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.

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 (*n*L) 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 *n*L, 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 *n*L 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 *n*L 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)

β -1

for 0 ≤ *x *≤ 1,

(1a)

Γ(α) Γ(β)

= 0

otherwise,

(1b)

where Γ is the gamma function.

10