File generated with AMS Word template 2.0 SIGNIFICANCE STATEMENT Negative scaling, a decrease of extreme precipitation at high local temperature, is a poorly understood phenomenon. It was suggested that the negative scaling may be a reflection of precipitation's influence on temperature. Here we show based on observational data, reanalysis data and climate models that the negative scaling results primarily from the impact of high temperature-induced saturation deficit on precipitation over land and from storm-induced temperature variations over the ocean. In hot weather when moisture is limited (as is over land), large saturation deficit reduces precipitation intensity by slowing down the convective updraft condensation rate and accelerating condensate evaporation, leading to a negative scaling. The same mechanism can also contribute to increased compound drought and heat events.

As the global climate warms, observational data have shown an increase in the intensity and frequency of extreme precipitation (Fischer and Kutti 2016;Easterling et al. 2017), and this trend is expected to continue (Meehl et al. 2007;Allan and Soden 2008;Kharin et al. 2017;Prein et al. 2017). Because extreme precipitation is intrinsically related to low-level moisture convergence and tends to occur when the atmosphere is close to saturation, its intensity is often proportional to the moisture-holding capacity of the air near the surface of the Earth. Therefore, the Clausius-Clapeyron (C-C) relationship, which dictates the increase with temperature in the capacity of the atmosphere to hold moisture, can be used as a first-order approximation for the scaling of precipitation extremes with warming (Trenberth 1999).

The relationship between extreme precipitation intensity and concurrent local temperature (EPI-T), however, is confounded by several other factors and processes, including atmospheric stability, precipitation efficiency, orographic effect, convective organization, moisture limitation, and latent heat release feedback on storm intensity (e.g., O'Gorman and Schneider 2009; Loriaux et al. 2013;Muller 2013;Singh and O'Gorman 2014;O'Gorman 2015;Dai and Soden 2020). Therefore, it does not, and is not expected to, conform to the C-C scaling (Lenderink and van Meijgaard 2008;Sugiyama et al. 2009;Hardwick Jones et al. 2010;Chen et al. 2011;Utsumi et al. 2011;Mishra et al. 2012;Berg et al. 2013;Prein et al. 2017;Bao et al. 2017;Wang et al. 2017;Da Silva et al. 2020). Specifically, in the context of climate variability and at daily and sub-daily timescales over most of the globe, extreme precipitation increases with local temperature up to a certain threshold, beyond which a lower magnitude of extreme precipitation is associated with higher temperatures. This leads to a peak-shaped relationship curve, with negative scaling at higher temperatures. As the climate warms, both the magnitude of the extreme precipitation peak and the threshold temperature at which extreme precipitation reaches its peak are projected to increase, leading to an upper-rightward shift of the curve relating the two, especially for the increasing branch of the scaling curves (Prein et al. 2017;Wang et al. 2017;Drobinski et al. 2018) (Figure 1). For the descending branch, however, its variation with warming can be more elusive (Drobinski et al. 2018), and the negative scaling is projected to become spatially more widespread in a warmer climate (Wang et al. 2017). Wang et al. (2017) suggested that the C-C scaling is more likely to hold at the peak precipitation intensity (indicated by dots in Figure 1b), since the most intense File generated with AMS Word template 2.0 precipitation event tends to occur when the atmosphere is close to saturation, a condition conducive to C-C scaling (Wang & Sun, 2022). The negative scaling of extreme precipitation at high temperature, although well documented in numerous studies, is poorly understood. Many factors may contribute to it, ranging from artificial effects of the data resolution and the methodology used to analyze the data to true physical mechanisms linking precipitation processes with temperature (e.g., Barbero et al. 2018;Bao et al. 2018;Visser et al., 2021). If higher temperature led to precipitation events that were more intense but spatially or temporally more concentrated (Long et a., 2021), data at coarse resolution would not capture the true response of precipitation intensity to temperature (Utsumi et al. 2011;Wasko et al. 2015;Visser et al., 2021). Mixing data from different seasons might lead to the clustering of large-scale precipitation at low or medium temperature on one end and convective precipitation at high temperature on the other end, which complicates the results (Drobinski et al. 2016;Ali et al. 2018). For physical processes underlying the negative scaling, some have hinted at the possible role of moisture limitation in precipitation at high temperature (Hardwick Jones et al. 2010;Prein et al. 2017;Wang et al. 2017;Wang & Sun, 2022), but this mechanism may not work over oceans, where moisture supply is usually not a limiting factor. Some have pointed to the response of nearsurface air temperature to synoptic conditions and precipitation processes, including warming associated with anticyclonic weather systems (Trenberth and Shea 2005;Chan et al. 2016) and cooling during heavy precipitation events (Bao et al. 2017), but this notion is a subject of inconclusive debate (Barbero et al. 2018;Bao et al. 2018). The lack of a consistent relationship File generated with AMS Word template 2.0 between surface air temperature and atmospheric moisture content may also cause the negative scaling between precipitation extremes and temperature (e.g., Roderick et al. 2019).

Despite the many studies on the relationship between extreme precipitation and temperature, the very nature of the negative scaling is not clearly understood; while not without exception (Visser et al., 2021), comments on the possible causes for negative scaling are often given without direct substantiating evidence. The projected increase in the spatial extent of negative scaling is subject to a similar lack of understanding (Wang et al. 2017). In the current study we aim to establish clear evidence for the negative scaling of extreme precipitation at high temperature, understand the nature of this negative scaling, assess its sensitivity (or the lack of such) to non-physical factors such as spatiotemporal resolution and seasonality, and tackle the physical mechanisms that underlie the negative scaling and its potential implications for future changes. We demonstrate that, for most regions over land at the weather timescale, the intensity of warm-season precipitation extremes decreases at high temperature, and this negative scaling is primarily a reflection of precipitation intensity being suppressed by temperature-induced large saturation deficit. Over oceans except for the subtropical dry zones, negative scaling is also found and results primarily from storm-induced temperature variations stemming from the combined impact of evaporative cooling and cloud radiative effect. As illustrated in Figure 1, the negative scaling at the weather timescale does not contradict the observed and predicted warming-induced increase of extreme precipitation at the climate timescale. The remainder of this article is organized as follows. Section 2 provides a description of the datasets and models used, while Section 3 details the methodologies applied, including the binned scaling analysis and diagnostics related to atmospheric convection. Section 4 presents a thorough examination of the robustness of negative scaling at high temperature, and illustrates the underlying physical mechanisms by exploring the interactions between temperature and precipitation processes, as well as the role of large-scale systems. Conclusions and discussion are given in Section 5.

Data from four sources are used in this study. These include the observational Integrated Multi-satellitE Retrievals for Global Precipitation Measurement (IMERG, Final Run version 6, Huffman et al. 2019), the European Centre for Medium-Range Weather Forecasts (ECMWF) fifth generation reanalysis data (ERA5, Hersbach et al. 2020), output from global simulations carried out for this study using the Community Earth System Model (CESM) version 1.2.2.1, File generated with AMS Word template 2.0 and output from the National Center for Atmospheric Research (NCAR) continental-scale convection-permitting modeling of North America (Liu et al. 2017) using the Weather Research and Forecasting (WRF) model version 3.4.1 (Skamarock et al. 2008).

The half-hourly, 0.1º resolution IMERG is the successor of the Tropical Rainfall Measuring Mission (TRMM) 3B42 precipitation data (Huffman et al. 2007) from the National Aeronautics and Space Administration (NASA). It is an adjusted precipitation product based on estimates from various precipitation-relevant satellite passive microwave sensors comprising the Global Precipitation Measurement (GPM) constellation; it is available for the period June 2000 to near the present and nominally covers the entire globe (primarily for unfrozen surfaces between 60º S and 60º N). The global ERA5 is the successor of ECMWF interim reanalysis (ERA-Interim, Dee et al. 2011) and uses a more advanced assimilation scheme. The ERA5 precipitation at approximately 30 km grid spacing is model simulated and available at every hour from 1950 to near real time; the 2-m air temperature in ERA5 is a reanalysis product that assimilates observed surface air temperature. Also available from ERA5 are dewpoint temperature and surface pressure, which are used to derive the 2-m saturation deficit following the approach of Byrne and O'Gorman (2018). As in Wang et al. (2017), the IMERG precipitation is paired with ERA5 2-m air temperature or 2-m saturation deficit to support the analysis on observed scaling, which we refer to here as "IMERG"; we refer to scaling analysis as "ERA5" if both precipitation and 2-m air temperature or saturation deficit are from ERA5. For comparison purposes, all IMERG and ERA5 analyses are also repeated based on TRMM and ERA-Interim.

The CESM global simulation is performed at f19 spatial resolution (approximately 1.9º × 2.5º) and over the period 1986-2013 (with the first five years deemed model spin-up), using prescribed sea surface temperature and sea ice fraction according to observations from the Hadley Centre and the National Oceanic and Atmospheric Administration (NOAA) (Hurrell et al. 2008). The atmospheric component is the Community Atmosphere Model, version 5.3 (Neale et al. 2012), with 30 vertical levels; the land component is the Community Land Model 4.5 with satellite phenology (Oleson et al. 2013). To represent present-day climate, the land surface is initialized according to year 2000 conditions (Oleson et al. 2013), and aerosol concentration, CO2, and other trace gases are all fixed at their year 2000 levels. In addition to daily and 3-hourly model output for the entire simulation period, model output is also saved for every time step (30 minutes) during the five-year period from 1991 to 1995 to examine the sensitivity of extreme precipitation scaling analysis to temporal resolution.

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The WRF convection-permitting simulation is conducted at 4-km grid spacing for the contiguous United States (and is referred to as "WRF4km" hereafter), driven with initial and boundary conditions from ERA-Interim for the period October 2000 to September 2013 (Rasmussen and Liu 2017;Liu et al. 2017). In this study, both the hourly and the aggregated 3-hourly and daily WRF4km data are used to examine the sensitivity of the scaling relationship to temporal resolution.

Figure S1 compares the precipitation climatology for the June-July-August (JJA) and December-January-February (DJF) seasons from all four data sources at their native resolution.

Both CESM and WRF reproduce the large-scale precipitation climatology reasonably well.

Discrepancies in certain regions can be large, especially for CESM. Precipitation during DJF, for example, is strongly underestimated by CESM over the Amazon basin, a common global model deficiency also found in other studies (e.g., Zhang et al. 2017). Moreover, CESM also captures the global pattern of extreme precipitation in comparison with IMERG and ERA5, although the magnitude is much lower as expected from coarse-resolution (~200 km) simulations (not shown).

Using data from each of the four sources respectively, we identify and track the extreme precipitation events under different temperatures, and analyze how extreme precipitation scales with temperature and other variables (e.g., saturation deficit) at different lead/lag times. For CESM, additional diagnostics related to precipitation and convection are examined to further understand the physical processes underlying the negative scaling of precipitation extremes at high temperature. In addition to global analysis, 16 sample regions (Figure S2) over land and ocean spanning the tropics and extratropics are chosen for more detailed analysis. Due to computational constraint, especially for event tracking, we aggregate the half-hourly IMERG, hourly ERA5 and hourly NCAR WRF model output as 3-hourly data for most of the analysis.

In section 4a, we demonstrate that this treatment does not impact the results because the sensitivity to temporal resolution is minimal as also found in previous studies (e.g., Drobinski et al. 2018). It should be noted that the focus of this study is on extreme precipitation scaling with temperature and therefore the surface air temperature is used as the covariate of precipitation intensity. Some past studies used dewpoint temperature as the precipitation covariate (see Fowler et al. 2021 for a comprehensive review). However, since dewpoint is a measure of specific humidity, it is not suitable for this study.

File generated with AMS Word template 2.0 a. Binned scaling analysis Our primary EPI-T scaling analysis is based on sub-daily data and conditional on nearsurface air temperature (taken as local 2-m air temperature), following the approach of Wang et al. (2017). Rather than using daily averaged temperature and sub-daily precipitation to reduce the imminent impact of precipitation on temperature as in Drobinski et al. (2018) andDa Silva et al. (2020), we analyze both temperature and precipitation at the sub-daily timescale to explore their interactions. This choice is also necessitated by our event tracking and lead-lag analysis that require sub-daily data. Specifically, all sub-daily precipitation data in each specific area within the analysis period are first binned according to the corresponding nearsurface air temperature, and a bin size of 0.5º C is used. For each temperature bin, the 99 th percentile of precipitation is identified, and the extreme intensity is then defined as the average of precipitation rates that exceed the 99 th percentile within the bin, and the corresponding nearsurface air temperatures are averaged to represent the bin temperature. Temperature bins with fewer than 1,000 data points, typically found at the lowest and highest ends of local temperature variations, are discarded. The resulting precipitation extremes are smoothed (using a three-bin moving average) to characterize the scaling relationship between precipitation extremes and near-surface air temperature, and to identify the temperature at which extreme precipitation peaks, denoted as Tpeak. A similar binned analysis is also conducted to derive the relationship between sub-daily precipitation and near-surface saturation deficit (EPI-SD), using a bin size of 0.5 g kg -1 .

For all precipitation events underlying each "extreme" data point within each temperature bin, we then track the temporal variation of precipitation, temperature, and some convectionrelated variables to assess the timing and magnitude of changes of temperature (and other variables) during storm development. This analysis enables us to evaluate whether the temperature differences between storm events in different bins are already present before storm development or caused by the storm, and to quantify how much of the difference can be attributed to the storm.

The aforementioned analyses are conducted globally and for each of the 16 representative regions as well. The global analysis is not based on each individual grid cell; instead, data from 25 grid cells centering around each grid cell is pooled together to increase the sample size in the extreme analysis. To compare data from the four different sources, the scaling analyses are conducted over their common period, December 2000 to August 2013, focusing on the warm season (JJA for the Northern Hemisphere and DJF for the Southern Hemisphere) when convective precipitation is dominant. Because of differences in spatial resolution, the number of grid cells needed to cover a specific representative region can differ dramatically across different datasets. To ensure similar spatial coverage for each region across all datasets, some resampling is necessary. For study regions within the contiguous United States, we resample IMERG, ERA5, and WRF4km to a 64-km resolution on the WRF grid (WRF64km-G or simply WRF). For regions outside the contiguous United States, we resample the IMERG precipitation to the ERA5 grid. To preserve the characteristics of precipitation extremes, no spatial interpolation is conducted; instead, resampling simply takes the raw data from the closest grid point. Overall, 169 (13 × 13) grid cells from WRF64km-G and 1089 (33 × 33) grid cells from ERA5 occupy an area similar to that of 25 (5 × 5) grid cells from CESM (Figure S2). Subject to computer memory constraint, the ERA5 grid has to be resampled at every other grid point before conducting scaling analysis. This leads to a total of 289 (17 × 17) grid cells that are eventually used for the scaling analysis based on the ERA5 grid. As is evident from Figures S3 andS4, the details of the resampling process do not influence the qualitative scaling behavior of precipitation extremes. This result is consistent with Drobinski et al. (2018), showing minimal sensitivity of EPI-T scaling to spatial resolution.

To explore the physical processes underlying the negative scaling of precipitation extremes at high temperature, we analyze diagnostics directly related to atmospheric convection, including the cumulus updraft condensation rate, cumulus downdraft evaporation rate, and downdraft convective available potential energy. Limited by the availability of data for the needed variables, the diagnostics described here are based on CESM output only.

Following Houze et al. (1980)

where p is atmospheric pressure, i p is the pressure from which the parcel starts to descend, n p is surface pressure or the pressure where a descending parcel achieves neutral buoyancy (whichever is smaller), d R is the gas constant for dry air, and e T ρ and p T ρ are the density temperature of the environment and air parcel, respectively (Emanuel 1994). Because the maximum kinetic energy that a descending parcel can achieve is proportional to DCAPE, DCAPE can be used as an indicator of maximum downdraft strength within storms: the higher the value of DCAPE, the stronger the downdraft could potentially be. DCAPE for each temperature bin is estimated using the average air temperature and water vapor mixing ratio corresponding to the extreme precipitation rates in that temperature bin. We adapt the DCAPE calculation from Emanuel (1994), which eliminates the need for total water mixing ratio information by assuming that the parcel is cooled isobarically through a wet-bulb process before descending pseudo-adiabatically with just enough evaporation to keep it saturated.

DCAPE, as an indicator of maximum downdraft when precipitation supply is sufficient and background wind shear is absent, is not a direct measure of the actual downdraft strength.

However, its response to temperature variation is consistent with that of the estimated cumulus downdraft evaporation rate d E (as shown later in the Results section), lending confidence to the accuracy of both diagnostics and their relevance as a metric for downdraft strength.

For the EPI-T relationship based on data from all seasons, the negative scaling at high temperature is dominated by precipitation events from the warm season (which coincides with the wet season in many regions) (Wang et al. 2017). Lumping data from warm and cold seasons together mixes convective and large-scale precipitation regimes, which may lead to an artificial negative scaling that does not reflect a true physical process relating extreme precipitation to temperature. We therefore focus on the warm season only, when convective precipitation is abundant and dominant. The 16 regions in Figure S2 are used to sample different climate regimes in the tropics and extratropics.

Figure 2 compares the EPI-T relationship for the 16 sample areas using sub-daily data from all four sources during their overlapping period (2001)(2002)(2003)(2004)(2005)(2006)(2007)(2008)(2009)(2010)(2011)(2012)(2013). The magnitude of precipitation extremes differs remarkably among the four sources and generally increases as the native resolution of the data becomes finer from CESM to ERA5 to IMERG and WRF. Relative to the observational reference IMERG, CESM substantially underestimates the intensity of extreme precipitation at sub-daily timescales, while WRF overestimates the extreme precipitation intensity compared with ERA5, which shows an overall agreement with IMERG (solid lines in Figure 2). Despite these rather substantial differences among the four data sources in the magnitude of precipitation extremes, and despite the vastly varying climate regimes of the 16 sample regions, the EPI-T relationships derived from all data sources for all sample regions are qualitatively similar and feature a negative scaling at high temperature (solid lines in Figure 2). The increasing branch of the scaling curves at lower temperatures can be minimal or even absent because the near-surface air temperature during the warm season is mostly above the threshold temperature at which the extreme precipitation peaks (Tpeak). The increasing branch would be more prominent and dominated by winter precipitation if the scaling curves were derived using data from all seasons (e.g., Wang et al. 2017). File generated with AMS Word template 2.0

The negative EPI-T scaling relationship is robust against the data temporal and spatial resolutions. As the temporal resolution changes from sub-hourly to hourly, three-hourly, and daily, the intensity of the precipitation extremes from all four data sources decreases, but qualitatively, the overall EPI-T relationship does not change (Figure 4

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To assess the impact of precipitation and its associated weather systems on near-surface air temperature, we track all individual storm events underlying the identified "extremes" within each temperature bin to examine how temperature and other variables evolve during a storm's lifetime. In this "storm tracking" analysis, we apply a 24-hour moving average to all time series to remove the diurnal cycle and focus on storm-induced variations. For most regions, nearsurface air in the warm and hot bins generally experiences slight cooling (or even warming) before the time of the storm peak, while near-surface air in the cold and threshold bins experiences stronger cooling. Most of the temperature changes occur within the 24 hours before the storm peak, as shown in Figure 5 using the U.S. Southern Great Plain as an example. Results for all sample regions are presented in supplementary Figures S6-S9 for IMERG, ERA5, CESM, and WRF, respectively. This cooling is closely related to cloud radiative effects that are the strongest within 24 hours before and after the storm peak (as evident from the surface insolation plot in Figure S10 using CESM as an example). In CESM for most sample areas, cloud content is much higher during storm events in the cold and threshold bins than those in the warmer bins, and the transition from predominantly low-level clouds to medium-and highlevel clouds (reflecting the transition from shallow to medium and deep convection) occurs within one day before the storm peak (Figures S11-S12). The other cooling process, through evaporation of rain droplets in the lower troposphere and water at the surface, occurs more imminently to the precipitating process. Therefore, one day before the storm peak is sufficient to capture most of the storm's impact on temperature; earlier temperature differences between bins reflect variations not directly related to the imminent storm events. In most land areas, the range of temperature variation in the absence of storm events is large (as reflected by the distance between lines at -1 day in Figure 5 and Figures S6-S9), and File generated with AMS Word template 2.0 the bin-to-bin temperature difference at the storm peak results from the combination of stormfree temperature variations and storm-induced temperature changes. Based on data from all four sources, over most of the land regions examined, less than 25% of the temperature differences at the storm peak between the cold (or threshold) and hot bins are attributable to the storm-induced temperature changes (Figure 6). Over most oceanic areas sampled, temperature variation in the absence of storm events is small or negligible as indicated by the small temperature difference across different temperature bins one day ahead of the storm events (e.g., in the subtropical Pacific (East), Figures S6-S9); and storm-induced temperature change generally accounts for over 60% of the differences between temperature bins (Figure 6). So the impact of precipitation process (or the lack of it) on temperature plays an essential role in shaping the EPI-T relationship over oceans. While results from the four data sources show some quantitative differences, they are remarkably similar in terms of the clear contrast between land and ocean, with a substantially higher fraction of temperature differences attributable to storm-induced variations over oceans than over land. T - ∆ at one day (24 hours) ahead.

The storm's impact on near-surface air temperature has been emphasized in previous studies focusing on the negative scaling of extreme precipitation. In general, heavier precipitation tends to produce stronger evaporative cooling, and this cooling unavoidably would shift the events toward lower temperature bins (Bao et al. 2017). To eliminate the impact of storm-induced temperature change, we adjust the EPI-T curve in Figure 2 by shifting extreme precipitation data to a bin pertaining to the temperature 24 hours before the storms' peak; this results in the dashed lines in Figure 2. For most areas over land, even though using File generated with AMS Word template 2.0 the antecedent temperature does shift extreme events among temperature bins, the adjusted EPI-T curve (with storm-induced cooling or warming removed; dashed lines in Figure 2) retains the general shape of the original, with a negative scaling at high temperature.

Differences between the original and adjusted curves are more substantial over oceanic areas. This further confirms that storm-induced temperature change is not the primary cause of the negative scaling over land, although it plays an important role over oceans. This strong contrast between land and ocean might be due to the abundance of low-level clouds over oceans during the development of heavy storms (Figures S11-S12), which tends to produce an overall cooling effect. In combination with evaporative cooling, the impact of precipitation process on nearsurface air temperature is thus amplified over the ocean.

To assess the impact of temperature on precipitation, we analyze the lagged EPI-T relationship on various sub-daily timescales, with near-surface air temperature leading precipitation by up to 18 hours to reduce or eliminate the impact of precipitation process on temperature. As the lead time increases from zero to 18 hours, the presence of negative scaling at high temperature and the general shape of the scaling curve are qualitatively preserved for all regions. This holds regardless of whether data from IMERG, ERA5, CESM, or WRF are used (Figure 7 using the U.S. Southern Great Plain as an example; results for all 16 sample areas in Supplementary Figures S13-S16). These results, together with the high degree of similarity between the solid and dashed curves in Figure 2, suggest that temperature's impact on precipitation plays an important role in the negative scaling of precipitation extremes at high temperature.

In Figure 7 and Supplementary Figures S13-S16, as the lead time increases, the curves shift and the corresponding Tpeak values change accordingly. Over most land areas and relative to the scaling curve with lead time zero, the deviation generally increases with lead time in CESM, but increases and then decreases with lead time in IMERG, ERA5 and WRF. Based on data at the sub-daily resolution, the scaling curve (especially Tpeak) is influenced by the diurnal cycle of temperature. If heavy precipitation tends to occur at a certain time of the day (e.g., in IMERG, ERA5 and WRF), the scaling curve will shift away from the concurrent curve as the lead time increases from zero and shift back towards the concurrent curve when the lead time approaches 24 hours. This does not occur in CESM, indicating that heavy precipitation might not have a clear "preferred time" in the coarse-resolution CESM simulation. Based on the comparison of the CESM results with those from IMERG and ERA5 (Figures 234567), it is evident that, although CESM does underestimate the Tpeak percentile, it is capable of capturing the negative scaling of extreme precipitation at high temperature. We therefore make use of CESM to study atmospheric convection under high temperature. At the process level, the decrease in extreme precipitation at high temperature in CESM is dominated by a decrease in the cumulus updraft condensation rate, with a minor contribution from enhanced evaporation in the atmosphere (Figure 8). Consistent with observational studies (Berg et al. 2013), in the high temperature range, the CESM-simulated extreme precipitation (gray lines in Figure 8) is primarily from cumulus convection (black lines), and the decrease in extreme precipitation at high temperature is dominantly a decrease in extreme convective precipitation with temperature. The convective precipitation relationship with temperature closely tracks the cumulus updraft condensation rate (blue lines), which increases with temperature and then decreases or levels off as temperature exceeds a certain threshold. Meanwhile, the cumulus downdraft evaporation rate (magenta lines), albeit small in magnitude, either increases with temperature or decreases more slowly than precipitation in most selected areas. This is consistent with the column maximum downdraft convective available potential energy (DCAPE) that peaks at high temperature (Figure S17). As large DCAPE tends to produce strong downdrafts that bring drier air from upper levels, evaporation tends to be stronger when temperature is high. Adding the downdraft evaporation back to extreme precipitation leads to a scaling curve (black dashed lines) with a flattened descending branch (relative to the EPI-T scaling curve) but is insufficient to qualitatively change the nature of the scaling. These results indicate that the slowing down of cumulus updraft condensation rate at high temperature is the dominant process underlying the negative scaling of extreme precipitation in CESM. Further inspection of the cumulus updraft condensation rate reveals that its variation is primarily associated with variations in convective motion: the contribution of saturated ascent to condensation rate (2nd term of Eq. 1 in section 3b) is one order of magnitude greater than the direct impact of mixing dry air from the environment (1st term of Eq. 1 in section 3b)

(results not shown). This suggests that the negative scaling is due to suppression of convection at high temperature. Compared with the cold and threshold bins, where the entire air column is close to saturation in all 16 sample regions, the atmosphere in the warm and hot bins features greater saturation deficit (Figure S18). As convective updraft is typically saturated, the entrained air with greater saturation deficit at high temperature tends to deplete cloud buoyancy more efficiently (Brown and Zhang 1997;Redelsperger et al. 2002;Derbyshire et al. 2004;Takayabu et al. 2010). Moreover, as in high-resolution simulations (Romps 2010), in our study the updraft entrainment rate in CESM is also strong for weak convective activities at high File generated with AMS Word template 2.0 temperature (Figures S19-S20). Therefore, the enhanced saturation deficit is an important cause for the suppressed convection (consequently, negative scaling) at high temperature in CESM.

Atmospheric saturation deficit (SD) can be quantified using the difference between the saturation water vapor mixing ratio ( * r ) and the actual water vapor mixing ratio ( r ): r r = -) reflecting differences in water vapor mixing ratio. Figure 9 shows the vertical profile of ΔSD in CESM and the contribution of its two components using four sample regions as examples; results for other regions are similar (Figure S21). Across the whole vertical profile of the atmosphere, SD increases from the threshold bin to warm (blue lines in Figures 9 andS21) and hot bins (pink lines in Figures 9 andS21), and this increase is dominated by the temperature-controlled term (dotted lines) below ~600 hPa. Compared with the threshold bin, storm events in the warm and hot bins generally feature more water vapor in the lower troposphere, which tends to reduce the saturation deficit (i.e., 2 ΔSD is negative, dashed lines); the magnitude of this decrease, however, cannot offset the large increase induced by higher temperature (i.e., 1 ΔSD , dotted lines). At upper levels, the comparison is more complex, as temperature differences between different bins might not be consistent with the near-surface air temperature differences. The results in Figures 9 and S21 are consistent with the notion that r generally increases with temperature more slowly than * r does due to moisture limitation (Sherwood and Fu 2014). Based on results from our analysis of extreme precipitation binned according to nearsurface saturation deficit, extreme precipitation decreases monotonically as the saturation deficit increases over land (Figure 10). Over the ocean, a similar trend is found at relatively large saturation deficit, with some exceptions in the northern Atlantic and tropical Pacific (West) in IMERG and ERA5 when the atmosphere is close to saturation. Relative to the land areas, saturation deficit is much smaller over oceans due to the abundant moisture supply from the surface, with a sharp contrast of extreme precipitation over a small range of saturation deficit. Similar to temperature variation over oceans being dominated by storm-induced temperature change, the relationships in Figure 10 over the ocean are possibly a result of descending motion that brings dry air from aloft, which is to be further examined in Section 4d. This is consistent with the fact that the saturation deficit profiles over oceans are rather homogeneous across the low-and mid-troposphere (Figure S18). Over land, due to limited moisture supply and higher temperature, saturation deficit is large in the lower troposphere below ~600 hPa and rapidly diminishes with altitude. On the other hand, the impact of precipitation process (or the lack of it) on saturation deficit might also contribute to the relationship curves in Figure 10, including for example moistening by evaporation of rain and drying due to subsidence. These effects, however, are important over oceans only and are not the dominant process underlying the relationship shown in Figure 10 over land. This is confirmed through tracking the near-surface saturation deficit prior to and during extreme precipitation events . Over most land areas, the nearsurface saturation deficit contrasts among different temperature bins already exist prior to the development of storm events, and precipitation processes modify the saturation deficit differences only slightly . This is a strong indication that the relationship shown in Figure 10 for the land areas is a result of saturation deficit influencing extreme precipitation, not the other way around. Over the ocean, however, the near-surface saturation deficit is similar among the various temperature bins prior to the storm events, and differences among the bins develop during and after the storm events. The relationship shown in Figures 10 and 11 for oceanic areas is therefore a reflection of temperature (and saturation deficit) responding to precipitation process over the ocean. This notion is further corroborated by the breakdown of a monotonic relationship between saturation deficit and extreme precipitation in the northern Atlantic and tropical Pacific (West) in IMERG and ERA5 (Figure 10).

As both temperature and precipitation respond to large-scale systems, a negative EPI-T scaling at high temperature may result from anomalous large-scale conditions. In any given region, for instance, near-surface air temperatures are usually high during dry spells, when heatwaves are prevalent and moist convection tends to be suppressed; similarly, large-scale descending motion suppresses convection (precipitation) and meanwhile induces adiabatic warming of the land surface. In some regions, climatological conditions have a specific subseasonal pattern that may cause an apparent negative scaling. Taking the U.S. Midwest as an example, July and August are generally warmer than June, while the large-scale setting in June is more favorable for convection and precipitation. To examine the impact of a large-scale system on the EPI-T relationship through its influence on both temperature and precipitation, we experiment using two additional approaches to derive the binned EPI-T scaling curves. In one, we randomly sample the temperature and precipitation data in time to break continuous dry spells and use only one-third of the rainy season data from each source (Figure S26). In the File generated with AMS Word template 2.0 other, we derive the scaling curves for each month separately to eliminate the effects of climatological sub-seasonal variations (Figure S27). Regardless of which data source we use, the results (Figures S26-S27) are all qualitatively similar to those based on all wet season data in Figure 2 (solid lines), suggesting that anomalous large-scale conditions are not the dominant cause for the overall shape (and the negative scaling) of the EPI-T relationship.

The CESM 850-hPa geopotential height ( 850Z ) anomalies (Supplementary Figures S28- S29) also show no clear cyclonic-anticyclonic contrast between the cold bin (or threshold bin)

and the hot bin (or warm bin). In the warm bins, cyclonic (as opposed to anticyclonic) largescale systems occur more frequently than the warm season mean condition over all regions, as indicated by the negative 850 Z anomalies, except for the Amazon; in the hot bins, the negative 850 Z anomalies persist in most regions, except for the Amazon, the U.S. Midwest, and Central

Europe. Over the tropical Pacific (East and West) and tropical Atlantic, the overall impact of large-scale systems is minimal, as indicated by the correspondingly small magnitude of 850 Z anomalies. These results, in combination with the lack of anticyclonic anomalies in the northern Atlantic and tropical Indian (Figure S29), suggest that subsidence makes limited contributions in shaping the rather homogeneous vertical profiles of saturation deficit over the ocean (Figure S18). Instead, the rather uniform vertical profile of saturation deficit might be a result of other processes, such as dry air intrusion in the middle troposphere.

These results, in combination with results from the randomized and month-specific scaling analyses, suggest that, while variations of large-scale systems may contribute to the negative EPI-T scaling at very high temperature (hot bins) in some regions, they are not the fundamental cause for the negative scaling documented in this study.

Based on analysis of the observational IMERG data, the ERA5 reanalysis product, and output from the coarse-resolution CESM and convection-permitting NCAR WRF simulations, we show that the negative scaling of extreme precipitation at high temperature is a robust feature of the precipitation-temperature relationship at the weather timescale during the warm season. Although the magnitude of extreme precipitation varies with data source and spatiotemporal resolution, the negative scaling nature of the precipitation-temperature relationship remains qualitatively the same. These statements hold over both land and ocean.

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The primary mechanisms underlying the negative scaling differ between land and ocean.

We conclude that the negative scaling of warm-season precipitation extremes at high temperature over land results primarily from the heat-induced suppression of precipitation intensity. We base this conclusion on the concurrent and lead-lag relationships between temperature and extreme precipitation, and on the temporal evolution of temperature and saturation deficit during heavy storm events. Precipitation cooling and cloud radiative effects play a secondary role in the negative scaling over land, but are more fundamental over oceans.

Over land, temperature and saturation deficit differences between extreme precipitation events are already in place prior to the development of the storms; over oceans, such differences emerge during the development and occurrence of the storms. These conclusions, as well as the robustness of negative scaling at high temperature, remain unchanged when the analysis is based on alternative data versions, TRMM 3B42 and ERA-Interim (results not shown).

At the process level and at the weather scale, results from CESM diagnostics indicate that high temperature reduces precipitation intensity through the suppression of convective updraft condensation rate and the acceleration of condensate evaporation, both due to increased saturation deficit over land at high temperature. Over oceans, both the saturation deficit and its range of variation are small and have limited impact on convection and precipitation. Instead, the large contrast in extreme precipitation over a small range of saturation deficit over the ocean is a reflection of saturation deficit responding to evaporation of precipitation. To examine the robustness of this conclusion and its potential model dependence, one could repeat the convection-related diagnostics using output from the NCAR WRF convection-permitting simulation, but some variables needed for such analysis are not available from the fineresolution NCAR WRF model output (or similarly from ERA5 either). Nevertheless, the consistency between the diagnosed cumulus downdraft evaporation rate (Figure 8) and the DCAPE (Figure S17) lends certain confidence to our CESM-based process analysis.

The local processes shaping the relationship between extreme precipitation and temperature are always under the influence of large-scale systems. Large-scale weather systems (that persist for weeks or longer) may influence both precipitation and temperature, leading to an apparent negative scaling of extreme precipitation with temperature even in the absence of a causaleffect relationship between the two. Results from both the randomized analysis (that reduces the large-scale effects) and the month-specific analysis (that limits data to those under the climatologically same or similar synoptic settings) suggest that large-scale systems are likely File generated with AMS Word template 2.0 not a fundamental cause for the negative scaling. The analysis of 850-hPa geopotential height anomalies during heavy storms in different temperature bins supports a similar conclusion.

With the influence of large-scale systems, the precipitation-temperature relationship and its characteristics (e.g., the threshold temperature) may change quantitatively, but would likely remain qualitatively similar.

While this study focuses on the intensity of heavy precipitation, binned analysis on mean precipitation intensity (MPI, Figure 12) and number of rainy days (not shown) indicates that precipitation amount and frequency follow a similar scaling behavior with temperature, although the corresponding threshold temperatures differ. At the event level, precipitation duration, spatial coverage, and spatiotemporal distribution are important characteristics that may confound the precipitation scaling relationship with temperature. Long et al. (2021) based on station data found that rain events under high temperature tend to be more concentrated in space and time, which would favor more intense precipitation over a short duration or over a small area. Therefore, using data with a spatiotemporal resolution much finer than available to the current study may alleviate the negative scaling. Visser et al. (2021) found that negative scaling can be eliminated if the intensity scaling analysis is conditioned on short rain duration.

On the other hand, even at spatiotemporal resolutions as coarse as used in the current study, Wang and Sun (2022) found a monotonic increase of extreme precipitation intensity with temperature when the scaling analysis was conditioned on saturated atmosphere, consistent with the important role of saturation deficit proposed in this study. However, as rain duration cannot be reliably derived from coarse resolution gridded data, a comparison between the roles of rain duration and saturation deficit is beyond the scope of this study and will be tackled in follow-up research.

In the context of climate variability, temperature is not the only predictor for precipitation characteristics. Many other factors are at play and confound the scaling of precipitation with temperature, and soil moisture is one such factor. Closely coupled with local temperature, soil moisture influences precipitation processes through positive or negative feedbacks, depending on temporal and spatial scales (e.g., Barros and Hwu 2002;Findell and Eltahir 2003;Kim and Wang 2007;Koster et al. 2011;Mei and Wang 2011;Taylor et al. 2012). Functioning as an additional moisture source for the atmosphere, wetter soil enhances evapotranspiration and increases atmospheric moisture content, thus reducing saturation deficit. This may alleviate the negative scaling and shift the threshold temperature toward higher values. Another important File generated with AMS Word template 2.0 confounding factor is aerosol, through its direct effect on surface radiative budget (therefore temperature) and indirect effect on clouds (therefore precipitation) (e.g., Stevens and Feingold 2009;Tao et al. 2012;Rosenfeld et al. 2014;Khain et al. 2015;Da Silva et al. 2020). Specifically, Da Silva et al. (2020) showed that, due to the indirect effect of aerosols, high aerosol concentrations tend to suppress convective precipitation at low temperatures, leading to a super-CC scaling rate on the increasing branch of the EPI-T scaling curves. This effect, however, is likely not fundamental to the negative scaling at high temperature when clouds tend to be less frequent (Figures S11-S12). In fact, negative scaling is captured in the CESM simulation that prescribes aerosol concentrations (Section 2). Findings from this study have significant implications concerning the understanding of extreme events such as flood, drought, and heatwaves and for projecting their future changes.

In a warmer climate, Wang et al. (2017) and Drobinski et al. (2018) found that the peak-shaped extreme precipitation-temperature scaling curve, especially for its increasing branch, would shift upward and rightward (Figure 1), with increases predicted in both the peak of extreme precipitation and the threshold temperature at which the precipitation peaks. In fact, numerous studies have shown evidence from both modeling and observational perspectives for an increase in precipitation extremes with global warming, leading to increased flood risks (e.g., Allan and Soden 2008;Fischer and Kutti 2016;Prein et al. 2017;Wang et al. 2020;Wang & Sun, 2022). As warming continues, because the rate of warming is faster over land than over oceans and much of the moisture over land originates from oceans, the atmospheric relative humidity is expected to decrease and the saturation deficit to increase over land (Sherwood and Fu 2014).

Based on results from our study, this increased saturation deficit may lead to more widespread negative scaling of precipitation intensity with temperature, which provides a theoretical basis for the model-projected increase in the spatial extent of negative scaling (Wang et al. 2017).Because negative scaling occurs for both the extremes (Figure 2) and mean precipitation (Figure 12), this also means the combination of high temperature with low or lack of precipitation may become more prevalent, leading to increased co-occurrence of drought and heatwaves (Mazdiyasni and AghaKouchak 2015;Zscheischler and Seneviratne 2017), another important consequence of climate change for which this study offers a possible explanation.