Bathymetry correction using an adjoint component of a coupled nearshore wave‐circulation model: Tests with synthetic velocity data

Abstract

[1] The impact of assimilation of wave-averaged flow velocities on the bathymetric correction is studied in tests with synthetic (model-generated) data using tangent-linear and adjoint components of a one-way coupled nearshore wave-circulation model. Weakly and strongly nonlinear regimes are considered, featuring energetic unsteady along-beach flows responding to time-independent wave-averaged forcing due to breaking waves. It is found that assimilation of time-averaged velocities on a regular grid (mimicking an array of remotely sensed data) provides sensible corrections to bathymetry. Even though the wave data are not assimilated, flow velocity assimilation utilizes adjoint components of both the circulation and wave models. The representer formalism allows separating contributions of these two components to the bathymetric correction. In a test case considered, involving a beach with an alongshore varying bar, the adjoint wave model contribution was mainly to determine the cross-shore position of the bar crest. The adjoint circulation model provided an additional contribution, mostly adding to alongshore variability in the shape of the bar. The array mode analysis reveals that there are very few modes that can be effectively corrected, given the assumed data error level. Bathymetry perturbations associated with these modes are a mixture of near-coast intensified modes as well as modes extending their influence to deep water (along the background wave characteristics). Additional tests show the utility of different observational arrays in providing the bathymetric correction.

Surf zone bathymetry and circulation predictions via data assimilation of remote sensing observations

“…Note this also limits the ability of the system to develop long decorrelation lengths in C hh as more data are assimilated over time, even if they exist in reality. This is a general limitation of the ensemble-based technique compared to exact adjoint-based schemes [e.g., Feddersen et al, 2004;Zaron et al, 2011;Kurapov and € Ozkan-Haller, 2013].…”

“…[] have applied Kalman filtering schemes to assimilate pseudoobservations of depth (i.e., observations derived from an explicit depth‐inversion) from remote sensing, with excellent results. Others have implemented more complex data assimilation schemes, including variational [ Zaron et al ., ; Kurapov and Özkan‐Haller , ], and ensemble‐based [ Wilson et al ., ; Wilson and Özkan‐Haller , ; Landon et al ., ], which are capable of assimilating general observations such as currents, wave height, etc. The work of Wilson et al .…”

Surfzone State Estimation, with Applications to Quadcopter-Based Remote Sensing Data

“…An advantage shared by the 1DVar method and several other bathymetry inverse methods (van Dongeren et al 2008;Wilson et al 2010;Kurapov and Özkan-Haller 2013) is that it is capable of assimilating multiple types of hydrodynamic data, in this case wave height and longshore current. This can serve to compliment other methods of bathymetry estimation, particularly methods based on inversion of remotely sensed wave celerity via the linear wave dispersion relationship (Bell 1999;Stockdon and Holman 2000;Holman et al 2013).…”

“…Veeramony et al (2010) and Orzech et al (2013) estimated boundary wave spectra in a nearshore model from observations of wave spectra in the model interior, assuming known bathymetry, and similar techniques have also been used in larger-scale coastal applications, for example, O'Reilly and Guza (1998) and Crosby et al (2017). Finally, several authors have developed methods for estimating surfzone bathymetry from a variety of in situ and remotely sensed observation types while assuming wave boundary conditions are known (van Dongeren et al 2008;Wilson et al 2010;Kurapov and Özkan-Haller 2013;Birrien et al 2013;Wilson et al 2014).…”

Modeling the Morphodynamics of Coastal Responses to Extreme Events: What Shape Are We In?

“…Data assimilation is being increasingly incorporated into coastal morphology models. Direct inference of bathymetry from observations of the sea surface has been used since World War II (Williams 1947) and is now based on estimates of wave dissipation and/or wave celerity, current velocity, and shoreline location derived from video imagery (e.g., Stockdon & Holman 2000;Alexander & Holman 2004;van Dongeren et al 2008;Wilson et al 2010Wilson et al , 2014Birrien et al 2013;Kurapov & Özkan-Haller 2013;Brodie et al 2018Brodie et al , 2019Wilson & Berezhnoy 2018;Collins et al 2020). So far, data assimilation has been coupled with relatively simple morphological models: Plant & Holland (2011) used a Bayesian approach to assimilate bathymetry, bar location, and wave breaking into a surf-zone wave-propagation model; Vitousek et al (2017) used an extended Kalman filter to assimilate historical shoreline data into a model for predicting shoreline change; and Ghorbanidehno et al (2019) demonstrated a fast Kalman filter for assimilating wave data into a bathymetry model.…”