DO BOX INVERSE MODELS WORK

The performance of a box inverse model is tested using output from a n ear-eddy-resolving numerical model. Conservation equations are written in isopycnal layers for,three properties: mass, heat, and salt anomal y. If the equations are free of error and the vertical exchange of pro perties between layers is negligible or known, the reference level vel ocity structure is quite accurately reproduced despite the underdeterm ined nature of the problem. If the interlayer fluxes of properties are not negligible and they are ignored, the solution for the reference l evel velocities is poor. If the interlayer fluxes of properties are in cluded as additional unknowns in the inversion, they can be accurately estimated provided the column weights are chosen appropriately. Colum n weights that minimize the ratio of largest to smallest singular valu e (the ''condition number'') result in the best solutions for interfac ial fluxes, and generally also for lateral fluxes. This choice of colu mn weights also makes the inversion insensitive to data error: Inversi ons containing typical errors can be solved at full rank, obviating th e need to estimate the rank. The choice of number of layers, and wheth er these layers are isopycnals or geopotentials, does not affect the a ccuracy of the inversion provided that interlayer fluxes are included as unknowns in the inversion. A reasonable estimate of solution accura cy is available by using the statistical approach to inverse problems, although this method can be sensitive to the choice of prior statisti cs. Box inverse models do work, provided that they include interfacial fluxes as unknowns and that these are weighted appropriately. Such a model can successfully determine interfacial fluxes and, in some cases , horizontal fluxes. However, the model will not generally reproduce t he detailed structure of the reference level velocities.