Empirical model development for the estimation of clearness index usingmeteorological parameters

Abstract

The clearness index is an indispensable parameter required for the design and analysis of solar energy systems. In the absence of measured values for a specific location, the clearness index can be estimated from other measured meteorological variables. In this study three meteorological parameters, sunshine hours, monthly mean values of the temperature difference ($\Delta$T), and cloudiness, are used to develop empirical models for the estimation of clearness index. The empirical models are developed for five major cities in Pakistan (Karachi, Multan, Lahore, Islamabad, and Quetta). For empirical model development, long-term data (1991 to 2010) of monthly average clearness index, sunshine hours, average daily minimum and maximum temperatures, and cloudiness have been used. The accuracy of the models has been tested by statistical indicators that include mean percentage error (MPE), coefficient of determination (R$^2$), mean absolute relative error (MARE), mean bias error (MBE), and root mean square error (RMSE). The error analysis revealed that the proposed models are suitable for the estimation of the clearness index. It is also concluded that multiple regression models give better estimates of clearness index for all the stations (0.80 $\leq$ R$^{2}$ $\leq$ 0.86) compared to single parameter model and therefore are recommended. The study indicated that clear sky conditions prevail throughout the months at all the investigated sites (0.58 $\leq$ K$_T$ $\leq$ 0.68), which is a good indicator for solar energy utilization. The statistical indicators also suggest that multilinear regression model M-3 gives a better representation of the climate system and using three parameters reduces the uncertainties in the developed model.