Coastal ocean models play a major role in forecasting coastal inundation due to extreme events such as hurricanes and tsunamis. Additionally, they are used to model tides and currents under more moderate conditions. The models numerically solve the shallow water equations, which describe conservation of mass and momentum for processes with large horizontal length scales relative to the vertical length scales. The bottom stress terms that arise in the momentum equations can be defined through the Manning's n formulation, utilizing the Manning's n coefficient. The Manning's n coefficient is an empirically derived, spatially varying parameter, and depends on many factors such as the bottom surface roughness. It is critical to the accuracy of coastal ocean models, however, the coefficient is often unknown or highly uncertain. In this work we reformulate a statistical data assimilation method generally used in the estimation of model state variables to estimate this model parameter. We show that low-dimensional representations of Manning's n coefficients can be recovered by assimilating water elevation data. This is a promising approach to parameter estimation in coastal ocean modeling.
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