Investigating the thermal state of permafrost with Bayesian inverse modeling of heat transfer

Long-term measurements of permafrost temperatures do not provide a complete picture of the Arctic subsurface thermal regime. Regions with warmer permafrost often show little to no long-term change in ground temperature due to the uptake and release of latent heat during freezing and thawing. Thus, regions where the least warming is observed may also be the most vulnerable to permafrost degradation. Since direct measurements of ice and liquid water contents in the permafrost layer are not widely available, thermal modeling of the subsurface plays a crucial role in understanding how permafrost responds to changes in the local energy balance. In this work, we first analyze trends in observed air and permafrost temperatures at four sites within the continuous permafrost zone, where we find substantial variation in the apparent relationship between long-term changes in permafrost temperatures (0.02–0.16 K yr−1) and air temperature (0.09–0.11 K yr−1). We then apply recently developed Bayesian inversion methods to link observed changes in borehole temperatures to unobserved changes in latent heat and active layer thickness using a transient model of heat conduction with phase change. Our results suggest that the degree to which recent warming trends correlate with permafrost thaw depends strongly on both soil freezing characteristics and historical climatology. At the warmest site, a 9 m borehole near Ny-Ålesund, Svalbard, modeled active layer thickness increases by an average of 13 ± 1 cm K−1 rise in mean annual ground temperature. In stark contrast, modeled rates of thaw at one of the colder sites, a borehole on Samoylov Island in the Lena River delta, appear far less sensitive to temperature change, with a negligible effect of 1 ± 1 cm K−1. Although our study is limited to just four sites, the results urge caution in the interpretation and comparison of warming trends in Arctic boreholes, indicating significant uncertainty in their implications for the current and future thermal state of permafrost.</p

A probabilistic analysis of permafrost temperature trends with ensemble modeling of heat transfer

Over the past few decades, polar research teams around the world have deployed long-term measurement sites to monitor changes in permafrost environments. Many of these sites include borehole sensor arrays which provide measurements of ground temperature as deep as 50 meters or more below the surface. Recent studies have attempted to leverage these borehole data from the Global Terrestrial Network of Permafrost to quantify changes in permafrost temperatures at a global scale. However, temperature measurements provide an incomplete picture of the Earth's subsurface thermal regime. It is well known that regions with warmer permafrost, i.e. where mean annual ground temperatures are close to zero, often show little to no long-term change in ground temperature due to the latent heat effect. Thus, regions where the least warming is observed may also be the most vulnerable to rapid permafrost thaw. Since direct measurements of soil moisture in the permafrost layer are not widely available, thermal modeling of the subsurface plays a crucial role in understanding how permafrost responds to changes in the local energy balance. In this work, we explore a new probabilistic method to link observed annual temperatures in boreholes to permafrost thaw via Bayesian parameter estimation and Monte Carlo simulation with a transient heat model. We apply our approach to several sites across the Arctic and demonstrate the impact of local landscape variability on the relationship between long term changes in temperature and latent heat

Learning Soil Freeze Characteristic Curves with Universal Differential Equations

Permafrost thaw is considered one of the major climate feedback processes and is currently a significant source of uncertainty in predicting future climate states. Coverage of in-situ meteorological and land-surface observations is sparse throughout the Arctic, making it difficult to track the large-scale evolution of the Arctic surface and subsurface energy balance. Furthermore, permafrost thaw is a highly non-linear process with its own feedback mechanisms such as thermokarst and thermo-erosion. Land surface models, therefore, play an important role in our ability to understand how permafrost responds to the changing climate. There is also a need to quantify freeze-thaw cycling and the incomplete freezing of soil at depth (talik formation). One of the key difficulties in modeling the Arctic subsurface is the complexity of the thermal regime during phase change under freezing or thawing conditions. Modeling heat conduction with phase change accurately requires estimation of the soil freeze characteristic curve (SFCC) which governs the change in soil liquid water content with respect to temperature and depends on the soil physical characteristics (texture). In this work, we propose a method for replacing existing brute-force approximations of the SFCC in the CryoGrid 3 permafrost model with universal differential equations, i.e. differential equations that include one or more terms represented by a universal approximator (e.g. a neural network). The approximator is thus tasked with inferring a suitable SFCC from available soil temperature, moisture, and texture data. We also explore how remote sensing data might be used with universal approximators to extrapolate soil freezing characteristics where in-situ observations are not available

An energy conserving method for simulating heat transfer in permafrost with hybrid modeling

Rapid climate change has lead to widespread warming of land surface temperatures throughout the Arctic, thereby accelerating the thawing of perennially frozen, carbon-rich soil, most commonly referred to as permafrost. Subsurface modeling of heat and water transport plays a key role in understanding how past, present, and future changes in the climate affect the rate and extent of permafrost thaw. We propose a novel hybrid modeling approach for solving by reparameterizing it as a universal partial differential equation, where the inverse enthalpy operator is represented by a universal approximator. Such a method would alleviate one of the major numerical difficulties in the simulation of two-phase heat transport and would allow for efficient and flexible modeling of permafrost at large time scales

Rapid climate change drives soil temperature warming and permafrost thaw on Svalbard

Svalbard is a hotspot of climate change in the rapidly warming Arctic. The strong air temperature warming coincides with a multitude of changes in other climate variables such as liquid precipitation, snow cover, and the surface energy budget components. These changes have highly complex effects on the soil temperature and freezing conditions. We investigate seasonal patterns of change in climate and soil conditions at the Bayelva study site close to Ny-Ålesund, Svalbard for the period 1998-2020. We use Bayesian inference to estimate trends in monthly mean values of air and soil temperature, radiation fluxes, sensible and latent heat flux, liquid precipitation, snow depth, and soil moisture. We then apply PCMCI+, a recently developed causal inference framework, in order to quantify the contributions of all meteorological variables to soil warming. Air temperature at the Bayelva site rose in all months of the year in the last 23 years (1998-2020). This trend has been particularly strong in April (1.3°C/10years), September (1.5°C/10years) and October (1.9°C/10years). The strong changes in spring and autumn led to earlier snowmelt (-14 days/10 years, 2007-2020) and more snow free days (+26 days/10years, 2007-2020). We observe later soil freezing in October and lower snow depth. Furthermore, strong rain events have become more frequent in winter, which contributed to soil warming. As a result of changes in air temperature, water fluxes, and the energy budget, top soil temperature increased in particular during spring (May/June 1.4°C/10years, 1998-2020). Our results illustrate how rapid climate change drives soil warming and permafrost thaw. They can help to validate results from climate and land surface models as well as aid in future predictions of landscape changes in Svalbard