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In-Depth Information
hydraulic roughness is typically about 1/30 the “grain size” of the elements con-
tributingroughness.For theportionsofthe SHEBA floe awayfrompressureridges
and leads,
z
0
=
6mm would imply a “grain size” of about 20cm, hence is not
inconsistentwith ourlimitedobservations.
The question remains:what is the “aggregate”roughnessof a typicalmulti-year
Arctic ice floe in the region traversed by SHEBA? The previousanalysis (McPhee
2002) utilized the cluster nearest the interface (nominally 4m until summer, when
itwasraisedto2m),andusedanestimateofthemixinglengththeretoadjustshear
between the interface and measurementlevel, which tended to decrease
z
0
from its
LOW value at SHEBA site 1 (Novemberto mid-March), and increase it slightly at
site2(mid-MarchthroughSeptember)relativetotheLOWestimate.Measurements
at the former site were obviously affected by a pressure ridge keel that was often
“upstream”as the station driftedwest and later north,while site 2 was fartherfrom
anyapparentfeatures.Whenaveragedovertheentiresite1deployment,therewasa
monotonicincreaseinaverage
u
∗
withdepthfromclusters1to3(nominally4-12m
fromtheice).
To address the SHEBA “scaling up” problem, we speculated that a technique
analogous to that developed to characterize the ISPOL floe could be adapted for
the SHEBA data. The approachsettled on was somewhatdifferent. Although there
was an acoustic Doppler profiler at SHEBA, its data return rate over the course of
the deploymentwas disappointing, and there often appeared to be spurious returns
in the upper portion of the current profiles that contaminatedmeasurementswithin
thewellmixedlayer.We choseinsteadtouseReynoldsstressandcurrentmeasure-
mentsfromTIC2ontheturbulencemast,alongwithT/SprofilesfromtheSHEBA
automatedprofilertosolvetheSLTCmodelforeach3-haverageintheperiodfrom
15November1997to1June1998whenicedriftspeed(withouttheinertialcompo-
nent)exceeded0
1ms
−
1
.Cluster2waschosenbecauseitwasatadepth(nominally
8mfromtheice)thoughttominimizetheimpactofupstreamheterogeneityandbe-
cause it had the most samples (clusters 3 and 4 were sometimes below the well
mixedlayer,andwerenotredeployedaftertheMarch1998breakup).
A time series of log
.
for each of 249, 3-h model realizations meeting the
minimumvelocityrequirements(alsoexcludingabout24sampleswherethederived
z
0
was smaller than 6mm) is shown in Fig. 9.11, along with averages in ten-day
bins. The mean value with standard deviation error bars is log
(
z
0
)
0.
Themeanvalueisthusabout4.9cmwitharangeimpliedbythestandarddeviation
oflog
(
z
0
)=
−
3
.
0
±
1
.
6cm.
The dimensionless surface velocity
(
z
0
)
,
1
.
6
≤
z
0
≤
14
.
u
∗
0
, shown in Fig. 9.12 for each
model realization, is the complex inverse of a “geostrophic drag coefficient” that
includes turning angle as well as magnitude. In terms of a more conventional
quadratic drag coefficient,
c
w
(where
Γ
=
V
0
/
u
∗
0
2
c
w
V
0
), the mean magnitude of
=
=
τ
0
=
.
Γ
0056. This is nearly equal to the value of 0.0055 derived in a
different manner from the free-drift force balance for the AIDJEX stations in the
central Beaufort Gyre in 1975 (McPhee 1980). The latter depended on a relatively
highvalueforthe10-mwinddragcoefficientbasedonanalysisofballoonsoundings
duringAIDJEX(Leavitt1980;Carsey1980).Themeanturningangleinferredfrom
theAIDJEXfree-driftforcebalancewas slightlyless: 23
◦
.
implies
c
w
0
