Climate change is a consequence of the current radiative imbalance at the top of the atmosphere, which delivers an excess amount of energy to the Earth's system in comparison with preindustrial conditions . Nonetheless, the energy imbalance presents an interhemispheric asymmetry that is larger in the Southern Hemisphere . This asymmetry causes an increase in the heat uptake by the ocean surface in the Southern Hemisphere in comparison with the ocean heat uptake in the Northern Hemisphere. Hence, a cross-equatorial northward transport of heat emerges to compensate for this asymmetry , in addition to the global meridional heat transport caused by the different radiation levels reaching the tropical and polar oceans . The hemispheric distribution of heat uptake, heat storage, and heat transport is expected to change under different emission scenarios , meaning that characterizing where the heat enters the system (uptake), where the heat is allocated (storage), and where the heat is redistributed (transport) is of critical importance to understand the evolution of climate change.

The vast majority of excess heat due to the Earth's energy imbalance is stored in the ocean (84 %–93 %), followed by the cryosphere (4 %–7 %) and the continental subsurface (2 %–5 %), with the atmosphere showing less heat storage term (1 %–4 %) . Therefore, extensive resources are devoted to monitoring and understanding the evolution of the ocean heat content, since it is also an indirect method to study the magnitude and variations of the energy imbalance at the top of the atmosphere that contributes to sea level rise . The rest of the components of the climate system have relevant roles in the Earth's heat inventory, despite their small contribution to storage . For instance, some energy-dependent processes are permafrost stability and the associated permafrost carbon feedback , changes in circulation patterns , and sea level rise from ice melting . The additional energy in the atmosphere, cryosphere, and continental subsurface also affects near-surface conditions, having important consequences for society. Increases in atmospheric heat content produce warmer surface air temperature and larger amounts of water within the atmosphere that can impact crop yields and consequently global food security as well as degrading human health due to heat stress . Floods induced by extreme precipitation events, the frequency and intensity of which are affected by the amount of water in the atmosphere, and floods induced by sea level rise caused by the thermal expansion of the ocean and melting of Greenland and Antarctica ice sheets are likely to impact human settlements . Furthermore, all these alterations of surface environmental conditions may enhance the spread of diseases , among other potential risks.

Long-term global estimates of heat storage within the continental subsurface have been previously estimated from borehole temperature profile (BTP) measurements. Changes in the energy balance at the land surface add or remove heat from the upper continental crust, changing the long-term subsurface equilibrium temperature profile . Such temperature changes propagate through the ground by conduction and are recorded in the subsurface as perturbations to the quasi-steady-state vertical temperature profile. Borehole climatology consists of estimating variations in ground surface temperature and heat flux from these recorded alterations in the subsurface thermal regime. Ground surface temperature histories and ground heat flux histories have been retrieved from BTP measurements at both regional and hemispheric scales for multi-century to multi-millennial time periods , constituting a useful reference for evaluating climate simulations performed by atmosphere–ocean coupled general circulation models beyond the observational period , as well as for evaluating reconstructions derived from other paleoclimate data .

Previous global estimates of GHC, ground heat flux histories, and ground heat temperature histories were retrieved from BTP measurements nearly 2 decades ago , including a limited characterization of uncertainties. Meanwhile, advances in borehole methodology have allowed researchers to assess the uncertainty in borehole reconstructions induced by a series of factors: the presence of advection and freezing phenomena, the sampling rate and the depth range used in the determination of the quasi-equilibrium profile, the depth of the log, the different logging dates of the profiles, the noise in the measured profile, the number of retained eigenvalues for obtaining stable solutions, the spatial distribution of borehole measurements, and the transient variations in the subsurface thermal regime due to the end of the last glacial cycle . These advances, together with the availability of new BTP measurements, make necessary an update of the global long-term evolution of ground heat content from borehole data.

Here, we use an expanded borehole database to estimate global ground surface temperature histories, ground heat flux histories, and ground heat content within the continental subsurface for the last 4 centuries. Surface temperature and heat flux histories are retrieved from each BTP using a singular value decomposition (SVD) algorithm, one of the standard borehole methodologies employed in previous analyses , and a new approach based on generating an ensemble of inversions for each temperature profile to explore additional sources of uncertainty unaddressed in previous global borehole reconstructions.

We find higher values of surface temperature, ground heat flux at the surface, and ground heat content from borehole data than previously reported. The estimated global surface temperature change since preindustrial times is in agreement with meteorological observations, proxy reconstructions, and general circulation model simulations. The higher continental heat storage implies that a larger amount of the additional energy gained by the Earth system is allocated within the continental subsurface than previously thought. These results reinforce the necessity of monitoring continental heat storage and the need for improving the representation of the land component of the Earth's heat inventory within long-term climate simulations.

Ground surface temperature histories estimated using a 25-year inversion model, together with the standard approach and the new GST_PPIT ensemble, show temperature increases that are particularly large during the second half of the 20th century in comparison with preindustrial conditions (Fig. a). This is in agreement with meteorological observations of surface air temperatures (red and orange lines in the mentioned figure) and with previous studies using both borehole temperature profiles and proxy data . Both approaches used to retrieve ground surface temperature histories from temperature profiles display remarkable agreement during the whole period and similar temperature changes as those shown by SAT_CRU temperatures for the observational period. Global mean temperature changes between 1950–1975 and 1975–2000 CE reach 0.3 K for the GST_PPIT ensemble and 0.4 K for the GST_Standard ensemble (Table ), with mean temperature changes from SAT_CRU data of approximately 0.4 K using both the entire dataset and the locations and dates containing BTP inversions.

Ground surface temperature histories present slightly higher temperature changes since preindustrial times than previously reported, with results ranging from 1.0±0.1 K to 1.2±0.2 K for the last part of the 20th century considering results from the three inversion models (Tables , S1, and S2) in comparison to the ∼0.9 K reported in previous works . Furthermore, ground surface temperature histories show a temperature increase of around 0.5±0.3 K using the GST_Standard ensemble and 0.3±0.5 K using the GST_PPIT ensemble at the beginning of the instrumental period relative to preindustrial times (∼1900 CE; Fig. a). Thus, 67 % and 81 % of the land warming occurs after 1900 CE in the GST_Standard ensemble and the GST_PPIT ensemble, respectively, indicating an accelerated land warming during the 20th century, in agreement with other reconstructions of past changes in surface temperature .

As in the case of surface temperature histories, the three approaches providing ground heat flux histories from BTP measurements are in good agreement during the entire period, although they present higher uncertainties than for temperatures (Fig. b and Table ). Global results from are also displayed in Fig. b (purple line), reaching similar values in comparison with ground heat flux histories in the GHF_Standard, GHF_PPIT, and GHF_PPIF ensembles except for the second half of the 20th century. Global heat flux change reaches 70±20, 60±50, and 60±40 mW m-2 for the GHF_Standard, GHF_PPIT, and GHF_PPIF ensembles, respectively (Table ), in contrast to 39±4 mW m-2 presented in and ∼33 mW m-2 from . The large number of recently acquired profiles included in our analysis may explain the larger flux estimates in comparison with previous works, since BTP measurements recorded before the 1980s did not capture the large disturbances in the surface energy budget from recent decades . Global changes in ground heat content were estimated from the GHF_Standard, GHF_PPIT, and GHF_PPIF ensembles by scaling these fluxes to the continental areas except Antarctica and Greenland, where there are no BTP measurements, which results in three new sets of results: the GHC_Standard, GHC_PPIT, and GHC_PPIF ensembles. Changes in ground heat content of 15±5, 10±10, and 13±8 ZJ (1 ZJ = 1021 J) are obtained for the period 1950–2000 CE using the GHC_Standard, GHC_PPIT, and GHC_PPIF ensembles, respectively, in comparison with 9±1 ZJ in and 7 ZJ in . As expected, these estimates of continental heat storage are larger than previously reported since the heat flux histories also present higher values. The small uncertainty for heat flux histories, and therefore for estimates of continental heat storage, shown by the standard and PPI approaches at the beginning of the period (Fig. ) is artificially imposed by Eq. (), since the heat flux estimate for the first temporal step is set to zero by default. Therefore, the GHF_PPIF and GHC_PPIF ensembles provide a more realistic estimate of the uncertainty in the global ground heat flux histories and ground heat content estimates for the first half of the period, with larger uncertainties for all ensembles in the second half of the period.

Although the borehole database used here contains BTP measurements recorded after 2000 CE, results are shown until the end of the 20th century, since the number of available logs decreases sharply afterwards and the remaining profiles are located mainly at high latitudes in North America and Australia (Fig. ). We use the trend for the period 1970–2000 CE to extrapolate the heat flux histories until 2018 CE, providing an estimate of the accumulated heat content in the continental subsurface from 1960 CE to the present (Fig. ). The global mean change in heat flux for the entire period is approximately 90 mW m-2 considering all inversion approaches, while the global heat flux change since 2000 CE is ∼120 mW m-2. Thus, the accumulated heat within the global continental subsurface obtained from these flux estimates reaches 20 ZJ for the entire period and ∼9 ZJ for 2000–2018 CE. That is, if the global heat flux increase during the first decades of the 21st century resembled the trend of the period 1970–2000 CE, half of the total increase in energy storage within the continental subsurface in the last 58 years would have occurred during the last 2 decades, a remarkably similar result in comparison with the accelerated ocean heat uptake in the last decades .

Ground surface temperature and ground heat flux histories retrieved by the three inversion models used here show similar evolutions since preindustrial times and yield similar estimates of ground heat content for all continental areas without considering Antarctica and Greenland (Figs. , S2, and S3; Tables , S1, and S2). Nonetheless, the surface temperature, heat flux, and heat storage results are larger than previous global estimates of ground surface temperature histories, ground heat flux histories, and ground heat content from borehole data . The main reason for the higher values reported here is the inclusion of additional temperature profiles measured at more recent dates than those employed in the literature, since logs acquired after the 1980s and 1990s recorded larger changes in the subsurface thermal regime due to larger variations in the surface energy balance . That is, more than 250 high-quality logs have been measured or made available for the community since the early 2000s, including profiles from scarcely represented areas in the Southern Hemisphere. Additionally, there have been improvements in the aggregation and treatment of borehole profiles, contributing to the differences between our estimates and previous works . We have truncated all logs to the same depth before performing the analysis in contrast to previous studies, which used profiles including a range of bottom depths, therefore including estimates of ground surface temperature histories and ground heat flux histories with different periods of reference.

The larger differences in uncertainties in heat flux estimates from the GHF_PPIT ensemble in comparison with those from the GHF_PPIF ensemble are caused by the criteria to discard unrealistic inversions in the PPI approach (Figs. b, S2b, and S3b). That is, the heat flux estimates for the GHF_PPIT ensemble were not filtered out using the flux criterion (0.51 W m-2) of the PPI approach but the temperature criterion (2.57 K). Applying these different criteria is necessary since heat flux estimates from the GHF_PPIT ensemble result from applying Eq. () to the previously retrieved surface temperature histories in the GST_PPIT ensemble, while the heat flux histories considered in the GHF_PPIF ensemble result from direct inversions of heat flux profiles, as explained in Sect. .

Borehole temperature profiles demonstrate a unique ability to integrate multi-centennial changes in the surface energy balance , which makes borehole inversions an important source of information about preindustrial conditions. The depth range considered here (from 15 to 300 m) allows us to retrieve information from ∼700 years before the logging date of each log, i.e., several centuries before industrialization. Thus, all surface temperature histories displayed in Figs. a, S2a, and S3a are relative to approximately 1300–1700 CE, as the subsurface quasi-equilibrium profile is estimated here from the 200–300 m depth range for all profiles . The ground surface temperature increases relative to preindustrial conditions from the three GST_PPIT ensembles analyzed here are ∼1.0 K for the last part of the 20th century, as previously shown in the Results section and Tables , S1, and S2. This is not, however, an estimate of the global temperature change, since land temperature changes at a higher pace than the temperature at the surface of the ocean due to their different thermal properties. The ratio between land temperature change and ocean temperature change is estimated in based on an ensemble of long-term general circulation model simulations performed under different external forcings, resulting in land temperature changes ∼2.36 times larger than ocean temperature changes. Thus, the ocean temperature change corresponding to the land temperature change retrieved from borehole temperature profiles can be approximated as ∼0.4 K, which suggests a global temperature change of ∼0.7 K since preindustrial times. Such a temperature change from preindustrial conditions is in good agreement with the estimates of 0.55–0.8 K discussed in using observations, general circulation model simulations, and proxy databases, even for a preindustrial period much further in the past in comparison with the periods analyzed in .

These new estimates of continental heat storage and ground heat flux from BTP inversions have implications for the assessment of the Earth's heat inventory and for comparison with general circulation model simulations. The ocean heat flux is still much larger than the ground heat flux, with an ocean flux of ∼900±100 mW m-2 in contrast to the ∼129±28 mW m-2 ground heat flux (Fig. ) for the period 1993–2018 CE. Nevertheless, although the ocean is still the largest component of the Earth's heat inventory (89 %), the contribution of the continental subsurface is higher than previously reported 6 % instead of 2 %–5 %;, reinforcing the necessity of monitoring and accounting for the rest of the components in the inventory. Furthermore, previous assessments have shown that general circulation model simulations are unable to represent changes in continental heat storage due to their shallow land surface model components . The new estimates of continental heat storage emphasize the demand for deeper subsurfaces in general circulation models in order to generate global transient simulations capable of correctly reproducing the Earth's heat inventory.

The distribution of BTP measurements used in this analysis is especially scarce in zones of Africa, South America, and the Middle East, which may raise doubts about the global representativity of the assembled borehole dataset. Previous works have assessed the spatial distribution of BTP measurements using transient climate simulations performed by general circulation models at millennial timescales and borehole databases aggregated using different techniques , with all studies concluding that the effects of limited regional sampling on estimates of global changes should be minor. Additionally, surface air temperatures from SAT_CRU data present markedly similar values considering both the full domain and the locations and dates containing BTP inversions (see red and orange lines in Fig. ), supporting the claim that borehole temporal and spatial distributions are representative of global conditions. Nevertheless, repeating measurements at previously logged borehole sites and obtaining new records at zones with a reduced density of BTP data would improve the global estimates of ground surface temperature and ground heat flux histories from borehole temperature profiles.

The magnitude of the retrieved changes in ground surface temperature in this analysis supports the claim that the Earth's surface has warmed by ∼0.7 K since preindustrial times. The new estimates also reveal that the continental subsurface stored more energy during the last part of the 20th century than previously reported, reaching around 12 ZJ. This evidences the need to include deeper land surface model components in transient simulations performed by general circulation models in order to correctly reproduce the land component of the Earth's heat inventory and potentially powerful carbon feedbacks related to energy-dependent processes of the continental subsurface, such as the stability of the soil carbon pool and permafrost evolution.