Inverse methods for assessing ship-of-opportunity networks and estimating circulation and winds from tropical expendable bathythermograph data

Inverse methods for estimating the surface ciculation of the equatorial Pacific by combining a linear reduced-gravity shallow-water model with the Tropical Ocean-Global Atmosphere ship-of-opportunity expendable bathythermograph (TOGA SOP XBT) observing program are examined. It is demonstrated that a simple linear model of the upper circulation of the equatorial Pacific can be successfully used as a weak constraint when smoothing the TOGA SOP XBT data. A circulation is sought as the weighted least squares fit to the dynamics and the data. The solution method is an expansion in representer functions, and the generalized inverse problem is thereby reduced from a functional problem to an algebraic problem for the coefficients of the representer. A specific inverse calculation using synthetic forcing and data is presented.