ESTIMATING TOTAL CLOUD AMOUNT IN THE WINTER
Although the spatial and temporal variability of Arctic clouds are some of the
poorest documented parameters required for modeling the polar atmosphere and
sea ice cover, numerical experiments with atmospheric general circulation models
show that these models have the highest sensitivity to just these parameters (e.g.,
Cess et al. 1989). To improve and validate regional sea ice models and atmospheric
general circulation models, it is therefore crucially important to develop an adequate
description of cloud parameters and their spatial and temporal variability.
One possible way to increase the reliability of cloud descriptions is a method of
statistical modeling that we have developed based on a correlation analysis using
surface-layer air temperature (T) and total cloud amount during the winter. Our
analyses of archival data from the North Pole drifting stations show that the cor-
relation coefficients between T and total cloud amount (n) and between T and low
cloud amount (nL) for observations from November to March are, on average, 0.6
with a significance level of 0.1 in the central Arctic.
It should be noted that, because on the drifting stations there were 48 observa-
tions per day, proximate observations may be correlated. That is, all the paired
temperature and cloud observations may not be independent. To test whether this
inherent correlation affected our analysis, we repeated the correlation analysis
twice, first using only one observation per day and then using one observation
every five days. These analyses, however, yielded the same correlation coefficient
that we gave above.
We also calculated the correlation coefficients between air temperature and cloud
amounts in time series for individual months from November to March. Again,
the correlation coefficients, on average, exceed 0.6. For October data, we also found
significant correlation between temperature and cloud amounts, but the correla-
tion was a little lower.
Based on the significant correlation between T and n and between T and nL, it
might seem possible to use a linear equation to estimate 3-hour cloud amounts
from 3-hour temperature data. Such a method, however, is not justified since tem-
perature is nearly normally distributed while cloud amount has a U-shaped dis-
tribution. Quite simply, if a random variable is normally distributed (in this case,
air temperature), any new random variable obtained from it with a linear trans-
formation (presumably the cloud amount) will also be normally distributed. Thus,
because we require that any predicted time series of n or nL have a U-shaped dis-
tribution, we cannot use standard statistical modeling methods to exploit the
observed high correlation between T and n and between T and nL but must,
instead, use a more complicated statistical algorithm.
For predicting cloud amounts using air temperature data, we begin with the
explicit form of the frequency distribution of total cloud amount in the Arctic
Basin. This is U-shaped; we fit it with a beta distribution. The probability density
function of a beta distribution, f(x), for random variable x in the interval [0,1] is
(e.g., Harr 1977, Aivazyan et al. 1983)
Γ(α + β)
xα -1 (1 - x)
β -1
f (x) =
for 0 ≤ x ≤ 1,
(1a)
Γ(α) Γ(β)
= 0
otherwise,
(1b)
where Γ is the gamma function.
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