Improving our knowledge of the last millennium (LM) climate variability is key for a better understanding of the mechanisms that determine the Earth system response to natural (solar, volcanic and orbital) and anthropogenic (land use and atmospheric composition changes) external forcings . Instrumental records represent the most adequate alternative to study past climate variations. However, they only provide coverage since the mid-19th century e.g.,. Therefore, to understand the nature of climate variability operating on longer temporal scales, LM reconstructions from a variety of proxy data e.g., tree-rings, corals, preserved pollen, ice cores, etc.; and simulations using general climate models (GCMs) are generally employed.

The current available LM temperature reconstructions agree, depicting a general pattern of temperature evolution going from a relatively warmer period at the beginning of the LM (MCA; Medieval Climate Anomaly) to a colder period from about 1450 to ca. 1850 (LIA; Little Ice Age), which is interrupted by the industrial warming in the 19th century . Despite this general agreement, there is still a large range of uncertainty that stems from different sources, including different reconstruction methods, various calibration and verification processes, spatial and temporal coverage, the different proxy locations (land, land and ocean, etc.) and the alternative statistical methods employed e.g.,. For instance, the range of uncertainty during the MCA regarding reconstructing Northern Hemisphere (NH) temperature is about 0.6 ∘C. Furthermore, estimate that the cooling during the Maunder Minimum (1645–1745) relative to present is about 0.7 ∘C, while report a colder LIA (1.4 ∘C) which is similar to findings by .

Addressing the range of uncertainties in reconstructing past temperature changes is relevant not only for assessing our understanding of past temperature changes and the confidence we have on available estimates , but also for model–data comparison exercises e.g., and for constraining the range of estimates of the system response to changes in the external forcing, i.e., the sensitivity of the climate system .

Borehole temperature inversion is a well-established reconstruction technique and leans on two main assumptions: first, surface air temperatures (SAT) are expected to be closely coupled to ground surface temperatures (GST); second, variations in SAT propagate downward through the subsurface via conduction . As a result, a thermal signature of the surface temperature is imprinted in the subsurface. This reconstruction technique is limited to recovering only the low-frequency information (decadal, and longer timescales) since the soil acts as a low-pass filter and progressively filters out the higher-frequency variations with depth. Oscillations with periods on the order of days only penetrate ∼50 cm deep , seasonal cycles are solely observed close to the surface (<10 m depth), decadal variations propagate within the upper 50 m and multi-centennial changes within the LM are observed in the upper 500 m below the surface .

As with every type of reconstruction method, the borehole technique is also subject to diverse sources of uncertainty. One of them is that the assumption of a conductive heat transfer may not always be substantiated, as non-conductive processes such as advection and convection may influence or even dominate the subsurface thermal regime in areas with important groundwater flows or geothermal activity. Nevertheless, a number of studies suggest that the impacts of such processes can be reduced with the appropriate treatment of the affected borehole temperature logs e.g

Additionally, the most important contributions to uncertainty arise from changes in surface processes that affect the SAT–GST coupling. Snow cover is especially important since it insulates the ground surface from the cold winter air causing large differences between the soil and air temperatures e.g.,. The impact of this effect on borehole theory has caused considerable discussion. argued that borehole-based reconstructions may be substantially biased by this seasonal influence of snow cover. Hence, under changing snow cover conditions GST may be not completely representative of SAT variations. argued against this based on the assumption that SAT and GST coupling is strong at longer than seasonal timescales; therefore, snow biases would only influence the high-frequency oscillations. Additionally, the long-term SAT–GST coupling has also been supported by observations and modeling assessments . Besides snow cover, other land surface and soil properties such as soil water content, vegetation and land use land cover (LULC) changes also have the potential to impact SAT–GST coupling. For instance, deforestation, afforestation and other land cover changes modify the land-surface properties including albedo, roughness and evapotranspiration altering the energy transfer between the atmosphere and the ground . In a recent study, found that deforestation tends to warm the ground surface mainly by reducing the transport of heat away from the surface. They also found that such continuous vegetation changes would result in long-term surface temperature anomalies; thus, deforestation should be considered as a possible source of bias for temperature reconstructions from subsurface temperatures.

One way of addressing the uncertainties of paleoclimate reconstruction methods is by using climate model simulations as a surrogate reality in which pseudoproxy records of varying complexity are created and reconstruction methods are replicated in pseudoproxy experiments (PPEs) mimicking real-world cases . The robustness of using the borehole method for reconstructing past SAT variations has been tested in PPEs e.g.,. investigated the relationship between simulated SAT and GST from interannual to centennial timescales in a forced climate simulation of the LM (1000–1900 common era; CE) using the ECHO-G GCM . They found that in spite of the seasonal and longer-term variability of snow cover, the coupling was stable for decadal and longer timescales, meaning that GST should be a good proxy for long-term SAT variations. extended this analysis by implementing the borehole method in the simplified reality of the same model. They simulated underground temperature perturbation profiles using a heat-conduction forward model driven by simulated GST. Then, they applied an inversion approach to reconstruct ground surface temperature histories from the simulated profiles. Their results supported the overall performance of the borehole methodology.

employed a similar approach to in order to retrieve past GST variations from GCMs: both studies applied an inversion method. They simulated global synthetic temperature profiles using a one-dimensional conductive model driven by simulated GST as an upper boundary condition from the CMIP5/PMIP3 Coupled Model Intercomparison Project phase 5 / Paleoclimate Modeling Intercomparison Project phase 3; LM simulations. Unlike the GCMs used in the early works that do not incorporate some external forcings, the PMIP3/CMIP5 simulations include a larger representation of LM forcings than pre-PMIP3 experiments incorporating a variety of land-surface model components. Their results have reinforced the reliability of recovering past global surface temperature variations from subsurface temperature measurements using current state-of-the-art GCMs.

The previous analyses support estimations of global/hemispheric past temperature obtained from borehole temperature inversions. First, they support the overall performance of the methodology in retrieving past GST histories from borehole profiles. Second, the use of up-to-date forcing representations in CMIP5 model ensembles also ensures that long-term alterations of surface properties like those induced by LULC changes, the effect of anthropogenic aerosols cooling and the potential long-term snow cover feedbacks induced by both forcings, do not seem to bias inversion results at global/hemispheric scales. In spite of these positive results, the analysis of last generation model experiments, including the complete set of agreed CMIP5 forcings in the so-called “all-forcing” experiments, does not allow for insights into the individual effect of each of the forcings and the related feedbacks, at either global/hemispherical or continental/regional scales. This would be desirable in order to quantify the effect of the individual forcings on SAT–GST coupling and to obtain estimates of its particular temporal evolution which would allow for the disentanglement of its contribution from that of other forcings. Therefore, the present work considers all-forcing and single-forcing types of experiments in order to address how state-of-the-art climate models simulate SAT–GST coupling from global to regional scales and to evaluate the potential influence of the external forcings on the SAT–GST relationship. This will also provide information about where and when a decoupling of SAT–GST may exist, with implications for borehole inversion practices at different spatiotemporal scales. For this purpose, we use the Community Earth System Model–Last Millennium Ensemble CESM-LME;, which is the largest existing ensemble of LM simulations with a single model to date and has not been used in previous assessments of this kind. The CESM-LME includes all- and single-forcing experiments that jointly or separately consider the transient evolution of solar variability, volcanic activity, orbital changes, greenhouse gases (GHGs), anthropogenic aerosols and LULC (see details in Sect. )

Using all-forcing simulations (ALL-F hereafter) allows for the evaluation of the SAT–GST relationship throughout the LM with a realistic representation of real-world conditions. Additionally, the single-forcing experiments are suitable for identifying the specific role that each forcing might play and its “fingerprint” on the presence of biases in the SAT–GST coupling. Most external natural (solar and volcanic variability) and anthropogenic (GHGs, LULC and aerosols) forcings have the potential to indirectly affect SAT–GST thermodynamics through snow cover feedbacks . Moreover, LULC changes can also have a direct influence on SAT–GST. Over the LM the Earth′s land cover has been substantially modified by the replacement of natural ecosystems with agricultural land, especially since the industrial period . Such land use changes have the potential to alter the surface energy balance by modifying energy fluxes and moisture budgets leading to direct impacts on the atmosphere and ground–surface temperature relationship . Furthermore, vegetation changes may additionally lead to indirect non-linear effects that are relevant in the borehole context. The most important of these is the fact that deforestation at high latitudes leads to an increase in snow cover; this is due to the fact that low vegetation accumulates continuous snow cover more readily than forests in early winter favoring its permanence longer in spring . The local-, regional- and large-scale implications of these interactions on long-term climate variability and specifically on the validity of the borehole method assumptions have not been explored so far.

The first part of this paper (Sect. ) describes the CESM-LME simulations and forcings used in the experiment. Subsequently, Sect.  describes the methodological approach employed for the analysis of the coupling between SAT and GST during the LM. Section  presents the main results in the analysis of the global covariance of SAT, GST and soil temperature (ST) at different model depths throughout the LM. This analysis includes the global SAT–GST long-term coupling at annual and seasonal timescales. The latter helps identify the impacts of seasonality on the SAT–GST coupling. In addition, the spatial distribution of the covariance structure, as well as the SAT–GST offset, are illustrated. This allows for the detection of possible failures in the air–ground temperature coupling at regional and local scales. The spatial analysis is extended to investigate the heat transfer within the shallow subsurface by comparing GST relative to deep model layers. Section  specifically addresses the long-term trend of the SAT–GST relationship in order to evaluate whether this association experiences variation with time during the simulated LM. Finally, Sect.  provides a discussion about the implications of decoupling processes at different temporal and spatial scales for the borehole temperature reconstruction method.

This analysis considers LM simulations produced with version 1.1 of CESM CESM1;. The Community Atmosphere Model version 5 is used as the atmospheric component, the Parallel Ocean Program version 2 represents the ocean component, including the Los Alamos sea ice model . The horizontal resolution of the CESM-LME is ∼2∘ over the atmosphere and land and ∼1∘ in the ocean and sea ice .

The land surface component in the CESM1 is the Community Land Model version 4 CLM4; which incorporates some improvements relative to the previous version CLM 3.5; regarding the representation of land surface processes that are important for the energy transfer between the atmosphere and the soil . Some of these include a better description of ground evaporation, thermal and hydrologic properties of organic soil, the ground depth, snow albedo, snow cover fraction and burial fraction of vegetation by snow . In addition, The CLM4 has the deepest bottom boundary condition placement (BBCP) among the current land surface models to date, placed at a depth of 42.1 m, discretized into 15 layers (see Table ) and including up to 5 additional layers in the overlying snowpack. This is relevant for borehole reconstruction applications because previous studies have shown that shallow bottom boundary conditions may not reliably represent the downward propagation of the temperature signal corrupting the amplitude attenuation and the phase shift , particularly for trends at timescales longer than decadal, from the comparison of energy storage in model simulations and borehole profiles e.g.,. Therefore, this improved and deeper land surface model allows for the analysis of the coupling between SAT and GST in a more realistic atmosphere–subsurface heat transfer scheme.

The CESM-LME incorporates ALL-F simulations with natural and anthropogenic forcings that were chosen following those used in . The model is composed of a total of 30 simulations including a subset of 10 simulations that incorporate all of the LM external forcings and smaller subsets of single-forcing simulations that consider each forcing individually (see Table  for details and references therein). The simulations used in this study and how they trace back to the original experiment names produced by are shown in Table .

In the present work the LM refers to the period from 850 to 2005 CE while the periods from 850 to 1850 CE and 1851 to 2005 CE refer to preindustrial and industrial, respectively. The 2 m air temperature is used for SAT, and the first land model level (Table ) represents GST. Additionally, the ST at different depths, denoted by the subscript notation STL2, STL3, …, STL15, is used to address different aspects of the subsurface heat transport within the CESM-LME. The simulated ST does not include data over the Antarctic region; therefore, this region is excluded from the analysis.

The relationship between SAT and GST is analyzed from two complementary perspectives. First, the covariance during the LM of the global SAT and GST anomalies relative to the 1851–2005 CE period is assessed at an interannual scale. Similarly, the spatial patterns of the correlation between SAT and GST are also analyzed. This spatial analysis is extended to the differences between the SAT and GST LM mean values, as this gives an additional measure of the energy exchange across the air–ground interface that may help characterize a potential air–ground temperature decoupling. In addition, the same spatial analysis is carried out for the differences between GST and STL8 in order to gain insight into processes affecting the pure conductive subsurface transport assumption within the shallow subsurface. For specific cases where SAT and GST exhibit some kind of decoupling, a description of the main processes that lead to this decoupling at local and regional scales is presented. For this purpose, the evolution of SAT, GST and ST at different depths is assessed over the last 105 years of the simulation period (1900–2005 CE) for the cases of interest. In some particular examples, additional variables (e.g., latent and sensible heat fluxes or snow cover) are also included for a better description of the physical processes. The purpose of such analyses is to provide some examples rather than detailing the minutiae of the processes that lead to different SAT–GST responses at many different locations. For the analysis described above the ALL-F ensemble will be used. This provides a more complete and realistic representation of real world conditions than the single forcing runs, from the point of view of the forcings considered. It also allows for the use of the surrogate reality of the CEMS-LME model as a test bed for detecting potential sources of deviations in the SAT–GST relationship during the LM.

We then focus on the assessment of the long-term trend in the SAT–GST relationship. Non-stationarity in such an association at long timescales (multi-decadal to multi-centennial) might imply that GST variations would not be representative of the SAT variations; therefore, this would result in unreliable inferences of past climate change . A two-phase regression model is applied to address this issue, which allows for the detection of changes in the long-term trend of the SAT–GST relationship without imposing any a priori temporal condition on their occurrence. The year of change is identified, as well as the trend before and after the change. The timing of change and the magnitude of trends are suggestive of long-term changes in the surface coupling. Initially, this assessment is performed at a global scale by analyzing the LM evolution of global SAT minus GST anomalies. The analysis of the long-term trend is then extended starting from the independent evaluation of SAT and GST linear trends during the industrial period, as the largest changes are expected to occur within this period. In this section of the study, besides the ALL-F ensemble, we also considered the GHG-only, LULC-only and OZ/AER-only ensembles because they have the highest potential for altering the land surface characteristics. This allows for the identification of the influence of each forcing on the LM SAT–GST coupling, including changes in snow cover, soil moisture, and latent and sensible heat variations. The linear trend analysis of SAT and GST gives a general view of their evolution through industrial times and a first glance at the most important areas where long-term SAT–GST decoupling may exist in response to changes in external forcings and related feedbacks. Although these types of processes have mostly taken place during industrial times, GHGs and land use also experienced notable changes before 1850 CE . The application of the two-phase regression to the complete LM permits for the identification of changes that occurred before 1850 CE.

CESM-LME supports the assumption that SAT is tightly coupled with GST at global scales and longer than multi-decadal scales. Figure a illustrates the stability of the coupling at global scales during the LM using the ALL-F2 ensemble member as an example. Results are comparable for other ALL-F ensemble members. The LM evolution of global continental SAT, GST, STL8 and STL15 anomalies relative to the 1850–2005 mean are shown. For STL15 non-filtered model output is represented and evidences the low-pass filter influence of the heat conduction below the surface, whereas for SAT, GST and STL8 31-year running mean low-pass filter outputs are shown. Subsurface temperature anomalies closely track SAT anomalies with relative small differences between them; this indicates that air and soil temperature are coupled above multi-decadal timescales. The correlation coefficients for the 31-year filtered series in Table  indicate high correlation (p<0.05) for the soil layers close to the surface that diminishes slightly with depth, as expected, due to the phase shift of the signal. Table  also indicates that the correlation considering the high-frequency variations (yearly; left column) is only high at the levels close to the surface, whereas at the deepest layer the correlation is low since the high-frequency variations are progressively filtered out and phase shifted as depth increases. Hence, the assumption of conductive heat transfer within the subsurface is realistically represented in the CESM-LME simulations.

Despite the strong coupling between air and subsurface temperatures at global scales, the existence of a relatively small offset between SAT and GST that grows backwards in time is evident for the annual (Fig. a) averages. This indicates a slight long-term decoupling between SAT and GST. Previous works have argued that the nature of this offset arises from the changes in snow cover and its influence insulating the ground from very cold air temperatures e.g.,. In order to explore the influence of processes such as this on the global SAT–GST relationship, this analysis is extended to consider the boreal winter and boreal summer seasons (DJF and JJA hereafter) independently (Fig. c, e). The offset between SAT and GST observed in the annual plot is only apparent in the DJF season. Indeed, the differences are larger during this season than in the annual data, whereas the JJA evolution of SAT and GST anomalies is virtually identical. In addition, even if SAT and GST are highly correlated and significant for both seasons, Table  suggest a slightly lower correlation for DJF than for JJA. This feature and the largest offset occurring in DJF suggest an important role for snow cover. Figure b, d, f further illustrate the strong relation between the SAT–GST offset and snow cover by displaying the 31-year low-pass filter outputs of the LM evolution of global snow cover and SAT–GST differences. Note that in DJF, due to its influence on annual averages, the decrease (increase) in snow cover leads to a decrease (increase) in the SAT–GST offset. This is due to the insulating effect of snow that keeps GST close to zero while SAT can reach large negative values. Thus, an increase in snow cover leads to larger negative SAT–GST differences. For JJA on the contrary, an in-phase relationship is found at all timescales. Long-term trends change in both snow cover and in SAT–GST after the end of the 19th century. During the boreal summer increases in snow also enhance SAT–GST differences due to the insulation of the ground from the warmer summer SAT, whilst the opposite is noted for snow cover decreases. This effect dominates the global average over that of the JJA austral winter during which SAT–GST and snow cover changes experience an anti-phase relationship as described above. Therefore, the NH influences anti-phase covariability of snow cover and SAT–GST during DJF (detrended correlations, r=-0.52; p<0.05) and annual (r=-0.67; p<0.05) and in-phase covariability during JJA (r=0.62; p<0.05).

Beyond the anti- and in-phase covariability at multi-decadal to centennial timescales, changes in the longer-term relationship between SAT and GST can play an important role in decoupling with implications for the borehole theory. At global scales, the long-term offset is relatively small, as shown in Fig. , and therefore has very limited implications. Nevertheless, it is interesting to asses the consistency and relative magnitude of changes in snow cover and SAT–GST. Two-phase regression in annual and seasonal SAT–GST (Fig. b, d, f) shows consistent date of change during the 18th century. All changes are towards smaller SAT–GST differences and are significant for annual and DJF (p<0.05). For snow cover trends, using the same dates of change as for SAT–GST, indicate anti-phase (in-phase) relationships for the annual and DJF (JJA) periods as in the multi-decadal timescales described above. However, changes in snow cover trends during the last centuries are small and can hardly be invoked to solely account for the comparatively larger SAT–GST trend changes. This calls for the consideration of other possible mechanisms and a more spatial perspective.

The spatial variability of the relationship between SAT and GST gives further insights into the role of different processes on the SAT–GST coupling. Figure  shows the spatial distribution of the differences between mean LM SAT and GST as well as the correlation coefficients for the annual, DJF and JJA averages in the ALL-F ensemble. In the case of the annual temperatures (Fig. a), GST is generally warmer than SAT with the differences being low over most of the globe (less than 2 ∘C) except in the NH mid- and high-latitude areas where the differences are higher (up to 15 ∘C). The correlation maps (Fig. b) provide a similar pattern with high and significant values over most of the globe (>0.8 in regions located between 45∘ N and 90∘ S) and lower correlations over NH mid- and high-latitudes, especially over eastern Siberia. Similar behavior is seen in the DJF season although it is more pronounced. During these months, GST is much warmer than SAT, reaching differences up to 30 ∘C in the northernmost parts of North America and Eurasia (Fig. c). Differences are smaller at mid- and low-latitudes. The influence of the ocean over coastal areas providing larger SAT relative to GST is noticeable. Similarly, the correlation is lower over the northern snow covered areas (Fig. d), while over the rest of the globe it remains high. In contrast, Fig. e, f show that during JJA, when the snow cover is scarce, the SAT–GST coupling is strong globally with temperature differences lower than 2 ∘C and high correlation coefficients (>0.9). Consequently, the role of snow cover in decoupling SAT and GST is highlighted. Positive correlation values are low over borderline areas where snow cover is more variable, which produces variability in the SAT–GST offset and thereby alters the covariance structure. Close to these areas in central Asia the high negative correlation within the Tibetan Plateau is noteworthy (see discussion below).

Figure  illustrates the SAT–GST decoupling due to the snow cover at the local scale for a particular grid point as an example. The grid point is located over a region with considerable snow cover during the boreal cold season (northeastern Russia). The DJF and JJA evolutions of SAT, GST and ST at different depths and the snow cover for the last 105 years from the ALL-F2 simulation are shown. Note that in DJF snow covers 100 % of the grid cell during almost the whole period. Thus, the soil is insulated and the difference between SAT and GST is ∼-15 ∘C on average. The temperature of the deeper layers is presented in order to illustrate the amplitude attenuation and phase shift with the depth of the temperature signal. Note that during DJF, GST is only slightly below 0 ∘C, and the agreement of its variations with those of SAT is only noticeable in the largest changes of both, while STL6 and deeper STs are above 0 ∘C. In JJA, SAT and GST are very similar and their low frequency variability propagates to deeper levels, all above 0 ∘C.

Some aspects of the SAT–GST spatial distribution deserve further attention. One of the most noteworthy of these is the fact that over the Tibetan Plateau region temperature differences between SAT and GST are as large as in the mid- and high-NH latitudes for both annual and DJF periods (Fig. a, c). However, SAT and GST are negatively correlated for annual and DJF seasonal resolution data (Fig. b, d), with the Tibetan Plateau being the only region of the globe where this occurs. Nevertheless, the correlation for JJA is positive and high (Fig. e). The nature of this opposite phase arises from discontinuous snow cover over this region and the very low air temperatures during DJF. Usually, the snow cover insulates the soil from the colder air, avoiding the heat exchange with the atmosphere (as shown in Fig. ). Nevertheless, discontinuous snow cover only partially insulates the soil, leading to this particular SAT–GST interaction. Figure  displays this behavior for a grid point located over the Tibetan Plateau. SAT, GST, ST at different depths, snow cover and surface sensible heat flux (SHFLX) are shown. In DJF during periods of low snow cover the fraction of surface exposed to the atmosphere allows for energy exchange from the warmer soil to the colder air. Conversely, when snow cover is high, the large fraction of insulated soil reduces almost completely the heat transfer from the soil to the atmosphere. Therefore, with lower (higher) fractions of snow cover, higher (lower) heat transfer takes place with GST decreasing (increasing) and SAT increasing (decreasing). Indeed, there is a high negative correlation (-0.84; p<0.05) between the snow cover fraction and SHFLX which is the main way that energy dissipates within this region since latent heat fluxes (LHFLX) are negligible. Higher/lower albedo due to variations in snow cover fraction also contribute to the negative SAT–GST correlation over this region (not shown). Horizontal model resolution does not seem to be an issue since a higher resolution version of the model CCSM4; produces a similar behavior which other models of similar resolution do not show . During JJA in comparison, snow cover is negligible and SAT–GST coupling is consequently strong. Note that GST and all ST are above zero and GST is higher than SAT as it is warmed by radiative gain and the transfer of heat to the atmosphere, hence the positive correlation (0.5; p<0.05) between SAT–GST and SHFLX.

The spatial SAT–GST differences during JJA (Fig. e) depict other relevant aspects that have an influence on the SAT–GST relationship at relatively short timescales. SAT is generally colder than GST globally. However, for JJA, there are large areas inland, mainly located in the southeastern US, some parts of central and eastern Europe and eastern Asia, with warmer SAT relative to GST. Variations in LHFLX from DJF to JJA drive this effect. Figure  shows that the areas where LHFLX increases in JJA relative to DJF are related to the same areas where SAT is higher than GST in JJA (Fig. e). Therefore, there is a direct relation between the increase in evapotranspiration in JJA and the ground temperature response at these locations. The time series in Fig.  display this behavior for a grid point located over southeastern China. During JJA the surplus of energy due to higher solar radiation reaching the surface is mostly dissipated as latent heat leading to a net heat loss at the ground surface. Note the anticorrelation between the surface soil moisture and LHFLX (-0.46; p<0.05) during JJA as well as the large SHFLX values that occur when soil moisture is at its lowest and evapotranspiration is limited. Therefore, the high rate of LHFLX contributes to cool the surface and GST tends to be lower relative to SAT. Soil water content also exhibits large changes during JJA consistent with the large evapotranspiration (Fig. a) and provides a source of moisture that contributes to temperate SAT and cool GST. Large variations in evapotranspiration from DJF to JJA are also present at midlatitudes of the SH summer continents (America, Africa and Australia), although only a very limited impact on Fig. e is perceived, especially over the western coast. Over these regions, high incoming energy impinging the surface during SH summer (not shown) supports high rates of latent heat fluxes. However, as soil water becomes a limiting factor, more energy is dissipated as sensible heat and the ground surface is warmed. Therefore, GST experiences higher temperature than SAT on average. Figure  also shows high evapotranspiration over the tropical rainforest in America and Africa, both in DJF and JJA, which does not translate to positive SAT–GST differences. Over the rainforest, the energy fluxes at the surface do not vary significantly from DJF to JJA since incoming radiation is relatively constant throughout the year, and is transferred to evaporation and evapotranspiration within the canopy, while soils are well watered by precipitation to support the large amounts of evapotranspiration. This situation leads to a small range of variation in both SAT and GST with very small differences between them and higher GST relative to SAT.

Figure a, c, e show similar higher SAT values relative to GST at some coastal areas in both JJA and DJF. During DJF the effect is mainly present in the NH midlatitudes, such as in most European coastal areas, both the east and the west coasts of North America, and in Japan and the east coast of China. During JJA, in comparison, this behavior is mostly seen in the SH midlatitudes, such as southern South America, South Africa and southern Australia. Interestingly, higher SAT relative to GST is also evident in some coastal areas over tropical regions; this applies for both JJA and in DJF, and is mainly observed over southeastern Asia, the southern areas of the Indian subcontinent, the Gulf of Guinea and some areas of South and Central America. In the CESM-LME the atmospheric grid box of the coastal areas is partitioned into land and ocean fractions. For the areas with sea ice formation, an additional sea ice fraction is considered . This configuration of the coastal grid points leads to a partition of the energy fluxes at the surface into those of the land fraction and those of the ocean fraction. During the cold season, partitioning such as this determines the higher SAT warming relative to GST, as the relatively low net radiation that impinges the surface at mid- and high-latitudes limits the ground surface heating as well as the energy fluxes out of the land surface fraction. In contrast, the energy fluxes from the ocean surface to the air above are large, primarily as a result of the temperature difference between the water and the comparatively colder air above. The dissipation of energy from the ocean fraction to the atmosphere warms the air, so the net effect is higher SAT relative to GST in the winter season. Over the tropical coasts that exhibit the same behavior, the energy fluxes out of the ocean fraction of each grid point also contribute to the higher warming of the air relative to the ground surface. Nevertheless, at these locations high rates of evapotranspiration all year long also play an important role as they generate evaporative cooling of the ground surface, as seen in the example described in Fig. .

The different examples used to illustrate the most important processes that may influence the air and soil temperature relationship at short timescales also depict relevant information about the propagation with depth of the annual cycle. For instance, at the grid point located over southeast China in Fig. , both in DJF and JJA, the temperature offset between contiguous levels is noticeable with a gradient of about 5 ∘C in the first meter of the ground and of about 10 ∘C down to the lowest level. Comparable pictures with some differences in the magnitude of gradients can be seen in the previous figures.

Therefore, it is interesting to also understand the propagation of temperature below the surface. GCMs simulate purely conductive regimes, and the temperature variations that propagate to deeper soil layers are established at or near the ground surface . Thus it is important to asses the propagation of the temperature signal within the shallow subsurface. This issue is addressed by analyzing the relationship between GST and STL8.

Figure a provides a spatial view of the temperature differences between GST and ST_L8 for annual, DJF and JJA periods. The correlation is also shown in the right panels. SAT–GST differences, for DJF and JJA show the yearly cycle of temperature with negative (positive) SAT–GST for the NH (SH) in DJF and vice-versa for JJA, illustrating the conductive regime within the shallow subsurface. The annual temperature differences are low and the correlation is high almost globally as it is the balance between the respective patterns in JJA and DJF. However, the northernmost part of the globe exhibits larger temperature differences (between 4 and 5 ∘C) and lower correlation coefficients. The DJF and JJA patterns show that the annual offset and correlations for this part of the globe are mostly the result of the larger weight of those in JJA given that, during these months, the temperature differences for a latitudinal band at ca. 60–70∘ N are as large as 15 ∘C and the correlation coefficients are close to zero. describe a similar behavior in some of the GCMs used in their analysis, detected over areas where frozen ground persists during JJA. Indeed, the nature of the large departure in the temperature response at the shallow subsurface at these locations arises from non-conductive processes related to latent heat release/uptake of freezing and thawing of the water content above a depth of 1 m that may account for the subsurface heat transfer .

To illustrate this mechanism, Fig.  shows the temperature evolution of SAT, GST and ST at different depths as well as the soil ice content (SIC) in the upper soil layers for a grid point located in the north of Canada. Over these areas the SIC in the upper 1 m of soil increases (decreases) during the cold (warm) season. During JJA, SAT and GST increase/decrease at the same rate since no ice is present at the ground surface so it is warmed by radiative gain and heat is transferred to the atmosphere. However, for deeper soil layers, the energy available is employed to melt the SIC (note the lower SIC in L6 during JJA relative to DJF), and latent heat is required so that these layers do not experience a temperature increase like the shallowest layers. Therefore the temperature at L8 (∼1 m depth) is kept below/near 0 ∘C during the warm season due to the zero-curtain effect , while GST is centered around 12 ∘C, leading to differences of ca. 15 ∘C between GST and ST_L8 and a low correlation coefficient (0.28 for this grid point) during JJA. In turn, during DJF, SAT sits around -35 ∘C and the frozen ground experiences skin temperatures of about -8 ∘C and of about -4 ∘C at a depth of 1 m. Consequently, the temperature offset between GST and STL8 is largest in JJA. As a result, there are some non-conductive processes associated with permanent frozen soils in the shallow subsurface that are included in the CLM4 parameterization and that play an important role in heat transport. The higher SIC in L8 during JJA relative to DJF (Fig. ) arises from the fact that freezing of the active layer begins in late autumn and, due to the release of the latent heat of fusion, the freezing front is inhibited and only reaches L8 in spring when SIC at this layer peaks. Then, as the thawing front penetrates downward in JJA, ice in the shallowest soil is melted, but it does not reach L8 until autumn when SIC at this layer is lowest. Therefore, due to the thawing–freezing processes, seasonal changes at the upper and deeper subsurface levels are phase-shifted.

This work evaluates the stationarity of the coupling between SAT and GST temperatures as simulated by the CESM in an ensemble of experiments spanning the LM. The initial motivation for this work is rooted on previous literature that addresses the realism of the borehole hypothesis for climate reconstruction, namely, that SAT and GST vary synchronously and that reconstructing past GST changes from borehole temperature profiles is a good proxy for past SAT variations. The use of the CESM-LME allows for the analysis of the influence of forcing changes on the SAT–GST covariability, both individually and as a group, by considering the different all-forcing and single-forcing ensembles. Additionally, having several experiment ensemble members for each given forcing type allows for the disentanglement of the effects of internal variability from those of the forcing response. Ultimately, the coupling between SAT and GST is assessed at a global and also at regional/local scales. This assessment requires the consideration of different mechanisms that contribute to SAT–GST variability within different climate types. In doing this, a variety of factors and conditions that contribute to the surface energy balance via different mechanisms are provided.

The CESM-LME shows that at global scale the SAT–GST coupling is strong above multi-decadal timescales since GST tracks SAT throughout the LM, as found in previous studies. However, in spite of the strong coupling, the CESM-LME also reflects that the SAT–GST relationship has not remained constant throughout the whole LM at these spatiotemporal scales. Hence, the nature of such variation is evaluated.

Globally, snow cover is the most important agent in modulating the connection between SAT and GST. Therefore the variation of the SAT–GST relationship described by the CESM-LME simulations should, in principle, be driven by variations in global snow cover. Nevertheless, the simulated snow cover remains relatively stable at the time when SAT–GST coupling varies; thus, this change cannot be solely explained by the influence of the snow cover. With this in mind, we explored, in some detail, different processes that may influence the SAT–GST relationship at different spatiotemporal scales. Firstly, we address processes acting at seasonal timescales that were identified from a spatial analysis of the SAT–GST differences and correlations. Secondly, the long-term evolution of the SAT–GST relationship is evaluated in the ALL-F, LULC-only, GHG-only and OZ/AER-only ensembles.

Several processes over different regions relevant during either DJF or JJA play an important role in impacting the SAT–GST coupling, such as snow cover over mid- and high-latitudes, discontinuous snow cover over the Tibetan Plateau region and seasonal variations in the energy fluxes at the surface. Although these processes are important for disrupting the SAT–GST relationship at seasonal scales, they have no implications on the long-term coupling if they are stationary. Nonetheless, if they experience variations with time the SAT–GST long-term relation may be impacted.

As discussed in Sect.  some of the anthropogenic external forcings have the potential to impose long-term variations on processes that regulate the relationship between SAT and GST. Among them, LULC changes are the most important of these forcings as they modify the energy fluxes at the ground–air interface, and consequently corrupt the SAT–GST coupling locally and regionally at various timescales. One example is the response to the deforestation processes triggered by the expansion of agriculture mainly during the industrial period at mid- and high-latitudes, where SAT and GST long-term coupling is impacted due to the variations in the albedo, surface roughness and hydrology. Similar decoupling processes related to LULC changes are found over different regions around the globe, such as those described in Sect.  over northeastern Brazil, and over some areas in Africa and the Indian subcontinent. All of these examples are driven by the long-term modifications of the energy fluxes at the surface, either from increased evapotranspiration, reduced energy dissipation via sensible heat or other factors. Besides these kinds of decoupling processes induced by individual forcings, the interactions of a variety of mechanisms and feedbacks from different external forcings can also exert an influence on the long-term SAT–GST relationship at different spatial scales. For instance, the effect of GHGs leads to a reduction of the snow cover during industrial times that is counterbalanced by the opposite effect of both LULC and OZ/AER forcings. As a consequence, the snow cover remains relatively stable over some regions during the industrial period in the presence of a warmer climate. This situation leads to a difference in the SAT–GST long-term evolution during the industrial period, since the snow cover insulates the soil from a warmer SAT. This effect is present over the NH high-latitudes of North America, Fennoscandia and northeastern Russia. Indeed, at a global scale, the combination of steady snow cover under warmer climate conditions is the dominant effect for explaining the variations in the long-term SAT–GST relationship.

Our findings indicate that the assumption of a strong relationship between SAT and GST may be impacted from local to regional scales by different mechanisms especially by the influence of LULC changes due to the modification of the energy balance at the surface. Therefore, the interpretation of temperature reconstructions from borehole measurements at these spatial scales must consider LULC changes as a source of possible bias. The effects of additional external forcings may also exert some influence on processes such as variations in the snow cover, hydrology and other land surface properties, which may in turn feedback on the SAT–GST long-term coupling. At a global scale, the influence of such local and regional decoupling processes is only ca. 0.05 ∘C; hence, the SAT–GST coupling at this spatial scale is supported by the CESM-LME.

The analysis using different GCMs may yield different levels of impacts. Overall, some consistency in the impacts among the available simulations of the LM with different GCMs can be expected. This is due to the fact that the external forcings considered in the PMIP3/CMIP5 LM simulations are similar and should have a similar contribution to the extent that the impacts on the SAT–GST long-term relationship are mainly driven by the external forcings. Nevertheless, not all model simulations consider exactly the same set of forcings. Some consider land use land cover changes and aerosols, and other do not (Masson-Delmotte et al., 2013). In addition, different model climate sensitivities and differences in the representation of surface processes (e.g., snow cover or soil moisture) may also contribute to produce different responses. Even if the role of external forcings should be dominant in a long-term context, addressing this issues from a multi-model ensemble approach would help with understanding the uncertainties associated with all the factors of variation described above. The CMIP6/PMIP4 offers an opportunity to explore better sensitivity to different models, as larger ensembles of the LM with a more systematic sampling of forcings and processes would be expected.