Ocean Data Assimilation Towards Submesoscales

Historically, ocean data assimilation systems have focused on fitting only larger, mesoscale features because of the relatively coarse nature of the observing networks. Recent, novel observing systems, such as the Surface Water Ocean Topography (SWOT) satellite, have created the opportunity to extend data assimilation skill towards smaller scales. However, assumptions embedded in long-standing assimilation systems, valid for larger scales, create a hard boundary for the types of features that can be corrected in the model background. Ocean assimilation systems must be adapted for these new observations that provide small-scale information. Three ‘multi-scale’ approaches are detailed and demonstrated, each with the intent of extending ocean assimilation skill to smaller scales without sacrificing skill at larger scales. The first technique continuously adapts the horizontal scales corrected by observations: large-scale corrections around relatively coarse observations and small-scale corrections around relatively fine observations. The second approach employs a two-step correction method: a large-scale corrections step that is then further adjusted based on smaller scale corrections provided by the smaller scale observations. The final method employs a wavelet-based approach. Both the model and the observations are brought into the same mathematical space and the model correction is calculated in that alternate space. This allows for the simultaneous correction of most horizontal scales present in both the model and the observations. Each method is shown to be beneficial, and their own strengths and weaknesses are discussed.