Scale-dependent Air-Sea Mechanical Coupling: Resolution Mismatch and
Spurious Eddy-Killing
Abstract
Mechanical coupling of the atmosphere to the ocean surface in general
circulation models is represented using bulk wind stress formulations.
The stress is often based on either absolute wind velocity, τa, or the
more correct wind velocity relative to the ocean surface currents, τr.
Here, we use coarse-graining to disentangle wind work by these
formulations at different length-scales. We show that both can be
reasonably accurate in forcing the ocean at length-scales larger than
the mesoscales, with τa overestimating wind work by 10%. However, τa
and τr show stark and opposing systematic biases in how they drive the
mesoscales; τa does negligible (albeit positive) work on the mesoscales,
while τr yields eddy-killing (negative work) that is artificially
exaggerated by a factor of ≈4. We derive an analytical criterion for
eddy-killing to occur, which shows that exaggerated eddy killing is due
to resolution mismatch between the atmosphere and ocean. Our criterion
highlights the disproportionate effect small-scale winds Ο(100)km can
have on the dynamics of mesoscale ocean eddies, despite the dominant
atmospheric motions being at length-scales larger than Ο(103) km. The
eddy-killing criterion shows that large-scale winds do not necessarily
cause eddy-killing but are merely an amplification factor for wind work
on the mesoscales, which can be either positive or negative depending on
the local alignment of small-scale winds with the ocean eddies. We
propose a simple reformulation of τr, without introducing tuning
parameters, to remove spurious eddy-killing from air-sea resolution
mismatch that is often present in climate models.