Geoscience Reference
In-Depth Information
Solar radiation was introduced into the model water column by taking a fixed
fraction
measuredatthe SHEBA
Project Office site, and distributing it with an exponential attenuation in the upper
oceanwith ane-foldingdepth
(
f
SW
)
of the incomingsurface solar radiation
(
I
0
)
SW
=
4m,togeneratea sourceterm
f
SW
I
0
SW
z
SW
Q
H
=
e
Parameters important in the interface submodel were assigned values:
α
h
=
9
.
3
×
10
−
3
6psu.
Themainpointofthemodelingexercisewastogaugehowmuchoftheincoming
radiation measured at the surface had penetrated the ice cover, in order to realisti-
cally account for both the diurnal variation and the secular trend in upper ocean
temperature. The model results, run with three different values of
f
SW
as shown
in Fig. 8.4, indicate that about 8-10% of the short-wave radiation made its way
throughthemultiyearicefloe.Withthesefractions,themodelresultsindicateabout
therightamountof total heatingoverthe four-dayperiod(Fig. 8.4a),and showthe
same pattern of diurnal variation, although the model appears to somewhat under-
estimate the nocturnal cooling. Modeled friction velocity at 8m is fairly accurate;
mean values differ by less than 0
,
α
s
=
α
h
/
35,and
S
ice
=
2mms
−
1
. At 4m (not shown) average modeled
.
5mms
−
1
, perhapsnotsurprisingbecause
z
0
inthe
model is substantially larger than estimated for the smooth ice surrounding Site 2
(McPhee2002).
Downwardheatfluxnearmaximumsunangleismodeledreasonablywellat8m
(Fig.8.4c);however,thenocturnalupward(positive)heatfluxislargerinthemodel
than observed. At night the main heat sink in the system is basal melting, which
in the model is consistent throughout the simulation period, so this might suggest
that modeled basal heat flux is too large (i.e.,
u
∗
exceedsmeasuredbyabout0
.
α
h
is too large). This interpretation,
however,is at oddswith the relatively rapid observednocturnalcooling (compared
withthemodels)inFig.8.4a.Amorelikelyexplanationisthaticeinthevicinityof
the turbulence mast is smooth enough compared with the overall roughness of the
floe (and model with
z
0
=
8cm) that the heat extraction from the water column
is smaller than the averagefor the whole floe. Temperatureof the well mixed layer
wouldrepresentanintegratedeffect.
For the model run with
f
SW
=
4
.
09, the mean basal heat flux was about
17Wm
−
2
,which,whenreducedbythesmallconductivefluxintheice,impliedice
melt of around 2cm over the four days. This produced an average buoyancy flux
at the interface,
0
.
10
−
8
Wkg
−
1
, which had little effect on turbulence near
the surface, but produced a mean value for
w
b
0
≈
µ
∗
of about 2.7 (Section 4.2.3). This is
enoughtoreducethedynamicboundarylayerextentslightly(seeFig.4.8).
When we first did these simulations, we were surprised that as much as 10%
of the incoming solar radiation was making its way into the water. At the time,
estimatesfromaerialphotographyputthefractionoficeareacoveredbyopenleads
intheSHEBAregionatabout2.5%(Perovichetal.2002,theirFig. 8.6),providing
effectively a lower limit on
f
SW
. By mid June melt ponds had formed and were
estimated to cover 15-20% of the surface (Perovich et al., op. cit.). Melt ponds
