can be used with confidence for estimation purposes, since the values of the standard error of estimates are very small. REFERENCES 1. M. Iqbal, Correlation of average diffuse and beam radiation with hours of bright sunshine. Solar Energy 23, 169-173 (1979). 2. S. Barbaro et al., Diffuse solar radiation statistics for Italy. Solar Energy 26, 429-435 (1981). 3. A. Angstrom, Solar and atmospheric radiation. Q.T.R.M. Soc. 20, 121-126 (1924). 4. Pakistan Meteorological Department, Geophysical Centre, Quetta (1987). 5. Firoz A h m a d and S. A. Husain, A study of availability and seasonal variation of diffuse solar radiation on horizontal and inclined surface at Karachi. Pak. J. Sei. Ind. Res. 27(I), 14~16 (1984).