1. Introduction

In a warming climate, predicting the rate at which global-mean precipitation scales, termed hydrologic sensitivity (HS), is one of the greatest challenges of climate science. The theoretical estimate for HS is about 2% K⁻¹, dictated by constraints in the global energy budget (Allen and Ingram 2002; Held and Soden 2006; Vecchi and Soden 2007). HS may be measured as the sensitivity of global precipitation directly to temperature (Kramer and Soden 2016; Pendergrass 2020) or can include fast adjustments of precipitation to radiative forcings (Fläschner et al. 2016; Yeh et al. 2021). The latter tends to be lower because CO₂ forcing suppresses the increase in radiative cooling with warming, thus slowing the rate of precipitation increase (Kramer and Soden 2016). Projections from global climate models (GCMs) are much more uncertain for the direct response to temperature (0.2%–4.6% K⁻¹) than including fast adjustments to radiative forcings (0.7%–2.3% K⁻¹) (Kramer and Soden 2016). Observation-based studies have reported values of HS at 6% K⁻¹ (Wentz et al. 2007), 3.4% ± 0.9% K⁻¹ (Allan et al. 2014), 2.8% ± 0.9% K⁻¹ (O’Gorman et al. 2012), and 2.0% ± 0.5% K⁻¹ (Allan et al. 2020), with the disagreement arising from the period studied and the choice of precipitation dataset. These observational estimates include both the fast response of precipitation to radiative forcing and the direct response to warming, which are highly challenging to disentangle.

The short observational record is rich in natural climate variability, associated with large temperature anomalies. In particular, El Niño–Southern Oscillation (ENSO) causes variability of global-mean surface temperature on the time scale of 5–10 years (Gu and Adler 2013; Adler et al. 2017). In addition, global cooling was observed following the eruptions of El Chichón and Mount Pinatubo in 1982 and 1991, respectively. Also, Pacific decadal variability (PDV) has contributed a cooling signature from the late 1990s onward (Gu and Adler 2013). This added uncertainty raises the question of HS in the context of internal variability. In particular, how much does global precipitation increase/decrease per degree of a global-temperature anomaly? This issue is complex because precipitation variability tracks temperature variability more closely during some periods than others (Gu and Adler 2013).

Different studies have placed importance on different terms on the right-hand side in determining the GCM spread in HS. For example, unrealistic representation of the surface term, SH, has a tendency for GCMs to mute HS (Richter and Xie 2008). Regarding the SWA term, Pendergrass and Hartmann (2012) found that differences in black carbon forcing across GCMs causes a range in dSWA/dT and hence HS. Also regarding the SWA term, DeAngelis et al. (2015) showed that, due to differences in radiative transfer schemes, GCMs vary in their rate of dSWA/dT, and also in dSWA/dPW, where PW is precipitable water. In a warming climate, enhanced water vapor increases shortwave absorption. Given that the observations suggest that the GCMs generally underestimate dSWA/dPW, they concluded that dSWA/dT is underestimated in CMIP5, which would overestimate HS in the absence of biases in the other terms in (1). However, this relationship between dSWA/dT and dSWA/dPW weakened in CMIP6 (Pendergrass 2020), which could indicate progress in the GCMs’ representations of this process.

The longwave cooling term is perhaps the greatest contributor to model spread in HS and dictates that HS associated with internal variability is greater than that associated with long-term warming. In particular, unlike the internal variability case, HS associated with long-term warming is driven by increasing CO₂ levels, which suppress the increase in radiative cooling with warming; hence the precipitation increase is supressed (Kramer and Soden 2016). Many studies have focused on trying to quantify the radiative-cooling strength or identify model errors associated with it. Watanabe et al. (2018) argued that GCMs overestimate HS due to an underestimate of the low-level longwave cloud radiative effect, resulting in excessive longwave cooling. However, Pendergrass (2020) argued that this constraint does not apply to HS because it only impacts the surface, and not the top-of-atmosphere (TOA), radiative budget. By contrast, Mauritsen and Stevens (2015) suggested that the GCMs underestimate HS due to an underestimate in the rate of tropical high-cloud shrinkage with warming (dCF/dT_s), which results in more outgoing longwave radiation (OLR), the so-called iris effect (Lindzen et al. 2001). This effect could result from the projected tightening of the intertropical convergence zone (ITCZ) and expansion of the Hadley circulation, resulting in more of the tropics having clearer skies. Based on this effect, Su et al. (2017) found that GCMs whose ascending branch of the Hadley circulation contracts more per degree of warming are also those whose dCF/dT_s is more negative (i.e., with more high-cloud shrinkage per degree of warming). This relationship enabled them to constrain the projections of HS, in particular suggesting that only the GCMs with the largest values are realistic.

Instead of the full observational record, the above study employed observational data just during 1995–2005. The authors chose this period because there were no major volcanic eruptions and it contains the highest correlation between global temperature and precipitation anomalies in the observational record. Hence, HS is more easily isolated than in other periods. Perhaps most relevantly, this period contained a major El Niño event, followed by prolonged strong La Niña conditions. The latter forced an intensification of the Walker circulation and contributed to suppressed global warming over 1999–2013 (Kosaka and Xie 2013; Merrifield 2011; L’Heureux et al. 2013). The fact that an emergent constraint on HS was found during this period of intense ENSO activity, both positive and negative anomalies, suggests that years of pronounced ENSO variability may be analogous to long-term warming, in terms of the global precipitation response. It is well documented that under anthropogenic forcing, GCMs project a slowdown of the Walker circulation and El Niño–like warming (Ying et al. 2016; Zheng et al. 2016). We hypothesize that as the Walker circulation weakens (intensifies) during El Niño (La Niña), the resulting positive (negative) anomalies of global-mean precipitation in a given GCM are a predictor of its HS under Walker circulation weakening in the future. In particular, we seek to answer the following: 1) Can HS under ENSO be diagnosed using preindustrial climate simulations that isolate natural variability? 2) Is there a relationship across GCM ensembles between HS diagnosed under ENSO versus future warming? 3) If so, can observational estimates be used to constrain projections of future hydrological intensification?

We address these questions by calculating HS in the latest CMIP6 ensemble, both in simulations purely representing internal variability and those representing anthropogenic forcing. We show the intermodel correlation between HS under ENSO versus anthropogenic forcing, as well as diagnosing HS under ENSO according to observations.

2. Data and methodology

a. CMIP6 experiments

This study uses monthly data of sea surface temperature (SST), surface air temperature T_s, and precipitation P from a suite of idealized CMIP6 experiments, in addition to the historical and projected twenty-first-century simulations. SST is required to calculate ENSO, while T_s and P are required to calculate HS. To calculate hydrologic sensitivity under ENSO, we use the piControl simulations (Eyring et al. 2019). These are centuries-long simulations in which atmospheric greenhouse gas concentrations are kept fixed at preindustrial levels. This enables us to isolate the climate system’s internal variability in the absence of any long-term warming trend. We use all CMIP6 models archiving piControl data of SST, T_s, and P for at least 500 years. Because some models exhibit variability during the first 200 years or so that resembles model spinup, we discard the first 200 years of output in each model and analyze years 201–500.

We use both the 1pctCO2 and abrupt-4xCO2 simulations (Eyring et al. 2019) to calculate hydrologic sensitivity in the context of anthropogenic forcing. In 1pctCO2 simulations, atmospheric CO₂ concentrations are initially at preindustrial levels, then increase by 1% yr⁻¹. This experiment allows an analysis of the response of precipitation to warming in the context of transient external forcing. In abrupt-4xCO2 simulations, preindustrial levels are instantaneously quadrupled and then held fixed. This experiment allows an analysis of how precipitation responds to warming in the context of a quasi-equilibrium response to external forcing. We retain the output for the first 150 years (the period archived for most models) of both the 1pctCO2 and abrupt-4xCO2 simulations. We discard any models archiving fewer years than this.

We discard any models that do not meet the above-specified requirements for all of piControl, 1pctCO2, and abrupt-4xCO2. This strategy ensures that the same ensemble of GCMs (34 in number) is analyzed for each of the experiments. We analyze the first realization for each GCM and experiment (r1i1p1f1 where available; see Table 1).

Table 1

CMIP6 models used in the study.

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In addition to the idealized experiments, we use the GCMs that archive monthly T_s and P for both the historical and the Shared Socioeconomic Pathway (SSP) 5–8.5 experiments. SSP5–8.5 is a high-emissions scenario from 2015 to 2100 (O’Neill et al. 2016). Combined with the historical simulations, this provides a 250-yr simulation of historical and projected anthropogenic warming, hereafter Hist + SSP585. Of the 34 GCMs identified based on the idealized experiments, 29 archive the required data for Hist + SSP585 (Table 1). Our focus in this study is on the idealized experiments, but we include the Hist + SSP585 data for reference.

We calculate area-weighted global-mean time series of T_s and P for each GCM and experiment, averaging over each GCM’s native grid. These are denoted T_G and P_G. For piControl, because we are analyzing internal variability, we calculate the time series of monthly-mean T_G and P_G. However, for the climate change experiments, because we are interested in the long-term trends, we calculate the annual-mean time series and apply a 10-yr running mean.

We then normalize the time series. For the anthropogenic-forcing simulations, we calculate anomalies relative to the beginning of the time series:

$T_{\mathit{G}}^{\mathbf{\prime }}=T_G-T{0}_G,\hspace{1em}{P}_{\mathit{G}}^{\mathbf{\prime }}=\frac{P_G-P{0}_G}{P{0}_G},$(2)

where T0_G and P0_G denote the first nonmissing value of T_G and P_G after applying the 10-yr running mean. Thus, these anomalies represent the degrees of warming and percentage increase of precipitation for each year, relative to the preindustrial climate. We found there to be no sensitivity of the calculation of HS to the length of baseline climate (e.g., if averaging over the first 20 or 30 years rather than 10 years to calculate T0_G and P0_G).

For piControl, we calculate anomalies from the monthly climatology of the time series:

$T_G^{\mathbf{\prime }}=T_G-\overline{T_G},\hspace{1em}{P}_G^{\mathbf{\prime }}=\frac{P_G-\overline{P_G}}{\overline{P_G}}.$(3)

Overbars denote the time mean of the time series for the given calendar month. Thus, these anomalies represent the degrees of temperature deviation and percentage of precipitation deviation from the monthly climatologies.

Having deseasonalized the piControl time series, we apply a 5–10-yr bandpass filter to $T_G^{\mathbf{\prime }}$ and $P_G^{\mathbf{\prime }}$ (Fig. 1a). This is because calculating HS from raw values places too much emphasis on high-frequency variability. The 5–10-yr filter is designed to represent the response of global temperature and precipitation to ENSO variability. We experimented with other filter time scales and briefly discuss this sensitivity in section 3. The bandpass filter renders the last decade or so of the time series as near zero, even if the unfiltered $T_G^{\mathbf{\prime }}$ and $P_G^{\mathbf{\prime }}$ are large over that time. For the piControl simulations, with 300 years of retained data, this could be easily remedied by removing those last few years. However, for the observational estimates (see section 2b), this would remove a significant amount of the data period. Thus, to be consistent between the GCMs and observations, we make the $T_G^{\mathbf{\prime }}$ and $P_G^{\mathbf{\prime }}$ periodic prior to applying the bandpass filter. Upon visual inspection of the filtered versus raw time series, we find that this technique preserves the occurrence of maxima and minima in the final decade (not shown), which would be near zero without making the time series periodic.

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The relationship in CMIP6 between HS under ENSO vs anthropogenic forcing: (a) $T_G^{\mathbf{\prime }}$ and $P_G^{\mathbf{\prime }}$ in piControl; (b) as in (a), but discarding calendar years without an ENSO event of magnitude > 1.5 (ENSO is overlaid in gray; the y axis spans 4.0 to −4.0); and (c) $T_G^{\mathbf{\prime }}$ and $P_G^{\mathbf{\prime }}$ in 1pctCO2. Note that (a)–(c) are shown for CESM2 as an example, with the resulting HS quoted above each panel. (d),(e) The analysis in (a)–(c) is repeated for all GCMs, yielding the intermodel comparison between HS in piControl vs 1pctCO2. In (d) HS in piControl is calculated as in (a); in (e), it is calculated as in (b). In (d) and (e) the least squares regression line is plotted and the Spearman rank order correlation coefficient is quoted above the panel. In (e), INM-CM4-8 is excluded because its piControl simulation does not include any ENSO events of magnitude > 1.5.

Citation: Journal of Climate 35, 21; 10.1175/JCLI-D-21-0842.1

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Finally, for each GCM and experiment, we perform a least squares linear regression between the $T_G^{\mathbf{\prime }}$ and $P_G^{\mathbf{\prime }}$ time series to calculate the hydrologic sensitivity. Meanwhile, we define ENSO by the Oceanic Niño Index (the 3-month running-mean monthly anomaly of SST, averaged over 5°N–5°S, 120°–170°W).

We also analyze multiple variables from the 1pctCO2 and piControl simulations at each grid cell. Monthly anomalies of these variables are calculated at a given grid cell, after bilinearly interpolating each model grid to a uniform 2° × 2° latitude–longitude grid. Thus, for some variable X we calculate X′ = X − X0 for 1pctCO2 and $X^{\prime }=X-\overline{X}$ for piControl, with X0 and $\overline{X}$ defined the same as for T_G and P_G, but at each individual grid cell (and, in the case of 3D variables, at the given pressure level). Finally, the time series of X′ is regressed against that of $T_G^{\mathbf{\prime }}$, with the 5–10-yr filter previously described applied to both variables, to give the local sensitivity of the given variable to global surface temperature. These variables are precipitation, surface temperature, zonal and meridional wind speed, and vertical velocity. For each variable there is a small number of the 34 models for which data are unavailable (Table 1), so that the ensemble is slightly smaller than that for HS. This analysis allows us to analyze the differences between GCMs in how they represent the changing global circulation under anthropogenic forcing and ENSO, in relation to the GCM spread in HS.

3. Evaluation of hydrologic sensitivity under internal variability versus anthropogenic forcing

We begin by computing HS across CMIP6 in both the anthropogenic forcing and internal variability cases. In Fig. 1c, we show the time series of $T_G^{\mathbf{\prime }}$ and $P_G^{\mathbf{\prime }}$ in 1pctCO2 in one GCM, CESM2, as an example. In accordance with the linear increase in CO₂, temperature quasi-linearly increases through the 150-yr simulation. In this GCM, there is a 5.8-K warming after 150 years. However, this is variable across GCMs (Fig. S1 in the online supplemental material), reflecting the CMIP6 spread in climate sensitivity (Flynn and Mauritsen 2020; Zelinka et al. 2020). The precipitation trend closely follows the temperature trend, increasing by 9% by the end of the simulation. Regressing the precipitation anomalies against temperature, this gives a HS of 1.6% K⁻¹. Similarly, in the piControl run of the same GCM, the precipitation anomalies closely follow the temperature anomalies at a near-constant ratio, with a HS of 2.5% K⁻¹ (Fig. 1a). Performing the same analyses for all 34 GCMs, we regress the calculated HS values in piControl versus 1pctCO2 (Fig. 1d). The model spreads in HS in piControl (0.8–4.2% K⁻¹) and 1pctCO2 (1.1–2.2% K⁻¹) are similar to those in 1pctCO2 in CMIP5 (Kramer and Soden 2016). There is a significant positive Spearman rank order correlation, hereafter r, across the ensemble (0.41, p < 0.05), indicating some tendency for high-HS GCMs under internal variability to also simulate high HS under anthropogenic forcing.

The 5–10-yr filter applied to the piControl time series isolates relatively low-frequency ENSO variability (ENSO is overlaid in Fig. 1a). Performing the same intermodel comparison as in Fig. 1d but for varying filter time scales we find that 5–10 years is optimal for relating HS between piControl and 1pctCO2 (Fig. S2). With this time scale, although the frequency is too low to capture every ENSO oscillation, it is sufficient to capture the maxima and minima of T_G and P_G associated with major El Niños and La Niñas.

The large ENSO threshold applied in Fig. 1 is necessary to differentiate high- from low-HS_ENSO GCMs. In particular, the intermodel correlation between HS_future and HS_ENSO is 0.40, 0.44, 0.56, and 0.66 for ENSO thresholds of 0.5, 1.0, 1.5, and 2.0, respectively (Fig. S4). However, the 2.0 threshold reduces the piControl simulations to very low samples in many GCMs (Fig. S3), preventing a robust representation of intermodel spread. Thus, 1.5 is deemed the highest reliable threshold for HS_ENSO. Similar results are found when filtering by El Niño and La Niña individually; that is, for El Niño we filter by years with ENSO > 0.5, 1.0, 1.5, and 2.0, and for La Niña we filter by years with ENSO < −0.5, −1.0, −1.5, and −2.0 (Figs. S5 and S6). For both El Niño and La Niña the relationship is maximized for a threshold of 1.5, likely due to the small samples of El Niño/La Niña events of magnitude > 2.

We find similar results by correlating HS_ENSO in piControl against HS_future abrupt-4xCO2 (see Fig. S7, which is equivalent to Fig. S4 except with HS diagnosed from abrupt-4xCO2 instead of 1pctCO2), with the relationship maximized (r = 0.57) for the ENSO threshold of 1.5. Note that the higher values of HS in abrupt-4xCO2 than 1pctCO2 match those of Pendergrass (2020), who also used abrupt-4xCO2 as the anthropogenic forcing scenario in their study. This is because abrupt-4xCO2 represents the direct response of the hydrological cycle to warming, while 1pctCO2 includes the damping effect of CO₂ forcing, occurring simultaneously with the warming. We proceed for the remainder of the study based on the comparison between piControl and 1pctCO2. This is because the intermodel variations in HS in 1pctCO2 are much better correlated with those in Hist + SSP585 and with similar values of HS (Fig. S8; r = 0.88 for 1pctCO2 versus 0.54 for abrupt-4xCO2). This indicates that the HS diagnosed from 1pctCO2 is a much better proxy for the projected twenty-first-century HS, a quantity of great societal relevance.

The requirement of a high ENSO threshold is because it reduces the events to those with a maximum positive (negative) SST anomaly in the central Pacific under El Niño (La Niña). Figure 2 (top row) shows the distributions of longitude in the equatorial Pacific at which the maximum SST anomaly is found, hereafter lon_SSTmax, based on various El Niño thresholds. Among years where the ENSO maximum is 0.0–1.0, there is a relatively even distribution of lon_SSTmax across the Pacific. But as we move to more extreme El Niños, lon_SSTmax becomes increasingly concentrated between about 170° and 120°W (i.e., the Niño-3.4 region). Similar results are found based on the longitude of maximum negative SST anomaly (lon_SSTmin) under La Niña (Fig. 2, second row). Among La Niñas between 0.0 and −1.0, lon_SSTmin is frequently in the far west and far east equatorial Pacific. But the more extreme La Niñas are increasingly centered in the central Pacific. It is not surprising that the events with the highest ENSO magnitudes should consist of a maximum anomaly within the Niño-3.4 region, given that this is the region upon which ENSO was defined. However, when filtering ENSO events by lon_SSTmax and lon_SSTmin we find that HS under central Pacific ENSO events is indeed a much better predictor for HS_future (r = 0.62) than HS under east Pacific ENSO events (r = 0.34) (bottom row of Fig. 2). An alternative way of making this comparison is to repeat the analysis thus far performed, but with ENSO defined by the Niño-3 region (i.e., the equatorial east Pacific; Fig. S9). This method reaffirms that HS under east Pacific ENSO events is a poorer predictor (cf. Fig. S4, based on Niño-3.4). Thus, HS under central Pacific ENSO events, with ENSO defined by the Niño-3.4 region, is the best predictor of HS_future.

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(top) The distribution of longitude at which the maximum positive SST anomaly is found in the equatorial Pacific (5°N–5°S, 150°E–80°W), conditioned on El Niño years where the ENSO maximum is in the given ranges. (middle) As in the top row, but for the longitude of maximum negative SST anomaly, conditioned on La Niña years where the ENSO minimum is in the given ranges. Each distribution is calculated for each GCM then averaged over all GCMs, excluding those that do not simulate any El Niño/La Niña events of the given magnitude. The bin size is 10°, where the given value on the x axis is the lower bound of the bin. (bottom) As in Fig. 1e, but just sampling years where the longitude of the maximum positive (negative) SST anomaly for El Niño (La Niña) is west of 120°W (central Pacific ENSO) and east of 120°W (east Pacific ENSO).

Citation: Journal of Climate 35, 21; 10.1175/JCLI-D-21-0842.1

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4. Observational evaluations of hydrologic sensitivity

Given that the GCM spread in HS under anthropogenic forcing is related to that under ENSO, we turn our attention to HS_ENSO in the observational record. The observational record deemed reliable (see section 2) is just 34 years long, a small fraction of the 300 years of unperturbed climate represented by the retained piControl simulations. Although we remove the long-term trend from the observational T_G and P_G, there is large uncertainty separating low-frequency variability from the long-term trend for such a short period. Moreover, the observational record used consists of a prolonged period of La Niña conditions sandwiched by major El Niños in 1997/98 and 2015/16. Hence it is not a fully representative sample of internal variability. However, by filtering by the magnitude of ENSO events, in both the observations and GCMs, we expect to account for this issue to some extent. We also note the caveat that GPCP is primarily based on satellite estimates over ocean but rain gauges over land, which have nonuniform biases. This caveat is particularly relevant for studying ENSO events in which the proportions of global precipitation falling over land versus ocean may change. This adds further uncertainty in the calculation of global-mean precipitation under El Niño versus La Niña. Noting these limitations, we employ the observations to derive our best possible estimate of HS_ENSO.

In Fig. 3, we plot the monthly time series of $T_G^{\mathbf{\prime }}$ and $P_G^{\mathbf{\prime }}$ during 1988–2021. These time series are deseasonalized, detrended, and 5–10-yr bandpass filtered to match the piControl simulations (Fig. 1a). Under |ENSO| > 0.5, almost the entire observational record is retained (Fig. 3a). However, with the transition to greater ENSO thresholds, an increasingly large fraction is discarded, so that under |ENSO| > 2.0, only the El Niños of 1997/98 and 2016/17 are retained. The HS_ENSO varies slightly between the |ENSO| > 0.5 (7.2% K⁻¹), |ENSO| > 1.0 (6.4% K⁻¹), and |ENSO| > 1.5 (7.7% K⁻¹) thresholds. But under |ENSO| > 2.0 there is a large reduction to 5.1% K⁻¹, due to the small amount of available data, similar to the piControl simulations. The lack of robustness under |ENSO| > 2.0 is demonstrated in Fig. 3e in which bootstrapping methods are employed to identify the 95% confidence interval of HS_ENSO under the varying ENSO thresholds. Up to the |ENSO| > 1.5 threshold, the uncertainty is within 15% of the calculated value. However, for |ENSO| > 2.0 the uncertainty range is 2.1%–7.3% K⁻¹, illustrating that the observational record is insufficient to robustly estimate HS under such strong ENSO events. For each ENSO threshold the GCM values of HS_ENSO are overlaid. These illustrate that, up to |ENSO| > 1.5, the observations robustly represent much greater HS than the GCMs. In particular, even the lower bound of the observational uncertainty is almost double that of the highest-HS GCMs.

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(a)–(d) HS_ENSO calculated in the observational record based on varying ENSO thresholds, discarding calendar years without an ENSO event of magnitude above the given threshold. The y-axis scale for ENSO is 3.0 to −3.0. (e) The uncertainty of HS_ENSO based on bootstrapping of the observations. For each threshold, N samples with replacement of monthly $T_G^{\mathbf{\prime }}$ and $P_G^{\mathbf{\prime }}$ are performed (with each sample of $T_G^{\mathbf{\prime }}$ and $P_G^{\mathbf{\prime }}$ taken at the same time step as one another), where N is the number of retained months plotted in (a)–(d). Then HS is calculated based on those N samples, and the process is repeated 1000 times. The shaded region spans the 2.5th–97.5th percentiles of HS, based on the 1000 replications. The HS_ENSO values calculated from each GCM’s piControl simulation (shown as scatterplots in Fig. S4) are overlaid, with the multimodel median (MMM) plotted in bold. The curve for one GCM (INM-CM4-8) only goes up to 1.0 on the x axis because this is the largest ENSO threshold to be exceeded in its piControl simulation.

Citation: Journal of Climate 35, 21; 10.1175/JCLI-D-21-0842.1

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The comparison presented above is restrictive because the recent historical climate represented by the observational record has been perturbed by anthropogenic forcing, in contrast to the preindustrial climate represented by the piControl simulations. Thus, for a more direct comparison, we repeat the analysis, but calculating HS_ENSO from Hist + SSP585 over the same years as the observations (1988–2021). Because this 34-yr period within Hist + SSP585 constitutes a small fraction of the ENSO events represented by piControl, these GCM results are noisier. Nevertheless, similar major underestimates of HS_ENSO by the GCMs, according to the observations, are evident (Fig. S10).

5. Changes to global circulation in high- versus low-HS GCMs

We subsequently attempt to understand the high intermodel correlation between HS_future and HS_ENSO. We begin by comparing the spatial patterns of different variables under future warming versus ENSO (Fig. 4). Under ENSO, the regression of local SST against T_G, averaged across GCMs, unsurprisingly exhibits a large maximum in the central Pacific, with the rest of the Pacific resembling the positive phase of the Pacific decadal oscillation (Fig. 4a). Under anthropogenic forcing, the El Niño–like warming is maximized in the east Pacific (Fig. 4b), as already documented for climate change experiments in CMIP6 (Tebaldi et al. 2021). Therefore, it may be surprising that HS under central Pacific ENSO is the best proxy for HS_future (Fig. 2). However, despite the differences in maximum SST anomalies, the Walker circulation responses are highly similar between central Pacific ENSO and future warming (Figs. 4e,f). In both regimes, there are enhanced low-level westerlies (vectors) and ascent (colors) over the equatorial Pacific, reduced ascent over the warm pool, enhanced low-level easterlies over the Indian Ocean, and enhanced ascent over the west Indian Ocean. These features all indicate a weakened tropical circulation, which arises to balance the greater rate of moisture increase than precipitation increase under warming (Held and Soden 2006). Consequently, under both ENSO and anthropogenic forcing, the maximum precipitation sensitivity is in the equatorial Pacific (Figs. 4c,d). And both consist of drying over the warm pool and wetting over the west Indian Ocean/East Africa, due to the well-known positive Indian Ocean dipole under El Niño (Mason and Goddard 2001; Barlow et al. 2002; Nazemosadat and Ghasemi 2004; Mariotti 2007; Hoell and Funk 2013; Moore et al. 2017).

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The local sensitivity of different variables to (left) global temperature under ENSO (calculated from years of piControl with an ENSO event of magnitude > 1.5) and (right) future warming (calculated from 1pctCO2), averaged across all available GCMs. (top) Shown are (a) the regression of local SST against $T_G^{\mathbf{\prime }}$ (hence dimensionless) and (b) the local rate of SST warming. (middle) The regression of local precipitation against $T_G^{\mathbf{\prime }}$. (bottom) The regression of 500-hPa ω (colors) and 850-hPa wind vectors (missing where the 850-hPa level is below the surface) against $T_G^{\mathbf{\prime }}$. For the bottom panels, the ensemble is slightly smaller depending on available data (see Table 1).

Citation: Journal of Climate 35, 21; 10.1175/JCLI-D-21-0842.1

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To explain the spread in HS across CMIP6, in Fig. 5 we compare maps of different variables between high- and low-HS GCMs under ENSO. The tropical precipitation response is magnified in the high-HS compared to low-HS GCMs (cf. Figs. 5a and 5c; differences are shown in Fig. 5e). In particular, the high-HS GCMs consistently (illustrated by stippling) have greater enhancement of precipitation in the equatorial Pacific, greater reduction in the East Indian Ocean, and greater enhancement in the west Indian Ocean. The high-HS GCMs also show greater reduction of precipitation in the subtropical Pacific in both hemispheres, indicating Hadley circulation expansion.

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(left) As in Fig. 4c, but averaged over high-HS and low-HS GCMs, with differences in (e) [note different color scale from (a) and (c)]. Stippling indicates that the high-HS composite shows greater or lower values than at least 80% of low-HS GCMs. (right) As in Fig. 4e, but averaged over high-HS and low-HS GCMs, with differences in (f) [note different color and vector scales from (b) and (d)]. The High-HS GCMs are CAMS-CSM1-0, CanESM5, CIESM, CMCC-CM2-SR5, E3SM-1-0, EC-Earth3-Veg, and NESM3. The low-HS GCMs are AWI-CM-1-1-MR, BCC-CSM2-MR, CESM2-WACCM, CNRM-CM6-1, CNRM-ESM2-1, FGOALS-g3, MIROC6, MPI-ESM-1-2-HAM, MPI-ESM1-2-HR, and MPI-ESM1-2-LR. These GCMs are selected as being high or low HS under both ENSO and future warming (Fig. 1e). However, the high-HS GCMs exclude HadGEM3-GC31-LL, HadGEM3-GC31-MM, MCM-UA-1-0, and UKESM1-0-LL, which are among the highest HS but for which the given variables are not all archived (Table 1).

Citation: Journal of Climate 35, 21; 10.1175/JCLI-D-21-0842.1

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These precipitation comparisons are explained by the magnified circulation features in high- versus low-HS GCMs (cf. Figs. 5b and 5d; differences are shown in Fig. 5f). High-HS GCMs exhibit a greater Walker circulation weakening and Hadley circulation expansion per degree of global temperature. These are indicated by the greater low-level westerlies (easterlies) over the equatorial Pacific (Indian) Ocean, as well as vertical velocity differences (shown by colors) matching those of precipitation. These comparisons between high- and low-HS GCMs can be seen in both the longitude–pressure plane along the equator, representing the Walker circulation (Fig. S11), as well as in the latitude–pressure plane over the Pacific, representing the Hadley circulation (Fig. S12). The greater Hadley circulation expansion in high-HS GCMs is consistent with Su et al. (2017), who found that higher-HS GCMs tend to simulate more contraction of the ascending branch of the Hadley circulation, under both internal variability and anthropogenic forcing.

Altogether, these analyses illustrate that the high-HS GCMs have greater sensitivity of the tropical circulation, and hence tropical precipitation, to global temperature variations under ENSO than the low-HS GCMs. This is shown explicitly in Fig. 6a, showing a correlation of 0.84 between HS_ENSO and the sensitivity of tropical (30°N–30°S) precipitation to $T_G^{\mathbf{\prime }}$ under ENSO (i.e., the y axis is equivalent to HS_ENSO except precipitation is just averaged over the tropics). Applying the same analysis but for extratropical precipitation, there is no relationship (r = 0.11; Fig. 6b). Under anthropogenic forcing, a similar relationship exists between HS_ENSO and the sensitivity of tropical precipitation to future warming (r = 0.89; Fig. 6c). And, unlike under ENSO, the sensitivity of extratropical precipitation is also highly correlated with HS (r = 0.80; Fig. 6d). Thus, under ENSO HS is determined by tropical but not extratropical precipitation anomalies, whereas under future warming HS is determined by both. To this effect, Fig. 4 illustrates that, outside of the tropics, there is almost no resemblance between ENSO and future warming in either the circulation or precipitation response. However, because tropical precipitation constitutes a majority of global precipitation, the relationship in the tropics alone is sufficient to generate an intermodel relationship in HS.

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(top) The regression between HS_ENSO and the sensitivity of (a) tropical (30°N–30°S) and (b) extratropical (global minus tropical) precipitation to $T_G^{\mathbf{\prime }}$, based on piControl. The values on the y axes are derived by calculating HS_ENSO, but replacing $P_G^{\mathbf{\prime }}$ with anomalies of tropical-mean and extratropical-mean precipitation. (bottom) As in the top row, but for HS_future, based on 1pctCO2. In each panel the least squares regression line is plotted and the Spearman rank order correlation coefficient is quoted above the panel. A missing regression line means that the correlation is insignificant at the 5% level.

Citation: Journal of Climate 35, 21; 10.1175/JCLI-D-21-0842.1

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6. Summary and discussion

A key aspect of future climate change is how much more precipitation will result per degree of warming. This is commonly represented by hydrologic sensitivity (HS), defined as the percent increase of global-mean precipitation P_G per degree increase of global-mean surface temperature T_G. GCMs project a wide spread in HS in simulations of anthropogenic forcing (1.1%–2.2% K⁻¹ in 1pctCO2 simulations of CMIP6, similar to the CMIP5 spread documented by Kramer and Soden (2016). To better understand this spread, HS was also calculated under ENSO in piControl simulations, which simulate the preindustrial climate in the absence of anthropogenic forcing, isolating internal variability.

There is a significant positive correlation between HS under internal variability and under future warming (HS_future) in CMIP6 (r = 0.41; Fig. 1d). This relationship improves when only years with strong ENSO events (|ENSO| > 1.5) are retained (r = 0.56; Fig. 1e). And from the intermodel regression, we derive the formula: HS_future ≈ 1.1 + 0.18 × HS_ENSO, where HS_ENSO and HS_future denote HS under ENSO and future warming, respectively. A similar relationship is found if using abrupt-4xCO2, instead of 1pctCO2, to derive HS_future.

As documented by previous studies, the projected twenty-first-century climate exhibits El Niño–like warming. Somewhat unexpectedly, HS under central Pacific ENSO events is a better predictor for HS_future (r = 0.62) than HS under east Pacific ENSO events (r = 0.34) (Fig. 2), despite future warming being maximized in the east Pacific. However, there are similar anomalies of tropical circulation and precipitation between central Pacific ENSO and future warming (Fig. 4). In particular, there is enhanced ascent over the equatorial Pacific and west Indian Ocean/East Africa, and enhanced descent over the warm pool, indicating a weakened Walker circulation. There is also enhanced descent in the subtropical Pacific, indicating Hadley circulation expansion. Farther poleward, however, there is little resemblance, which limits the intermodel relationship between the two forms of HS. For high-HS GCMs, these features are enhanced (i.e., greater Walker circulation weakening and greater Hadley circulation expansion; Fig. 5). Therefore, higher-HS GCMs are those with greater sensitivity of the tropical (but not extratropical) circulation to global temperature anomalies under ENSO (Fig. 6). A natural question that arises is whether large perturbations to the climate system, other than ENSO anomalies, can distinguish high- from low-HS GCMs, which we did not investigate.

The observational record with reliable data is short (34 years) and cannot be used as a fair comparison to the multicentury piControl simulations. Nevertheless, in this study, we produced the best possible estimate of HS_ENSO in the observations as a frame of reference. The observations show HS of 7.2% K⁻¹ (|ENSO| > 0.5), 6.4% K⁻¹ (|ENSO| > 1.0), and 7.7% K⁻¹ (|ENSO| > 1.5), which are robust in their sampling (Fig. 3). Under each of these ENSO thresholds, even the lower bound of observational uncertainty is about double that of any GCMs, suggesting that the GCMs simulate much too low HS_ENSO. Given the intermodel correlation between HS_ENSO and HS_future, it is thus likely that GCMs are underestimating HS_future, the metric that we wish to constrain. This is similar to Su et al. (2017), who constrained HS in CMIP5, finding that only the GCMs with the largest HS are credible.

It is thus implied that a given GCM’s representation of HS largely results from its own unique transformation of the tropical circulation. And, in general, the GCMs that project more weakening of the tropical circulation are those that simulate higher HS. However, the relationship between the GCM spread in HS and that in the circulation response does not prove causality in either direction. Examining in more detail the circulation anomalies that each GCM simulates in response to warming across GCMs, in the context of both the Hadley and Walker circulations, and how this impacts global precipitation, would appear to be a fruitful future research avenue. In particular, can changes to the two circulations be disentangled and their contributions to HS isolated, both in observations and across a GCM ensemble? And what time scales of internal variability govern each, in order to provide the best proxy for anthropogenic forcing? Such a breakdown in the observations and GCMs could help to fundamentally address the relationship between internal variability and anthropogenic forcing, and whether the changing circulation under anthropogenic forcing in the GCMs is reliable.

An examination of the global energy budget is also required to address the spread in HS, as conducted in previous studies (Richter and Xie 2008; Pendergrass and Hartmann 2012; DeAngelis et al. 2015; Mauritsen and Stevens 2015; Kramer and Soden 2016; Su et al. 2017; Pendergrass 2020; Watanabe et al. 2018), which was not done in this study. From Eq. (1), an intensification of the hydrological cycle may occur in line with enhancements to longwave cooling, shortwave absorption, or surface sensible heat. Future study should address what similarities or differences exist in the energy budget under ENSO versus future warming, and the extent to which future projections of HS can be constrained via analysis of the energy budget under ENSO.

Data availability statement.

The CMIP6 data are available from the Earth System Grid Federation (ESGF) archive (https://esgf-node.llnl.gov/search/cmip6/). HadCRUT5 data are available at https://www.metoffice.gov.uk/hadobs/hadcrut5/; GPCP data are available at https://climatedataguide.ucar.edu/climate-data/; ENSO data are available at https://origin.cpc.ncep.noaa.gov/.