Abstract The weathering crust is a layer of porous ice that can form at the surface of an ice sheet. It grows and decays in response changing weather and climate conditions, affecting the albedo, the melt rate and the transport of meltwater across the surface. To understand this behaviour, we seek time-dependent solutions to a continuum, thermodynamic model for the porosity, temperature and thickness of the weathering crust, and the internal and surface melt rates. We find solutions using a numerical enthalpy method, presented in this study. We use idealized ‘switching’ and sinusoidal forcings to explore the different dynamics exhibited during growth and decay, the timescales involved, and the impact of diurnal vs. annual variations. The results demonstrate qualitative agreement with observations, and provide insight into the relative importance of different surface heat fluxes during the growth and decay of the crust. The model therefore provides a useful tool for exploring the response of the weathering crust to climate change.