Analytical prediction of active-layer thaw and subsidence under seasonal thermal forcing: application to Svalbard permafrost

Land Mccormick, Dina Schmidt

Seasonal thaw of the active layer and the resulting ground subsidence strongly influence Arctic hydrology, soil-carbon release, and the stability of northern infrastructure. Lunardini (1987) derived an exact similarity solution for one-dimensional thaw in frozen soil that consolidates as it thaws. Although physically elegant, the solution has remained difficult to use in practice: usable limiting formulas are lacking, parameter sensitivities remain unquantified, and performance under transient seasonal forcing has not been independently tested. Its field-scale value for active-layer and thaw-settlement prediction therefore remains largely unresolved. Here we revisit Lunardini’s solution with these needs in mind. We derive closed-form small- and large-Stefan-number approximations for the thaw parameter, with errors of about 2% in the small-Stefan permafrost regime and about 1.3% in the large-Stefan regime. We then quantify dimensionless sensitivity coefficients and show that the thaw parameter responds sub-proportionally to all major inputs, with the largest controls coming from the Stefan number and the degree of initial subcooling. An independent enthalpy finite-difference model reproduces the exact solution with a mean error of 2.5%, providing a check on the implementation and a tool for transient forcing. When the similarity solution is applied to a season-mean surface temperature, it overpredicts the end-of-season active-layer thickness by roughly 8% and advances the thaw trajectory by about 2 weeks. In an illustrative Svalbard application at the Calypsostranda CALM site in Bellsund, using representative seasonal forcing and independently specified fine-soil properties, the model predicts an active-layer thickness close to the reported historical mean and a drained kinematic thaw-settlement estimate of about 5.5 cm. These results turn an exact but underused analytical solution into a practical tool for rapid active-layer and thaw-settlement estimates, while also defining when a transient numerical model is still needed.