Review of the limitations and potential empirical improvements of the parametric group method of data handling for rainfall modelling

This study furthers the utilisation of the parametric group method of data handling (GMDH) in assessing the possibility of rainfall modelling and prediction, using publicly available temperature and rainfall data. In using ordinary GMDH approaches, the modelling is inconclusive with no clear consistency demonstrated through coefficients of determination and analysis of variance. Hence, an empirical assessment has been undertaken to provide an explanation of the inconsistency. In doing so, state variable distribution, their classification within the fuzzy context, and the need to integrate the principle of incompatibility into the GMDH modelling format are all assessed. The mathematical foundations of GMDH are discussed within the heuristic framework of data partitioning, partial description synthesis, the limitations of the least-squares coefficient of determination, incompleteness theorem, and the necessity for an external criterion in the selection procedure for polynomials. Methods for modelling improvement include the potential for hybridisation with least square support vector machines (LSSVM), the application of filters for parameter estimation, and the combination with signal processing techniques, ensemble empirical mode decomposition (EEMD), wavelet transformation (WT), and wavelet packet transformation (WPT). These have been investigated in addition to the implementation of enhanced GMDH (eGMDH) and fuzzy GMDH (FGMDH). The inclusion of exogenous data and its application within the GMDH modelling paradigm are also discussed. The study concludes with recommendations to enhance the potential for future rainfall modelling study success using parametric GMDH. SUPPLEMENTARY INFORMATION: The online version contains supplementary material available at 10.1007/s11356-022-23194-3.