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 2Â 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
