Little Change in Apparent Hydrological Sensitivity at Large CO2 Forcing

Apparent hydrological sensitivity (ηa), the change in the global mean precipitation per degree K of global surface warming, is a key aspect of the climate system's response to increasing CO2 forcing. To determine whether ηa depends on the forcing amplitude we analyze idealized experiments over a broad range of abrupt CO2 forcing, from 2× to 8× preindustrial values, with two distinct climate models. We find little change in ηa between 2× and 4×CO2, and almost no change beyond 5×CO2. We validate this finding under transient CO2 forcing at 1%‐per‐year, up to 8×CO2. We further corroborate this result by analyzing the 1%‐per‐year output of more than 15 CMIP5/6 models. Lastly, we examine the 1,000‐year long LongrunMIP model output, and again find little change in ηa. This wealth of results demonstrates that ηa is a very weak function of CO2 forcing.

One might ask if ECS and HS are related.Watanabe et al. (2018) suggested an anti-correlation between ECS and HS due to the low cloud response in a warmer world.More recently, however, Pendergrass (2020) revisited this connection using Phase 6 of the Coupled Model Intercomparison Project (CMIP6, Eyring et al. (2016)) and found no correlation between ECS and HS.Nonetheless, since ECS was found to be strongly affected by the magnitude of CO 2 forcing, one might ask if HS, as another aspect of the climate response, could also be affected in the same way, even if ECS and HS are not related.
We are aware of only one study which explored this subject (Good et al., 2012), which reported that HS decreases at higher CO 2 concentrations.However, that finding was obtained with a single climate model.Furthermore, the range of CO 2 forcing explored in that study was limited, as the authors only considered three values of CO 2 (0.5×, 2×, and 4×CO 2 ).Whether the finding of Good et al. (2012) can be confirmed with different climate models and over a broader range of CO 2 , remains to be determined.
The goal of our study, therefore, is to answer this question.We do this by using two fully-coupled models, analyzing the changes in HS under abrupt CO 2 forcing, ranging from 2× to 8×CO 2 .We also study changes in HS under the more realistic transient 1%/year CO 2 forcing scenario, with both models, and additionally in over 15 CMIP5 and CMIP6 models.And, finally, we examine HS under abrupt 2×, 4×, and 8×CO 2 in several LongrunMIP models, each run for 1,000 years.In all these, we find little change in HS with increased CO 2 forcing, especially under the stronger forcing cases.

Methods
We analyze output from the fully-coupled atmosphere-ocean-sea-ice-land model versions of the Community Earth System Model (CESM-LE, Hurrell et al. (2013)) and the NASA Goddard Institute for Space Studies ModelE (GISS E2.1-G, Kelley et al. (2020)).We use output that was previously analyzed by Mitevski et al. (2021) which performed a series of abrupt CO 2 forcing runs, with 2×, 3×, 4×, 5×, 6×, 7×, and 8×CO 2 with respect to the PI value, with all other natural and anthropogenic forcings fixed at PI values.Each run is 150 years long, as per the CMIP standard prescription for abrupt4xCO2 runs.We also analyze transient 1%/yr (1pctCO2) experiments for both CESM-LE and GISS E2.1-G from 1× to 8×CO 2 previously performed by Mitevski et al. (2021).
In addition to these two models, we also analyze output from both CMIP5 (Taylor et al., 2012) and CMIP6 (Eyring et al., 2016) models forced under the 1pctCO2 scenario.The list of models used can be found in Tables S2 and  S3 in Supporting Information S1.Furthermore, we analyze five LongrunMIP models (Rugenstein et al., 2019): MPI-ESM1.2,HadCM3L, CCSM3, CESM1.0.4,and FAMOUS.For each of these models we analyze 1,000 years after the abrupt 2×, 4×, and 8×CO 2 increase (with the exception of FAMOUS, for which only the abrupt 2× and 4×CO 2 experiments were run to 1,000 years).
In all cases, we define global-averaged precipitation and surface temperature changes (ΔP and ΔT) as the difference from the PI control values.For the abrupt n×CO 2 , following Fläschner et al. (2016), one can define the HS η as the slope of the linear regression of ΔP versus ΔT, that is, where A is the fast adjustment of the precipitation to CO 2 increase.However, since variables η and A, as defined in Equation 1, can only be calculated in abrupt increase in CO 2 experiments, we here prefer to use the apparent HS (this is referred to as endpoint η a in Fläschner et al. ( 2016)); η a is simply the ratio ΔP/ΔT.The advantage of η a is that it can be calculated for both the transient and abrupt runs.For the abrupt runs, the ratio η a is computed over the last 10 years of the model runs, following Fläschner et al. (2016); for the transient runs, η a is just an instantaneous value.The quantities η and η a are illustrated in Figure S1 in Supporting Information S1, which shows ΔP versus ΔT for the abrupt CO 2 forcing runs of the CESM-LE model.

Results
We start by examining how HS varies with CO 2 increase in the abrupt forcing experiments.Figure 1 shows the value of η a for the fully-coupled CESM-LE runs (solid blue, values can be found in Table S1 in Supporting Information S1).One can see only small variations with CO 2 forcing, with the line becoming basically flat beyond 4×CO 2 .This fact-which constitutes the key result of our paper-is corroborated by the runs performed with the 10.1029/2023GL104954 3 of 7 fully-coupled GISS E2.1-G model (solid red, Table S1 in Supporting Information S1).The lack of changes in HS at high CO 2 forcing is not dependent on the definition of HS.Using the second definition of HS, η in Equation 1, also reveals basically flat lines beyond 5×CO 2 (Figure S2a and Table S1 in Supporting Information S1).Note that the values of η a are smaller than those of η, as the former includes the fast adjustment (Fläschner et al., 2016).
The reader might wonder about the small kink at 4×CO 2 in the CESM-LE runs, and 3×CO 2 in the GISS E2.1-G runs (Figure 1).To understand this behavior, we analyze additional experiments with identical forcings but with the slab-ocean configuration of both models where the ocean heat transport is fixed.We find that the kinks disappear in the slab-ocean runs (Figure 1, dashed lines), indicating that the non-monotonicity is due to changes in the ocean circulation.Mitevski et al. (2021) analyzed these runs in more detail and attributed the non-monotonic behavior to the formation of the North Atlantic Warming Hole caused by the collapse of the Atlantic Meridional Overturning Circulation (AMOC).The changes in η a associated with AMOC collapse are relatively small for the CESM-LE model, less than 10%, and a little more substantial for the GISS E2.1-G model, ∼20% (Figure 1).The key point, however, is that these changes disappear at larger CO 2 forcing.
In Figure S2b in Supporting Information S1 we show the fast adjustment A, calculated as the y-intercept of the regression of ΔP versus ΔT (see Equation 1), as a function of CO 2 forcing.A is the precipitation response before the surface temperature has had time to warm.The black line in Figure S2b in Supporting Information S1 is the linear regression of A versus the log of the CO 2 forcing.For both models we find that A is proportional to the log of the CO 2 concentration (with the exception of 4×CO 2 in CESM-LE and 3×CO 2 in GISS E2.1-G) as expected, considering that A is caused by the CO 2 radiative forcing, which is approximately a logarithmic function of its concentration.
Having obtained a robust result from the abrupt forcing experiments, we next explore the more realistic transient forcing experiments.In Figure 2 we show η a in the transient 1pctCO2 experiments, for both models, with CO 2 Figure 1.Apparent hydrological sensitivity, η a calculated from fully coupled (solid lines) and slab ocean (dashed lines) CESM-LE (blue) and GISS E2.1-G (red) abrupt 2× to 8×CO 2 runs.Data is globally and annually averaged.Error bars denote 95% confidence intervals.
Figure 2. Time series of the apparent hydrological sensitivity, η a , calculated from fully coupled 1pctCO2 CESM-LE (a, blue line) and GISS E2.1-G (b, red line) runs.Gray dots mark η a calculated from the abrupt runs (Figure 1) and the dashed line marks the mean of 3-8×CO 2 .
ranging from PI to 8×CO 2 values.Beyond 3×CO 2 , the value of η a is constant (note that we have added an additional x-axis to show the CO 2 values over time).The gray dots in that figure show the values of η a from the abrupt forcing experiments at the corresponding CO 2 value.The agreement between the abrupt and transient values of η a corroborates our key finding, that HS is very nearly constant at large CO 2 forcing.
Next, we confirm that the lack of change in HS with CO 2 holds true over a larger set of climate models.We plot η a in the 1pctCO2 scenario in 31 CMIP5 and 15 CMIP6 models, showing individual models in colored lines, and the multi-model mean in black, in Figure 3.Even though the CMIP models are run only up to 150 years and only up to 4×CO 2 , we can see the flattening of the η a line, so that HS becomes almost constant at the end of the models' run.
Finally, we address the question of time scales.Some might argue that, in the abrupt experiments, 150 years is not enough to reach an equilibrated state, and thus to obtain the full effect of the slow response on the hydrological cycle.To address this concern, we thus analyze all the LongrunMIP models for which 1,000 years are available (there are five such models, see Section 2).With solid lines in Figure 4 we show η a , averaged over the last 10 years of the runs, calculated for these five models for the abrupt 2×, 4×, and 8×CO 2 experiments (note that the FAMOUS model lacks the abrupt8× data point).Similarly to the results shown above over the shorter 150 year period, we find very small changes in HS in these LongrunMIP models, with one outlier (HadCM3L).For that model, we note that η a changes more than in the other four (by 31% from 2 to 8).However, its value of η a lies well outside the range of the other four at 2×CO 2 .Also, at 4×CO 2 -where we have an additional 6 models available-that model is again the outlier.Leaving that model aside, therefore, we conclude that even for much longer time scales, HS is largely independent of CO 2 forcing.

Summary and Discussion
The key finding of this paper is that HS is a weak function of CO 2 forcing, especially at large concentrations.Analyzing idealized experiments with abrupt CO 2 increases in two models, we find some variations in η a between 2× and 4×CO 2 (roughly 8% in CESM-LE, and 20% in GISS E2.1-G), but η a becomes almost completely insensitive to the magnitude of CO 2 forcing beyond 5×CO 2 .These findings are confirmed by transient 1pctCO2 experiments, with both models, and with more than 15 CMIP5 and CMIP6 models.Finally, 4 LongrunMIP models show almost no change in HS with CO 2 forcing even for long time scales.
Our findings are in good agreement with Good et al. (2012), who reported a change in HS of about 10% between 2× and 4×CO 2 in the HadCM3 model.We have confirmed their quantitative findings.However, by examining many models under different scenarios, and a much larger range of CO 2 forcing, we have reached a different conclusion, that is, that the HS is only a weak function of CO 2 .
For the sake of consistency we have, up to this point, focused most of our attention on the apparent HS η a , and only briefly discussed HS as measured by η, which can only be computed for the abrupt forcing runs.Digging a little deeper, it can be seen by contrasting panels a and b of Figure S3 in Supporting Information S1, that η shows a somewhat stronger dependence on the CO 2 forcing than η a .However, this result appears to be model dependent: over the range 2× to 8×CO 2 η varies by 6% for the CESM-LE model but 22% for the GISS E2.1-G model.Since η and η a are related by: (2) (using Equation 1 and substituting ΔP in the definition of η a ) we can use this expression to calculate η a using η, ΔT, and A. The result of this calculation is shown in panel d of Figure S3 in Supporting Information S1 which agrees very well with η a computed as the ratio ΔP/ΔT, in panel a.The smaller variations of η a compared to η with CO 2 are a consequence of a compensation from the term A/ΔT, as shown in panel c.This compensation explains why ECS is a strong function of CO 2 while η a is insensitive to CO 2 forcing.
The reader may also wonder whether the key finding of our study, which pertains to the global mean precipitation, might also apply to distinct geographical regions.A very preliminary look at the model output analyzed above reveals that HS is also a weak function of CO 2 over land, in both the abrupt and 1%/yr cases in the CESM-LE model, but a full examination of this question is beyond the scope of this short paper.
Finally, it is important to keep in mind that CO 2 is not the only forcing of the climate system.Whether other forcings are able to alter HS in a substantial way remains to be determined.Richardson et al. (2018) examined the HS in 10 models forced with carbon dioxide, methane, sulfates, aerosols, and others, and reported little difference in HS across these forcings (except for black carbon).MacIntosh et al. ( 2016), using the HadGEM3 model, found that ozone is able to produce a fast precipitation response.More recently, McCoy et al. (2022) suggested that the absorbing aerosols might be able to affect the HS via the fast response, similar to the findings in Richardson et al. (2018).While a careful analysis of HS changes using single forcing runs remains to be done, we have examined the largest CO 2 forcing scenarios in both CMIP5 (RCP8.5)and CMIP6 (SSP5-8.5) to determine if our key finding remains valid in a more realistic setting, that is, in the presence of other climate forcings.As shown in Figure S4 in Supporting Information S1 (List of models used is in Tables S4 and S5 in Supporting Information S1), the CMIP models show small changes in η a in the second half of the 21st century, when the CO 2 forcing is the largest, confirming our finding.Needless to say, changes in these scenarios are difficult to interpret, as CO 2 is not the only forcing, and it is conceivable that specific forcings may be able to affect HS in specific decades, when the CO 2 forcing is not as strong.That question, however, is beyond the scope of this study.

Figure 3 .
Figure 3.Time series of the apparent hydrological sensitivity, η a , for CMIP5 and CMIP6 data, 1pctCO2 experiment (colored lines).Black line is the model mean.

Figure 4 .
Figure 4. Apparent hydrological sensitivity parameter for abrupt ×CO 2 in LongrunMIP model runs.For 6 of these models, only the 4×CO 2 output is available.