Climate models and some observational studies show that, as climate warms, elevated surfaces tend to warm more rapidly than non-elevated surfaces . This elevation-dependent warming (EDW) suggests that the impacts of a changing climate will be amplified for elevated surfaces, with implications for societies and ecosystems in mountainous regions as well as for glaciers and meltwater runoff .

Amplified warming (or, more generally, differential warming) of elevated regions implies that the energetic forcing and feedback processes which control radiatively forced temperature trends e.g. vary systematically with surface elevation. Proposed drivers of EDW based on this energetic perspective include the surface albedo feedback , the temperature dependence of longwave emission i.e. the Planck feedback;, and cloud feedbacks . Radiative effects associated with increasing water vapour, in particular variations in this feedback with surface elevation, have also been cited as a possible contributor to EDW , as has the height dependence of free-tropospheric warming . Some of these proposed EDW drivers are well understood. For example, the surface albedo feedback – a positive feedback on forced temperature changes – is expected to be more important for high-elevation regions where surface snow and ice are plentiful and near the freezing point. Using high-resolution simulations, identified this albedo feedback as the primary driver of EDW in the Rocky Mountains. The negative Planck feedback is also temperature dependent and expected to be weaker in colder elevated regions, thereby favouring EDW . Other factors, including radiative forcing due to aerosols, are important for regional EDW according to some studies , yet their influence on large scales and importance relative to other EDW drivers are less clear. As-yet undiscovered mechanisms could also influence the relative warming of elevated versus non-elevated surfaces: for example, CO2 radiative forcing is weaker in elevated regions including the Tibetan Plateau but has received little attention in the EDW literature. In summary, despite intensive research over recent decades, a comprehensive and quantitative understanding of the physical processes driving EDW remains elusive.

In this study, we examine EDW over the historical period using gridded observations, atmospheric reanalysis, and climate models. Our focus is on understanding the large-scale EDW signal in the tropics and subtropics (averaged from 40° S to 40° N), the consistency across observational and model datasets, and the processes influencing EDW. We focus on the tropics and subtropics where the EDW signal is strong and where meridional gradients in surface temperature trends – which have the potential to complicate interpretation of the EDW signal – are relatively weak (e.g. compared to northern middle and high latitudes where polar amplified warming manifests; ). We begin by introducing the data and analysis techniques (Sect. 2) before quantifying EDW using surface air temperatures and assessing trends across observations, models, and seasons (Sect. 3). Using large ensembles of climate simulations, in Sect. 4 we assess the following: (i) the influence of radiative forcing versus internal variability on EDW and (ii) the roles of specific forcing agents in driving EDW, in particular greenhouse gases and aerosols. In Sect. 5 we quantify and interpret the physical processes influencing EDW using a forcing–feedback framework before finishing with a summary and conclusions (Sect. 6).

A range of monthly resolved observational and model datasets are analysed to gain insight into the historical EDW signal and its physical drivers. On the observational side, gridded surface air temperature anomalies from the HadCRUT5 dataset at 5°×5° resolution; are analysed along with surface air temperature estimates from the ERA5 reanalysis

Note that the ERA5 temperature data analysed here were accessed from the Copernicus Climate Data Store on 21 December 2023.

To analyse EDW, for each dataset the land-surface air temperatures (or land-surface air temperature anomalies in the case of HadCRUT5) are first binned by surface elevation. All grid boxes comprising more than 90 % land are included. For ERA5 and CESM1-LE, surface elevations are derived from the surface geopotential data. Surface elevations for HadCRUT5 are obtained by regridding the ERA5 geopotential data to the HadCRUT5 grid. For CMIP6, surface elevations are taken from the GFDL-CM4 model's orography file and are regridded before being used with the other models. A total of 11 elevation bins are defined, with equally spaced lower bounds of 0 m surface elevation for the lowest bin and 5000 m for the highest bin; the highest bin has no upper bound and includes all grid boxes higher than 5000 m. Temperatures are averaged over each calendar year (or each 3-month local season) and in each elevation bin, with area weighting, prior to the multi-decadal trends being computed using ordinary least-squares regression. Binned data are plotted as a function of the mean surface elevation in each bin (e.g. Fig. a). Using the standard error of the slope and the t statistic, confidence intervals are estimated for the trends under typical assumptions for ordinary least squares (e.g. normality of residuals). We repeated many of our analyses using a robust linear regression designed to be less sensitive to outliers, as implemented in the statsmodels robust linear models module v0.14.0; that uses a Huber T norm with a generalised maximum likelihood method (M estimation) to estimate the regression coefficients. Our conclusions are insensitive to this choice of regression model, but we state below any instances where slopes changed notably with the choice of statistical model.

Over our tropical–subtropical region, reanalysis and gridded station data show quantitatively similar pronounced warming over elevated surfaces. Specifically, when land-surface air temperatures are binned by surface elevation and then averaged spatially and over each calendar year, as described above, linear trends over the 1959–2014 period generally increase with height (Fig. a). Although central estimates of the linear trends differ between the station data (HadCRUT5) and reanalysis (ERA5) in many elevation bins, the 95 % confidence intervals of these trends always overlap. Spatial sampling differed substantially between the reanalysis and gridded station data due to their different resolutions (0.25 and 5°, respectively) and some spatio-temporal gaps in the station data; one effect of this can be seen in the different mean surface elevations within each elevation bin (this is especially prominent between 3 and 4.5 km surface elevation in Fig. a).

The magnitude of the EDW signal, and any differences in its value between datasets, can be quantified by an “EDW index”. Specifically, we define the EDW index as the slope obtained by regressing the warming trend in each elevation bin onto the mean surface elevation within each bin (this metric is similar to the “elevational gradient” analysed by ). This yields, for example, EDW indices of 0.0089±0.0080 K per decade per kilometre for ERA5 and 0.0189±0.0169 K per decade per kilometre for HadCRUT5 (Fig. b; the uncertainties listed here correspond to 95 % confidence intervals). These values are not statistically distinct from each other, and both have confidence intervals that do not include 0 (the p values are 0.043 and 0.042, respectively). Using a robust linear model instead of ordinary least squares yields slightly smaller central estimates of the EDW indices, 0.0087 K per decade per kilometre for ERA5 and 0.0180 for HadCRUT5, with respective p values of 0.058 and 0.035.

All of the above results were for annual mean temperatures, and the EDW indices vary by season (Fig. b). Local autumn and winter values are larger than local spring and summer values in both datasets; in HadCRUT5 only the autumn and winter seasons are statistically distinct from 0 at the 95 % level. The larger EDW signal in cool seasons is consistent with the larger contribution to EDW of mechanisms that are stronger at colder temperatures (i.e. the Planck feedback) and when surface snow and ice are prevalent (i.e. the surface albedo feedback); these effects are discussed in Sect. 5 below.

Upon examining the historical CMIP6 simulations, we find that the ensemble median EDW indices and warming trends in each elevation bin are roughly similar to those of our two observational datasets (Fig. a). This simulated EDW signal, averaged across the tropics and subtropics, is consistent with regional modelling studies focused on tropical EDW . For the warming trends, error bars for the two observational datasets fall within the interquartile range of the CMIP6 models in every elevation bin. The CMIP6 median EDW index falls within the error bars of the two observational datasets for annual mean data (Fig. b), although the model ensemble spans a large range with four models exhibiting reduced warming over elevated surfaces (negative EDW index) and a few models having EDW indices that are roughly an order of magnitude larger than observed. Models exhibit the largest EDW in winter, like observations, and the median values for summer and autumn are also broadly consistent with the observational estimates. There is less agreement in spring, with the CMIP6 median EDW index falling outside the HadCRUT5 error bars.

Do these measures of differential warming have geographic correspondence between the models and our two observational datasets? Annual mean warming trends (over the same 1959–2014 period used above) are the largest over many of the same orographic regions in all three datasets: the Tibetan and Iranian plateaus, the North American Cordillera, and the Brazilian Highlands in eastern South America (Fig. ). Warming is also strong over the Arabian Peninsula and Sahara in all datasets; although parts of these regions contain high orography, there does not seem to be a strong relation between the warming rate and surface elevation over Africa and the Arabian Peninsula. Since factors other than surface elevation are expected to influence the warming rate, such as surface aridity , we do not expect the map of warming rate to have the same pattern as the map of surface elevation. Given the prominence of enhanced warming over off-equatorial regions, particularly in the Northern Hemisphere (Fig. ), it seems worthwhile to assess whether the EDW signal seen in Fig.  might be an artefact of the polar amplification of warming that is seen primarily in the Northern Hemisphere e.g.. We assess this possibility in the Appendix, showing that the association of latitude with warming is insufficiently large to explain the majority of the observed EDW signal.

Is the historical EDW described in Sect. 3 a forced response of the climate system (e.g. to increasing greenhouse gases)? Or is it potentially an artefact of internal variability? To address these questions, we analyse data from the CESM1-LE simulations (1959–2005) to isolate the relative contributions of external radiative forcing and natural internal variability to historical EDW. Across the all-forcing ensemble, 17 out of 20 members show a positive EDW index (i.e. enhanced warming at elevation; Fig. ), implying that historical EDW is very likely, at least in part, to be radiatively forced. The EDW index varies substantially across members in the all-forcing ensemble, from +0.0288 to -0.0082 K per decade per kilometre (Fig. b). This suggests an important role for internal variability in affecting the magnitude of the historical EDW signal, consistent with . The EDW indices from the HadCRUT5 and ERA5 datasets are 0.0140±0.0189 and 0.0099±0.0096 K per decade per kilometre, respectively (Fig. b), which are similar to the ensemble-mean all-forcing EDW index (0.0135 K per decade per kilometre) and fall within the ensemble spread (these HadCRUT5 and ERA5 values differ from those given in the previous section because here we use an analysis period ending in 2005). These results suggest that both radiative forcing and internal variability have played an important role in shaping historical EDW.

Greenhouse gases and anthropogenic aerosols, two important radiative forcing agents , can both drive regional patterns of surface temperature change . To advance understanding of EDW, it is important to assess which forcing agent is responsible for the large-scale EDW signal over the historical period. To this end, we analyse the CESM1-LE single-forcing simulations, wherein greenhouse gases or aerosols are prescribed to pre-industrial levels so as to isolate the contributions of these forcing agents to historical trends (see Sect. 2). We find that greenhouse gases are the dominant driver of historical EDW (cf. grey and red markers in Fig. b). Aerosol forcing has only a weak influence on large-scale EDW (blue markers in Fig. b) but could potentially be important on regional scales e.g.. Inter-member correlations between tropical mean temperature trends and the EDW index are weak, for both the all-forcing and single-forcing experiments (Fig. b), suggesting that the internal variability influencing tropical mean warming is different in character from the variability controlling EDW, and that the magnitude of EDW is not simply determined by the rate of overall tropical warming.

EDW has been studied for over 2 decades, yet debate persists on the physical processes driving this phenomenon and its robustness across datasets. In this study, we examine historical EDW using gridded observations, reanalysis data, and climate models. Averaged over the tropics and subtropics, positive annual mean EDW indices (i.e. larger surface air warming trends for high-elevation regions) are identified in HadCRUT5 observations, ERA5 reanalysis, and across the CESM1-LE and CMIP6 ensembles. The EDW index varies substantially across seasons, with local winter showing the strongest relative warming of high-elevation surfaces. The warming trends binned by surface elevation are reasonably consistent across the datasets, suggesting that EDW is a robust response of the climate system to historical warming that is broadly captured by climate models. A simple calculation is used to argue that the majority of the EDW signal cannot be explained by elevated regions being situated further poleward where the warming trend is larger. Rather, EDW appears to be a phenomenon that is at least partially distinct from polar amplified warming.

Two approaches are taken to understand the mechanisms controlling annual mean EDW. First, analysis of 20 ensemble members from the CESM1-LE indicates – consistent with previous work – that historical EDW is likely to be a radiatively forced response of the climate system and not an artefact of internal variability. Furthermore, internal multi-decadal variability produces uncorrelated changes in the magnitude of EDW and the tropics-wide temperature trend; in other words, the magnitude of EDW is not simply set by the rate of overall tropical warming. Single-forcing CESM1-LE simulations also demonstrate that EDW, at least on large scales, is primarily driven by radiative forcing associated with increasing greenhouse gas concentrations rather than anthropogenic aerosols.

Second, a forcing–feedback framework based on TOA energy balance is used to directly quantify the physical processes contributing to, and opposing, EDW in the historical CMIP6 simulations. Consistent with previous studies, the surface albedo and Planck feedbacks favour amplified warming of elevated surfaces. The analysis also demonstrates that the (positive) water vapour feedback is weaker for high-elevation regions and therefore opposes EDW. This result contrasts with other studies, which argue (e.g. based on statistical relationships between water vapour and downwelling longwave fluxes in models; ) that the radiative effects of water vapour favour EDW. Here we use radiative kernels to isolate the influence of water vapour on EDW; this difference in methodology compared to previous studies may explain the differing results. The effect of the water vapour feedback on EDW is largely cancelled by the lapse rate feedback, as expected from physical reasoning. Cloud feedbacks are shown to strongly oppose EDW, a result which also contrasts with previous work. The forcing–feedback framework reveals two additional contributors to EDW that have received little attention to date. The first is radiative forcing, which is shown to oppose EDW because it is weaker (i.e. less positive) over cold, elevated surfaces. The second is energy transport by the atmospheric circulation, which favours EDW in the majority of CMIP6 models – a result which can be interpreted using diffusive arguments – but exhibits considerable inter-model uncertainty.

The analyses presented here provide new, quantitative insights into the processes driving EDW. However the large-scale approach taken in this study, using global datasets at relatively coarse spatial resolutions, has limitations. For example, in regions of complex terrain, the EDW signal is likely not well sampled by observational networks underpinning the HadCRUT5 and ERA5 datasets. Complex terrain is also an issue for global climate models e.g., potentially leading to biases in the simulation of processes known to be important for EDW, including mountain snow accumulation and orographic clouds. Future research could investigate the influence of such finer-scale effects on EDW using high-resolution models; work along these lines is already underway . More generally, this study could be expanded by examining EDW signals across different large ensemble projects, reanalysis products, and observational datasets. How EDW connects to warming of the tropical troposphere, which also increases with height, consistent with moist adiabatic adjustment, is another important and open question. The forcing–feedback framework presented here could be extended to examine the processes controlling EDW in specific seasons, specific regions, beyond 40° N and 40° S, and in simulations of both past and future climate states. The results in this study suggest that uncertainty in future EDW may be driven primarily by uncertainties in how atmospheric energy transport over land responds to climate change, along with uncertainties in surface albedo and cloud feedbacks. Improved understanding of how these processes vary with surface elevation is essential for building reliable EDW projections, with benefits for communities living in mountainous regions.