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

Abstract

Abstract. 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 K yr−1 to 0.16 K yr−1) and air temperature (0.09 K yr−1 to 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 thaw depth 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 and variations in latent heat is heavily dependent on both local soil properties as well as historical climatology. At the warmest site, a nine meter borehole near Ny-Ålesund, Svalbard, modeled annual maximum thaw depth increases by an average of (12 ± 1) cm K−1 rise in mean annual ground temperature. In stark contrast, modeled thaw rates for a borehole on Samoylov Island in the Lena River Delta (northeastern Siberia) appear far less sensitive to temperature change, with an almost negligible increase 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 substantial uncertainty in their implications for the current and future thermal state of permafrost.

Ground Heat Flux Reconstruction Using Bayesian Uncertainty Quantification Machinery and Surrogate Modeling

“…However, in both studies, forward model results are directly used in the calibration process or in the likelihood function, which can be computationally costly for complex models. Cleary et al (2021) and Groenke et al (2022) have applied the ensemble Kalman sampling (EKS) algorithm to generate approximate samples from the parameter posterior. The EKS method requires a multivariate Gaussian prior distribution over parameters (which may not usually be the case) and will underestimate posterior variance with finite algorithm iterations.…”

“…(2021) and Groenke et al. (2022) have applied the ensemble Kalman sampling (EKS) algorithm to generate approximate samples from the parameter posterior. The EKS method requires a multivariate Gaussian prior distribution over parameters (which may not usually be the case) and will underestimate posterior variance with finite algorithm iterations.…”