Data assimilation and bathymetric inversion in a two‐dimensional horizontal surf zone model

A methodology is described for assimilating observations in a steady state twodimensionalhorizontal (2‐DH) model of nearshore hydrodynamics (waves and currents),using an ensemble‐based statistical estimator. In this application, we treat bathymetry as amodel parameter, which is subject to a specified prior uncertainty. The statistical estimatoruses state augmentation to produce posterior (inverse, updated) estimates of bathymetry,wave height, and currents, as well as their posterior uncertainties. A case study is presented,using data from a 2‐D array of in situ sensors on a natural beach (Duck, NC). The priorbathymetry is obtained by interpolation from recent bathymetric surveys; however, theresulting prior circulation is not in agreement with measurements. After assimilating data(significant wave height and alongshore current), the accuracy of modeled fields isimproved, and this is quantified by comparing with observations (both assimilated andunassimilated). Hence, for the present data, 2‐DH bathymetric uncertainty is an importantsource of error in the model and can be quantified and corrected using data assimilation. Herethe bathymetric uncertainty is ascribed to inadequate temporal sampling; bathymetricsurveys were conducted on a daily basis, but bathymetric change occurred on hourlytimescales during storms, such that hydrodynamic model skill was significantly degraded.Further tests are performed to analyze the model sensitivities used in the assimilation and todetermine the influence of different observation types and sampling schemes.

This work was supported by the Office of Naval Researchgrants N00014‐02‐1‐0198, N00014‐07‐1‐0852, and N00014‐09‐1‐0121.