Statistical approach to the proposition and validation of daily diffuse irradiation models

This paper explores the prospects of using sunshine duration and cloud cover in estimations of daily diffuse irradiation besides the conventional use of global irradiation, where all the parameters are gathered from typical ground-based measurements and proposes optimal region-based models. Data from eight locations across four countries are used for model proposition and subsequent evaluation. Daily sunshine fraction (SF) and daily cloudiness factor (CF) are used along with daily clearness index (Kt) by inter-combination to develop a series of diffuse ratio (K) empirical models for each site. Various statistical tools are employed to establish the criterion of best performing model. Each model's performance is initially assessed, based on the data it is derived from, and then validated against an independent dataset. This validation is demonstrated by two means: first by testing the models developed for one site against another site in the same region and, secondly by testing the models derived from one section of data against a reserved section from the same site covering a different period of time. The accuracy of prediction is evaluated using three statistical measures (AS, SD, t-statistic). The final assessment also includes calculated versus measured diffuse irradiation plots and indicators such as percent MBD and percent RMSD for potential models. It was found that a model based on Kt and SF (and/or CF) performs better than a model based on Kt alone within the same data set. However, if these models are tested against the data belonging to a different period of time or a different site, the improvement is less significant. Such model-specificity can be attributed to the fact that the proposed models involve more than one measured parameter, hence greater uncertainty, as against the single-input Kt model. Given the climatological variants that differ from site-to-site and measurement uncertainties owing to the poor meteorological standards within the same dataset, validation of such models becomes a challenging task. Nevertheless, it is found that the Kt, SF model is an optimum choice when estimating diffuse radiation for independent data, as it yields improved results even over the local K-Kt model. Thus, this investigation establishes the improvement in estimation of daily diffuse irradiation that can possibly be achieved through incorporating effective variables along with global radiation for both local as well as independent sites.