Explaining the Statistical Properties of Salt Intrusion in Estuaries Using a Stochastic Dynamical Modeling Approach

Determining the statistical properties of salt intrusion in estuaries on sub-tidal time scales is a substantial challenge in environmental modeling. To study these properties, we here extend an idealized deterministic salt intrusion model to a stochastic one by including a stochastic model of the river discharge. In the river discharge model, two types of stochastic forcing are used: one independent (additive noise) and one dependent (multiplicative noise) on the river discharge state. Each type of forcing results in a non-Gaussian response in the salt intrusion length, which we consider here as the distance of the 2 psu isohaline contour to the estuary mouth. The salt intrusion model including both types of stochastic forcing in the river discharge provides a satisfactory explanation of the multi-year statistics of observed salt intrusion lengths in the San Francisco Bay estuary, in particular for the skewness of its probability density function.