  Numerical and observational evidence indicates that, in regions where
mixed-layer instability is active, the surface geostrophic velocity is largely
induced by surface buoyancy anomalies. Yet, in these regions, the observed
surface kinetic energy spectrum is steeper than predicted by uniformly
stratified surface quasigeostrophic theory. By generalizing surface
quasigeostrophic theory to account for variable stratification, we show that
surface buoyancy anomalies can generate a variety of dynamical regimes
depending on the stratification's vertical structure. Buoyancy anomalies
generate longer range velocity fields over decreasing stratification and
shorter range velocity fields over increasing stratification. As a result, the
surface kinetic energy spectrum is steeper over decreasing stratification than
over increasing stratification. An exception occurs if the near surface
stratification is much larger than the deep ocean stratification. In this case,
we find an extremely local turbulent regime with surface buoyancy
homogenization and a steep surface kinetic energy spectrum, similar to
equivalent barotropic turbulence. By applying the variable stratification
theory to the wintertime North Atlantic, and assuming that mixed-layer
instability acts as a narrowband small-scale surface buoyancy forcing, we
obtain a predicted surface kinetic energy spectrum between $k^{-4/3}$ and
$k^{-7/3}$, which is consistent with the observed wintertime $k^{-2}$ spectrum.
We conclude by suggesting a method of measuring the buoyancy frequency's
vertical structure using satellite observations.
