Relationship between Extreme Precipitation and Temperature in Two Different Regions: The Tibetan Plateau and Middle–East China

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  • Corresponding author: Yunfei FU, fyf@ustc.edu.cn
  • Funds:

    Supported by the National Natural Science Foundation of China (91837310) and National Key Research and Development Program of China (2017YFC1501402 and 2018YFC1507200)

  • doi: 10.1007/s13351-019-8181-3

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  • The change of extreme precipitation with temperature has regional characteristics in the context of global warming. In this study, radiosonde data, co-located rain gauge (RG) observations, and Tropical Rainfall Measuring Mission (TRMM) precipitation radar (PR) products are used to explore the relationship between extreme precipitation intensity and near-surface temperature in Middle–East China (MEC) and the eastern Tibetan Plateau (TP) during 1998–2012. The results show that extreme precipitation intensity increases with increasing temperature at an approximate Clausius–Clapeyron (C–C) rate (i.e., water vapor increases by 7% as temperature increases by 1°C based on the C–C equation) in MEC and TP, but the rate of increase is larger in TP than in MEC. This is probably because TP (MEC) is featured with deep convective (stratiform) precipitation, which releases more (less) latent heat and strengthens the convection intensity on a shorter (longer) timescale. It is also found that when temperature is higher than 25°C (15°C) in MEC (TP), the extreme precipitation intensity decreases with rise of temperature, suggesting that the precipitation intensity does not always increase with warming. In this case, the limited atmospheric humidity and precipitable water could be the primary factors for the decrease in extreme precipitation intensity at higher temperatures.
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  • Fig. 1.  Geographical locations of the selected IGRA radiosonde stations (denoted by red dots) in Middle–East China (MEC) and the Tibet Plateau (TP). The shadings represent the topography (in m).

    Fig. 2.  Distributions of the daily precipitation (a) samples and (b) intensity with temperature from the rain gauge (RG) data in Middle–East China (MEC; red color) and eastern Tibet Plateau (TP; blue color) during 1998–2012.

    Fig. 3.  Relationships between the daily precipitation intensity and near-surface temperature from the rain gauge (RG) data in (a) Middle–East China (MEC) and (b) east Tibet Plateau (TP) during 1998–2012. The ordinate axis ranges from 1 to 200 mm day–1 on a logarithmic scale; the blue, red, and purple lines denote the variation of 75th, 90th, and 95th percentiles of daily precipitation intensity with the near-surface temperature, respectively; the gray dashed lines indicate the C–C rate; and the black solid vertical lines indicate the temperature transition values.

    Fig. 4.  Regression slopes for the logarithmic daily precipitation intensity and temperature for the (a) 75th, (b) 90th, and (c) 95th percentiles of daily precipitation intensity at the selected stations shown in Fig. 1 during 1998–2012.

    Fig. 5.  As in Fig. 3 but for the near-surface precipitation intensity of different precipitation types from the new merged precipitation radar (PR) dataset including (a) convective and (c) stratiform precipitation in MEC; (b) deep convective and (d) shallow precipitation in the TP during 1998–2012. The ordinate axis ranges from 0.5 to 100 mm h–1 on a logarithmic scale.

    Fig. 6.  The relationship between the daily depression of the dew point (DDP) and near-surface temperature in (a) MEC and (b) the TP during 1998–2012. The blue, red, and purple lines denote the variation of 75th, 90th, and 95th percentiles of DDP with the near-surface temperature, respectively; and the black solid vertical lines indicate the temperature transition values.

    Fig. 7.  As in Fig. 6, but for the daily specific humidity (SH) in (a) MEC and (b) the TP, and the relative humidity (RH) in (c) MEC and (d) the TP during 1998–2012.

    Fig. 8.  As in Fig. 4, but for the daily specific humidity (SH).

    Fig. 9.  As in Fig. 2, but for the precipitable water (PW) samples and intensity. The purple and green lines indicate the regression lines for PW intensity and temperature in MEC and the TP, respectively

    Fig. 10.  The relationship between the daily precipitation intensity and precipitable water (PW) intensity from the rain gauge (RG) data in (a) MEC and (b) the TP during 1998–2012 (denoted by the black solid regression lines). The ordinate axis ranges from 0.5 to 100 mm day−1 on a logarithmic scale.

    Fig. 11.  As in Fig. 3, but for the daily precipitable water (PW) intensity. The ordinate axis ranges from 1 to 200 mm day−1 on a logarithmic scale.

    Fig. 12.  The PW intensity trends corresponding to precipitation events at the selected stations shown in Fig. 1 during 1998–2012.

    Fig. 13.  As in Fig. 4, but for the PW intensity.

    Table 1.  Regional average correlation coefficients between daily extreme precipitation intensity and temperature for the 75th, 90th, and 95th percentiles in MEC and TP

    75th percentile90th percentile95th percentile
    MEC0.770.850.85
    TP0.820.840.91
    Download: Download as CSV

    Table 2.  Samples of different precipitation types derived from the new merged dataset in MEC and TP

    ConvectiveStratiformDeepShallow
    MEC11422684
    TP832363
    Download: Download as CSV
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Relationship between Extreme Precipitation and Temperature in Two Different Regions: The Tibetan Plateau and Middle–East China

    Corresponding author: Yunfei FU, fyf@ustc.edu.cn
  • 1. School of Earth and Space Sciences, University of Science and Technology of China, Hefei 230026, China
  • 2. Anhui Meteorological Information Center, Anhui Institute of Meteorological Sciences, Hefei 230061, China
  • 3. School of Atmospheric physics, Nanjing University of Information Science & Technology, Nanjing 210044, China
  • 4. International Arctic Research Center and Department of Atmospheric Sciences, University of Alaska Fairbanks, Fairbanks, AK 99775, USA
Funds: Supported by the National Natural Science Foundation of China (91837310) and National Key Research and Development Program of China (2017YFC1501402 and 2018YFC1507200)

Abstract: The change of extreme precipitation with temperature has regional characteristics in the context of global warming. In this study, radiosonde data, co-located rain gauge (RG) observations, and Tropical Rainfall Measuring Mission (TRMM) precipitation radar (PR) products are used to explore the relationship between extreme precipitation intensity and near-surface temperature in Middle–East China (MEC) and the eastern Tibetan Plateau (TP) during 1998–2012. The results show that extreme precipitation intensity increases with increasing temperature at an approximate Clausius–Clapeyron (C–C) rate (i.e., water vapor increases by 7% as temperature increases by 1°C based on the C–C equation) in MEC and TP, but the rate of increase is larger in TP than in MEC. This is probably because TP (MEC) is featured with deep convective (stratiform) precipitation, which releases more (less) latent heat and strengthens the convection intensity on a shorter (longer) timescale. It is also found that when temperature is higher than 25°C (15°C) in MEC (TP), the extreme precipitation intensity decreases with rise of temperature, suggesting that the precipitation intensity does not always increase with warming. In this case, the limited atmospheric humidity and precipitable water could be the primary factors for the decrease in extreme precipitation intensity at higher temperatures.

    • Precipitation releases latent heat and affects radiation in the earth–atmosphere system (Fu et al., 2003; Zhou and Yu, 2005; Zhao et al., 2006; Li et al., 2013; Guo et al., 2018). In recent years, in the context of global warming, the global climate has been featured with frequent occurrence and heavy intensity of precipitation (Knapp et al., 2008; Jian et al., 2011; De Lima et al., 2013; Huang and Cui, 2015; Ye et al., 2015; Fu et al., 2016). Owing to the significant impact of extreme precipitation on the earth’s environment and human activities, more research has been focusing on extreme precipitation and associated climate variability. For instance, Curtis et al. (2007) evaluated the changes in ENSO that affected extreme precipitation in tropical regions. They found a significant correlation between the frequency of daily extreme precipitation and the variation in sea surface temperature in the Niño3.4 region. Allan and Soden (2008) revealed that the observed amplitude of extreme precipitation with temperature was higher than the result of a climate mo-del simulation, suggesting that the development of extreme precipitation could be more intense in the future than predicted by models. In China, technological improvements in the past decades have facilitated research on extreme precipitation. For example, some studies have evaluated the uncertainty involved in quantifying extreme precipitation in China and demonstrated that obvious discrepancies existed between observations and mo-del simulations. Moreover, it is indicated that the frequency and intensity of extreme precipitation showed significant increasing trends (Zhai et al., 2007; Wang Y. J. et al., 2017; Zhou et al., 2018).

      From a different perspective, the correlation between water vapor and temperature can be described theoretically by the Clausius–Clapeyron (C–C) equation. This equation suggests that water vapor increases by approximately 7% as the temperature increases by 1°C under the assumption of constant relative humidity (RH). This is also known as the C–C rate (Trenberth et al., 2003; Zhao et al., 2012). As with water vapor, previous results also indicate that extreme precipitation intensity increases with temperature at the C–C rate, even close to double of the C–C rate. In addition, the rate of increase changes with the season (Lenderink and van Meijgaard, 2008; Shaw et al., 2011; Mishra et al., 2012; Ali and Mishra, 2017; Schleiss, 2018). Some studies have simulated the relationship by using models and predicted the tendency of extreme precipitation with temperature in the future. For instance, Kendon et al. (2014) and Chan et al. (2016) simulated the characteristics of hourly extreme precipitation in UK based on a climate model. The rate of change was about 6.5% K–1, and they demonstrated that extreme precipitation intensity might continue to increase in the coming decades. Drobinski et al. (2016) reported that extreme precipitation showed a positive relationship with temperature at low temperatures but a negative relationship at high temperatures in the French Mediterranean region. Furthermore, factors that influence extreme precipitation and temperature have also been discussed. For example, Blenkinsop et al. (2015) and Lepore et al. (2015) concluded that the change in extreme precipitation with temperature was restricted by the general circulation, dew point temperature, and unstable energy, in UK and eastern USA, respectively. Lochbihler et al. (2017) revealed that extreme precipitation, humidity, and cloud scale to mesoscale circulations were all embedded in regional climate change. It is important to study the variation of extreme precipitation with temperature under the background of global warming.

      The Tibetan Plateau (TP) is famous for its “heat pump” and “water tower” characteristics, and climate change in the TP region has long been a hot topic of research in the scientific community (Luo and Yanai, 1983; Liu and Yin, 2001; Mao and Wu, 2006; Bao et al., 2011; Zhang et al., 2013). Meanwhile, Middle–East China (MEC) is influenced by the East Asian monsoon with frequent precipitation (Fu and Liu, 2003; Zhu et al., 2011; Xu, 2013; Zhang et al., 2016; Yang et al., 2019). Previous studies have focused mainly on the distribution patterns and interannual scale changes of precipitation in the TP and MEC regions. For example, based on the precipitation radar (PR) data from the Tropical Rainfall Measurement Mission (TRMM), Lu et al. (2016) discussed the interannual changes of precipitation in eastern China and surrounding regions. More recently, Fu et al. (2018) revealed the characteristics of precipitation and the topographical effect on precipitation over the southern slope of TP by using a dataset that combined TRMM PR and Visible and Infrared Scanner measurements.

      Because of the complexity of topography and the high altitude of terrain, climate of the TP has a unique dyna-mic and thermal structure. Moreover, latent heat and water vapor over the TP affect the nature of climate in its downstream regions. In addition, precipitation occurs frequently in MEC, and the characteristics of precipitation there are significant and complicated. Obviously, the precipitation characteristics differ between MEC and TP. However, recognition of the relationship between extreme precipitation and temperature in these two specific regions situated at approximately the same latitude remains incomplete. In the present study, the relationship between extreme precipitation and temperature in MEC and TP based on observational data is analyzed and compared, with an intention to provide a reference for model simulation in the two regions. Specifically, the relationship is to be examined by using radiosonde data, co-located rain gauge (RG) data, and TRMM PR observations during 1998–2012 in both regions. The focus will be on how the extreme precipitation intensity during the study period responds to the temperature change in MEC and TP and how it differs in the two regions. Furthermore, how the atmospheric humidity and precipitable water (PW), which are the primary factors that affect the change in extreme precipitation intensity in the two regions, change with increasing temperature is also examined. Following this introduction, the data and methods are described in Section 2. The relationship between extreme precipitation and temperature is revealed in Section 3, with discussion presented in Section 4. Section 5 provides a summary of the key findings and draws the final conclusions.

    2.   Data and methods
    • Radiosonde data derived from the Integrated Global Radiosonde Archive (IGRA), provided by the National Climatic Data Center (NCDC) of USA, were used to obtain the temperature and humidity in MEC and TP. IGRA has since 1960 provided pressure, temperature, humidity, wind speed, wind direction, and other meteorological parameters twice daily (0000 and 1200 UTC; Durre et al., 2006, 2009). The precipitation data were derived from quality-controlled RG observation data (Yu et al., 2007) provided by the National Meteorological Information Center of China Meteorological Administration (CMA-NMIC), which were co-located with the IGRA radiosonde station data.

      TRMM PR 2A25 products, obtained by Goddard Space Flight Center (GSFC), provide near-surface precipitation data with a vertical resolution of 0.25 km and horizontal resolution of 5 km (Kummerow et al., 1998; Schumacher and Houze, 2003). The TRMM PR 2A25 products have been widely applied in three dimensional precipitation studies in tropical and subtropical regions (Zhou et al., 2008; Rapp et al., 2011; Fu et al., 2017).

      Precipitation types, such as convective and stratiform precipitation, can be distinguished easily by TRMM PR. In order to investigate the different types of extreme precipitation change with increasing temperature in MEC and TP, TRMM PR precipitation products were chosen. The gauge precipitation data were also employed, and the TRMM PR products were used to match with the IGRA data. In this study, TRMM PR 2A25 precipitation products were merged with IGRA dataset at each IGRA station within a 0.25° gridded spatial range, and the sounding times of TRMM PR were merged with IGRA within two hours over 1998–2012. For more details, please refer to the work by Wang and Fu (2017). Moreover, Guo and Ding (2008, 2009) suggested that the minimum data requirement for sounding observation data is 80% for a single station. Therefore, IGRA radiosonde data with a missing rate of less than 20% for each station were selected. Ultimately, there are nine stations in MEC and three in TP (Fig. 1). Based on the new merged dataset, different precipitation types in MEC and TP regions were identified.

      Figure 1.  Geographical locations of the selected IGRA radiosonde stations (denoted by red dots) in Middle–East China (MEC) and the Tibet Plateau (TP). The shadings represent the topography (in m).

      Previous studies that worked on the concept of extreme precipitation have revealed that precipitation intensity P is proportional to the precipitation efficiency E, the vertical velocity w during precipitation process, and the atmospheric moisture content q: PE w q (Doswell III et al., 1996; Drobinski et al., 2016). Combined with the C–C equation, the change in atmospheric moisture content acts as a bridge linking the variation in precipitation intensity with the temperature when E and w are assumed to be constant. Thus, the change in extreme precipitation intensity with temperature is expected to follow the C–C rate (Lenderink and van Meijgaard, 2010; Panthou et al., 2014). Moreover, considering the diurnal variation of temperature and the energy accumulation prior to the process of precipitation (Shaw et al., 2011; Sun et al., 2013; Park and Min, 2017), daily temperature and precipitation data were utilized in this study.

      Following previous studies, precipitation intensity larger than 0.1 mm day−1 was considered as a valid precipitation event (Berg et al., 2009; Hardwick Jones et al., 2010; Xiao et al., 2016). Furthermore, only temperature values larger than 0°C were considered, in order to avoid snow events (Panthou et al., 2014; Molnar et al., 2015). The daily precipitation intensity was extracted directly from RG observations at each station. Because the RG stations were co-located with the IGRA stations, the precipitation intensity corresponding to near-surface temperature was easily sorted out. Accordingly, the daily precipitation intensity and corresponding daily temperature data were combined from nine stations in MEC during 1998–2012 for the subsequent analysis. Similarly, the data of three stations in TP were processed in the same manner. Considering the regional difference in extreme precipitation intensity, it is objective to choose the equal-temperature bin method to determine the threshold of extreme precipitation (Lenderink and van Meijgaard, 2008; Bürger et al., 2014; Lepore et al., 2015). Specifically, the daily precipitation intensity corresponding to daily temperature with an interval of 2°C was binned. Additionally, sensitive analysis of extreme precipitation intensity and near-surface temperature with an interval of 1°C was carried out. The change in extreme precipitation intensity for 1°C temperature bins showed a similar pattern with that for 2°C temperature bins. However, the extreme precipitation intensity fluctuated more with 1°C temperature bins than that with 2°C temperature bins, and the extreme precipitation intensity varied more smoothly with an interval of 2°C. Furthermore, there were more precipitation samples in each 2°C temperature bin. Thereby, temperature with an interval of 2°C was selected to carry out the investigations in this study. Then, the 95th, 90th, and 75th percentiles of precipitation intensity were extracted as the extreme precipitation intensity from each precipitation–temperature bin.

      Moreover, the change in extreme precipitation intensity with temperature was analyzed by using regression method (De Lima et al., 2013; Miao et al., 2016). As suggested by previous studies (Hardwick Jones et al., 2010; Utsumi et al., 2011; Schroeer and Kirchengast, 2018), the logarithmic precipitation intensity is a linear function of temperature:

      $$ {\rm{ln}} \; P = {b_0} + {b_1}T, $$ (1)

      where P is the precipitation intensity, T is the near-surface temperature, and b0 and b1 are the regression coefficients. This expression of relation is followed and the change in extreme precipitation with temperature is investigated in the following sections.

    3.   Results
    • The distributions of daily precipitation samples and precipitation intensity at near-surface temperature range in MEC and TP during 1998–2012 are shown in Fig. 2. Clearly, precipitation occurred more frequently in MEC than in TP (Fig. 2a). The precipitation samples were larger than 500 and distributed from 0°C to 32°C in MEC. The sample peaks were near 6°C and 26°C in MEC. For TP, precipitation events were mainly distributed from 0°C to 22°C, with the sample peak at 16°C. Figure 2b displays the distribution of daily precipitation intensity in each 2°C temperature bin. Precipitation was more intense in MEC, and the precipitation intensity even exceeded 50 mm day−1 from 18°C to 30°C. By comparison, the precipitation intensity in TP was smaller than 50 mm day−1 and distributed almost evenly in each temperature bin.

      Figure 2.  Distributions of the daily precipitation (a) samples and (b) intensity with temperature from the rain gauge (RG) data in Middle–East China (MEC; red color) and eastern Tibet Plateau (TP; blue color) during 1998–2012.

      Figure 3 shows the relationship between daily precipitation intensity and near-surface temperature in MEC and TP during 1998–2012. In general, all precipitation intensities at the 95th, 90th,and 75th percentiles in MEC were larger than corresponding percentiles in TP. The extreme precipitation became more intense as the temperature increased at an approximate C–C rate, especially when the temperature was higher than 12°C in MEC and 6°C in TP. The extreme precipitation intensity reached its peak value when the temperature was close to 25°C and 15°C in MEC and TP, respectively. However, the precipitation intensity showed negative variation against temperature as the temperature became even higher. The temperature of 25°C and 15°C were the transition values for the MEC and TP regions, respectively. It is applicable to describe the C–C relationship of extreme precipitation intensity and temperature when the temperature is lower than the transition value. In contrast, the variation of extreme precipitation with temperature agrees with a peak-like structure in previous studies. The extreme precipitation intensity has been shown to reach a peak value when temperature is around 25°C in the eastern United States, South Korea, Mediterranean, and Mahanadi River basin (Lepore et al., 2015; Park and Min, 2017; Peleg et al., 2018; Sharma and Mujumdar, 2019). The locations of these regions, as with MEC, are all coastal. Compared with the result reported by Wang et al. (2018), the temperature transition value is similar in MEC, whereas is lower in TP. In addition, the relationship between temperature and precipitation intensity at the 95th percentile was closer to the C–C rate than the other two percentiles, suggesting that the C–C rate is suitable for describing the relationship between stronger precipitation and temperature.

      Figure 3.  Relationships between the daily precipitation intensity and near-surface temperature from the rain gauge (RG) data in (a) Middle–East China (MEC) and (b) east Tibet Plateau (TP) during 1998–2012. The ordinate axis ranges from 1 to 200 mm day–1 on a logarithmic scale; the blue, red, and purple lines denote the variation of 75th, 90th, and 95th percentiles of daily precipitation intensity with the near-surface temperature, respectively; the gray dashed lines indicate the C–C rate; and the black solid vertical lines indicate the temperature transition values.

      Based on fitting of the relational expression [Eq. (1)] between precipitation intensity and temperature in Section 2, the correlation coefficient of extreme precipitation intensity and temperature at each selected station was obtained by regression analysis in MEC and TP. Then, the regional average correlation coefficients were calculated. Note that only the extreme precipitation events with daily temperature below the transition value were chosen to calculate the correlation coefficients with temperature. The results are listed in Table 1. With increased precipitation intensity, the correlation coefficient of precipitation intensity and temperature increased gradually, both in MEC and TP. This indicates that changes in precipitation intensity with temperature are more significant for heavy precipitation. In addition, the correlation between extreme precipitation and temperature is more robust in TP than in MEC.

      75th percentile90th percentile95th percentile
      MEC0.770.850.85
      TP0.820.840.91

      Table 1.  Regional average correlation coefficients between daily extreme precipitation intensity and temperature for the 75th, 90th, and 95th percentiles in MEC and TP

      Figure 4 shows the regression slopes (rate of increase) for extreme precipitation intensity and temperature at the selected stations in MEC and TP during 1998–2012. The rate of increase at MEC stations ranged from 3%–6% °C−1, 2%–6% °C−1, and 2%–4% °C−1 at the 95th, 90th, and 75th percentile of precipitation intensity, respectively. Meanwhile, the equivalent ranges for TP were 5%–14% °C−1, 5%–12% °C−1, and 8%–11% °C−1. By comparison, the rate of increase of extreme precipitation intensity with near-surface temperature was much larger in TP than that in MEC. These rates are smaller in MEC and larger in TP than previously reported based on hourly precipitation data during 1991–2012 (Miao et al., 2016).

      Figure 4.  Regression slopes for the logarithmic daily precipitation intensity and temperature for the (a) 75th, (b) 90th, and (c) 95th percentiles of daily precipitation intensity at the selected stations shown in Fig. 1 during 1998–2012.

    4.   Discussion
    • To reveal the possible mechanisms responsible for the different rates of increase in MEC and TP, we examined the roles of different precipitation types during extreme precipitation events in the two regions. Table 2 shows samples of different precipitation types based on the new merged PR dataset (see Section 2) in MEC and TP. There were 1142 and 2684 samples for convective and stratiform precipitation in MEC respectively, whereas there were only 832 and 363 samples for deep convective and shallow precipitation in TP respectively. In general, stratiform precipitation was the dominant form of precipitation in MEC, whereas the precipitation in TP was mainly deep convective precipitation, which is consistent with previous results (Fu et al., 2008a, b, 2018; Pan and Fu, 2015).

      ConvectiveStratiformDeepShallow
      MEC11422684
      TP832363

      Table 2.  Samples of different precipitation types derived from the new merged dataset in MEC and TP

      Figure 5 shows the relationship between the near-surface precipitation intensity for different precipitation types and the near-surface temperature using the new merged PR dataset in MEC and TP during 1998–2012. The convective and stratiform precipitation intensity increased with increasing temperature and decreased when temperature exceeded the transition value in MEC (similar to Fig. 3). It is clear that the rate of increase for convective precipitation with temperature was larger than that for stratiform precipitation (Figs. 5a, c). The variation of deep convective precipitation intensity with temperature in TP (Fig. 5b) showed a similar pattern with the result in Fig. 3. However, the shallow precipitation intensity decreased with increasing temperature, which was different to what was found for deep convective precipitation (Fig. 5d).

      Figure 5.  As in Fig. 3 but for the near-surface precipitation intensity of different precipitation types from the new merged precipitation radar (PR) dataset including (a) convective and (c) stratiform precipitation in MEC; (b) deep convective and (d) shallow precipitation in the TP during 1998–2012. The ordinate axis ranges from 0.5 to 100 mm h–1 on a logarithmic scale.

      The rate of change exceeding the C–C rate for extreme precipitation intensity with temperature is mainly caused by convective precipitation (Haerter and Berg, 2009; Berg and Haerter, 2013; Berg et al., 2013; Huang et al., 2017). Vertical activity is strong during convective precipitation, and releases more latent heat than other types of precipitation (Mitovski and Folkins, 2014). The latent heat released by convective precipitation heats the whole tropospheric layer and enhances upward movement, which can result in relatively high levels of condensation and increased precipitation intensity on a short timescale (Sheng et al., 2003; Beck and Bárdossy, 2013; Gao et al., 2018). Due to the short duration of convective precipitation, the phenomenon of the rate of increase being greater than the C–C rate is captured more easily by hourly than daily observations. Furthermore, the rate of increase being greater than the C–C rate is more obvious when the precipitation intensity is more intense. As shown in Fig. 5a, the convective precipitation intensity clearly increased more significantly with temperature at the 95th and 90th percentiles.

      Generally, stratiform precipitation forms via large-scale uplift and condensation. The vertical structure shows that latent heat only occurs above the melting level. In addition, cooling anomalies appear in the lower troposphere, and this cooling can last a long time because of the long duration of stratiform precipitation (Houze, 1997; Hu et al., 2011; Wang and Fu, 2017; Li et al., 2019). Thereby, the rates of change in stratiform precipitation with temperature at the three precipitation percentiles are not as robust as for convective precipitation. On the other hand, MEC is dominated by stratiform precipitation according to Table 2. Eventually, the rate of increase in extreme precipitation intensity with temperature could be reduced by stratiform precipitation in MEC.

      Although the classification of precipitation differs between MEC and TP, the precipitation types basically correspond. That is, deep convective precipitation and shallow precipitation correspond to convective precipitation and stratiform precipitation respectively. Accordingly, the mechanism responsible for the change in extreme precipitation intensity with temperature in TP is similar to that in MEC. Differently, the shallow precipitation intensity decreases with temperature more obviously. Because the number of samples of deep convective precipitation was more than double those of shallow precipitation in TP, the rate of increase extreme precipitation intensity with temperature was mainly contributed by deep convective precipitation.

    • As mentioned in Section 2, atmospheric humidity is the link between extreme precipitation and temperature according to the C–C equation and concept of extreme precipitation. To further investigate how atmospheric humidity affects the relationship between precipitation intensity and near-surface temperature in MEC and TP, the relationship between the near-surface depression of the dew point (DDP) and temperature is demonstrated. The DDP is a way to characterize atmospheric humidity, wherein a small DDP means the atmosphere is close to being saturated and a large DDP means the atmosphere tends towards being dry. The change in the near-surface DDP with temperature is shown in Fig. 6. Although there was little fluctuation, the DDP generally decreased with increasing temperature below the temperature transition values in MEC and TP. Then, DDP increased sharply with temperature after the transition value in the two regions, but particularly in TP. The pattern of change in DDP with temperature was an opposite to that of the structure of extreme precipitation intensity and temperature. Atmospheric humidity decreased with increasing temperature, which could possibly weaken the precipitation intensity. It is also worth noting that the atmospheric humidity was more sensitive to the change in the temperature in TP, since DDP increased more significantly above 15°C in this region.

      Figure 6.  The relationship between the daily depression of the dew point (DDP) and near-surface temperature in (a) MEC and (b) the TP during 1998–2012. The blue, red, and purple lines denote the variation of 75th, 90th, and 95th percentiles of DDP with the near-surface temperature, respectively; and the black solid vertical lines indicate the temperature transition values.

      The change in specific humidity (SH) with temperature in MEC and TP was further analyzed to support the above analysis (Figs. 7a, b). As the temperature increased, SH increased approximately exponentially in the two regions below the temperature transition value; whereas, the variation in SH increased slowly after 25°C in MEC, but decreased obviously at 15°C in TP. Similarly, Figs. 7c, d show the change in RH with temperature. As we can see, RH decreased significantly as temperatures grew larger than 25°C in MEC. RH also decreased with increasing temperature in TP and decreased sharply after 15°C. When atmospheric humidity does not increase, an air mass can only rise if it reaches saturation. As a consequence, the maximum water vapor content at upper levels is smaller than the water vapor content at lower levels (Drobinski et al., 2016; Barbero et al., 2018). Additionally, water vapor condenses into rain drops and generates into precipitation, which results in loss of atmospheric water vapor. This could affect the precipitation efficiency and further weaken the decreasing precipitation intensity because of the reduction in humidity against the background of global warming (Ye et al., 2014). The rates of change in DDP, SH, and RH with temperature at the C–C rate were calculated, and the results showed that the DDP or RH did not change with the C–C rate, only the SH maintained at approximately the C–C rate with increasing temperature below the temperature transition value in MEC and TP (Fig. 8). The result corresponds with those in Figs. 6, 7. Due to the direct correlation between SH and water vapor pressure, the SH and temperature presented a good C–C relationship.

      Figure 7.  As in Fig. 6, but for the daily specific humidity (SH) in (a) MEC and (b) the TP, and the relative humidity (RH) in (c) MEC and (d) the TP during 1998–2012.

      Figure 8.  As in Fig. 4, but for the daily specific humidity (SH).

    • As a measurement of water vapor, the PW influences the variation of precipitation. Previous studies have revealed that extreme precipitation is associated with PW under a warming climate (Ye et al., 2014, 2015). The effect of PW on extreme precipitation in MEC and TP was investigated, and the results are discussed as follows. Figure 9a presents the distribution of PW samples (corresponding to precipitation events) in each 2°C temperature bin in MEC and TP. It is apparent that the distribution pattern of PW number was the same as with the precipitation number. The distribution of PW intensity across the temperature range shows that atmospheric PW intensity monotonously with temperature (Fig. 9b). However, PW intensity varied with temperature with a different monotonic function in MEC and TP. Specifically, PW intensity increased exponentially with increasing temperature in MEC, whereas it tended to change linearly with increasing temperature in TP. As the essential element of precipitation, water vapor has a significant positive correlation with precipitation (Zhai and Eskridge, 1997; Wang R. et al., 2017). Figure 10 shows the relationship between the precipitation intensity and PW intensity in MEC and TP, revealing consistency with previous results in that the precipitation intensity had a significantly positive and near linear correlation with PW intensity. This suggests that precipitation intensity increases with increasing PW intensity. Moreover, the precipitation intensity increased more obviously with PW intensity in TP than in MEC.

      Figure 9.  As in Fig. 2, but for the precipitable water (PW) samples and intensity. The purple and green lines indicate the regression lines for PW intensity and temperature in MEC and the TP, respectively

      Figure 10.  The relationship between the daily precipitation intensity and precipitable water (PW) intensity from the rain gauge (RG) data in (a) MEC and (b) the TP during 1998–2012 (denoted by the black solid regression lines). The ordinate axis ranges from 0.5 to 100 mm day−1 on a logarithmic scale.

      The relationship between PW intensity and temperature was analyzed at the 95th, 90th, and 75th percentile. As shown in Fig. 11, the natural relationship of PW intensity with temperature was similar to that of extreme precipitation intensity with temperature. Specifically, PW intensity increased with the increasing temperature at the C–C rate when temperatures were lower than 28°C and 18°C in MEC and TP, respectively, and decreased with increasing temperature when they were higher than 28°C and 18°C. Moreover, the relationship between PW intensity and temperature was closer to C–C rate than the relationship between extreme precipitation intensity and temperature. Because of latent heat released during the process of condensation, the upper atmosphere becomes heated and the water vapor content increases accordingly (Fujita and Sato, 2017). Thus, the rate of change in PW intensity with temperature was closer to the C–C rate.

      Figure 11.  As in Fig. 3, but for the daily precipitable water (PW) intensity. The ordinate axis ranges from 1 to 200 mm day−1 on a logarithmic scale.

      Figure 12 shows the trend of PW intensity corresponding to precipitation events for each selected station in MEC and TP during 1998–2012. It is clear that the trends in PW intensity were negative at most stations during this period. The decreasing PW intensity led to decreasing atmospheric humidity and could have had a positive effect on the decrease in precipitation intensity. Therefore, the extreme precipitation intensity was not only restricted by near-surface humidity, but also was affected by the PW intensity, which is the amount of water vapor in the local atmospheric column. The regression slope for PW intensity and temperature ranged from 5%–6% °C−1 and 6%–9% °C−1 in MEC and TP (Fig. 13). This again verified that the increasing rate of PW intensity with temperature was closer to the C–C rate than that of extreme precipitation intensity and temperature, and the change in PW intensity with temperature can be more robustly described by the C–C relationship.

      Figure 12.  The PW intensity trends corresponding to precipitation events at the selected stations shown in Fig. 1 during 1998–2012.

      Figure 13.  As in Fig. 4, but for the PW intensity.

    5.   Summary and conclusions
    • Based on the IGRA radiosonde data, co-located RG observation data, and a new merged dataset derived from TRMM PR products and IGRA, the relationship between extreme precipitation intensity and near-surface temperature on the daily timescale was investigated from a thermodynamics perspective over the MEC and TP regions during 1998–2012. Meanwhile, we compared the relationship in MEC with that in TP. Moreover, we analyzed the humidity and PW as possible factors that influenced the change in the relationship between extreme precipitation and temperature in MEC and TP. The main results are summarized as follows.

      Observational data analyses indicate that extreme precipitation intensity increased with increasing temperature at an approximate C–C rate in MEC and TP. The rate of increase was significantly closer to C–C rate when the precipitation intensity was larger, which suggests that the C–C rate is more suitable for describing the relationship between extreme precipitation and temperature. In contrast, the rate of increase in extreme precipitation intensity with rise of temperature was larger in TP than that in MEC, probably because of different types of precipitation that occur in the two regions. Specifically, deep convective precipitation occurs frequently in TP while stratiform precipitation dominates MEC, and convective precipitation releases more latent heat to enhance upward motion and may therefore produce more precipitation in a short period. However, when temperatures were higher than 25°C in MEC and 15°C in TP, the variation of extreme precipitation intensity with temperature did not follow the C–C rate, and the precipitation intensity decreased with increasing temperature. This implies that precipitation intensity does not always increase with climate warming.

      According to the C–C equation and the concept of extreme precipitation, atmospheric humidity is the connection between extreme precipitation and temperature. Therefore, the effect of atmospheric humidity on extreme precipitation was discussed. We found that the relationship of the DDP, SH, and RH with temperature was similar to that of the change in extreme precipitation intensity with temperature. The extreme precipitation intensity increased along with increasing humidity at lower temperature ranges, whereas precipitation intensity decreased at higher temperatures because of a loss of humidity. In addition, PW, which characterizes the atmospheric water vapor, also showed a peak-like structure across the temperature range, similar to change in extreme precipitation intensity with temperature. Moreover, PW intensity showed negative trends at most stations in recent years, indicating that decreasing water vapor might influence the precipitation intensity. Hence, the changes in near-surface humidity and column-integrated water vapor could have critical impacts on the changes in extreme precipitation intensity against the background of warming in MEC and TP.

      Undoubtedly, investigating the relationship between extreme precipitation and temperature is complicated and challenging. For instance, atmospheric stability and aerosols are two other key elements for the formation of precipitation, and more works will need to focus on weather systems, the effects of aerosols, and other factors that affect the change in extreme precipitation with temperature over MEC and TP in the future.

      Acknowledgments. We appreciate the NCDC, CMA-NMIC, and GSFC for providing the IGRA radiosonde data, RG precipitation data, and TRMM PR 2A25 products. We also appreciate the valuable comments by the Editor and two anonymous reviewers.

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