Applicability of Rice’s Formula in Stochastic Hydrological Modeling

Abstract

The evaluation of crossing probability for a given threshold level of a discrete process is an important modeling issue in stochastic hydrology. Rice’s formula is a tool to measure the instantaneous crossing rate for a given threshold level in a continuous Gaussian process. This paper examines the discrete application of Rice’s formula to estimating the up-crossing probability in typical discrete stationary univariate Gaussian processes. The results based on Rice’s formula are found to follow a biased pattern relative to the exact solutions, and perform poorly in important scenarios, particularly for estimating resilience in these numerical experiments.