Variations in permafrost thickness in response to changes in paleoclimate

Abstract

Solutions to the Stefan problem for the motion of the base of ice‐bearing permafrost in response to changes in paleoclimate were obtained using perturbation, finite difference, and finite element methods. Paleotemperature models were used to investigate the thickness response, to compare solution methods, to determine the current state of the permafrost, and to determine constraints on the models. The perturbation and finite difference methods used the approximation of linear temperature profiles, while the finite element method did not. There was a transient thickness response of about 41 kyr, implying that paleotemperature records of greater length are needed for models and that the permafrost loses its “memory” of past conditions for much longer times. Faster thawing rates, slower freezing rates, and greater variations in thickness were found for the perturbation and finite difference solutions compared to the finite element solution. These results appear to be caused by the simplifying assumptions in the former solutions. A lag (about 20 kyr) exists between changes in surface temperature and thickness response, and a small thermal offset is apparent in the finite element solution. Small asymmetries exist in the freezing and thawing rates and the thickness response. Paleotemperature models based on ice cores predict current permafrost thicknesses that are too large. Models with the long‐term mean surface temperature of permafrost within a few degrees of the current value of −11°C and with the last glacial period temperatures no more than 6°–8°C lower are compatible with current Prudhoe Bay conditions. These include models developed for East Siberia, from isotopic profiles in deep‐sea sediments, and for Barrow, Alaska, modified for Prudhoe Bay. These models predict that the permafrost thickness at Prudhoe Bay varied by about ±10% or less (±60 m) over the last glacial cycle. Freezing and thawing rates were less than 6 mm yr−1. At present this permafrost should be near its long‐term equilibrium thickness and thawing at <1 mm yr−1.

Advancement toward coupling of the VAMPER permafrost model within the Earth system model &lt;I&gt;i&lt;/I&gt;LOVECLIM (version 1.0): description and validation

“…In these cases, a larger time step in their numerical simulations (usually 1 month or 1 year) (e.g., Osterkamp and Gosink, 1991;Lebret et al, 1994;Lunardini, 1995;Delisle, 1998) is assumed since they only need to force the models with the low-frequency changes in air temperature or ground temperature that occur over millennia. At this timescale, it is not necessary to use a sub-annual time step.…”

Past climate changes and permafrost depth at the Lake El'gygytgyn site: implications from data and thermal modeling

“…In this paper, we focus on the characterization of the thermal field beneath and around the lake, studying the influence of variations of thermal properties and past ground surface temperature changes using numerical modeling techniques (e.g. Osterkamp and Gosink, 1991;Galushkin, 1997;Mottaghy and Rath, 2006;Holmén et al, 2011). In the recent years, the impact of climate change on permafrost formation and evolution has become a particular subject of interest.…”

Coupled Northern Hemisphere permafrost–ice-sheet evolution over the last glacial cycle

“…17). A slow convergence with a timescale longer than 100 kyr for permafrost thickness has been already shown by Osterkamp and Gosink (1991) for a deep permafrost site in Alaska using idealized surface temperature forcing over the past three glacial cycles. The present-day permafrost thickness simulated starting during different past interglacials shows a particularly slow convergence over some deep permafrost regions (Fig.…”

“…Since rock is always water-free in the model and thus no phase changes can occur, the presence of permafrost in rock does not affect heat conduction and just indicates that the temperature conditions would potentially be favorable for water, if present, to freeze. In other models, permafrost is defined by the −1 • C isotherm (Kitover et al, 2013;Osterkamp and Gosink, 1991) or by the melting point temperature (Tarasov and Peltier, 2007).…”

“…Assuming that the geothermal heat flow did not notably change over the Quaternary, the present permafrost state has been shaped mainly by past surface ground temperature variations (Osterkamp and Gosink, 1991). The formation time of deep permafrost can take several 100 000 years, and it is therefore possible that some, perhaps most, of current permafrost had its origin at the beginning of the Pleistocene era (Lunardini, 1995).…”