[1] A methodology is described for assimilating observations in a steady state twodimensional horizontal (2-DH) model of nearshore hydrodynamics (waves and currents), using an ensemble-based statistical estimator. In this application, we treat bathymetry as a model parameter, which is subject to a specified prior uncertainty. The statistical estimator uses 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 prior bathymetry is obtained by interpolation from recent bathymetric surveys; however, the resulting prior circulation is not in agreement with measurements. After assimilating data (significant wave height and alongshore current), the accuracy of modeled fields is improved, and this is quantified by comparing with observations (both assimilated and unassimilated). Hence, for the present data, 2-DH bathymetric uncertainty is an important source of error in the model and can be quantified and corrected using data assimilation. Here the bathymetric uncertainty is ascribed to inadequate temporal sampling; bathymetric surveys were conducted on a daily basis, but bathymetric change occurred on hourly timescales during storms, such that hydrodynamic model skill was significantly degraded.Further tests are performed to analyze the model sensitivities used in the assimilation and to determine the influence of different observation types and sampling schemes.

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Observations are presented of the wave shear stress hũwi on a steeply sloping beach. Above the wave boundary layer (WBL), positive values of hũwi were observed and are attributed to a combination of both wave shoaling due to the large-scale bed slope, and dissipation due to wave breaking, in agreement with the wave theory of . Within the WBL, observed vertical profiles of hũwi were also in good agreement with theory, in cases where the wave height was small. As wave heights increased, however, the WBL profile of hũwi generally did not agree with theory. Near-simultaneous rotary sonar observations of the bed suggest the disagreement with theory was due to the presence of orbital-scale ripples, which the present theory does not accommodate.

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A coherent Doppler profiler was used to measure coincident time series of velocity (u,w), sediment mass concentration (c), and sediment grain size (d), above mobile sand dunes in unidirectional flow (∼1 m/s, ∼1 m water depth). The measurements are used to extract statistical distributions of sediment concentration and flux just above the bed. Observed mass fluxes (uc,wc) were well fit by quasi‐exponential distributions, at all positions along the dune profile, similar to previous observations of single‐particle momenta for bed load over flat beds. Observed concentrations of moving particles were well fit by negative‐binomial distributions, also similar to previous observations over flat beds. These probability distributions relate to two recent stochastic theories, previously derived and verified for uniform flow over flat beds. It is hypothesized that these theories may also be used as a local approximation in natural‐scale flows with bed forms.