Multi-scale assimilation of simulated SWOT observations

We use an Observing System Simulation Experiment (OSSE) to quantify improvements in ocean state estimation due to the assimilation of simulated Surface Water Ocean Topography (SWOT) observations using a multi-scale 3DVAR approach. The sequential multi-scale assimilation first generates a large-scale analysis and then updates that analysis with smaller scale corrections. Since we use temperature and salinity depth profiles as proxies for sea surface height (SSH) observations, the results are idealized. Skill metrics consistently show that the multi-scale analysis is superior to the single-scale analysis, specifically because it improves small-scale skill without sacrificing skill at larger scales. The analysis skill over a range of spatial scales is determined using wavenumber spectral analysis of 100 m temperature, SSH, and mixed layer depth (MLD). For MLD, the multi-scale assimilation of SWOT data reduces the minimum constrained wavelength from 158 km to 122 km, a 36 km reduction, compared to a single-scale assimilation of the same data. For SSH, the multi-scale approach only reduces constrained scales from 73 km to 72 km, a 1 km reduction. This small increase in skill is caused by the steep wavenumber spectral slope associated with SSH, which suggests that SSH variability is concentrated at long wavelengths. Ultimately, the small-scale update in the multi-scale assimilation has less to correct for SSH. In contrast, MLD has a relatively flat spectral slope. The multi-scale solution can make a more substantial update to the MLD field because it has more small-scale variability. Thus, our results suggest that the magnitude of the skill improvement provided by the multi-scale solution is negatively correlated with the spectral slope of the ocean variable.