A Direct Method for Assimilating Sea Surface Height Data into Ocean Models with Adjustments to the Deep Circulation

Abstract

There is as yet no consensus an the best method for inserting surface data into ocean models so that appropriate information is transmitted to the deeper layers in a rapid and efficient manner. First we consider the correlation of sea surface pressure (which is related to sea surface height as measured by altimeters) and the surface and subsurface currents within the framework or a four-layer quasi-geostrophic model. We begin by suggesting that the homogenization of potential vorticity, q, in the unforced layers discussed by Rhines and Young, ensures that the potential vorticity anomalies in the deep ocean are weak. It follows that instantaneous q information from thew deep layers may not need to be accurately known in order to reconstruct the deep eddy currents, i.e., climatological q information may be sufficient. Taking the fields from the model we use the instantaneous surface streamfunction, ?1, data along with various approximate subsurface q climatologies and attempt to reconstruct the lower layer flow fields, including the eddies, to the best of our ability. We judge the success of the results both visually and by using the global measure of rms errors. This process is remarkably successful showing that much of the information on the deep eddy currants is contained in the surface ?1, field. We also try to use instantaneous surface q1 information to reconstruct the deep flow but with much less success. This is because the barotropic mode streamfunction ?B is not well constrained by q1 information alone whereas ?1 information does constrain ?B to some extent. A new method of directly inserting data within the time integration scheme of the model is then suggested in which the q fields in the subsurface model layers are left unchanged by the assimilation procedure, and the method is tested with a twin experiment (i.e., a control ocean is defined by the same model at a different time in its evolution). In the assimilation run the top layer q1 field is changed so as to make the consistent ?1 field coincide with the control ocean values. The appropriate q1 is not the same as the control ocean q1 as it must compensate for the incorrect q fields below. The assimilation run is found to converge rapidly to the control ocean even with total surface data coverage every 40 days. The q fields in the deeper layers (particularly at the bottom) converge as the model evolves in between the data assimilation times. The method works very well because of the q homogenization in the unforced model layers; however, we argue that it would also be suitable under the less stringent constraint that the eddy q fields be uncorrelated in the vertical. Finally we discuss the two commonly used methods of nudging and direct insertion in the light of these results and consider whether this new method can be extended into a primitive equation framework.