Optimizing spectral wave estimates with adjoint-based sensitivity maps

A discrete numerical adjoint has recently been developed for the stochastic wave modelSWAN. In the present study, this adjoint code is used to construct spectral sensitivitymaps for two nearshoredomains. The maps display the correlations of spectral energy levels throughout the domain with the observed energy levels at a selected location or region of interest (LOI/ROI), providing a full spectrum of values at all locations in the domain. We investigate the effectiveness of sensitivity maps based on significant wave height(H s ) in determining alternate offshore instrument deployment sites when a chosen nearshorelocation or region is inaccessible. Wave and bathymetrydatasets are employed from one shallower, small-scale domain (Duck, NC) and one deeper, larger-scale domain (San Diego, CA). The effects of seasonal changes in wave climate, errors in bathymetry, and multiple assimilation points on sensitivity map shapes and model performance are investigated. Model accuracy is evaluated by comparing spectral statistics as well as with an RMS skill score, which estimates a mean model–data error across all spectral bins. Results indicate that data assimilation from identified high-sensitivity alternate locations consistently improves model performance at nearshoreLOIs, while assimilation from low-sensitivity locations results in lesser or no improvement. Use of sub-sampledor alongshore-averaged bathymetryhas a domain-specific effect on model performance when assimilating from a high-sensitivity alternate location. When multiple alternate assimilation locations are used from areas of lower sensitivity, model performance may be worse than with a single, high-sensitivity assimilation point.