  We present an analysis of the model by Gnanadesikan [1999] for the pycnocline
depth in the ocean. An analytic solution for the overturning strength as a
function of the meridional pressure difference is derived and used to discuss
their mutual scaling. We show that scaling occurs only in two unphysical
regimes of the model. In the absence of the Southern Ocean (SO) processes, i.e.
for a northern overturning cell, the volume transport is proportional to the
square root of the pressure difference. Linear scaling is seen when the
overturning is restricted entirely to the SO, i.e. when no northern downwelling
exists. For comparison, we present simulations with the coupled climate model
CLIMBER-3$\alpha$ which show linear scaling over a large regime of pressure
differences in the North Atlantic (NA). We conclude that the pycnocline model
is not able to reproduce the linear scaling between its two central variables,
pressure and volume transport.
