Snow topography on undeformed Arctic sea ice captured by an idealized model

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, and provides a source of meltwater for melt ponds during summer that decrease the ice's albedo. Here, we develop a simple model of pre-melt ice surface topography that accurately describes snow cover on flat, undeformed ice. 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 Popovic 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.