Testing the Altitude and Latitude Based Solar Irradiance Models in Kenya

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The OPEC oil embargo of the 1970s sparked off the era of innovative development of renewable energy technologies with solar energy being one of the principal components. A major input in solar energy technology is solar radiation composed of direct and diffuse components whose sum is known as global radiation. In some countries only a few meteorological stations measure solar radiation and this has necessitated more research and development (R&D) of various models that estimate direct, global, and diffuse radiation using measured solar radiation and other meteorological parameters. This paper assesses both Tiwari’s Latitude and Gopinathan’s Altitude Models derived from the regression of measured clearness index () against fraction of bright sunshine duration () in the classical Angstrom-Prescott type regression model. Measured solar radiation and sunshine duration data from four Kenyan meteorological stations of Dagoretti, Eldoret, JK Airport, and Voi was processed for consistency and statistical quality. The clearness index and the fraction of bright sunshine were calculated for each station and curve-fitted to obtain the quadratic form of Angstrom-Prescott equation () where  are the coefficients that are altitude dependent on one hand and latitude dependent on the other. Model performance was measured using goodness of fit statistics that included; Pearson correlation coefficient (r), coefficient of determination (R²), Mean Bias Error (MBE), Root Mean Square Error (RMSE), Students- t-statistic, and the t-test. For each of the four stations investigated the model equation of the form,  are presented and discussed. It emerged that out of the four sites assessed, Voi produced the best performing Altitude model (t-statistic = .070) while Eldoret produced the best overall performing Latitude model (t-statistic = .547). It was recommended that the 8 models produced could be used to estimate the irradiance at these sites with the fraction of sunshine duration being considered to be the only input.