| 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. |
