The Assimilation of CFOSAT Wave Heights Using Statistical Background Errors

This paper discusses the assimilation of significant wave height (Hs) observations from the China France Oceanography SATellite (CFOSAT) into the Global Deterministic Wave Prediction System developed by Environment and Climate Change Canada. We focus on the quantification of background errors in an effort to address the conventional, simplified, homogeneous assumptions made in previous studies using Optimal Interpolation (OI) to generate Hs analysis. A map of Best Correlation Length, L, is generated to count for the inhomogeneity in the wave field. This map was calculated from pairs of Hs forecasts of two grid points shifted in space and time from which a look-up table is derived and used to infer the spatial extent of correlations within the wave field. The wave spectra are then updated from Hs analysis using a frequency shift scheme. Results reveal significant spatial variance in the distribution of L, with notably high values located in the eastern tropical Pacific Ocean, a pattern that is expected due to the persistent swells dominating in this region. Experiments are conducted with spatially varying correlation lengths and a set correlation length of eight grid points in the analysis step. Forecasts from these analyses are validated independently with the Global Telecommunications System buoys and the Copernicus Marine Environment Monitoring Service (CMEMS) altimetry wave height observations. It is found that the proposed statistical method generally outperforms the conventional method with lower standard deviation and bias for both Hs and peak period forecasts. The conventional method has more drastic corrections on Hs forecasts, but such corrections are not robust, particularly in regions with relatively short spatial correlation length scales. Based on the analysis of the CMEMS comparison, the globally varying correlation length produces a positive increment of the Hs forecast, which is globally associated with forecast error reduction lasting up to 24 h into the forecast.