  We present a mathematical model describing the evolution of sea ice and
meltwater during summer. The system is described by two coupled partial
differential equations for the ice thickness $h$ and pond depth $w$ fields. We
test the sensitivity of the model to variations of parameters controlling
fluid-dynamic processes at the pond level, namely the variation of turbulent
heat flux with pond depth and the lateral melting of ice enclosing a pond. We
observe that different heat flux scalings determine different rates of total
surface ablations, while the system is relatively robust in terms of
probability distributions of pond surface areas. Finally, we study pond
morphology in terms of fractal dimensions, showing that the role of lateral
melting is minor, whereas there is evidence of an impact from the initial sea
ice topography.
