Sunshine duration ( S ) based empirical equations have been employed in this study to estimate the daily global solar radiation on a horizontal surface ( G ) for six meteorological stations in Burundi. Those equations include the Å ngstr ö m-Prescott linear model and four amongst its derivatives, i.e. logarithmic, exponential, power and quadratic functions. Monthly mean values of daily global solar radiation and sunshine duration data for a period of 20 to 23 years, from the Geographical Institute of Burundi (IGEBU), have been used. For any of the six stations, ten single or double linear regressions have been developed from the above-said five functions, to relate in terms of monthly mean values, the daily clearness index ( ) to each of the next two kinds of relative sunshine duration (RSD): and . In those ratios, G 0 , S 0 and stand for the extraterrestrial daily solar radiation on a horizontal surface, the day length and the modified day length taking into account the natural site’s horizon, respectively. According to the calculated mean values of the clearness index and the RSD, each station experiences a high number of fairly clear (or partially cloudy) days. Estimated values of the dependent variable ( y ) in each developed linear regression, have been compared to measured values in terms of the coefficients of correlation ( R ) and of determination ( R 2 ), the mean bias error ( MBE ), the root mean square error ( RMSE ) and the t-statistics. Mean values of these statistical indicators have been used to rank, according to decreasing performance level, firstly the ten developed equations per station on account of the overall six stations, secondly the six stations on account of the overall ten equations. Nevertheless, the obtained values of those indicators lay in the next ranges for all the developed sixty equations: ; ; ; , with . These results lead to assert that any of the sixty developed linear regressions (and thus equations in terms of and ), fits very adequately measured data, and should be used to estimate monthly average daily global solar radiation with sunshine duration for the relevant station. It is also found that using as RSD, is slightly more advantageous than using for estimating the monthly average daily clearness index, . Moreover, values of statistical indicators of this study match adequately data from other works on the same kinds of empirical equations.
KeywordsClearness IndexTwo Kinds of Relative Sunshine Duration&Aring
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m-Prescott Linear Model and Four Derivatives
Statistical Tests
Six Burundian Stations
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