The most dynamic electromagnetic coupling between the magnetosphere and
ionosphere occurs in the polar upper atmosphere. It is critical to
quantify the electromagnetic energy and momentum input associated with
this coupling as its impacts on the ionosphere and thermosphere system
are global and major, often leading to considerable disturbances in
near-Earth space environments. The current general circulation models of
the upper atmosphere exhibit systematic biases that can be attributed to
an inadequate representation of the Joule heating rate resulting from
unaccounted stochastic fluctuations of electric fields associated with
the magnetosphere-ionosphere coupling. These biases exist regardless of
geomagnetic activity levels. To overcome this limitation, a new
multiresolution random field modeling approach is developed, and the
efficacy of the approach is demonstrated using SuperDARN data carefully
curated for the study during a largely quiet 4 hours period on February
29, 2012. Regional small-scale electrostatic fields sampled at different
resolutions from a probabilistic distribution of electric field
variability conditioned on actual SuperDARN LOS observations exhibit
considerably more localized fine-scale features in comparison to global
large-scale fields modeled using the SuperDARN Assimilative Mapping
procedure. The overall hemispherically integrated Joule heating rate is
increased by a factor of about 1.5 due to the effect of random regional
small-scale electric fields, which is close to the lower end of
arbitrarily adjusted Joule heating multiplicative factor of 1.5 and 2.5
typically used in upper atmosphere general circulation models. The study
represents an important step towards a data-driven ensemble modeling of
magnetosphere-ionosphere-atmosphere coupling processes.