A drier than expected future, supported by near-surface relative humidity observations

Abstract

Despite continuous progress in climate modeling, global projections of the terrestrial water cycle remain highly model dependent. Here, we use quality-controlled gridded observations of temperature and humidity to constrain projected changes in continental near-surface relative humidity across the 21st century. Results show that the projections are poorly constrained when using surface temperature observations only and argue for mitigation policies that are not only rooted in global warming levels. Projections constrained with both near-surface temperature and relative humidity observations show an inevitable continental drying, especially in the northern midlatitudes where anthropogenic aerosols have, however, countered this long-term response until the late 1980s. A “strong drying” storyline is then used to highlight the urgent need for careful adaptation strategies and to suggest a possible contribution of land surface processes to model uncertainties.

Climate models underestimate both recent and future near-surface air drying over land, even when scaled with global warming.

INTRODUCTION

Almost 10 years ago, a commentary in Science (1) warned that changes in precipitation do not tell the whole story of hydrological changes caused by human-induced global warming: “Many regions will get more rain, but it appears that few will get enough to keep pace with the growing evaporative demand.” This suggestion was grounded in the predicted decrease in annual mean near-surface relative humidity (RH) over most land regions. It was heeded by the first working group of the Intergovernmental Panel on Climate Change (IPCC), which released last year its sixth assessment report (AR6). Chapter 8 pointed out that water cycle changes result not only from changes in precipitation patterns but also from an increase in the atmospheric evaporative demand because of greater warming over land than over the ocean and, consequently, a reduction in continental near-surface RH (2–4). However, both observed and simulated changes in evapotranspiration, and in precipitation minus evaporation (P − E), are still very uncertain, even when globally averaged over land (2, 5, 6). Structural and parametric model uncertainties still dominate the overall uncertainty in climate projections (2, 7), and the gap between understanding and predicting water cycle changes has not been bridged from AR5 to AR6.

It is thus urgent to combine our improved theoretical understanding (3) with better constrained projections to provide more reliable climate information to decision-makers. As the climate warms, both theoretical (8) and modeling (9) studies predict that RH will remain approximately constant at the global scale, leading to an increase in specific humidity, a positive water vapor feedback, and an overall intensification of the global water cycle (2). An early formal attribution study identified a human-induced significant global-scale increase in surface-specific humidity, with RH remaining approximately constant (10). However, the constant near-surface RH hypothesis seems to be no more valid over land, at least since the early 21st century (11). Global projections from the fifth phase of the coupled model project (CMIP5) showed uncertain changes with contrasted geographical patterns (4). In the highest emission scenario, they revealed a strong land-ocean contrast in the response of near-surface RH to global warming, with a possible but model-dependent decrease over land. However, there were at least two studies suggesting that most CMIP5 models underestimate the projected drying over land given their limited ability to capture the observed negative trends in RH (i.e., a rising water vapor deficit) since the late 20th century (12, 13).

In the present study, we use a recent update of quality-controlled observations of surface temperature (HadCRUT5) (14) and RH (HadISDH) (15) to constrain global projections from the state-of-the-art CMIP6 climate models. Compared to CMIP5, CMIP6 models do not show any improvement in their ability to converge on the response of near-surface RH to global warming (fig. S1), even in the highest emission scenario where such uncertainties cannot be attributed to internal climate variability (7). Over most land areas, the range of model responses varies from limited wetting to substantial drying. Only a few regions, particularly the Mediterranean basin, South Africa, and Amazonia, are subject to a robust drying, whose magnitude is, however, still highly model dependent. Such uncertainties remain a major obstacle for adaptation strategies but can be potentially narrowed through the use of observational constraints. For this purpose, we use the KCC (Kriging for Climate Change) Bayesian statistical method inspired from data assimilation (16). This package has been recently enriched to combine two observational constraints (17, 18). The method relies on a probabilistic assessment in which a CMIP ensemble of GCMs is taken as the “prior” distribution of projected anomalies, which is then narrowed with observations. This is a strong but common assumption that neglects the possibility that the models are all wrong, especially if they share common flaws in their structure or historical forcings. While this may lead to overconfident constrained projections, we will show that consistent results are obtained using either CMIP6 or previous-generation CMIP5 models. Moreover, KCC also accounts for observational uncertainties and may be, thus, less sensitive to this assumption than previously proposed Bayesian methods. More details about the KCC method can be found in the final Materials and Methods section.

RESULTS

We first illustrate the method using the global mean land surface response of RH (hereafter referred to as LSRH) projected by a subset of 32 CMIP6 models with only one realization of the historical experiment and the SSP5-8.5 high-emission scenario (Fig. 1). It should be emphasized here that KCC aims at constraining the forced model response, after discarding the contribution of internal climate variability. In Fig. 1A, we first check that the HadCRUT5-observed estimates (200 members) of the historical (1850–2021) warming allow us to constrain the projected increase in the global mean near-surface air temperature (GSAT). A 33% narrowing of the 5 to 95% confidence interval is obtained at the end of the 21st century and a downward shift of the best estimate, in good agreement with a previous assessment based on a larger subset of CMIP6 models (16).

Fig. 1. Constrained versus unconstrained annual forced changes in GSAT and global mean LSRH.

Mean (solid lines) and 5 to 95% range (shading) of the prior and posterior distributions of the annual forced GSAT and LSRH response to both natural and anthropogenic radiative forcings in historical simulations and SSP5-8.5 projections from 32 CMIP6 models: (A) HadCRUT-only observational constraint on GSAT, (B) HadCRUT-only observational constraint on LSRH, (C) HadISDH-only observational constraint on LSRH, and (D) HadCRUT and HadISDH observational constraints on LSRH. After the constraint, the 5 to 95% interval at the end of the 21st century is reduced by 33, 17, 22, and 37% in (A) to (D), respectively. The mean observed anomalies are show as black (gray) filled circles when they are (not) used for constraining the model response.

Our results, however, show that the same HadCRUT5 observations poorly constrain the projections of the LSRH response. Even the sign of the constrained LSRH response remains uncertain across the 21st century (Fig. 1B), and the confidence interval of the posterior is only narrowed by 17% at the end of the century compared to the prior. This narrowing is mostly the result of an upward shift of the lower 5% percentile. This limited constraint is consistent with the fact that the projected global warming does not tell the whole story about regional climate change (19). Even aggregated over global land, RH is not strongly constrained by HadCRUT5 observations despite the theoretical expectation that trends in continental humidity are directly linked to the ocean warming (20). Similar results are found when replacing HadCRUT5 by global sea surface temperature (SST) observations (HadISST1). This result confirms that there may be a gap between our physical understanding of climate change and our ability to deliver accurate projections (21).

The RH record from the HadISDH dataset, although being available only since 1973, provides another potential constraint on the projected LSRH anomalies (Fig. 1C). As for GSAT, we here take advantage of the estimated observational uncertainty estimate in each 5° by 5° grid cell of HadISDH to generate 200 estimates of LSRH (cf. the Supplementary Materials). Compared to the prior, the HadISDH observations allow us to narrow by 22% the posterior distribution of LRSH projections at the end of the 21st century. Beyond the reduced intermodel spread and unlike the GSAT observational constraint, the observational constraint here rules out a possible future increase in LSRH, with an ensemble mean response that is close to −3%. Combining the HadCRUT5 and HadISDH constraints has a limited effect on the ensemble mean response but reduces the intermodel spread by 37% in 2100 (Fig. 1D). This substantial narrowing of the model uncertainties highlights the power of the KCC method and the complementarity of the proposed observational constraints, although the obtained reduction of the intermodel spread is not fully additive.

Similar conclusions can be drawn from the intermediate emission scenario (SSP2-4.5; fig. S2) and further reinforce our confidence in the results. The constrained ensemble mean drying found in the high-emission scenario is greater (−4% in 2100) when averaging RH in the northern midlatitudes (fig. S3) and even stronger (−5% in 2100) when focusing on the June to September season (fig. S4). In this region and season, where and when a large fraction of the global food production is concentrated, the land surface drying is inevitable, all the more so as greenhouse gas (GHG) emissions are unabated and potentially associated with considerable ecological and agricultural impacts (22). Compared to LSRH, the boreal summer midlatitude drying is even less constrained by the observed global warming. However, the combined effect of the HadCRUT5 and HadISDH observational constraints is still substantial as evidenced by a 30% reduction in the intermodel spread. In all cases, none of the available CMIP6 models is able to capture the magnitude of the early 21st century drying. As discussed in the first KCC study (16), this remark highlights one possible limitation common to all Bayesian statistical methods: the fact that the prior distribution may not provide a comprehensive sampling of uncertainty.

However, and unlike most alternative methods, the KCC method allows recent and future climate change to be constrained in a consistent manner. If we now focus on a subset of nine CMIP6 models that have provided at least three realizations of the historical simulations with individual radiative forcings (cf. the Supplementary Materials), then the double observational constraint provides an unequivocal demonstration that human emissions of GHGs have been responsible for the recent continental near-surface drying (Fig. 2). This drying has been, however, countered by both anthropogenic and natural (volcanic) aerosols over much of the 20th century, which may explain why it has not been observed before the 1990s. This finding is consistent with the latest IPCC report (2) and with previous evidence of a strong anthropogenic aerosol influence on the global water cycle across the 20th century (23, 24).

Fig. 2. Temperature dependence and attribution of recent changes in global LSRH based on nine models.

(A) Scatterplot of recent changes in LSRH (%) versus GSAT (K). Recent changes are simply estimated as the difference between the 2001–2020 and 1979–1998 climatology, respectively. Individual CMIP6 models are shown as cyan crosses, while the ensemble mean and ensemble spread of their prior and posterior distributions are shown as crosses and ellipses in blue and red, respectively. The red solid line shows the linear regression fit of the posterior joint distribution. Observed trends and related uncertainties are shown in black. The gray dotted lines denote four illustrative rates of decrease ranging from 0 to −1.5%/K. (B) Constrained (solid lines) and unconstrained (dashed lines) time series of the LSRH response to natural (NAT), greenhouse gas (GHG), other anthropogenic (OA), and anthropogenic (ANT = GHG + OA) forcings over the period 1850–2020. All anomalies are estimated relative to the 1995–2014 baseline period.

As most CMIP6 models used in Fig. 1, the selected subset used in Fig. 2 tends to overestimate the observed global warming, but tends to underestimate the observed continental drying (Fig. 2A). Although the prior average drying varies depending on which model ensemble is chosen, their results are very close once the observational constraints are applied. However, the structural LSRH versus GSAT dependence across the nine CMIP6 models do not allow the KCC method to produce a scaled drying that is fully consistent with the observations. Looking at the best estimates, the posterior drying remains close to −0.5%/K, while observations rather suggest a threefold −1.5%/K scaling (Fig. 2A). Similar results are found when all available CMIP6 models shown in Fig. 1 are considered (fig. S5), thereby indicating that the underestimation of the scaled drying is not an artifact of the model subset used in Fig. 2. This mismatch highlights the need for large ensembles of independent models within CMIP and the importance of accounting for observational errors in KCC.

Compared to the prior ensemble mean response (dashed lines), the posterior response (solid lines) is not much different for non-GHG forcings but suggests an overestimated sensitivity to the GHG forcing over the period covered by the HadISDH dataset (Fig. 2B). At first glance, this result is not consistent with the underestimated response found in Fig. 1 but would be consistent if Fig. 1 had been produced with the subset of only nine models available for detection-attribution (not shown). In the northern midlatitudes (fig. S6), the observed recent drying is underestimated, in agreement with the KCC results obtained across the 21st century (fig. S3D). Expectedly, the influence of the anthropogenic aerosols is more pronounced than at the global scale. However, the response to both natural and anthropogenic aerosols is not much influenced by observations, which mostly constrain the response to the GHG forcing. This finding is consistent with a substantial narrowing of the CMIP6 projections using KCC given the increasing influence of GHGs across the 21st century in both intermediate and high-emission scenarios.

DISCUSSION

Our results show that the continental drying projected by the CMIP6 models is highly model dependent and that the multimodel ensemble mean is not necessarily the most likely response. Constraining the projections with both HadCRUT5 and HadISDH observations allows us not only to narrow model uncertainties but also to predict a stronger than simulated decrease in RH, especially in the northern midlatitudes. In contrast, the ensemble mean continental drying conditional to the observed historical warming only is weaker than simulated, and the associated intermodel spread is not much reduced compared to the prior distribution. This finding highlights a potential drawback of the current mitigation policy framings, based on global warming levels alone (25). Other policy-relevant metrics could be considered, not only because of the uncertain hydrological consequences at a given global warming level (2) but also given the plausible vulnerability of the mitigation options compatible with the Paris Agreement to the forthcoming water cycle changes (21).

As an illustration, Fig. 3 provides a storyline of plausible climate changes associated with the top 10 CMIP6 models projecting a strong continental drying across the 21st century (fig. S7). The SSP5-8.5 high-emission scenario is used again to illustrate this storyline approach. Compared to the full set of CMIP6 models (fig. S8), the selected models show, as expected, a stronger recent drying, but which is also more realistic with respect to the best guess estimate derived from the HadISDH multimember dataset (fig. S5). Although they are, thus, more credible than the “hot models” (16, 25), they also project a stronger surface warming (Fig. 3B), especially over the continental areas that exhibit a stronger drying (Fig. 3A). Significant differences in the projected precipitation anomalies are found over both land and ocean surfaces, including a lesser increase in the boreal midlatitudes and contrasted patterns in the tropics (Fig. 3C).

Fig. 3. Strong drying storylines.

Difference in the ensemble mean anomalies (2081–2100 minus 1995–2014 climatology) between a subset of 10 CMIP6 models showing the strongest global mean continental drying in the SSP5-8.5 scenario and the full set of available CMIP6 models for the same scenario: (A) near-surface RH (%), (B) near-surface temperature (K), (C) total precipitation (mm/day), and (D) total surface evaporation (mm/day). Stippling denotes the regions where the difference is significant at the 5% level.

More unexpectedly, total evapotranspiration anomalies show an overall weaker increase over land but a stronger increase over the ocean (Fig. 3D). This land-sea contrast is intriguing because it is sometimes assumed that surface evaporation will increase proportionally to the control evaporation under warmer conditions (6). However, possible changes in both soil moisture and plant stomatal conductance can invalidate this hypothesis over land. The weaker increase in land surface evapotranspiration despite a stronger near-surface drying (Fig. 3A) suggests a key role for land surface processes. This hypothesis is consistent with a detailed analysis of the RH response to an abrupt quadrupling of atmospheric CO₂ in the standard configuration of the CMIP6 global climate model from the Centre National de Recherches Météorologiques (CNRM-CM6-1), where a direct CO₂ effect on plant transpiration was identified as a key factor for understanding a stronger continental drying than in the previous-generation CNRM-CM5 model (26). However, a key question that could not be investigated in this study based on atmosphere-only simulations was the extent to which the land surface processes can influence the projected global warming.

In the understanding of changes in climate sensitivity between successive generations of global climate models, land surface processes have been rarely mentioned as one of the possible causes (27). However, our current understanding of climate variability at shorter time scales highlight that land surface anomalies can have remote and circumglobal effects (28). Idealized deforestation experiments also reveal nonlocal effects, including a global ocean cooling in the CMIP6 models where deforestation first leads to a widespread and significant cooling above the deforested areas (29). Such a possible land surface influence on global mean temperature is also consistent with Fig. 3B that shows an enhanced near-surface warming over the ocean in the strong-drying storyline. Such an interpretation remains, however, highly speculative given the strong overlap between the 10 hottest and 10 driest models within CMIP6 (fig. S7). We just note here that both storylines are not mutually exclusive and that land surface feedbacks can contribute to amplify global warming.

Looking again at all available CMIP6 models (Fig. 4), there is a clear emergent relationship between near-surface drying and near-surface warming globally averaged over land (Fig. 4A). Such a relationship does not imply a causality but is consistent with a possible amplification of global warming. Note that this emergent relationship would be much stronger if the four configurations of the European Centre for Medium-Range Weather Forecasts (ECMWF) model (i.e., the only models that show an unrealistic increase in LSRH according to KCC) were discarded from the CMIP6 ensemble. Even without these four models, the linear regression fit would show a nonzero offset that is consistent with a fast adjustment (i.e., drying) induced by increased CO₂ levels (26). The possible outliers highlight the well-known weakness of emergent constraints that are not necessarily robust across successive generations of models (30). In contrast, the KCC method is based on direct observational constraints and was shown to be relatively robust (16, 18). This is further supported by the present study that shows similar conclusions for CMIP6 (Fig. 2) and CMIP5 (fig. S9) models.

Fig. 4. Scatterplots of global land anomalies versus changes in LSRH.

(A) Near-surface air temperature (°C), (B) total precipitation (mm/day), (C) total evapotranspiration (mm/day), and (D) ratio between annual runoff and annual precipitation (%). All anomalies are estimated as differences between the 2081–2100 and 1995–2014 climatologies in the SSP5-8.5 high-emission scenario. Each symbol represents one of the 32 CMIP6 models (not all models are available for all variables). Red bars denote ±1 SD of interannual variability. If the squared intermodel correlation (R²) exceeds 0.25, then a linear regression fit is drawn as a black solid line.

An emergent constraint based on model biases in LSRH (fig. S10A) would be also consistent with the KCC results regarding the possible underestimation of the projected drying by a significant fraction of the available CMIP6 models. However, the link between model climatologies and model responses is much weaker across CMIP5 models (fig. S10B). This result agrees with the growing evidence that emergent constraints based on model biases may lead to overconfident projections (30). It does not contradict our previous conclusions and our “strong-drying” storyline because KCC is based on projected anomalies relative to a reference climatology and, thus, does not explicitly consider model errors in mean climate. However, it may suggest that the calibration of coupled models should be based not only on radiative equilibrium at the top of atmosphere and resulting SSTs but also on the water budget at the land surface and resulting soil moisture.

Coming back to Fig. 4, there is overall no clear link between LSRH and precipitation over land (Fig. 4B). In contrast, there is a strong emergent relationship between LSRH and land surface evapotranspiration (Fig. 4C). Because local evaporation does not strongly control local RH (because of moisture advection), Fig. 4C may be interpreted as the signature of a soil moisture and/or stomatal influence on both evapotranspiration and RH. Moreover, a stronger near-surface drying is generally associated with a strong ratio between annual runoff and annual precipitation (Fig. 4D), thereby further suggesting that changes in the land surface water budget may influence LSRH. Again, this emergent relationship would be stronger if the multiple configurations of the ECMWF model were not considered. These four models had been already noticed in Fig. 4A where they contribute to weaken the relationship between projected changes in RH versus Tair over land. Our results therefore support the claim that potential outliers may lead to spurious emergent constraints and overconfident projections across a limited set of models (30). However, our more robust KCC method and the relationships shown in Fig. 4 also advocate for a stronger attention paid to the representation of land surface processes in global Earth system models (31) and highlights the potential need for a stronger structural diversity therein.

MATERIALS AND METHODS

HadISDH and HadCRUT5 observations

HadISDH is a global gridded monthly mean surface humidity dataset. Quality-controlled and homogenized/bias-adjusted monthly mean anomalies (relative to a 1991–2020 base period) are provided alongside uncertainty estimates (observation and grid box sampling). Actual values, climatological mean, and SD are also provided. The dataset begins in January 1973 and is updated annually. Here, we use the 1973–2021 time series and focus over land only. HadISDH uses simultaneous subdaily temperature and dew point temperature data from >4500 quality-controlled HadISD stations that have sufficiently long records. All humidity variables, including RH, are calculated at hourly resolution, and monthly means are created. Monthly means are then homogenized using a pairwise algorithm to detect and adjust for features within the data that do not appear to be of climate origin. Stations with very large (>15% for RH) adjustments applied are removed. Measurement, climatological, and homogeneity adjustment uncertainty is estimated for each month. Climatological averages over the 1991–2020 period are calculated and monthly mean climate anomalies obtained. These anomalies (in addition to climatological mean and SD, actual values, and uncertainty components) are then averaged over 5° by 5° grid boxes. Given the uneven distribution of stations over time and space, sampling uncertainty is estimated for each grid box month. Although the coverage of land areas is not complete even at a 5° resolution (e.g., some limited gaps in the tropics), we consider that the whole time series are representative of the global land domain. This is consistent with our previous finding (26) that applying a HadISDH mask to the ERA5 reanalysis does not alter the annual mean time series compared to the full-coverage ERA5 global land values (cf. their figure 1). Regarding observational uncertainties, HadISDH does not directly provide multiple members as for the HadCRUT5 datasets. However, we have implemented a simple method to generate 200 estimates of the 1973–2021 annual mean time series. We have assumed no strong seasonality in the observational uncertainties so that the annual mean values of the monthly uncertainty estimates have been used to generate 200 members of annual mean values assuming a normal distribution. In doing so, we keep the steep reduction in observational uncertainties across the 1973–2021 period, with much larger uncertainties in the early record.

HadCRUT5 is one of the main datasets used to monitor global and regional surface temperature variability and trends and is here only briefly described (more details can be found at www.metoffice.gov.uk/hadobs/hadcrut5/). It is a global surface temperature product that combines gridded land surface weather station air temperatures with gridded ship and buoy SSTs. The observations have been quality controlled and bias adjusted to remove nonclimatic artifacts. HadCRUT5 is a departure from its predecessors in that two different versions are offered. Both versions include monthly anomalies over 1850 present on a 5° by 5° latitude-longitude grid. The first version has no interpolation of missing grid box values. Hence, there are wide coverage gaps in the polar regions and in the interiors of some continents such as Africa and South America. The second version is a spatially complete, infilled, or “analyzed” version with (almost) no coverage gaps and is the most suitable version to use for direct comparisons with climate model outputs (as in the present study). Both versions include a 200-member ensemble that samples the distribution of the systematic observational uncertainty and the analysis uncertainties.

CMIP6 and CMIP5 models

We make use of a large set of global climate models from both CMIP6 and CMIP5. We took all models providing at least one historical simulation and the corresponding SSP5-8.5 high-emission scenario for CMIP6 [or a similar representative concentration pathway (RCP8.5) for CMIP5] for both tas and hurs monthly mean variables, corresponding to near-surface air temperature and RH, respectively. As a result, we considered 32 CMIP6 models (slightly less for the intermediate SSP2-4.5 scenario; cf. missing models in fig. S7): ACCESS-CM2, ACCESS-ESM1-5, CESM2-WACCM, CMCC-CM2-SR5, CMCC-ESM2, CNRM-CM6-1-HR, CNRM-CM6-1, CNRM-ESM2-1, CanESM5, EC-Earth3-CC, EC-Earth3-Veg-LR, EC-Earth3-Veg, EC-Earth3, FGOALS-f3-L, FGOALS-g3, FIO-ESM-2-0, GFDL-CM4, GFDL-ESM4, GISS-E2-1-G, HadGEM3-GC31-LL, HadGEM3-GC31-MM, INM-CM4-8, INM-CM5-0, IPSL-CM6A-LR, KACE-1-0-G, MIROC-ES2L, MIROC6, MPI-ESM1-2-HR, MPI-ESM1-2-LR, MRI-ESM2-0, NorESM2-MM, and UKESM1-0-LL. Alternatively, we also used a subset of nine CMIP6 models for the detection and attribution analysis in Fig. 2 (ACCESS-ESM-1-5, CanESM5, CNRM-CM6-1, FGOALS-g3, GFDL-ESM4, HadGEM3-GC31-LL, IPSL-CM6A-LR, MIROC6, and MRI-ESM2-0). These nine models were selected because they provide at least three realizations for the following four experiments: hist-ALL (historical simulations with all natural and anthropogenic forcings), hist-GHG (simulations driven by evolving GHG concentrations only), hist-AER (simulations driven by evolving anthropogenic aerosol loadings only), and hist-NAT (simulations driven by evolving solar and volcanic forcings only). Historical simulations and the corresponding RCP8.5 high-emission scenario from only 20 CMIP5 models (bcc-csm1-1-m, BNU-ESM, CanESM2, CCSM4, CESM1-CAM5, CNRM-CM5, CSIRO-Mk3-6-0, GISS-E2-H, GISS-E2-H-CC, GISS-E2-R, GISS-E2-R-CC, HadGEM2-ES, inmcm4, MIROC5, MIROC-ESM, MIROC-ESM-CHEM, MRI-CGCM3, MRI-ESM1, NorESM1-M, and NorESM1-ME) have been also used. All model outputs have been retrieved from the Institut Pierre-Simon Laplace platform (https://mesocentre.ipsl.fr/plate-forme-physique/). Annual mean anomalies have been estimated relative to the 1995–2014 baseline reference period, as in the latest IPCC report. A bilinear regridding to a common horizontal grid (T127 grid of the medium-resolution CNRM-CM6-1 model) has been used for the global mapping of the multimodel ensemble statistics (e.g., fig. S1 and Fig 3), but the GSAT and global land average RH time series have been calculated from raw model outputs.

KCC method

The observational constraint method, called KCC, has been previously applied to global and regional warming (16, 17), as well as to global total precipitable water (18). It can deal with at least two different variables (17, 18), and there is no need that related observations cover the same period of time. KCC consists of three steps. First, the forced response of each climate model is estimated over the whole 1850–2100 period (after concatenation of historical simulations with corresponding 21st century projections). To also get attribution statements, the responses to ALL (all forcings), NAT (natural forcings only), and GHG forcings are estimated separately. Second, the sample of the forced responses from available climate models is used as a prior of the real-world forced response, assuming that “models are statistically indistinguishable from the truth.” Third, observations are used to derive a posterior distribution of the past and future forced response–given observations. This Bayesian method can be summarized using the following equation

$$\mathbf{y}=\mathbf{H}\mathbf{x}+\epsilon$$

where y is the time series of observations (a vector), x is the time series of the forced response (a vector), H is an observational operator (matrix), ɛ is the random noise associated with internal variability and measurement errors (a vector), and ɛ ∼ N(0, Σ_y), where N stands for the multivariate Gaussian distribution. In the case of two variables (as in the present study), x and y are simply built as the concatenation of the related time series. Climate models are used to construct a prior on x: π(x) = N(μ_x, Σ_x). Then, the posterior distribution given observations y can be derived as p(x|y) = N(μ_p, Σ_p). μ_p and Σ_p are available in closed-form expressions.

In the following, we mostly assess the forced response of annual and global mean LSRH, as well as the response to specific subsets of radiative forcings (attribution). These forced responses are then constrained by Global Mean Surface Temperature records (GMST, a blending of near-surface air temperature over land and sea ice and of SST over the ice-free ocean, therefore a good surrogate for GSAT) and/or by observations of LSRH. The same technique can be easily applied to selected regions (e.g., the northern midlatitudes) and seasons (e.g., June to September).

Therefore, we consider the following CMIP vector

$$\mathbf{x}=({\mathbf{T}}_{\mathrm{all}},{\mathbf{R}\mathbf{H}}_{\mathrm{all}},{\mathbf{R}\mathbf{H}}_{\mathrm{ghg}},{\mathbf{R}\mathbf{H}}_{\mathrm{nat}})$$

where each element is an entire 1850–2100 time series of the forced response, and T and RH stand for GSAT and LSRH, respectively. “all,” “ghg,” or “nat” are the subsets of external forcings considered. Similarly, we define an observed vector as

$$\mathbf{y}=({\mathbf{T}}_{\mathrm{obs}},{\mathbf{R}\mathbf{H}}_{\mathrm{obs}})$$

i.e., only observed time series are used in y. The length of these time series varies: 1850–2021 for GMST and 1973–2021 only for LSRH. As a result, x is a very long vector, and all attribution or projection diagnoses presented below can be derived from the posterior distribution p(x|y). Following (16), μ_x and Σ_x are estimated as the sample mean and covariance of the forced responses. Σ_y requires statistical modeling of internal variability and measurement errors, and we use a mix of autoregressive processes of order 1 to model internal climate variability. The intrinsic variance of both GMST and LSRH is derived from observations after subtracting the multimodel mean estimate of the forced response of GSAT and LSRH, respectively. We also assume dependence between GMST and LSRH internal variabilities, by accounting for the correlation between the two residuals in Σ_y. Such a dependence is, however, limited (correlation of 0.156) when assessed over the common 1973–2021 period of the HadCRUT5 and HadISDH dataset. The assessment of measurement uncertainty is based on the HadCRUT5 ensemble for GMST (200 members), while we have also generated 200 time series of LSRH from the HadISDH dataset (see previous HadISDH section).

Supplementary Materials

This PDF file includes:

Figs. S1 to S10