Table 9. Modeled characteristics of a sea ice cover based on various longwave
parameterizations and the data from North Pole 25 from October 1982 to Oc-
tober 1983. Computed sea ice variables are the maximum and minimum thick-
ness, the amplitude (∆h) of the annual variation in thickness, and the dates
on which melting first begins in the snowpack and cooling in the sea ice be-
gins.
∆h
Maximum
Minimum
Experiment
(m)
(m)
(m)
Melting
Cooling
1.
Brunt, eq 7, day*
6.50
5.78
0.72
May 20
Sept 10
2.
Marshunova, eq 9, day
4.40
3.45
0.95
May 25
Sept 11
3.
Maykut, eq 10, day
4.96
4.19
0.77
May 24
Sept 10
4.
Satterlund, eq 11, day
5.09
4.17
0.92
May 24
Sept 12
5.
KL&A, eq 12, day
3.94
2.93
1.01
May 26
Sept 12
6.
KL&A, eq 12, day, rec
3.87
2.85
1.02
May 25
Sept 12
7.
KL&A, eq 12, month
4.67
3.83
0.84
May 24
Sept 11
8.
KL&A, eq 12, month, sum
4.61
3.77
0.84
May 25
Sept 11
9.
KL&A, eq 12, month, win
3.99
2.97
1.02
May 25
Sept 12
10.
Marshunova, eq 9, month
4.36
3.39
0.97
May 29
Sept 11
11.
Marshunova, eq 9, month, sum
4.37
3.41
0.96
May 27
Sept 11
12.
Marshunova, eq 9, month, win
4.38
3.42
0.96
May 27
Sept 11
* To identify the different numerical experiments, we use the following shorthand: "day" used
daily averaged observations of total cloud amounts; "day, rec" used daily averaged total cloud
amounts for winter reconstructed from air temperature using eq 4; "month" used monthly cloud
data interpolated to daily values; "month, sum" used daily averaged data for the winter but
monthly averaged cloud data interpolated to daily values for the summer; "month, win" used
daily averaged data for the summer but monthly averaged data interpolated to daily values
for the winter.
also be possible to estimate daily averaged total cloud amount on an arbitrary grid
throughout the basin.
The method for describing cloud amount can, of course, have a significant
influence on the computed longwave radiation balance in particular. The
parameterizations for Fdn and B by Brunt, Marshunova, and Satterlund account
for clouds with linear functions. Therefore, monthly averaged values of Fdn and B
should not differ regardless of whether they were obtained from 3-hour cloud
observations averaged to daily values or from monthly cloud amounts interpo-
lated to daily values--provided, of course, that the monthly cloud values are based
on the same 3-hour observations. In contrast, Maykut and Church's and KL&A's
parameterizations for Fdn and B depend nonlinearly on cloud amount. For these,
the type of averaging is crucial.
Table 9 lists numerical model calculations of the equilibrium sea ice thickness
and related variables computed using the various parameterizations for longwave
radiation that we have been discussing and the various ways of representing cloud
data. All the other meteorological information used in these numerical experiments,
including the incoming shortwave radiation, are daily averages computed from
3-hour observations.
We see in Table 9 that the spread in the computed maximum and minimum ice
thicknesses based on the various parameterizations for Fdn (i.e., experiments 15)
is rather large. The seasonal amplitude in ice thickness also varies widely--from
0.72 m with the Brunt parameterization to 1.01 m with the KL&A parameteriza-
tion. The KL&A parameterization (i.e., experiment 5) yields an equilibrium thick-
ness closest to the usually accepted value (e.g., Semtner 1976, Hibler 1979). The
results of experiment 6 in the table are also very interesting. Here the cloud amounts
20
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