Probabilistic graphical modeling method for inferring hydraulic conductivity maps from hydraulic head maps

The ability to design and employ groundwater distribution models plays an important role in the development and application of regional water management policies and resource exploration. This paper presents a probabilistic reasoning approach for estimating groundwater levels over a geological map based on a limited number of available observations of hydraulic head and conductivity levels. The approach adapts, expands, and combines non-Euclidean distance kriging, probabilistic graphical modeling, and expectation maximization to provide a viable alternative to the currently existing, simulation-based methods of spatial interpolation. Upon outlining a conceptual framework for the proposed approach, this paper investigates the feasibility of using its key component, the Markov random field, with a flexible (learned) structure that recovers hydraulic conductivity maps from the knowledge of hydraulic head on those maps. The model is trained on a medium-sized data set of simulated hydraulic maps, and returns promising results. The paper also motivates future work in the area, pointing out several research directions.