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.