Abstract

The objective of this work is to develop empirical correlations describing Diffuse Fraction (DF) as a function of (1) Sunshine Fraction (SF), (2) Clearness Index (CI) and (3) both SF and CI. Four years instantaneously measured data was changed to monthly data at five locations belonging to five different climatic regions in Pakistan which was used as training dataset and nine correlations for each location (a total of forty-five) were formulated and their performance was assessed. Moreover, nine general empirical models were developed using the entire dataset (11 years) for five locations which were termed as Generalized Correlations (GCs). These GCs were validated by applying them to five other locations and comparing the generated results with measured results for those locations (validation dataset). The best model among GCs were found as GC8 which was, then applied to compute DF for five more locations for which short term (8 months) measured data was also available and thus a reasonable comparison could be made. Results showed that (1) new models were better than literature models, (2) GCs correlations were found in good agreement and (3) 2nd degree multivariate polynomial models are the best performance models with minimum errors e.g. Mean Absolute Biased Error (MABE), Mean Absolute Percentage Error (MAPE), Root Mean Square Error (RMSE), Sum of Square of Relative Error (SSRE) and Standard Relative Error (SRE) for GC8 were estimated as 0.018, 6.397, 0.021, 0.006 and 0.022 respectively (all values for Karachi).

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