Abstract 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.

中文翻译：

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模拟 SWOT 观测的多尺度同化

摘要 我们使用观测系统模拟实验 (OSSE) 来量化由于使用多尺度 3DVAR 方法对模拟地表水海洋地形 (SWOT) 观测进行同化而对海洋状态估计的改进。顺序多尺度同化首先生成大规模分析，然后用更小尺度的修正更新该分析。由于我们使用温度和盐度深度剖面作为海面高度 (SSH) 观测的代理，因此结果是理想化的。技能指标一致表明，多尺度分析优于单尺度分析，特别是因为它在不牺牲大规模技能的情况下提高了小尺度技能。使用 100 m 温度的波数谱分析、SSH、和混合层深度（MLD）。对于 MLD，与相同数据的单尺度同化相比，SWOT 数据的多尺度同化将最小约束波长从 158 公里减少到 122 公里，减少了 36 公里。对于 SSH，多尺度方法仅将约束尺度从 73 公里减少到 72 公里，减少了 1 公里。技能的这种小幅增长是由与 SSH 相关的陡峭波数光谱斜率引起的，这表明 SSH 可变性集中在长波长上。最终，多尺度同化中的小尺度更新对 SSH 的修正较少。相比之下，MLD 具有相对平坦的光谱斜率。多尺度解决方案可以对 MLD 领域进行更实质性的更新，因为它具有更多的小尺度可变性。因此，