Thermodynamically inconsistent extreme precipitation sensitivities across continents driven by cloud-radiative effects

Domain: earth_science
Published: 2024-12-11
Editorial outcome: major_revision

Abstract
Extreme precipitation events are projected to intensify with global warming, threatening ecosystems and amplifying flood risks. However, observation-based estimates of extreme precipitation-temperature (EP-T) sensitivities show systematic spatio-temporal variability, with predominantly negative sensitivities across warmer regions. Here, we attribute this variability to confounding cloud radiative effects, which cool surfaces during rainfall, introducing covariation between rainfall and temperature beyond temperature’s effect on atmospheric moisture-holding capacity. We remove this effect using a thermodynamically constrained surface-energy balance, and find positive EP-T sensitivities across continents, consistent with theoretical arguments. Median EP-T sensitivities across observations shift from −4.9%/°C to 6.1%/°C in the tropics and −0.5%/°C to 2.8%/°C in mid-latitudes. Regional variability in estimated sensitivities is reduced by more than 40% in tropics and about 30% in mid and high latitudes. Our findings imply that projected intensification of extreme rainfall with temperature is consistent with observations across continents, after confounding radiative effect of clouds is accounted for.

Introduction
Extreme precipitation events can lead to catastrophic floods and are expected to intensify with global warming following the increase in atmospheric moisture at the rate of 7%/K (Clausius-clapeyron (CC) rate)1,2. While the climate models have been largely able to simulate such an increase3–6, observational evidence to validate these changes is challenged by diverging trends and the inhomogeneity of rainfall records7. Alternatively, studies test this response in observations by estimating extreme precipitation sensitivities with respect to local near-surface air temperatures, forming an equivalent relationship to the Clausius-Clapeyron equation8–11. These so-called “extreme precipitation-temperature (EP-T) scaling rates” show significant deviations from the CC rate of 7%/K with systematic zonal variations. EP-T scaling shows a monotonic increasing relationship at high latitudes, “hook” like structures in mid-latitudes, and a monotonic decreasing EP-T relationship in the tropics12–16. Consequently, EP-T sensitivities remain largely negative over most of the tropical regions in contrast to positive changes projected by climate models and observed trends7,17–19.

A number of factors have been argued to cause deviations in the EP-T scaling, including shifts in atmospheric dynamics3, atmospheric stability20, change in rainfall types from stratiform to convective21, extreme rainfall event duration22,23, cooling effect of rain24–26, availability of moisture27 and saturation deficits at high temperatures28. Alternative scaling variables, like atmospheric and upper tropospheric air temperatures29,30, and moisture indicators such as dew point temperature and integrated water vapor31–33, have been proposed but offer only marginal enhancements in scaling. Using dew point temperatures showed improvements34, but it underestimates rainfall-depth information35, fails to fully address negative scaling and peak structures in tropical regions16,36,37, and provides limited insights on rainfall sensitivity to increasing temperatures26,38. As a result, there remain large uncertainties in using present-day scaling to project changes in future precipitation extremes.

Here, we show that a large part of this uncertainty in EP-T scaling can be explained by the confounding radiative effect of precipitating clouds on surface temperature. Clouds associated with rainfall events significantly alter the local surface energy budget as they reflect the shortwave radiation to space while they absorb and re-emit longwave radiation back to the surface. Consequently, they cause changes in surface temperatures mostly resulting in a net cooling across warmer regions and periods. This cooling makes observed temperatures covary with precipitation and thereby affects the causal nature of precipitation-temperature scaling relationships. As a result, scaling rates not only show how precipitation changes with temperature but also reflect how the synoptic conditions associated with the rainfall event affect temperature. The primary objective of this study is to quantify to what extent the covariation between clouds and temperatures affects the regional EP-T sensitivities.

We evaluate this effect by combining observationally derived daily gridded rainfall and temperature datasets from the Climate Prediction Center (CPC) and Global Precipitation Climatology Project (GPCP – 1.3)39 with satellite-based daily observations of cloud-area fraction and radiative fluxes from the NASA-CERES dataset40,41. The consistency of results was also checked with ERA-5 reanalysis data. To remove the effect of clouds on surface temperatures, we used a surface energy balance model where the vertical turbulent exchange is explicitly constrained by the thermodynamic limit of maximum power42,43. By using this additional constraint together with the “all-sky” and “clear-sky” radiative fluxes as forcings, we estimate changes in surface temperatures associated with cloud radiative effects during rainfall events. Subsequently, we use them to evaluate the impact of clouds on rainfall-temperature scaling.

Results
We start by estimating the extreme precipitation-temperature (EP-T) scaling rates across the global land grids using the quantile regression (QR) method9. It involves fitting a QR model between the logarithmic precipitation and temperature values at the target quantile of 95%, 99%, and 99.9%. The EP-T sensitivity (scaling rate) is then calculated by the exponential transformation of the slope coefficient (see “Methods”). Figure 1A shows the map of estimated sensitivities from the CPC observations for the 95th percentile13,36, along with their zonal variations (Fig. 1B). Positive sensitivities were found at high latitudes, while in the tropics, the sensitivities remained mostly negative. The sensitivities were particularly negative in the tropical humid regions of India, Nothern Australia, Central Africa, Western US, and Amazonia (Fig. 1A). These patterns were consistent across different rainfall quantiles, including the 99th and 99.9th percentiles, and for the GPCP and ERA-5 reanalysis data as well (Supplementary Figs. S1, S9, and S10). Sensitivities estimated using ERA-5 data were generally more negative than those derived from CPC and GPCP rainfall observations (Supplementary Fig. S10).

To further look at distinct patterns in EP-T relationships, we use LOWESS (locally weighted scatter plot smoothing regression) for the 95th percentile daily rainfall events (hereafter P95) and corresponding near-surface air temperature at each grid cell12 and identified three distinct scaling behaviors. This includes a monotonic decreasing (MD) relationship, a hook-shaped (HS) relationship, and a monotonic increasing (MI) relationship. The MD and HS characteristics were predominant in the tropics and mid-latitudes, while the MI relationship was mainly found over grids at high latitudes. Figure 1C–E illustrates the EP-T scaling for all the grids (depicted by light orange lines) in the tropics, mid-latitudes, and high-latitudes respectively. Most of the grid cells in the tropics showed a monotonic decreasing relationship. In mid-latitudes, most of the grid cells showed “peak structures” such that extreme precipitation increases with temperature up to a certain threshold of around 20°C, after which the scaling breaks down and the EP-T relationship becomes negative. The high latitudes showed a monotonic increasing relationship but the rate of increase remained lower than CC rates. Note that the tropics were characterized as regions from 23S to 23N, mid-latitudes as regions from 23N–55N and 23S–55S, and high-latitudes as regions beyond 55S and 55N.

The negative sensitivities in the warmer tropics, systematic zonal variation in observed sensitivities and the three distinct characteristics shown by EP-T scaling as depicted in Fig. 1 are consistent with what has already been reported by previous studies12,15,16,24,37.

We next show that these distinct patterns in EP-T scaling can be reproduced alone by how the radiative effect of clouds during rainfall events affects temperatures. To illustrate this, we calculated the cloud radiative effects (CRE), which we defined as the difference between “clear-sky” and “all-sky” radiative fluxes. The positive value implies a reduction in radiative heating at the surface by clouds, indicating cooling, while the negative values indicate warming of the surface. We estimated the CRE for both shortwave and downwelling longwave radiation during the extreme rainfall (P95) events. The global distribution of shortwave and longwave CRE are shown in Supplementary Fig. S2. When plotted as a function of rainfall (Supplementary Fig. S3), we found that the shortwave CRE shows a statistically significant increase as the rainfall intensity increases leading to a reduction of more than 100 W/m2 of energy from reaching the Earth’s surface and thereby exerting a strong cooling effect. The strength of CRE was proportional to the intensity of the rainfall event. The CRE of downwelling longwave radiation had an opposite warming effect, but the magnitude remain much lower in comparison to shortwave CRE. It further remains largely insensitive to changes in rainfall (Supplementary Fig. S3). This insensitivity can be partly explained by the compensating effects of emissivity and atmospheric heat storage in shaping downwelling longwave radiation44. The net effect of clouds on the surface is then diagnosed by adding the CRE of both shortwave and longwave radiation and is referred to as the net CRE. The global distribution of the net CRE is shown in Fig. 2A. It shows a systematic spatial and zonal variability across the globe such that the humid tropical regions where the averaged extreme rainfall can exceed 40 mm/day are associated with a very large CRE of more than 120 W/m2, whereas in the dry regions, the heavy rainfall is largely limited by available moisture and show a reduced CRE of less than 40 W/m2 (Supplementary Fig. S2). It also shows a systematic zonal variation with higher CRE in the tropics compared to higher latitudes (Fig. 2B).

We then generated the scaling curves for radiation-temperature scaling (hereafter “CRE-T scaling”) curves equivalent to EP-T scaling (Fig. 2C–E). We find that the tropical regions showed a monotonic decreasing relationship for CRE-T scaling. Mid-latitudes showed a “hook-structure” in CRE-T scaling as well, while high latitudes showed a monotonic increasing CRE-T scaling. These curves are similar to EP-T scaling but have quite a different interpretation. The relationships of CRE and temperature clearly reflect that temperatures covary with extreme rainfall events and are lowered during the strongest events primarily because of the reduction in radiative heating of the surface due to clouds. As a result of this cooling, the strongest rainfall events are shifted to lower temperature bins, causing the bin-shifting effect—where the apparent sensitivity of precipitation to temperature gets biased by the redistribution of extreme events into cooler bins. This effect leads to an overestimation of precipitation sensitivity at cooler temperatures and an underestimation at warmer temperatures, skewing the perceived precipitation-temperature relationship24,26. This effect is strongest in the tropics and at the higher temperature bins in the mid-latitudes where the slope of CRE-T scaling is negative. This shows that the three distinct EP-T scaling curves shown in Fig. 1C–E do not only indicate how the rainfall events change with temperature but also reflect the covariation induced by how the radiative conditions associated with these events affect temperatures.

To quantify how much the changes in CRE affect surface temperatures, we use a thermodynamically constrained surface energy balance model, forced it with radiative fluxes for “all-sky” and “clear-sky” conditions, and estimated “all-sky” and “clear-sky” temperatures that include and excludes the radiative effects of clouds respectively (see details in Ghausi et al. 26 & methods section)26. This model captures the observed day-to-day variation of land surface temperature derived from NASA-CERES reasonably well with the R2 of 0.96 and mean RMSE of 3.8 K (Supplementary Fig. S4). The sensitivity of surface temperatures to changes in cloud cover was also very well captured with an R2 of 0.93 (Supplementary Fig. S5). The residual errors between the model and observations were comparable and only slightly larger than those between observations and ERA-5 reanalysis data (Supplementary Figs. S4C, S5B). The cooling effect of clouds given by ΔTclouds was then quantified as the difference between clear-sky and all-sky temperatures. This temperature difference (ΔTclouds) varies as a function of precipitation (Supplementary Fig. S6) with the heaviest rainfall associated with the strongest amount of cooling. However, at very high rainfall levels, this effect tends to saturate, which is likely due to a saturation in the cloud-area fraction and associated radiative effects. The global variation of this cooling effect is shown in Supplementary Fig. S7. We found that the humid tropical regions experience the most significant cooling and the effect dampens as we move towards drier regions and higher latitudes. The reduction in cooling at high latitudes is because of an increasing compensating role of enhanced downward longwave radiation compared to the reduction in absorbed solar radiation, while over dry regions it is simply because of the lack of clouds.

We then evaluated the changes in the EP-T scaling rates and their variations after the cloud effects on temperatures were removed. The adjustment to temperatures was made by adding the estimated temperature difference by clouds (ΔTclouds) to the observations of air temperature during rainy days (see “Methods”). The global distribution of precipitation temperature scaling rates for the 95th percentile rainfall events, estimated after adjusting for the cloud-cooling effects, is shown in Fig. 3A. We found positive sensitivities over most of the global land regions. The zonal variation showed positive values across the latitudinal range (Fig. 3B). These results were consistent across different rainfall quantiles, including the 99th and 99.9th percentiles, and for the GPCP and ERA-5 reanalysis data as well (Supplementary Figs. S8–S10). The breakdown in scaling at high temperatures also disappeared in the scaling curves, and rainfall extremes showed a monotonic increase closely aligning with the CC rate of 7%/°C throughout the temperature range (Fig. 3C–E). The most significant change in scaling was found in the tropics where the radiative effects of clouds are the strongest. Diametric change in sensitivities from negative to positive was found over the tropical humid regions of India, Southeast Asia, Nothern Australia, Central Africa, and Amazonia. These positive sensitivities are consistent with the regional climate model projections and observed trends over these regions24,45,46. Notably, some grids in Eastern China showed positive EP-T sensitivities for both observed and clear-sky scaling (Figs. 1A, 3A), despite experiencing a strong cloud-radiative effect (Fig. 2A). We believe that this effect is likely related to the different regimes of how cloud-radiative effects vary with increasing rainfall and the seasonality of monsoon-rainfall and its effect on pre-monsoon temperatures (see Supplementary Fig. S12 for more detail). Other studies have reported a similar spatial pattern in observed scaling over Eastern China as well16,47. Different scaling between the Himalaya Mountain regions and southeast Asia can also be attributed to topographic changes that have been shown to affect rainfall dynamics and scaling patterns48. The clear-sky scaling also showed a variation with aridity such the scaling rates remain lower/negative across the dry regions. This can be seen over the regions of the Middle East Asia and Western United States that still showed negative scaling (Fig. 3A and Supplementary Fig. S16). We note that this pattern cannot be explained by the effect of clouds alone and may likely relate to the moisture-availability limitations27. The mid-latitudes exhibited weaker scaling at low temperatures but showed a sharp increase at higher temperatures closely aligning with CC rates. This increase in scaling between 10°C to 20°C is consistent with other studies and has been argued to be a result of changing rainfall type from stratiform rainfall at low temperatures to convective rainfall at high temperatures21,49. The scaling over high latitudes remained positive and largely unchanged due to weak cloud radiative effects. Similar results were obtained when the analysis was repeated with the GPCP rainfall data (Supplementary Fig. S8). These findings suggest that the argued intensification of extreme rainfall with temperatures is consistent with observations across global land after the covariation between clouds and temperatures is corrected.

Figure 4A then closely compares the observed and derived scaling rates with and without the effect of clouds, respectively. Results show that after removing the cloud-temperature covariation, the median scaling rates in the tropics changed from –5.1%/°C to 4.5%/°C in the CPC data (Fig. 4A) and from –4.7%/°C to 7.6%/°C in the GPCP data (Fig. 4C). The change in mid-latitudes were from –2%/°C to 2.4%/°C in the CPC data (Fig. 4A) and 0.9%/°C to 3.1%/°C in GPCP data (Fig. 4C). The variability in the estimates of scaling rates was also substantially reduced. The interqauartil range (IQR) of the estimated sensitivities was reduced by about 40% in the tropics, while the total range was reduced by more than 50%, where the cloud radiative effects are the strongest (Fig. 4B). The IQR was reduced to about 30% in mid and high latitudes. Similar reductions were also observed using GPCP rainfall data (Fig. 4D). The reduction in variability was statistically significant for all three zones, as determined by an F-test (p < 0.0001), where p represents the probability of obtaining the observed difference in variances under the null hypothesis of equal variances. In addition, we diagnosed the residuals between the observations and fitted quantile regression. The residuals consistently showed lower values for estimates where the cloud effects on temperatures were removed across the latitudinal range, with the most significant reduction occurring in the tropics (Fig. 4B) for both CPC and GPCP data. This then relates back to our interpretation that the primary source of uncertainty in observed EP-T response arises from the covariation of rainfall and temperature through the confounding radiative effect of clouds.

There still exists regional variability and deviations from the CC rate in the estimated “clear-sky” sensitivities over land. Studies attribute these regional deviations to dynamic factors, particularly to changes in vertical pressure velocities11,50. To assess the impact of dynamics on regional variations in EP-T sensitivities, we analyzed standardized anomalies of vertical pressure velocity (w) on extreme rainfall days, using ERA-5 data at 650 hPa. The results reveal a positive correlation such that stronger anomalies in vertical velocity lead to positive deviations from the CC rate, particularly between 30N and 30S, where dynamic effects have been shown to be more pronounced11 (Supplementary Fig. S14). These changes in vertical velocities are tightly coupled to updrafts within the clouds, where greater power from condensation heating drives deeper convection and increased rainfall. We further explored this by examining the difference between cloud-base and cloud-top temperature as a proxy for moist convection and found a clearer, monotonic increasing relationship with deviations in EP-T sensitivities (Supplementary Fig. S14B, D). This highlights the role of dynamics in regulating regional variability in EP-T sensitivities, consistent with previous research11,50.

Most negative EP-T scaling also occur over tropical oceans16,51. To investigate the impact of cloud radiative cooling on these scaling estimates, we extended our analysis to include oceans using rainfall-temperature data from ERA-5 reanalysis and radiative fluxes from NASA-CERES. Our energy-balance model was able to reproduce sea-surface temperatures across oceans reasonably well (Supplementary Fig. S12A, B). The scaling became positive across the tropical oceans after the cloud effects were removed (Supplementary Fig. S12C, D). These estimates were consistent with what has been reported using dew-point temperatures as a scaling variable over oceans16. These results confirm that the negative scaling in oceans can be explained in parts by cloud-radiative effects as well. However, it is to be noted that cooling over oceans may also result from factors like wind-induced upwelling, turbulent mixing, and heat extraction by storms which remain unaccounted for in our current approach.

We found that the number of grids exhibiting sensitivities greater than the Clausius-Clapeyron rate (super-CC scaling) over land increases more than threefold, after removing the cloud radiative effects from temperature (Supplementary Fig. S13). Most of this change occurred in the tropics, with regional patterns being consistent across observations (CPC) as well as ERA-5 reanalysis data (Supplementary Fig. S13). The super CC scaling cannot be explained by the thermodynamic constraints on saturation vapor pressure alone and has been attributed to the dynamic factors including enhanced moisture convergence and increased moist updrafts within clouds8,52. These results suggest that the presence of super-CC scaling in observed EP-T sensitivities is largely underestimated when cloud effects on temperatures are not taken into account.

In the mid and high latitudes, the scaling rates were positive and showed a monotonic increase with temperatures but remained less than the CC rate across most grids. While the monotonic increase has already been attributed to the predominance of thermodynamic factors shaping EP-T sensitivities over these regions, the negative deviations from CC rate over these grids can be due to many other factors that have been shown to cause discrepancies in observed EP-T scaling and are not accounted for here. This primarily includes consideration of rainfall-event duration22,23, changing rainfall types21, shifts in atmospheric dynamics50, the role of topography48, and lack of moisture availability27. While these factors also affect scaling, our finding shows that the systematic zonal variation with negative tropical sensitivities and breakdown in scaling at high temperatures can be largely explained by accounting for the cloud radiative effects alone. It is crucial to clarify that the objective of this study is not to explain all the variability in EP – T scaling but to quantify to what extent the covariation of rainfall and temperature alone affect these estimates. Our results revealed that after removing the cloud radiative effects, the EP-T sensitivities yielded physically consistent estimates and showed a significant reduction in their spatial variability.

The role of the cooling effect of rainfall in impacting the EP-T scaling has also been argued before24,25,28,37. However, no study has explicitly attributed this effect to the observed zonal variation in the global scaling rates. Part of it is due to the complexities associated with quantifying this cooling effect across the global scale, particularly over regions where we lack rainfall-temperature data at high temporal resolution. To correct this effect, atmospheric moisture measures like dew-point temperature31 have been suggested as an alternative scaling variable to dry bulb temperatures. Dew-point temperature showed improved scaling, but they do not entirely account for confounding synoptic changes within the atmosphere38. It was shown that while the effect of clouds may not be directly visible in extreme precipitation-dewpoint scaling, the breakdown occurs in how dew-point scales with observed temperatures26,33,38. Time-lagged daily temperatures have also been used to minimize the cooling effect24. While they show some improvement in scaling, they do not entirely remove the negative sensitivities. We show in Supplementary Fig. S15 that explicitly correcting for cloud effects using radiation data, clearly outperforms time-lagged temperature estimates of EP-T scaling. Other methodologies to correct for the cooling effect of rainfall on temperatures had been largely statistical, relying on the very fine temporal resolution of temperature and precipitation data25,37, which may not be available in all the regions. While we agree that the use of fine-resolution data may improve the scaling estimates53, it remains an emerging challenge, particularly for future projections in data-scarce regions. On the contrary, our physics-based approach to remove the cloud cooling effect relies only on globally available satellite observations of radiative fluxes and provides an efficient tool to correct this effect across the globe and provide physically consistent estimates of global and regional EP-T sensitivities.

Our results imply that the “hook structures” and high-temperature thresholds at which the scaling breakdown or negative scaling occurs (also called “peak temperatures”), will not limit the intensification of extreme rainfall in a future climate. This is consistent with the reported shift in peak temperatures towards warmer and wetter conditions diagnosed using climate model projections51,54,55. However, the extent to which the modeled shift in peak temperatures relates to cloud-radiative effects in climate model projections remains a potential area for future research.

Our findings can also be extended to address the observed inconsistency between extreme rainfall and streamflow sensitivities to increase in temperatures13,15,56. This inconsistency has largely been attributed to factors such as rainfall duration and antecedent soil moisture conditions15,57, however the role of clouds in affecting these differences has not been explored yet. Given that the time of concentration can vary significantly across catchment sizes, the temperatures sampled for rainfall and streamflow extremes may correspond to different radiative conditions influenced by cloud effects, potentially playing a key role in affecting these sensitivities. Our approach, which removes the confounding effect of clouds on temperatures, thus provides an efficient tool for diagnosing the sensitivities of other hydrological variables beyond rainfall extremes as well.

To conclude, our analysis demonstrates that the observations across global land are consistent with the argued intensification of rainfall extremes with global warming after the covariation between clouds and temperature is accounted for. Cloud radiative effects can explain most of the observed variability in the extreme precipitation-temperature sensitivities including negative scaling rates in the tropics and the breakdown in scaling at high temperatures. This resolves the discrepancy between the apparent negative scaling rates in observations and the projected increase in precipitation extremes by climate models. More work is still needed to understand the existing uncertainties about observed changes in the rainfall dynamics with global warming in order to reliably extrapolate observationally derived EP-T sensitivities directly into the future3,11. Our findings further highlight that the rising threat of increased rainfall extremes with global warming across continents is already evident in observations, emphasizing the urgent need for more effective strategies for climate adaptation and disaster preparedness.

Methods
Datasets used
We used daily rainfall data from CPC – global daily precipitation dataset58 which is available at 0.5°x0.5° resolution. This dataset is derived using gauge-based observations across the globe. The results were also validated using the daily rainfall data from the Global Precipitation Climatology Project (GPCP – 1.3)39 available at 1°x1° resolution. This dataset is combined using satellite-based products and in situ observations. Observed gridded temperature data was used from the CPC-global daily temperature dataset available at 0.5°x0.5° resolution. The analysis was also repeated using rainfall-temperature data from the ERA-5 reanalysis interpolated at 1°x1° resolution. Surface and top-of-atmosphere radiative fluxes data for “all-sky” and “clear-sky” conditions were obtained from NASA CERES – Syn1deg dataset40,41 available at 1°x1° resolution. The analysis was performed on a daily scale over the years from 2001 to 2023.

Physical model behind scaling
The scaling of extreme rainfall with temperature is widely adopted to understand extreme precipitation-temperature sensitivities across regions and has been extensively reviewed11,59,60. The physical equation arises using the vertically integrated dry static energy budget (derived in Muller et al.61) and can be expressed as:

Pe = ϵ ∫ ∂qsat/∂z w dz (1)

Where Pe is the rate of extreme precipitation, ϵ denotes the precipitation efficiency such that ϵ=1 indicates that all condensation precipitates out. ρ denotes the mean density, w is the vertical velocity and qsat is the saturation mixing ratio. Assuming small changes in vertical velocities and precipitation efficiency with warming, the fractional change in rainfall can then be written as

δP/P ≈ δqsat(Tsurface)/qsat(Tsurface) (2)

This indicates that the changes in extreme rainfall can be approximated to follow changes in saturation vapor pressure (qsat) at the surface which is an exponential function of surface temperatures (Clausus-Clapeyron equation). As a result, one can isolate extreme rainfall events and analyze their rate of change in observations using the exponential relationship with local surface temperatures8,9,13.

Estimation of scaling rates
EP-T sensitivities were estimated by using the quantile regression (QR) method, which calculates the conditional quantile of the dependent variable (in this case, precipitation) based on given values of the independent variable (temperature). This methodology to estimate EP-T sensitivities has been widely adopted by previous studies8,9,12. The first step involved fitting a QR model between the logarithmic precipitation and temperature values at the target quantile (n) (95%, 99%, and 99.9% in our case)

Log(Pi) = βn0 + βn1(Ti) (3)

Here Pi denotes the daily rainfall intensity and Ti is the observed daily temperature. The βn0 and βn1 are the regression coefficients. The slope coefficient βn1 is then exponentially transformed and is referred to as the scaling rate (α1).

α1 (%/°C) = 100 * (eβn1 – 1) (4)

Quantifying the cloud radiative effects on surface temperatures
To remove the effect of cloud cooling from surface temperatures, we used a thermodynamically constrained surface energy balance model. The thermodynamic constraint arises by setting the vertical turbulent exchange to operate at the thermodynamic limit of maximum power. This approach has already been evaluated against observations and showed excellent agreement in reproducing turbulent fluxes and surface temperatures43,62,63. We force this model with absorbed solar radiation, downwelling longwave radiation at the surface, and outgoing longwave radiation at the top of the atmosphere for both “all-sky” and “clear-sky” conditions. These fluxes are a standard product in the NASA-CERES dataset, where ‘all-sky’ fluxes reflect the observed conditions, including cloud radiative effects while “clear-sky” fluxes are derived by eliminating the cloud effects from the radiative transfer. The temperature difference associated with clouds was estimated by the difference in the modeled temperature for “clear-sky” and “all-sky” conditions. This difference was then added to the observed temperatures during rainy days in order to eliminate the cloud-cooling effect. A detailed description of this approach can be found in Ghausi et al. 26 and briefly below.

Thermodynamic constraint on turbulent flux exchange
The vertical turbulent flux exchange was conceptualized as an outcome of a heat engine operating between the two reservoirs – the hot surface and the cooler atmosphere. The surface is heated by absorbed solar radiation (Rs) and downwelling longwave radiation (Rld) which makes it warmer at temperature (T). This energy is released back to the atmosphere but at a much colder temperature (Tr) described by outgoing longwave radiation at the top of the atmosphere (Rl,toa). This heat engine performs work to sustain the convective motion. The work done by this engine is proportional to the temperature difference between the two reservoirs. At the same time, the more work the engine performs, it leads to more vertical turbulent exchange between surface and atmosphere, which in turn depletes the driving temperature difference. This flux-gradient feedback then leads to an optimal turbulent flux that maximizes the total work done. This limit is termed as the maximum power limit42.

After writing the first and second law of thermodynamics for this conceptualized heat engine (see details in ref. 26 and ref. 43), the total power generated by this heat engine can be written as

G = (Jin – dU/dt) * (Rs + Rld – σ(Jin/σ)1/4 – 1) (5)

Here, Jin is the vertical turbulent flux exchange, dU/dt denotes the heat storage changes within the heat engine, and σ is the Stefan–Boltzmann constant with the value of 5.67*10−8 Wm−2 K−4. The optimal turbulent flux (Jopt) that maximizes the power generation (G) was estimated by numerically maximizing Eq. (5) with respect to Jin. This approach has already been evaluated against observations and has shown excellent agreement in reproducing turbulent fluxes and surface temperatures43,62,64,65. Additional evaluation is shown in Supplementary Figs. S4, S5.

After estimating the optimal turbulent fluxes Jopt, the surface temperatures at the maximum power limit can be calculated by using the surface energy balance as described in Eq. (6).

Tmaxpower = (Rs + Rld – Jopt) / σ)1/4 (6)

To estimate the effect of clouds on surface temperatures, the maximum power model is forced with the radiative fluxes for “all-sky” and “clear-sky” conditions. We use these fluxes to estimate “all-sky” and “clear-sky” surface temperatures using Eqs. (7) and (8).

Tallsky = (Rs,allsky + Rld,allsky – Jopt,allsky) / σ)1/4 (7)

Tclearsky = (Rs,clearsky + Rld,clearsky – Jopt,clearsky) / σ)1/4 (8)

The effect of clouds on surface temperatures was then calculated as the difference between “all-sky” and “clear-sky” temperatures as

ΔTclouds = Tclearsky – Tallsky (9)

Finally, we apply this correction to the Eq. (2) to estimate changes in extreme precipitation as

δP/P ≈ δqsat(Tsurface + ΔTclouds) / qsat(Tsurface + ΔTclouds) (10)

Peer review rounds
[{"round": 1, "reviewer_comments": {"reviewer_1": "Review Report of NCMMS-24-33469\nExtreme precipitation is projected to intensify with global warming. However, estimated extreme precipitation-temperature\nsensitivities exhibit negative behaviors in tropics and a ‘hook’ structure in mid-latitudes. Previous studies have reported\nvarious reasons causing these deviations from the Clausius-Clapeyron relationship: changes in rainfall types, varying\nduration of rainfall events, availability of moisture, cooling effect of rain, etc. This manuscript explored the behind\nmechanisms over global land areas and reveals that negative sensitivities in warm periods and regions are primarily results\nfrom confounding cloud radiative effects on surface temperatures during the rainfall events. This topic regarding\ninvestigating why ‘negative precipitation-temperature’ relationships is interesting; the authors do provide a strong KEY\nfinding contribute to improve the understanding of extreme precipitation physics. The language is fluent and the whole\nstoryline is coherent. However, I still have some concerns that need to be addressed before the article being accepted at\nsuch a high-impact journal.\nMAJOR COMMENTS:\n1. The authors used a thermodynamically constrained surface-energy balance approach to remove the effect of clouds on\ntemperature; and they found median EP-T sensitivities shifted from negative to positive; the mid-latitudes saw an increase in\nthe sensitivities. This is really interesting. However, existing studies also mentioned that atmospheric dynamics (e.g., vertical\nvelocity) play dominant roles in regulating deviations of extreme precipitation sensitivity from CC relationships and is the\nmain driver of spatial variability (e.g., Pfahl et al., 2017; Gu et al., 2023). Can the authors further explore how the clouds\naffect the atmospheric dynamics of the extreme precipitation sensitivities?\nPfahl, S., O’Gorman, P. A., & Fischer, E. M. (2017). Understanding the regional pattern of projected future changes in\nextreme precipitation. Nature Climate Change, 7(6), 423-427.\nGu, L., Yin, J., Gentine, P., Wang, H. M., Slater, L. J., Sullivan, S. C., ... & Guo, S. (2023). Large anomalies in future extreme\nprecipitation sensitivity driven by atmospheric dynamics. Nature Communications, 14(1), 3197.\n2. The authors investigate the observed scaling rates (before removing the effects from clouds) over the global land areas\ntend to be all smaller than 7%/K (Fig. 1 and Fig. S1); which is kind of strange, previous studies also reported that there is\nsuper CC scaling for precipitation-temperature relationships (e.g., Yin et al., 2018; Ali et al., 2022) ; Can the authors explain\nwhy in their studies there is only negative-sub CC scaling?\nYin, J., Gentine, P., Zhou, S., Sullivan, S. C., Wang, R., Zhang, Y., & Guo, S. (2018). Large increase in global storm runoff\nextremes driven by climate and anthropogenic changes. Nature communications, 9(1), 4389.\nAli, H., Fowler, H. J., Pritchard, D., Lenderink, G., Blenkinsop, S., & Lewis, E. (2022). Towards quantifying the uncertainty in\nestimating observed scaling rates. Geophysical Research Letters, 49(12), e2022GL099138.\n3. The observed scaling rates is negative over the India while positive over the southeast Asia (Fig. 1). However, both\nregions show strong net cloud radiative effect (Fig. 2). Then after removing the net cloud radiative effect, the scaling rates\nover the India become strongly positive while the scaling rates over the southeast Asia almost stay unchanged (Fig. 3). Why\nthis happens? I mean, why the strong cloud radiation effect cannot affect the scaling over the southeast Asia? If they do, the\nscaling rates after adjustment should also sharply increase. I notice the authors say that the cloud effects dampen towards\ndrier regions and higher latitudes (e.g., western North America). This makes sense since the CRE (cloud radiation effect) is\nweak there; but since the CRE is really strong over the southeast Asia, why it cannot affect the scaling rates? Please explain\nmore details.\n4. The authors explore the regimes behind negative precipitation-temperature scaling relationships over global land areas.\nThis is no doubt meaningful. However, actually, most negative scaling also emerges over tropical oceans (e.g., Wang et al.,\n2017). Can the authors also extend to discuss whether the cloud effects can explain the negative scaling over tropical\noceans?\nWang, G., Wang, D., Trenberth, K. E., Erfanian, A., Yu, M., Bosilovich, M. G., & Parr, D. T. (2017). The peak structure and\nfuture changes of the relationships between extreme precipitation and temperature. Nature Climate Change, 7(4), 268-274.\n5. My final concern is that, the analysis is performed over 2001-2016, only involving 17 years data. The common analysis\ninvolves 20-30 years data; since short-term analysis can involve large uncertainty from internal climate variability. To make\ntheir results more robust, can the authors extent the analysis period? Or at least can they use some model simulations (e.g.,\nCMIP6 model outputs) to provide further evidence of their results?\nSPECIFIC COMMENTS:\n1. Line 30: consistent with model projections. This sounds weird. Please change to ‘consistent with observed trends’ or\nsomething like that. The model projections are not always tell the truth. And the adjusted results are consistent with model\nprojections cannot prove the explanation is reasonable.\n2. Line 139-140: the humid tropical regions are associated with CRE of more than 120 W/m2 whereas the dry regions show\na reduced CRE of less than 40 W/m2. How the authors define humid tropical regions? where the dry regions refer to? The\nauthors should define these regions at least in the supplementary.\n3. Line 211-214, the median scaling rates in the tropics changed from -3%/k to 5%/k. The change in mid-latitudes from\n0.8%/K to 3.2%/K. Again, the authors need to clarify these regions either in the methods section of in the supplementary.\n4. In Figure 4, again, I feel strange, why observed scaling rates over tropics, mid-latitudes, high-latitudes both show negative\nto sub-CC scaling rates? This is inconsistent with previous findings. Please clarify this.\n5. The authors only use one extreme quantile, 95%, to exhibit their findings. To make the results more robust, I suggest they\nperform the analysis using varying extreme quantiles, e.g., 99%, 99.9%.", "reviewer_2": "This study explores the climate-scale cloud radiative effects on surface temperature during rainfall and quantifies their\nimpacts through a thermodynamically constrained surface energy balance model. The study is an extension of the authors’\nprevious works about estimate of heat flux based on a thermodynamically constrained energy balance model, and the cloud-\nradiative effect on surface temperatures and turbulent fluxes over land (Ghausi et al. 2023). The major results suggest that\nthe projected intensification of extreme rainfall with temperature in tropics is closer to the ideal pattern of Clausius-Clapeyron\nrate when the cloud radiative effects are removed. While the overall results do provide certain evidence to support the\nexplanation of the inconsistent relationship between temperature increase and extreme rainfall increase in observations, we\nhave concerns about applying the thermodynamically constrained energy balance model to daily data at finer grid scale to\nseek relation between surface temperature (with and without cloud effect) and extreme rainfall (P95). Although the authors\nclaim that the approach have already been evaluated against observations and showed excellent agreement in reproducing\nturbulent fluxes and surface temperatures (Kleidon & Renner 2017; Ghausi et al., 2023), it appears that these evaluations\nare done based on data at longer time scale not at daily time scale. If true, there is no guarantee that the approach works on\ndaily time scale because the simple energy balance may not hold in local convective processes for extreme rainfall. This is\nshown in the highly scattered EP-T relation in Fig. 3. In fact, there is no physical base to expect EP-T to follow\nthermodynamic relation. There are few studies to suggest the P-T relation slower than the q-T relation in global energy\nbalance condition, but no existing theories explain the EP-T relation. Even the q-T relation varies in different climate regimes\n(e.g., super greenhouse effect over the tropical warm pool). Therefore, I would expect to see some justification or evaluation\nof the thermodynamically constrained energy balance approach. Such an evaluation requires an estimate of quality of daily\nvariables of solar and terrestrial radiative fluxes at surface, the surface temperature (that is different from near surface air\ntemperature), and turbulent fluxes.\nA related question is about the change of water cycle with environment warming. For completeness, it is desirable to see the\nsame analysis over oceans. The SST, air-sea fluxes, and rainfall are all available over oceans. It is physically more suitable\nand practically easier to apply the method to search EP-T relation over oceans.\nBesides the above major concerns, we wonder whether the cloud cooling effect is the most important factor influencing EP-\nT. The authors mentioned some other explanations in the text. Is it possible to isolate the EP-T under greenhouse warming\nin the current climate?\nOverall, the objectives and findings of this study are quite interesting but the applicability of the method needs be justified to\nensure the major conclusions are reasonable. In addition, some statistics, physical discussions, and method descriptions\nare unclear and must be revised. Therefore, I recommend that this article be considered for publication after the above\nconcerns are adequately addressed.\nSpecific comments:\n1. The extreme precipitation-temperature (EP-T) sensitivities, scaling rate, and quantile regression should be briefly\nintroduced/defined in the main text, although they are described in the section of Data and Methods.\n2. Please add more physical discussion about possible mechanisms causing the different effects among the tropics, mid-,\nand high-latitudes.\n3. Please highlight the potential applications of the findings in this study or the expansion of our physical understanding in\nthe last 2-3 paragraphs. They are unclear in the current manuscript.\n4. The “significant results” (e.g., lines 129, 244, 274, Fig 4, Fig S3, S4, S7) should be examined by a statistical significance\ntest to precisely mention and compare their significant differences or regressions.\n5. Please add a brief description of “the bin-shifting effect” in line 152 to the main text or an example figure in the\nsupplement.\n6. Line 199: Fig S5 should be Fig S6.\n7. CPC should be in full name when it first appears.\n8. Each possible mechanism mentioned in lines 235-237 should have corresponding references or brief descriptions.\n9. Please ensure that either °C or K is used consistently throughout the manuscript.\n10. Lines 240-242: It should be also highlighted in the Introduction.\n11. Line 246: has\n12. Line 260: remains\n13. Line 265: suggest\n14. Line 272: highlight\n15. Line 274: show\n16. Line 283: induced\n17. Line 285 shows\n18. Please check and add many missing references, such as Emory & Brown., 2005; Lenderink et al., 2010; Dhara et al.,\n2016; Kleidon & Renner 2017; Wasko et al., 2018; Wasko & Nathan 2019; Tian et al., 2023a, b …etc.", "reviewer_3": "I co-reviewed this manuscript with one of the reviewers who provided the listed reports. This is part of the Nature\nCommunications initiative to facilitate training in peer review and to provide appropriate recognition for Early Career\nResearchers who co-review manuscripts.", "reviewer_4": "The observed scaling relationship between surface temperature and extreme precipitation daily amount is revisited at global\nscale. The temperature is corrected for, thanks to a surface budget equation, to remove the cooling effect of the cloudiness\nassociated with the extreme precipitation event. The resulting correction improves the scaling, in particular in the tropics.\nThe authors should be commended for connecting the cloud radiative effect of the precipitating system to the surface\ntemperature in the scaling relationhsip. This is a timely addition to the debate on the usefullness of such scaling laws for\nassessing climate models prédictions of future extreme precipitation.\nWhile this reviewer is rather in favor of publication of this paper, it will increase the impact of this work if the paper would\ninclude a discussion about:\n- physical model behind the scaling (e.g. Muller and Takayabu, 2020) and how the corrected temperature actually enters the\nscaling equation?\n- alternative to this correction. In particular using time lagged temperature instead of contemporaneous ones over both land\n(Bao et al., 2017) and ocean (De Meyer and Roca, 2021) and how the present correction does a better job at characterizing\nthe surface condition staht yield to the extreme precipitation event?\nOn a miscalleneaous note, I would suggest to state early in the manuscript the source of the precip data and the scale (daily)\nas well as the scale upon which the cloud radiative effect is computed.\nReferences\n-Bao, J., Sherwood, S., Alexander, L. et al. Future increases in extreme precipitation exceed observed scaling rates. Nature\nClim Change 7, 128–132 (2017). https://doi.org/10.1038/nclimate3201\n-De Meyer, V. and R. Roca, 2021: Thermodynamic scaling of extreme daily precipitation over the tropical ocean from\nsatellite observations. J. Meteor. Soc. Japan, 99, 423-436.\n-Muller, C. J., & Takayabu, Y. (2020). Response of precipitation extremes to warming: what have we learned from theory and\nidealized cloud-resolving simulations, and what remains to be learned? Environmental Research Letters.\nhttps://doi.org/10.1088/1748-9326/ab7130"}, "author_response": "We thank the reviewer for investing their time and effort and for providing a positive and\nthoughTul assessment of our work. The reviewer suggested important points that needed\nmore analysis and clarifications. We have now accordingly revised the manuscript with the\npoint by point response mentioned in this document. The reviewer comments are shown in\nBlack and our responses are shown in Blue. All the reviewer comments have been marked for\nreference as R1_M1, R1_M2, R1_M3 respectively. Each reply is composed of a “response” to\nthe comment and “action” taken in the main manuscript/supplementary file.\nMAJOR COMMENTS:\nR1_M1: The authors used a thermodynamically constrained surface-energy balance approach\nto remove the effect of clouds on temperature; and they found median EP-T sensitivities\nshifted from negative to positive; the mid-latitudes saw an increase in the sensitivities. This is\nreally interesting. However, existing studies also mentioned that atmospheric dynamics (e.g.,\nvertical velocity) play dominant roles in regulating deviations of extreme precipitation\nsensitivity from CC relationships and is the main driver of spatial variability (e.g., Pfahl et al.,\n2017; Gu et al., 2023). Can the authors further explore how the clouds affect the atmospheric\ndynamics of the extreme precipitation sensitivities?\nPfahl, S., O’Gorman, P. A., & Fischer, E. M. (2017). Understanding the regional pagern of\nprojected future changes in extreme precipitation. Nature Climate Change, 7(6), 423-427.\nGu, L., Yin, J., Gentine, P., Wang, H. M., Slater, L. J., Sullivan, S. C., ... & Guo, S. (2023). Large\nanomalies in future extreme precipitation sensitivity driven by atmospheric dynamics. Nature\nCommunications, 14(1), 3197.\nResponse:\nThis is an important point about the spatial variability in EP-T sensitivities. While, we show in\nfigure 4 (main manuscript) that the regional variability in the extreme precipitation-\ntemperature (EP-T) sensitivities is reduced after removing the cloud radiative effect from\ntemperatures, there still exist regional variations and deviations from CC rate in the estimated\n“clear-sky” sensitivities. Studies have shown that these deviations arise due to the dynamic\ncomponent characterized by changes in vertical pressure velocities (Pfahl et al., 2017; Gu et\nal., 2023).\nTo test how much changes in dynamics affect the regional variations of EP-T sensitivities in our\nstudy, we looked at standardized anomalies of vertical pressure velocity (w) isolated on\nextreme rainfall days at each grid point. Vertical pressure velocity at 650 hpa were used from\nERA-5 reanalysis data. We ploged it against the spatial deviation in the “clear-sky” EP-T\nsensitivities from CC rates (Fig. R1A). We found an increasing relationship indicating that the\nstronger anomalies in vertical pressure velocity leads to positive deviations in sensitivities\nfrom CC rate while lower values lead to negative deviations. The relationship becomes clearer\nand stronger when the grids between 30N and 30S were isolated (Fig. R1C). This is the same\nregion where the dynamic effects of changes in vertical velocities have been shown to be\npredominant (Gu et al., 2023).\nThese changes in vertical pressure velocities are tightly coupled to updrafts within the clouds.\nHeat release during condensation generates power within clouds to perform work to generate\nmotion and dehumidify the atmosphere. The greater power the clouds generate, deeper is\nthe convection and higher is the rainfall. To analyse these differences in cloud updrafts, we\nused the differences between cloud base and cloud top temperatures (obtained from NASA-\nCERES observations) as a proxy for moist convection within clouds. The higher are the\nupdrafts, deeper the cloud grows and higher is the difference between cloud-base and cloud-\ntop temperatures. We show in Fig. R1 B, D that the spatial deviation in EP-T sensitivities shows\na clear monotonic increasing relationship with standardized anomalies in the cloud\ntemperature differences on extreme rainfall days. This relationship is similar and clearer to\nthe relationship found using anomalies in vertical pressure velocities.\nThis shows that dynamics play an important role in regulating deviations in EP-T sensitivities,\nconsistent with findings of other studies (Pfahl e al., 2017; Gu et al., 2023). However, in order\nto estimate the magnitude of this effect on EP-T sensitivities, one has to explicitly account for\nan analytical expression of moist convection within clouds and estimate its rate of change with\ntemperatures. While we believe that this will be a really interesting result, it remains beyond\nthe scope of the current study which is focused on the impact of cloud-radiative effects on the\nthermodynamic scaling. However, it remains an important area for potential extension of this\nresearch.\nAction:\nDiscussion is added in lines 269-282 of the new manuscript. Fig. R1 (below) have been added\nas a new supplementary figure S14.\nFigure R1: Deviation in EP-T sensitivities (P95) from CC rate (7%/K) after correcting for cloud-effects as a\nfunction of (A) standardized anomalies in vertical pressure velocity at 650 hpa on extreme rainfall (P95) days\nand (B) standardized anomalies in the temperature difference between cloud-base and cloud-top on extreme\nrainfall days (P95). (C, D) same as (A, B) but for grids between 30S and 30N.\nR1_M2: The authors investigate the observed scaling rates (before removing the effects from\nclouds) over the global land areas tend to be all smaller than 7%/K (Fig. 1 and Fig. S1); which\nis kind of strange, previous studies also reported that there is super CC scaling for\nprecipitation-temperature relationships (e.g., Yin et al., 2018; Ali et al., 2022); Can the authors\nexplain why in their studies there is only negative-sub-CC scaling?\nYin, J., Gentine, P., Zhou, S., Sullivan, S. C., Wang, R., Zhang, Y., & Guo, S. (2018). Large increase\nin global storm runoff extremes driven by climate and anthropogenic changes. Nature\ncommunications, 9(1), 4389.\nAli, H., Fowler, H. J., Pritchard, D., Lenderink, G., Blenkinsop, S., & Lewis, E. (2022). Towards\nquantifying the uncertainty in estimating observed scaling rates. Geophysical Research\nLegers, 49(12), e2022GL099138.\nResponse:\nWe thank the reviewer for the comment. The reviewer correctly points out that previous\nstudies have reported super CC scaling (EP-T sensitivities > 7%/K) in the tropics and mid-\nlatitudes. However, our analysis found only a limited number of grids exhibiting super-CC\nscaling. We agribute this primarily to the daily time scale of the datasets used.\nTo clarify this, we have isolated the grids where super-CC scaling is observed and presented\nthem in Fig. R2. The grid is classified to follow super CC scaling when the sensitivity is greater\nthan 7%/K. The le] column in Fig. R2 displays grids with super-CC scaling before accounting\nfor the cloud-cooling effects on temperature, using the CPC dataset (A) and ERA-5 (C). The\nright column shows the grids with super-CC scaling after correcting for cloud-cooling effects,\nagain for both the CPC dataset (B) and ERA-5 (D).\nFirst, we would like to emphasize that our estimates of scaling that includes cloud effects at\nthe daily time scale, are consistent with the findings of previous studies (Utsumi et al., 2018;\nYin et al., 2018; Tian et al., 2023). The specific locations where super-CC scaling occurs are\nconsistent across datasets (CPC and ERA-5) and align very well with the previous research\n(Utsumi et al., 2011). The differences in our scaling estimates, compared to studies that\nconduct analyses at sub-daily time scales (e.g., Ali et al., 2022), are primarily in the magnitude\nof scaling. The impact of storm duration on higher scaling rates has been widely discussed\n(Ghausi et al., 2020). However, it is important to note that the occurrence of negative\nsensitivities in the tropics is consistent regardless of the temporal scale of analysis (Tian et al.,\n2023).\nSecondly, we observe that the number of grids exhibiting super-CC scaling increased more\nthan threefold after removing the cloud radiative effects from temperature. This pagern is\nalso consistent across both the observations (CPC) and reanalysis (ERA-5) datasets. These\nresults suggest that the presence of super-CC scaling at daily scale is largely underestimated\nwhen cloud effects on temperatures are not taken into account.\nAction: Text is added in the lines 294-303 of the revised manuscript. Fig. R2 (below) have been\nadded as new supplementary figure S13.\nFigure R2: Grids exhibiting super CC scaling (EP-T sensitivity > 7%/K) in observations (A,B) and ERA-5 reanalysis\n(C,D) with cloud-effects (A,C) and after correcting for cloud-effects (B,D).\nR1_M3: The observed scaling rates is negative over the India while positive over the southeast\nAsia (Fig. 1). However, both regions show strong net cloud radiative effect (Fig. 2). Then after\nremoving the net cloud radiative effect, the scaling rates over the India become strongly\npositive while the scaling rates over the southeast Asia almost stay unchanged (Fig. 3). Why\nthis happens? I mean, why the strong cloud radiation effect cannot affect the scaling over the\nsoutheast Asia? If they do, the scaling rates after adjustment should also sharply increase. I\nnotice the authors say that the cloud effects dampen towards drier regions and higher\nlatitudes (e.g., western North America). This makes sense since the CRE (cloud radiation\neffect) is weak there; but since the CRE is really strong over the southeast Asia, why it cannot\naffect the scaling rates? Please explain more details.\nResponse: This is a very good point. This leads to even broader question why two regions with\nsimilar strong cloud radiative effect behave differently to observed EP-T scaling. We looked\ninto this, by isolating the grids over Southeast Asia. Fig. R3 shows the observed scaling (C) with\nclouds and (E) after correcting for the cloud radiative effects (CRE). The map of net CRE\n(defined as the sum of shortwave and longwave CRE) isolated over this region and averaged\nover all extreme rainfall days is shown in panel (D). While the scaling after removing the cloud\neffects is positive everywhere, the question is why the south east humid region of China (solid\nblack box in the Fig. R3C) shows positive scaling and regions of Thailand, Laos, Vietnam (doged\nblack box in Fig. R3C) shows negative observed scaling despite having similar CRE (Fig. R3D).\nIt should also be noted that other studies have reported a similar spatial pagern in observed\nscaling over Southeast Asia as well (Tian et al., 2023; Moghari et al., 2022).\nWe show that this effect can be explained by the different regimes of how cloud radiative\neffects varies with rainfall (Fig. R3B and R3F). In the southeast humid region of China, the net\nCRE increases with rainfall but saturates at high values implying no further change in cooling\nwith increasing rainfall (Fig. R3B). As a result, when extreme rainfall is scaled against observed\ntemperatures, the observed scaling (red line in Fig. R3A) also flagens at high temperature bins\nleading to positive sensitivities. This bin-shifting effect even leads to an apparent super-CC\nscaling at low temperature bins (see also Li et al., 2023), but it disappears after cloud effects\nare removed. However, in regions of Vietnam/Laos the CRE keeps on increasing with rainfall\n(Fig. R3F) resulting in a monotonic decreasing scaling of rainfall with temperatures (Fig. R3E)\nand negative sensitivities.\nThese different regimes of how CRE scales with rainfall may likely relate to the contribution\nfrom large scale and convective rainfall events. Convective rainfall is localized and\nconcentrated with ligle spatial spread and may not entirely saturate the grid with clouds\nhowever more contribution from stratiform rainfall will result in more cloud saturation of the\ngrid. It may also relate to a latitudinal effect of higher solar insolation for grids closer to\nequator leading to increased reflectance of top of atmosphere solar-radiation by clouds. We\nfind this an important effect that can be further explored using higher resolution regional\ndatasets.\nAction: Discussion is added in lines 220-224 of the revised manuscript. Fig. R3 (below) is added\nas new supplementary figure S11.\nFigure R3: Maps of EP-T sensitivities for observations (C), Net cloud radiative effect on extreme rainfall (P95)\ndays (D) and EP-T sensitivities after correcting for cloud-effects (E) isolated over Southeast Asia region. Black\nsolid and black doXed boxes further separate these regions into two parts. (A, E) shows the scaling curves of\nextreme precipitation with observed temperatures (red line) and temperatures corrected for cloud-effects\n(blue-line) for grids within black solid box and black doXed box respectively. (B, F) shows the variation of net\ncloud radiative effect with rainfall for grids within black solid box and black doXed box respectively.\nR1_M4: The authors explore the regimes behind negative precipitation-temperature scaling\nrelationships over global land areas. This is no doubt meaningful. However, actually, most\nnegative scaling also emerges over tropical oceans (e.g., Wang et al., 2017). Can the authors\nalso extend to discuss whether the cloud effects can explain the negative scaling over tropical\noceans?\nWang, G., Wang, D., Trenberth, K. E., Erfanian, A., Yu, M., Bosilovich, M. G., & Parr, D. T. (2017).\nThe peak structure and future changes of the relationships between extreme precipitation\nand temperature. Nature Climate Change, 7(4), 268-274.\nResponse:\nThe reviewer correctly mentions that most negative scaling has also emerged over tropical\noceans (Wang et al., 2017; Tian et al., 2023). To test to what extent cloud radiative cooling\naffect the scaling estimates over ocean, we have now extended our analysis to oceans as well.\nWe used ERA-5 reanalysis rainfall-temperature data and together with the radiative fluxes\nfrom NASA-CERES to estimate the EP-T sensitivities with and without the effect of clouds.\nObserved EP-T scaling over oceans is shown in Fig. R4C. We find that the negative scaling\ndominates across the tropical oceans, with regional pagerns being consistent with what have\nbeen reported by other studies (Wang et al., 2017; Tian et al., 2023; Gu et al., 2023). To\nestimate the effect of cloud-cooling over oceans, we used our thermodynamically constrained\nsurface energy balance forced with “all-sky” and “clear-sky” radiative fluxes. The evaluation\nof the estimated surface temperatures with observations from CERES is shown in Fig.R4 A, B.\nWe find that the residual errors were higher than that compared to land. This can be agributed\nto the surface heat -storage effect within the oceans that remain unaccounted for in our\napproach (more details in Kleidon & Renner, 2017). However, this will lead to systematic bias\nwhich should not affect the difference between “clear-sky” and “all-sky” temperatures which\nis quantified as cloud-radiative cooling. Thus, our approach can be used to diagnose the effect\nof clouds on ocean temperatures as well.\nEP-T scaling over oceans after removing the effect of cloud are shown in Fig. R4D. The scaling\nbecame positive across the tropical oceans. These estimates were consistent with what have\nbeen reported using dew-point temperatures as a scaling variable over oceans (Tian et al.,\n2023). However, it should also be noted that apart from clouds, ocean surface temperatures\ncan also cool due to wind-induced upwelling of deep sea-water, turbulent mixing of the ocean\nlayers and heat extraction by storm during the rainfall event which remain unaccounted for in\nour approach. So, while we show that the cloud-cooling effects explains negative sensitivities\nin tropical oceans, we note that the net estimated cooling of surface temperature over oceans\nmay be underestimated by accounting for the effect of clouds alone. A more detailed analysis\nto quantify the cooling effect of storm over ocean will require a different formulation of\nsurface energy-balance model that explicitly accounts for the heat-storage and wind mixing\neffects over the ocean.\nAction: Text is added in the lines 283-293 of the revised manuscript. Fig. R4 is added as a new\nsupplementary figures S12.\nFigure R4: (A) Comparison of estimated daily sea surface temperatures with the energy balance model with\ntemperatures derived from (NASA-CERES). Root mean squared error (RMSE) between daily estimated and\nobserved temperatures from CERES across all the oceanic grids. Global map of extreme precipitation-\ntemperature sensitivities over oceanic grids with (C) observed temperatures and (D) temperatures corrected\nfor cloud-effects.\nR1_M5: My final concern is that, the analysis is performed over 2001-2016, only involving 17\nyears data. The common analysis involves 20-30 years data; since short-term analysis can\ninvolve large uncertainty from internal climate variability. To make their results more robust,\ncan the authors extent the analysis period? Or at least can they use some model simulations\n(e.g., CMIP6 model outputs) to provide further evidence of their results?\nResponse: We thank the reviewer for the comment. We have now extended the whole\nanalysis to the period from 2001 to 2023 for both CPC and GPCP data. Additionally, we have\nnow also used the ERA-5 data over both land and ocean to check the robustness of the results.\nThe primary limitation that constrains the analysis period is the availability of observed\nsatellite radiative flux data from NASA-CERES which only starts from 2001. All the results in\nthe new analysis (with extended period) are consistent with the previous finding and does not\naffect our final conclusions. The use of climate models has been kept out of scope for the\npresent study in order to avoid the uncertainties arising with the representation of day-to-day\ncloud radiative fluxes in climate model projections which may add to the spread and will\nrequire a separate evaluation.\nAction: Whole analysis is extended for the years (2001 – 2023). All the main and\nsupplementary figures are modified accordingly. New supplementary figure S10 is added.\nSPECIFIC COMMENTS:\n1. Line 30: consistent with model projections. This sounds weird. Please change to ‘consistent\nwith observed trends’ or something like that. The model projections are not always telling the\ntruth. And the adjusted results are consistent with model projections cannot prove the\nexplanation is reasonable.\nResponse: Thanks for pointing this out. The suggested change is made.\nAction: Text is accordingly modified in the revised manuscript.\n2. Line 139-140: the humid tropical regions are associated with CRE of more than 120 W/m2\nwhereas the dry regions show a reduced CRE of less than 40 W/m2. How the authors define\nhumid tropical regions? where the dry regions refer to? The authors should define these\nregions at least in the supplementary.\nResponse: We apologize for not being clear. We have now added modified the supplementary\nfigure S2 and explicitly isolated the CRE for each region and described how the region is\nclassified. These regions are described in the figure caption.\nAction: Figure R5 is added as new supplementary figure S2.\nFigure R5: Global map of cloud radiative effects (defined as the difference between the “clear-sky” and “all-sky” radiative\nfluxes) isolated on extreme rainfall days for absorbed shortwave (A) and downwelling longwave (C) radiation. Box plots for\n(B) shortwave CRE and (D) downwelling longwave CRE separated into different climate zones. The tropical regions are\nclassified as grids between 23S and 23N, mid-latitudes as grids from 23S-55S and 23N-55N and high-latitudes as grids\nbeyond 55S and 55N. The classification into humid and arid regions is derived from the Budyko Aridity index, which is\ncalculated as the ratio of mean annual potential evapotranspiration to mean annual precipitation. The region is classified as\nhumid when aridity index is less than 1 and arid when it is greater than 1.\n3. Line 211-214, the median scaling rates in the tropics changed from -3%/k to 5%/k. The\nchange in mid-latitudes from 0.8%/K to 3.2%/K. Again, the authors need to clarify these\nregions either in the methods section of in the supplementary.\nResponse: Thanks for pointing this out. We refer to tropics as regions from 23S to 23N. The\nmid-latitudes are characterized as regions from 23N – 55N and 23S – 55S. Regions higher than\n55N and 55S are classified as high-latitude regions. We have now added this into the main\ntext.\n4. In Figure 4, again, I feel strange, why observed scaling rates over tropics, mid-latitudes, high-\nlatitudes both show negative to sub-CC scaling rates? This is inconsistent with previous\nfindings. Please clarify this.\nAddressed in comment R1.M2\n5. The authors only use one extreme quantile, 95%, to exhibit their findings. To make the\nresults more robust, I suggest they perform the analysis using varying extreme quantiles, e.g.,\n99%, 99.9%.\nResponse: We agree that performing analysis for different quantiles adds to the robustness of\nthe results. We have now extended the analysis to 99th percentile and 99.9th percentile rainfall\n(shown in figure below) in addition to 95th percentile (shown in main figures). The key findings\nremain same for all the percentiles.\nAction: Text is accordingly modified in the revised manuscript. Fig. R6 (below) is added as new\nsupplementary figure S9.\nFigure R6: Global map of extreme precipitation – temperature (EP-T) sensitivities for 99th percentile rainfall\n(A,C) and 99.9th percentile rainfall (B,D) with observed temperatures (A,B) and with corrected temperatures for\ncloud-effects (C,D).\nReferences:\nTian, B., Chen, H., Yin, J., Liao, Z., Li, N., & He, S. (2023). Global scaling of precipitation extremes\nusing near-surface air temperature and dew point temperature. Environmental Research\nLegers, 18(3), 034016.\nHosseini-Moghari, S. M., Sun, S., Tang, Q., & Groisman, P. Y. (2022). Scaling of precipitation\nextremes with temperature in China’s mainland: Evaluation of satellite precipitation data.\nJournal of Hydrology, 606, 127391.\nLi, X., Wang, T., Zhou, Z., Su, J., & Yang, D. (2023). Seasonal characteristics and spatio-temporal\nvariations of the extreme precipitation-air temperature relationship across China.\nEnvironmental Research Le2ers, 18(5), 054022.\nPfahl, S., O’Gorman, P. A., & Fischer, E. M. (2017). Understanding the regional pagern of\nprojected future changes in extreme precipitation. Nature Climate Change, 7(6), 423-427.\nGu, L., Yin, J., Gentine, P., Wang, H. M., Slater, L. J., Sullivan, S. C., ... & Guo, S. (2023). Large\nanomalies in future extreme precipitation sensitivity driven by atmospheric dynamics. Nature\nCommunications, 14(1), 3197.\nReviewer #2 (Remarks to the Author):\nThis study explores the climate-scale cloud radiative effects on surface temperature during\nrainfall and quantifies their impacts through a thermodynamically constrained surface energy\nbalance model. The study is an extension of the authors’ previous works about estimate of\nheat flux based on a thermodynamically constrained energy balance model, and the cloud-\nradiative effect on surface temperatures and turbulent fluxes over land (Ghausi et al. 2023).\nThe major results suggest that the projected intensification of extreme rainfall with\ntemperature in tropics is closer to the ideal pattern of Clausius-Clapeyron rate when the cloud\nradiative effects are removed. While the overall results do provide certain evidence to support\nthe explanation of the inconsistent relationship between temperature increase and extreme\nrainfall increase in observations, we have concerns about applying the thermodynamically\nconstrained energy balance model to daily data at finer grid scale to seek relation between\nsurface temperature (with and without cloud effect) and extreme rainfall (P95).\nWe thank the reviewer for investing their time and effort in reviewing our manuscript and for\nthe thoughTul assessment of our work. The reviewer has raised some concerns about\napplying the thermodynamically constrained model at daily timescale. We have now\nperformed additional evaluation to justify our approach. The analysis is extended to oceans\nas well (as suggested by the reviewer). The manuscript is accordingly revised with the point-\nby-point response mentioned in this document. The reviewer comments are shown in Black\nand our responses are shown in Blue. All the reviewer comments have been marked for\nreference as R2_M1, R2_M2 respectively. The reply is composed of a “response” to the\ncomment and “action” taken in the main manuscript/supplementary file.\nR2_M1: Although the authors claim that the approach have already been evaluated against\nobservations and showed excellent agreement in reproducing turbulent fluxes and surface\ntemperatures (Kleidon & Renner 2017; Ghausi et al., 2023), it appears that these evaluations\nare done based on data at longer time scale not at daily time scale. If true, there is no\nguarantee that the approach works on daily time scale because the simple energy balance\nmay not hold in local convective processes for extreme rainfall. This is shown in the highly\nscattered EP-T relation in Fig. 3.\nResponse:\nThanks for the comment. The reviewer correctly points out that the evaluation in the previous\nstudies (Kleidon & Renner 2017 and Ghausi et al., 2023) were done at coarser temporal scales.\nIn Ghausi et al., (2022), it was performed at daily time-scale but was limited to a small region.\nWe have now added here the global evaluation of this approach at the daily scale.\nFig. R1A (below) shows the comparison between the daily values of estimated surface\ntemperatures from the thermodynamically constrained surface energy balance model with\nobservations of surface temperatures derived from NASA-CERES dataset. Fig. R1B shows the\nmap of root mean squared error (RMSE) between estimated surface temperature and\nobservations from NASA-CERES, computed for the daily timeseries at each grid. While some\nbiases exist, our approach reasonably captures the day-to-day variability in temperatures with\nmean RMSE of 3.8K. We have further added the comparison between ERA-5 reanalysis data\nand NASA-CERES observations (Fig. R1C and R1D). We do this to highlight that residual errors\nin our model estimates are comparable and only slightly larger than those between the\nobservations and reanalysis data.\nAction:\nFigure R1 is added to the supplementary information as Fig. S4. Text is added in the revised\nmanuscript (lines 187-192).\nFigure R1: (A) Comparison of daily estimated surface temperatures using the thermodynamically constrained\nsurface energy balance model against observations from the NASA-CERES dataset.(B) Global map of root mean\nsquared error (RMSE) between the estimated surface temperatures and NASA-CERES observations, computed\nfor the daily timeseries at each grid point. (C, D) same as (A, B) but for the comparison between ERA-5\nreanalysis data and NASA-CERES observations.\nR2_M2: In fact, there is no physical base to expect EP-T to follow thermodynamic relation.\nThere are few studies to suggest the P-T relation slower than the q-T relation in global energy\nbalance condition, but no existing theories explain the EP-T relation. Even the q-T relation\nvaries in different climate regimes (e.g., super greenhouse effect over the tropical warm pool).\nTherefore, I would expect to see some justification or evaluation of the thermodynamically\nconstrained energy balance approach. Such an evaluation requires an estimate of quality of\ndaily variables of solar and terrestrial radiative fluxes at surface, the surface temperature (that\nis different from near surface air temperature), and turbulent fluxes.\nResponse: We thank reviewer for the comment. We agree with the reviewer that in the global\nenergy balance conditions, mean precipitation increases at rates much slower than q-T\nrelation due to the energetic constraints. The thermodynamically constrained approach used\nin our study was able to analytically reproduce these sensitivities as well (see Kleidon et al.,\n2013). However, the primary physical basis for rainfall extremes to follow the thermodynamic\nrelation comes from the Clausius-Clapeyron equation that suggest atmospheric moisture to\nincrease at the rate of 7%/K (Trenberth et al., 2003) at the assumption of small changes in\nrelative humidity (Held & Soden, 2006). Climate models have shown rainfall extremes to\nincrease at higher rates compared to mean rainfall but with regional variability as also\nmentioned by the reviewer. The deviations from the thermodynamic relation at regional\nscales have been attributed to the dynamic factors such as the strength of vertical velocity and\nmoist convection (O’Gorman & Schneider, 2009; Pfahl et al., 2017; Gu et al., 2023).\nTo justify our thermodynamically constrained approach we would like it to support it with two\nlines of evaluation. First, we show that our thermodynamically constrained surface energy\nbalance model effectively captures the observed day-to-day sensitivity of surface\ntemperatures to changes in cloud-cover and comparable to that by ERA-5 reanalysis data.\nSecondly, we show that the regional deviations in EP-T sensitivities from the thermodynamic\nrelation relates to the dynamics characterized by changes in vertical pressure velocities and\nthese affects are very well captured in the changes in cloud base and cloud top temperatures.\n1) We estimated the first-order sensitivity of daily surface temperature to changes in\ncloud cover at each grid point using temperatures derived from CERES, our\nthermodynamically constrained energy balance model, and ERA-5 surface\ntemperatures. Fig. R2A compares the sensitivities of the temperatures estimated by\nour model with those derived from CERES, where each black dot represents the\nsensitivity at a specific grid point. Similarly, Fig. R2B compares the cloud-cover\nsensitivities of ERA-5 surface temperatures with those of CERES. Our results\ndemonstrate that our model accurately captures the observed sensitivity from CERES\nwith R2 of 0.93 (Fig. R2A), and the residual errors were comparable to those in the\nsensitivities of ERA-5 and observations (Fig. R2B).\n2) To assess the impact of dynamic changes on regional variations in EP-T sensitivities,\nwe analysed standardized anomalies of vertical pressure velocity (w) on extreme\nrainfall days at each grid point. Vertical pressure velocity data at 650 hPa was taken\nfrom ERA-5 reanalysis. We ploJed these anomalies against the spatial deviation in\n\"clear-sky\" EP-T sensitivities from CC rates (Fig. R3A, C). Our analysis revealed a\npositive relationship, indicating that the stronger anomalies in vertical pressure\nvelocity led to positive deviations in sensitivities from the CC rate, while lower\nanomalies correspond to negative deviations. These findings are consistent with what\nhave been reported by other studies as well (Pfahl et al., 2017; Gu et al., 2023). Note\nthat, this relationship become clearer when the grids between 30°N and 30°S are\nisolated. This is the same region where the dynamic effects of changes in vertical\nvelocities are most significant, as shown by Gu et al. (2023). We then show that these\nvariations in vertical pressure velocities are closely linked to updrafts within clouds and\nare very well captured in the CERES cloud-base and cloud-top temperature data.\nCondensational heating generates power within the clouds to drive vertical motion\nand dehumidify the atmosphere. The more power clouds generate, the deeper the\nconvection and the higher the rainfall. To analyse these differences in cloud updrafts\nwith increasing vertical velocities, we used the difference between cloud base and\ncloud top temperatures (obtained from NASA-CERES observations) as a proxy for moist\nconvection within clouds. The stronger the updrafts lead to a greater temperature\ndifference between the cloud base and cloud top. Fig. R3B, D demonstrate that the\nspatial deviation in EP-T sensitivities exhibits a clear, monotonic increasing relationship\nwith cloud temperature differences as well. This relates back to the reviewer’s point\nthat the EP-T relation can deviate from the thermodynamic scaling at regional scales.\nWe show that these changes can be attributed to changes in the atmospheric\ndynamics.\nAction: Discussion is added in the main text (lines 187-192 and 269-282). Fig. R2 and Fig. R3\n(below) are added as new supplementary figures Fig. S5 and Fig. S14.\nFigure R2: (A) Comparison of the first-order sensitivity of daily surface temperatures to changes in cloud cover,\nestimated by the thermodynamically constrained energy balance model, with those derived from NASA-CERES\nobservations. Each black dot represents the sensitivity at each grid point over land. (B) Same as (A) but for the\ncomparison of cloud-cover sensitivities of ERA-5 surface temperatures with those derived from CERES\nobservations.\nFigure R3: Deviation in EP-T sensitivities (P95) from CC rate (7%/°C) after correcting for cloud-effects as a\nfunction of (A) standardized anomalies in vertical pressure velocity at 650 hpa on extreme rainfall (P95) days\nand (B) standardized anomalies in the temperature difference between cloud-base and cloud-top on extreme\nrainfall days (P95). (C, D) same as (A, B) but for grids between 30S and 30N.\nR2_M3: A related question is about the change of water cycle with environment warming. For\ncompleteness, it is desirable to see the same analysis over oceans. The SST, air-sea fluxes, and\nrainfall are all available over oceans. It is physically more suitable and practically easier to\napply the method to search EP-T relation over oceans.\nResponse: As per reviewer’ suggestion, we have now extended the analysis to oceans as well.\nWe used rainfall-temperature data from ERA-5 reanalysis, together with the radiative fluxes\nfrom NASA-CERES to estimate the EP-T sensitivities with and without the effect of clouds.\nObserved EP-T scaling over oceans is shown in Fig. R4C (below). We find that negative scaling\ndominates across the tropical oceans. These estimates are consistent with what have been\nreported by other studies (Wang et al., 2017; Tian et al., 2023; Gu et al., 2023). To estimate\nthe effect of cloud-cooling over oceans, we used our thermodynamically constrained surface\nenergy balance forced with “all-sky” and “clear-sky” radiative fluxes. The evaluation of the\nestimated daily surface temperatures with observations from CERES over oceans is shown in\nFig. R4 A, B. We find that the residual errors were higher than that compared to land. This can\nbe attributed to the surface heat -storage effect within the oceans as well as the oceanic heat\ntransport that remain unaccounted for in our approach (more details in Dhara et al., 2016 &\nKleidon & Renner, 2017). However, this will likely lead to a systematic bias (Dhara et al., 2016)\nwhich should not affect the difference between the “clear-sky” and “all-sky” temperatures\nwhich is quantified as cloud-radiative cooling. Thus, our approach can be used to diagnose the\neffect of clouds on ocean temperatures as well.\nEP-T scaling over oceans aner removing the effect of clouds are shown in Fig. R4D. The scaling\nbecame positive across the tropical oceans. These estimates were consistent with what have\nbeen reported using dew-point temperatures as a scaling variable over oceans (Tian et al.,\n2023) as well as the climate model projections (Chang et al., 2022). However, it should also be\nnoted that apart from clouds, ocean surface temperatures can also cool due to wind-induced\nupwelling of deep sea-water, turbulent mixing of the oceanic layers and heat extraction by\nstorm during the rainfall event. So, while we show that the cloud-cooling effects explains\nnegative sensitivities in tropical oceans as well, we note that the net estimated cooling of\nsurface temperature over oceans may be underestimated by accounting for the effect of\nclouds alone. A detailed analysis to quantify the cooling effect of storm over ocean will require\na different formulation of surface energy-balance model that explicitly accounts for the heat-\nstorage and wind mixing effects over the ocean and remain a potential area for future\nresearch.\nAction: Text is added in lines 283-292 of the revised manuscript. Figure R4 (below) is added\nas new supplementary figure Fig. S12.\nFigure R4: (A) Comparison of estimated daily sea surface temperatures using the energy balance model with\ntemperatures derived from NASA-CERES observations. Root mean squared error (RMSE) between daily\nestimated and observed temperatures from CERES across all the oceanic grids. Global map of extreme\nprecipitation-temperature sensitivities over oceanic grids with (C) observed temperatures and (D)\ntemperatures corrected for cloud-effects.\nR2_M4: Besides the above major concerns, we wonder whether the cloud cooling effect is the\nmost important factor influencing EP-T. The authors mentioned some other explanations in\nthe text. Is it possible to isolate the EP-T under greenhouse warming in the current climate?\nResponse: We thank reviewer for the comment. In this study, we show that the negative\nextreme precipitation-temperature sensitivities in observations across the tropics arises\npredominantly due to the cloud-cooling effect. However, it necessarily does not mean that\ncloud-cooling effect is the most important factor influencing other aspects of EP-T sensitivities\nas well, for e.g., the regional variability and deviations from CC scaling. While, we show in\nfigure 4 (main manuscript) that the regional variability in the extreme precipitation-\ntemperature (EP-T) sensitivities is reduced aner removing the cloud radiative effect from\ntemperatures, there still exist regional variations and deviations from CC rate in the estimated\n“clear-sky” sensitivities. Studies have shown that these deviations arise due to the dynamic\ncomponent characterized by changes in vertical pressure velocities (Pfahl et al., 2017; Gu et\nal., 2023). We have now also demonstrated in Fig. R2A (above) that regional deviations from\nCC scaling correlates with changes in vertical pressure velocities and moist updrafts within\nclouds. Other aspect is the existence of super CC rates which cannot be explained by effect of\nclouds alone and are related to the strengthening of moist convections.\nTo isolate EP-T response under greenhouse warming in the current climate is not possible\nusing our thermodynamic energy balance model as it does not simulate precipitation directly\nbut rather the surface temperatures and turbulent fluxes of sensible and latent heat\nassociated with changes in radiative forcings. This model has been used to obtain sensitivities\nof global mean evaporation and have been found to reproduce the sensitivities from climate\nmodel simulations very well (see Kleidon & Renner 2013, Kleidon et al., 2014). However, we\nnote that other studies using optimal fingerprint techniques with climate model runs have\nshown that observed intensification of extreme rainfall is attributable to greenhouse induced\nwarming (Zhang et al., 2013; Paik et al., 2020).\nAction: Text is added in lines 269-282.\nOverall, the objectives and findings of this study are quite interesting but the applicability of\nthe method needs be justified to ensure the major conclusions are reasonable. In addition,\nsome statistics, physical discussions, and method descriptions are unclear and must be\nrevised. Therefore, I recommend that this article be considered for publication aner the above\nconcerns are adequately addressed.\nThank you, these are helpful comments and we hope we have now addressed your concerns\nadequately.\nSpecific comments:\n1. The extreme precipitation-temperature (EP-T) sensitivities, scaling rate, and quantile\nregression should be briefly introduced/defined in the main text, although they are described\nin the section of Data and Methods.\nResponse: Thanks for the suggestion. We have made this change.\nAction: Text is added in lines 94-97 of the revised manuscript.\n2. Please add more physical discussion about possible mechanisms causing the different\neffects among the tropics, mid-, and high-latitudes.\nResponse: The suggested change is made.\nAction: Text is accordingly modified in the discussion section.\n3. Please highlight the potential applications of the findings in this study or the expansion of\nour physical understanding in the last 2-3 paragraphs. They are unclear in the current\nmanuscript.\nResponse: Thanks for the suggestion. We have now added the potential applications of the\nfindings in this study in the last paragraphs.\nAction: Text is accordingly modified in the discussion section.\n4. The “significant results” (e.g., lines 129, 244, 274, Fig 4, Fig S3, S4, S7) should be examined\nby a statistical significance test to precisely mention and compare their significant differences\nor regressions.\nResponse: Thank you for the suggestion.\nFor the relationship between precipitation and cloud radiative effects, as well as changes in\ntemperature, we have now reported the p-value for the estimated slope coefficient to\ndemonstrate the statistical significance of the results.\nFor the variability in precipitation-temperature sensitivities, we performed an F-test, which\ncompares the variances an determine if the variability between two datasets is significantly\ndifferent. The F-test revealed that the reduction in variability in extreme-precipitation-\ntemperature sensitivities aner removing the cloud radiative effects was statistically significant\n(p < 0.0001).\nAction: Text is added in lines 143 and 254-257 of the revised manuscript.\n5. Please add a brief description of “the bin-shining effect” in line 152 to the main text or an\nexample figure in the supplement.\nResponse: Thanks for the suggestion. We have now added a description about the bin-shining\neffect in the main text.\nAction: Text is added in lines 165-167 of the revised manuscript.\n6. Line 199: Fig S5 should be Fig S6.\nResponse: Thanks for pointing this out. The suggested change is made.\n7. CPC should be in full name when it first appears.\nResponse: The suggested change is made.\n8. Each possible mechanism mentioned in lines 235-237 should have corresponding\nreferences or brief descriptions.\nResponse: The suggested change is made.\n9. Please ensure that either °C or K is used consistently throughout the manuscript.\nResponse: The suggested change is made. We have used °C at all the places where EP-T\nsensitivity is discussed.\n10. Lines 240-242: It should be also highlighted in the Introduction.\nResponse: The suggested change is made.\n11. Line 246: has\nAction: Changed\n12. Line 260: remains\nAction: Changed\n13. Line 265: suggest\nAction: Changed\n14. Line 272: highlight\nAction: Changed\n15. Line 274: show\nAction: Changed\n16. Line 283: induced\nAction: Changed\n17. Line 285 shows\nAction: Changed\n18. Please check and add many missing references, such as Emory & Brown., 2005; Lenderink\net al., 2010; Dhara et al., 2016; Kleidon & Renner 2017; Wasko et al., 2018; Wasko & Nathan\n2019; Tian et al., 2023a, b …etc.\nAction: Thanks for pointing this out. The missing citations have been added.\nReferences:\nChang, M., Liu, B., Wang, B., Mar4nez-Villalobos, C., Ren, G., & Zhou, T. (2022). Understanding\nfuture increases in precipitation extremes in global land monsoon regions. Journal of Climate,\n35(6), 1839-1851.\nKleidon, A. and Renner, M.: A simple explanation for the sensitivity of the hydrologic cycle to\nsurface temperature and solar radiation and its implications for global climate change, Earth\nSyst. Dynam., 4, 455–465, hJps://doi.org/10.5194/esd-4-455-2013, 2013.\nKleidon, A., Kravitz, B., & Renner, M. (2015). The hydrological sensitivity to global warming and\nsolar geoengineering derived from thermodynamic constraints. Geophysical Research Le0ers,\n42(1), 138-144.\nZhang, X., Wan, H., Zwiers, F. W., Hegerl, G. C., & Min, S. K. (2013). AJribu4ng intensification\nof precipitation extremes to human influence. Geophysical Research LeJers, 40(19), 5252-\n5257.\nPaik, S., Min, S. K., Zhang, X., Donat, M. G., King, A. D., & Sun, Q. (2020). Determining the\nanthropogenic greenhouse gas contribution to the observed intensification of extreme\nprecipitation. Geophysical Research LeJers, 47(12), e2019GL086875.\nWe thank the reviewers for investing their time and effort in reviewing our manuscript and for\nthe positive and though8ul assessment of our work. The manuscript is accordingly revised as\nper reviewer’s comments and suggestions, with the point-by-point response mentioned in this\ndocument. The reviewer comments are shown in Black and our responses are shown in Blue.\nAll the reviewer comments have been marked for reference as R3_M1, R3_M2 respectively.\nThe reply is composed of a “response” to the comment and “action” taken in the main\nmanuscript/supplementary file.\nThe observed scaling relationship between surface temperature and extreme precipitation\ndaily amount is revisited at global scale. The temperature is corrected for, thanks to a surface\nbudget equation, to remove the cooling effect of the cloudiness associated with the extreme\nprecipitation event. The resulting correction improves the scaling, in particular in the tropics.\nThe authors should be commended for connecting the cloud radiative effect of the\nprecipitating system to the surface temperature in the scaling relationhsip. This is a timely\naddition to the debate on the usefullness of such scaling laws for assessing climate models\nprédic0ons of future extreme precipitation.\nThank you for the positive feedback.\nWhile this reviewer is rather in favor of publication of this paper, it will increase the impact of\nthis work if the paper would include a discussion about:\nR3_M1: - physical model behind the scaling (e.g. Muller and Takayabu, 2020) and how the\ncorrected temperature actually enters the scaling equation?\nResponse: This is a very good suggestion. We have now included a brief background on the\nphysical model behind scaling in the methods section and related how corrected temperature\nenters this equation. Discussion about this have also been added in the main text.\nAction: Text is added in lines 388-409 of the revised manuscript.\nR3_M2: alternative to this correction. In particular using time lagged temperature instead of\ncontemporaneous ones over both land (Bao et al., 2017) and ocean (De Meyer and Roca,\n2021) and how the present correction does a be[er job at characterizing the surface condition\nstaht yield to the extreme precipitation event?\nResponse: Thanks for the comment. The reviewer correctly points out that studies have tried\nto minimize the cooling effect of rain by using time-lagged values of surface temperatures.\nWhile this leads to some improvement in the scaling, it has been shown that it does not\nentirely remove the negative scaling over land (Bao et al., 2017).\nTo test this in our study, we repeated the analysis by using 1-day lagged temperature to\nestimate the extreme precipitation scaling rates over land. The results are presented in Fig. R1\n(below). The box plots in Fig. R1 (bo[om-row) compare the sensitivities obtained using\nobserved (red), time-lagged (orange) and corrected temperatures after removing the cloud-\neffects (blue). Although, the sensitivities improved after using lagged temperatures, they were\nstill negative across most regions of the tropics. Similar pagern was found in the residual error\nbetween observations and fitted quantile regression. The residuals were lower for time-lagged\ntemperatures compared to observation but higher than those obtained after removing the\ncloud-radiative effects. This shows that while using lagged-temperatures minimize cooling for\nsome events, it does not entirely eliminate the cooling effect particularly where the time-scale\nof cooling is longer than a day or few like the monsoon-systems (Ghausi et al., 2022). Secondly,\nthe cloud-formation does not necessarily imply the storm-event occurrence. As a result, any\ndelay between cloud-formation and storm will not be accounted for while using lagged\ntemperatures but will be effectively removed using our approach.\nAction: Text is added in lines 330-334 of the revised manuscript. Figure R1 (below) is added\nas a new supplementary figure S15.\nFigure R1: (Top row) Global map of extreme precipitation-temperature sensitivities estimated using quantile\nregression with (A) observed temperatures, (B) 1-day time lagged temperatures and (C) temperatures\ncorrected for cloud-radiative effects. (BoFom row-D) Comparison of EP-T scaling rates estimated using\nobserved temperatures (red), time-lagged temperatures (orange) and with temperatures corrected for the\ncloud-cooling effect (blue) for tropics, mid-latitudes and high-latitudes. (E) same as (D) but for the residuals\nbetween observations and fitted quantile regression\nOn a miscalleneaous note, I would suggest to state early in the manuscript the source of the\nprecip data and the scale (daily) as well as the scale upon which the cloud radiative effect is\ncomputed.\nResponse: We thank the reviewer for the suggestion. We have now added the information\nabout the precipitation data sources and the temporal scales of the analysis at the end of the\nintroduction section.\nAction: Text is added in lines 80-83 of the revised manuscript.\nReferences added:\nBao, J., Sherwood, S., Alexander, L. et al. Future increases in extreme precipitation exceed\nobserved scaling rates. Nature Clim Change 7, 128–132 (2017).\nh[ps://doi.org/10.1038/nclimate3201\nDe Meyer, V. and R. Roca, 2021: Thermodynamic scaling of extreme daily precipitation over\nthe tropical ocean from satellite observations. J. Meteor. Soc. Japan, 99, 423-436.\nMuller, C. J., & Takayabu, Y. (2020). Response of precipitation extremes to warming: what have\nwe learned from theory and idealized cloud-resolving simulations, and what remains to be\nlearned? Environmental Research Le[ers. h[ps://doi.org/10.1088/1748-9326/ab7130"}, {"round": 2, "reviewer_comments": {"reviewer_1": "1. The authors address most of mine concerns, this is good. However, I still have some doubts regarding the scaling patterns\nacross India and southeast China. The authors argue that ‘different regimes of how CRE scales with rainfall may likely relate to the\ncontribution from large scale and convective rainfall events.’ Since it is tropics, I would like to believe large scale circulation plays a\nminor role while small scale circulation and convection can be more important. Moreover, is this phenomenon can be related to\n‘monsoons’? However, even during monsoon seasons, strong precipitation across the India and southeast China can be the same…\nCan the authors discuss or analyze more details about how the monsoon affect the different scaling across India, southeast China,\nand Indonesia, respectively?\n(https://scied.ucar.edu/learning-zone/storms/monsoons)\n2. Secondly, I still consider that in the main text, dividing all scaling patterns into tropics, mid-latitude, high latitudes are not\nthat appropriate? Maybe it’s not a big problem, but since the authors have already global maps, why they always tend to\ngroup the results into 3 region boxes? Since there are discernable zonal differences of the scaling rates. Further, does the\naridity can affect the scaling rates or cloud effects? For example, how does the observed scaling rates varies and how cloud\ncooling affects the eastern North America (belongs to humid areas) and the western North America (belongs arid areas),\nrespectively? Finally, it seems that topography can also affect scaling (e.g., different scaling between the Himalaya mountain\nregions and southeast Asia). Although it is not the target of this research, the authors can have a short discussion.", "reviewer_2": "The revised manuscript addresses all my comments adequately. I recommend the manuscript be accepted for publication\nafter some very minor changes as stated below. I do not need to see the revision again.\n1. The descriptions about figure S4ab are unclear and confusing. I do not understand NASA-CERES temperature. From the\n“dataset used”, I see CPC temperature but no NASA-CERES temperature.\n2. In LINE 465, equation (S3) is referred but nonexistent. Please check equation numbers in the text.", "reviewer_3": "I co-reviewed this manuscript with one of the reviewers who provided the listed reports. This is part of the Nature\nCommunications initiative to facilitate training in peer review and to provide appropriate recognition for Early Career\nResearchers who co-review manuscripts."}, "author_response": "We thank the reviewers for investing their time and effort in reviewing our manuscript and for\nthe positive and though8ul assessment of our work. The manuscript is accordingly revised as\nper reviewer’s comments and suggestions, with the point-by-point response mentioned in this\ndocument. The reviewer comments are shown in Black and our responses are shown in Blue.\nAll the reviewer comments have been marked for reference as R1_C1, R1_C2 respectively. The\nreply is composed of a “response” to the comment and “action” taken in the main\nmanuscript/supplementary file.\nReviewer #1 (Remarks to the Author):\nR1.C1: The authors address most of mine concerns, this is good. However, I s0ll have some\ndoubts regarding the scaling paNerns across India and southeast China. The authors argue\nthat ‘different regimes of how CRE scales with rainfall may likely relate to the contribu0on\nfrom large scale and convec0ve rainfall events.’ Since it is tropics, I would like to believe large\nscale circula0on plays a minor role while small scale circula0on and convec0on can be more\nimportant. Moreover, is this phenomenon can be related to ‘monsoons’? However, even\nduring monsoon seasons, strong precipita0on across the India and southeast China can be\nthe same… Can the authors discuss or analyze more details about how the monsoon affect\nthe different scaling across India, southeast China, and Indonesia, respec0vely?\nResponse: Thanks for the comment. We agree with the reviewer that in the tropics small-scale\ncircula0on and convec0on will play a major role. We believe that different regime of how\ncloud radia0ve effects (CRE) scales with rainfall mainly relate to spa0al structure of cloud-\ncover and its areal spread. NASA-CERES data only provides a spa0al CRE across a 1°x1° grid\nresolu0on and might not be able to truly represent the small-scale dynamics of cloud-cover.\nWe believe this is an important effect but will ideally require Flux-tower observa0ons across\nthese regions to diagnose this at local scales and have been kept out of scope for present\nstudy.\nAbout the role of monsoon: this is a very good point. We looked more into how monsoon can\naffect scaling over these regions. We isolated the grid across south Asia into three regions:\nIndian region, Eastern China and South Eastern countries Thailand, Laos and Vietnam. While\nthe scaling aaer removing the cloud-radia0ve effects is posi0ve and quite uniform\neverywhere, the eastern humid region of China also showed posi0ve scaling with observed\ntemperatures (Fig. R1, below). We have already aNributed it to how CRE scales with\nprecipita0on over these regions (Supp. Fig. S11).\nWe then also looked at the seasonal cycles of precipita0on, temperature and cloud-radia0ve\neffects over these regions. We find that the Indian and South east asia region shows a strong\nskewness in the annual temperature varia0ons (due to strong monsoon seasonality) leading\nto high pre-monsoon temperatures (extreme lea and right column in figure R1), while this\neffect is absent across the Eastern China region which despite having a monsoonal seasonality\nalso receives some rainfall throughout the year. The presence of high pre-monsoon\ntemperatures has already been argued to exacerbate nega0ve scaling by intensifying the bin-\nshiaing effects (Ali & Mishra, 2017; Ghausi et al., 2022; Dash & Maity, 2022) and this effect\nwas found to be absent across Eastern China region.\nAction: Text is added in lines 221-225 of the revised manuscript.\nFigure 1: (top row) Maps of Extreme precipita3on sensi3vi3es before and a8er removing the radia3ve effect of clouds\nrespec3vely. (BoAom row) Seasonal cycles of precipita3on, temperature and cloud-radia3ve effects over (le8) Indian\nmonsoon region, (middle) Eastern China region and (right) South Eastern countries: Thailand, Laos and Vietnam.\nR1.C2: Secondly, I s0ll consider that in the main text, dividing all scaling paNerns into tropics,\nmid-la0tude, high la0tudes are not that appropriate? Maybe it’s not a big problem, but since\nthe authors have already global maps, why they always tend to group the results into 3 region\nboxes? Since there are discernable zonal differences of the scaling rates.\nResponse: Thanks for the comment. We totally agree with the reviewer that there are\ndiscernable zonal differences in the scaling rates visible from the maps. However, we chose to\ngroup the results into three regional categories (tropics, mid-la0tudes, and high la0tudes) for\ntwo main reasons:\n1) Reduce variability: Displaying scaling curves globally, especially for each land grid,\nintroduces substan0al interzonal variability. By categorizing into tropics, mid-la0tudes,\nand high la0tudes, we significantly reduce this variability, resul0ng in clearer and more\ninterpretable visualiza0ons.\n2) Maintain consistency with other studies: Monotonic decreasing scaling in the tropics,\nhook-shaped scaling in the mid-la0tudes and monotonic increasing scaling at high\nla0tudes have been widely argued in literature (Utsumi et al., 2011; Yin et al., 2018).\nRecent studies that address this issue have divided the scaling in similar la0tudinal bins\n(Tian et al., 2023). To maintain the consistency of results with other studies we\nadopted a three-region approach.\nR1.C3: Further, does the aridity can affect the scaling rates or cloud effects? For example, how\ndoes the observed scaling rates varies and how cloud cooling affects the eastern North\nAmerica (belongs to humid areas) and the western North America (belongs arid areas),\nrespec0vely?\nResponse: This is a very good point. First, we would like to point out that aridity is closely\nrelated to cloud-cover. Temperature varia0ons across aridity gradient have been shown to be\nstrongly modulated by cloud-radia0ve effects (Ghausi et al., 2023). This also makes cloud-\nradia0ve effects to differ considerably across dry and humid regions.\nSecondly, Nega0ve scaling has been widely argued to be due to moisture limita0ons (higher\naridity). While we show that cloud radia0ve effects can clearly explain nega0ve scaling across\nmost global land regions. There s0ll exist some dry regions where nega0ve scaling persists\neven aaer removing the cloud-cooling effects. This can be seen in arid region of western North\nAmerica and Sahara. This means that over these regions the moisture limita0on (aridity) may\nbe the major driver of nega0ve scaling compared to the effect of clouds. We have already\nnoted this point in lines (225-228) of the manuscript, but agree that a more comprehensive\nanalysis of aridity's role could strengthen the discussion.\nTo first demonstrate specifically about North America that reviewer pointed out, we show in\nfigure R2, the maps of aridity, net cloud radia0ve effects, observed and clear-sky scaling over\nthis region. We can clearly see that in the arid western region (figure R2 A), the cloud radia0ve\neffects are much less strong (Fig. R2 B). Ini0ally the nega0ve precipita0on scaling persists\nacross the whole regions (Fig. R2 C). However, aaer removing the cloud radia0ve effects,\nscaling across most of the eastern humid regions became posi0ve while some nega0ve scaling\ns0ll remained over western arid region (Fig. R2 D). We believe that this scaling is due to\nmoisture availability limita0ons and cannot be explained by the effect of clouds.\nTo demonstrate this effect at the global scale, we first show in figure R3A that the net cloud\nradia0ve effects become weaker as we go towards drier regions indica0ng less clouds. The\neffect of clouds in modula0ng surface temperatures across the aridity gradient have been\ndescribed in detail in Ghausi et al., (2023). Secondly, we show that clear-sky extreme\nprecipita0on-temperature sensi0vi0es also shows a first-order reduc0on as we go towards\ndrier regions (Fig. R2B). This shows that moisture availability limita0on could s0ll play an\nimportant role in explaining nega0ve/reduced scaling over dry regions.\nAction: Text is added in lines 229-233 of the revised manuscript. Fig. R3 is added as new\nsupplementary figure S16.\nFigure R2: Maps over North America grids for (A) Budyko Aridity Index (defined as the ra3o between mean net radia3on\nand the energy equivalent to mean annual precipita3on),where higher values indicate more arid condi3ons. (B) Net Cloud\nRadia3ve Effect (W/m²). (C) Observed extreme precipita3on- temperature Scaling (D) Extreme precipita3on-temperature\nscaling a8er removing the effect of clouds.\nFigure R3: Varia3on along the Budyko aridity index (defined as the ra3o between mean net radia3on and the energy\nequivalent to mean annual precipita3on),where higher values indicate more arid condi3ons of (A) Net Cloud radia3ve\neffects (W/m2) and (B) Extreme precipita3on-temperature scaling a8er removing the effect of clouds.\nR1.C4: Finally, it seems that topography can also affect scaling (e.g., different scaling between\nthe Himalaya Mountain regions and southeast Asia). Although it is not the target of this\nresearch, the authors can have a short discussion.\nResponse: Thanks for the comment. The topography indeed plays an important role in\naffec0ng the scaling due to several reasons:\n1) The presence of orographic liaing can substan0ally deviate precipita0on sensi0vi0es\nto follow the thermodynamic scaling and the dynamic factors become much more\nimportant over these regions (Moustakis et al., 2020).\n2) Due to changes in the local radia0ve environment at high eleva0on regions, the\nsensi0vity of surface temperatures to changes in cloud-cover can vary significantly\ncompared to low eleva0on regions. For instance, high eleva0on regions have been\nshown to be much more sensi0ve to changes in the atmospheric emissivity and\ndownwelling longwave radia0on which can influence the magnitude of net cloud\nradia0ve effects associated with rainfall events.\nAction: We have added a short discussion about it in the main text. Text added in lines 226-\n228 and 317.\nReviewer #2 (Remarks to the Author):\nThe revised manuscript addresses all my comments adequately. I recommend the\nmanuscript be accepted for publication after some very minor changes as stated below. I do\nnot need to see the revision again.\nR2.C1: The descriptions about figure S4ab are unclear and confusing. I do not understand\nNASA-CERES temperature. From the “dataset used”, I see CPC temperature but no NASA-\nCERES temperature.\nResponse: We apologize for not being clear. From NASA-CERES temperatures, we refer to\nthe surface temperatures diagnosed using upwelling longwave equation from NASA-CERES\ndataset. We have now clarified it in the caption.\nAction: Caption of figure S4a, b is revised.\nR2.C2: In LINE 465, equation (S3) is referred but nonexistent. Please check equation\nnumbers in the text.\nResponse: Thanks for pointing this out. We have made the correction.\nAction: We have corrected the text."}, {"round": 3, "reviewer_comments": {"reviewer_1": "All my concerns have been well addressed and I consider at this stage it can be accepted."}, "author_response": ""}]

Decision letter