Table 7. Monthly averages of the coefficient cM for use in eq 9, derived by Marshunova (1961)
from observations at various Arctic stations.
J
F
M
A
M
J
J
A
S
O
N
D
Tikhaya Bay
0.27
0.29
0.29
0.24
0.24
0.22
0.19
0.19
0.21
0.25
0.26
0.28
Cape Zhelaniya
0.29
0.29
0.29
0.24
0.24
0.22
0.19
0.18
0.21
0.22
0.26
0.28
Chetyrekhstolbovoy Island
0.27
0.27
0.25
0.24
0.22
0.19
0.16
0.19
0.22
0.25
0.25
0.27
Cape Schmidt
0.25
0.25
0.20
0.25
0.24
0.18
0.16
0.19
0.22
0.25
0.27
0.26
NP-3, NP-4, 1954-1957
0.30
0.30
0.30
0.28
0.27
0.24
0.22
0.23
0.27
0.29
0.30
0.30
tic. The coefficients aM and bM are different, however, and accounting for the in-
fluence of clouds occurs directly in the formula for Fdn:
(
) (1 + cM n) ,
ε * = aM + bM e1/2
(9)
where n is again the fractional total cloud amount. Tables 6 and 7 list the aM, bM,
and cM coefficients that Marshunova obtained from monthly averaged values of B
and n observed at several polar stations and on drifting stations NP-3 and NP-4 in
19541957.
We see from Tables 6 and 7 that the empirical coefficients in eq 9 have clear spa-
tial and temporal variability and are, thus, not universal. The variations in cM (Table
7) are especially pronounced. The variability in aM, bM, and cM is likely connected
with the types of air masses and clouds prevalent in a region, a variability we
earlier documented in Table 1.
Maykut and Church's method
On analyzing 3000 hourly observations of air temperature, humidity, incoming
longwave radiation, and cloud amount collected during a year at Barrow, Alaska,
Maykut and Church (1973) developed the following expression for the effective
emittance of the polar atmosphere:
ε* = 0.7855 (1+0.2232n2.75) ,
(10)
where, as above, n is the fractional total cloud amount. The difference between this
and previous parameterizations is that here the influence of water vapor on incom-
ing longwave radiation is taken into account indirectly in the empirical coefficients.
Satterlund's method
For parameterizing the effective emittance, Satterlund (1979) offers a function
of air temperature and vapor pressure that Brutsaert (1982) claims describes
longwave radiation well at low temperatures:
[
)] ,
(
ε * = 1.08 1 - exp -eT/2016
(11)
where T is in kelvins and e is in millibars. As with Brunt's method, Satterlund
accounts for cloud effects by using a multiplier in the longwave radiation balance
as in eq 8.
Knig-Langlo and Augstein's method
For effective emittance, Knig-Langlo and Augstein (1994; henceforth, KL&A)
suggest
ε * = aK + bK n3 ,
(12)
15
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