Crossing Theory for Non‐Gaussian Stochastic Processes With an Application to Hydrology

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Abstract
The theoretical properties of level crossings for stationary Gaussian processes have been applied in the past to model empirical crossing behavior of streamflow data with some success. However, when the marginal distributions exhibit departures from normality, such as high coefficients of skewness, the theoretical Gaussian results perform poorly in modeling empirical crossing behavior. In this paper we present theoretical results for crossings of levels by two non‐Gaussian processes, namely, the chi‐square process and the lognormal process. The chi‐square process does not appear to have been applied previously in the hydrologic literature. We apply both models to a skewed annual flow series. Comparisons with the Gaussian model are made and noticeable improvements are found in both cases.

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