Applied Latin Hypercube stochastic method to quantify the uncertainty in groundwater equation model simulations

¹ Laboratories of mathematical and analysis, noncommutative geometry and applications, Faculty of Science, Ibn Tofail University, Campus Maamora, BP.133, 1400 Kénitra, Maroc.
² Laboratory of hydroinformatics, Faculty of Sciences, University Ibn Tofail, Campus Maamora, BP. 133 1400 Kenitra, Morocco.

Abstract

It is accepted that digital models simplify the physical reality that is the object of the modeling. Hydrodynamic modeling is an approach with high uncertainties in this context. Indeed, the deterministic modeling approach assumes the existence of a functional relationship between the observed variables. The variables are observed by a series of measurements riddled with errors. Because of this, there is always a significant amount of uncertainty associated with a hydrogeological model. This uncertainty can be associated with the conceptual model or with the data and parameters associated with the different components of the model. Some model parameters such as hydraulic conductivity and recharge are particularly susceptible to uncertainty. Stochastic modeling of the hydrodynamics of a groundwater reservoir is an adequate response to allow us to take a step back on the significance of the results. The study is based on the development of a direct problem-solving model which represents the best estimate of the real hydrodynamic system. This model is used to make predictions. With a stochastic approach, a set of models is constructed where each model, as a whole, is considered to be equally likely. Each model is then used to make the prediction or simulate a given scenario. The MODFLOW-STOCHASTIC-GMS code allows us to do randomization simulations (Latin Hypercube method) and with parameter indicators.