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Many activities require accurate wind and wave forecasts in the coastal ocean. The assimilation of fixed buoy observations into spectral wave models such as SWAN (Simulating Waves Nearshore) can provide improved estimates of wave forecasts fields. High-frequency (HF) radar observations provide a spatially expansive dataset in the coastal ocean for assimilation into wave models. A forward model for the HF Doppler spectrum based on first- and second-order Bragg scattering was developed to assimilate the HF radar wave observations into SWAN. This model uses the spatially varying wave spectra computed using the SWAN model, forecast currents from the Navy Coastal Ocean Model (NCOM), and system parameters from the HF radar sites to predict time-varying range-Doppler maps. Using an adjoint of the HF radar model, the error between these predictions and the corresponding HF Doppler spectrum observations can be translated into effective wave-spectrum errors for assimilation in the SWAN model for use in correcting the wind forcing in SWAN. The initial testing and validation of this system have been conducted using data from ten HF radar sites along the Southern California Bight during the CASPER-West experiment in October 2017. The improved winds compare positively to independent observation data, demonstrating that this algorithm can be utilized to fill an observational gap in the coastal ocean for winds and waves. [ABSTRACT FROM AUTHOR]