An analytical coupled ice-cream model is considered which is forced by a specified wind stress acting on the open ocean as well as the ice. The analysis supports the conjecture that the upwelling dynamics at ice edges can be understood by means of a simple analytical model. In similarity with coastal problems it is shown that the ice edge upwelling is determined by the net mass flux at the boundaries of the considered region. The model is used to study the sensitivity of the upwelling dynamics in the marginal ice zone to variation in the controlling parameters. These parameters consist of combinations of the drag coefficients used in the parameterization of the stresses on the three interfaces atmosphere-ice, atmosphere-ocean, and ice-cream. The response is shown to be sensitive to variations in these parameters in that one set of parameters may give upwelling while a slightly different set of parameters may give downwelling.