International Journal of Sustainable and Green Energy
Volume 4, Issue 2, March 2015, Pages: 47-53

Solar Radiation Estimation from the Measurement of Sunshine Hours over Southern Coastal Region, Bangladesh

Shuvankar Podder1, Md. Minarul Islam2

1Department of Electrical and Electronic Engineering, Bangladesh University ofEngineering and Technology, Dhaka, Bangladesh

2Department of Electrical and Electronic Engineering,Shahjalal University of Science and Technology, Sylhet, Bangladesh

Email address:

(S. Podder), (Md. M. Islam)

To cite this article:

ShuvankarPodder, Md. Minarul Islam. Solar Radiation Estimation from the Measurement of Sunshine Hours over Southern Coastal Region, Bangladesh. International Journal of Sustainable and Green Energy. Vol. 4, No. 2, 2015, pp. 47-53. doi: 10.11648/j.ijrse.20150402.14

Abstract: In this study,the global solar radiation over the southern coastal region of Bangladesh is estimated from the duration of relative sunshine hours. Five models are considered to estimate the solar irradiance. These models are modified form of classical Angstrom – Prescott regression equation. A quadratic logarithmic model, relating the relative solar radiation and the relative sunshine hours is proposed for southern coastal region of Bangladesh. NASA Surface Meteorology and Solar Energy (SSE)have record of solar radiation data all over the world, measured from satellite. As Bangladesh Meteorological Department or any other organization has no record of measured solar radiation data for the considered locations, the estimated solar irradiance from the proposed regression model is compared with the data recorded by NASA SSE. Also t – statistics is applied to the estimated results to determine whether or not they are statistically significant at a particular confidence level.

Keywords: Solar Radiation, Sunshine Hours, Coastal Region, Nonlinear Relation, Hybrid

1. Introduction

According to renewable energy policy 2009, the Government of Bangladesh is committed to facilitate both private and public sector investments in renewable energy projects to substitute indigenous non- renewable energy supplies and scale up contributions existing renewable energy based electricity production. The policy envisions that 5% of the total energy production will have to be achieved by 2015 and 10% by 2020 using renewable resources. There is a good scope for solar, wind, biomass and mini-hydro power generation in Bangladesh. Among these solar and wind possess most potential for electricity generation [1].

The reliability of electric power encourages hybridization of two or more renewable energy systems because of its intermittent nature.Solar-wind hybrid system is an universal one. Bangladesh Power Development Board (BPDB) has launched 7.5 MW off-grid solar-wind hybrid systems in Hatiya Island, Noakhali. BPDB has planned to install 1 MW off-grid solar-diesel based hybrid plant in Kutubdia Island and a 500 kW photovoltaic plant at Sandwip. 8 MW grid-connected and 2 kW off-grid photovoltaic plants are ongoing projects at Rangamati and Noakhali, respectively.BPDB has also lined up installation of MW range wind power stationatCox’s Bazar [1]

Adequate assessment of renewable resource data are essentials for planning and designing renewable energy based power systems. At present, solar radiation data are available from (1) Renewable Energy Research Centre (RERC), Dhaka University; it has recorded long-term hourly solar irradiance of Dhaka city with Eppley Precision Pyrometer. (2)Bangladesh Meteorological Department (BMD); it has 35 sunshine recording stations [2] situated generally in towns and cities. BMD has no record of solar radiation on the abovementioned solar projects areas. Solar radiation reaching the earth’s surface depends upon climatic conditions. Thus a mathematical model can be developed relating climatic factors with solar radiation. A number of studies [3-4] have computed solar radiation from observation of cloud cover. Other studies [5-8] have estimated solar radiation from sunshine hours. BMD has record of daily bright sunshine hours at the abovementioned places.

Some studies havecorrelated sunshine hours and solar radiation over some major cities in Bangladesh [9-10]. But no attempt has yet been made to estimate solar radiation of the places in Bangladesh where the prospect of solar-wind hybrid system has promising potential. In this paper, five models relating solar radiation and relative sunshine hours have been analyzed andsolar radiation is predicted at Rangamati, Sandwip, Noakhali, Kutubdia and Cox’s Bazar. Resultsare compared with the data reported by NASA Surface Meteorology and Solar Energy (SSE) [11] on that places.

2. Experimental Data

Solar radiation arriving on the horizontal earth surface and duration of bright sunshine hours are two main experimental data in this study.Data of sunshine hours for the years 1983 to 2013 have been collected from BMD.As solar radiation data is not available at BMD, they have been collected from NASA SSE. In this paper, the target locations for analyzing solar radiation are Rangamati, Sandwip, Noakhali, Kutubdia and Cox’s Bazar. The geographical parameters of those five locations are shown in Table 1. The relative sunshine hours of five places are shown in Table 2.

Table 1. Geographical parameters.

Stations Latitude Longitude Elevation
Rangamati 22.63 92.2 14
Sandwip 22.48 91.48 7
Noakhali 22.70 91.10 12
Kutubdia 21.82 91.86 50
Cox’s Bazar 21.58 92.02 3

Table 2. Relative sunshine hours.

Month Ranga-mati Sand-wip Noak-hali Kutub-dia Cox’s Bazar
January 0.6635 0.6826 0.6225 0.7362 0.7998
February 0.6906 0.6758 0.6626 0.7370 0.7880
March 0.6361 0.6490 0.6324 0.6962 0.7255
April 0.6050 0.6181 0.5929 0.6379 0.6814
May 0.4679 0.4789 0.4804 0.5270 0.5358
June 0.3194 0.3513 0.2821 0.3156 0.2929
July 0.2815 0.3270 0.2657 0.2886 0.2710
August 0.3609 0.3739 0.3486 0.3514 0.3355
September 0.4227 0.4239 0.3935 0.4711 0.4665
October 0.5545 0.5725 0.5584 0.6031 0.6292
November 0.6527 0.6890 0.6598 0.7252 0.7560
December 0.6677 0.6780 0.6478 0.7556 0.7620

3. Methodology

According to World Meteorological Organization(WMO) the sunshine duration is defined as the period during which the direct solar irradiance exceed a threshold value of 120 W/m2-day or 2.88 KWh/m2-day [12]. Solar radiation of a certain period is proportional to sunshine duration. Different models describing solar radiation and sunshine hours are paraphrased here.

3.1. Angstrom Model

The relation between solar radiation and sunshine duration was first proposed by Angstrom in 1924.The original Angstrom equation is given by [13]


Where = monthly average daily global radiation (Wh/m2/day),  = monthly average clear sky daily global radiation for the location, = monthly average daily maximum bright sunshine duration in hours, = actual sunshine duration in a day in hours, and, are empirical coefficients. These coefficients are location specific.

A basic difficulty in this model is to determine, clear sky radiation. To avoid this difficulty a modified model was presented by Prescott [14] in 1940.

3.2. Angstrom-Prescott Model

Popularly known Angstrom-Prescott model is given by


where,are same as equation (1) and= monthly average daily extraterrestrial radiation at the specific location. The ratio of solar radiation at the surface of the Earth (H) to extraterrestrial radiation (𝐻0), that is, 𝐻/𝐻0, is called the clearness Index and the ratio n/N is referred to as the cloudless index.

Monthly average daily extraterrestrial radiation is calculated from following equation:



 the solar constant = 1.367 kW/m2

 the day of a year (a number between 1 to 365, starting from 1st January)

 the latitude in degree

 the solar declination in degree

the sunset hour angle in degree.

The solar declination is calculated according to the following equation:


The sunset hour angle is calculated using the following equation:


The average  for the month is calculated as follows:



the average extraterrestrial horizontal radiation for the month in kWh/m2/day

the number of days in the month

The maximum possible sunshine duration N in hours for a horizontal surface is given by:


3.3. Akinoglu and Ecevit Model

Akinoglu BG et el [15] constructed a quadratic relation between H/Ho and n/N from modified Angstrom model. According to Akinoglu BG et el:


3.4. Newland Model

Newland et el [16] separated global solar irradiance into its components for the southern coastal region Macau, China. He showed that a non linear relation between (n/N) and (H/Ho) gives better prediction of global irradiance. His proposed relation is


3.5. Ampratwum and Dorvlo Model

Ampratwum et el [17] studied five stations in Oman and proposed a logarithmic relationship between (n/N) and (H/Ho). His proposed model is


3.6. Proposed Model

In this paper, another non-linear model is proposed. The proposed model relating (H/Ho) and (n/N) is


The coefficients a,b,c of different models are calculated by least square regression. Five models considered for estimating global solar irradiance on five southern coastal region of Bangladesh aretabulated in Table 3. MATLAB simulationis used in determining regression coefficient.

Table 3. Considered models.

Models Regression Equations

Akinoglu and Ecevit

Ampratwum and Dorvlo


Proposed Model

4. Model Performance

Stone [18] concluded that the t-statistics test might be taken as a statistical indicator for the evaluation and comparison of solar models. The smaller the value of t, the better is the model’s performance. If the calculated value of t-stat is less than a critical value tc, then it can be concluded that estimation is significant to (n-1) degree of freedom at the (1- α) confidence level. Stone recommend that t-statistics may be used in conjunction with Mean Bias Error (MBE), Root Mean Square Error (RMSE) and Mean Absolute Percentage Error (MAPE) to access the relative model performance.The mostly used statistical indicator MBE, RMSE and MAPE are defined as





where,Hic , and Him are the estimated and measured monthly average global solar radiation for the ith month. The average of the deviations E (= Hic – Him) is MBE and gives information about the long- term performance of the correlations. MAPE is a measure of the goodness of each correlation, while RMSE measures the short-term prediction quality of the correlations [19].

5. Result and Discussion

As shown in Table 1, the five study regions are geographically close to one another andthey are mainly southern coastal belt of Bangladesh. Therefore, a general relation between solar radiation and sunshine hours can be developed for these places.

The regression coefficients of five models for the considered locations are shown in Table 4.The physical significance of the regression coefficients `a' and `b' is that `a' is a measure of the overall atmospheric transmission for total cloud conditions (n/N=0), and is a function of the type and the thickness of the cloud cover, while `b' and `c' are the rate of increase of (H/Ho) with (n/N). The sum (a+b) denotes the overall atmospheric transmission under clear sky conditions.

Statistical evaluations of five models are summarized inTable 5. It is seen that the regional correlation has minimum error in all models. MBE, RMSE and MAPE are lowest in "Akinoglu and Ecevit" model for all locations. Also value of r is highest in "Akinoglu and Ecevit"-model for all locations indicate that this model best fit the sunshine hour data with solar radiation. The value of t-stat lies far below the critical value tc(at α=0.01) indicating correlation models performance is statistically significant at 99% level of significance.

The proposed model in this paper shows statistically good performance. The value of t-stat for all locations in this model is lower than linear and logarithmic models. This indicates that proposed model is better in estimating solar radiation than that proposed by Angstrom and Ampratwum et el.

Table 4. Regression coefficients in different models.

  Model a b c a+b+c
Rangamati Angstrom-Prescott 0.1733 0.6619   0.8352
Akinoglu & Ecevit 0.4166 -0.4181 1.0930 1.0915
Ampratwum &Dorvlo 0.7299 0.3041   1.034
Newland -0.6133 1.5878 -0.4370 0.5375
Proposed 0.9107 0.8560 0.3508 2.1175
Sandwip Angstrom-Prescott 0.1305 0.6898   0.8203
Akinoglu & Ecevit 0.3240 -0.1174 0.7807 0.9873
Ampratwum &Dorvlo 0.7249 0.3401   1.0650
Newland -0.4791 1.3937 -0.3517 0.5629
Proposed 0.8689 0.8155 0.3309 2.0153
Noakhali Angstrom-Prescott 0.1757 0.6457   0.8214
Akinoglu & Ecevit 0.3952 -0.3909 1.0983 1.1026
Ampratwum &Dorvlo 0.7083 0.2815   0.9898
Newland -0.6030 1.5796 -0.4186 0.5580
Proposed 0.9061 0.8490 0.3372 2.0923
Kutubdia Angstrom-Prescott 0.1423 0.6750   0.8173
Akinoglu & Ecevit 0.2578 0.1845 0.4647 0.9070
Ampratwum &Dorvlo 0.7293 0.3291   1.0584
Newland -0.2779 1.1545 -0.2390 0.6376
Proposed 0.8472 0.7483 0.2835 1.8790
Cox’s Bazar Angstrom-Prescott 0.1730 0.5868   0.7598
Akinoglu &Ecevit 0.2792 0.1299 0.4245 0.8336
Ampratwum & Dorvlo 0.6889 0.2861   0.9750
Newland -0.1898 0.9957 -0.2048 0.6011
Proposed 0.7819 0.6459 0.2413 1.6691

The estimated annual radiations on considered locations along with measured radiation are shown in Table 6.

A general relation relating relative sunshine hours (n/N) and relative solar radiation (H/Ho) has been developed according to proposed model for these southern coastal regions. To determine the coefficients of general relation, least square regression has been used combining all the data of five locations. The proposed general correlation equation for southern coastal region is


To validate the proposed general correlation, the estimated solar radiation for considered five locations along with measured radiation has been shown in figure 1 to 5. From those figures it is evident that the predicted radiations according to equation (16) are sufficiently close to that measured by NASA SSE.

Table 5. Statistics of five models.

  Model r MBE RMSE MAPE t-stat tc
Rangamati Angstrom-Prescott 0.9595 0.0108 0.1855 0.0334 0.1933 3.106
Akinoglu and Ecevit 0.9770 0.0061 0.1243 0.0019 0.1642
Ampratwum and Dorvlo 0.9226 0.0163 0.2611 0.0208 0.2076
Newland 0.9751 0.0065 0.1322 0.0221 0.1639
Proposed 0.9729 0.0067 0.1399 0.0234 0.1587
Sandwip Angstrom-Prescott 0.9676 0.0069 0.1527 0.0283 0.1502 3.106
Akinoglu and Ecevit 0.9692 0.0036 0.1351 0.0233 0.0875
Ampratwum and Dorvlo 0.9534 0.0110 0.1959 0.0377 0.1858
Newland 0.9686 0.0042 0.1383 0.0242 0.1000
Proposed 0.9678 0.0047 0.1416 0.0251 0.1102
Noakhali Angstrom-Prescott 0.9516 0.0158 0.2151 0.0016 0.2443 3.106
Akinoglu and Ecevit 0.9676 0.0098 0.1575 0.0012 0.2068
Ampratwum and Dorvlo 0.9155 0.0209 0.2863 0.0026 0.2425
Newland 0.9676 0.0114 0.1617 0.0014 0.2354
Proposed 0.9670 0.0119 0.1668 0.0289 0.2378
Kutubdia Angstrom-Prescott 0.9763 -0.0035 0.1591 0.0288 0.0726 3.106
Akinoglu and Ecevit 0.9859 -0.007 0.1359 0.0228 0.1732
Ampratwum and Dorvlo 0.9458 0.0047 0.2469 0.0461 0.0630
Newland 0.9869 -0.007 0.1366 0.0235 0.1768
Proposed 0.9854 -0.006 0.1387 0.0250 0.1578
Cox’s Bazar Angstrom-Prescott 0.9771 0.0015 0.1534 0.0288 0.0330 3.106
Akinoglu and Ecevit 0.9849 -0.004 0.1256 0.0196 0.0965
Ampratwum and Dorvlo 0.9443 0.0098 0.2542 0.0511 0.1276
Newland 0.9841 -0.002 0.1276 0.0207 0.0578
Proposed 0.9827 -0.002 0.1321 0.0229 0.0418

Table 6. Comparison of estimated and measured radiation

Stations Models Annual Estimated Radiation Annual Measured Radiation
Rangamati Angstrom-Prescott 4.7266 4.72
Akinoglu and Ecevit 4.7220
Ampratwum and Dorvlo 4.7321
Newland 4.7224
Proposed 4.7225
Sandwip Angstrom-Prescott 4.5642 4.56
Akinoglu and Ecevit 4.5619
Ampratwum and Dorvlo 4.5693
Newland 4.5625
Proposed 4.5630
Noakhali Angstrom-Prescott 4.5741 4.56
Akinoglu and Ecevit 4.5681
Ampratwum and Dorvlo 4.5792
Newland 4.5698
Proposed 4.5703
Kutubdia Angstrom-Prescott 4.7707 4.77
Akinoglu and Ecevit 4.7669
Ampratwum and Dorvlo 4.7789
Newland 4.7669
Proposed 4.7677
Cox’s Bazar Angstrom-Prescott 4.6915 4.69
Akinoglu and Ecevit 4.6863
Ampratwum and Dorvlo 4.6998
Newland 4.6878
Proposed 4.6883

Figure 1. Estimated and measured radiation on Rangamati.

Figure 2. Estimated and measured radiation on Sandwip.

Figure 3. Estimated and measured radiation on Noakhali.

Figure 4. Estimated and measured radiation on Kutubdia.

Figure 5. Estimated and measured radiation on Cox’s Bazar.

The accuracy of the estimated radiation according to equation (16)has also been determined by statistical means. The MBE, RMSE, MAPE and t-stat for estimated radiation according to proposed equation has been shown in Table 7. It is found fromTable 7 that the values of t-stat are far below from tc at 99% confidence level. This indicates that the general correlation is statistically significant.

Table 7. Statistics of proposed equation.

Stations r MBE RMSE MAPE t-stat tc (α=0.01)
Rangamati 0.972 -0.106 0.171 0.030 2.638 3.106
Sandwip 0.961 0.062 0.164 0.032 1.358 3.106
Noakhali 0.960 -0.102 0.199 0.023 1.991 3.106
Kutubdia 0.984 0.033 0.155 0.028 0.719 3.106
Cox’s Bazar 0.979 0.126 0.198 0.037 2.752 3.106

In this paper, correlation between relative sunshine hour and solar radiation has been developed for southern coastal region of Bangladesh. Using this correlation, global solar radiation on any southern coastal region of Bangladesh can be estimated from relative sunshine hours. To determine the correctness of proposed relation, solar radiation has been estimated on another southern coastal region Patenga, Chittagong. Patenga is situated at 22.70 latitude and 91.80 longitudes.

Figure 6. Estimated and measured radiation on Patenga.

Table 8. Radiation on Patenga.

Month n/N H0 Hmeasured Hestimated
January 0.7246 7.1764 4.4207 4.5251
February 0.7345 8.2196 4.9811 5.2379
March 0.6491 9.4823 5.4428 5.4914
April 0.5696 10.4854 5.5048 5.5032
May 0.4809 10.9736 5.1137 5.1079
June 0.3311 11.0921 4.1595 4.1955
July 0.3054 10.9962 4.0356 4.0380
August 0.3724 10.6154 4.1825 4.2380
September 0.4549 9.7876 4.0227 4.3914
October 0.5751 8.5646 4.2823 4.5271
November 0.6648 7.2901 4.2493 4.3000
December 0.7215 6.8279 4.2811 4.2910
Average     4.5563 4.6539

Table 9. Statistics of estimated radiation on Patenga.

Station r MBE RMSE MAPE t-stat tc(α=0.01)
Patenga 0.9749 0.1024 0.1558 0.0238 2.8905 3.106

The estimated solar radiation on Patenga according to equation (16) along with measured solar radiation has been shown in figure 6. The relative sunshine hours, measured solar radiation and estimated solar radiation over the year on Patengahas been shown in Table 8. The statistical parameters MBE, RMSE, MAPE and t-stat for estimated solar radiation according to proposed correlation on Patengahas been shown in Table 9. It is found that estimated global solar radiation is statistically satisfied.

6. Conclusion

In this analysis, five models relating global solar radiation and relative sunshine hours have been considered for predicting the global solar radiation pattern over the southern coastal region of Bangladesh. The level of performance of five models has been studied by statistical measures. The t-statistics have been applied to test the significance of applicability of these models.

A nonlinear logarithmic model has been proposed for estimating the global solar radiation from sunshine hour data. Statistical tests show that proposed model gives fairly good result and can be applied to southern coastal areas of Bangladesh. Few articles correlate the global solar radiation with sunshine ours over Bangladesh. But developing a nonlinear model for estimating solar radiation over southern coastal region of Bangladesh is quiet new. This work emphasis on this region considering the potential of generating electricity from hybrid solar-wind based renewable energy system. The accuracy of prediction can be further developed by considering the fog density, cloud cover and atmospheric scattering effect.


  1. Development of Renewable Energy Technologies by BPDB, accessed at 15 January 2015,available:
  2. Solar and Wind Energy Resource Assessment (SWERA) project report, pp. 13-14, accessed at 10 January 2015,available
  3. S. Rangarajan, M. S. Swaminathan and A. Mani, Computation of solar radiation from observations of cloud cover.Solar Energy, Vol. 32, No. 4, pp. 553-556, (1984)
  4. A. Nyberg, Determination of global radiation with the aid of observations of cloudiness. Acta Agric.Scand, Vol. 27, pp. 297-300.
  5. M. R. Rieltveld, A new method for estimating the regression coefficients in the formula relating solar radiation to sunshine. Agr.Meteorol. vol - 19, pp243-252(1978).
  6. K. K. Gopinathan, A general formula for computing the coefficient of the correlation connecting global solar radiation to sunshine duration. Solar Energy, Vol. 41. No. 6, pp. 499-502. (1988)
  7. P. R. Benson, M. V. Paris, J. E. Serry and C. G. Justus, Estimation of daily and monthly direct, diffuse and global solar radiation from sunshine duration measurement , SolarEnergy, Vol. 32, No.4, pp:523-535(1984).
  8. H. Ogelman, A. Ecevit and E. Tasdemiroglu, A new method for estimating solar radiation from bright sunshine data. Solar Energy, Vol. 33, No.6, pp. 619-625, (1984)
  9. H R Ghosh, S M Ullah, S K Khadem, N C Bhowmik and M Hussain, Measurement and estimation of sunshine duration for Bangladesh. Renewable Energy Research Center, University of Dhaka, Bangladesh
  10. Debazit Datta, Bimal Kumar Datta, Empirical model for the estimation of global solar radiation in Dhaka, Bangladesh. International Journal of Research in Engineering and Technology, Volume: 02 Issue: 11, pp. 649-653.
  11. NASA Surface Meteorology and Solar Energy; accessed at 15 January 2015, from
  12. Guide to Meteorological Instruments and Method of Observation, accessed at 15 January 2015, available
  13. A. Angstrom, Solar and terrestrial radiation, Quarterly Journal of the Royal Meteorological Society, vol. 50, no. 210, pp. 121-126, 1924
  14. J. A. Prescott, "Evaporation from water surface in relation to solar radiation," Transactions of The Royal Society of South Australia, vol. 40, pp.114–118 (1940).
  15. Akinoglu BG, Ecevit A. Construction of a quadratic model using modified Angstrom coefficients to estimate global solar radiation. Solar Energy 1990, Vol. 45, pp. 85-92.
  16. Newland FJ. A study of solar radiation models for the coastal region of South China. Solar Energy 1989, Vol. 43(4), pp. 227-235.
  17. David B. Ampratwum, Atsu S.S. Dorvlo, Estimation of solar radiation from the number of sunshine hours, Applied Energy, Vol. 63 (1999), pp. 161-167
  18. Stone RJ, Improved statistical procedure for the evaluation of solar radiation models. Solar Energy 1993, Vol.51, pp. 289 – 291
  19. B.G. Akinoblu andA. Ecevit, A further comparison and discussion of sunshine-based models to estimate global solar radiation. Energy, Vol. 15, No.10, pp. 865-872, 1990
  20. Srivastava SK, Sinoh OP, Pandy GN, Estimation of global solar radiation in Uttar Pradesh (India) and comparison of some existing correlations. Solar Energy (1993), Vol. 51, pp. 27 – 29.

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