Method and System for Multi-scale Assimilation of Surface Water Ocean Topography (SWOT) Observations

A method of forecasting an ocean state via a multi-scale two-step assimilation of Surface Water Ocean Topography (SWOT) observations. The method may include receiving data associated with a prior ocean state forecast associated with SWOT observations, determining a large-scale increment state variable based on a large scale correction associated with the prior ocean state forecast, and determining a small scale initial input value based on (i) a combination of the background state associated with the prior ocean state forecast and (ii) the determined large-scale increment state variable. The method may include generating, based on the determined small scale initial input value, a small scale correction associated with the prior ocean state forecast, determining a small-scale increment state variable based on the small scale correction, and generating a current ocean state forecast based on at least some of this information.