Future precipitation increase constrained by climatological pattern of cloud effect

Domain: earth_science
Published: 2023-10-11
Editorial outcome: major_revision

Abstract
The fractional increase in global mean precipitation (\Delta P/P) is a first-order measure of the hydrological cycle intensification under anthropogenic warming. However, \Delta P/P varies by a factor of more than three among model projections, hindering credible assessments of the associated climate impacts. The uncertainty in \Delta P/P stems from uncertainty in both hydrological sensitivity (global mean precipitation increase per unit warming) and climate sensitivity (global mean temperature increase per forcing). Here, by investigating hydrological and climate sensitivities in a unified surface-energy-balance perspective, we find that both sensitivities are significantly correlated with surface shortwave cloud feedback, which is further linked to the climatological pattern of cloud shortwave effect. The observed pattern of cloud effect thus constrains both sensitivities and consequently constrains \Delta P/P. The 5%-95% uncertainty range of \Delta P/P from 1979-2005 to 2080-2100 under the high-emission (moderate-emission) scenario is constrained from 6.34\pm3.53% (4.19\pm2.28%) in the raw ensemble-model projection to 7.03\pm2.59% (4.63\pm1.71%). The constraint thus suggests a higher most-likely \Delta P/P and reduces the uncertainty by ~25%, providing valuable information for impact assessments.

Introduction
Global mean precipitation (P) is projected to increase under anthropogenic warming, but the magnitude of increase is highly uncertain. The fractional increase in mean precipitation over the 21st century (\Delta P/P) varies from 3.3 to 11.6% in models under the high-emission scenario (RCP8.5/SSP5-8.5) and from 1.9 to 7.4% under the moderate-emission scenario (RCP4.5/SSP2-4.5). This large uncertainty in \Delta P/P must be constrained for credible assessments of hydrological impacts.

The uncertainty in \Delta P/P stems from uncertainty in both hydrological sensitivity (HS) which represents the fractional increase in global mean precipitation per degree of warming (\Delta P/P / \Delta T) and climate sensitivity (CS) which represents the increase in global mean temperature per anthropogenic forcing (\Delta T). CS and HS contribute roughly equally to uncertainty in global precipitation change, both varying by a factor of two among models (ratio between the highest and lowest values). An accurate estimate of future precipitation increase thus requires constraining uncertainty in both HS and CS.

A common approach to constraining uncertainty in climate-model projections is the so-called “emergent constraint” (EC), which utilizes statistical and/or physical relationships between the observable current climate and a future projection. For CS, several ECs have been proposed from various perspectives, such as linking future temperature change to its seasonal or interannual variability, relating cloud feedbacks to the climatological distribution or properties of clouds, and using correlations with other observable features. For HS, two ECs have been proposed based on the atmosphere-energy-balance perspective that relates changes in global precipitation to changes in atmospheric radiative cooling. They show that HS is correlated with feedbacks from clear-sky shortwave absorption and longwave cloud radiation. However, a more recent analysis finds that, in the latest generation of climate models, the correlation of HS to clear-sky shortwave feedback weakens substantially (r = −0.45) and the correlation to longwave cloud feedback no longer holds (r = -0.12). Furthermore, the constraints on HS and CS have not been integrated into a full constraint on \Delta P/P. It was challenging to do so as the ECs on HS and CS were based on different but potentially correlated observables.

Using a rather different approach, some studies have directly constrained \Delta P/P by relating it to the observed historical temperature trend. The rationale is that future precipitation increase should be correlated with future temperature increase and future temperature increase should be correlated with forced temperature trend over recent decades. Interestingly, the correlation of \Delta P/P to historical precipitation trend is lower and the resultant EC is less effective. Thus, their ECs mainly utilized the CS part while the potential to constrain the HS part was not harnessed. Furthermore, as the observed trend contains not only the forced response but also natural variability, the forced temperature trend must be estimated as a range, which introduces further uncertainty.

Is it possible to build an EC on \Delta P/P that integrates constraints on both CS and HS? Here, unlike previous studies that consider HS and CS separately from the perspectives of atmosphere and top-of-the-atmosphere, we investigate them in a unified surface-energy-balance perspective. This allows us to correlate CS and HS with the same observable and upon that build an EC on \Delta P/P. Specifically, we reveal that the sensitivity of surface shortwave cloud effect to anthropogenic warming is responsible for a large part of the uncertainty in both HS and CS. We further show that the uncertainty in cloud sensitivity is dominated by the temperature-mediated feedback and can be inferred from the climatological pattern of cloud shortwave effect. The observed pattern of cloud shortwave effect thus provides an effective EC on \Delta P/P. The resultant EC indicates a higher most-likely \Delta P/P than the ensemble model projection and reduces the 5%-95% uncertainty range of \Delta P/P by ~25%.

Results
A surface-energy-balance perspective for understanding HS and its uncertainty
Because the increase in global precipitation is strongly correlated with the increase in global ocean evaporation (Fig. S1), one can understand HS from the perspective of ocean surface energy balance. Specifically, according to a reformulated Penman equation, ocean evaporation is linked to surface energy fluxes and relative humidity as,

L_v E = f[SW + LW - G + \xi(1 - RH)]

where SW and LW are the net shortwave and longwave radiative fluxes received by ocean surface; G is the ocean heat uptake; RH is the near-surface relative humidity; f is an energy allocation factor that depends only on temperature and increases with warming (reflecting an increased ratio of latent to sensible surface fluxes); and \xi is a scale parameter that varies with aerodynamic resistance. A derivation with detailed definitions of f and \xi is provided in Methods. The Penman equation allows us to attribute future change in ocean evaporation and its intermodel uncertainty to individual factors.

We first affirm that the Penman equation well captures the historical climatology (Fig. S2) and future change (Fig. 1) of the model-simulated ocean evaporation. The spatial patterns of the estimated and simulated evaporation are correlated at r = 0.99 for historical climatology (Fig. S2a–c) and r = 0.98 for future change (Fig. 1a, b). Across models, the global mean values of the estimated and simulated evaporation are correlated at r = 0.78 for historical climatology (Fig. S2d) and r = 0.93 for future change (Fig. 1c).

We then attribute future change in ocean evaporation and its uncertainty to individual factors such as surface air temperature (which controls the energy allocation factor f), surface radiative fluxes, relative humidity, ocean heat uptake, and surface wind speed (which affects aerodynamic resistance and then the parameter \xi). As summarized in Fig. 1d, the model ensemble projects a 1.87\pm0.46 % K–1 increase in global ocean evaporation (\Delta E_o / E_o / \Delta T), where \pm indicates the 5–95% uncertainty range (Methods). The increase is contributed by the warmer temperature that increases the energy allocation factor f and the increasing net longwave flux as a more humid atmosphere enhances air emissivity, but is partially offset by the ocean heat uptake and relative humidity increase (see Fig. S3 for the spatial patterns of changes in individual factors and their contributions to ocean evaporation change). While surface shortwave flux only contributes weakly to the mean change, it is the largest source of uncertainty, leading to a \pm0.61% K–1 intermodel spread in global ocean evaporation change. The contribution of surface shortwave flux is further decomposed into contributions from surface albedo, clear-sky downward shortwave flux, and cloud effect on downward shortwave flux (hereafter denoted as surface shortwave cloud effect, or SSCE). Of these, SSCE is by far the largest source of the uncertainty, leading to a \pm0.72% K–1 spread in global ocean evaporation change (Fig. 1d; see Fig. S4 for the contribution of individual factors in each model). Note that the \pm0.72% K–1 uncertainty due to the SSCE change is larger than the total 0.46% K–1 uncertainty in HS, indicating potential compensations from other factors. In particular, the intermodel uncertainty due to SSCE is partially (~0.3) compensated by that due to surface net longwave radiation (Fig. S5).

Surface shortwave cloud feedback regulates future precipitation change by affecting both CS and HS
Due to the dominant contribution of SSCE to the projection uncertainty, the increase in global ocean evaporation per unit warming (\Delta E_o / E_o / \Delta T) is significantly correlated with that contributed solely by the SSCE change (\Delta E_o^SSCE / E_o / \Delta T) across models (Fig. S6; r = 0.75). As a result, \Delta E_o / E_o / \Delta T is significantly correlated with global ocean SSCE change per unit warming (\Delta SSCE / \Delta T) (Fig. 2a; r = 0.72). Models with a larger \Delta SSCE / \Delta T tend to project a larger \Delta E_o / E_o / \Delta T, that is, a higher HS in term of ocean evaporation increase.

According to surface energy balance, a larger \Delta SSCE / \Delta T would also enhance the degree of surface temperature warming under anthropogenic forcing (\Delta T), implying a potential positive correlation between \Delta SSCE / \Delta T and CS. Indeed, CS is significantly correlated with \Delta SSCE / \Delta T across models (Fig. 2b; r = 0.61). Models with a larger \Delta SSCE / \Delta T tend to project a larger global mean surface warming \Delta T. As both \Delta E_o / E_o / \Delta T and \Delta T are correlated with \Delta SSCE / \Delta T, \Delta E_o / E_o (Fig. 2c; r = 0.76) and thus \Delta P/P (Fig. 2d; r = 0.70) are correlated with \Delta SSCE / \Delta T. All these correlations are significant among both the individual and combined ensemble of CMIP5 and CMIP6 (see correlation coefficients in Fig. 2). The high correlation between \Delta SSCE / \Delta T and \Delta P/P suggests that if there is an observational constraint on \Delta SSCE / \Delta T, we can also constrain the uncertainty in \Delta P/P under anthropogenic warming.

\Delta SSCE / \Delta T is the change in global ocean SSCE per unit warming under the RCP8.5/SSP5-8.5 scenario, which includes the effects of both rapid adjustment and temperature-mediated feedback (feedback here refers to the temperature-mediated change in SSCE, without corrections for non-cloud factors as in the radiative-kernel method). By diagnosing these two effects from the piControl and Abrupt4xCO2 experiments (Methods), we can see that the effect of rapid adjustment of SSCE (normalized by ocean warming) is much less uncertain compared to the temperature-mediated feedback of SSCE, hereafter referred to as SSCF (Fig. 2e). As a result, the intermodel uncertainty in \Delta SSCE / \Delta T is largely due to that of SSCF, with the intermodel correlation between \Delta SSCE / \Delta T and SSCF at r = 0.9 (Fig. 2f). Subsequently, \Delta E_o / E_o / \Delta T, \Delta T, \Delta E_o / E_o and \Delta P/P are all significantly correlated with SSCF (Fig. S7).

An emergent constraint on future precipitation increase
Now, we explore potential correlations of \Delta SSCE / \Delta T to observable quantities and build ECs for \Delta SSCE / \Delta T and \Delta P/P. The shortwave cloud radiative effect and its feedback have been widely studied from the top-of-the-atmosphere (TOA) perspective. Previous work finds that the intermodel uncertainty in TOA shortwave cloud feedback can be attributed to distinct climatological patterns of cloud effect. Particularly, models that exhibit lower (higher) climatological cloud reflection in warm (cool) regions tend to project a more positive shortwave cloud feedback at the TOA. Because the uncertainty in \Delta SSCE / \Delta T is dominated by the temperature-mediated feedback and both shortwave cloud effect and feedback are highly correlated between surface and TOA (Fig. S8), we explore a similar correlation between \Delta SSCE / \Delta T and the climatological pattern of SSCE.

To visualize the potential relation between \Delta SSCE / \Delta T and the climatological pattern of SSCE, we compare model groups with the highest and lowest \Delta SSCE / \Delta T (Fig. 3). The two groups present distinct climatological patterns of SSCE and local \Delta SSCE / \Delta T. For the climatological SSCE pattern, the group of high \Delta SSCE / \Delta T exhibits a larger spatial variance of SSCE, that is, stronger SSCE (more negative than that in an average model) over the cold midlatitudinal region where SSCE is climatologically strong and weaker SSCE over the warm tropical region (except the deep convective regions) where SSCE is climatologically weak (Fig. 3a, c, e). For local \Delta SSCE / \Delta T, the group of high \Delta SSCE / \Delta T exhibits more positive \Delta SSCE / \Delta T over subtropical regions where the climatological SSCE exhibits strong spatial gradients (Fig. 3b, d, f). The relation between \Delta SSCE / \Delta T, local \Delta SSCE / \Delta T, and climatological SSCE can be interpreted similarly as those at the TOA. Specifically, as the warm tropical region with lower climatological SSCE expands poleward with warming, a larger spatial gradient in the climatological SSCE induces an anomalously positive \Delta SSCE / \Delta T in the subtropical transition regions (Fig. 3f), consequently leading to a higher \Delta SSCE / \Delta T.

A consistent picture is seen from the regression of the climatological SSCE onto \Delta SSCE / \Delta T across models. A higher \Delta SSCE / \Delta T is associated with lower (less negative) climatological SSCE over the warm tropical regions and higher (more negative) climatological SSCE over cold midlatitudinal regions (Fig. 4a). Thus, an index that measures how much a model climatology favors high \Delta SSCE / \Delta T can be derived as the pattern correlation between the climatological SSCE (anomaly relative to the multi-model mean) and Fig. 4a. This index of climatological SSCE pattern, denoted as C, is significantly correlated with \Delta SSCE / \Delta T across models (r = 0.72; Fig. 4b). The ISCCP and CERES datasets provide satellite measurements of surface radiative flux and their climatological values of Index C are 0.25 and 0.28, respectively. An EC on \Delta SSCE / \Delta T is then derived by applying the observational values of C to the regression line. The resultant EC constrains the 5%-95% uncertainty range of \Delta SSCE / \Delta T from 0.39\pm1.20 Wm−2 K−1 in the raw ensemble-model projection (black vertical error bar in Fig. 4b) to 0.63\pm0.83 Wm−2 K−1 (red vertical error bar in Fig. 4b).

As \Delta P/P is significantly correlated with \Delta SSCE / \Delta T and \Delta SSCE / \Delta T is significantly correlated with Index C, \Delta P/P is significantly correlated with Index C (Fig. 4c; r = 0.68). We then derive an EC on \Delta P/P by applying the observational values of C to the regression line between C and \Delta P/P. The resultant EC constrains the 5%-95% uncertainty range of \Delta P/P between 1979-2005 and 2080-2100 under the RCP8.5/SSP5-8.5 scenario from 6.34\pm3.53% in the raw ensemble-model projection (black vertical error bar in Fig. 4c) to 7.03\pm2.59% (red vertical error bar in Fig. 4c). This indicates a higher increase in global mean precipitation than the ensemble-model projection and reduces the intermodel uncertainty by 27%.

As the climatological SSCE affects \Delta SSCE / \Delta T through its spatial gradient between warm and cold regions, we further construct a simpler index of the climatological SSCE pattern based on the difference in the mean SSCE between the region with SST > 25oC and 0 < SST < 25oC. This simple Index D drops the need to compute the pattern correlation and can be easily applied to other warming scenarios and future CMIP ensembles. As shown in Fig. S9, Index D effectively constrains \Delta SSCE / \Delta T and \Delta P/P. The resultant ECs indicate similar results as those of Index C, demonstrating the robustness of the proposed EC.

Relation and difference between different warming scenarios
Our EC also works well for the moderate-emission scenario of RCP4.5/SSP2-4.5. HS, CS and \Delta P/P are all significantly correlated with \Delta SSCE / \Delta T (Fig. S10), and \Delta P/P can be constrained by the climatological index of SSCE (Fig. S11). The proposed EC constrains the 5%-95% uncertainty range of \Delta P/P under RCP4.5/SSP2-4.5 from 4.19\pm2.28% in the raw ensemble projection to 4.63\pm1.71%. This indicates a higher increase in global mean precipitation than the ensemble-model projection and reduces the projection uncertainty by 25%.

Methods
Future projection of global climate models
Future changes under anthropogenic warming are projected by climate models from the Coupled Model Intercomparison Project Phase 5 (CMIP5) and Phase 6 (CMIP6) under the Representative Concentration Pathway 4.5 and 8.5 warming scenarios (RCP4.5 and RCP8.5) for CMIP5 and under the Shared Socioeconomic Pathway 4.5 and 8.5 warming scenarios (SSP2-4.5 and SSP5-8.5) for CMIP6 (Table S1). Future changes are estimated from the differences in climatology between the historical period (1979-2005) and the future period (2080-2100). All outputs have been interpolated into a common 2.5o x 1.5o grid before analyses.

Effects of rapid adjustment and temperature-mediated feedback
The piControl and Abrupt4xCO2 simulations from the above 36 models are used to estimate the direct (i.e., rapid adjustment) and indirect (i.e., temperature-mediate) effect of the CO2 increase. Here, piControl refers to the pre-industrial control simulation with non-evolving pre-industrial conditions and it serves as a baseline for perturbation simulations that branch from it. Abrupt4xCO2 refers to the perturbation simulation in which an instantaneous quadrupling of CO2 is imposed and then held fixed.

The temperature-mediated feedback is estimated from the change normalized by ocean warming after year 1, i.e.,

Temp-mediated Feedback = \Delta z_{1-80} / \Delta T_{1-80} (1)

where \Delta T_{1-80} is the increase in global mean ocean surface temperature from year 1 to year 80 and \Delta z_{1-80} is the change in global mean of a specific variable (i.e., SSCE or precipitation) from year 1 to year 80. The effect of rapid adjustment is computed as

Rapid Adjustment = \Delta z_1 - Feedback * \Delta T_1 (2)

where \Delta z_1 is the change in a variable in year 1 of Abrupt4xCO2, and \Delta T_1 is the temperature increase in year 1. When comparing the relative importance of rapid adjustment and the temperature-mediated feedback for the RCP/SSP scenario, we normalize the effect of rapid adjustment by the total degree of ocean warming.

The reformulated Penman equation
The Penman equation estimates evaporation (E) over open water as

L_v E = \Delta / (\Delta + \gamma) * (SW + LW - G) + \gamma / (\Delta + \gamma) * \kappa e* (1 - RH) (3)

where L_v is the latent heat of vaporization, e* is the near-surface saturation vapor pressure, \Delta = \partial e* / \partial T = L_v e* / (R_v T^2) measures the increase of e* with temperature, \gamma is the psychrometric constant, \kappa = \rho C_p / r_a is the aerodynamic resistance, T and RH are the near-surface air temperature and relative humidity, SW and LW are the net downward surface shortwave and longwave radiative fluxes, and G is the ocean heat uptake. Following Refs. 25,29, the Penman evaporation can be rewritten as,

L_v E = f[SW + LW - G + \xi(1 - RH)] (4)

where f = \Delta / (\Delta + \gamma) is the energy allocation factor and \xi = R_v T^2 \kappa / \gamma scales the RH effect.

As saturation vapor pressure e* increases exponentially with warming, \Delta increases with warming at the rate of d ln \Delta / dT = L_v / (R_v T^2) \approx 5.8% K−1, and consequently the energy allocation factor f \approx \Delta / (\Delta + \gamma) increases with warmer temperature at the rate of d ln f / dT \approx (1 - f) d ln \Delta / dT. That is, a warmer temperature will increase the energy allocation of total available energy to surface latent flux and contribute to future evaporation increase.

The Penman-based estimates of evaporation are computed from Eq. 4 using monthly mean air temperature, relative humidity, surface radiative flux, ocean heat uptake and surface wind speed in each model. The aerodynamic resistance in \kappa is computed from the surface wind speed as r_a = 1.0 x 10^-3 (1 + 0.7 U), which fits the simulation climatology well. Because it is difficult to directly compute the ocean heat uptake, G is diagnosed as the residual of the surface energy balance, i.e., G = SW + LW - L_v E - SH. In climatology of models (1979-2005), the global mean G is ~1.34\pm0.8 Wm−2 while SW + LW is ~115\pm3.5 Wm−2 and SSCE is 59\pm5.5 Wm−2. When estimating the contribution of a particular factor to the ocean evaporation change, we change its values in the Penman equation from those in historical climate to those in future climate while other factors are unchanged.

Estimation of uncertainty ranges
For the raw multi-model ensemble estimate, the 5%-95% uncertainty range is estimated from the \pm1.64 s.d. of the intermodel spread, assuming the spread generally follows a Gaussian distribution. For the emergent constraint, the uncertainty range is estimated using the s.d. of residual variance after regression and we compute the s.d. of residual variance using the hierarchical statistical framework following Refs. 22,38. Let z be the future changes, x be the parameter C in climate models, and y be the observed values of C (here we only have two data points from CERES and ISCCP). The observationally constrained mean E(z|y) and s.d. \delta(z|y) is calculated by the following equations,

E(z|y) = u_z + \rho \delta_z / \delta_x * (y - u_x) (5)

\delta(z|y) = \delta_z \sqrt{1 - \rho^2} (6)

where u and \delta refer to the mean and s.d., and \rho is the correlation between x and z.

Peer review rounds
[{"round": 1, "reviewer_comments": {"reviewer_1": "Summary:\nThis paper aims to constrain the projection uncertainty of global mean precipitation change, by\nconstraining its two components – the hydrological sensitivity (∆P/∆T) and the climate sensitivity.\nUsing a unified surface-energy-balance framework, it is found that both sensitivities are significantly\ncorrelated with surface cloud shortwave feedback, which can be constrained using the observed\npattern of climatological cloud effect. This is a physically strong emergent constraint. It reduces the\nprojection uncertainty by more than 25% in the CMIP5/6 ensemble.\nThe emergent constraint is effective and novel, because it applies to both the hydrological\nsensitivity and the climate sensitivity. The main conclusions are well supported by the analyses. My major\ncomments focus on the analysis of hydrological sensitivity, including the applicability of the\nemergent constraint in transient and “quasi-stabilized” climate change scenarios, and the scenario\ndependency of hydrological sensitivity. These are fundamental issues in the hydrological cycle\nchange.\nMajor comments:\n1. The emergent constraint of hydrological sensitivity (∆P/∆T) is applied to the median emission\nscenario (RCP4.5/SSP2-4.5). Under RCP4.5/SSP2-4.5 scenarios, global mean temperature increases in\nthe near-term and then stabilizes. That is, it includes two types of climate change under\nRCP4.5/SSP2-4.5 – transient climate change in the first stage and “quasi-stabilized” climate change in\nthe second stage (I use “quasi-stabilized” because only the global mean temperature is stabilized but\nnot in the ocean state). Thus, the hydrological sensitivity (∆P/∆T) is different in these two stages.\nHow does this affect the constraint? Does the emergent constraint apply to both stages?\n2. As the hydrological sensitivity (∆P/∆T) depends on external forcings, it should differ between\ndifferent emission scenarios. Please add some discussions on the scenario dependency of\nhydrological sensitivity (in raw simulations and in constrained results).\n3. There have been several studies providing constrained projections of hydrological sensitivity or\nglobal mean precipitation change. How do the quantitative results compare with each other? Please\nadd some discussions on this.\nMinor comments:\n4. Fig. S1: Please clarify which experiments were used for CMIP5 and CMIP6.\n5. L126 and L157: Please use the full term “global surface shortwave cloud feedback” instead of\nGSSCF in the subtitle.", "reviewer_2": "This paper presents a new emergent constrain on global hydrologic sensitivity by utilizing\nthe relationship between the pattern of surface climatological shortwave cloud radiative effect and the\nprojected global precipitation response under future emission scenarios. The relationship is rooted\nin the physics that tie the climatological cloud pattern, shortwave cloud feedback, oceanic energy\nbudget (and thus global evaporation), and climate sensitivity together. To my knowledge, the\nrelationship between global precipitation and shortwave cloud effect has not been\ndiscovered/shown previously. An emergent constraint utilizing satellite measurements of the\nclimatological shortwave cloud effect pattern results in a small constraint on the model spread of\nthe projected global precipitation response. While the final constraint is marginal, I think this study is\nvaluable for revealing a new emergent constraint that can be utilized in other model ensembles and\nobservational datasets in the future. Also, the study uses a large and robust collection of climate\nmodels and reasonable metrics to perform the constraint. Nonetheless, I think some revisions are\nwarranted to improve the robustness and physical interpretation of the results, as described below. I\nthink the paper may be suitable for publication in Nature Communications if the authors can address\nthese concerns.\n1. A reasonable assumption may be that the relationships shown for the RCP emissions scenarios\nhere (e.g., Figs. 2, 4, S6, S7) are rooted in the response of the relevant quantities (clouds,\nprecipitation, evaporation) to planetary warming. In other words, I wonder if the temperature-\nmediated responses [i.e., the changes that only result from global (predominantly oceanic) warming\nand that exclude potential contributions from rapid adjustments due to changes in the forcing itself\n(from greenhouse gases, aerosols, etc.)] are largely responsible for the relationships. Is this true?\nThis could be diagnosed with simulations that abruptly increase CO2 initially then leave it constant,\nor with simulations that just increase SST but not radiatively active atmospheric constituents,\nallowing one to examine the response to just the warming itself (e.g., see refs. 17, 18, and 21).\nShowing that these inter-model relationships also exist in the temperature-mediated framework\nwould help to 1) show their robustness, and 2) better pin down their physical basis. I suggest the\nauthors consider doing this (and perhaps showing the results as supplementary figures), which\nwould help strengthen their conclusions and allow for a more direct comparison with previous\nstudies that constrain hydrologic sensitivity on the basis of temperature-mediated responses.\n2. Regarding the evaporation calculations: can the authors expand on the ocean heat uptake (G)\ncalculation a bit more in methods? If it is computed as a residual, this implies that it uses model-\ngenerated SW, LW, and E. How then is model-generated E different from the E computed from the\nPenman equation? Is one expected to be a better estimate than the other? Also, do the SW and LW\nterms appear twice or cancel out if one were to expand G in equation (2). In short, I wonder how\nstrongly the model-generated and Penman E are dependent on each other (due to the way G is\ncomputed) and whether this dependence could explain the apparently good agreement between\nthese quantities (e.g., Fig. S2).\n3. Has the sensitivity to the definition of C (the metric used for the emergent constraint) been\nexplored? Currently, C depends on the relationship between GSSCF and climatological SSCE itself\n(Fig. 4a). Would a metric that is independent of this relationship (say, just the difference between\nclimatological SSCE between the low and high latitudes) give the same tight relationships as in (b)\nand (c) of Fig. 4? Not only would this demonstrate robustness, but also allow one to compute the\nmetric in other ensembles without the need to first generate Fig. 4a based on that ensemble.\nSpecific/minor comments:\nL45-46: “a more recent analysis suggests that the statistical relationships underlying these two ECs\ndo not hold up among the latest generation of climate models” – This claim is not entirely true. As\nstated in the abstract of ref. 21: “The constraint based on clear-sky shortwave absorption sensitivity\nto water vapor has weakened, and it is argued that a proposed constraint based on surface low\ncloud longwave radiative effects does not apply to HS.” Ref. 21 does not suggest that both ECs no\nlonger apply or that all key related relationships no longer exist.\nL52-54: “The rationale is that future precipitation increase is correlated with future temperature\nincrease and the latter is correlated with the forced trend over recent decades” – Did you mean to\nsay “the former” rather than “the latter” is correlated…?\nL54-55: “That said, only the CS part has been utilized in the EC to constrain DP/P while the potential\nto constrain the HS part has not been harnessed.” I'm not sure this is true since that study (ref. 22),\naccording to its abstract, uses trends in DP itself to constrain future DP. It is thus constraining the\ntotal DP directly, which has contributions from HS and CS as the authors state earlier.\nFigs. 1, S2, and possible others: It would help to state the time periods that are plotted in the figure\ncaptions.\nL126: I would avoid using such a long acronym (GSSCF) in the section title, especially since this\nacronym has not been defined yet.\nL158-160: “The shortwave cloud feedback, widely considered as a major uncertainty source for CS,\nhas been often studied from the perspective of the top of the atmosphere (TOA).” What is the\nrelationship between the TOA and SFC SW cloud feedback? It is assumed here that these should be\nessentially the same, qualitatively and perhaps even quantitatively, to some extent? If so, this should\nbe stated explicitly.", "reviewer_3": "Several major revisions and comments are provided for the manuscript, as I found it unconvincing:\nAbstract: what exactly is meant by climatological cloud effect? This is very vague and I don´t know\nwhat exactly it is about clouds that is meant\nLine 27: Give a clear definition of what ΔP/P stands for (the fractional change in mean precip\nnormalized by the mean precip)\nLine 33: “varying by a factor of 2” is unclear language.\nLine 41: Emergent constraints should be constructed only with observable quantities, but this\nsentence seems to imply anything can be used?\nLine 48-49: “under different frameworks” and “different but likely dependent observables” are oddly\nworded and unclear.\nLine 51: Not sure this is necessary, seems like a rehash of previous paragraph? Also co-dependencies\nof terms within the EC as explained in previous paragraph?\nLine 59: All ECs should be physically guided, so this statement is unnecessary. That said, why a\nsurface energy balance framework – what is new and of value here, as opposed to ECs based on the\nTOA budget, for example.\nLines 36-57: The manuscript could be better motivated. It is good to explain what ECs are, but the\nfocus is supposed to be on finding an EC for precipitation increases with warming, so why spend so\nmuch time discussing ECs for CS and HS? It`s distracting, focus instead on ECs for precipitation\nincrease specifically. That said, I believe there has been other rather recent work in addition to Ref.\n22 on ECs for precipitation increase, and the manuscript alludes to how this EC is different from\nother studies; this should be further discussed. What makes this framework for developing an EC in\nthis manuscript new and of value? The motivation for using ocean evaporation and the surface\nenergy budget is particularly missing.\nLine 60-62: It`s not necessary for an EC to constrain both HS and CS first in order to well constrain\nfuture precipitation increases (so long as a physical relationship exists between the observed\nquantity and the precipitation increase). This seems convoluted and potentially misguided. Why this\napproach?\nLine 124: compensation from other factors maybe deserves to be explored – if we reduced\nuncertainty in SSCE then how much would it really matter given these other factors (ok, at least the\ndiscussion section acknowledges this, but this issue still needs to be addressed).\nLine 131: Calling the change in SSCE with warming a “cloud feedback” is misleading, since this\nincludes feedbacks and adjustments but isn´t quite itself a feedback, it´s a change in shortwave cloud\nradiative effects as seen by the surface. A different analysis is needed to isolate the surface\nshortwave cloud feedbacks.\nLines 145: There actually seems to a deterioration between the CMIP5 and CMIP6 ensembles in the\ncorrelation between GSSCF and change in evaporation and change in precipitation with warming,\nbut especially for precipitation. The deterioration is fairly large for precipitation, and appears to be\ndriven by two models. Which are these and why do they depart so starkly from the other CMIP6\nmodels? Doesn´t this negatively impact the EC constructed for precipitation, or is r=0.67 still a high\nenough correlation?\nLine 158: This approach seems odd – since GSSCF is correlated with ΔP/P, why not just find an\nobservable variable that is highly correlated or linked to shortwave cloud feedback and build the EC\nfor precipitation with that variable directly? That seems to me to be the standard way to construct\nan EC, rather than build an EC on top of an EC (constraining GSSCF to then constrain precipitation\nchange), which may be a misguided approach. If this is what was done, this needs to be made more\nclear, because it does not read this way.\nLine 160: Need to make clear what understanding/advancement is gained by examining from a\nsurface energy balance perspective rather than TOA.\nLine 162: Again, what exactly is meant by climatological cloud pattern? Just their geographical\ndistribution, and/or optical thickness, etc.?\nLines 167-168: Why ignoring the models in between these two groups?\nLine 224: does EC break down for low emission scenario and why?\nHow does this compare to ECs based on TOA framework?? Like in ref 22\nLine 237: this wasn´t shown for f, wasn’t it the definition?? Also this wasn’t shown or discussed at all\nreally anyway\nFig. 4, remainder of EC construction, and Discussion: the EC presented in Fig. 4 seems veeeeeeery\nhand-wavey. The climatological SSCE index is heavily derived parameter, based on quantities that\nare observed but can have a high uncertainty, while ECs ideally should be constructed with\nobservable parameters/variables that at the least are not so derived or directly measured, and the\nobservable´s uncertainty range tells something about the plausible range of the parameter being\nconstrained by highlighting its values that fall into that range. I do not see that with the EC as\npresented in Fig. 4 for precipitation change with warming. The horizontal error bars in Fig. 4 appear\nto be missing in fact, so that this plausible range of precipitation change values does not seem like it\ncan be easily estimated despite the uncertainty value given in the text. It´s really the horizontal error\nbars on the climatological index and NOT the vertical bars that we´re after with an EC\nanyway, and so the uncertainty range given in the text appears to be misestimated; we want to see which values\nof the precipitation change are associated with the range of index values over its uncertainty range –\nthis is the uncertainty range on the precipitation change rather than the calculation underlying the\nvertical error bars in Fig. 4. I remain unconvinced by this EC because of the amount of derivation\nrequired and the misguided uncertainty/constraint estimation.\nMinor Comments:\nFig. S4: what is the x-axis?? The model “number?”"}, "author_response": "Dear Reviewers:\nThank you so much for your insightful comments and detailed suggestions. They are very\nhelpful to us for improving the manuscript. We have revised the manuscript accordingly.\nThe major changes include:\n1. Diagnose the effects of rapid adjustment and the temperature-mediated feedback\nbased on the piControl and Abrupt4xCO2 simulations of CMIP5/6 models, and use\nthem to further understand the response under the RCP scenarios\n2. Illustrate the relation and difference among different warming scenarios and\nperiods, and demonstrate the usefulness of the proposed EC to different scenarios\nand periods.\n3. Introduce a simple index of the climatological pattern of SSCE based on the SSCE\ndifference between regions with SST>25oC and 0oC<SST<25oC. This simple Index\nD does not involve the computation of pattern correlation and shows the\nrobustness of the EC.\n4. Add more detailed comparison with previous ECs on HS and ∆𝑃#/𝑃# and highlight\nthe advantage of the proposed EC\n5. The uncertainty of the observations is already included in Fig. 4 (for Index C) and\nFig. S9 (for the new simple Index D). As a benefit of using the climatological pattern\nas the final observable, the uncertainty from the observations is very small so the\nuncertainty of the EC is mainly from the unexplained variance by the correlation.\n6. Correct the computation of Index C by only using the ocean grid points (as we are\ntalking about surface energy balance and evaporation over ocean). This correction\nslightly increases the most-likely ∆𝑃#/𝑃# constrained by the EC.\nOur point-by-point responses are provided below (the original review in black and the\nauthors’ responses in red).\nResponse to Reviewer #1:\nThis paper aims to constrain the projection uncertainty of global mean precipitation\nchange, by constraining its two components – the hydrological sensitivity (∆P/∆T) and\nthe climate sensitivity. Using a unified surface-energy-balance framework, it is found\nthat both sensitivities are significantly correlated with surface cloud shortwave feedback,\nwhich can be constrained using the observed pattern of climatological cloud effect. This\nis a physically strong emergent constraint. It reduces the projection uncertainty by more\nthan 25% in the CMIP5/6 ensemble.\nThe emergent constraint is effective and novel, because it applies to both the hydrological\nsensitivity and the climate sensitivity. The main conclusions are well supported by the\nanalyses. My major comments focus on the analysis of hydrological sensitivity, including\nthe applicability of the emergent constraint in transient and “quasi-stabilized” climate\nchange scenarios, and the scenario dependency of hydrological sensitivity. These are\nfundamental issues in the hydrological cycle change.\nMajor comments:\n1. The emergent constraint of hydrological sensitivity (∆P/∆T) is applied to the median\nemission scenario (RCP4.5/SSP2-4.5). Under RCP4.5/SSP2-4.5 scenarios, global mean\ntemperature increases in the near-term and then stabilizes. That is, it includes two types\nof climate change under RCP4.5/SSP2-4.5 – transient climate change in the first stage\nand “quasi-stabilized” climate change in the second stage (I use “quasi-stabilized”\nbecause only the global mean temperature is stabilized but not in the ocean state). Thus,\nthe hydrological sensitivity (∆P/∆T) is different in these two stages. How does this affect\nthe constraint? Does the emergent constraint apply to both stages?\nWe thank the reviewer for raising this important question. In response to your comment,\nwe have conducted additional analyses and added supplementary figures to illustrate the\ntwo stages of climate change in RCP4.5 and demonstrate that the EC applies to both\nstages.\nThe climate response to the RCP forcing can be understood as a combination of the direct\n(i.e., rapid adjustment) and indirect (i.e., temperature-mediated) effects. Fig. R1a shows\nthe temporal evolutions of ∆T and ∆P/P in RCP4.5, RCP8.5 and Abrupt4xCO2 and Fig.\nR1b plots ∆T versus ∆P/P over time (the slope of the regression line indicates HS).\nAccording to Abrupt4xCO2 in Fig. R1a, the direct effect reduces P (as seen in the rapid\nresponse at year 1) while the temperature-mediated effect increases P (as seen in the\nresponse after year 1). For RCP4.5, the CO2 increase stabilizes in the late 21st century,\nso the temperature-mediated effect becomes more dominant than the effect of rapid\nadjustment, and HS becomes larger (Fig. R1b). Nevertheless, HS in the early (2049-2069\nminus 1979-2005) and late (2080-2100 minus 2049-2069) periods are highly correlated\namong models (Fig. R1e,f) and so are CS in the two periods (Fig. R1g,h). As shown in\nFig. R2, for both stages, the intermodel uncertainty in both HS and CS are significantly\ncorrelated with that of ∆𝑆##𝑆##𝐶##𝐸#/∆𝑇#, and Index C works well to constrain ∆P/P.\nWe have added a new section to discuss the relation and difference among different\nwarming scenarios. The early and late stages in RCP4.5 are discussed in the second\nparagraph of that section. We have included Fig. R1 and Fig. R2 as Fig. S12 and Fig.\nS14 in Supplementary Information.\nFigure R1: a, Temporal evolution of the global mean temperature (∆𝑇#, solid) and precipitation\n(∆𝑃#/𝑃#, dashed) under RCP8.5 (red), RCP4.5 (blue) and Abrupt4xCO2 (black). b, Relationship\nbetween changes in temperature and precipitation (the slope indicates hydrological sensitivity\n∆𝑃#/𝑃#/∆𝑇#) under RCP8.5 (red), RCP4.5 (blue) and Abrupt4xCO2 (black). c, Relationship between\nchanges in temperature and precipitation under RCP8.5 for individual models. The slopes of\nHS=1.2% K-1 and HS=3.2% K-1 are plotted for reference. d. As c but for RCP4.5. e. Intermodel\nscatterplot of HS in the early (Mid-Future minus Historical, i.e., 2049-2069 minus 1979-2005,\ndenoted as MF - H) and late (Future minus Mid-Future, i.e., 2080-2100 minus 2049-2069, denoted\nas F - MF) periods of RCP8.5. f. As e but for RCP4.5. g,h, As e,f but for CS. The open and filled\ndots are the CMIP5 and CMIP6 results, respectively.\nFigure R2: a,e, Intermodel scatterplot between ∆#𝑆#𝑆##𝐶##𝐸#/∆𝑇# and ∆𝐸# /𝐸# /∆𝑇#. b,f, Intermodel\n! !\nscatterplot between ∆𝑆##𝑆##𝐶##𝐸#/∆𝑇# and ∆𝑇#. c,g, Intermodel scatterplot between ∆#𝑆#𝑆##𝐶##𝐸#/∆𝑇# and\n∆𝑃#/𝑃#. d,h, Intermodel scatterplot between Index C and ∆𝑃#/𝑃#. a-d are for the early period of the\n21st century under RCP4.5 (Mid-Future minus Historical, 2049-2069 minus 1979-2005) while e-\nh are for the late period of the 21st century under RCP4.5 (Future minus Mid-Future, 2080-2100\nminus 2049-2069). The open and filled dots are the CMIP5 and CMIP6 results, respectively.\n2. As the hydrological sensitivity (∆P/∆T) depends on external forcings, it should differ\nbetween different emission scenarios. Please add some discussions on the scenario\ndependency of hydrological sensitivity (in raw simulations and in constrained results).\nAs the CO2 increase stabilizes in the late stage of RCP4.5, the temperature-mediated\neffect becomes more dominant, and HS becomes larger than that in RCP8.5 which\nfeatures a nearly linear CO2 increase. Nevertheless, HS is highly correlated between\nRCP4.5 and RCP8.5 (Fig. R3). We have added a new section “Relation and difference\namong different warming scenarios” to address Comments 1 and 2. The application of\nthe EC to RCP4.5 is described in the first paragraph of that section and summarized in\nFig. S11 and Fig. S11.\nFigure. R3: Intermodel scatterplot between HS’s in RCP8.5 and RCP4.5\nIn response to both Comments 1 and 2, we would like to note that while the temporal\nevolution of the anthropogenic forcing differs among different periods and warming\nscenarios, all the models run share the same forcing given a specific scenario/period and\nhere we build ECs to constrain the intermodel uncertainty. The ECs work well for different\nperiods and warming scenarios, because the intermodel uncertainty in ∆ 𝑃#/𝑃# is\nconsistently dominated by the uncertainty in ∆#𝑆#𝑆##𝐶##𝐸#/∆𝑇#, and ∆#𝑆#𝑆##𝐶##𝐸#/∆𝑇# is correlated with\nthe climatological pattern of SSCE.\n3. There have been several studies providing constrained projections of hydrological\nsensitivity or global mean precipitation change. How do the quantitative results compare\nwith each other? Please add some discussions on this.\nIn the manuscript, we have reviewed two constraints on HS (Ref. 17 and 18) and one\nconstraint on global mean precipitation increase (Ref. 22). These three references, to\nour knowledge, present the most updated ECs on future precipitation increase.\nRef. 17 and 18 are based on CMIP5. Ref. 21 shows that, in CMIP6, the correlation\nproposed by Ref. 17 has substantially weakened (r = -.045) and the correlation proposed\nby Ref. 18 no longer holds (r =-0.01). We have now explicitly mentioned these correlations\nin Introduction. We have discussed in detail how our EC is different from the EC in Ref.\n22 (second paragraph in Discussion). Because our EC constrains both HS and CS and\nbecause our final observable is a climatological pattern instead of a trend which is more\nuncertain, our EC reduces ~25% of the intermodel uncertainty in ∆P/P, while Ref. 22\nreduces only ~13%. Note that Ref. 22 reports a ~25% “reduction in variance”, which is\nequivalent to a ~13% reduction in uncertainty range.\nMinor comments:\n4. Fig. S1: Please clarify which experiments were used for CMIP5 and CMIP6.\nWe have clarified that Fig. S1 is based on RCP8.5. Also, we have stated in the last\nparagraph of Introduction that the main result focuses on RCP8.5. The results of RCP4.5\nare discussed in the section before Discussion.\n5. L126 and L157: Please use the full term “global surface shortwave cloud feedback”\ninstead of GSSCF in the subtitle.\nWe have modified the two subtitles to “Surface shortwave cloud feedback regulates future\nprecipitation changes by affecting both CS and HS” and “An emergent constraint on future\nprecipitation increase”.\nResponse to Reviewer #2:\nThis paper presents a new emergent constrain on global hydrologic sensitivity by utilizing\nthe relationship between the pattern of surface climatological shortwave cloud radiative\neffect and the projected global precipitation response under future emission scenarios.\nThe relationship is rooted in the physics that tie the climatological cloud pattern,\nshortwave cloud feedback, oceanic energy budget (and thus global evaporation), and\nclimate sensitivity together. To my knowledge, the relationship between global\nprecipitation and shortwave cloud effect has not been discovered/shown previously. An\nemergent constraint utilizing satellite measurements of the climatological shortwave cloud\neffect pattern results in a small constraint on the model spread of the projected global\nprecipitation response. While the final constraint is marginal, I think this study is valuable\nfor revealing a new emergent constraint that can be utilized in other model ensembles\nand observational datasets in the future. Also, the study uses a large and robust collection\nof climate models and reasonable metrics to perform the constraint. Nonetheless, I think\nsome revisions are warranted to improve the robustness and physical interpretation of\nthe results, as described below. I think the paper may be suitable for publication in Nature\nCommunications if the authors can address these concerns.\nThank you for your review and appreciation of our work. By constraining both CS and HS,\nour ECs reduce the intermodel uncertainty in ∆P/P by 25%-27%, which to our knowledge\nis more effective than any previously proposed ECs. Also, our EC indicates a higher most-\nlikely ∆P/P than the mean ensemble-model projection. These results would provide\nimportant information for credible assessment of hydrological impacts of climate change.\n1. A reasonable assumption may be that the relationships shown for the RCP emissions\nscenarios here (e.g., Figs. 2, 4, S6, S7) are rooted in the response of the relevant\nquantities (clouds, precipitation, evaporation) to planetary warming. In other words, I\nwonder if the temperature-mediated responses [i.e., the changes that only result from\nglobal (predominantly oceanic) warming and that exclude potential contributions from\nrapid adjustments due to changes in the forcing itself (from greenhouse gases, aerosols,\netc.)] are largely responsible for the relationships. Is this true? This could be diagnosed\nwith simulations that abruptly increase CO2 initially then leave it constant, or with\nsimulations that just increase SST but not radiatively active atmospheric constituents,\nallowing one to examine the response to just the warming itself (e.g., see refs. 17, 18,\nand 21). Showing that these inter-model relationships also exist in the temperature-\nmediated framework would help to 1) show their robustness, and 2) better pin down their\nphysical basis. I suggest the authors consider doing this (and perhaps showing the results\nas supplementary figures), which would help strengthen their conclusions and allow for a\nmore direct comparison with previous studies that constrain hydrologic sensitivity on the\nbasis of temperature-mediated responses.\nThank you so much for your suggestion! We have analyzed the Abrupt4xCO2 simulation\nand related it to the RCP scenarios. We find that the temperature-mediated part is largely\nresponsible for the proposed constraint under RCP, and the constraint does apply to the\ntemperature-mediated change in Abrupt4xCO2.\nWe use the piControl and Abrupt4xCO2 simulations to estimate the direct (i.e., rapid\nadjustment) and indirect (i.e., temperature-mediated) effect of the CO2 increase. The\ntemperature-mediated feedback is estimated from the change normalized by ocean\nwarming after year 1, i.e.,\nFeedback =\n∆\"!\"#$ \n∆#!\"#$ \nwhere ∆𝑇 is the increase in global mean ocean surface temperature from year 1 to\n$%&' \nyear 80 and ∆𝑧 is the change in global mean of a specific variable (i.e., SSCE or\n$%&' \nprecipitation) from year 1 to year 80. The effect of rapid adjustment is computed as\nRapid Adjustment = ∆𝑧 −Feedback×∆𝑇\n$ $ \nwhere ∆𝑧 is the difference between year 1 in Abrupt4xCO2 and the piControl mean, and\n$ \nFeedback×∆𝑇 represents the temperature-mediated effect in year 1, estimated as the\n$ \ntemperature-mediated feedback multiplied by the temperature increase in year 1. When\ncomparing the relative importance of rapid adjustment and temperature-mediated\nfeedback, we normalize the effect of rapid adjustment by the total degree of ocean\nwarming.\nFig. R4a depicts the different CO2 forcing under Abrupt4xCO2 and RCP8.5, and Fig.\nR4b,c show the temporal evolution of changes in different terms associated with surface\nenergy balance under Abrupt4xCO2 and RCP8.5, respectively. The Abrupt4xCO2\nscenario begins with rapid adjustment and then experiences the temperature-mediated\nchanges. The response of individual terms under RCP8.5 shows the same trend as the\ntemperature-mediated change in Abrupt4xCO2, indicating the temperature-mediated\neffect dominates over the direct CO2 effect. The intermodel s.d. of the changes in these\nterms is summarized in Fig. R4d, for the rapid adjustment and temperature-mediated part\nof Abrupt4xCO2 and for RCP8.5. We can see that SSCE is the dominating factor that\ncontributes to the uncertainty in the change of HFS (latent + sensible heat flux). Fig. R4e\ncompares the rapid adjustment and the temperature-mediated feedback of SSCE in\nindividual models. The effect of rapid adjustment is much less uncertain compared to the\ntemperature-mediated feedback (i.e., SSCF). As a result, ∆#𝑆#𝑆##𝐶##𝐸#/∆𝑇# in RCP8.5 is highly\ncorrelated with SSCF diagnosed from Abrupt4xCO2 among models (Fig. R4f, r=0.9).\nSubsequently, ∆𝐸# /𝐸# /∆𝑇# , ∆𝑇# , ∆𝐸# /𝐸# and ∆𝑃#/𝑃# in RCP8.5 are all significantly\n( ( ( ( \ncorrelated with SSCF (Fig. S7). The temperature-mediated ∆𝑃#/𝑃# in Abrupt4xCO2 is\nsignificantly correlated with SSCF and the climatological Index of SSCE works well to\nconstrain SSCF and consequently the temperature-mediated ∆𝑃#/𝑃# (Fig. R4g-i).\nWe have added a new paragraph (Line 166-173, copied below) to highlight that the\ntemperature-mediated feedback dominates the uncertainty in the change of SSCE. In this\nparagraph, Fig. R4e,f is included as Fig. 3e,f and Fig. R5 is included as Fig. S7.\n“∆#𝑆#𝑆##𝐶##𝐸#/∆𝑇# is the change in global ocean SSCE per unit warming under the RCP scenario,\nwhich includes the effects of both rapid adjustment and temperature-mediated feedback.\nBy diagnosing these two effects from the piControl and Abrupt4xCO2 experiments\n(Methods), we can see that the effect of rapid adjustment of SSCE (normalized by ocean\nwarming) is much less uncertain compared to the temperature-mediated feedback, i.e.,\nsurface shortwave cloud feedback or SSCF (Fig. 2e). As a result, the intermodel\nuncertainty in ∆𝑆##𝑆##𝐶##𝐸#/∆𝑇# is largely due to that of SSCF, with the intermodel correlation\nbetween ∆𝑆##𝑆##𝐶##𝐸#/∆𝑇# and SSCF at r = 0.9 (Fig. 2f). Subsequently, ∆𝐸# /𝐸# /∆𝑇#, ∆𝑇#, ∆𝐸# /𝐸#\n( ( ( ( \nand ∆𝑃#/𝑃# are all significantly correlated with SSCF (Fig. S7).”\nWe have also added a new section before Discussion to talk about the relation and\ndifference among different warming scenarios, with the help of this decomposition of\ndirect and indirect effects. Fig. R4 is included as Fig. S15 in this section.\nFigure R4: a, Temporal evolutions of the atmospheric CO2 concentration under Abrupt4xCO2 and\nRCP8.5. b, Temporal evolutions of different terms associated with surface energy balance, i.e., global\nmean 𝑆𝑊 , 𝑆𝑊 , 𝐿𝑊, 𝐺 and 𝐻𝐹𝑆, to Abrupt4xCO2. The solid line shows the ensemble model mean\n!\"# !\"$ \nand the shading indicates the intermodel s.d. c, As b but for RCP8.5. d, Ensemble model mean and\nintermodel s.d. of the changes in 𝑆𝑊 , 𝑆𝑊 , 𝐿𝑊, 𝐺 and 𝐻𝐹𝑆 under Abrupt4xCO2 (separated into\n!\"# !\"$ \nrapid adjustment and temperature-mediated effects) and under RCP8.5. e, Intermodel scatterplot\nbetween rapid adjustment and temperature-mediated feedback of SSCE under Abrupt4xCO2. To\ncompare their relative effects, the effect of rapid adjustment has been normalized by global ocean\nwarming. f, Intermodel scatterplot between the temperature-mediated feedback of SSCE diagnosed\nfrom Abrupt4xCO2 (i.e., SSCF) and ∆𝑆,,𝑆,,𝐶,,𝐸,/∆𝑇, under RCP8.5. g, Intermodel scatterplot between\nSSCF and the temperature-mediated precipitation increase under Abrupt4xCO2. h. Intermodel\nscatterplot between Index C and SSCF. i, Intermodel scatterplot between Index C and the\ntemperature-mediated precipitation increase under Abrupt4xCO2. The open and filled dots are the\nCMIP5 and CMIP6 results, respectively.\nFigure R5: Same as Fig. 2a-d but with SSCF diagnosed from Abrupt4xCO2 as the x axis.\n2. Regarding the evaporation calculations: can the authors expand on the ocean heat\nuptake (G) calculation a bit more in methods? If it is computed as a residual, this implies\nthat it uses model-generated SW, LW, and E. How then is model-generated E different\nfrom the E computed from the Penman equation? Is one expected to be a better estimate\nthan the other? Also, do the SW and LW terms appear twice or cancel out if one were to\nexpand G in equation (2). In short, I wonder how strongly the model-generated and\nPenman E are dependent on each other (due to the way G is computed) and whether this\ndependence could explain the apparently good agreement between these quantities (e.g.,\nFig. S2).\nThe model-simulated E and the projected change are what the Penman equation tries to\ncapture. The Penman equation, as a theoretical equation, allows us to understand how\nindividual factors contribute to the model-projected E change and its intermodel\nuncertainty.\nTo clarify the computation of G, we would like to review the derivation of the Penman\nequation. Evaporation over open water can be written as,\n𝐿 𝐸 = 𝜅(𝑒∗ −𝑒) = 𝜅∆(𝑇 −𝑇)+𝜅𝑒∗(1−𝑅𝐻),\n) * * \nwhere ∆≡\n,-∗\n=\n.&-∗\nmeasures the slope of the 𝑇−𝑒∗ curve and 𝜅 ≡\n01(.\n,# /&#' 23) \nGiven sensible heat flux 𝑆𝐻 = 𝜅𝛾(𝑇 −𝑇), and surface energy balance 𝐿 𝐸 +𝑆𝐻 = 𝑅 −\n* ) 4 \n𝐺, Penman solves evaporation by eliminating 𝑇 −𝑇. That is,\n* \n∆ 𝛾\n𝐿 𝐸 = (𝑅 −𝐺)+ 𝜅𝑒∗(1−𝑅𝐻),\n) ∆+𝛾 4 ∆+𝛾 \n4 \nwhere 𝑅 = 𝑆𝑊 +𝐿𝑊 is the net surface radiation.\n∆\nrepresents the energy part which allocates of total available energy (𝑅 −𝐺) to E and\n4 \n∆52 \nthe second term represents the aerodynamic part which reflects the effect of RH.\nIn model climatology (1979-2015), the global mean 𝐺 is ~1.34±0.8 W/m2 while 𝑅 is\n4 \n~115±3.5 W/m2 (SSCE, -59±5.5 W/m2). Thus, 𝐺 does not have a notable impact on the\nmagnitude of global mean E and contributes secondarily to the intermodel spread.\nBecause it is difficult to directly compute G, we diagnose 𝐺 as 𝐺 = 𝑅 −𝐿 𝐸 −𝑆𝐻, so\n4 ) \n𝑅 −𝐺 = 𝐿 𝐸 +𝑆𝐻, reflecting the total energy for surface turbulent heat flux. With 𝐺\n4 ) \ndiagnosed, the Penman equation can be used to estimate how much the individual factors\ncontribute to the intermodel spread in the E change. As shown in Fig. 1d, the increase in\n∆\n𝐸 is dominated by the increase in . This effect is independent of the change in 𝑅 −𝐺,\n4 \n∆52 \ni.e., 𝐿 𝐸 +𝑆𝐻. The intermodel uncertainty in the E increase is dominated by SSCE and\n) \n𝐺 plays a secondary role (Fig. 1d).\nHope this clarifies our computation of G and we have described the computation of G\nmore clearly in Methods.\n3. Has the sensitivity to the definition of C (the metric used for the emergent constraint)\nbeen explored? Currently, C depends on the relationship between GSSCF and\nclimatological SSCE itself (Fig. 4a). Would a metric that is independent of this relationship\n(say, just the difference between climatological SSCE between the low and high latitudes)\ngive the same tight relationships as in (b) and (c) of Fig. 4? Not only would this\ndemonstrate robustness, but also allow one to compute the metric in other ensembles\nwithout the need to first generate Fig. 4a based on that ensemble.\nThank you for your suggestion! We have now introduced a simple index as the difference\nin the climatological SSCE between the region with observed annual-mean SST>25oC\nand the region with observed annual-mean SST>0oC but <25oC. As shown in Fig. R6,\nthis simple index is significantly correlated with Index C, and is able to constrain the\nintermodel uncertainty of ∆#𝑆#𝑆##𝐶##𝐸#/∆𝑇#and ∆𝑃/𝑃. The resultant ECs indicate similar results\nas those of Index C, demonstrating the robustness of the proposed EC. We have included\nFig. R6 as Fig. S9 and presented the related result at the end of the EC section.\nFigure R6: Same as Fig. 4 but using the simple climatological index of SSCE, Index D. The red\ncontour in a indicates the contour of 25oC.\nSpecific/minor comments:\nL45-46: “a more recent analysis suggests that the statistical relationships underlying\nthese two ECs do not hold up among the latest generation of climate models” – This\nclaim is not entirely true. As stated in the abstract of ref. 21: “The constraint based on\nclear-sky shortwave absorption sensitivity to water vapor has weakened, and it is\nargued that a proposed constraint based on surface low cloud longwave radiative\neffects does not apply to HS.” Ref. 21 does not suggest that both ECs no longer apply\nor that all key related relationships no longer exist.\nWe have edited the sentence as follow: However, a more recent analysis21 finds that, in\nthe latest generation of climate models, the correlation of HS to clear-sky shortwave\nfeedback weakens substantially (r = -0.45) and the correlation to longwave cloud\nfeedback no longer holds (r = -0.01).\nL52-54: “The rationale is that future precipitation increase is correlated with future\ntemperature increase and the latter is correlated with the forced trend over recent\ndecades” – Did you mean to say “the former” rather than “the latter” is correlated…?\nSorry for the confusion. We mean ” future precipitation increase should be correlated with\nfuture temperature increase and future temperature increase should be correlated with\nforced temperature trend over recent decades”. We have modified the sentence to clarify\nour point.\nL54-55: “That said, only the CS part has been utilized in the EC to constrain DP/P while\nthe potential to constrain the HS part has not been harnessed.” I'm not sure this is true\nsince that study (ref. 22), according to its abstract, uses trends in DP itself to constrain\nfuture DP. It is thus constraining the total DP directly, which has contributions from HS\nand CS as the authors state earlier.\nIn Ref. 22, the correlation between future ∆𝑃/𝑃 and recent ∆𝑃 is only 0.49, smaller than\nthe correlation r=0.6 between future ∆𝑃/𝑃 and recent ∆𝑇. As a result, their paper mainly\nfocused on the constraint using recent ∆𝑇− future ∆𝑃/𝑃. That said, the potential to\nconstrain HS is not harnessed. The correlation between future ∆𝑃/𝑃 and recent ∆𝑃 is\nmainly from the correlation between future ∆𝑃/𝑃 and recent ∆𝑇, and the correlation is\nsmall likely because precipitation trend is more variable. We have edited the paragraph\nto clarify these points.\nFigs. 1, S2, and possible others: It would help to state the time periods that are plotted in\nthe figure captions.\nWe have stated the time periods in the figure captions of Fig. 1 and Fig. S1 (but not other\nfigures to avoid redundancy). The time periods are also stated in the last paragraph of\nIntroduction and in Methods.\nL126: I would avoid using such a long acronym (GSSCF) in the section title, especially\nsince this acronym has not been defined yet.\nWe have edited the section title to “Surface shortwave cloud feedback regulates future\nprecipitation change by affecting both CS and HS”.\nL158-160: “The shortwave cloud feedback, widely considered as a major uncertainty\nsource for CS, has been often studied from the perspective of the top of the atmosphere\n(TOA).” What is the relationship between the TOA and SFC SW cloud feedback? It is\nassumed here that these should be essentially the same, qualitatively and perhaps even\nquantitatively, to some extent? If so, this should be stated explicitly.\nAs shown in Fig. R7 (included in manuscript as Fig. S8), cloud SW effects/feedback are\nspatially correlated between TOA and SFC. The TOA SW cloud feedback can be\nconstrained by its climatological patten (Siler et al., 2018) and so is the SFC SW cloud\nfeedback (this work). We have mentioned the correlation between TOA and SFC cloud\nshortwave effect in Line 183-184. But we would like to note that, to build the\nconstraint on SFC SW feedback, there is no need to first link SFC to TOA.\nFigure R7: The shortwave cloud effect and feedback at the TOA and SFC.\nResponse to Reviewer #3:\nSeveral major revisions and comments are provided for the manuscript, as I found it\nunconvincing:\nAbstract: what exactly is meant by climatological cloud effect? This is very vague and I\ndon´t know what exactly it is about clouds that is meant\nSorry for the confusion. We mean “the climatological pattern of cloud shortwave effect”\nand we have modified the text.\nLine 27: Give a clear definition of what ΔP/P stands for (the fractional change in mean\nprecip normalized by the mean precip)\nWe have edited the sentence to clearly describe ΔP/P as “the fractional increase in mean\nprecipitation”.\nLine 33: “varying by a factor of 2” is unclear language.\nWe have edited the sentence to “varying by a factor of two among models (ratio between\nthe highest and lowest values)”.\nLine 41: Emergent constraints should be constructed only with observable quantities, but\nthis sentence seems to imply anything can be used?\nIt seems to us that we did not mention any unobservable quantities in this sentence\n(copied below).\n“For CS, several ECs have been proposed from different perspectives8, such as linking\nfuture change in temperature to its seasonal9 or interannual variability10, relating cloud\nfeedbacks to its climatological pattern11,12 and properties13,14, or using correlations with\nother observable features15,16.”\nThe observable quantities here are the seasonal or interannual variability of temperature\nand the climatological pattern or properties of cloud effect, and other observable\nquantities. To construct ECs, one first identifies correlations between future projection\nand some quantity in the model ensemble and then use the observations of that quantity\nto constrain model projection. Please let us know if we misunderstand this comment.\nLine 48-49: “under different frameworks” and “different but likely dependent observables”\nare oddly worded and unclear.\nWe have modified the sentence to “It was challenging to do so as the ECs on HS and CS\nwere based on different but potentially correlated observables”.\nLine 51: Not sure this is necessary, seems like a rehash of previous paragraph? Also co-\ndependencies of terms within the EC as explained in previous paragraph?\nThe previous paragraph talks about ECs on HS (∆𝑃/𝑃/∆𝑇) and CS (∆𝑇), while this\nparagraph talks about ECs that directly constrain ∆𝑃/𝑃. We have edited both paragraphs\nto make our points clearer.\nLine 59: All ECs should be physically guided, so this statement is unnecessary. That said,\nwhy a surface energy balance framework – what is new and of value here, as opposed\nto ECs based on the TOA budget, for example.\nWe have deleted “physically guided” and edited the sentences to highlight the surface\nperspective (Line 61-65). Furthermore, the benefit of the surface perspective is\nemphasized in Discussion.\nLines 36-57: The manuscript could be better motivated. It is good to explain what ECs\nare, but the focus is supposed to be on finding an EC for precipitation increases with\nwarming, so why spend so much time discussing ECs for CS and HS? It`s distracting,\nfocus instead on ECs for precipitation increase specifically. That said, I believe there has\nbeen other rather recent work in addition to Ref. 22 on ECs for precipitation increase, and\nthe manuscript alludes to how this EC is different from other studies; this should be\nfurther discussed. What makes this framework for developing an EC in this manuscript new\nand of value? The motivation for using ocean evaporation and the surface energy budget is\nparticularly missing.\nLine 60-62: It`s not necessary for an EC to constrain both HS and CS first in order to well\nconstrain future precipitation increases (so long as a physical relationship exists between\nthe observed quantity and the precipitation increase). This seems convoluted and\npotentially misguided. Why this approach?\nThese two comments are closely related, so we will answer them together.\n∆𝑃/𝑃 can be written as ∆𝑃/𝑃 = HS ×CS. It may be possible to directly constrain ∆𝑃/𝑃\nwithout explicitly considering HS and CS. But we believe it is meaningful and helpful to\nattribute the uncertainty in ∆𝑃/𝑃 to those in HS and CS.\nFirst, as shown in Fig. R8, ∆𝑃/𝑃 in individual models are scaled by ∆𝑇, so it makes sense\nto first isolate the uncertainty from CS.\nFigure R8: Intermodel scatterplot between ∆𝑇 and ∆𝑃/𝑃.\nSecond, for our work, the EC works well to constrain ∆𝑃/𝑃 because it constrains both HS\nand CS, so we would like to introduce our work from this perspective.\nFinally, HS and CS are widely recognized parameters that have important physical\nmeanings. HS is useful in itself for assessment of hydrological impact of climate change,\nbecause sometimes we would like to know the climate impact at specific degrees of\nwarming (e.g., 2oC) instead of under specific warming scenarios. For example, in IPCC\nAR6, both global warming levels and scenarios are used to discuss climate change.\nRef. 22 directly constrains ∆𝑃/𝑃 by linking it to the historical temperature trend. This is\nbased on the relations that ∆𝑃/𝑃 is correlated with ∆𝑇 and ∆𝑇 is further correlated with\nforced temperature trend over recent decades. So, the EC is mainly based on the CS.\nThey did try constraining ∆𝑃/𝑃 by linking it to the historical precipitation trend, but the\ncorrelation is lower than that using the temperature trend. We found another study that\nprovides some sort of constraint on ∆𝑃/𝑃, but that was also based on the relation between\n∆𝑃/𝑃 and ∆𝑇 (Fig. 2 in Allen& Ingram, 2002).\nLine 124: compensation from other factors maybe deserves to be explored – if we\nreduced uncertainty in SSCE then how much would it really matter given these other\nfactors (ok, at least the discussion section acknowledges this, but this issue still needs to\nbe addressed).\nThank you for your comment. As now shown in Fig. S5, we find that the intermodel\nuncertainty due to SSCE is partially compensated by that due to surface net longwave\nradiation. We have explicitly mentioned this compensation in Line 119-120.\nWe’d like to note that the effect of this compensation is already included in the\nregression line between ∆#𝑺#𝑺##𝑪##𝑬#/∆𝑻H and ∆𝑬H/𝑬H/∆𝑻H and consequently included in the\nresultant EC. Specifically, given the regression slope 𝛽 = \n∑(8*%8̅)(;*%;<)\n, the compensation\n∑(8 %8̅)'\n* \nreduces the regression slope between ∆𝑆##𝑆##𝐶##𝐸#/∆𝑇# and ∆𝐸#/𝐸#/∆𝑇#. The correlation between\n∆𝑆##𝑆##𝐶##𝐸#/∆𝑇# and ∆𝐸#/𝐸#/∆𝑇# should be less impacted, given 𝑟 = ∑(8*%8̅)(;*%;<) and (𝑦 −\n=∑(8 %8̅)'∑(; %;<)' >\n* * \n𝑦#) is in both nominator and denominator. The correlation between ∆#𝑆#𝑆##𝐶##𝐸#/∆𝑇# and\n∆𝐸#/𝐸#/∆𝑇# is r=0.76, so the uncertainty due to SSCE explains about 0.65 (i.e., √1−𝑟?) of\nthe uncertainty of ∆𝐸/𝐸/∆𝑇.\nLine 131: Calling the change in SSCE with warming a “cloud feedback” is misleading,\nsince this includes feedbacks and adjustments but isn´t quite itself a feedback, it´s a\nchange in shortwave cloud radiative effects as seen by the surface. A different analysis\nis needed to isolate the surface shortwave cloud feedbacks.\nFollowing your suggestion, we directly use the term ∆𝑆##𝑆##𝐶##𝐸#/∆𝑇# to refer to the change in\nSSCE with warming. Furthermore, we have computed the effect of rapid adjustment and\ntemperature-mediated feedback based on the piControl and Abrupt4xCO2 simulations of\nthe CMIP models (see details in Methods). We show that the intermodel uncertainty in\n∆𝑆##𝑆##𝐶##𝐸#/∆𝑇# is dominated by the temperature-mediated feedback (Line 166-173).\nLines 145: There actually seems to a deterioration between the CMIP5 and CMIP6\nensembles in the correlation between GSSCF and change in evaporation and change in\nprecipitation with warming, but especially for precipitation. The deterioration is fairly large\nfor precipitation, and appears to be driven by two models. Which are these and why do\nthey depart so starkly from the other CMIP6 models? Doesn´t this negatively impact the\nEC constructed for precipitation, or is r=0.67 still a high enough correlation?\nThe correlation between GSSCF (now ∆𝑆##𝑆##𝐶##𝐸#/∆𝑇#) and ∆𝐸# /𝐸# /∆𝑇 decreases from r=0.8\n( ( \nin CMIP5 to r=0.74 in CMIP6 (Fig. 2c) and the correlation between ∆𝑆##𝑆##𝐶##𝐸#/∆𝑇# and\n∆𝑃#/𝑃#/∆𝑇 decreases from r=0.82 in CMIP5 to r=0.67 in CMIP6. The two models\nresponsible for the decreased correlations in CMIP6 are CanESM5 and EC-Earth3. For\nCanESM5 (the model that departs from others in Fig. 3c), it projects a larger ∆𝐸# /𝐸# /∆𝑇\n( ( \nthan that expected from ∆𝑆##𝑆##𝐶##𝐸#/∆𝑇# . As shown in Fig. 1d, while ∆#𝑆#𝑆##𝐶##𝐸#/∆𝑇# is the\ndominating factor for the uncertainty in ∆𝐸# /𝐸# /∆𝑇, other factors can also contribute. For\n( ( \nEC-Earth3, its ∆𝐸# /𝐸# /∆𝑇 is as expected from its ∆𝑆##𝑆##𝐶##𝐸#/∆𝑇#, but its ∆𝑃#/𝑃#/∆𝑇 is higher\n( ( \nthan expected. While we expect a close correlation between ∆𝐸 /𝐸 /∆𝑇 and ∆𝑃/𝑃/∆𝑇,\n( ( \nthey are not identical due to factors such as land processes.\nIf we remove these two models from the calculation, the correlation between ∆𝑆##𝑆##𝐶##𝐸#/∆𝑇#\nand ∆𝐸# /𝐸# /∆𝑇 increases from 0.74 to 0.82 in CMIP6 (from 0.76 to 0.81 in combined\n( ( \nCMIP), and the correlation between ∆#𝑆#𝑆##𝐶##𝐸#/∆𝑇# and ∆𝑃#/𝑃#/∆𝑇 increases from in CMIP6\nfrom 0.67 to 0.78 (from 0.70 to 0.79 in combined CMIP).\nLine 158: This approach seems odd – since GSSCF is correlated with ΔP/P, why not just\nfind an observable variable that is highly correlated or linked to shortwave cloud feedback\nand build the EC for precipitation with that variable directly? That seems to me to be the\nstandard way to construct an EC, rather than build an EC on top of an EC (constraining\nGSSCF to then constrain precipitation change), which may be a misguided approach. If\nthis is what was done, this needs to be made more clear, because it does not read this\nway.\nThank you for your comment. We did not build an EC on top of another EC. We build an\nEC for ∆𝑆##𝑆##𝐶##𝐸#/∆𝑇# based on the correlation between Index C and ∆𝑆##𝑆##𝐶##𝐸#/∆𝑇# (Fig. 4b) and\nan EC for ΔP/P based on the correlation between Index C and ΔP/P (Fig. 4c). To avoid\nconfusion, we have modified the sentence as “Now, we explore potential correlations of\n∆𝑆##𝑆##𝐶##𝐸#/∆𝑇# to observable quantities and build ECs for ∆#𝑆#𝑆##𝐶##𝐸#/∆𝑇# and ∆𝑃#/𝑃#”.\nLine 160: Need to make clear what understanding/advancement is gained by examining\nfrom a surface energy balance perspective rather than TOA.\nThank you for your suggestion. The surface-energy-balance perspective allows us to link\nthe shortwave cloud effect to both HS and CS. The TOA perspective is usually used for\nunderstanding CS, but it does not offer an easy way to interpret the intermodel spread of\nHS. The advantage of the surface perspective is now emphasized in both Introduction\nand Discussion.\nLine 162: Again, what exactly is meant by climatological cloud pattern? Just their\nclimatological distribution, and/or optical thickness, etc.?\nSorry for the confusion. We mean the climatological pattern of cloud shortwave effect.\nWe have edited the sentence.\nLines 167-168: Why ignoring the models in between these two groups?\nThe comparison between the two distinct groups (Fig. 3) is used for illustrating how\nintermodel uncertainty in ∆#𝑆#𝑆##𝐶##𝐸#/∆𝑇# may be associated with the differences in the\nclimatological SSCE. We later use regression (include all models, Fig. 4) to further show\nthe dependency of ∆#𝑆#𝑆##𝐶##𝐸#/∆𝑇# on the spatial pattern of the climatological SSCE.\nLine 224: does EC break down for low emission scenario and why?\nHow does this compare to ECs based on TOA framework?? Like in ref 22\nFor low emission scenario RCP2.6, the global mean temperature increases by ~1oC by\n2100 and the global mean precipitation increases by ~2%. It is challenging (and maybe\nnot meaningful) to constrain the intermodel uncertainty as the natural variability becomes\ncomparable to the forced change, and ECs are used to constrain the forced change due\nto model uncertainty.\nWe have discussed in detail how our EC is different from the EC in Ref. 22 (second\nparagraph in Discussion). Particularly, because our EC constrains both HS and CS and\nbecause our final observable is a climatological pattern, our EC reduces ~25% of the\nprojection uncertainty in ∆P/P, while the EC in Ref. 22 reduces only 13% (which\ncorresponds to a ~25% reduction in variance, as reported in their paper).\nLine 237: this wasn´t shown for f, wasn’t it the definition?? Also this wasn’t shown or\ndiscussed at all really anyway\nThe energy allocation factor 𝑓 was introduced in Line 87-89 and described in detail in\nMethods. It has also been used when we describe Fig. 1d. As derived in Methods, a\nwarmer temperature will increase the energy allocation of total available energy to surface\nlatent flux and contribute to future evaporation increase. We now use “the increasing\nenergy allocation” in this line.\nFig. 4, remainder of EC construction, and Discussion: the EC presented in Fig. 4 seems\nveeeeery hand-wavey. The climatological SSCE index is heavily derived parameter,\nbased on quantities that are observed but can have a high uncertainty, while ECs ideally\nshould be constructed with observable parameters/variables that at the least are not so\nderived or directly measured, and the observable´s uncertainty range tells something\nabout the plausible range of the parameter being constrained by highlighting its values\nthat fall into that range. I do not see that with the EC as presented in Fig. 4 for precipitation\nchange with warming. The horizontal error bars in Fig. 4 appear to be missing in fact, so\nthat this plausible range of precipitation change values does not seem like it can be easily\nestimated despite the uncertainty value given in the text. It´s really the horizontal error\nbars on the climatological index and NOT the vertical bars that we´re after with an EC\nanyway, and so the uncertainty range given in the text appears to be misestimated; we\nwant to see which values of the precipitation change are associated with the range of\nindex values over its uncertainty range – this is the uncertainty range on the precipitation\nchange rather than the calculation underlying the vertical error bars in Fig. 4. I remain\nunconvinced by this EC because of the amount of derivation required and the misguided\nuncertainty/constraint estimation.\nIn response to your concern, we have introduced a simpler Index D that measures the\ngradient of the climatological pattern of cloud shortwave effect. Specifically, the index is\ncomputed as the difference in the climatological SSCE between the region with observed\nannual-mean SST>25oC and the region with observed annual-mean 0oC<SST<25oC.\nIndex D can be directly computed without pattern correlation or the exact knowledge of\nthe regression map (Fig. 4a). As shown in Fig. S9 (copied here as Fig. R9), Index D\neffectively constrains ∆#𝑆#𝑆##𝐶##𝐸#/∆𝑇# and ∆𝑃#/∆𝑃#, and the resultant ECs indicate similar\nresults as those of Index C. This demonstrates the robustness of the proposed EC and\nwe have presented these results at the end of the EC section (Line 228-234).\nFor both Indices C and D, the uncertainty in observations is small, and particularly, much\nsmaller than the uncertainty among models. Specifically, Index C is 0.28 in CERES and\n0.25 in ISCCF but varies from -0.81 to 0.75 in models. Index D is 0.89 in CERES and\n0.84 In ISCCF but varies from -0.99 to 1.94 in models. The error bars of the observations,\nas shown in Fig. 4 and Fig. S9, are thus very short. As a result, the uncertainty of the\nconstrained ∆𝑃/𝑃 is mainly from the residual variability that is unexplained by the\ncorrelation, instead of the uncertainty in observations. This reflects the advantage of\nusing a climatology as the final observable. In Ref. 22, the final observable is the\nforced historical temperature trend, which includes substantial uncertainty itself. When\ncomputing the uncertainty range of the EC, we do include the effect of the uncertainty in\nobservations (see Methods).\nFigure R9: Same as Fig. 4 but using the simple climatological index of SSCE, Index D. The red\ncontour in a indicates the contour of 25oC.\nMinor Comments:\nFig. S4: what is the x-axis?? The model “number?” Yes, it is the model number. We have\nadded this in the figure caption. Thank you for pointing this out.\nREVIEWERS' COMMENTS\nReviewer #1 (Remarks to the Author):\nSummary:\nI thank the authors for the additional analyses which have well addressed my concerns and\nimproved the robustness of the results. I have only a few minor suggestions.\n1. Following my previous Major comment #1, the authors added a new section to discuss the\ndifference between transient and quasi-stabilized stages under RCP4.5/SSP2-4.5 scenarios, which is\nhelpful for understanding the hydrological responses under median emission scenarios. But in the\ntext and figures, to be accurate, you should refer to “RCP4.5/SSP2-4.5 and RCP8.5/SSP5-8.5” rather\nthan “RCP4.5 and RCP8.5”, because both CMIP5 and CMIP6 models are used.\n2. Discussion section: The comparison between the ECs in this paper (based on ECs on both HS and\nCS) and in Ref. 22 (mainly based on EC on CS alone) has further implications. In this paper, the EC\nbased on both HS and CS leads to a larger ∆P/P after constraint; while the EC based on CS alone\nleads to a smaller ∆P/P after constraint in Ref. 22. The difference between the two methods might\nimply that for the projection uncertainty of precipitation change, even though CS exhibits a\nsignificant correlation with ∆P/P across models, CS alone may not be sufficient to constrain the inter-\nmodel uncertainty of precipitation projections, because other processes related to precipitation\nchange are also important. I think this point is worth to be mentioned. In a broader sense, this\nactually indicates that one needs to be more careful when establishing emergent constraints.\nReviewer #2 (Remarks to the Author):\nThe authors have made substantial improvements to the manuscript and have addressed my\nprevious major concerns. In particular, the assessment of the Abrupt4xCO2 experiments helps with\nthe interpretation of the physical origin of the emergent constraints. The authors also show the\nrobustness of their results by demonstrating that a simpler observable metric leads to the same\nconclusions. I have only a few remaining minor comments:\n1. I recommend being careful when referring to the temperature-mediated surface SW cloud\nradiative effect (SSCE) response to warming (DSSCE/DT) as the surface shortwave cloud feedback, as\nthe term “feedback” in this context usually refers to the SW cloud radiative effect that is corrected\nfor non-cloud factors (or could masking, e.g., Soden et al. 2008,\nhttps://doi.org/10.1175/2007JCLI2110.1). I thus suggest avoiding using the word “feedback” as it\npertains to clouds and explicitly saying “temperature-mediated component of DSSCE/DT” or\nsomething similar. Though it will add more words, it will avoid misinterpretation of what is being\ncalculated.\n2. In Methods, I suggest listing the models in a table rather than embedding the model names in a\nparagraph as currently written.\n3. L206-208: rather than saying “A higher DSSCE/DT is associated with lower climatological SSCE over\nthe warm tropical regions and higher climatological SSCE over cold midlatitudinal regions,” I suggest\nreplacing “lower” with “less negative,” and “higher” with “more negative.”\n4. There are a number of typos and grammatical errors throughout the study, many likely introduced\nduring the latest round of revisions. I suggest the authors thoroughly proofread and edit the text.\nBelow are a few examples, though the following list is not exhaustive:\nL111: Change “they are the largest…” to “it is the largest…”\nL157, Fig. 2 caption: “in term of” should be “in terms of”\nFig. S7 caption: “Abript4xCO2” -> “Abrupt4xCO2”\nL290: “we compares” -> “we compare”\nL344 in Methods: change “hold fixed” to “held fixed”\nReviewer #3 (Remarks to the Author):\nThe authors' responses to my comments and the other reviewer's comments and their changes to\ntheir manuscript are satisfactory.\nResponse to Reviewer #1:\nSummary:\nI thank the authors for the additional analyses which have well addressed my concerns\nand improved the robustness of the results. I have only a few minor suggestions.\n1. Following my previous Major comment #1, the authors added a new section to discuss\nthe difference between transient and quasi-stabilized stages under RCP4.5/SSP2-4.5\nscenarios, which is helpful for understanding the hydrological responses under median\nemission scenarios. But in the text and figures, to be accurate, you should refer to\n“RCP4.5/SSP2-4.5 and RCP8.5/SSP5-8.5” rather than “RCP4.5 and RCP8.5”, because\nboth CMIP5 and CMIP6 models are used.\nFollowing your suggestion, we have replaced “RCP4.5 and RCP8.5” with “RCP4.5/SSP2-\n4.5 and RCP8.5/SSP5-8.5” throughout the manuscript and Supplementary Information.\n2. Discussion section: The comparison between the ECs in this paper (based on ECs on\nboth HS and CS) and in Ref. 22 (mainly based on EC on CS alone) has further\nimplications. In this paper, the EC based on both HS and CS leads to a larger ∆P/P after\nconstraint; while the EC based on CS alone leads to a smaller ∆P/P after constraint in\nRef. 22. The difference between the two methods might imply that for the projection\nuncertainty of precipitation change, even though CS exhibits a significant correlation with\n∆P/P across models, CS alone may not be sufficient to constrain the inter-model\nuncertainty of precipitation projections, because other processes related to precipitation\nchange are also important. I think this point is worth to be mentioned. In a broader sense,\nthis actually indicates that one needs to be more careful when establishing emergent\nconstraints.\nThank you for your suggestion. We have highlighted in the second point that “our EC\nutilizes both the HS and CS components to constrain ∆𝑃#/𝑃# while the EC in ref. (Shiogama\net al., 2022) mainly utilizes the CS component”. At the end of this discussion, we have\nadded the following sentence: “Caution is thus needed when interpreting the EC based\nsolely on the observed temperature trend.”\nResponse to Reviewer #2:\nThe authors have made substantial improvements to the manuscript and have addressed\nmy previous major concerns. In particular, the assessment of the Abrupt4xCO2\nexperiments helps with the interpretation of the physical origin of the emergent constraints.\nThe authors also show the robustness of their results by demonstrating that a simpler\nobservable metric leads to the same conclusions. I have only a few remaining minor\ncomments:\n1. I recommend being careful when referring to the temperature-mediated surface SW\ncloud radiative effect (SSCE) response to warming (DSSCE/DT) as the surface shortwave cloud\nfeedback, as the term “feedback” in this context usually refers to the SW cloud radiative effect that is\ncorrected for non-cloud factors (or could masking, e.g., Soden et al. 2008,\nhttps://doi.org/10.1175/2007JCLI2110.1). I thus suggest avoiding using the word “feedback” as it\npertains to clouds and explicitly saying “temperature-mediated component of DSSCE/DT” or\nsomething similar. Though it will add more words, it will avoid misinterpretation of what is being\ncalculated.\nThank you for your suggestion. We understand that, when quantifying climate feedbacks\nusing the radiative-kernel method (e.g., Soden et al., 2008), cloud feedback is estimated\nfrom <the change in the cloud radiative effect> minus <the effect of clouds on the TOA\nradiation anomaly induced by the changes in the non-cloud factors>. However, we also\nnotice that in other studies of cloud effects, “feedback” is used generally to refer to the\nsensitivity of the total change in cloud radiative effect to temperature (e.g., Zelinka et al.,\n2017; Siler et al., 2018; Watanabe et al., 2018; Ceppi & Nowack, 2021).\nIn the manuscript, we have used the terms “the temperature-mediated feedback (of\nSSCE)” and “surface shortwave cloud feedback” but avoided the exact short term “cloud\nfeedback”. We feel that replacing all “feedback” to “the temperature-mediated component\nof ∆#𝑆#𝑆##𝐶##𝐸#/∆𝑇#” would affect the readability of some sentences, so after some consideration\nwe choose to keep the “feedback” term but clarify its definition when we first introduce it\n(Line 169-172):\n\"∆#𝑆#𝑆##𝐶##𝐸#/∆𝑇# is the change in global ocean SSCE per unit warming under the\nRCP8.5/SSP5-8.5 scenario, which includes the effects of both rapid adjustment and\ntemperature-mediated feedback (feedback here refers to the temperature-mediated\nchange in SSCE, without corrections for non-cloud factors as in the radiative-kernel\nmethod).”\nCeppi, P., & Nowack, P. (2021). Observational evidence that cloud feedback amplifies\nglobal warming. Proceedings of the National Academy of Sciences, 118(30),\ne2026290118. https://doi.org/10.1073/pnas.2026290118\nShiogama, H., Watanabe, M., Kim, H., & Hirota, N. (2022). Emergent constraints on\nfuture precipitation changes. Nature, 602(7898), Article 7898.\nhttps://doi.org/10.1038/s41586-021-04310-8\nSiler, N., Po-Chedley, S., & Bretherton, C. S. (2018). Variability in modeled cloud\nfeedback tied to differences in the climatological spatial pattern of clouds.\nClimate Dynamics, 50(3), 1209–1220. https://doi.org/10.1007/s00382-017-3673-2\nWatanabe, M., Kamae, Y., Shiogama, H., DeAngelis, A. M., & Suzuki, K. (2018). Low\nclouds link equilibrium climate sensitivity to hydrological sensitivity. Nature\nClimate Change, 8(10), Article 10. https://doi.org/10.1038/s41558-018-0272-0\nZelinka, M. D., Randall, D. A., Webb, M. J., & Klein, S. A. (2017). Clearing clouds of\nuncertainty. Nature Climate Change, 7(10), Article 10.\nhttps://doi.org/10.1038/nclimate3402\n2. In Methods, I suggest listing the models in a table rather than embedding the model\n\nnames in a paragraph as currently written.\nFollowing your suggestion, we have listed the models using a table (Table S1).\n3. L216-218: rather than saying “A higher DSSCE/DT is associated with lower\nclimatological SSCE over the warm tropical regions and higher climatological SSCE over\ncold midlatitudinal regions,” I suggest replacing “lower” with “less negative,” and “higher”\nwith “more negative.”\nWe have edited the sentence following your suggestion.\n4. There are a number of typos and grammatical errors throughout the study, many likely\nintroduced during the latest round of revisions. I suggest the authors thoroughly proofread\nand edit the text. Below are a few examples, though the following list is not exhaustive:\nL111: Change “they are the largest…” to “it is the largest…” Corrected\nL157, Fig. 2 caption: “in term of” should be “in terms of” Corrected\nFig. S7 caption: “Abript4xCO2” -> “Abrupt4xCO2” Corrected\nL290: “we compares” -> “we compare” Corrected\nL344 in Methods: change “hold fixed” to “held fixed” Corrected\nWe have corrected the typos above and proofread the text carefully. Thank you!"}]

Decision letter