Thaw lake expansion in a two‐dimensional coupled model of heat transfer, thaw subsidence, and mass movement

Abstract

Thaw lakes, widespread in permafrost lowlands, expand their basins by conduction of heat from warm lake water into adjacent permafrost, subsidence of icy permafrost on thawing, and movement of thawed sediment from lake margins into basins by diffusive and advective mass wasting. We describe a cross‐sectional numerical model with thermal processes and mass wasting. To test the model and provide an initial investigation of its utility, the model is driven using historical daily temperatures and permafrost conditions for the northern Seward Peninsula, Alaska (NSP; thick syngenetic ice, mean annual air temperature (MAAT) −6°C) and Yukon coastal plain (YCP; thin epigenetic ice, MAAT −10°C). In the model, lakes develop dynamic equilibrium profiles that are independent of initial morphology. These profiles migrate outward episodically and match the morphology of profiles from lakes that were measured at each site. Modeled NSP lakes expand more rapidly than YCP lakes (0.26 versus 0.10 m a−1) under respective modern climates. When identical climates are imposed, NSP lakes still grow more rapidly because their deeper basins and steeper bathymetric slopes move thawed insulating sediment away from the lake margin. In sensitivity tests, an increase of 3°C in MAAT causes 2.5× (NSP) and 1.6× (YCP) faster expansion of lakes. An 8°C decrease essentially halts expansion for both sites, consistent with paleostudies which attribute basins to postglacial warming. In the model, basins expand monotonically but lakes do not. The 1σ interannual variability of lake expansion is 0.51 (NSP) and 0.44 m a−1 (YCP), with single year rates of up to ±8 m occurring because of instabilities from thermal/mass movement coupling even under a stationary climate. This variability is likely a minimum estimate, compared to natural variability, and suggests that long measurement time series, of basins not lake surfaces, would best detect thermokarst acceleration resulting from a climate change.