Wavelet Ocean Data Assimilation

The ocean remains severely under sampled. However, recent high-resolution observations (such as SWOT) have increased the availability of “dense but patchy” data. These dense data sets have motivated research into so-called multi-scale data assimilation methods. Here, we demonstrate a new assimilation approach utilizing the wavelet transform that is multi-scale by nature and only requires a single analysis step. To produce a relatively simple proof-of-concept, we utilize observational sources that has strong spatial coverage and is high-resolution. The current standard when assimilating observations of this nature is to first perform super observations. The super-observation approach reduces a dense field to weighted averaged points that are a correlation scale away from each other. The process typically reduces the observational information to less than 10% of what they originally were, leading to large-scale corrections of the ocean model. Our advancement instead uses the wavelet transform as an “observational operator”. The wavelet transform allows the innovation to occur in wavelet space, and wavelet thresholding allows us to retain all of the spatial information, down to scales that are not well represented by the horizontal resolution of the ocean model. In order to test the validity of using wavelets in data assimilation, an Observing System Simulation Experiment (OSSE) was used. We find that the wavelet-based assimilation produces less root mean square (RMS) error with respect to depth than the more traditional super-observation approach. Additionally, we evaluated the spatial scales constrained by each assimilation approach. We find that the wavelet-based approach constrains smaller horizontal scales than the super-observation approach. We expect this is due explicitly to the fact that the wavelet transform allows the assimilation to consider many more spatial scales than is possible using the super-observation approach.