densely packed roughness elements, such as

crops, trees or other vegetation, *d*/*h *is typically

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 *C*DN10.

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 *C*S10 to *C*Sh in the section on *Parti-*

ridges 1 to 4 m high accounted for most of the

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-

sponds mainly to two variables, τR/τ and *C*Dh;

ness elements. Pressure ridges, however, will

probably be important in establishing an areally

linearly with *C*Dh2 . The peak in *d*/*h *near 2030

1/

averaged or effective roughness length, *Z*0. 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 *C*Dh has its maxi-

offered some thoughts on inferring *Z*0 from *z*0.

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 *z*0 or

These model results and the behavior of *C*DN10

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 *z*0 (e.g., Brutsaert 1982, p. 113;

scheme for parameterizing *C*DN10. 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

wind builds sastrugi and therefore streamlines

tion of R92's model has 11 adjustable parameters:

the surface in the mean wind direction. Figure 4

shows how *C*DN10 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

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