Altimetric assimilation with water property conservation

A simple method for assimilating surface pressure data into a 21-level, eddy-resolving Cox model in a double-gyre configuration [see Cox, 1985] is introduced. A conservation principle is used to derive the new water column structure based on rearrangement of the preexisting water masses. This respects the long timescales required to modify water properties on deeper isopycnals, while still allowing for immediate changes in isopycnal geometry and associated currents. Water columns are displaced vertically by an amount which reduces the surface pressure update to zero at the bottom. Current updates are then calculated geostrophically. An identical twin experiment is performed for 1 year with complete surface pressure data assimilated every 9 days. Thermocline temperature and current errors decrease rapidly after a single assimilation of surface pressure. Errors in subthermocline currents and isopycnal potential vorticity (stratification) within the thermocline decrease only after model integration. Deep current (3000 m) RMS errors are, after 1 year, reduced by up to 60%. A mixed layer scheme is added to the simple assimilation procedure to account better for changes in water properties near the surface (where property conservation is less realistic). Assimilation, with both surface pressure and surface temperature data provided, is also described. Surface temperature data have the biggest immediate impact on the circulation where the mixed layer is deep, e.g., in the subtropical gyre or in the far north, although after 1 year it does not contribute much over surface pressure assimilation alone. We speculate that the surface temperature data will contribute more for temporally varying surface boundary conditions, where it influences water properties subducted into the thermocline. This assimilation scheme should be easy to implement in any model framework and can be modified to incorporate an error analysis for use with real data sets.