Introduction

The global hydrological cycle’s responses to rising temperatures driven by increasing greenhouse gas concentration significantly impact human activities and Earth’s ecosystems1,2,3,4,5,6,7,8. Extreme rainfall events are becoming more intense9,10,11, raising serious concerns for human vulnerability12. Furthermore, damaging floods and drought frequency are projected to increase13,14. The magnitude and rate of changes for regional hydrological events directly impact infrastructure, agriculture, and health15,16,17.

Previous studies examined precipitation changes in warmer climates by analyzing Coupled Model Intercomparison Projection Phase 5 (CMIP5) climate models. These climate change simulations are characterized by a wet-get-wetter/dry-get-drier pattern18,19,20 or a warmer-get-wetter pattern21,22 over the oceans. Water vapor content at typical lower troposphere temperatures is constrained to increase by no more than 7% K−1 18, which is the limit set by the Clausius–Clapeyron equation for saturation vapor pressure. Changes in the rate of global precipitation and evaporation response to warming differ significantly from water vapor content changes2,3,18. Most CMIP5 models predict hydrological sensitivity around 1–3% K−117. The discrepancy between water vapor content changes and hydrological sensitivity can be explained by net radiative surface and atmospheric energy balance constraints that limit latent heat flux increases driven by a warmer climate2, an important consequence of which is atmospheric circulation slowdown18,23. Although this perspective explains the hydrological cycle changes reasonably well, the scientific community requires more detailed understanding of hydrological cycle sensitivity to transient climate change24.

Studies investigating hydrological sensitivity to atmospheric CO2 removal are of importance, because they provide climate mitigation plans and emission reduction replacements25,26,27,28,29. Some climate mitigation studies assume a linear relationship between temperature and precipitation with respect to increasing or decreasing atmospheric CO2 concentrations30,31. The global hydrological cycle, however, demonstrates known hysteresis behavior and this has important implications for atmospheric emission reductions and carbon capture32. Furthermore, it is important to differentiate the hydrological cycle’s response over oceans and land in a changing CO2 pathway. In this study, we focus on understanding the physical processes associated with hydrological sensitivities to idealized transient CO2 increases and removal over land and oceans, respectively, which has never been attempted in a previous study. We used 28 climate simulation ensemble sets along with a present-day climate simulation (PD simulation) using the standard Community Earth System Model version 1.2.2 (CESM1) (see “Methods”).

A standard metric for assessing the sensitivity of climate to radiative forcing is the Equilibrium Climate Sensitivity, which quantifies the global average surface temperature change resulting from a doubling of CO2 concentration from a pre-industrial period after the climate system equilibrates. However, in the present study we are interested in examining the physical processes determining hydrological sensitivity and how this determines global water cycle changes over time, thereby providing information relevant for ongoing climate mitigation and adaptation plans from the present climate condition.

Unless stated otherwise in the text, all analyses use the annual mean of the 28-member ensemble with the deviation obtained by subtracting the PD simulation climatology from the ensemble mean.

Results

Changes in precipitation and temperature to CO2 forcing

Figure 1a displays changes in CO2 concentration including an increase (ramp-up) and decrease (ramp-down) period. The CO2 concentration during the stabilization period is identical to that in the PD simulation. Global mean precipitation increases during the CO2 ramp-up period and continues to increase for almost two decades after peak CO2 concentration (Fig. 1a, b).

Fig. 1: Mean precipitation and temperature changes for a changing CO2 pathway.
figure 1

a Changes in CO2 concentration for an increase (ramp-up) period, a decrease (ramp-down) period, and a stabilization period. b Changes in global, land, and ocean mean precipitation from the ramp-up period to the stabilization period compared to the PD simulation. c Same as b, except for surface temperature anomaly. d Changes in global mean precipitation from the ramp-up period to the stabilization period compared to the PD simulation (black) and the estimated global mean precipitation (green) using a simple conceptual model (see “Methods”).

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Although the changes in global mean precipitation are almost identical to the changes in ocean precipitation, land precipitation changes are almost symmetric in a changing CO2 pathway (Fig. 1b). During the stabilization period, neither the global mean precipitation nor ocean and land precipitation returns to the present climate conditions, as the adjustment back to the PD simulation is likely to be slow after 280 continuous years of excess heating, much of which is stored in the deep ocean.

The precipitation is 2% higher than the present climate conditions after 120 years of stabilization in both land and ocean (Fig. 1b). This indicates that the precipitation responses to a changing CO2 pathway are not symmetric33,34. Similar behavior is seen for global mean surface temperature (Fig. 1c). The evolution of the temperature is largely corresponding to changes in CO2, suggesting a linear response, although its peak is delayed some years because of the heat capacity of the ocean, and the rate of temperature decrease in the ramp-down period is smaller in magnitude than the rate of increase in the ramp-up period27,35. We demonstrate that the hydrological cycle hysteresis is different for oceans and land (Fig. 1b). Ocean and land temperature changes in response to changing CO2 are similar, except for their magnitudes (Fig. 1c), which is mainly due to a large heat capacity in the ocean. Consequently, there is an almost linear relationship between precipitation and temperature change for land in response to a changing CO2 concentration (Supplementary Fig. 1 and see also Fig. 2b), which contrasts with the asymmetric relationship of precipitation and temperature change over the ocean (Supplementary Fig. 2 and see also Fig. 2c). We discuss the detailed physical processes later.

Fig. 2: Precipitation and temperature relationship changes during CO2 ramp-up, ramp-down, and stabilization periods.
figure 2

a The percentage change of global mean precipitation and the global mean surface temperature anomaly during CO2 ramp-up, ramp-down, and stabilization periods. b–d Same as a, except they are over land, ocean, and land minus ocean, respectively. Each dot represents the annual mean anomaly obtained by subtracting the PD simulation climatology from the ensemble mean. The percentage anomaly is defined as the difference between the ensemble mean and PD simulation divided by PD simulation.

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Global mean precipitation response to CO2 concentration changes is a combination of an initial fast (days to weeks) atmospheric adjustment to radiative forcing and a slower response to surface temperature change34. This has previously been explained by considering the atmospheric and surface energy budgets36, and it can be illustrated using a simple conceptual model (see “Methods” for details). It is found that the estimated global mean precipitation response based on the atmospheric and surface energy budgets is well matched with the global mean precipitation response simulated in CESM1 (Fig. 1d). This implies that the precipitation response (ΔP) is explained by the fast (ΔPfast) and slow (ΔPslow) precipitation response to temperature change in a CESM1. It is noteworthy that Δ indicates the deviation from PD simulation climatology. Therefore, we obtain the following equation

$${\Delta}P = \kappa {\Delta}T = {\Delta}P_{\mathrm{fast}} + {\Delta}P_{\mathrm{slow}} = {\Delta}P_{\mathrm{fast}} + \alpha {\Delta}T$$
(1)

Here, κ is an apparent hydrological sensitivity, which represents the total change of precipitation per degree surface warming compared to PD climate. α is a hydrological sensitivity, which is defined by the increase in precipitation solely due to a given change in temperature and it can be estimated from the stabilization phase where ΔPfast = 0. This equation can be applied to global, ocean, or land, respectively.

An apparent global hydrological sensitivity (κglobal) is 1.35% K−1 for the CO2 ramp-up period and it is significantly reduced to 1.09% K−1 for the CO2 ramp-down period (Supplementary Fig. 3a, b, d). However, κglobal increases to 2.54% K−1 during the stabilization period (Supplementary Fig. 3c, e and Table 1). This is consistent with energetic arguments in previous studies showing that global precipitation response to temperature change is larger when CO2 concentrations are constant than when they change over time34,37. It is noteworthy that the CO2 changes suppress the apparent global hydrological sensitivity below 2.54% K−1 equally in ramp-up and ramp-down. However, the delayed temperature response, which is mostly due to the ocean heat capacity, tends to suppress this response more in the ramp-down period (Fig. 2a and Table 1). Therefore, removing atmospheric CO2 may cause a significant climate mitigation side effect by reducing the magnitude of precipitation to the ensuing cooling due to the mitigation and then abruptly increasing hydrological cycle sensitivity once the CO2 concentration stabilizes. This indicates a need for careful climate mitigation and emission reduction planning.

Table 1 Summary of hydrological sensitivity and apparent hydrological sensitivity in a CESM1.
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Contrasting hydrological sensitivity over land and ocean

Subsequently, we calculate the precipitation response to atmospheric adjustment, to radiative forcing over oceans and land, respectively, following Eq. (1).

$${\Delta}P_{\mathrm{ocean}\,{\mathrm{fast}} \uparrow } = \left( {\kappa _{\mathrm{ocean} \uparrow } - \alpha _{\mathrm{ocean}}} \right){\Delta}T_{\mathrm{ocean}}$$
(2)
$${\Delta}P_{\mathrm{ocean}\,{\mathrm{fast}} \downarrow } = \left( {\kappa _{\mathrm{ocean} \downarrow } - \alpha _{\mathrm{ocean}}} \right){\Delta}T_{\mathrm{ocean}}$$
(3)
$${\Delta}P_{\mathrm{land}\,{\mathrm{fast}}} = \left( {\kappa _{\mathrm{land}} - \alpha _{\mathrm{land}}} \right){\Delta}T_{\mathrm{land}},$$
(4)
$$\left( { \uparrow :\,\mathrm{ramp - up}\,{\mathrm{period}},\, \downarrow :\,\mathrm{ramp - down}\,{\mathrm{period}}} \right)$$

αocean, αland, κland, κocean↑, and κocean↓ values are summarized with those in the globe in Table 1.

Here, the characteristics of the apparent hydrological sensitivity over the ocean (κocean) and land (κland) are different during the ramp-up and ramp-down periods (Fig. 2b, c and Table 1). Although κocean is not the same for the CO2 ramp-up (κocean↑ = 1.32% K−1) and ramp-down (κocean↓ = 0.86% K−1) periods (Figs. 2c and 3a), κland (1.59% K−1) is nearly identical over land for both periods (Figs. 2b and 3b) (see also “Methods”). This implies that CO2 changes equally influence the apparent hydrological sensitivity over land in ramp-up and ramp-down, which is in contrast to oceans.

Fig. 3: Ocean and land hydrological sensitivity for each ensemble member.
figure 3

a Box-and-whisker diagram of apparent ocean hydrological sensitivity (κocean) during CO2 ramp-up and ramp-down periods. The box plot and whiskers represent quartiles with median and total range, respectively, in each period. b Same as a, except apparent land hydrological sensitivity (κland).

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On the other hand, land precipitation changes from rising temperatures, which are influenced by tropospheric temperature adjustments to CO2 radiative forcing, are increased by 0.38% K−1 (κland (1.59% K−1) − αland (1.21% K−1)). That is, the CO2 radiative forcing drives an additional increase in precipitation as land temperatures rise. This phenomenon could be related to land–ocean temperature contrast (Fig. 2d), i.e., warmer land than ocean may lead to more convergence over land, resulting in an additional increase in precipitation. In contrast, ocean precipitation changes from CO2 radiative forcing are suppressed by 1.77% K−1 during the CO2 ramp-up period (κocean↑ (1.32% K−1) − αocean (3.09% K−1)) and 2.23% K−1 during the CO2 ramp-down period (κocean↓ (0.86% K−1) − αocean (3.09% K−1)), implying that the CO2 radiative forcing drives an additional decrease in precipitation as ocean temperatures rise. These results indicate that CO2 radiative forcing leads to a contrast in the fast precipitation response between land and oceans38,39. Furthermore, the CO2 radiative forcing tends to suppress the precipitation changes over the ocean more in the ramp-down period than in the ramp-up period, which is due to the delayed ocean temperature response in the ramp-down period (Fig. 2d).

We used 28 climate simulation ensemble sets along with the PD simulation; therefore, a deviation in each ensemble from the ensemble mean could be due to internal climate variability40,41. We calculate the standard deviation (SD) of apparent ocean and land hydrological sensitivity in 28 climate simulation ensemble sets, respectively (Fig. 3 and see also Table 2). It is found that the SD of κocean↓ is significantly larger than that of κocean↑, implying that the role of internal climate variability on apparent ocean hydrological sensitivity is large during the CO2 ramp-down period compared to that during the CO2 ramp-up period. A similar phenomenon is also observed in apparent hydrological sensitivity over land (Table 2). However, the increase of SD over land from the ramp-up to the ramp-down period is smaller than the ocean. These results indicate that the role of internal climate variability on apparent hydrological sensitivity over the ocean and land is changing from the CO2 ramp-up to the ramp-down period and its contribution differs over the ocean and land, respectively.

Table 2 Summary of SDs of apparent hydrological sensitivity (κ) in 28 CESM1 ensemble members.
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Contrasting precipitation changes over land and ocean constrained by energy budget

As precipitation changes are constrained by atmospheric and surface energy budgets2,34,42,43, we also examine the land and ocean global surface energy budgets.

$${\Delta}Q_{\mathrm{L}} = {\Delta}R_{\mathrm{Lnet}} + {\Delta}R_{\mathrm{Snet}} - {\Delta}Q_{\mathrm{S}}:\,{\mathrm{Land}}$$
(5)
$${\Delta}Q_{\mathrm{L}} = {\Delta}R_{\mathrm{Lnet}} + {\Delta}R_{\mathrm{Snet}} - {\Delta}Q_{\mathrm{S}} + {\Delta}R_{\mathrm{TOA}}:\,{\mathrm{Ocean}}$$
(6)

Here, QL is latent heat flux from the surface, RLnet is net longwave radiation, RSnet is net shortwave radiation, and QS is the upward sensible heat flux. RTOA is the net radiation at the top of the atmosphere, which balances with ocean heat uptake (i.e., -RTOA)37 and we assume land heat uptake is negligible. The right-hand side of Eq. (5) can be seen in Fig. 4a. Changes in net longwave radiation (ΔRLnet) and net shortwave radiation (ΔRSnet) are compensated by changes in sensible heat flux (ΔQS). Consequently, changes in latent heat flux (ΔQL) balance with ΔRLnet, ΔRSnet, and ΔQS (Fig. 4b). As ΔQL changes are tied to land precipitation changes (Fig. 4c), we conclude that the almost symmetric land precipitation response (see also Supplementary Fig. 1) is mainly constrained by the symmetric change in surface energy terms ΔRLnet, ΔRSnet, and ΔQS (Fig. 4a). This implies that the overall land precipitation response is strongly constrained by the fast response to CO2 radiative forcing’s tropospheric temperature adjustment. Over land, the tropospheric temperature adjustments during CO2 ramp-up and ramp-down decreases atmospheric stability and increases convection compared to that during the present climate condition2,36,44, leading to increased precipitation45. This is also explained by an increased land–ocean temperature contrast with warming (see also Fig. 2d), which drives decreased atmospheric stability and dominates over the direct atmospheric and surface heating effect of elevated CO2 over land. The land–ocean warming contrast relating to differing thermal capacities of land and ocean but also contrasting surface feedbacks explains the increased hydrological sensitivity over land46 (i.e., 0.38% K−1).

Fig. 4: Changes in land and ocean surface energy budgets and precipitation changes.
figure 4

Changes in land a ΔRLnet, ΔRSnet, and ΔQS, b ΔQL and (ΔRLnet + ΔRSnet − ΔQS) during CO2 ramp-up, ramp-down, and stabilization periods. c Relationship between ΔQL and precipitation percentage change in land during CO2 ramp-up and ramp-down periods. Changes in ocean d ΔRLnet, ΔRSnet, and ΔQS, e ΔQL (ΔRLnet + ΔRSnet − ΔQS + ΔRTOA) and -ΔRTOA during CO2 ramp-up, ramp-down, and stabilization periods. f Relationship between ΔQL and precipitation percentage change in ocean during CO2 ramp-up and ramp-down periods. Δ indicates the deviation from the PD climatology simulation. Bracket values represent linear regression coefficients between ΔQL and the precipitation percentage change, which are statistically significant at a 99% confidence level.

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Figure 4d, e display the right-hand side of Eq. (6) (ΔRLnet, ΔRSnet, ΔQS, and ΔRTOA) for oceans, respectively. Figure 4e also shows ΔQL changes are identical to the four surface energy terms combined and it is also tied to ocean precipitation changes (Fig. 4f). Therefore, the ocean precipitation response is also constrained by changes in surface energy terms ΔRLnet, ΔRSnet, ΔQS, and ΔRTOA, consistent with land (Fig. 4b, e). In contrast to land, however, changes in sensible heat flux (ΔQS) are negative (i.e., downward) over the ocean during both CO2 ramp-up and ramp-down periods (Fig. 4d). This is because land warms more than ocean; therefore, the sea surface temperature is changing less than the atmosphere above it (Supplementary Fig. 4). This is also associated with the suppression of (κocean − αocean) during both periods (Eqs. (2) and (3)), which is explained by the direct atmospheric heating by CO2 radiative forcing, while the land–ocean warming contrast partly offset this effect.

In addition, changes in both ocean heat uptake (-ΔRTOA) (Fig. 4e) and net shortwave radiation (ΔRSnet) (Fig. 4d) explain the asymmetric precipitation response to oceanic temperature changes (Fig. 4f). Unlike the symmetric ΔQS and ΔRLnet changes, both ΔRSnet and ΔRTOA changes are asymmetric. ΔRSnet changes its sign in the latter stages of the CO2 ramp-down period and the ocean receives more net shortwave radiation during the CO2 stabilization period (Fig. 4d). After peak atmospheric CO2 concentration, on the other hand, -ΔRTOA slowly decreases and changes sign in the middle of the CO2 ramp-down period (Fig. 4e). These characteristics contribute to the asymmetric precipitation response over the oceans. In particular, the oceans absorb heat until the middle of the CO2 ramp-down period despite the CO2 concentration decrease. In addition, the oceans continue to release heat despite a fixed CO2 concentration during the stabilization period. We speculate that this may contribute to increased ΔRSnet during and after the latter stages of the CO2 ramp-down (Fig. 4d). There is a possibility that ocean heat release into atmosphere may reduce the amount of low-level clouds over the oceans during the stabilization period (Supplementary Fig. 5) through enhanced low-level turbulence in boundary layer47. This may act to increase net shortwave radiation at the surface. However, we cannot exclude the possibility that the extra heat released to the atmosphere may destabilize it, enhance convection, leading to more cloudiness, and hence reduced shortwave radiation at the surface. It is therefore valuable to further analyze the detailed mechanisms, although it is beyond the scope of the present study.

Meanwhile, there is a contrast in both “slopes” and “direction” in the relationship between ΔQL and precipitation percentage change over land and the ocean during CO2 ramp-up and ramp-down periods, respectively (Fig. 4c, f). This implies that there is different moisture divergence from over the ocean and convergence over land during CO2 ramp-up and ramp-down periods. The low slopes over land (Fig. 4c) reflects weaker dependence of precipitation on evaporation than that over the ocean. Therefore, the enhanced precipitation must be due more to enhanced moisture convergence from the oceans (e.g., stronger monsoons) than to local evaporation. However, the increased latent heat loss through surface evaporation over land during the CO2 ramp-down period (Fig. 4c) does not reflect warmer or wetter land during this period, because temperature is relatively symmetric between the CO2 ramp-up and ramp-down periods (see Fig. 1b). Therefore, the increased latent heat loss over land could be explained by a smaller contribution of moisture import from the oceans to land precipitation during the CO2 ramp-down period. A smaller contribution of moisture convergence to precipitation over land during the CO2 ramp-down period then requires more surface evaporation over land for the same precipitation anomaly. On the other hand, the larger slopes in the relationship between ΔQL and precipitation percentage change over the ocean than land (Fig. 4c, f) indicates that precipitation over the ocean must be closely proportional to surface evaporation compared to that over land. Figure 4f also indicates that less surface evaporation over the ocean is required during the CO2 ramp-down period for the same precipitation anomaly compared with the CO2 ramp-up period, because there is less moisture export to land during the CO2 ramp-down period.

Discussion

The climate system response to changes in the Earth’s radiative balance depends on the timescale48. The transient climate response, which is formally defined as the global mean surface warming at the time of doubling of CO2 in an idealized 1% year−1 CO2 increase experiment, quantifies warming in response to a changing forcing prior to the deep ocean being in equilibrium with the forcing. On the other hand, the equilibrium climate sensitivity is defined as the warming for doubling CO2 in the atmosphere relative to pre-industrial climate, after the climate reached its new equilibrium49. To project correctly Earth’s future climate, therefore, it is fundamental to understand the transient climate response and equilibrium climate sensitivity50,51,52. In particular, the understanding of the hydrological cycle response to transient climate change is essential for successful adaptation and mitigation policies.

Although the response of the global hydrological cycle has been qualitatively examined by analyzing an atmospheric general circulation model and state-of-the-art climate models, there is little study to examine the contrast of hydrological cycle over land and ocean in a changing CO2 pathway with large ensemble simulations.

We found that there is an almost linear relationship between precipitation and temperature change for land in response to a changing CO2 concentration, which contrasts with the asymmetric relationship of precipitation and temperature change over the ocean. Our results indicate that ocean heat uptake and land–ocean warming contrast is the key to the contrasting precipitation responses between land and oceans. The oceans absorb heat until the middle of the CO2 ramp-down period and it continues to release heat despite a fixed CO2 concentration during the stabilization period, resulting in an asymmetric relationship of precipitation and temperature changes constrained by surface energy budget. In particular, the CO2 radiative forcing drives an additional increase in precipitation as land temperatures rise, which could be related to land–ocean temperature contrast. In contrast, ocean precipitation changes from CO2 radiative forcing are suppressed during the ramp-down period. This result implies that changing CO2 pathway mitigation and adaptive actions should incorporate the contrasting hydrological cycle responses of the land and ocean, and underlines the importance of confirming simulated responses in the hydrological cycle to CO2 across all timescale from days to decades. In addition, it would be necessary to examine the hydrological cycle to CO2 radiative forcing over the tropical vs. the extratropical to understand its regional characteristics.

All analyses used the annual mean of the 28-member ensemble in the present study; however, it would be valuable to understand how the seasonality of precipitation to CO2 forcing changes over land and the ocean. Transient climate changes and slow adjustment processes during the stabilization period were not found to substantially affect the seasonality of precipitation over both land and ocean, only the magnitude (Supplementary Fig. 6).

Although the ramp-up and ramp-down periods are symmetric in terms of CO2 concentrations, they are not symmetric at all in terms of forcing relative to the PD climate, as extra heating relative to the PD climate is occurring during both ramp-up and ramp-down periods. The climate system at the beginning of the stabilization period has already absorbed the integrated effects of extra heating during both ramp-up and ramp-down periods. Therefore, the stabilization period is unlike the PD climate in terms of heat content and distribution in the ocean in spite of the same CO2 concentration. This hysteresis of the global hydrological cycle is expected to be less apparent if assessing in the context of a symmetrical ramp-up and ramp-down in radiative forcing. In that case, there would be no net heat loss or gain after the 280 years relative to the PD climate in which any hysteresis could be weak. Although the present study focuses on the climate transition from CO2 ramp-up to ramp-down, it would be also necessary to understand the slow adjustment process during the stabilization period.

Methods

CESM1 experiments

To investigate the hydrological cycles’ contrasting response over land and ocean to CO2 emission ramp-up and ramp-down, we conducted experimental climate model simulations. The model used in this study is a fully coupled CESM1, which has the same component models and coupling of the CESM1 with the Community Atmosphere Model version 5 in CMIP5. CESM1 is the Community Atmosphere Model version 5 coupled to the Parallel Ocean Program version 2, the Community Land Model version 4, and the Los Alamos Sea Ice Model, all at ~1° horizontal resolution53. Vertical resolutions were 30 and 60 levels for the atmosphere and ocean, respectively. The land carbon cycle was also included54.

We performed two kinds of simulations. One is a PD simulation with a constant CO2 concentration (1× CO2, 367 p.p.m.) of over 900 years, where we extracted 28 initial conditions from the PD simulation. The 28 initial ocean condition was taken from the PD simulation arbitrarily. Also, a CO2 ramp-up and -down experiment was performed in each 28 ensemble member. This experiment employed an increasing atmospheric CO2 concentration at a rate of 1% year−1 until CO2 quadrupling (4× CO2, 1478 p.p.m., CO2 ramp-up simulation) and then a decreasing CO2 forcing to the same rate over 140 years until reaching the original value (1× CO2, 367 p.p.m., CO2 ramp-down simulation). In addition, we integrated a restoring run of 120 years with a constant CO2 concentration (1× CO2, 367 p.p.m., CO2 stabilization simulation).

Simple model for global precipitation response

Global mean precipitation response (ΔP) is balanced by the fast component (fΔF) in which the atmosphere rapidly adjusts to changes in top of atmosphere radiative forcing, ΔF, and a slow component (αglobalΔT), which quantifies the global mean precipitation response to the global mean surface temperature change, ΔT, as follows2:

$${\Delta}P\sim - f{\Delta}F + \alpha_{\mathrm{global}}{\Delta}T$$
(7)

where f is the fraction of radiative forcing manifest in the atmosphere and \(\alpha\)global is the global hydrological sensitivity that quantifies the global mean precipitation response to the global mean temperature warming alone. It is noteworthy that αglobal is obtained from the stabilization period in CESM1 experiment (Fig. 2a and Supplementary Fig. 3c, e), 2.54% K−1. f is 0.8 for the fraction of the CO2 forcing that heats the atmosphere36. In addition, the ΔF can be simplified as 5.35ln(CO2/367 p.p.m.)55 and ΔT is the model simulated surface temperature response in a CESM. Based on this simple model, we are able to calculate the estimated global mean precipitation response to a CO2 radiative forcing and compare with the results in CESM1 experiment (Fig. 1d).

Apparent hydrologic sensitivity over land

We define the proportionality constant, κ (i.e., the apparent hydrological sensitivity), as both the fast and slow precipitation response in the ocean and land during the CO2 ramp-up and ramp-down periods, respectively. However, land’s hydrological sensitivity is nearly identical during the ramp-up (↑) period (1.57% K−1) and ramp-down (↓) period (1.61% K−1) (see Fig. 3b), indicating the following relationship:

$${\Delta}P_{\mathrm{land}} = k_{\mathrm{land}}{\Delta}T_{\mathrm{land}}\left( {\mathrm{ramp - up}\left( \uparrow \right)\,{\mathrm{and}}\,{\mathrm{ramp - down}}\,\left( \downarrow \right)\,{\mathrm{periods}}} \right)$$
(8)

Here, κland = (κland↑ + κland↓)/2, i.e., 1.59% K−1.