Linkage Between Hourly Precipitation Events and Atmospheric Temperature Changes over China during the Warm Season

We investigated changes in the temporospatial features of hourly precipitation during the warm season over mainland China. The frequency and amount of hourly precipitation displayed latitudinal zonation, especially for light and moderate precipitation, which showed successive downward change over time in northeastern and southern China. Changes in the precipitation amount resulted mainly from changes in frequency rather than changes in intensity. We also evaluated the linkage between hourly precipitation and temperature variations and found that hourly precipitation extreme was more sensitive to temperature than other categories of precipitation. A strong dependency of hourly precipitation on temperature occurred at temperatures colder than the median daily temperature; in such cases, regression slopes were greater than the Clausius-Clapeyron (C-C) relation of 7% per degree Celsius. Regression slopes for 31.6%, 59.8%, 96.9%, and 99.1% of all stations were greater than 7% per degree Celsius for the 75th, 90th, 99th, and 99.9th percentiles for precipitation, respectively. The mean regression slopes within the 99.9th percentile of precipitation were three times the C-C rate. Hourly precipitation showed a strong negative relationship with daily maximum temperature and the diurnal temperature range at most stations, whereas the equivalent correlation for daily minimum temperature was weak.


Results
Temporospatial changes in hourly precipitation. Figure 1 presents the changes in the frequency, intensity, and total amount of precipitation between two periods (1991-2001 and 2002-2012) for four classes of precipitation event: light (< 5 mm/h), moderate (5-10 mm/h), heavy (10-20 mm/h), and extreme (> 20 mm/h). Changes in the frequency and amount of light precipitation measured on an hourly basis showed latitudinal zonation (Fig. 1a,c). Stations around 30°N-40°N covering the Huaihe River basin, the Yellow River basin, the southern part of the Haihe River basin, and the northern part of the Yangtze River basin experienced large increases in the number of hourly light precipitation events after 2002, leading to an overall increase of more than 20% compared with the period 1991-2001. In contrast, after 2002, there were decreases in the total amount of light precipitation and the frequency of light precipitation events in northeastern and southern China, especially in the southern part of the Southwest River drainage basin. For moderate events, the changes in precipitation were similar and also showed regional differences by latitude. The locations with the largest increases in both frequency and total amount were concentrated in the northern section of the Yangtze River basin and the middle reaches of the Yellow River basin. In contrast, relatively large decreases were observed in the lower reaches of the Yangtze River basin and the northwestern part of the Southeast River drainage basin. For heavy precipitation events, zonal changes in frequency and amount were relatively weak. Increases were observed in the Huaihe River basin and the northern part of the Yangtze River basin, with about a 25% incremental rise in heavy rainfall amount. Hourly heavy precipitation decreased after 2002 in the Liaohe River basin and over a large part of southeastern China. For extreme precipitation, changes tended to be at the local rather than zonal level. In southern China, changes in extreme precipitation intensity were relatively weak. Large changes in the amount of extreme precipitation were observed in the Yellow River basin and the Songhua River basin, presumably resulting from the remarkable changes in both frequency and intensity of extreme precipitation in those regions (Fig. 1j,l). In addition, we investigated changes in frequency and intensity in extreme values by comparing the 5-year return values in 1991-2001 and 2002-2012 periods. Results showed the changes in frequency are statistically significant in the Huaihe River and Yellow River basins; The changes in intensity of wet events were most apparent in the Liaohe River and Haihe River basins (Fig. S1).
Diurnal variations in precipitation provide information on the process of rain formation and its interaction with the local climate 11 . Two peaks in diurnal rainfall-one in the early morning and another in the late afternoon-have been identified over central eastern China 20 . However, this diurnal cycle of precipitation shows large spatial and seasonal variations 9,27 . Figure 2a shows an upward trend in the frequency of hourly wet events over China between 1991 and 2012, with positive rates of change for all hours throughout the day; the figure also shows that the rate of change was not the same at all times of day but that two distinct diurnal phases were evident. The rate of change in precipitation frequency was greater before noon than after noon [1300-1900 Local Standard Time (LST)]: the rates of change for these two phases were ~25-fold larger per annum and ~12-fold larger per annum, respectively. There was an overall downward trend in the intensity of precipitation for Scientific RepoRts | 6:22543 | DOI: 10.1038/srep22543 most times throughout the day, with positive rates of change occurring only around midnight LST (Fig. 2b). Combining the frequency and intensity changes for each local hour, the total amount of precipitation showed an upward trend for most hours, with the rate of change exceeding 40 mm per year between 2200 and 0700 (Fig. 2c). Downward trends were observed in the early afternoon (1300-1400) and at 1800 and 2000 LST. Hence, changes in the amount of precipitation resulted mainly from changes in frequency (at local time) rather than changes in intensity. In addition, we examined the change in precipitation frequency for the different precipitation classes. There were two distinct phases to the changes in the number of light precipitation events, similar to the phases in the overall frequency of precipitation (Fig. 2d) and the rate of change for light precipitation was greater than for the other classes. This indicates that changes in the overall frequency of precipitation resulted mainly from changes in the number of light precipitation events. At 0300 and 0900 LST, the rate of change for frequency of light precipitation reached statistical significance at the p < 0.05 level.
We similarly investigated trends in the diurnal frequency of hourly light, moderate, heavy, and extreme precipitation events for nine individual river basins between 1991 and 2012 (Fig. 3). The results show that the changes varied among regions. For all basins, the frequency of light events showed the greatest variability in rate of change across the day. Downward trends were observed in the Songhua River basin, the Yangtze River basin, and the Southwest River drainage basin. In the Songhua River basin, the most distinct changes were observed during the afternoon and night (1300-0000 LST), when decreases reached ~3-fold per annum. The Yangtze River basin showed the greatest downward trends in hourly light events, especially during the morning. In the Pearl River basin during the afternoon, the frequency of light events decreased but the frequency of extreme events increased. The Liaohe River, Haihe River, Yellow River, and Huaihe River basins showed upward trends in the frequency of light events for each of the 24 hours. The greatest changes were generally concentrated in the morning hours for the Liaohe River, Haihe River, and Huaihe River basins. The Yellow River basin showed a constant upward trend in the frequency of light events throughout the day, with increases of greater than 4-fold per annum for each of the 24 hours. The Southeast River drainage basin experienced an increase in the frequency of light events in the morning and late at night, but a decrease in the frequency of light events between 1700 and 2100 LST. All basins showed only slight variations in the frequency of moderate, heavy, and extreme events, similar to the pattern observed across the entire country (Fig. 2d).
Interactions between atmospheric temperature and hourly precipitation. The annual rates of change for the 75th, 90th, 99th, and 99.9th percentiles of hourly precipitation during the period 1991-2012 period over China were estimated (Fig. S2), and the change rates of precipitation were uneven in different percentiles of precipitation and different regions. Previous studies revealed as the atmosphere warms, increased atmospheric water vapor content generally encourages an increase in extreme precipitation events 19 . Figure 4 shows the distribution of regression slopes for the relationship between hourly extreme precipitation amount and mean temperature for all stations, for the period 1991-2012. For the 75th percentile of precipitation, the regression slopes for most stations were lower than the C-C rate of 7% per degree Celsius, with the amount of rainfall generally increasing by around 4-6% per degree Celsius. Only a few stations scattered in the Yangtze River basin and the Pearl River basin had slopes greater than the C-C rate (Fig. 4a). For the 90th percentile of precipitation, the dependency of hourly precipitation extremes on temperature exceeded the C-C rate at about 30% of all stations; these stations were mainly located in the middle reaches of the Yangtze River and Pearl River basins, with a small number found in other river basins (Fig. 4b). For the 99th and 99.9th percentiles of precipitation, regression slopes greater than the C-C rate were found at 41.4% (240/580) and 47.2% (274/580) of all stations, respectively ( Fig. 4c,d). These stations were concentrated in the Pearl River basin, the middle reaches of the Yangtze River and Yellow River basins, and the northern parts of the Huaihe River and Liaohe River basins. The corresponding regression slopes varied between 7% and 14% per degree Celsius. Overall, the regression slopes increased as the percentile of hourly precipitation increased, indicating that precipitation extremes were more sensitive to changes in temperature. Figure 5 shows the relationships between temperature and precipitation obtained from nine randomly selected stations, one in each of the nine river basins. The 75th, 90th, 99th, and 99.9th percentiles of precipitation intensity generally increased as temperatures increased, which suggests strong temperature dependency. However, a reduction in precipitation intensity was found when temperatures exceeded a higher temperature threshold, suggesting that the relationship between precipitation and temperature does not follow the C-C relationship. We therefore plotted the regression slopes for hourly precipitation and daily temperatures below the median daily temperature across mainland China ( Fig. 6) and found the regression slopes to be greater than those shown in Fig. 4. For the 75th, 90th, 99th, and 99.9th percentiles of precipitation, 31.6%, 59.8%, 97.0%, and 99.1% of all stations had regression slopes greater than 7% per degree Celsius. The mean regression slopes were greater than the C-C rate for the 90th (8.9% per degree Celsius), 99th (16.0% per degree Celsius), and 99.9th (22.5% per degree Celsius) percentiles of precipitation, with the latter being approximately three times the C-C rate. Overall, the slope values were higher than those shown in Fig. 4, indicative of a decrease in precipitation at temperatures above the median daily temperature. Precipitation is associated with cloudiness and soil moisture and thus can be strongly correlated with the DTR. As shown in Fig. 7, the daily maximum temperature (TX) and frequency of light precipitation events exhibited a strong negative correlation (correlation coefficients below − 0.6) over large regions for the period 1991-2012; correlations between the TX and other categories of precipitation event were weaker. The negative correlations for all four categories of precipitation event were stronger in southeastern China than in other regions. The correlations between daily minimum temperature (TN) and precipitation were weaker and also showed regional dependency. Stations located in the Yangtze River basin, Southeast River drainage basin, and parts of the Pearl River and Haihe River basins exhibited a negative relationship between TN and light precipitation, whereas weak positive correlations were found in northern China in the regions of the Huaihe River basin, the Yellow River basin, and the Songhua River basin. With increasing precipitation intensity, negative correlations decreased and positive correlations became more numerous. Only a few stations scattered in the lower Yangtze River basin showed a negative relationship between TN and precipitation for all four categories of precipitation. Changes in the DTR are sensitive to variations in TX and TN. Overall, the relationship between the DTR and hourly precipitation was consistent with that for TX and hourly precipitation; the frequency of hourly light events showed the strongest negative correlations with the DTR compared with the other precipitation categories, with the correlations for light precipitation being statistically significant at the p < 0.05 level for most stations . Our findings indicate that the frequency of hourly light precipitation has a range of effects on temperature variations.   (Fig. 8a). About half of the sites showed downward trends in hourly light precipitation events over the period 1991-2012, with upward trends in the corresponding maximum temperatures. Trends in TX related significantly to trends in the frequency of hourly light precipitation. For TN, upward trends of approximately 0 °C per year to 0.1 °C per year were observed at most stations (Fig. 8b). However, TN did not appear to be correlated with the frequency of light precipitation events, indicating that the changes in TN were not sensitive to precipitation change. The rates of change in TX and TN were not consistent at each station, with differences in trends varying from − 0.1 °C per year to 0.1 °C per year. The relationship between these differences and trends in the frequency of light precipitation events resembled the relationship between trends in TX and light precipitation events. Approximately half of the stations exhibited positive differences, resulting in an increase in the DTR. Changes in the DTR were linearly dependent on the differences between the trends in TX and the trends in TN (Fig. 8d).

Discussion
The frequency and magnitude of precipitation measured on an hourly basis over mainland China showed latitudinal zonation with three sequential areas apparent, involving the northeastern, northern, and southern regions of the country. This was particularly evident for light and moderate precipitation events, which showed downward trends over northeastern and southern China. These results are consistent with similar changes obtained from daily measures of precipitation by Wu et al., who attributed rain reduction to lower tropospheric temperatures and precipitation 28 . Previous studies have demonstrated that the diurnal variation in rainfall across China shows considerable regional fluctuations. Differences in the annual rates of change for daytime and nighttime precipitation could partly account for changes in diurnal variation. For instance, precipitation peaks in the late afternoon have previously been documented over southern and northeastern China 29 ; however, we observed downward trends in the frequency of precipitation in the Songhua River basin and Southeast River drainage basin in the late afternoon and upward trends during the morning, weakening the diurnal variation. In addition, changes in hourly heavy and extreme precipitation were unevenly distributed, indicating sensitivity to location. Short-duration extreme precipitation was most likely associated with terrain or terrain-induced local circulation, such as local mountain-valley wind circulation 8,30 .
Temperature and precipitation are two of the most important climate variables, and understanding their relationship is important for identifying precipitation-forming processes and for weather and climate forecasting 31 . Our investigation into the dependency of hourly precipitation on daily mean temperature in the warm season showed that the regression slopes at most stations were approximately 4-6% per degree Celsius for the 75th  percentile of precipitation and that only 41% (240/580) and 47% (274/580) of all stations showed regression slopes slightly greater than the C-C rate of 7% per degree Celsius for the 99th and 99.9th percentiles of precipitation, respectively. However, a stronger dependency of hourly precipitation on temperature occurred at temperatures colder than the median daily temperature, with 32%, 60%, 97%, and 99% of all stations exhibiting regression slopes greater than the C-C rate for the 75th, 90th, 99th and 99.9th percentiles of precipitation, respectively. The mean regression slope for the 99.9th percentile was three times the C-C rate. The results revealed that, at most stations, rainfall intensity increased with temperature up to a maximum and then decreased with temperature beyond that maximum. Precipitation formation involves processes acting at different spatial and temporal scales, such as large-scale atmospheric dynamics and meso-scale convection 17 . In China, compared with stratiform precipitation (such as larger-scale frontal precipitation), convective precipitation related to vigorous overturning tends to occur on warmer days and promotes heavier short-term rainfall. Stratiform events have no pronounced temperature dependence but convective events taken as a whole produce an increase in intensity of extreme events that exceeds the C-C rate 32 . Furthermore, in summertime, the tropical cyclone produces significant amounts of extreme rainfall in most coastal regions. These factors can partly explain the stronger dependency of hourly extreme precipitation (99.9th percentile) on temperature that was observed at most stations. However, our observation of a decrease in precipitation at high temperatures is contrary to the finding by Lenderink and Meijgaard that the dependency of hourly precipitation extremes on daily temperature was approximately twice the C-C rate for temperatures above 10 °C. Different geographical regions and seasons affect the relationship between temperature and precipitation 33 , so the appearance of a decrease in precipitation at high temperatures may be related to China's specific geographical features. In China, the climate is generally controlled by complex large-scale atmospheric circulation systems. For instance, the moisture supply in China is mainly dominated by the western Pacific subtropical high and the East Asia summer monsoon, especially in summertime 34,35 , with consequent effects on both temperature and precipitation. High temperatures and a lack of rain are the predominant conditions under the western Pacific subtropical high during the warm season. Furthermore, Utsumi et al. raised the possibility that the duration of wet events may be related to the relationship between temperature and precipitation. They showed that a decrease in the duration of precipitation events can explain the decrease in extreme daily precipitation intensity at high temperatures 36 . Inconsistencies remain between the precipitationtemperature relationships measured at the global scale compared with the regional scale. With global warming, it might be expected that more extreme precipitation may occur at both regional and global levels 37 . However, the findings of our study suggest that precipitation may in fact decrease after the temperature exceeds a threshold value (Fig. 5). The combined effect of higher temperatures and less precipitation could produce heat waves and droughts, and thus challenge societal development.
Our results showed a strong correlation between the DTR and hourly light precipitation. The DTR is by nature related to changes in TX and TN). Whereas TN is strongly dependent on net longwave radiation, TX is strongly controlled by surface solar heating and the partitioning of sensible and latent heat fluxes. Previous studies have revealed cloud, precipitation, and soil moisture as the main factors affecting variations in the DTR. Compared with clear-sky days, days with precipitation (often accompanied by cloud cover) affect TX during the daytime and TN at nighttime owing to the influence on surface solar heating and upward longwave radiation 38,39 . Furthermore, precipitation can increase the soil moisture content, which in turn contributes to changes in the DTR. Verdecch et al. revealed that in areas where soil moisture increases owing to an increase in precipitation there is a positive change in latent heat flux and a decrease in sensible heat flux 40 ; consequently, in areas with increased soil moisture, the increase in TX is smaller than the increase in TN, thereby causing a decrease in the DTR. In our study, hourly precipitation was significantly correlated with TX and the DTR at most stations, indicating that precipitation affects the DTR. In the warm season, short-term strong rainfall events, such as convective precipitation, were more sensitive to the changes in temperature. Overall, the frequency of hourly light precipitation had the strongest relationship with the DTR. Moreover, the correlation between precipitation and TN was weak. The rate of change in TX was generally inversely related to the rate of change of hourly precipitation frequency, especially for light precipitation events. It is likely that this relationship was primarily driven by reductions in solar heating owing to cloud cover and by increases in surface latent heat flux owing to increased surface wetness from precipitation 41 . However, the correlation between TX and precipitation frequency gradually weakened as hourly rainfall intensity increased from light to extreme. During the warm season, convective precipitation related to vigorous overturning can promote heavy rainfall over a short period of time. For convective precipitation, the maximum rainfall rate and peak intensity occur in the late afternoon 42 , which is generally later in the day than the time at which TX occurs. This partly explains the weaker relationship between TX and hourly heavy and extreme precipitation. Whereas Zhou et al. found a stronger relationship between increased precipitation and trends in TN and the DTR 20 , we have found a distinctive relationship between warm-season precipitation changes and trends in TX and the DTR. Other mechanisms that may contribute to changes in the DTR, such as clouds, aerosols, and land cover, should be explored in future studies. In this study, we used gauge observations of precipitation at a fine (hourly) temporal resolution. However, owing to a lack of available data, our study used limited data and relatively short time periods and this may have restricted the results. Furthermore, gauge measurements do not provide complete areal coverage and are not available over unpopulated land areas, especially in western China. Recently, some satellite-derived datasets that provide sub-daily precipitation measurements and more spatially homogeneous and temporally complete coverage of large areas of the globe have become available. These include the Tropical Rainfall Measuring Mission (TRMM) 43 , the Precipitation Estimation from Remotely Sensed Information using Artificial Neural Networks (PERSIANN) 44,45 , and Climate Prediction Center morphing technique (CMORPH) products 46 . Moreover, the Global Precipitation Measurement (GPM) Core Observatory was launched in early 2014 to explore global precipitation characteristics in more detail 47 , and a high-resolution and advanced Integrated Multi-satellitE Retrievals for GPM (IMERG) dataset was recently released. The increased temporal and spatial resolution provided by these satellite observations offers great potential for improving precipitation measurements to meet the various scientific and societal needs.

Data and Methods
Data. The dataset of hourly rainfall was obtained from the National Meteorological Information Center of the China Meteorological Administration, which maintains rain-gauge records from more than 2400 stations across China. Data on the daily mean temperatures, maximum temperatures, and minimum temperatures from 824 stations were collected from the SURF_CLI_CHN_MUL_DAY_V3.0 dataset, which was downloaded from the China Meteorological Data Sharing Service System (http://cdc.nmic.cn/home.do). The full dataset was subject to strict quality control and homogenized according to the methods described by Xu et al. 48 ; 580 stations providing synchronous hourly precipitation and temperature measurements were selected for this research (Fig. 9).

Analysis.
To detect the changes in precipitation, it was necessary to examine variations both in mean precipitation and in precipitation at different intensities. We divided all hourly precipitation events across China into four categories: light (< 5 mm/h), moderate (5-10 mm/h), heavy (10-20 mm/h), and extreme (> 20 mm/h) 8,49 . We compared the changes in mean precipitation amount, intensity, and frequency in these four categories between the periods 1991-2001 and 2002-2012. We focused on each wet event, defined as hourly precipitation greater than 0.1 mm. To better understand the hydrologic processes, we also estimated changes in temperature and precipitation in the different river basins separately (Fig. 9). These data were used to investigate temporal changes in precipitation. Owing to the very few stations distributed in the Northwest River drainage basin, results for this basin were excluded. We investigated trends in the frequency of light, moderate, heavy, and extreme precipitation events over nine different river basins.
Previous studies have noted that hourly extreme precipitation events show increases at more than the 7% C-C rate in a variety of regions 17 . The present study utilizes the method proposed by Mishra et al. 19 to investigate the relationship between mean daily temperature and hourly extreme precipitation events. For each station, all hourly precipitation events and the corresponding daily mean temperatures were extracted to calculate the relationships over the period 1991-2012. Hourly precipitation data were divided into bins of 1 °C width based on the daily mean temperature and, for each temperature bin, the 75th, 90th, 99th, and 99.9th percentiles of hourly precipitation were estimated. We used regression analysis to plot the logarithm of these hourly precipitation percentiles against the mean temperature to estimate the percentage change in hourly precipitation with temperature. Panthou et al. summarized the various relationships between precipitation and temperature as follows: (i) rainfall intensity increases monotonically with temperature, (ii) rainfall intensity decreases monotonically with temperature, (iii) rainfall intensity increases with temperature and levels off at high temperature (upper limit structure), and (iv) rainfall intensity increases with temperature and decreases after reaching a maximum (peak-like structure) 33 . We selected nine stations at random, one from each of the nine river basins, to examine the type of the relationship between temperature and precipitation. Noting that Isaac and Stuart found inconsistencies in the precipitation occurring at temperatures lower and higher than the median temperature 31 , we took the median daily temperature at each station as the threshold and analyzed the relationship between hourly precipitation and daily temperatures below and above this threshold. Previous studies have also demonstrated that precipitation affects the mean, maximum, and minimum temperatures, and hence the DTR 23,41 . We utilized the Pearson correlation coefficient to estimate the correlation between hourly precipitation and temperature variations, and linear regression to calculate the rate of change of these variables.