| Summary: | We present a model for the formation and evolution of melt ponds on sea ice, written as a dynamical system on a network. These ponds have long been suggested as a contributing factor to the discrepancy between observed and predicted sea ice extent; ponds have a lower albedo than bare ice, so they contribute to the ice-albedo feedback. Of particular interest here is the geometry and topology of the ponds as they grow and connect. It has been observed that there is a change in the fractal dimension of the pond system. Further, it has been suggested that pond systems go through a percolation process with ponds connecting across a whole oe at a phase transition, and that a percolation threshold plays a key role in pond dynamics. We present a physically based network model for systems of ponds, which can be used to examine both their individual and collective behaviour. Each pond initially occupies a distinct catchment basin, modelled as a node; a di erential equation represents the melting dynamics, and mass conservation governs the evolution of the pond volume and water level. Ponds can connect together through uxes of water between catchment basins, represented by edges. Ponds can also drain into the sea, through another form of edge. We use the model to explore how the evolution of pond area and hence melting depends on model parameters, and nd that it depends most sensitively on surface roughness and the timing of onset of drainage from the ponds. We qualitatively reproduce the observed transition in fractal dimension as the ponds grow, and the typical life-cycle of the pond system, with the areal coverage growing, then shrinking as the ponds drain to sea level, and then slowly increasing again. We examine the importance of percolation thresholds, and in some cases, nd evidence of anomalous percolation. We also use model results to predict the extent of pond coverage in the future, warming Arctic.
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