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. Thermokarst lake dynamics, which play an essential role in carbon releasedue to permafrost thaw, are affected by various geomorphological processes.In this study, we derive a three-dimensional (3D) Stefan equation tocharacterize talik geometry under a hypothetical thermokarst lake in thecontinuous permafrost region. Using the Euler equation in the calculus ofvariations, the lower bounds of the talik were determined as an extremum ofthe functional describing the phase boundary area with a fixed total talikvolume. We demonstrate that the semi-ellipsoid geometry of the talik isoptimal for minimizing the total permafrost thaw under the lake for a givenannual heat supply. The model predicting ellipsoidal talik geometry wascompared to talik thickness observations using transient electromagnetic(TEM) soundings in Peatball Lake on the Arctic Coastal Plain (ACP) ofnorthern Alaska. The depth : width ratio of the elliptical sub-lake talik cancharacterize the energy flux anisotropy in the permafrost, although the lakebathymetry cross section may not be elliptic due to the presence ofnear-surface ice-rich permafrost. This theory suggests that talikdevelopment deepens lakes and results in more uniform horizontal lakeexpansion around the perimeter of the lakes, while wind-induced waves andcurrents are likely responsible for the elongation and orientation ofshallow thermokarst lakes without taliks in certain regions such as the ACPof northern Alaska.

A new Stefan equation to characterize the evolution of thermokarst lake and talik geometry