Geoscience Reference
In-Depth Information
In the surface layer, kinematic surface stress is often expressed as a function of
windspeedsquared:
c
h
U
U
where
U
isthevelocityvector(relativetothesurface)atdistance
h
fromthebound-
ary,and
c
h
is the dragcoefficientappropriateto level
h
. Thisis equivalentto speci-
fying
z
0
since
τ
0
=
u
∗
0
u
∗
0
=
he
−
κ
/
√
c
h
z
0
=
and it might seem unnecessary to consider undersurface roughness at all; indeed,
mostice/oceanmodelsspecifyquadraticdragbetweentheiceandunderlyingocean,
sometimeswithaconstantturningangle(e.g.,Hibler1980).However,asexploredin
moredetailbelow,quadraticstress isprobablynotappropriateexceptwhenapplied
tocurrentsmeasuredormodeledwithinthethinsurfacelayer,confinedtotheupper
fewmetersfromtheinterface.
Howbesttospecifyundersurfaceroughnessforlargescalemodelsisstilllargely
unresolved,andbecauseimportantice/oceanexchangeparametersdependonit,the
problemcontinuesto drawattention. From practicalconsiderations,oceanographic
instrumentationismostoftendeployedunderreasonablysmoothiceawayfromob-
viousobstacles,andaconcernisthatwethussystematicallybiasestimatesofunder-
surface roughness (hence also stress and scalar flux estimates) downward. During
the planning and analysis of SHEBA data, there was much emphasis on “scaling
up”measurementsmadeatonelocality(theSHEBAstation)torepresentaregional
area commensurate with the practical grid scale of a large scale numerical model.
This is particularly germane in the case of surface roughness and will be explored
inmoredetailbelow.
4.1.3 Monin-Obukhov Similarity
The LOW (4.3) is valid only when buoyancy effects are negligible. In the at-
mospheric surface layer this precludes a large percentage of possible states; for
example, strong diurnal heating from incoming shortwave radiation, or nocturnal
surface cooling from outgoing longwave radiation. In the former case, buoyant air
parcels formed near the surface tend to enhance turbulence and increase the effi-
ciency of exchange, thus reducing shear; whereas in the latter case, a temperature
inversionmay form near the surface, much reducingthe frictionalcouplingand in-
creasing near surface shear. The ice/ocean interface exhibits analogous conditions
when thereis meltingor freezing(althoughrarelyto the same intensityas foundin
thedailycycleofthe mid-latitudeatmosphere).
The impact of buoyancy on the surface layer wind shear was first investigated
systematicallybyObukhov(1971,Englishtranslation;seealsoBusingerand Yaglom
1971).Forthepurposeshere,dimensionalanalysissufficestodefinethemainfeatures
of the problem.We postulate that wind (currentshear) in thesurface layer depends
on friction velocity, scaled distance from the interface, and buoyancy flux:
,
w
b
0
)
U
z
=
F
(
u
∗
0
,
κ
z
