Understanding compound extreme precipitations preconditioned by heatwaves over China under climate change

Compared with individual heatwaves or storm events, the compound extreme precipitations preconditioned by heatwaves (CHEPs) usually amplify their adverse repercussions on both ecosystems and society. However, little is known about the physical mechanisms of generations, especially considering precipitation types triggered by various factors and synoptic patterns. By classifying extreme precipitations based on duration, we conduct an event-based analysis and comprehensively assess CHEPs using the machine learning-constrained framework and binning scaling methods over China. We find the fraction of CHEPs to total extreme short-duration/long-duration precipitations (ESDPs/ELDPs) has substantially increased by 18%/15% from 1979 to 2021, when using dry-bulb temperature to identify heatwaves. More notably, the hotspots of CHEPs are generally consistent with those of ESDPs. The ESDPs play a dominant role in shaping CHEPs episodes, which are governed by enhancing atmospheric instability due to preconditioned heatwaves. The horizontal moisture advection and transient vertical dynamic motion of moisture, which are paramount to LDPs, is not significantly enhanced by the overheating atmosphere, leading to a small fraction of LDPs to CHEPs. In addition, the intensity of ESDPs tends to increase with air temperature at higher rates than that of ELDPs. As short-duration storms may trigger severe flash floods, ample attention should be paid to the escalating risks of CHEPs under climate change.


Introduction
Heatwaves and precipitation extremes are among the most common weather-related extreme events globally (Hu et al 2020, Wu et al 2023).Although numerous studies have investigated the characteristics and impacts of individual events, physical mechanisms underlying successive heatwaves and precipitation extremes are still poorly understood (Li et al 2023, Sauter et al 2023).Compared with univariate extremes, impacts of compound extreme precipitations preconditioned by heatwaves (CHEPs) on the society and ecosystem can be amplified (Zscheischler et al 2018(Zscheischler et al , 2020)).For example, heatwaves can provide favorable conditions for the breeding of vectors.If extreme precipitations occur successively, the related floods are prone to the wide spread of infectious diseases, such as malaria and dengue (Boyce et al 2016, Cheng et al 2021, Wang et al 2022).In addition, the sharp and rapid transition of weather extreme patterns means a short recovery time for society, putting an overwhelming strain on medical resources and decreasing the risk-resistance capacity (Raghavendra et al 2018, Raghavendra andMilrad 2021).
Numerous studies have reported that heatwaves may facilitate moisture conditions to feed extreme precipitations (Li et al 2023).According to the Clausius-Clapeyron (C-C) relationship, the saturation water vapor pressure increases with the air temperature at the rate of roughly 6.8% • C −1 , suggesting that the atmosphere can hold more water vapor after a heatwave (Wasko et al 2015, Visser et al 2020).In addition, the heatwave can increase atmospheric instability, thus favoring atmospheric convection and resulting in heavy rainstorms (Zhang and Villarini 2020).Previous studies also pointed out that rainfalls preconditioned by heatwaves can be more intense than those not being preconditioned by heatwaves in the central United States and the Yangtze River basin of China (Chen et al 2022, Zhang andVillarini 2020).Using high-resolution regional climate models, You and Wang (2021) revealed that CHEPs in China will be even more frequent and abruptly in the future warmer climate.
Most frameworks investigated CHEPs using ground-based meteorological observations, which are usually available only on a daily scale (Li and O'Gorman 2020, Li et al 2023).However, triggered by various factors and mechanisms, precipitation events can be classified into different types, which cannot be well captured based on the daily scale analysis.Previous studies utilized event durationbased classification to separate convective and largescale precipitations.Specifically, short-duration precipitations (SDPs) lasting several hours are frequently associated with local convective thunderstorms, while long-duration precipitations (LDPs) with a steady pour for a few days are usually generated by large-scale synoptic systems (Hatsuzuka et al 2021).The classification of storm types based on sub-daily datasets facilitates a deeper understanding of the heatwave's role in successive extreme precipitation events.However, to our knowledge, no studies have yet explored CHEPs by considering precipitation types.
In this study, we aim to understand CHEPs in China.We mainly focus on two scientific questions: (1) what are the characteristics of CHEPs with different types of precipitation? and (2) What are the underlying mechanisms for CHEPs generation?We carry out the event-based method to identify CHEPs at an hourly scale, which are then classified based on the duration of precipitation extremes.To explore the water-heat transport mechanism in CHEPs generation, we first detect determined meteorological factors driving different precipitation types and then quantify potential influence of heatwaves on these factors.By conducting these two steps, we build a cascade physical chain (heatwaves-key meteorological factors-precipitation extremes) to explain potential mechanisms of CHEPs.All abbreviations used in this study and the corresponding full names are presented in table S1.

Sub-regions and datasets
To better understand characteristics of CHEPs in different regions featured by various climate and terrain types, our study uses seven sub-regions (figure S1): northeast China (NE), north China (N), east China (E), south China (S), northwest China (NW), southwest China (SW), and Qinghai-Tibet Plateau (QT) (Wang and Li 2007).We spatially weight values of all grids within each sub-region by areas to derive regional mean values.
The fifth generation of the European Centre for Medium Range Weather Forecasts global reanalysis (ERA5) is utilized (Hersbach et al 2020).ERA5 provides abundant real-time hourly meteorological data covering a long-time range at a high spatial resolution globally, making the analysis of CHEPs at a sub-daily scale feasible (Gu et al 2022a).
We employ ERA5 hourly total precipitation, 2 m air temperature (T2m), 2 m dewpoint temperature (D2m), convective available potential energy (CAPE), surface air pressure (SAP), 500 hpa vertical velocity (VV, upward positive), and total column water vapor (TCWV) covering the period of 1979-2021.D2m and T2m are utilized to calculate the 2 m relative humidity (RH) and the vapor pressure deficit (VPD), and the 2 m specific humidity (SH) is calculated using also the SAP.We then compute the wet bulb temperature (TWB) based on both T2m and RH (text S1).
All meteorological variables except hourly total precipitation are averaged to daily values.We select VV at the 500 hpa level, as it is closely related to the precipitation process (Kunkel et al 2020, Li and O'Gorman 2020).Variables can be further classified into three types of factors dominant in the precipitation process: convective energy factors, represented by CAPE; moisture factors including RH, SH, VPD, and TCWV; and atmospheric dynamic factors, represented by VV (Yin et al 2022).

Identification of CHEPs
As heatwaves and extreme precipitation events usually occur in summer across most areas of China, we only focus on the warm season (May to September).We take the 90th percentile as the heat threshold, and a heatwave event occurs when the daily dry-bulb (wet-bulb) temperature exceeds the heat threshold for at least three consecutive days (Luo et al 2022).We then conduct an event-based analysis framework to identify precipitation events.Any two precipitation events are considered to be independent if they are separated by 3 or more dry hours.Precipitation event intensity (mm h −1 ) is defined as the total amount of precipitation divided by whole duration hours (Pérez Bello et al 2022).A precipitation extreme is identified if its intensity exceeds the 95th percentile in the population of events (You and Wang 2021).CHEPs are finally identified as extreme precipitations following heatwaves within a 3 d interval (You and Wang 2021, You et al 2023).More details of the CHEPs identification procedure can be seen in Text S2.
All precipitation events are classified into three types based on duration: SDPs, <6 h, middleduration (MDPs, >6 h & <12 h), and LDPs, >12 h (Pérez Bello et al 2022).Accordingly, extreme SDPs, MDPs, and LDPs events are represented by ESDPs, EMDPs, and ELDPs for short hereinafter.Based on the convective precipitation and large-scale precipitation variables in ERA5 datasets, we confirm precipitation events in our short/long-duration subsets are inherently generated by different regimes.As MDPs are a mixture of convective and synoptic-scale precipitation events, their overall characteristics would be vague, thus we do not put much weight on them in this study (text S3 and figure S2).

Moving-blocks bootstrap methods to conduct the significance test
When considering successive temporal compound events, it is important to explore whether the causal relationship exists among the occurrence of different events.You et al (2023) utilized the moving-blocks bootstrap framework to test whether the occurrence of heat-pluvial and pluvial-heat events is only a matter of chance.It puts the original series out of order to disrupt the potential causal relationship between meteorological variables.Based on this method, we also consider the spatial correlation of event series when conducting resampling.The steps to test the statistical significance of CHEPs from what would be randomly distributed are described in text S4.

Machine learning model to identify dominant factors governing the precipitation intensity
The random forest model is employed to identify the most important factors in governing the precipitation intensity (Gu et al 2022b).More detailed introductions of the random forest model can be seen in Text S5.Nine meteorological variables, RH, TWB, CAPE, D2m, SH, T2m, TCWV, VPD, and 500 hpa VV are selected as inputs of the random forest model to predict precipitation intensity and then we obtain the rank importance of these variables in precipitation generations.Following previous studies (Kunkel et al 2020, Chen et al 2022, Yin et al 2022, Li et al 2023, Tian et al 2023, You et al 2023), these meteorological variables are selected as candidates because they all demonstrated important roles in shaping precipitation events.One hundred regression trees are set in the bagged ensemble with five leaf nodes, which can balance the trade-off between the model prediction performance and overfitting (Green et al 2020).Note we use all precipitation events to train the random forest model as the limited-sampled extreme precipitation events are not enough to satisfy the big-data demand for such machine learning methods.

Scaling of precipitation intensity and various meteorological variables
The 'Binning scaling' method is widely used to disentangle the relationship between extreme precipitation and temperature (P-T).Previous studies have reported three types of P-T relationship: monotonic increase, monotonic decrease, and the hook structure where extreme precipitations increase first and decline thereafter (Yin et al 2018, Tian et al 2023).The inflexion point of the fitted line for P-T relationship in the hook structure is defined as the peak point temperature.We employ this method to assess the temperature scaling relationship of precipitation and some other meteorological variables that may play key roles in CHEPs.By doing this, we can figure out how overheating weather conditions influence the precipitation process by affecting various atmospheric thermodynamic and dynamic factors.Six variables including CAPE, SH, RH, VPD, TCWV, and VV are selected as candidates to investigate the meteorological variables-temperature (M-T) relationship.We analyze M-T binning scaling behavior both in the context of precipitation events and the context of CHEPs occurrence.Details can be seen in text S7.

The characteristics of CHEPs
Using ERA5 hourly reanalysis datasets, we first quantify the frequency of CHEPs during 1979-2021 in China.QT, SW, and NE are the hotspots of CHEPs, which show an average total frequency of 32, 21, and 20 counts, respectively (figure 1(a)).The frequency of CHEPs in NW is the lowest among all sub-regions, where more than 75% of grids occurred less than nine events.For all sub-regions, the frequency of CHEPs computed based on original series falls outside the 95% confidence interval of the resampling empirical distribution based on bootstrap, suggesting that CHEPs occur much more frequently than those happening only by chance.The results confirm that a causal relationship exists among the occurrence of heatwaves and extreme precipitations (figure 1(b)).Moreover, the fraction of CHEPs to total ESDPs (EMDPs and ELDPs) in China substantially increases from ∼8% (6%, 4%) in 1979 to ∼26% (24%, 19%) in 2021, of which linear trends are all significant at the 0.01 confidence level by using the student's t-test (figure 1(e)).
By exploring the total frequency of ESDPs and ELDPs as well as fractions of them to all extreme precipitations for 43 years, we find that hotspots of CHEPs are similar to those of ESDPs, such as QT, SW, and NE (figure S3).CHEPs occur rarely in E where extreme precipitation events are mostly characterized by long duration.In addition, by presenting the differential fraction of ESDPs and ELDPs in CHEPs (figures 1(c) and (d)), we find that the frequency of CHEPs with ESDPs notably outnumbers those with ELDPs in most areas, suggesting that ESDPs play the dominant role in shaping CHEPs.We verify this speculation by further investigating how the fraction of precipitation extremes in each duration subsetting (namely ESDPs, EMDPs, and ELDPs) changes with the T2m increase in sub-regions (figure S4).At higher T2m, ESDPs generally occupy the major share in extreme precipitation events, confirming heatwaves favor ESDPs occurrence, and thus the short duration is the main feature of precipitation events in CHEPs.
By exploring CHEPs using different heatwave indices (figure S5), we find that the national average coincidence rate based on wet-bulb temperature (25.9) is higher than that based on dry-bulb temperature (19.1).This result is somewhat expected, as wet-bulb temperature also introduces the information of atmospheric humidity and the high humidity in extreme wet-bulb temperature is usually the precursor to following extreme precipitations.However, the spatial distribution pattern is similar to the result based on dry-bulb temperature to define heatwaves, indicating our finding is robust with different heatwave indices.

The dominant factors of governing precipitation intensity
We select 9 meteorological variables as candidates, RH, TWB, CAPE, D2m, SH, T2m, TCWV, VPD, and VV to determine dominant factors driving precipitation processes for different types.The random forest has a generally good ability to predict the precipitation intensity in original series, with more than 75% of grids having RMSE less than 0.4 and R 2 larger than 0.56 (text S6 and figure S6).
For all precipitation events, the most important factor affecting precipitation intensity is VV in the east and CAPE in the west (figure 2(a)).If classifying precipitation events based on duration, we can find that CAPE is the predominant factor for SDPs intensity whereas VV is the most important to LDPs (figures 2(b) and (c)).For each variable, we calculate the proportion of grids to the total where this variable ranks top 3 of importance (figures 2(d)-(f)).Taking all precipitation events into consideration, CAPE, VV, and TCWV are the most important factors.For SDPs, CAPE is the predominant factor in precipitation intensity and it ranks top 3 over more than 90% grids.VV is also more important than other variables, but considerably less important than CAPE.In addition, variables presenting moisture conditions such as TCWV and SH play less important roles.Whereas for LDPs, the most important factor is VV with nearly 90% grids having it in the top 3 of importance ranking.TCWV also shows much importance and ranks top 3 over more than 58% grids.

Relationship between various meteorological variables and near-surface air temperature
In section 4.2, we detect most important variables governing different types of precipitation.In this section, we focus on relationships between meteorological variables and T2m to figure out how heatwaves influence extreme precipitations by affecting key meteorological variables to reveal potential underlying mechanisms of CHEPs.
Before disentangling complex interplays of various meteorological variables, we first outline the P-T relationship, which is the most basic relationship in CHEPs (figure S7).The scaling rate of SDPs in more than 65% grids of total is stronger than that of LDPs, suggesting warmer conditions can amplify the intensity of SDPs more effectively than LDPs.77% grids in QT show a monotonically increasing type in SDPs, whereas LDPs show low peak point temperatures and even monotonically decreasing structures, corresponding to the high proportion of ESDPs in CHEPs in QT.In other sub-regions, precipitation extremes are more likely to exhibit a hook-like behavior.If we pair the precipitation intensity with the antecedent T2m, more grids (+15%, 14%, and 10% for all, SDPs, and LDPs) show monotonically show the scaling rate distribution of 95th percentile meteorological variables with T2m using the binning scaling method.The barplot at the top left corner in each panel presents the proportion of grids that show monotonically increasing scaling behaviors (inc), decreasing behaviors (dec), or a hook-like structure with the peak point temperature.The grids filled in grey denote there are not enough precipitation event samples for binning scaling analysis.
increasing structure (figures S8(d)-(f)).The scaling rate of SDPs in more than 64% grids is still stronger than that of LDPs.
Figure 3 presents scaling relationships between the extremeness of meteorological variables and T2m in the context of precipitation events occurrence.CAPE increases significantly with the T2m increase in 80% grids of total at super C-C scaling rates, even larger than 20%/ • C in NE, N, SW, E, and S. RH has a negative relationship with T2m in most regions, in line with the positive correlation between VPD and T2m, especially discernible in low latitudes.SH and TCWV show sub-C-C scaling in NW, N, SW, E, and S, whereas near or super C-C scaling in NE and QT.VV in 500 hpa negatively correlated with T2m in more than 55% grids, and the scaling presents high spatial heterogeneity in the other areas.Generally, the M-T relationship behaves similarly in different precipitation types (figures S9 and S10), and the cooling effect of precipitation seems not pronounced (figures S11-S13).
We then focus on the relationship of meteorological variables with T2m in the context of CHEPs and compare the relative magnitude of these variables in SDPs and LDPs (figure 4).The CAPE, which presents the convective energy factor, has higher values in SDPs than LDPs for both 50th and 95th percentiles in most regions.As for moisture factors, RH and TCWV in LDPs are higher than SDPs and correspond to lower values of VPD, revealing abundant water vapor characteristics in LDPs.VV, a variable representing the atmospheric dynamic condition, has significant higher values in LDPs than in SDPs.The basic pattern of scaling relationship in the context of CHEPs is similar to that in the context of precipitation events: the increasing scaling of CAPE, SH, and TCWV in most sub-regions; decreasing scaling of RH and the inconsistent scaling relationship among sub-regions of VV with T2m.We find although most sub-regions show similar scaling patterns, the discrepancy does exist in other several sub-regions.The sample sizes, large-scale circulations, and orographic effects may be the reasons leading to these differences, deserving further investigation in future studies (Molnar et al 2015, Huang et al 2021, 2023).

The physical mechanism underlying CHEPs generation
We further conduct the moisture budget analysis to investigate how antecedent heatwaves influence moisture conditions for extreme precipitations, the details of this method can be seen in Text S8.Whether for extreme precipitations preconditioned by heatwaves or not, a positive horizontal advection anomaly is detected in most grids the day before the extreme precipitation day (figures S14(b) and (l)), while the vertical advection is significant on the extreme precipitation day (figures S14(h) and (r)).After breaking down the moisture advection anomalies into the thermodynamic and dynamic components, we find the preconditioned heatwaves have a positive effect on the thermodynamic component of the vertical advection anomalies (figure 5(c)), but have a limited influence on the dynamic component for both the horizontal and vertical advection anomalies (figures 5(b) and (d)).By classifying CHEPs events according to the Based on the results of the random forest model, binning scaling analysis, and moisture budget  equation, the mechanism for CHEP generations could be deeply understood (figure 6).The blocking weather patterns accompanied by heatwaves are not conducive to the dynamic component of water vapor advection (Fang and Lu 2020).However, heatwaves can stimulate the convective energy of the local atmosphere by heating air parcels, which is associated with the thermodynamic component of vertical moisture advection change.The SDPs, which do not need very abundant water vapor transports for occurrence, can be accelerated effectively after the passage of heatwaves.The continuous water vapor transports and dynamic lifting conditions are crucial in LDPs, which cannot be promoted significantly by heatwaves.Therefore, SDPs are more prevalent in CHEPs.Moreover, P-T relationships suggest that not only the intensity of SDPs can be enhanced by heatwaves; if atmospheric dynamic and moisture conditions are satisfied, heatwaves may also enhance the intensity of LDPs by facilitating the convective energy factor (figure S16).Although the peak point temperature exits in P-T relationships, it is near the maximum temperature for both SDPs and LDPs in most regions (figure S16), indicating that precipitation intensity can be enhanced by a heatwave in a wide range of surface air temperature.The potential mechanism of CHEP generation implies that risks of CHEPs would increase in warmer climates.

The reliability of ERA5 reanalysis for capturing CHEPs over China
Although the ERA5 reanalysis dataset has some uncertainty, it has high space-time resolution with multiple meteorological variables and has been widely used in previous studies on both a local and global scale (Hersbach et al 2020).The analysis based on station datasets may obtain more convincing results, but unfortunately, the time series of stationbased hourly precipitation publicly available are too short to investigate CHEPs.Moreover, when evaluating precipitation over extended areas, especially with complex terrain, station-based datasets are limited due to their representativeness issues.
To further validate the reliability of ERA5 datasets to capture the hourly precipitation and CHEP events in China, global precipitation measurement (GPM) satellite data is employed to compare with ERA5 (text S9 and figure S17).We find that the main distribution characteristics of ESDPs, ELDPs, and CHEPs are similar between the two datasets, presenting NE and QT are hotspots for ESDPs and CHEPs.However, GPM tends to detect more LDPs and less SDPs in S and SW.Li et al (2021) evaluated the performance of GPM satellite in capturing sub-daily precipitation events over China, and found that although GPM observed more precipitation events than gauge observations on average, it presented an underestimation of SDPs in SW and S, which is consistent with our results.Wu et al (2022) indicated that ERA5 hourly data captured more precipitation events and longer duration than gauge observations over China, but the variation pattern for zonal mean values is similar between ERA5 and sub-daily observations.They found both datasets show the precipitation events experienced an increase followed by a decrease for duration and a decrease followed by an increase for frequency from high to low latitudes.Although these studies did not focus on extreme precipitations, they still have referential values for our study as they used such an event-based analysis method and systematically evaluated the performance of these products in capturing the duration, frequency, and intensity of precipitation events.These results both support the robustness of our main results, although the comprehensive evaluation for CHEPs at the sub-daily scale using stationbased datasets is still urgently needed in future work.

Limitations and future works
We identify heatwaves in CHEPs only based on the surface air temperature at 2 m, which some other variables, such as RH, SH, and TWB, are also calculated based on.However, these variables may change with height, and the values in precipitation generation centers are probably different from the surface, which may lead to bias in our results of the random forest and scaling rates.Another caveat is that due to the burden from the storage space, except the hourly precipitation variable, other variables are all analyzed at a daily scale, whose variations in precipitation processes cannot be well captured.In addition, we only conduct univariate scaling analysis in this study, but we should note correlations among variables (Wang and Sun 2022).For example, CAPE closely depends on the surface humidity and temperature (Zhang and Villarini 2020).Variables capturing moisture factors, such as RH, SH, and TCWV, also contain duplicate information.Incorporating additional factors and disentangling these complex relationships in a multivariate scope may bring novel insights to CHEPs studies, which merits further investigation.Nonetheless, our work gives a comprehensive analysis of CHEPs and advances the understanding of various meteorological variables' roles in generating precipitation extremes as well as impacts of heatwaves on them.Although our analysis concentrates on China, the event identification method and mechanism analysis framework can be generalized to the global scale for more robust conclusions.
In the future, using numerical weather prediction models such as the Weather Research and Forecasting (WRF) model to simulate CHEPs would be beneficial, as we can investigate CHEPs at finer spatial scales even a convection-permitting resolution.It would provide more insights into how antecedent heatwaves influence the convective process of extreme precipitations (Zhu et al 2023).We can also conduct pseudo-global warming experiments to facilitate a deeper understanding of how climate change affects such compound events again using WRF (Tang et al 2023).From an artificial intelligence standpoint, investigating the interaction of antecedent heatwaves and precipitation extremes directly within a unified end-toend framework can be valuable.Besides the moisture budget analysis utilized in this study, the omega equation and energy budget analysis can be further adopted to analyze the water-heat transports in CHEPs in future work.

Conclusion remarks
For the first time, CHEPs, a kind of hazardous compound event, are investigated by classifying the precipitation events based on duration.We distinguish the response of precipitation extremes generated by different processes to preconditioned heatwaves.With intense rainfall rates concentrated at small spatial-temporal scales, short-duration thunderstorms can trigger rapid hazardous flash floods, which leaves little response time for emergency warnings and preparations.As CHEPs have already increased in recent decades, our work highlights urgent needs for policymakers and stakeholders to prepare adaptation and resistance strategies for future risks.
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Figure 1 .
Figure 1.The characteristics of CHEPs during 1979-2021 in China.Panel (a) presents total CHEPs frequencies during total 43 years.Panel (b) shows raincloud plots of significance test of regional-mean frequencies for CHEPs using moving-blocks bootstrap methods.The rain (circles) and the cloud (ridgeline) represent the frequency of CHEPs for 1000 resamples and their distribution, respectively.The upper dashed line denotes the 95% confidence interval for each sub-region.The figure above the cloud presents CHEPs frequency calculated based on the original series.Note the ordinates of (a) and (b) all represent the frequency of CHEPs.Panels (c), (d) show the fraction of ESDPs and ELDPs to total CHEPs.Panel (e) presents changes in the CHEPs count and the fraction of CHEPs to total extreme events with different precipitation types.Specifically, the CHEPs count for the left ordinate denotes the sum value of CHEPs frequency for all grids in each year, while the CHEPs fraction for the right ordinate denotes the fraction of CHEPs count with different durations to the extreme precipitations count with the corresponding duration in each year.All linear trends in Panel (e) are statistically significant at the 0.01 confidence level.

Figure 2 .
Figure 2. The most important factors governing precipitation events.Panels (a)-(c) show the spatial distribution of the predominant factor in each grid for all precipitation events (a), SDPs (b), and LDPs (c), respectively.The blue, red, and yellow bars in Panels (d)-(f) show the proportion of grids to the total where the importance of a particular meteorological variable ranks first, second, and third for all precipitation events (d), SDPs (e) and LDPs (f), respectively.

Figure 3 .
Figure3.Relationship between meteorological variables and T2m in the context of precipitation events occurrence.Spatial maps show the scaling rate distribution of 95th percentile meteorological variables with T2m using the binning scaling method.The barplot at the top left corner in each panel presents the proportion of grids that show monotonically increasing scaling behaviors (inc), decreasing behaviors (dec), or a hook-like structure with the peak point temperature.The grids filled in grey denote there are not enough precipitation event samples for binning scaling analysis.

Figure 4 .
Figure 4. Relationships between meteorological variables (vertical axes) and T2m (horizontal axes) in the context of CHEPs occurrence.A logarithmic vertical axis is used.Black dashed lines in each panel denote C-C scaling.The color coding of points presents precipitation events duration in CHEPs.Blue curves and red curves show the scaling for SDPs and LDPs, respectively, which are presented for the 50th and 95th percentiles and all smoothed using the LOWESS method.

Figure 5 .
Figure 5.The spatial cumulative distribution function for the thermodynamic (a) and (c) and dynamic (b) and (d) components of composite moisture advection anomalies on the extreme precipitation day.The spatial cumulative distribution function shows the cumulative probability of grids that have equal or less than a certain value for different budget terms.The legend CHEPs and no-CHEPs denote the extreme precipitations preconditioned by heatwaves and not.

Figure 6 .
Figure 6.The conceptual schematic diagram of the physical mechanisms for CHEPs.
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