Initialization of Thermal Models in Cold and Warm Permafrost

Equilibrium modelling, also known as spin-up, is a technique for initializing a stable thermal regime in ground temperature models for permafrost regions. The results act as a baseline for subsequent transient analyses of ground temperature response to climate change or infrastructure. In practice, spin-up procedures are often loosely described or neglected, and the criteria by which a stable thermal regime is evaluated are rarely defined or presented explicitly. In this paper, model results show that no single criterion based on thresholds of inter-cycle temperature change can be used to identify a stable thermal regime in all spin-up scenarios. Results from simulations using a wide range of initialization temperatures and conditions show the number of spin-up cycles can range between 10 to 10,000, and a spin-up criterion as fine as 0.00001 ^oC/cycle is required to achieve a stable thermal regime suitable for deeper warm permafrost models. The implications of selected threshold criteria are examined in follow-up transient analyses and show that warm permafrost models can be highly sensitive to initial temperature profiles based on the criterion utilized. The results alert scientists and engineers to the importance of initialization on site-specific and regional permafrost models for transient ground temperature analyses.

A New Mitigation Measure to Counter Thermal Instability of Air-Cooled Embankment in Sandy Permafrost Zones of Tibet Plateau

A crushed-rock revetment (CRR) with high permeability that can be paved on embankment slopes is widely used to cool and protect the subgrade permafrost. In this study, a traditional CRR over warm permafrost was selected to investigate its cooling characteristics based on the ground temperature observed from 2003 to 2014. A new mitigation structure (NMS) was designed to improve the cooling capacity of the CRR and to counter the pore-filling of the rock layer. Numerical simulations were conducted to evaluate the cooling performance and reinforcing capacity of the NMS based on a developed heat and mass transfer model. The results indicate that the traditional CRR can improve the symmetry of the permafrost subgrade and decrease the ground temperature of shallow permafrost. However, the CRR cannot generate strong enough cooling to influence the deep (below 10 m depth) and warm permafrost with a mean annual ground temperature above −1.0°C. The wind-blown sand can further weaken the cooling of the CRR and cause significant permafrost warming and thawing beneath the slopes, posing a severe threat to the long-term safe operation of the embankment. The proposed NMS can produce a significantly superior cooling performance to the CRR. If the CRR is reinforced by the new structure, it can not only effectively cool the underlying warm permafrost but also elevate the permafrost table. The new structure can also protect the rock layer on the slopes from sand-filling. The NMS can be used as an effective method for roadbed design or maintenance over warm permafrost.

Equilibrium Spin-up of Cold and Warm Permafrost Models

<p>Initialization (spin-up) of a numerical ground temperature model is a critical but often neglected step for solving heat transfer problems in permafrost. Improper initialization can lead to significant underlying model drift in subsequent transient simulations, distorting the effects on ground temperature from future climate change or applied infrastructure.  In a typical spin-up simulation, a year or more of climate data are applied at the surface and cycled repeatedly until ground temperatures are declared to be at equilibrium with the imposed boundary conditions, and independent of the starting conditions.</p><p>Spin-up equilibrium is often simply declared after a specified number of spin-up cycles. In few studies, equilibrium is visually confirmed by plotting ground temperatures vs spin-up cycles until temperatures stabilize; or is declared when a certain inter-cycle-temperature-change threshold is met simultaneously at all depths, such as ∆T ≤ 0.01<sup>o</sup>C per cycle. In this study, we investigate the effectiveness of these methods for determining an equilibrium state in a variety of permafrost models, including shallow and deep (10 – 200 m), high and low saturation soils (S = 100 and S = 20), and cold and warm permafrost (MAGT = ~-10 <sup>o</sup>C and >-1 <sup>o</sup>C). The efficacy of equilibrium criteria 0.01<sup>o</sup>C/cycle and 0.0001<sup>o</sup>C/cycle are compared. Both methods are shown to prematurely indicate equilibrium in multiple model scenarios.  Results show that no single criterion can programmatically detect equilibrium in all tested models, and in some scenarios can result in up to 10<sup>o</sup>C temperature error or 80% less permafrost than at true equilibrium.  A combination of equilibrium criteria and visual confirmation plots is recommended for evaluating and declaring equilibrium in a spin-up simulation.</p><p>Long-duration spin-up is particularly important for deep (10+ m) ground models where thermal inertia of underlying permafrost slows the ground temperature response to surface forcing, often requiring hundreds or even thousands of spin-up cycles to establish equilibrium. Subsequent transient analyses also show that use of a properly initialized 100 m permafrost model can reduce the effect of climate change on mean annual ground temperature of cold permafrost by more than 1 <sup>o</sup>C and 3 <sup>o</sup>C under RCP2.6 and RCP8.5 climate projections, respectively, when compared to an identical 25 m model. These results have important implications for scientists, engineers and policy makers that rely on model projections of long-term permafrost conditions.</p>