Exploring the added value of assimilating satellite altimeter measurements in a North Sea wave model using the Deterministic Ensemble Kalman Filter

Abstract This study reports on the impact of assimilating satellite altimeter measurements with the Deterministic Ensemble Kalman Filter (DEnKF) using a regional SWAN wave model for the North Sea. We assimilated satellite altimeter measurements over a 3-month period (December 2021 - March 2022) from the following satellites: nadir CFOSAT, Haiyang-2B, Cryosat-2, Jason-3, Sentinel-3, Saral and Altika. The wind forcing is used as control variable to represent system uncertainty and a coarse resolution wave model was used for computational efficiency. Validation against independent wave and wind observations shows a significant performance increase. The assimilation improves predictions of significant wave height with a mean RMSE reduction of 20 %. Unlike most wave data assimilation approaches, the full wave spectrum is used as the state, resulting in automatic adjustment of the full wave spectra and other integral wave parameters. Hence, we also found improvements in mean wave period (10 %) and peak period (5%). Modest improvements in wind speed and direction are found for part of the stations. The DEnKF updates the wave spectrum indirectly through ensemble-based covariances, significant wave height observations and wind forcing. This is most effective in unimodal sea states, which we attribute to the assimilation of significant wave height only. The mean time difference between pass-overs is approximately 3 hours, ranging from within one hour to approximately 14 hours and 46 minutes. Our results indicate that the accuracy decreases when time gaps between satellite pass-overs increase. Effective spectrum-wide corrections, while assimilating significant wave height only, can potentially be achieved with an improved wave model, refining the wind noise model, assimilating other integral wave parameters and potentially extending the wind model beyond wind forcing. The results highlight the added benefit of assimilating satellite altimeter measurements in a regional wave model with a DEnKF using the wave spectrum as the state. To make this a viable approach for operational forecasting, a reduction of the memory and compute requirements are needed. Other potential applications are reanalyses of past wave states for studies of risk and climate change, and more recently training Machine Learning models.