Nonlinear data assimilation for shallow water equations in branched channels

Abstract

A framework has been developed for the optimal combination of a network of time series observations with a numerical model of nonlinear shallow water wave propagation in branched channels. The model results and observations are weighted according to their reliability to produce estimates of surface elevation and transport. Two filtering techniques are adopted to perform the dynamic‐stochastic modeling. For weakly nonlinear conditions a modified incremental covariance Chandrasekhar‐type algorithm is employed, whereas for more strongly nonlinear dynamics a Bierman square root form of the extended Kalman filter is used. Numerical experiments performed using parameters from the Great Bay estuary in New Hampshire demonstrate that both filters successfully estimate the time‐ and space‐dependent elevation and transport distributions under conditions of stochastic forcing (model error) and measurement noise. Although the Chandrasekhar algorithm underestimates the covariances of the filter estimates, it performs nearly as well as the fully nonlinear algorithm, even for the significantly nonlinear test case. It is shown that the Chandrasekhar filter performance does not degrade when the algorithm is applied to systems in which the process noise and measurement noise structures are purely sinusoidal, thus violating the assumption of white noise under which the filter algorithm is derived.