Solar Radiation Estimation from the Measurement of Sunshine Hours over Southern Coastal Region, Bangladesh
Shuvankar Podder^{1}, Md. Minarul Islam^{2}
^{1}Department of Electrical and Electronic Engineering, Bangladesh University ofEngineering and Technology, Dhaka, Bangladesh
^{2}Department of Electrical and Electronic Engineering,Shahjalal University of Science and Technology, Sylhet, Bangladesh
Email address:
(S. Podder), (Md. M. Islam)
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. 4753. 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 minihydro 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.Solarwind hybrid system is an universal one. Bangladesh Power Development Board (BPDB) has launched 7.5 MW offgrid solarwind hybrid systems in Hatiya Island, Noakhali. BPDB has planned to install 1 MW offgrid solardiesel based hybrid plant in Kutubdia Island and a 500 kW photovoltaic plant at Sandwip. 8 MW gridconnected and 2 kW offgrid 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 longterm 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 [34] have computed solar radiation from observation of cloud cover. Other studies [58] 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 [910]. But no attempt has yet been made to estimate solar radiation of the places in Bangladesh where the prospect of solarwind 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.
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 
Month  Rangamati  Sandwip  Noakhali  Kutubdia  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/m^{2}day or 2.88 KWh/m^{2}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]
(1)
Where = monthly average daily global radiation (Wh/m^{2}/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. AngstromPrescott Model
Popularly known AngstromPrescott model is given by
(2)
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 (𝐻_{0}), that is, 𝐻/𝐻_{0}, 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:
(3)
where,
the solar constant = 1.367 kW/m^{2}
the day of a year (a number between 1 to 365, starting from 1^{st} 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:
(4)
The sunset hour angle is calculated using the following equation:
(5)
The average for the month is calculated as follows:
(6)
where,
the average extraterrestrial horizontal radiation for the month in kWh/m^{2}/day
the number of days in the month
The maximum possible sunshine duration N in hours for a horizontal surface is given by:
(7)
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:
(8)
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
(9)
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
(10)
3.6. Proposed Model
In this paper, another nonlinear model is proposed. The proposed model relating (H/Ho) and (n/N) is
(11)
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.
Models  Regression Equations 
AngstromPrescott 

Akinoglu and Ecevit 

Ampratwum and Dorvlo 

Newland 

Proposed Model 

4. Model Performance
Stone [18] concluded that the tstatistics 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 tstat is less than a critical value t_{c}, then it can be concluded that estimation is significant to (n1) degree of freedom at the (1 α) confidence level. Stone recommend that tstatistics 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
(12)
(13)
(14)
(15)
where,H_{ic} , and H_{im} are the estimated and measured monthly average global solar radiation for the i^{th} month. The average of the deviations E (= H_{ic} – H_{im}) 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 shortterm 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 tstat lies far below the critical value t_{c}(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 tstat 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.
Model  a  b  c  a+b+c  
Rangamati  AngstromPrescott  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  AngstromPrescott  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  AngstromPrescott  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  AngstromPrescott  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  AngstromPrescott  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
(16)
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.
Model  r  MBE  RMSE  MAPE  tstat  tc  
Rangamati  AngstromPrescott  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  AngstromPrescott  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  AngstromPrescott  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  AngstromPrescott  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  AngstromPrescott  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 
Stations  Models  Annual Estimated Radiation  Annual Measured Radiation 
Rangamati  AngstromPrescott  4.7266  4.72 
Akinoglu and Ecevit  4.7220  
Ampratwum and Dorvlo  4.7321  
Newland  4.7224  
Proposed  4.7225  
Sandwip  AngstromPrescott  4.5642  4.56 
Akinoglu and Ecevit  4.5619  
Ampratwum and Dorvlo  4.5693  
Newland  4.5625  
Proposed  4.5630  
Noakhali  AngstromPrescott  4.5741  4.56 
Akinoglu and Ecevit  4.5681  
Ampratwum and Dorvlo  4.5792  
Newland  4.5698  
Proposed  4.5703  
Kutubdia  AngstromPrescott  4.7707  4.77 
Akinoglu and Ecevit  4.7669  
Ampratwum and Dorvlo  4.7789  
Newland  4.7669  
Proposed  4.7677  
Cox’s Bazar  AngstromPrescott  4.6915  4.69 
Akinoglu and Ecevit  4.6863  
Ampratwum and Dorvlo  4.6998  
Newland  4.6878  
Proposed  4.6883 
The accuracy of the estimated radiation according to equation (16)has also been determined by statistical means. The MBE, RMSE, MAPE and tstat for estimated radiation according to proposed equation has been shown in Table 7. It is found fromTable 7 that the values of tstat are far below from t_{c} at 99% confidence level. This indicates that the general correlation is statistically significant.
Stations  r  MBE  RMSE  MAPE  tstat  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 22.7^{0} latitude and 91.8^{0} longitudes.
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 
Station  r  MBE  RMSE  MAPE  tstat  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 tstat 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 tstatistics 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 solarwind based renewable energy system. The accuracy of prediction can be further developed by considering the fog density, cloud cover and atmospheric scattering effect.
References