  Our ability to predict the future of Arctic sea ice is limited by ice's
sensitivity to detailed surface conditions such as the distribution of snow and
melt ponds. Snow on top of the ice decreases ice's thermal conductivity,
increases its reflectivity (albedo), and provides a source of meltwater for
melt ponds during summer that decrease the ice's albedo. In this paper, we
develop a simple model of pre-melt snow topography that accurately describes
snow cover of flat, undeformed Arctic sea ice on several study sites for which
data was available. The model considers a surface that is a sum of randomly
sized and placed "snow dunes" represented as Gaussian mounds. This model
generalizes the "void model" of Popovi\'c et al. (2018) and, as such,
accurately describes the statistics of melt pond geometry. We test this model
against detailed LiDAR measurements of the pre-melt snow topography. We show
that the model snow-depth distribution is statistically indistinguishable from
the measurements on flat ice, while small disagreement exists if the ice is
deformed. We then use this model to determine analytic expressions for the
conductive heat flux through the ice and for melt pond coverage evolution
during an early stage of pond formation. We also formulate a criterion for ice
to remain pond-free throughout the summer. Results from our model could be
directly included in large-scale models, thereby improving our understanding of
energy balance on sea ice and allowing for more reliable predictions of Arctic
sea ice in a future climate.
