Empirical models and artificial intelligence for estimating hourly diffuse solar radiation in the state of Alagoas, Northeastern Brazil

Diffuse solar irradiation (H_D) data are essential for the design and management of photovoltaic solar systems, biosphere-atmosphere modeling, and other applications. However, H_D observations are scarce in several locations, especially in tropical regions. Employing hourly diffuse solar irradiation ($H_D^h$) and global solar irradiation ($H_G^h$) data collected between 2002─2003 and 2007─2008 in Alagoas State, Northeast Brazil, this study assesses various modeling techniques. Empirical models, including third-degree polynomial, logistic, sigmoidal, and rational functions, were compared with AI methods such as artificial neural networks (ANN), support vector machine (SVM), and adaptive neuro-fuzzy inference system (ANFIS). Additionally, it explores how solarimetric and meteorological variables impact the performance of these models. The empirical models showed similar performance in estimating $K_D^h(=H_D^h/H_G^h)$ (r² > 0.726, modified Willmott – d_m > 0.704, and RMSD < 0.103), with the third-degree polynomial model standing out. The empirical models had difficulty estimating $K_D^h$ for hourly atmospheric transmittance $\left(K_T^h\right)$ > 0.80, which indicated that they are not able to adequately simulate clear sky conditions, mostly due to surface reflections and clouds at the end of the day. ANN (r² > 0.718, d_m > 0.702, and RMSD < 0.105) showed better precision and accuracy of estimates for a greater number of schemes in relation to SVM and ANFIS (r² > 0.704, d_m > 0.699, RMSD < 0.108) and to empirical models. AI methods were able to represent the complexity of these conditions, with overall performance in estimating $K_D^h$ superior or equivalent to empirical models. This study underscores the significance of exploring diverse methods for H_D estimation, demonstrating promising potential for accurate and reliable estimation of hourly diffuse solar irradiation.