DEVELOPMENT OF INFORMATION THEORY FORMULATION TO QUANTIFY PARAMETER UNCERTAINTY IN GROUNDWATER MODELING

We developed an Information Theory (IT) formulation to quantify uncertainty of optimized parameters for a groundwater model. The IT formulation constructs entropy as a measure of uncertainty at the most probable state of hydrogeologic conditions when a groundwater model is fully optimized. The entropy is subject to the error constraint and the normalization constraint imposed by observation data. We derive an analytical solution to calculate covariance of optimized parameters by maximizing the entropy. MODFLOW-2000 is implemented to optimize unknown parameters. After optimizing these parameters, we calculate the Hessian matrix of minimized error and its eigenvalues for the analytical solution. We apply IT to a three-dimensional synthetic model and the case of Kansas City Plant, Missouri in order to demonstrate how the IT approach effectively quantifies parameter uncertainty. Hydraulic conductivities are the input parameters to be optimized and hydraulic heads are the output to be observed. The IT approach constructs a multivariate probability distribution for given hydraulic head data and estimates variance, covariance, and correlation coefficient between input parameters. Example studies show that 1) the IT approach is able to determine whether the optimization process is reliable or not, 2) it is applicable to various purposes such as a sampling strategy for observation data, conditioning parameters, and a decision making process, and 3) the IT formulation is compatible with any model and any optimization process.