Improved station-independent correlations between diffuse irradiation and sunshine duration

Energy Convers. Mgmt Vol. 30, No. 2, pp. 173-177, 1990 Printed in Great Britain. All rights reserved

0196-8904/90 $3.00+ 0.00 Copyright © 1990 Pergamon Press pie

IMPROVED STATION-INDEPENDENT CORRELATIONS BETWEEN DIFFUSE IRRADIATION AND SUNSHINE DURATION M. HUSSAIN Renewable Energy Research Centre and Department of Physics, University of Dhaka, Dhaka-2, Bangladesh (Received 19 January 1988; receivedfor publication 28 November 1989)

Abstract--Regression fits between monthly average values of daily diffuse irradiation and bright sunshine duration have been obtained for monsoon, pre- and post-monsoon periods, collectively for stations in (1) the zone comprising arid and semi-arid regions and (2) the wet-and-dry zone in north and central India. Long-term data of eight stations situated near 20°N lat have been employed. The root mean square (r.m.s.) errors of the fits are between 3 and 7%. The present station-independent correlations do not require data on global radiation and provide highly satisfactory estimates of diffuse irradianee from sunshine duration. The technique of making collective fits, depending on seasons and climatic regions, may well be applied to different parts of the world with much advantage. Diffuse irradiation lations Albedo

Global irradiation Sunshine duration Turbidity Monsoon Pre-monsoon

Station independent correPost-monsoon

NOMENCLATURE D= Go = G= s= S= S' = a, b, c, d = r=

Diffuse irradiation on horizontal surface (kWh/m2 day) Extra-terrestrial irradiation on horizontal surface (kWh/m2 day) Global irradiation on horizontal surface (kWh/m2 day) Bright sunshine duration (h) Day length (h) Maximum period over which Campbell-Stokes recorders remain sensitive (h) Regression coefficients Correlation coefficient

INTRODUCTION D a t a on diffuse r a d i a t i o n are scarce, as these are r e c o r d e d at far a w a y places, due to the cost involved a n d the c o m p l e x i t y o f r e c o r d i n g d a t a c o n t i n u o u s l y a n d o f a n a l y s i n g t h e m with due corrections. L o n g - t e r m m o n t h l y a v e r a g e values o f diffuse i r r a d i a t i o n are needed to p l a n for the utilization o f solar energy c o n v e r s i o n devices at a n y location. This is d u e to the fact t h a t fiat solar collectors are a l m o s t a l w a y s k e p t tilted t o w a r d s the sun a n d values o f b o t h g l o b a l a n d diffuse i r r a d i a n c e are r e q u i r e d to c o m p u t e the a m o u n t o f solar r a d i a t i o n which m a y be received by them. A g a i n , for c o n c e n t r a t i n g collectors, one requires the a m o u n t o f incident direct r a d i a t i o n which is often c o m p u t e d f r o m d a t a on g l o b a l a n d diffuse irradiance. A s a consequence, a need often exists for e s t i m a t i n g diffuse i r r a d i a n c e f r o m b r i g h t sunshine d u r a t i o n d a t a which are available for a large n u m b e r o f locations. M o s t o f the c o r r e l a t i o n s [I-6], d e v e l o p e d for the p u r p o s e , require values o f g l o b a l r a d i a t i o n as well which are n o t a v a i l a b l e for m a n y stations. In this w o r k , a technique is p r e s e n t e d for p r e d i c t i n g m o n t h l y average values o f D w i t h o u t an i n p u t o f g l o b a l r a d i a t i o n d a t a . A linear c o r r e l a t i o n o f the f o r m D

Go

s

c + d~

(1)

is employed where the parameters c and d are to be evaluated for each season of the year, collectively for stations lying in a climatic region. 173

174

HUSSAIN: DIFFUSE IRRADIATION AND SUNSHINE DURATION Table I. Seasonal classification of data of different stations Station

Zone

Pre-monsoon period

Monsoon period

Post-monsoon period

Ahmadabad Bhavnagar Jodhpur New Delhi

A

April-June April-June April-June April-June

July-September July-September July-August July-September

October-March October-March September-March October-March

Bombay Calcutta Nagpur Vishakhapatnam

B

April-May April-May April-May April-May

June-September June-September June-September June-September

October-March October-March October-March October-March

For estimating the global irradiation, G, from sunshine duration, we found it very useful in an earlier work to obtain regression fits between G and s/S for data of each season for stations lying within a climatic zone [7]. The justification rests mainly on the fact that, under cloud free conditions, the transmission and scattering of the incoming radiation from the sun depend on seasons and climatic regions. Details about climatic and regional variations of physical quantities like water vapour content in the atmosphere and its turbidity and the albedo of the earth's surface and the sky, which affect global radiation, have been presented earlier [7] for a large part of India. Diffuse radiation arises from the scattering of beam radiation in the atmosphere and the multiple scattering of solar radiation between the earth's surface and the sky. D, therefore, depends largely on the turbidity of the atmosphere and the albedo of the earth and the sky [8]. These variables change with the period of the year for both the arid and semi-arid zone and the wet-and-dry zone [9-11] of north and central India. We make here an attempt to correlate the data of groups of stations lying within each climatic zone independently for monsoon, and pre- and post-monsoon periods (Table 1). A map showing the stations and the zones is available in the literature [7]. The idea reported earlier [12] is developed here using additional data and a careful division of the year into three periods. Equation (1) has also been employed by Garg and Garg [5]. They obtained the correlation parameters c and d for each of 11 stations in India using data over the year and also for a collective fit of all data. The standard errors for the stations were found to lie between 3-14% and 3-15% for the two types of fits. For some of the stations, the errors are rather large. An attempt has been made in this paper to study the adequacy of various other correlation formulae found in the literature for estimating D at Indian stations. Our technique is found to give far better estimates than others. DATA AND ANALYSIS

Data of eight stations (Table 1) in north and central India around 20°N lat have been used for the present study. At these stations, situated near sea level, long-term data on D have been recorded by the Indian Meteorological Department with the help of periodically calibrated thermopile pyranometers following standard procedures[5, l l]. The sunshine hour data[9] required for the analysis have also been obtained by them using Campbell-Stokes recorders. Information on the geographical location of the stations and the number of months of data recorded have been presented earlier [7]. It may be mentioned that four of the stations are situated in the arid and semi-arid regions, zone A, and the other four are in the wet-and-dry region, zone B (Table 1). Table 1 also shows the division of the year into three periods--monsoon, pre- and post-monsoon. For nearby months, the changes in the different physical variables may affect G and D by different amounts, and therefore, the grouping of months into three periods may not be exactly the same for correlating G and D. Our present classification differs slightly from the previous one for G. We now consider March as the last month of the post-monsoon season whereas earlier [7] it formed the first month of the pre-monsoon season. Another difference is that we consider July to be the first monsoon month for all stations in zone A, while earlier, we considered June to be the first month for two of the stations, Ahmadabad and Bhavnagar. Figures 1 and 2, showing least-square fits to equation (l) of monthly average values of daily D and s, clearly justify our classification.

HUSSAIN:

DIFFUSE IRRADIATION AND SUNSHINE DURATION

175

0.5

F

o./,

~

~

07

0.3

Pre-mom~on

8o

--

e6 7

9

e6 50

06

~

5e

0,2

•

9 Post-monsoon

0,1

I 0.25

~'e

f2

3 3"~e e~31211 2 /10 $ ~ e2 o "¢0~- I 10 12 "e~le 12 • • 2e'~ t0 ° t4 1t 011

1

0.50

I

0.75

1.00

s/S Fig. 1. A plot of

(D/Go) vs (s/S) for Ahmadabad, Bhavnagar, New Delhi and Jodhpur along with our seasonal fits using data of the four stations in zone A. RESULTS

AND

DISCUSSION

Table 2 presents the regression constants c and d for the two zones for each period o f the year, along with the correlation coefficient r, the r.m.s, error for each fit and the overall r.m.s, error for 0.5

0.3

•. ~ 7 0

~ 0 0 ~

• ......

7 6

o/

Monsoon

__/

7 0

8 O

9~ s

*

. ~ o -

-

e

= ~

0 ~

5~ e~

/'-

\/

\ 4

Pre-monsoon

e~

.

10 e

1 2 11 ee

3

/~ Post. monsoon /

0.2

-

5

" ~ : |

,o

e~:

'=~

,,

\

10 e e e e ~ "

•

3 3 " ~ = e I 02

le 2*~ee~ 2 12. t l ",,. 11 1212

0

I 0.25

I 0.50

I 0.75

s/S Fig. 2. A plot of (D/Go) vs (s/S) for Bombay, Calcutta, Nagpur and Vishakhapatnam along with our seasonal fits using data of the four stations in zone B.

176

HUSSAIN:

DIFFUSE IRRADIATION A N D SUNSHINE D U R A T I O N

Table 2. Linear regression fits between (D/Go) and (s/S) Zone

r

RMSE (%)

-0.240 - 0.281 -0.210

-0.87 - 0.96 -0.95

5 5 7

6

-0.102 -0.598 -0.266

-0.71 -0.94 -0.85

3 4 7

5

-0.96 -0.97 -0.92

3 3 4

3.5

-0.72 -0.98 -0.88

3 3 7

5

Period

c

d

A

Monsoon Pre-monsoon Post-monsoon

0.388 0.446 0.351

B

Monsoon Pre-monsoon Post-monsoon

0.315 0.667 0.394

A

Monsoon Pre-monsoon Post-monsoon

0.392 0.445 0.367

-0.263 -0.284 -0.229

B

Monsoon Pre-monsoon Post-monsoon

0.312 0.648 0.427

-0.095 -0.568 -0.309

Overall RMSE (%)

Four-station fits

Three-station fits

either zone. We used data of all the four stations in each region to obtain four-station fits to equation (1), while three-station fits (Table 2) do not employ data of Jodhpur, the only station with an arid climate, and of Vishakhapatnam, a station with a rather different latitude. Table 2 and Figs 1 and 2 show that it has been possible to find excellent correlations with station-independent regression parameters to predict D for a large part of the Indian subcontinent. We observe that the regression parameters for three-station fits have a close agreement with the four-station parameters. Computations show that three-station fits give fair predictions for Jodhpur and Vishakhapatnam too. These facts provide a test for our correlations. For three-station fits, r.m.s, errors in monthly estimates are 3.5 and 5% for the two zones, while for the four-station fits, these are slightly higher, 5 and 6%. We found an error of 23% in estimated D for a single month at Jodhpur. Excepting this, the maximum error for three and four-station fits is 16%. In order to compare our estimates with those from other correlation formulae, we made an attempt to use Page's relation [2] D G

--

=

1.00-

G Go

1.13

--

for our stations. Generally, low estimates of D were obtained, with errors > 30% in many cases. Based on Page's formula, Modi and Sukhatme [3] and Gupta e t al. [ 4 ] obtained the following correlations using Indian data D --

G =

1.411

-

G

169

--

(2a)

Go

D

G = 1 . 3 5 4 - 1.570 - - . G Go

(2b)

--

In Table 3, we compare the deviations in estimates of D from measured value for correlations (2a) and (2b), along with the deviations for our technique. We have used four-station regression Table 3. Deviation between measured and estimated D (D in kWh/m -~ day) Dest), May

(D .... - D,~,), November

(Dm~s- Dest)2, all months

A

B

Ours

A

B

Ours

A

B

Ours

-0.57 -0.57 +0.18 -0.24 -0.57 -0.49 -0.81 -0.80

-0.45 -0.32 +0.02 -0.10 -0.34 -0.25 -0.62 -0.58

+0.05 +0.07 -0.04 -0.01 -0.01 -0.10 +0.06 -0.15

+0.26 +0.44 +0.14 +0.14 +0.17 +0.09 -0.07 +0.08

+0.33 +0.56 +0.28 +0.31 +0.31 +0.25 +0.07 +0.24

-0.04 +0.18 -0.07 +0.07 +0.07 +0.03 -0.04 +0.20

0.77 0.74 0.22 0.41 1.20 0.99 1.84 2.31

0.79 0.93 0.59 0.60 0.70 0.58 1.20 1.32

0.16 0.13 0.07 0.16 0.10 0.03 0.05 0.31

(D Station Calcutta Bombay Nagpur Vishakhapatnam Ahmadabad Bhavnagar New Delhi Jodhpur

. . . .

- -

HUSSAIN: DIFFUSE IRRADIATION AND SUNSHINE DURATION

177

parameters for Jodhpur and Vishakhapatnam and three-station parameters for the other six stations. Table 3 shows that the present method leads to much better estimates. The first three columns show that, for the m o n t h of May, a pre-monsoon month, correlations (2a) and (2b) give large underestimates, while the next three columns show for them large overestimates for a postmonsoon month, November. The last three columns indicate that correlation (2a) gives marginally better fits than (2b) for the wet-and-dry region and worse fits for the arid and semi-arid regions, and that both give rise to much larger errors compared to our correlations. G a r g and G a r g [6] recently obtained the correlation constants a and b of Page's formula D

G

--=a+b-G Go

for individual stations using monthly average values over the year. This procedure gave r.m.s. errors of 6 - 1 2 % for four stations in India. As a and b vary from location to location, considerable uncertainties would arise in extrapolating or interpolating their values for a place where the diffuse radiation is to be estimated. A different approach for estimating D for north Indian stations had an additional variable in the correlation formula [13] D

s

Go

a + b - ~ + cw

where w is the water content in the atmosphere and S ' is the period over which a Campbell-Stokes recorder remains sensitive over a day. As w varies with the season and the climatic region, this relation partially takes into account seasonal and regional effects on the scattering of solar radiation. The r.m.s, error for a collective fit of data for seven stations was found to be 11%, which is again quite large. An attempt was also made to use the correlation developed by Collares-Pereira and Rabl [14]. An estimate of D for New Delhi showed excellent results for off-monsoon months, but predictions fail for the m o n s o o n months. F o r June-August, we computed D using the technique for our eight stations and found that the values obtained are, in each case, lower than the measured ones and the errors in monthly estimates lie between 16 and 33%. We find that a number of correlations available in the literature for estimating D are inadequate for Indian stations. The technique presented in this paper gives smaller errors and shows no seasonal bias. We conclude that the present correlations allow one to obtain highly satisfactory estimates of diffuse irradiance (Table 2) for locations in the northern and central parts of the Indian subcontinent, having data on sunshine hours. The technique may well be applied to different parts of the world. REFERENCES I. 2. 3. 4. 5. 6. 7. 8. 9. 10. I1. 12. 13. 14.

B. Y. Liu and R. C. Jordan, Sol. Energy 4, 19 (1960). J. K. Page, Proc. U.N. Conf. on New Sources of Energy, Paper No. S/98 (1961). Vijay Modi and S. P. Sukhatme, Sol. Energy 22, 407 (1961). C. L. Gupta, K. Usha Rao and T. A. Reddy, Energy mgmt 3, 299 (1979). H. P. Garg and S. N. Garg, Energy Convers. Mgmt 25, 409 (1985). H. P. Garg and S. N. Garg, Sol. Wind Technol. 4, 113 (1987). M. Hussain, Energy Convers. Mgmt 30, 163 (1990). J. E. Hay, Sol. Energy 23, 301 (1979). A. Mani and S. Rangarajan, Solar Radiation Over India. Allied Publishers, New Delhi (1982). A. Mani, O. Chacko and S. Hariharan, Tellus XXI, 6 (1969). A. Mani, Handbook of Solar Radiation Data for India. Allied Publishers, New Delhi (1980). M. Hussain, Proc. ENERGEX Conf., Regina, Canada, pp. 393-396 (1984). M. Hussain, Sol. Energy 23, 217 (1984). M. Collares-Pereira and A. Rabl, Sol. Energy 22, 155 (1979).