Do Box Inverse Models Work?

Abstract

Abstract The performance of a box inverse model is tested using output from a near-eddy-resolving numerical model. Conservation equations are written in isopycnal layers for three properties: mass, heat, and salt anomaly. If the equations are free of error and the vertical exchange of properties between layers is negligible or known, the reference level velocity structure is quite accurately reproduced despite the underdetermined nature of the problem. If the interlayer fluxes of properties are not negligible and they are ignored, the solution for the reference level velocities is poor. If the interlayer fluxes of properties are included as additional unknowns in the inversion, they can be accurately estimated provided the column weights are chosen appropriately. Column weights that minimize the ratio of largest to smallest singular value (the “condition number”) result in the best solutions for interfacial fluxes, and generally also for lateral fluxes. This choice of column weights also makes the inversi...