Comparison of different pilot point parameterization strategies when measurements are unevenly distributed in space
Abstract
Effective groundwater modeling requires appropriate parameterization of hydraulic properties that are spatially distributed. A commonly employed method involves estimating hydraulic properties at a limited number of pilot points and interpolating the values at each model cell. However, identifying the optimal number and distribution of pilot points is a crucial and unresolved issue that significantly affects the effectiveness of the method.
We present an approach for achieving optimal pilot points parameterization by minimizing the number of parameters while maximizing data assimilation. We compare the performance of different pilot point distributions using a synthetic groundwater model, examining regular grids of pilot points with varying spacings and adaptive grids with different refinement criteria. We consider both prior and iterative refinements, with a parameter estimation step between successive refinements. Parameter estimation is conducted using the Gauss–Levenberg–Marquardt Algorithm, and the strategies are evaluated based on the number of model calls required to achieve the target objective function.
The strategy that provides the best fit with the measurement dataset at the lowest computational cost involves using an adaptive grid of pilot points with prior refinement based on measurement density. This strategy is successfully demonstrated on a regional, multilayered groundwater flow model in the French South-West geological basin.