An approximation to statistical analysis of recession curves of a karst system in a plain

Abstract

A number of models exists to analyze discharge recession curves (RC), such as Boussinesq (BM) and Maillet (MM) models, which were derived from theoretical equations of groundwater flow. This paper presents the results of a study, analyzing water table recession curves, whose objective was to determine the model that best represents the dynamics of the karst aquifer in the northern plain of Yucatan, Mexico. The above was achieved defining statistical criteria to select the model; implementing a statistical analysis strategy to compare the estimates of the parameters of greatest hydrological interest of the chosen decay models. Two scenarios were considered for the analysis: I.- Two wells with the same time intervals with standardized data of: different initial hydraulic head (ho); similar ho; modified ho. II.- A single well, starting from an established hydraulic head and discharge in the same period of time. Numerical methods were used to fit models to the observed RCs and a maximum likelihood function for parameters estimation. Statistical criteria were established to choose the best model. The Boussinesq model proved to be the most appropriate, whose estimates of the parameter α were explored, using fixed values of the parameter n. The comparison between the estimates of α was made based on hypothesis tests (t to compare between two values of α and F for the comparison between more than two values of α). Quasiprobability distributions obtained by a maximum likelihood estimator were also used. The best estimates of α(BM) are obtained with values of the parameter n between 0.5 and 2.