Calculating Lateral Frost Front Penetration in a Rapidly Retreating Cliff of Fine Sediments

Abstract

An adapted version of the Stefan equation (CLIFFSE) was tested to predict lateral progression of the frost front into cohesive sediments that form coastal cliffs along the north shore of the maritime estuary and gulf of the St Lawrence River (Quebec, Canada). The equation was adapted to accommodate the influence of cliff erosion on lateral penetration of freezing and thawing into vertical cliff faces. As the cliff erodes, freezing and thawing are initiated from the newly revealed surface. Frost progression and erosion were measured with an automated thermal erosion pin system. Measured observations agreed with predictions from the adapted equation (78 to 99% of the variability explained). Erosion associated with thawing front progression during winter warm spells led to a relative reduction in the frost front depth. Subsequently, progression of the frost front into the cliff contributed to an additional 50 cm of sediment freezing and erosion by the end of the cold season, which was not predicted by the original Stefan equation. Our findings support the hypothesis that multiple warm spells influence the amount of lateral penetration of the frost front in vertical cliffs. Copyright © 2015 John Wiley & Sons, Ltd.