Due to an imbalance between incoming and outgoing radiation at the top of the atmosphere, excess heat has accumulated in Earth's climate system in recent decades, driving global warming and climatic changes. To date, it has not been quantified how much of this excess heat is used to melt ground ice in permafrost. Here, we diagnose changes in sensible and latent ground heat contents in the northern terrestrial permafrost region from ensemble-simulations of a tailored land surface model. We find that between 1980 and 2018, about 3.9+1.4-1.6 $3.9\genfrac{}{}{0pt}{}{+1.4}{-1.6}$ ZJ of heat, of which 1.7+1.3-1.4 $1.7\genfrac{}{}{0pt}{}{+1.3}{-1.4}$ ZJ (44%) were used to melt ground ice, were absorbed by permafrost. Our estimate, which does not yet account for the potentially increased heat uptake due to thermokarst processes in ice-rich terrain, suggests that permafrost is a persistent heat sink comparable in magnitude to other components of the cryosphere and must be explicitly considered when assessing Earth's energy imbalance.

Permafrost is a key element of the cryosphere and an essential climate variable in the Global Climate Observing System. There is no remote-sensing method available to reliably monitor the permafrost thermal state. To estimate permafrost distribution at a hemispheric scale, we employ an equilibrium state model for the temperature at the top of the permafrost (TTOP model) for the 2000-2016 period, driven by remotely-sensed land surface temperatures, down-scaled ERA-Interim climate reanalysis data, tundra wetness classes and landcover map from the ESA Landcover Climate Change Initiative (CCI) project. Subgrid variability of ground temperatures due to snow and landcover variability is represented in the model using subpixel statistics. The results are validated against borehole measurements and reviewed regionally. The accuracy of the modelled mean annual ground temperature (MAGT) at the top of the permafrost is +/- 2 degrees C when compared to permafrost borehole data. The modelled permafrost area (MAGT 0) is around 21 x 10(6) km(2) (22% of exposed land area), which is approximately 2 x 10(6) km(2) less than estimated previously. Detailed comparisons at a regional scale show that the model performs well in sparsely vegetated tundra regions and mountains, but is less accurate in densely vegetated boreal spruce and larch forests.