Reconstructing historical climate change from deep ground temperature measurements in cold regions is often complicated by the presence of permafrost. Existing methods are typically unable to account for latent heat effects due to the freezing and thawing of the active layer. In this work, we propose a novel method for reconstructing historical ground surface temperature (GST) from borehole temperature measurements that accounts for seasonal thawing and refreezing of the active layer. Our method couples a recently developed fast numerical modeling scheme for two-phase heat transport in permafrost soils with an ensemble-based method for approximate Bayesian inference. We evaluate our method on two synthetic test cases covering both cold and warm permafrost conditions as well as using real data from a 100 m deep borehole on Sardakh Island in northeastern Siberia. Our analysis of the Sardakh Island borehole data confirms previous findings that GST in the region have likely risen by 5-9 degrees C between the pre-industrial period of 1750-1855 and 2012. We also show that latent heat effects due to seasonal freeze-thaw have a substantial impact on the resulting reconstructed surface temperatures. We find that neglecting the thermal dynamics of the active layer can result in biases of roughly -1 degrees C in cold conditions (i.e., mean annual ground temperature below -5 degrees C) and as much as -2.6 degrees C in warmer conditions where substantial active layer thickening (>200 cm) has occurred. Our results highlight the importance of considering seasonal freeze-thaw in GST reconstructions from permafrost boreholes. Plain Language Summary Long-term changes in the temperature of the atmosphere are recorded in the solid Earth due to the insulating properties of soil and rock. As a result, it is possible to estimate past changes in temperature at the interface between the ground and the atmosphere by measuring ground temperatures deep below Earth's surface. In cold regions, the presence of permafrost, that is, ground that remains frozen throughout the year, complicates such analyses due to the effects of water freezing and thawing in the soil. In this work, we present a new method for reconstructing past changes in ground surface temperature from boreholes situated in permafrost using a computational model of heat flow that accounts for these effects. We evaluate our method on both synthetic test cases as well as real data from a 100 m deep borehole in northeastern Siberia. Our results demonstrate that annual freezing and thawing of water near the surface has a substantial impact on the reconstructed ground surface temperature (GST), especially in regions where permafrost is thawing. The proposed method is the first to be widely applicable to ground temperatures measured in permafrost and thus constitutes a valuable new tool for understanding past and present climate change in cold regions.

Understanding varying climate responses in tree-ring data across tree ages is important, but little is known about tree-age effects on climate responses in tree-ring stable isotopes. To detect whether age differences in tree-ring delta C-13 and delta O-18 could lead to differing climate responses, we measured tree-ring cellulose delta C-13 and delta O-18 (1901-2010) from Schrenk spruce (Picea schrenkiana) trees in northwestern China with ages ranging from 110 to 470 years, which we binned into three age groups. Tree-ring delta C-13 (pin-corrected) and delta O-18 exhibited similar year-to-year variability between age groups and did not feature age-related trends. delta C-13 series from old trees (270-470 years) showed stronger legacy effects, reflecting influences from the antecedent period (due to carbohydrate reserves and climate), compared to young trees (110-125 years). Both tree-ring delta C-13 and delta O-18 values decreased with increasing relative humidity (RH) and precipitation and with decreasing mean and maximum temperatures during the main growing season (May-August). delta C-13 and delta O-18 exhibited age-dependent climate responses: Young trees had a stronger climate response in delta C-13 but a weaker or similar climate response in delta O-18 compared to old trees. We developed multiple growing-season RH reconstructions based on composite chronologies using delta C-13 and delta O-18 series from different age groups. In particular, we found that including delta C-13 from young trees improved the skill of RH reconstructions because of the age-specific mechanisms driving the delta C-13-climate relationship, but that caution is warranted with regard to extreme values. We therefore suggest that young trees should be considered when using stable isotopes, particularly in delta C-13, for climate reconstruction.

Borehole temperature-depth profiles contain a record of surface ground temperature (SGT) changes with time and complement surface air temperature (SAT) analysis to infer climate change over multiple centuries. Ground temperatures are generally warmer than air temperatures due to solar radiation effects in the summer and the insulating effect of snow cover during the winter. The low thermal diffusivity of snow damps surface temperature variations; snow effectively acts as an insulator of the ground during the coldest part of the year. A numerical model of snow-ground thermal interactions is developed to investigate the effect of seasonal snow cover on annual ground temperatures. The model is parameterized in terms of three snow event parameters: onset time of the annual snow event, duration of the event, and depth of snow during the event. These parameters are commonly available from meteorological and remotely sensed data making the model broadly applicable. The model is validated using SAT, subsurface temperature from a depth of 10 cm, and snow depth data from the 6 years of observations at Emigrant Pass climate observatory in northwestern Utah and 217 station years of National Weather Service data from sites across North America. Measured subsurface temperature-time series are compared to changes predicted by the model. The model consistently predicts ground temperature changes that compare well with those observed. Sensitivity analysis of the model leads to a nonlinear relationship between the three snow event parameters (onset, duration, and depth of the annual snow event) and the influence snow has on mean annual SGT.