A Probabilistic Reasoning Approach for Constructing Underground Water Maps with Varying Local Hydraulic Conductivity

The ability to design and efficiently 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 given geological map based on a limited number of available observations of hydraulic head and conductivity levels on the map. The approach adapts, expands and combines such methodologies as non-Euclidean distance kriging, probabilistic graphical modeling and expectation maximization, to provide a viable alternative to currently existing, simulation based methods of special interpolation. In addition to motivating and providing a conceptual framework for the proposed approach, this paper investigates the feasibility of using its key component, a Markov random field with a flexible (learnt) structure, for predicting hydraulic conductivity maps based on the knowledge of hydraulic head on those maps. The model is trained on a medium-sized dataset of simulated hydraulic maps and returns promising results on a number of test maps. The paper also motivates future work in the area, pointing out several key research directions.