Practical Probabilistic Ground‐Water Modeling

Abstract

Abstract The major obstruction to the effective use of probabilistic models is the determination of the statistical properties of unknown model parameters. In this paper we use the principle of minimum relative entropy (MRE) to determine the prior pdf, p(m) of a set of model parameters, (m) based on limited information. The pdf is of the form of a multivariate truncated exponential distribution. In this paper we use p(m) in Monte Carlo simulations to provide expected values in field variables such as drawdowns, pumping rates, and confidence limits. The examples presented illustrate some dangers associated with the practice in probabilistic modeling of assigning Gaussian pdf's as priors. First, such an assumption for the input parameters actually injects more information into the problem than may actually exist, whether consciously or unconsciously. This fact is born out by comparison with minimum relative entropy theory. Second, the output parameters as suggested from the Monte Carlo analysis cannot be assumed to be Gaussian distributed even when the prior pdf is in Gaussian form. In a practical setting, the significance of this result and the approximation of Gaussian form would depend on the cost, risk, and consequences of the decision being made.