One-dimensional models for the closure of a coastal latent heat polynya

One-dimensional models for the closure of a coastal latent heat polynya due to the onshore drift of frazil ice and consolidated ice are presented in this paper. The models predict the width of a polynya during an opening and closing cycle and include the cases in which the collection thickness of consolidated new ice at the polynya edge (during opening) or at the coast (during closing) is (a) a prescribed constant or (b) parameterized in terms of the depth of frazil ice arriving at the polynya edge (during opening) or the coast (during closing) and the relative velocity of the frazil ice with respect to the "convergence boundary" (i.e., the consolidated ice during opening or the stationary coastal wall during closing). Four dimensionless parameters specify the opening and closing cycle of a polynya, and throughout most of the four-dimensional parameter space the closing timescale is shorter than the opening timescale. In this case, it is found that the heat released from the polynya to the atmosphere during opening exceeds that during closing. However, this inequality for the opening/closing heat fluxes can be reversed when the frazil ice production rate during closing exceeds that during opening. Two processes contribute to polynya closure: the onshore advection of consolidated new ice and the pileup of interior frazil ice at the coastal wall. Parameter regimes are identified where pileup of interior frazil ice at the coast plays a minor role in the closure of the polynya. The impact on the polynya closure time of rearrangement of the initial interior frazil ice distribution is also studied. It is also demonstrated that when meteorological conditions are such that the frazil ice production rate during polynya closing is negligible, the closing time is independent of the initial interior frazil ice distribution, provided that its volume per unit alongshore length is fixed and that the collection depth of consolidated new ice is constant. This invariance of the polynya closing time is found not to hold using the aforementioned parameterization for the collection depth. The model is used to simulate two opening and closing polynya events off the northern coast of Svalbard. The parameter values required for the simulations are estimated from time series of wind stress and air temperature, and the results are compared with published simulations in the refereed literature. For both events, the closing time is found to be much shorter than the opening time.