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estimatesoficevelocityanddeformationonauniform5kmgridcoveringadomain
about 200km by 200km, in the vicinity of the SHEBA drift station. An example
of the velocity field product derived from two RGPS scenes spaced about one day
apartis shownin Fig. 2.8.Thecoloredcontourmapaccentuatesthe boundariesbe-
tween threecomparativelyuniformvelocity zones, with the moresoutherlybound-
ary passing near theship trajectoryfrom 77.75to 78.73,i.e., duringthe time of the
upwellingevent.
Using Rossby-similarity (see Section 4.2.2)to relate ocean stress to ice velocity
(assumingthatgeostrophiccurrentwassmallinthisregion),wecalculatedagridded
map of kinematic stress corresponding to the velocities of the 5-km RGPS grid
(Fig2.8a).Wethencalculatedalowerlimitonthekinematicstresscurlaccordingto
× τ 0 ∆τ 0 y
x ∆τ 0 x
y
where the differentials are approximated by differences over the grid scale
x
=
5km, with results shown in Fig. 2.8b. Although, the RGPS analysis can-
not estimate shear (or stress curl) on scales smaller than 5km, our observations
from the ship and by analysis of SAR images in the vicinity of the ship suggested
thattheshearoccurredacrossscalesatleastanorderofmagnitudeless(i.e.,500m).
If the numerical value of stress curl from Fig. 2.8b, evaluated in the vicinity of the
ship,ismultipliedby10,theresultingpycnoclinedisplacementisaboutthesameas
observed (McPhee et al. 2005), and we thus inferred that the March 19 upwelling
eventwasa resultofEkmanpumping.
It is remarkable that the zones of intense stress curl, manifested locally at the
shipbya dramaticshearacrossanarrowlead,extendatleast200kminalongmore
or less parallel arcs. The strength of the ice appears to provide a mechanism by
which gradientsin the forcingwind field are concentratedinto narrowshear zones,
which by Ekman pumping induce substantial isopyncnal displacement and much
enhanced mixing of heat and salt in the upper ocean. The RGPS analysis reveals
that these concentrated shear zones extend for long distances and are a ubiquitous
featureinthe Arcticicepack(Kwok2001).
y
=
2.7 The Equation of State for Seawater
In polar oceans, a layer of cold, less saline water nearly always overlies water that
isbothwarmerandsaltier.Thisnegativetemperaturegradientbyitselfisdestabiliz-
ing, 4 sostratificationismaintainedbythenegativesalinitygradient(i.e.,increasing
withdepth).Theequationofstateforseawaterisbyconventionexpressedasafunc-
tionof temperature,salinity asunitsof the practicalsalinity scale (abbreviated psu ,
4 In fresh water, thermal expansion changes sign at about 4 C, so fresh (or brackish water) may
remain stable despite a negative temperature gradient near the surface. This does not hold for
seawater withsalinitiesinexcess ofabout 24 unitson the practical salinity scale.
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