Efficient Calibration of Categorical Parameter Distributions using Subspace Methods

Categorical parameter distributions are common-place in hydrogeological systems consisting of rock-types / aquifer materials with distinct properties, eg: sand channels in a clay matrix. Model calibration is difficult in such systems because the inverse problem is hindered by the discontinuities in the parameter space. In this paper, we present two approaches based on sub-space methods to generate categorical parameter distributions of aquifer parameters that meet calibration constraints (eg:- measured water level data, gradients) while honoring prior geological constraints.

In the first approach, the prior geological information and acceptable parameter distributions are encapsulated in a simple object-based model. In the second approach, a Multiple-Point Statistics simulator is used to represent the prior geological information. Sub-space methods in conjunction with dynamic pilot points are then employed to explore the parameter space and determine the parameter combinations that optimally honor geologic and calibration constraints.

Using a simple aquifer system, we demonstrate that the new approach is capable of quickly generating multiple multiple parameter distributions that honor both geological and calibration constraints. We also explore the underlying parameter and predictive uncertainty using Null Space Monte Carlo techniques.