Assimilating in-situ Measurements into a Reduced-Dimensionality Model of an Estuary- Plume System.

A very fast, model independent, fully non-linear extension to the reduced space Kalman filter has been recently proposed and demonstrated for the assimilation of the non-linear circulation in both a synthetic estuary and in the river-dominated Columbia River estuary. Here, we extend the application to another complex problem the simulation of a coupled estuary-plume system.

Our data assimilation method is based on the same three stages as in our previous work: (1) generate a database of hindcast runs with a forward numerical circulation model like SELFE; (2) use examples from the hindcast database to train a fast, non-linear neural network model surrogate that approximates the dynamics of the forward model; and (3) use a Sigma Point Kalman filter, incorporating the model surrogate dynamics, to estimate the true state of the system. Both model surrogates (2) and state estimation (3) operate in the reduced space spanned by the Empirical Orthogonal Functions (EOFs, aka principal components). The key modifications that we are introducing are the improved EOF analysis for more accurate dimension reduction in the plume region, a more compact noise model for faster DA, and the improved treatment of wetting and drying. The resulting data assimilation system is ~100 faster than the forward model and ~10000 faster than the existing variational and sequential methods for data assimilation.

As a test of the system, we assimilate in-situ data from four offshore moorings and 14 estuarine stations during May-September of 2004. For validation of the experiments we use cross-validation against in-situ data, data from research cruises, and satellite imagery. We show that data assimilation is effective for improving the simulation of at least three highly non-linear processes: the dynamics of the estuarine salt-wedge, the response of the plume to wind shifts, the propagation of the shallow water tides, and wetting and drying of tidal flats.