densely packed roughness elements, such as
DISCUSSION
crops, trees or other vegetation, d/h is typically
Primary roughness elements
reported to be about 0.7 (Stanhill 1969, Thom
The obvious (and, perhaps, surprising) conclu-
1971, Fazu and Schwerdtfeger 1989). For the
sion from the calculations described in the last
more widely spaced sastrugi that I am consider-
section is that roughness elements with heights of
ing, however, d/h is 0.150.35. This is also rough-
only 10 cm can have a dominant effect on CDN10.
ly what R92 (his Figure 5) computed for λ values
This is essentially the same conclusion that Jack-
in the range relevant to this problem, 0.010.06.
son and Carroll (1978) reached. Arya's (1973,
These plots justify my use of d/h = 0.3 when I
1975) model, in contrast, predicted that pressure
had to convert CS10 to CSh in the section on Parti-
ridges 1 to 4 m high accounted for most of the
tioning the Stress. They also show that, for sastru-
form drag that determined the large-scale rough-
gi typically 10 cm high, d is usually less than 3
ness and drag coefficient over Arctic sea ice.
cm. We were thus safe to ignore d in analyzing
My calculations provide a theoretical basis for
our wind speed profiles in AC95. For the lowest
the empirical result that Banke et al. (1976, 1980)
profiling level used in AC95, 0.5 m, including a
obtained, eq 1. Their roughness parameter ξ re-
displacement height of 3 cm in a computation
flects the small-scale roughness; they reported ξ
based on eq 29 would yield a u value roughly
values of 313 cm, where ξ came from integrating
*
1% larger than a computation with d = 0. For the
the roughness spectrum over all wavelengths
higher levels, the difference would be even less.
shorter than 13 m (also see Andreas et al. 1993).
Since the nominal uncertainty in our wind speed
Such wavelengths are far smaller than either Arc-
measurements was 5 cm/s, this small bias in
tic or Antarctic ridge spacings (Lytle and Ackley
our computations is negligible.
1991). Thus, eq 1 and my calculations point to the
Figure 6 shows that d has some interesting
same conclusion: Pressure ridges are relatively
structure--it is not a constant for all wind direc-
unimportant in setting the local drag coefficient;
tions. Equation 46 explains this behavior: d/h re-
CDN10 responds primarily to sastrugi-size rough-
sponds mainly to two variables, τR/τ and CDh;
ness elements. Pressure ridges, however, will
d/h increases linearly with τR/τ but decreases
probably be important in establishing an areally
linearly with CDh2 . The peak in d/h near 2030
1/
averaged or effective roughness length, Z0. Fied-
corresponds to the rapid increase in τR/τ in this
ler and Panofsky (1972), Arya (1975), Overland
range (Fig. 5), while the broad minimum
(1985), and Claussen (1991), among others, have
centered near 100 is where CDh has its maxi-
offered some thoughts on inferring Z0 from z0.
mum (Fig. 4). Another curious feature in Figure 6
But pursuing that connection is beyond my scope
is that the d values in this broad minimum are
here.
usually less than the values for head-on flow.
Clearly, d does not change in concert with z0 or
Parameterizing the drag coefficient
CDh--parameters that quantify the aerodynamic
These model results and the behavior of CDN10
roughness of the surface. This is an important
over snow-covered sea ice that we documented in
conclusion because others have claimed that d is
AC95 suggest what might be necessary in a
a linear function of z0 (e.g., Brutsaert 1982, p. 113;
scheme for parameterizing CDN10. The snow sur-
Sugita and Brutsaert 1990).
face is not in general isotropic, especially during,
In summary, the Raupach's Model Adapted to
or for some time after, high wind events. The
Drifting Snow section explains that my adapta-
wind builds sastrugi and therefore streamlines
tion of R92's model has 11 adjustable parameters:
the surface in the mean wind direction. Figure 4
h, m, n, γ, CS10, CR1, CR2, CR3, c, cw and cd. With
shows how CDN10 behaves for various wind di-
reasonable choices for these and with little fine-
rections once the surface has been streamlined.
tuning, I have demonstrated that that model fits
Thus, the key is to estimate the dominant di-
our ISW observations quite well. I do not mean
rection of the sastrugi without the benefit of in
to imply here, however, that the model is infalli-
situ observations. Maybe in the future, satellites
bly accurate--only that it seems to capture the
will provide real-time information on ice-surface
essential physics of how wind transfers momen-
roughness, including any preferential alignment
tum to snow-covered sea ice.
of the roughness elements. But for now, all we can
10
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