Estimation of Global Radiation using Angstrom-Type Models at Selected Sites in Kenya

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The 1970s energy crisis stirred a world-wide interest in, and development of, renewable and sustainable energy including solar energy. Solar radiation data is an important input component in the design and implementation of solar energy systems. Only a few scattered meteorological stations in Kenya measure solar radiation on a continuous basis. The use of models to estimate solar radiation is one way to get around this problem. The Angstrom-Type Model is obtained from measured global solar radiation on a horizontal surface situated on Earth’s surface. Using solar radiation and duration of sunshine data from 11 Kenyan meteorological stations, this study tested seven Angstrom-Prescott type regression models for their suitability to estimate clearness index for normal skies(K₀) . The Angstrom-Prescott type models were obtained by regressing sunshine duration against clearness index and obtaining curves of best fit. Linear, quadratic, exponential, power and logarithmic fits were obtained. Model performance was measured using goodness of fit statistics. These included Pearson correlation coefficient (r), coefficient of determination (R²), Mean Bias Error (MBE), Root Mean Square Error (RMSE), Student t-statistic, and the t-test. Out of the 11 stations considered only data from Dagoretti, Eldoret, JKI Airport, and Voi meteorological stations showed high R² values and these were used to produce modified Angstrom-Prescott models whose long-term, short-term, and overall performances were measured using MBE, RMSE, and t-statistic respectively. For each of the four stations with high R² values 10 pairs of equations, one each for(K₀) are presented. These equations maybe used in estimating clearness indices at the four stations using measured fraction of duration of sunshine as the only input. The correlation coefficients for the linear model of the Angstrom type for JKI Airport and Eldoret were 0.274, 0.354 and 0.309, 0.465 respectively while those for the quadratic model for the same two stations were respectively 0250, 0.430, -0.075 and 0.210, 0.800, -0.270. Recommendations on the use of these models is all models derived from data from Dagoretti, Eldoret, JK Airport, and Voi and expressed in equation form (Eqn. 7 to Eqn. 22) may be used to estimate the clearness indices K₀ for sites at or near the four locations. Equations 23 to 26, pertaining to the Logarithmic model must be used with caution as they do not guarantee best short-term or long-term performance in any of the stations.