On the Use of Information Theory to Quantify Parameter Uncertainty in Groundwater Modeling

We applied information theory to quantify parameter uncertainty in a groundwater flow model. A number of parameters in groundwater modeling are often used with lack of knowledge of site conditions due to heterogeneity of hydrogeologic properties and limited access to complex geologic structures. The present Information Theory-based (ITb) approach is to adopt entropy as a measure of uncertainty at the most probable state of hydrogeologic conditions. The most probable conditions are those at which the groundwater model is optimized with respect to the uncertain parameters. An analytical solution to estimate parameter uncertainty is derived by maximizing the entropy subject to constraints imposed by observation data. MODFLOW-2000 is implemented to simulate the groundwater system and to optimize the unknown parameters. The ITb approach is demonstrated with a three-dimensional synthetic model application and a case study of the Kansas City Plant. Hydraulic heads are the observations and hydraulic conductivities are assumed to be the unknown parameters. The applications show that ITb is capable of identifying which inputs of a groundwater model are the most uncertain and what statistical information can be used for site exploration.