Penitentes and suncups are structures formed as snow melts, typically high in the mountains. When the snow is dirty, dirt cones and other structures can form instead. Sunlight, heating from air, and dirt all play a role in the formation of structure on an ablating snow surface. Recently, laboratory experiments by Vance Bergeron and Charles Berger reproduced penitente-like structures in a controlled environment. In this talk I'll present a minimal model for the formation of ablation morphologies as a function of measurable parameters. The model gives a single-parameter expression for the melting rate as a function of dirt thickness, which agrees well with a set of measurements by Driedger. The dependence of ablation morphologies on weather conditions and initial dirt thickness are studied, including the initial growth of perturbations away from a flat surface and the nonlinear development and evolution of spatial structure. I will also discuss other applications of this type of modeling.