Reply on RC1

Noriaki Ohara

doi:10.5194/tc-2021-192-ac1

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.

Highlights

Thermokarst lakes are abundant in regions underlain by ice-rich permafrost including the Arctic Coastal Plain (ACP) of northern Alaska, northwestern Canada and Siberia (Grosse et al, 2013)
The theory presented here addresses the origin of the thermokarst lake ellipticity on the ACP. Elliptic lake geometry results from minimizing overall thawing energy consumption for a given incoming energy load
As the vertical temperature slope diminishes with talik maturation, the depth546 width ratio of the talik becomes larger creating a deeper talik; much of incoming energy is 547 likely consumed for vertical rather than horizontal expansion

Summary

Introduction

Thermokarst lakes are abundant in regions underlain by ice-rich permafrost including the Arctic Coastal Plain (ACP) of northern Alaska, northwestern Canada and Siberia (Grosse et al, 2013). If the lake bed has a mean annual temperature greater than 0 ֯C, the sub-lake permafrost will begin to thaw (Burn, 2002; Arp et al, 2016) This typically occurs in lakes deeper than the maximum winter ice thickness, where the ice cover floats above an unfrozen water body. In this case, unfrozen lake bed sediments persist and the thaw front continues to penetrate deeper into the underlying permafrost. The talik increases in thickness and lake bed subsidence continues as long as the thawing permafrost is ice-rich

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