k2
CHr =
[ln(r / z0 ) - ψ m (r / L)] [ln(r / zT ) - ψ (r / L)]
,
(14a)
h
k2
CEr =
[ln(r / z0 ) - ψ m (r / L)][ln(r / zQ ) - ψ h (r / L)] .
(14b)
Here z0, zT, and zQ are the roughness lengths for wind speed, temperature, and
humidity, respectively, and L is the Obukhov length, a stability parameter.
For the semiempirical stability functions for momentum (ψm) and heat (ψh) in
eq 14, we use the following:
For stable stratification, r / L ≡ ς ≥ 0 (Launiainen and Vihma 1990),
[
]
ψ m (ς) = ψ h (ς) = - 0.7 ς + 0.75 (ς - 14.3) exp(-0.35 ς) + 10.7 ;
(15a)
For unstable stratification, ς ≥ 0 (Paulson 1970),
[(
) ]
[
]
ψ m (ς) = 2 ln (1 + y) / 2 + ln 1 + y 2 / 2 - 2 arctan(y) + π /2
(15b)
[(
) ]
ψ h (ς) = 2 ln 1 + y 2 / 2 ,
(15c)
where
y = (1 - 16ς)
1/4
.
(15d)
We ran the model with cyclic boundary conditions such that the thicknesses of
the ice and snow at the end of a year were used as inputs to the new year with the
same one-year (i.e., October 1982 to October 1983) NP-25 meteorological data
repeating. Computations ended when the ice thickness reached equilibrium.
In modeling sea ice there are usually two main problems. First, as mentioned
above, is choosing parameterizations for the main components of the surface heat
budget. Second is the external meteorological information. Because the iterative
procedure in models typically uses a one-day time step, daily averaged values of
the external parameters are necessary. Such information can be obtained in two
ways. One way is to average the 3-hour meteorological observations for each day.
Another is to interpolate the monthly averaged fields computed from many years
of data and tabulated in an atlas, Gorshkov (1983) for example, to obtain daily
values. The input data that this second method yields are more smooth than data
from the first method but less accurate.
For example, interpolating monthly data to daily values must produce a time
series of cloud amount that varies monotonically through the month in the same
manner year after year. Such a series is of little use for investigating interannual
variability.
On the other hand, producing 3-hour observations for the entire Arctic Basin
requires accurately interpolating daily averaged data measured at nonuniformly
distributed drifting buoys and polar stations. We mentioned above that, in prin-
ciple, daily averaged surface temperature, at least, should be available for the
entire basin from these sources. Then, using the method described above, it should
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