Karst spring discharge evaluation supported by a grey-box data driven based method

Most part of groundwater in Central Italy, as in the whole Apennine Mountains chain, is stored in karst aquifers. In last decades, the most important water resources in Italy are affected by sensitive depletion, mostly due to the increasing of anthropogenic activities and the impacts of climate changes.In the field of simulation models of hydrological and hydrogeological processes, physical hydrological models are based on physical laws. Data-driven approaches, on the contrary, do not rely, directly, on explicit physical knowledge of the process, but they build a purely empirical model, linking input and output variables. Using various learning algorithms data-driven approaches provide a flexible way to model complex phenomena such the spring discharge. Many approaches proposed to analyze the relationships between the rainfall time series over the recharge area and the spring outflow. Research studies, concerning karst springs, employed time-series analysis studying transfer function between rainfall and spring discharge, obtained by black-box models. These ones are often based on continuous and discrete wavelet analysis, cross-correlation analysis, or machine learning models, such as artificial neural network. In this paper, primary factors governing spring discharge patterns related to rainfall input are modeled by a grey-box on data driven model trained by an evolutionary algorithm. The model uses monthly rainfall (P−1, P−2,…, P−k) and temperature (T−1, T−2,…, T−k) time series as input data for the evaluation of spring discharges. The first step of the pre-processing procedure in order to take into account of derived phenomena and the magnitude of the data processed. In addition, in order to take into account the evapotranspiration phenomenon, the temperature values are used in the preliminary non-linear normalization of the effective rainfall. Input and output data are supposed to be related by a linear relationship having a polynomial form, where the progressive variables, P_i, are the previous monthly rainfall data, considered for a best period chosen by the performance on the assumed number of back months. A long time series of available data (at least 60 months) is necessary for the algorithm training in which monthly average flow rates (Qi) must be known for the first phase of coefficients determination. Subsequently, the model frees from flow rate values validating the accuracy of discharge estimation on a different time window.