Preprints
https://doi.org/10.5194/tc-2021-192
https://doi.org/10.5194/tc-2021-192

  30 Aug 2021

30 Aug 2021

Review status: this preprint is currently under review for the journal TC.

Three-Dimensional Stefan Equation for Thermokarst Lake and Talik Geometry Characterization

Noriaki Ohara1, Benjamin M. Jones2, Andrew D. Parsekian3,1, Kenneth M. Hinkel4, Katsu Yamatani5, Mikhail Kanevskiy2, Rodrigo C. Rangel3, Amy L. Breen6, and Helena Bergstedt2 Noriaki Ohara et al.
  • 1Department of Civil and Architectural Engineering, University of Wyoming, Laramie, WY, 82071, USA
  • 2Institute of Northern Engineering, University of Alaska Fairbanks, Fairbanks, Alaska,99775, USA
  • 3Department of Geology and Geophysics, University of Wyoming, Laramie, WY 82071, USA
  • 4Department of Geological and Mining Engineering and Sciences, Michigan Technological University, Houghton, MI 49931, USA
  • 5Department of Urban Science, Meijo University, 4-102-9 Yataminami, Higashi, Nagoya 461- 8534, Japan
  • 6International Arctic Research Center, University of Alaska Fairbanks, Fairbanks, Alaska

Abstract. Thermokarst lake dynamics, which plays an essential role in carbon release due to permafrost thaw, is affected by various geomorphological processes. In this study, we derive a three-dimensional (3D) Stefan equation to characterize talik geometry under a hypothetical thermokarst lake in the continuous permafrost region. Using the Euler equation in the calculus of variations, the lower bounds of the talik were determined as an extremum of the functional describing the phase boundary area with a fixed total talik volume. We demonstrate that the semi-ellipsoid geometry of the talik is optimal for minimizing the total permafrost thaw under the lake for a given annual heat supply. The model predicting ellipsoidal talik geometry was verified by talik thickness observations using transient electromagnetic (TEM) soundings in Peatball Lake on the Arctic Coastal Plain (ACP) of Alaska. The lake width-depth ratio of the elliptic talik can characterize the energy flux anisotropy in the permafrost although the lake bathymetry cross section may not be elliptic due to the presence of near-surface ice-rich permafrost. This theory suggests that talik development stabilizes thermokarst lakes by ground subsidence due to permafrost thaw while wind-induced waves and currents are likely responsible for the elongation and orientation of thermokarst lakes in certain regions such as the ACP of northern Alaska.

Noriaki Ohara et al.

Status: open (until 25 Oct 2021)

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Noriaki Ohara et al.

Noriaki Ohara et al.

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Short summary
New variational principle suggests that semi-ellipsoid talik shape (3D Stefan equation) is optimum for incoming energy. However, the lake bathymetry tends to be less ellipsoidal due to the ice rich layers near surface. Wind-wave erosion is likely responsible for the elongation of lakes while thaw subsidence slows the wave effect and stabilizes the thermokarst lakes. The derived 3D Stefan Equation was tested by the field observed talik thickness data using geophysical methods.