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Penitentes and suncups are structures formed as snow melts, typically high inthe mountains. When the snow is dirty, dirt cones and other structures can forminstead. Building on previous field observations and experiments, this workpresents a theory of ablation morphologies, and the role of surface dirt indetermining the structures formed. The glaciological literature indicates thatsunlight, heating from air, and dirt all play a role in the formation ofstructure on an ablating snow surface. The present work formulates amathematical model for the formation of ablation morphologies as a function ofmeasurable parameters. The dependence of ablation morphologies on weatherconditions and initial dirt thickness are studied, focusing on the initialgrowth of perturbations away from a flat surface. We derive a single-parameterexpression for the melting rate as a function of dirt thickness, which agreeswell with a set of measurements by Driedger. An interesting result is theprediction of a dirt-induced travelling instability for a range of parameters.Comment: 28 pages, 13 figure

Theory of structure formation in snowfields motivated by penitentes, suncups, and dirt cones