Pumping test interpretation by combination of Latin hypercube parameter sampling and analytical models

Pumping tests in groundwater reservoirs are a much used and recommended method to derive hydraulic properties of aquifers and aquitards at the field scale. Interpretation of pumping tests can be done by fitting analytical or numerical models to the obtained field data using optimisation procedures. In this paper, an interpretation methodology is presented and implemented in the form of a computer code that combines analytical solutions for confined, semi-confined and unconfined single and multiple layer schematisations, with random parameter generator routines to find best fitting parameter sets to measured pumping test data. As this requires a large number of Monte Carlo (MC) runs, the number of required simulations is restricted by using a stratified instead of a pure random sampling technique. Latin hypercube sampling (LHS) is used as the stratified random sampler. The analytical solutions are defined in the Laplace domain and inverted numerically using the well-known Stehfest algorithm. The program uses a number of iteration cycles during which parameters sets are generated within predefined limits using the LHS technique. Parameters sets which satisfy a chosen maximum value for a selected objective function (root mean square (RMSE) or mean relative deviation (MRD)) are retained and used to update parameter limits for the next cycle. The objective function criterion is decreased during subsequent cycles while the limits of the sampling intervals are adapted. The number of determinable parameters is dependent on the aquifer schematisation and conceptual model that is chosen. After each cycle, statistics of the parameter values of the realisations which satisfy the objective function criterion are calculated. The method is demonstrated with examples including synthetic datasets and field data. The synthetic data examples show that the program is able to retrieve the parameter values used for generating drawdown sets very well. Typical runtimes on a PC are no more than a few minutes. The program can easily be extended with additional analytical solutions for other schematisations.