Indian Journal of Radio & Space Physics Vol. 28, December 1999, pp. 277-285

Solar beam radiation estimate's correlation for Bangladesh

M M Rahman, M A Uddin & M W Islam

Department of Physics, University of Rajshahi, Rajshahi 6205, Bangladesh

Received 8 February 1999; revised 12 July 1999; accepted 16 September 1999

An empirical correlation has been developed which correlates the monthly average daily solar beam radiation with the maximum possible number of bright sunshine hours. Airmass exponential correlation is also established. The applicability of these models in climatic conditions of Bangladesh is also studied. Measured beam radiation and the bright sunshine hour data are analyzed to find out the regression co-efficient of these correlations using computer simulation programme by Gaussian elimination technique. Applying these correlations, solar beam radiation is computed for different locations in Bangladesh. Predicted results are compared statistically with the experimental observations considering different statistical errors. The t-statistics is also applied to test whether or not a model is statistically significant at a particular confidence level. On the basis of the analysis, a model has been recommended which is found to be bes~ suited to the climatic conditions of Bangladesh.

1. Introductioll With the i.ncreased interest in applications of solar

energy, quantitative values of solar insolation at the earth's surface are needed. In many applications of solar energy, solar engineers, architects, agriculturists and hydrologists require a reasonably accurate knowledge of the availability of the solar resources at the projected site. Since the behaviour of solar energy varies, both on a diurnal and seasonal scale, the estimation of the resource becomes essential for its effective utilization . Solar beam radiation is very important in some industrial applications, such as solar furnaces and other solar energy concentrating devices . Instantaneous fluxes of beam radiation may be needed in some research problems associated with solar energy.

The most important parameter that is often needed is the long-term average daily global (beam and diffuse) radiation. Unfortunately, the measurement of this parameter is .one oniy at a few places. For a place whe!'e no r,1easured data are avai lable, a common practice i." to a_ ess irradiance (direct and beam) co sidering appropriate correlations that are empirically established by using the measured data at some selected places. These correlations are based on more readily avai lable meteorologicaL climatological

d h· I \- \7 an geograp lca p"ramet;: rs . There are many parameters that change the amount

of beam and diffuse solar radiation, such as time, date, latitud . Ititu e, dedi. :1t1On angle, zenith angle,

atmospheric transrruttlvlty, water vapour, regional albedo, cloud condition, sunshine hours, maximum air temperature, relative humidity, elevation of the location, etc. It is very difficult to obtain a general formula in order to estimate direct and diffuse solar radiation by considering all these parameters simultaneously. On the other hand, some of the above mentioned parameters have little effect on solar radiation and can be neglected, and only important factors may be taken into account. Bright sunshine hours of a day are a frequently measured data in most of the places around the world and are,directly related to the amount of solar irradiance. Based on this parameter, the correlations of beam radiation estimates are not much developed and only a few works ll

.16 have been reported. Solar radiation data

(global or beam) of Bangladesh are not studied very well so far. In near future it would be very essential for the development and applications of solar energy devices in this country.

The objectives of the present work are to analyze the meteorological solar data to correlate the solar beam radiation with the commonly measured sunshine hour data. An airmass correlation has also been developed for the estimation of direct solar radiation for places where no measured data are available. The main characteristic of the airmass model is that this model needs no measured data, if the latitude of the location is known. The present work also carries out a statistical comparison of these

278 INDIAN J RADIO & SPACE PHYS. DECEMBER 1999

models and recommends one that is general and is most accurate for esti mating solar beam radiation over Bangladesh.

2 Experimental data This study consists of basic data involving monthly

average daily solar beam radiation ( HB

) arriving on

horizontal plane surface and the bright sunshine hours (5) collected over I I years (1983-93) from seven meteorological stations in Bangladesh . These stations are Barisal (BAR), Bogra (BOG), Comilla (COM), Dhaka (DHK), Mymensingh (MYN), Rangpur (RAN) and Sylhet (SYL), geographically distributed throughout the country. The geographical parameters of these locations are given in Table 1. The measured solar beam radiation and the bright sunshine hour data were collected from the Meteorological Department of Bangladesh (MDB). The percent of

poss ible sunshine (S / So) of a day and the monthly

average daily solar beam radiation ( HB ) data are

presented in Table 2 and 3, respectively.

Table 1- Geographical parameters of different locations of Bangladesh

Location Latitude ($) Longitude Elevation (h) ON °E m

Barisal (B AR) 22.75 90.22 02.10

Bogra (BOG) 24.85 89.22 18.00

Comilla (COM ) 23.43 89.22 18.00

Dhaka (DHK) 23.77 90.23 08.80

Mymensingh (MYN) 25.77 90.26 18.00

Rangpur (RAN) 25.73 89.14 18.00

Sylhet (SYL) 24.30 91.53 32.50

3 Methods of prediction

3.1 Iqbal polynomial model

To predict the solar beam rdl..!iatlOn, we have considered the Iqbal type polynomial correlation in

which the sunshine hour data (S ) are only the input parameter. The correlation is expressed as 11

where, a j , are the regression constants, (HB ) the

monthly mean daily solar beam radiation, Ho the monthly average daily extra-terrestrial radiation on horizontal surface and So the day length. The daily solar beam radiation is expressed as the ratio of

observed CHB ) to the value of Ho calculated for a

horizontal plane at the top of the atmosphere. Using

the ratio, (HB / H 0 ) rather than ( H B ) in regression

analysis, it is possible to assess whether the regression coefficients are independent of site and time of the year or noes. The monthly average daily extra-terrestrial radiation Ho is given by13

where, lse (=1.367 kW/m2 ) is the solar constant, Eo the eccentricity correction factor, <I> the latitude of the location, 0 the solar declination angle and ills the sunshine hour angle. The solar declination angle 8

Table 2- Measured values of monthly mean daily percent of possible sunshine ( S / So) for different locations in Bangladesh

Month S / So for locations

BAR BOG COM DHK MYN RAN SYL

Jan . 0.72 0.70 0.72 0.71 0.64 0.69 0.72

Feb. 0.72 0.72 0.69 0.73 0.66 0.69 0.71

Mar. 0.69 0.7 1 0.68 0.70 0.60 0.67 0.66

Apr. 0.66 0.63 0.60 0.62 0.54 0.58 0.52

May 0.55 0.52 0.54 0.56 0.44 0.48 0.43

June 0.33 0.38 0.39 0.38 0.31 0.40 0.30

July 0.27 0.29 0.29 0.31 0.28 0.30 0.26

Aug. 0. 34 0.40 0.41 0.41 0;34 0.41 0.35

Sep. 0.42 0.42 0.42 0.43 0.3 1 0.41 0.34

Oct. 0.61 0.64 0.60 0.63 0.56 0.62 0.62

Nov. 0.72 0.73 0.70 0.72 0.72 0.79 0.78

Dec. 0.73 0.74 0.72 0.73 0.69 0.73 0.77

...

RAHMAN el al. : CORRELATION OF SOLAR RADIATION ESTIMATES FOR BANGLADESH 279

Table 3-Measured values of monthly average daily solar beam radiation HB (kWhlm2) for different locations in Bangladesh

Month HB (kWhlm2

) for locations

BAR BOG COM

Jan. 2.616 2.876 2.577

Feb. 3.094 3.404 2.971

Mar. 3.727 3.947 3.616

Apr. 3.795 4.209 3.690

May 3.646 3.764 3.660

June 2.946 3.450 3.116

July 2.793 3.029 2.731

Aug. 2.892 3.398 3.171

Sep. 2.769 2.994 2.718

Oct. 2.849 3.127 2.973

Nov. 2.749 3.044 2.779

Dec. 2.594 2.733 2.585

(degrees) is assumed to be the same for every year and to have the value 8 = 0° on 21 March. It is computed by means of Fourier series l8

3 3

8 = ~>n cos(nt) + Idn sin(nt) · . . (3) n=O n= 1

21t t= (N D -80)

- 365 .24 · . . (4)

The values of Fourier co-efficients en and dn in Eq.(3) are given in the last column of Table 4. The eccentricity correction factor Eo is given by

Eo = I +0.0335cos D (

21t N ) 365 .24

· .. (5)

Here, ND is the number of the day sequence of the year starting from the first January: The sunshine hour angle COs and hence the day length, So , are computed by the relationsl4

· .. (6)

· . . (7)

The values of the regression constants a j of Eq. (1 ) have been determined using Gaussian elimination technique. These constants are listed in Table 4. The

DHK MYN RAN SYL

2.980 2.649 2.384 2.960

3.430 2.999 2.804 3.326

3.823 3.467 3.232 3.719

4.040 3.753 3.502 3.650

3.521 3.415 3.313· 3.659

3.342 2.988 3.062 3.285

3.187 2.744 2.690 3.270

3.312 2.753 2.964 3.421

2.996 2.508 2.477 2.901

3.167 2.918 2.665 3.220

3.096 2.814 2.658 3.128

2.852 2.828 2.379 2.871

constants a j are determined by fitting local data (regional fit) as well as by fitting integrated data of all the stations (general fit) .

3.2 Airmass exponential model The airmass correlation has also been established

for the prediction of solar beam radiation over Bangladesh. Two forms of this model (airmass model I and airmass model II) have been considered in this study.

3.2.1 AimUlSS model 1- The direct solar irradiance reaching the surface can be written as

... (8)

where, -r is the optical depth and m the air mass. When this is averaged over a day (different solar zenith angles during sunshine) and over a month, Eq. (8) has the form

(:: ) ~ (exp(-<m»)

which can be approximated as

. . . (9)

3.2.2 Airma~s model II-Another form of the airmass model, similar to model I, which has been considered here is as follows

280 INDIAN J RADIO & SPACE PHYS, DECEMBER 1999

Table 4-Parameter values of the polynomial correlation of Iqbal type [Eq. (I)]

Locati on at) al a2

BAR 1.248 -6.561 14.669

BOG 0.717 -2.772 06.857

COM 0.809 -3.795 09.361

DHK 1.203 ..:.5.455 11.402

MYN -0.285 3.505 -5.943

RAN -0.076 2.170 -3.489

SYL 0.414 -0.387 o 1.l 49

Bangladesh 0.232 0.600 -0.6 12

HB - I ... (10) -- = 0, exp(02m )

Ho

where, Q j are the regression constants and m is the average airmass of the location. The average ainnass m can be eva lu ated using the following equation as l9

CDS m=

cos 8 cos <I> cos CDs (tan CDs - CDs) ... (11)

The regression constants of Eqs . (9) and (10) can be obtamed by fitting experimental data of (HB IHo). The values of these constants obtained by using a computer programme are as follows: al= 0.552, a2 = - 0.273 and a, = 0.193, 02 = 0.992 for model I <lI1d model II, respectively.

4 Model performance The performance of the models used in this study

has been discussed considering some statistical errors such as root mean square error (RMSE) , mean bias error (M BE) , mean relative percentage errors (MRPE%). the I-statistics (t-stat ) and chi-square (X2

) . b 1 t' II ' . 1 14 20-23 given y til e 0 oWlllg expressIOns" .

I

[I n . 2 ] 2

RMSE = -;; ~ (P; -MJ _ .. . (12)

1 II

MBE= - L (P;-MJ n j

... (13)

I " P-M MRPE=-L j j ><100

n . M . I I

... (14)

a) i -10.252 0.145

-05.161 0.153

-07.075 0.114

-07.609 0.087

03 .074 0.112

01.657 0.172

-Ol.021 0.085

-00.300 1.262

I - -l (n-I)MBE

2

12 t stat - 2 2

RMSE -MBE

x2 = Iff>; _M j )2 . M . I I

Cn & d" [Eq. (3)]

Co = 0.386470

c, = -0.392624

C2 = 0.377853

c) = 0.030 124

d, = 23.259526

d2 = 0.131544

d) =-0.167013

... (15)

... (16)

where Pj and M j are the ith predicted and measured values of n observations. Generally, the lower the value of RMSE, the more accurate the model is. However, a few large errors in the sum can produce a significant increase in RMSE. The MBE test provides infonnation with respect to overestimation (positive value) or underestimation (negative value), but the lower the absolute value, the better is the model perfonnance. To determine whether a model' s estimation is statistically significant, one simply has to determine a critical value obtainable from standard statistical table, i.e. tan at the a level of significance and (11-1) degrees of freedom. For model's estimates to be judged statistically significant at the (1-a) confidence level , the predicted t-value must be less than its critical value Ie. The smaller the value of (­stat, the better is the model perfonnance. The parameter X2 controlled the quality of the fits with experimental observations. The lower value of X2 will indicate the better quality of the fits.

5 Results and discussion Solar meteorological data measured at different

places in Bangladesh have been analyzed to study the beam radiation pattern over the country. The local geographical parameters of different meteorological stations are given in Table 1. The possible sunshine

hour data ( SIS 0) and the measured values of solar

RAHMAN el at.: CORRELATION OF SOLAR RADIATION ESTIMATES FOR BANGLADESH 281

beam radiation HB are presented in Tables 2 and 3,

respectively. The (S / So) value varies from 0.26 to

0.77 and HB varies from 2.379 to 4.209 (kWhlm2)

for Bangladesh . For the computation of solar beam radiation theoretically over Bangladesh, two models namely Iqbal polynomial model [Eq. ( I)] and airmass exponential model [Eqs (9) and (10)] have been considered .

Using fraction of measured beam radiation

( H B / H 0 ) and the percent of possible sunshine

(S / So) data, the regression constants Q; of the Iqbal

model have been determined by computer fitting simulations. The constants Q . have been determined

I

by fitting the station wise data (regional fit) and their values are given in Table 4.

Typical behaviour of the predicted results obtained by using regional correlation of Iqbal type is shown in Fig. I only for the location Dhaka (Bangladesh), for example. The other stations have the same profile as in Fig.l . This figure shows that the obtained co­efficients Q; of regional correlation of Iqbal type give

values very close to the experimental observations except for the months of October and November. For these months, the proposed correlation gives slightly higher results than the experimental one. So, the regional correlations obtained for different locations can be used for the prediction of monthly average daily solar beam radiation with a deviation of less than 2% [see MRPE (%) in Table 5].

The countrywide regression constants have also been determined by fitting the observed data

- -(H B / H 0) and (S / So), taking integrated data of all

5 r-----------------------------------------------~

Fig. I-Compari son of predicted values with measured data of monthly mean daily solar beam radiation HB (kWh/m2) obtained from the Iqbal type (regional) correlation for the meteorological station Dhaka (Bangladesh).

Table 5-Statistical errors obtained from Iqbal type (regional) correlation

Location MBE RMSE MRPE (%) I-sIal Ic( a=O·OI )

BAR -0.036 0.336 0.257 0.359 3. 106

BOG 00.004 0.375 1.259 0.035 3. 106

COM 00.007 0.298 0.959 0.080 3. 106

DH K -0.001 0.28 1 0.599 0.0 16 3.1 06

MYN 00.002 0.291 0.832 0.022 3.106

RAN 00.002 0.326 1.2 18 0.022 3.106

SYL 00.006 0.253 0.637 0.073 3.106

282 INDIAN] RADIO & SPACE PHYS. DECEMBER 1999

the seven stations of Bangladesh. Hence, the countrywide general polynomial correlation of Iqbal type yields the form for Bangladesh as

HB = 0.232+0.60j S } 0.612( S )~ 0.30j S )3 H 0 vl So So ":l So

... (17)

The airmass exponential correlations for the prediction of monthly average daily', solar beam radiation over the country have been established. Here, the two forms of this model, i.e. airmass model I and II as illustrated in Eqs (9) and (10), respectively, are considered. The regression constants of these correlations can be obtained by fitting experimental

data of ( H B / H 0) with the monthly average values of

airmass (m) of the location .computed by Eg. (11) . The integrated data of all the seven stations of Bangladesh are used during' fitting procedure. Therefore, the airmass model takes the forms for Banglad.esh as

H _B_ = 0.552exp(-D.273m) Ho

H B = 0.193 exp(0.992m -I) Ho

... (18)

... (19)

Graphical behaviours of the predicted results oetained from the above mentioned correlations [Eqs (17)­(19)] are presented in Fig. 2 simultaneously also for the same meteorological station Dhaka (Bangladesh). Analysis shows that the airmass models give results very close to each other and one can use any form of the above mentioned models for the prediction of monthly average daily solar' beam radiation at any place in Bangladesh. The airmass models give slightly lower values than those corresponding to experimental observations, but better than the Iqbal model. Local values of regression constants Q i of the airmass models have not been evaluated. The countrywide general correlation of Iqbal type gives also lower values than the counterparts. Thus, Fig. 2 indicates that the airmass model yields the better performance.

The performance of the proposed correlations is evaluated statistically by finding the errors such as mean bias error (MB£) , root mean square error (RMS£) , mean relative percentage error (MRPE %), etc.[Eqs (12)-(14)]. There are some drawbacks in RMSE and MBE errors. In RMSE test, a few large errors in the sum can produce a significant increase in RMSE and it does not differentiate between underestimation and overestimation. In M BE test, overestimation of an individual observation will cancel underestimation in a separate observation. So, this test may not be an adequate indicator of the

5 ~--------------.-------------------------------,

4

3 Ne

~ ..I<:

Iii 2 ::t:

-+- Measured , ___ Iqbal model (general)

-'-Ainnass model I -*- Ainnass model II

0

2 3 4 5 6 7 8 9 10 11 12

MONTH

Fig, 2-Measured and predicted values of monthly mean daily solar beam radiation HB (kWh/m2) obtained from different correlations for the meteorological station Dhaka (Bangladesh).

RAHMAN el at.: CORRELATION OF SOLAR RADIATION ESTIMATES FOR BANGLADESH 283

model's performance. It is possible to have a large RMSE value and, at the same time, a small MBE or a relatively small RMSE and a large MBE. Another drawback of using thf' RMSE and MBE is that the dimension values of the indicators do not allow model testing under various meteo-climatic conditions2J

. To circumvent these problems, a relationship for (-statistics [Eq. (15)] has been developed as a function of widely used RMSE and MBE.

Table 5 summarizes the statistical errors to study the performance of the regional correlation of Iqbal type examined in this analysis. It is seen that the regional correlation has the minimum statistical errors and the values of t-stat lie far below the critical value tc' This indicates the better performance of the obtained correlation which is statistically significant at a particular level of confidence. Table 5 also indicates that the regional correlation of Iqbal type can predict the solar beam radiation accurately with a deviation of 2-3% in the considered locations.

Tables 6 and 7 give the comparison of statistical errors obtained from different correlations of Iqbal type (general) and airmass correlation · over the

country. It is observed that the airmass correlations have the lower statistical errors. The negative sign (-) of the statistical errors in Tables 5-7 indicates the underestimation of the results of correlations and the positive values indicate overestimation. For the convenience of analysis of the results, the maximum (Max) and minimum (Min) values of the statistical errors obtained from different models 'are listed in Table 8.

Table 8 clearly indicates that the airmass exponential model proposed in this work has the minimum statistical errors, thereby confirming the better performance of it. The two forms of the airmass exponential model , practically, give the same results and have the identical statistical errors. Graphical representations (Fig. 2) demonstrate also that the airmass correlation curves are indistinguishable from each other. Therefore, any of the forms of airmass model can be considered. Table 7 also indicates that the results are statistically significant at the particular confidence level ( l-a = 1-0.0 1 = 99%), since the t-stat error is less than its critical value tc' The critical tc value can be obtained from standard statistical Table24

. In some cases (for

Table 6-.Comparison of statistical errors MBE and RMSE obtained from different correlations.

MBE RMSE Location Iqbal model Airmass Airmass Iqbal Airmass Airmass

model I model II model model I model II

BAR -0.376 -0.100 -0.100 0.694 · 0.356 0.351

BOG -0.712 0.314 0.313 0.906 0.449 0.448

COM -0.317 -0.025 -0.025 0.564 0.296 0.292

DHK -0.658 0.251 0.251 0.834 0.353 0.352

MYN -0.161 0.006 0.004 0.480 0.327 0.324

RAN -0.201 -0.136 -0.138 0.523 0.301 0.297

SYL - 0.631 0.245 0.244 0.796 0.326 0.323

Table 7--Comparison of statistical errors MRPE (%) and I -sIal obtained from Iqbal type (general) and airmass correlations

MRPE(%) I-sIal Ie (a=O.OI ) Location Iqbal Airmass Airmass Iqbal Airmass Airmass

model model I model II model model I model II

BAR -11.048 - 04.662 -4.627 02.135 0.970 0.982 3.106

BOG -20.478 8.570 8.526 04.209 3.243 3.242 3.106

COM -09.554 -01.828 -1.820 02.255 0.283 0.286 3.106

DHK - 19.307 7. 124 7.116 0.4.265 3.356 3.368 3. 106

MYN -04.349 -0.760 -0.842 01.180 0.063 0.042 3.106

RAN -06.463 -05.727 -5 .812 01.383 1.678 1.740 3.106

SYL - 19.266 7.1 4 1 7.121 04.305 3.764 3.8 19 3.106

284 INDIAN J RADIO & SPACE PHYS, DECEMBER 1999

Table 8-Maximum (Max) and minimum (Min) variation limits of the statistical errors obtained from different correlations over the country.

Correlation MBE RMSE Max Min Max

Iqbal model 0.712 0.161 0.906

Airmass I 0.314 0.006 0.449

Airmass II 0.313 0.004 0.448

Iq bal(regional) 0.004 0.001 0.375

the locations Bogra, Dhaka and Sylhet), the t-stat has slightly higher values than te, but they are very close to each other. So, the results of these locations obtained from airmass correlation seem also to be statistically significant.

The quality of the fits with the experimental observations is controlled by the value of t evaluated during the fitting process by Eq.(l6). The values of t obtained from Iqbal model (general) and airmass exponential models I and II are 1.262, 1.003 and 0.985 , respectively. It is noted here that the lower the value of t, the more accurate is the model fits. In this analysis , airmass model has also the lower value of

t · The yearly average of monthly values of deviation

in percentage are evaluated by MRPE (%) and given in Tables 7 and 8. Iqbal model (general) has the maximum deviation of == 20%, whereas the airmass model has deviation less than 9.0% and obviously the general correlation of Iqbal type shows little worse performance. On the other hand, regional correlation of Iqbal type has the excellent performance (Table 5).

On the basis of the analysis, the overall evaluation of the correlations is that the airmass correlation has some privilege over the others where no measured data are available; and the airmass model needs no measured input data such as bright sunshine hours , temperature, humidity, etc., but needs only the geographical parameter (<1» , the latitude of the location .

6 Conclusions In thi s analysis , mainly two analytical mod .s

(Iqbal polynomial model and airmass exponential model) have been considered for studying the solar beam radiation pattern over Bangladesh and then their levels of performance have been studied. This type of work has been done for the fi rst time in Bangladesh. Che i-statistics (/·slat) has been applied to test the

MRPE(%) t·stat Min Max Min Max Min

0.480 20.480 04.350 4.305 1.180

0.296 08.570 0.760 3.764 0.063

0.292 08.526 0.842 3.819 0.042

0.281 01.259 0.599 0.359 0.016

significance of applicability of these ·models in the climatic conditions of Bangladesh.

Model performance shows that the airmass correlations give fairly good results and can be applied for the prediction of solar beam radiation at a place where no measured data are available. The main features of the airmass model is that it needs not any measured data if only the latitude of the location is known . Analysis indicates that the airmass model of either of the forms I and II is more significant than other correlations at a particular confidence level of a = 0.01 (i.e. 99%). Local correlation of Iqbal type [Eq. (1)] can also be applied to the respective locations safely . The local correlation predicts solar beam radiation accurately with a deviation of 2-3%. If more measured data of different locations in Bangladesh are obtained, an accurate and more suitable correlation could be established.

Ac~nowledgements

The authors are thankful to the anonymous referees for their valuable comments which have been very usefu l in revising the manuscript.

References I Sopian K & Othman M Y, Renew Energy (UK), 2 (1992)

329. 2 Reitvelt M R, Agr Meteorol (UK), 19 (1978) 243. 3 Hamdan M A & AI·Sayeh A I, Int J Sol Energy

(Switzerland), 10 (1991) 145. 4 Bahel Y, Srinivasan R & Baksh H, Energy (UK), 11 (1986)

985. 5 Gopinathan K K, Sol Wind Technol (UK), 5 (1988) 107. (. Alnaser WE, Energy (UK), 14 (1989) 409. 7 !laja 1 A &. Twidell J W, Sol Energy (USA ), 44 (1990) 63. IS Samuel T D M A, Sol Energy (USA), 47 (1991 ) 333. 9 Jain PC, Sol Energy (USA), 45 (1990) 30 I .

JO Khogali A, Sol Energy (USA), 31 (1 983) 45 . II Iqbal M, Sol Energy (USA), 23 (1979) 169. 12 Alnaser W E, Sol Energy (USA ), 34 (1 989) 409. 13 Turton S M, Sol Energy (USA), 38 (1 987) 353. 14 Rahman M M, Ind ian J Pure & Appl Phys, 35 (1997) 290. 1>5 Barr A G, Mcginn S M & Cheng S B, Sol En"18Y (USA), 56

(1996) 21 3.

RAHMAN et al.: CORRELATION OF SOLAR RADIATION ESTIMATES FOR BANGLADESH 285

16 Mani A & Rangarajan S, Solar Energy (USA), 31 (1983) 577 17 Mani A & Rangarajan S, Solar Radiation over India. (Allied

Pub Pvt Ltd, New Delhi, India), 1983. 18 Exell R H B, Sol Energy (USA), 26 (1981) 161. 19 Pereira M C & Rabl A, Sol Energy (USA), 22 (1979)155. 20 Canada 1, Renew Energj (UK). 2 (1992) 305

21 Alnaser W E, Renew Energy (UK). 3 (1993) 175.

22 Gopinathan K K, Sol Energy (USA). 49 (1992) 209

23 Stone R 1. Sol Energy (USA). 51 (1993) 289.

24 McClave 1 T & Benson P G. Statistics for Business and Economics (Dallen Pub. Co., USA), 1988. p.1197.