2020 年 98 巻 6 号 p. 1147-1162
The usefulness of Clausius–Clapeyron (CC) scaling in explaining extremely heavy precipitations is explored in the present-day climate and in pseudo-global-warming (PGW) conditions. This is analyzed by conducting regional-scale numerical simulations at 1-km grid resolution for two recent extreme rainfall events that occurred in Japan: the case in northern Kyushu during 5–6 July 2017 and the case in Shikoku Island during 5–8 July 2018. The Weather Research and Forecasting (WRF) model was used for the simulation, and the data samples were collected at each grid point individually for each hour over the two regions. We found that the frequency and intensity of extremely heavy precipitation associated with the two events are increased under PGW conditions. The extremely heavy precipitations (> 50 mm h−1) followed CC scaling for the temperatures up to 22°C in the present-day climate, while those under the PGW conditions followed CC-scaling up to 24°C. The peak intensity of the extremely heavy precipitations in the precipitation-temperature relationship is found as ∼ 140 mm h−1 at 25°C in the present-day climate, while the same with PGW conditions is projected as ∼ 160 mm h−1 at 27°C. The increasing rate of the extremely heavy precipitations in the present-climate condition is noticed as ∼ 3 % °C−1 and that under the PGW conditions is anticipated as ∼ 3.5 % °C−1. The increase in peak precipitation intensity and the rate of precipitation increase against temperature in future warming climate are attributed to the decrease in temperature lapse rate and increase in atmospheric water vapor and convective available potential energy. To our knowledge, this is one of the first quantitative investigations of CC scaling of extremely heavy precipitations based on case studies.
The Clausius–Clapeyron (CC) equation states that the moisture-holding capacity in the atmosphere increases at a rate of ∼ 7 % °C−1 (Trenberth et al. 2003). According to this equation, it is expected that the heavy rainfall events should scale with temperature when a constant relative humidity is assumed (Trenberth 2011; O'Gorman 2015). Recent studies on heavy rainfall events indicated that higher-percentile precipitation intensities mostly increase with temperature (Lenderink and Meijgaard 2008, 2010; Lenderink et al. 2011; Muller 2013; Berg et al. 2013; Nayak and Dairaku 2016; Taylor et al. 2017; Nayak et al. 2018; Nayak 2018; Nayak and Takemi 2019a).
According to previous studies (Haerter and Berg 2009; Singleton and Toumi 2013; Moseley et al. 2016), the hourly heavy rainfall events are often a result of the self-aggregation of local convective clouds into larger cloud clusters. When such organized convective cloud clusters remain over a place for a long time, it produces extremely large amount of rainfall (Schumacher 2009; Schumacher and Johnson 2009; Ricard et al. 2012; Unuma and Takemi 2016a, b; Takemi 2018) and therefore the risks of floods increase (Coumou and Rahmstorf 2012).
Recently, two extremely heavy rainfall events occurred during 5–6 July 2017 and 5–8 July 2018 in western parts of Japan and caused severe damages. These two events brought record-breaking torrential rainfall amounts of over 500 mm d−1 to Kyushu and Shikoku Islands of Japan (http://www.dpri.kyoto-u.ac.jp/disaster_report/#9491). Previous studies pointed out that the stationary convective systems over an identical location for a long time are the main causes of these extreme rainfall events (Takemi 2018; Kato et al. 2018; Tsuguti et al. 2019) although such flood events depend on many other factors such as moisture content, favorable synoptic situations, terrain and hydrological basin size (Ranalkar et al. 2016; Takemi 2018; Huang et al. 2019). However, many studies have revealed that a change in temperature certainly influences the local convective systems and therefore regulates the memory of past rainfall and inter-cloud dynamics, because the self-organization of precipitation at any given time is controlled by the atmospheric conditions resulting from past processes (Singleton and Toumi 2013; Moseley et al. 2016). Thus, by assuming that the extreme precipitations are controlled by the moisture already available in the atmosphere and its change due to temperature, it is reasonable to expect that the extreme precipitations during individual events will scale with temperature in roughly proportion with CC-scaling (Hardwick et al. 2010; Romps 2011; Singleton and Toumi 2013). CC-scaling refers to the scaling anticipated from the CC equation, which is roughly 7 % °C−1.
The relationship between precipitation and temperature have been explored for several cases over some regions in Japan from multi-decadal observational data and/or climate simulations (e.g., Utsumi et al. 2011; Yamada et al. 2014; Fujibe 2016; Nayak et al. 2018). Such studies examined the rainfall amounts as a daily basis. According to these studies, the daily precipitation in extreme ranges increases with temperature up to a certain degree (roughly 20–25°C) and decreases at higher temperatures. Nayak et al. (2018) analyzed multi-model ensemble datasets at 20-km spatial resolution and highlighted that daily precipitation extremes over Japan follow super-CC scaling (> 7 % °C−1) for temperatures below ∼ 10°C and sub-CC scaling (< 7 % °C−1) for temperatures above ∼ 10°C. On the other hand, Utsumi et al. (2011) analyzed the hourly and 10-min meteorological station observation data over North Island, Kyushu, and Southern Islands of Japan and found that the precipitation extremes in a sub-daily time-scale exhibit CC scaling and monotonically increases even at high temperatures, implying that higher temperatures will enhance the potential for precipitation extremes on shorter timescales, corresponding to extremely heavy precipitations in local areas.
An inherent weakness of using long-term rainfall dataset is that they are of coarse resolution and do not resolve the life cycle of individual extreme heavy rainfall events and do not also explicitly resolve the convective processes. Since temperature conditions play a crucial role in driving the convection processes within an individual heavy rainfall event itself by regulating the saturation vapor pressure and hence the amount of water vapor according to the CC equation. A few studies (e.g., Hardwick et al. 2010; Singleton and Toumi 2013; Attema et al. 2017) highlighted that CC scaling exists even in individual heavy rainfall events and the associated extreme precipitations also follow CC scaling when the temperature is below 24–26°C. Now, the question is whether extremely heavy precipitations induced by individual heavy rainfall events evaluated in short time-periods, e.g., an hourly time-scale, can be explained using the CC equation? Since extreme precipitations occur in Japan and the East Asian regions during the monsoon and summer seasons, it is scientifically interesting how CC scaling appears in the extreme precipitations during those warm seasons. In this sense, the two torrential rainfall events that occurred in western Japan during 5–6 July 2017 and 5–8 July 2018 (hereafter July 2017 and July 2018 events) are considered appropriate examples to investigate how in the extreme cases the precipitation-temperature relationship is compared with CC scaling.
In addition, it is anticipated that extremely heavy precipitations will intensify in the global warming climate. A recent study on the July 2018 event by Kawase et al. (2020) suggested that the total precipitation during this heavy rainfall event was increased by about 7 % owing to recent warming around Japan. Therefore, our question is further extended to an issue whether the response of CC scaling of extreme precipitations to future warming climate appears. As stated above, only a few studies investigated CC scaling of extreme precipitations, but evaluated in a daily timescale over Japan by taking into account all wet events (particularly defined as > 0.5−1 mm d−1) in present and future climates (e.g., Yamada et al. 2014; Nayak and Dairaku 2016; Nayak et al. 2018). However, CC scaling of extremely heavy precipitations, evaluated in a shorter timescale (e.g., > 50 mm h−1), are not well explored. Typically, neither models nor observational data have yet been analyzed for extremely heavy precipitations in an hourly timescale, although a few studies (e.g., Hardwick et al. 2010; Romps 2011; Singleton and Toumi 2013) highlighted about these concepts. According to Hardwick et al. (2010), CC-scaling exists between the surface temperatures up to between 20°C and 26°C and precipitation durations up to 30 minutes which implies possible existence of CC scaling in short time storm systems. Because CC scaling is derived from a thermodynamic law, the scaling should be a guide to quantify the increase in extreme precipitation amounts from a climatological aspect. From an impact assessment point of view, e.g., flash flooding, inundations, landslides, etc., with extreme precipitations in a shorter timescale, such as an hourly time scale should be considered. Therefore, CC scaling of extreme precipitations in an hourly time scale is important.
This study intends to understand the usefulness of CC scaling in explaining the extremely heavy precipitations (> 50 mm h−1) in the framework of the two above-mentioned torrential rainfall events. A regional meteorological model is used to reproduce the two heavy rainfall events. We also simulate those rainfall events under a future warmed climate condition. The warmed climate condition is generated by a pseudoglobal-warming (PGW) approach. Here PGW condition refers to a future warming scenario which is prepared by adding the warming increments of climatic variables to that in present reanalysis fields (Sato et al. 2007).
The Weather Research and Forecasting model version 4.0 (WRF V4.0, Skamarock et al. 2008) was configured in two-ways, i.e., two nested domains with grid spacings of 5 km (parent domain: d01) and 1 km (inner domain: d02) (Fig. 1). Four numerical experiments (two experiments for the July 2017 event in the present-day and future climates and two experiments for the July 2018 event in the present-day and future climates) are conducted for 16 days each, starting from the 25th June to 10th July of each year. For present-day climate simulations, the model was forced by 1.25° resolution Japanese 55-year Reanalysis (JRA55) data at 6-hour interval (Kobayashi et al. 2015). For future climate simulations, the warming increments of sea surface temperature (SST), geopotential height, and temperature were added to the present-day reanalysis fields of JRA55 which is referred as PGW conditions. The choice of the variables added to the JRA55 fields is based on the idea that thermodynamic fields play an important role in quantifying the convective response to the warmed conditions (Ito et al. 2016; Takemi 2016a, b, 2019; Nayak and Takemi 2019b, c). The warming increments were taken from MRI-AGCM3.2 climate simulations performed for the present-climate (1979–2003) and future-climate under the RCP8.5 scenario (2075–2099) (Mizuta et al. 2012, 2014). The mean difference between present climate (1975–2003) and future climate (2075–2099) are computed for temperature including SST and geopotential height at each grid point and added to JRA55 reanalysis data at each grid point. A brief overview of the model setup and configuration is given in Table 1. To validate the model results, we compared precipitation amounts and temperatures from the model simulations with Automated Meteorological Data Acquisition System (AMeDAS) station observations. We also compared the model simulated precipitation distributions with Radar-AMeDAS analyzed precipitation datasets.
Model domain (d01) and the location map of the study region. The inset red (blue) boxes corresponds to the inner model domain (d02) for July 2017 (July 2018) event. The purple (green) boxes (box 1 and box 2) corresponds to the study region of July 2017 (July 2018) event. The inset map in the model domain shows the location of 114 AMeDAS observation stations.
We sampled the precipitations at each grid points individually for each hour over the two boxed regions in d02 (Fig. 1). The box over Kyushu Island (box 1) contains 168 × 68 grid points and the box over Shikoku Island (box 2) contains 277 × 189 grid points. Previous studies (e.g., Berg et al. 2009 and Attema et al. 2017) also collected the samples in the same way. We identified the precipitations with different thresholds of intensities (1, 10, and 50 mm h−1) at each grid point and categorized them into light, moderate and extremely heavy precipitation types according to their intensities exceeding 1, 10 and 50 mm h−1 respectively and analyzed each type separately. It is noted that various studies have used various precipitation thresholds and there is no standard threshold. In our study, we used three different thresholds (1, 10 and 50 mm h−1), while we did not consider the precipitations with intensities below 1 mm h−1 in the CC analysis. It is also noted that 1, 10 and 50 mm h−1 precipitation intensities roughly correspond to 50th, 85th and 99th percentile of precipitation distribution respectively (see Sections 3 and 4). We then paired the precipitation intensity (P), separately for each threshold, with the corresponding hour's temperature (T) at each grid point (P, T) for all hourly time steps from 0000UTC to 2300UTC 5 July 2017 and from 0000UTC 5 July 2018 to 2300UTC 7 July 2018. We combined all the (P, T) pairs obtained from the two events (the July 2017 and July 2018 cases) and analyzed precipitation-temperature characteristics from the total (P, T) pairs. The total number of the (P, T) pairs are about 4,050,000 (168 × 68 grid points for July 2017 event for 24 hours and 277 × 189 grid points for July 2018 event for 72 hours). We stratified the precipitation intensities into different temperature bins of 1°C interval and computed the 99th percentile in each temperature bin for each categorized precipitation type (light, moderate and extremely heavy). We set the lowest sample size in each bin to 400 (∼ 0.01 % of total sample size) to minimize the sampling error. So the bins with less than 400 samples are not included in the analysis. Finally, we applied a least squared linear regression to the logarithm of precipitations (considering the temperature values up to peak precipitation intensities), separately for each categorized precipitation type, which will be similar to the following equation:
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This equation is computed from August-Roche-Magnus approximation for saturated vapor pressure, es:
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We first compared the model simulated precipitation and temperature with observations by analyzing the frequency distributions and different percentiles of precipitation intensities and temperature in the framework in the torrential rainfall events (July 2017 and July 2018).
3.1 Frequency distributionFigure 2a represents the frequency distribution of the precipitation intensities from 114 AMeDAS station observations and that from the model simulation at the grid points corresponding to the 114 AMeDAS stations. The precipitation intensities from the 1 km grid Radar_AMeDAS observation and that from the model simulation at 1 km grid is shown in Fig. 2b. The shape of frequency distributions of precipitation intensities looks different between AMeDAS (Fig. 2a) and Radar_AMeDAS (Fig. 2b), probably because of different sample points. It is noted that the total sample points in the station observation case are about 5000 (37 stations for July 2017 event for 24 hours and 77 stations for July 2018 events for 72 hours), while the total number of sample points for the simulation case is about 4 million because we considered all hourly time steps at each grid point (1 km resolution) over the two boxed regions in d02. We found that the distribution of precipitation intensities in the model simulation agrees well with that of in the observations in both cases (station and grid). The stronger precipitations have intensities above 100 mm h−1 (160 mm h−1) in AMeDAS station (Radar_AMeDAS) observations although their frequencies of occurrences are less. The difference in the precipitation intensities in AMeDAS and Radar_AMeDAS could be due to the limited number of AMeDAS stations compared with the large number of grids in Radar_AMeDAS. The frequency distribution of temperature is well represented in the model simulation for the temperatures above 25°C while it is slightly overestimated for temperatures below 22°C and underestimated for the temperature 23–24°C (Fig. 2c). The underestimation of temperature frequency for 23–24°C is perhaps due to the cold bias of WRF model for summer-days simulation (García-Díez et al. 2013). We also compared the model simulated precipitable water with the 50-km hourly data from Modern-Era Retrospective Analysis for Research and Applications (MERRA-2) and found a good agreement between them (Fig. 2d).
Frequency distribution of precipitation intensities (a) from WRF and AMeDAS station observations, and (b) from WRF and Radar-AMeDAS grid observations. (c) Frequency distribution of temperature from WRF and AMeDAS station observations. (d) Frequency distribution of precipitable water from WRF and MERRA-2 reanalysis. P (x) indicates the probability of (a, b) precipitation intensity, (c) temperature, and (d) precipitable water.
The extremes are examined at different percentiles of precipitation intensities and precipitable water starting from 50th to 99th from the model simulation and the observation (Fig. 3). The percentiles of precipitations are separately calculated with consideration of all intensities at all grid points (Figs. 3a, b) and the precipitations only with different thresholds (Figs. 3c, d). We found that the precipitations at higher percentiles (> 80 %) are overestimated by the model when all intensities are considered (Figs. 3a, b), while this overestimation is reduced when the intensities are considered with some thresholds (Fig. 3c, d). The overestimation at 99th percentile of the precipitations in the model corresponds up to ∼ 20 mm h−1 for all intensities, while it corresponds up to ∼ 15 mm h−1 in the case of 1 mm h−1 intensity threshold and up to ∼ 5 mm h−1 in the case of a 50 mm h−1 intensity threshold. However, in general all percentiles of extremely heavy precipitations (> 50 mm h−1) are well captured by the model. The 50th percentile corresponds to ∼ 60 mm h−1 precipitation intensity; however, the 90th and higher percentiles correspond to ∼ 100 mm h−1 or more. The correspondence of the simulated results both with Radar_AMeDAS gridded observation and AMeDAS station observation shows similar results. This indicates that the model reproduced the intensities of extremely heavy precipitations reasonably well.
Different percentiles of precipitations (a) from WRF and AMeDAS station observations, and (b) from WRF and Radar-AMeDAS grid observations considering all intensities. The results in (c) and (d) are the same as (a) and (b) respectively, but with 1 mm h−1 and 50 mm h−1 intensity thresholds. (e) Different percentiles of precipitable water from WRF and MERRA-2 reanalysis.
We also compared the model simulated precipitable water with MERRA-2 data at different percentiles and noticed a good agreement between them (Fig. 3e). The precipitable water refers to the amount of atmospheric water vapor in a column of the atmosphere. The absolute amount of water dissolved in the atmosphere is known as atmospheric water vapor. In general, extreme precipitations require large amounts of precipitable water which is determined from the atmospheric water vapor and the precipitable water has a positive correlation with precipitation (Lu et al. 2009). So in the following section, we will further examine the amount of precipitable water as well as other atmospheric factors during the extreme precipitations.
In this section, we first analyzed the spatial distribution of daily precipitation intensities and temperatures during the July 2017 and July 2018 events in the present-day climate condition and in the PGW climate. We then examined the occurrence of extremely heavy rainfall events and the associated temperatures. Subsequently we investigated the relationship between extreme precipitations and temperature during the two events and their connection with the CC equation.
4.1 Precipitation and temperature distributionThe spatial distributions of daily precipitation intensities and temperatures during the two events are shown in Fig. 4. We found that the two events under PGW climate produce more precipitations over the target regions with an exception for 07 July 2018 (Figs. 4a, b). The precipitation intensities on 7 July 2018 do not show significant changes in future climate, perhaps due to quick intermittent removal of atmospheric moisture by the extreme precipitations on previous two days in the future condition. Much intense precipitation implies more release of latent heat which may further supply more moisture and make the precipitating cycle more rapid although what happens to the duration is less clear. Closer looks on precipitation intensity during 6–7 July 2018 also indicates very intense precipitation over Shikoku Island on 6 July 2018 in future climate, which may drain away all the moisture in future condition. Previous studies (e.g., Trenberth et al. 2003) also reported that the intensity of extreme events may be strengthened and duration of extreme events may be shortened under global warming. Daily mean temperatures during these two events show an increase in future warming climate over almost all areas of the target region (Figs. 4c, d).
24-hours (00–23 UTC) accumulated precipitation of each day over the target boxed region (box 1 and box 2) of d02 in Fig. 1 in (a) present climate and (b) future climate; and 24-hours (00–23 UTC) mean temperature of each day over the target boxed region (box 1 and box 2) of d02 in Fig. 1 in (c) present climate and (d) future climate.
Figure 5a represents the frequency distribution of precipitation intensities in the present-day climate and under the PGW condition. Figure 5b illustrates different percentiles of precipitations with 50 mm h−1 intensity threshold in the present and future climates. We found that the strongest precipitation intensity under PGW reaches about 200 mm h−1, higher than the strongest intensity of around 180 mm h−1 in the present climate (Fig. 5a). All percentiles of the extremely heavy precipitations under PGW conditions correspond to an increase of ∼ 20 mm h−1 intensity compared with present-day climate (Fig. 5b). The normal probability distribution of extremely heavy precipitations (> 50 mm h−1) and the associated temperatures in the present-day climate condition and the same with the PGW condition are shown in Fig. 6. The normal probability distribution, f (x) was defined as:
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(a) Frequency distribution of precipitation in present climate and future climate; and (b) Different percentiles of precipitation intensities with 50 mm h−1 precipitation threshold in present climate and future climate. P (x) indicates the probability of precipitation intensity.
Probability distribution function (PDF) of (a) the extremely heavy precipitations with threshold of 50 mm h−1 intensity and (b) the temperature during the heavy precipitations. The values in each figure correspond to the mean (μ) and standard deviation (σ).
The results indicated that the occurrence of extremely heavy precipitations with intensity exceeding ∼ 80 mm h−1 are increased and the precipitations with intensity below ∼ 80 mm h−1 are decreased under PGW conditions (Fig. 6a). We noticed that during extremely heavy precipitations, the probability of temperatures above ∼ 23°C is increased and that of temperatures below ∼ 23°C is decreased under PGW condition (Fig. 6b). The intensity of some extremely heavy precipitations in future warming climate are expected to increase by ∼ 20 mm h−1 and the temperature associated with such precipitations under PGW conditions are expected to increase by ∼ 4°C (Fig. 6b). This indicates that future changes in the occurrences of extremely heavy precipitations are someway connected to the temperatures.
4.3 Relationship between extremely heavy precipitations and temperatureWe first analyzed the precipitation-temperature relationship at the AMeDAS observation stations and compared it with model simulated precipitation-temperature relationship at the grid points corresponding to the AMeDAS observation stations (Fig. 7a). Results indicated that the intensities of the extreme precipitations linked to temperature are overestimated for all precipitation types (light, moderate and extremely heavy) and show a relatively weaker peak compared with that of observation. However, both model and observation extreme precipitations linked to temperature have relatively similar peaks for light and moderate precipitation types. Extremely heavy precipitation type in the observation shows monotonically increasing characteristics with temperature compared with the light and moderate precipitation types, while shows similar behavior with slower rate compared with direct observation. It is worth mentioning that the relationship between extreme precipitations and temperature obtained from the samples of two torrential rainfall events does not look like the idealized relationship. This could be due to the less variability in temperature within the events and the topographic effect.
The 99th percentile of precipitations with different intensity thresholds as a function of temperature from (a) observation and model simulation in present climate, and (b) model simulation in present and future climates. (c) The 99th percentile of precipitable water as a function of temperature during the extreme precipitations. The dashed lines are obtained from the CC equation and used as reference.
Figure 7b represents the relationship between 99th percentile of three categorized precipitation types (light, moderate and extremely heavy) and temperature in present-day climate and future warming climate. The 99th percentile of light and moderate precipitations (i.e., > 1 and 10 mm h−1) does not show any significant change in intensities with temperatures below 23°C in present-day climate, while that of the extremely heavy precipitations (> 50 mm h−1) shows increase in intensity with temperature up to 25°C (Fig. 7b). Overall, we found a negative relationship between the extreme precipitations and temperature for light to moderate precipitation cases during July 2017 and July 2018 events.
In a study on extreme precipitations over Europe, Berg et al. (2009) also reported a negative relationship between extreme precipitation intensities during June, July, and August. Specifically, they found that the intensity of all categorized precipitation cases in future warming climate increases with temperature up to a certain temperature and then starts decreasing. We found that the peak intensity of the extremely heavy precipitations is ∼ 140 mm h−1 at 25°C in the present climate, while the same in future climate is ∼ 160 mm h−1 at 27°C. Nevertheless, the intensities of all categorized precipitation types are increased by ∼ 20 mm h−1 at higher temperatures in future warming climate.
Figure 7c shows the 99th percentile of precipitable water as a function of temperature during the precipitation cases. The 99th percentile of precipitable water during these rainfall events shows a sharp increase with temperature up to certain temperature in both climates (Fig. 7c). The results indicated that during extreme precipitations the dependence curves of the atmospheric water vapor on temperature are almost the same up to the peak intensity among all the thresholds of precipitations. In all the precipitation intensity categories, the peak amount of the precipitable water for the extreme precipitations is noticed as about 75 mm at 26°C in present-day climate, while that in future climate is expected as ∼ 95 mm at ∼ 28°C. This implies an increase of ∼ 20 mm of precipitable water in future warmer atmosphere with an increase of ∼ 2°C temperature which is consistent with the future changes in the intensities of extremely heavy precipitations.
4.4 CC-scaling of extremely heavy rainfall eventsFigure 8 shows the rate (i.e., α in Eq.1) of change of the 99th percentile of the light to extremely heavy precipitation cases in present-day climate and future warming climate. We computed the rates with the consideration up to peak intensities of each categorized precipitation type. We found that the heavier precipitations have higher increasing rates of intensities. The increasing rates of the light and moderate precipitations in the present-day climate are found as ∼ 0.5 % °C−1 and those in the future warming climate are projected as ∼ 1 % °C−1. On the other hand, the increasing rate of extremely heavy precipitations in the present climate was observed to be ∼ 3 % °C−1 and that in the future warming climate model was anticipated as ∼ 3.5 % °C−1. These results indicated that the rate of change of all the categorized precipitation cases in the future warming climate are expected to increase by ∼ 0.5 % °C−1 in addition to the rate in the present-day climate.
The rate of change of precipitations with 1, 10 and 50 mm h−1 thresholds of intensities.
Overall, the increasing rate of light and moderate precipitation cases linked to temperature is less significant compared with CC scaling (∼ 7 % °C−1). This is different from the results shown in the previous studies (Utsumi et al. 2011; Yamada et al. 2014; Nayak et al. 2018) over Japan which highlighted the increasing rate of 3–6 %. The reason could be due to the consideration of different time periods. For instance, the previous studies over Japan looked at the whole year when temperatures are largely different depending on the seasons, while we looked at only a few days in July, corresponding to the warm season. So much more similar events with less variability in temperature occurred in our study domain and can be possibly explained with the seasonal analysis (e.g., Berg et al. 2009). However, we found that the 99th percentile of extremely heavy precipitations follows CC scaling for the temperatures up to 22°C in present-day climate. On the other hand, our result is slightly different from that of the previous study of Singleton and Toumi (2013) who reported a CC scaling of extreme precipitations up to 24°C. This difference could be associated with the regionality and type of torrential rainfall events. The difference in the environmental conditions for the occurrence of precipitations may play a role in producing different responses of the extreme precipitation intensity to the increase in temperature in each climate condition, because the environmental conditions will strongly control the structure and intensity of precipitating cloud systems (e.g., Unuma and Takemi 2016a) and hence affect the extreme precipitation intensity. The environmental conditions will be examined in the next section, but detailed analysis is beyond the scope of this study.
All precipitations irrespective of intensity thresholds in future warming climate follow CC scaling up to 24°C (Fig. 7b). This indicates that the extremely heavy precipitations associated with the two torrential rainfall events in future warming climate will be more intense, probably due to the dynamic and thermodynamic effects on the moisture content (Dairaku and Emori 2006). Previous studies (e.g., Yamada et al. 2014; Nayak and Dairaku 2016) also documented an increase in precipitation intensities in future climate over Japan. Nayak and Dairaku (2016) reported an increase of extreme precipitation intensities 5–15 mm d−1 for temperatures above ∼ 21°C over Japan in the future climate. It should be pointed out that our analysis is a first step to explore CC scaling of extremely heavy precipitations by choosing two torrential rainfall events as a case study. However, to understand the robustness of CC scaling of extremely heavy precipitations in torrential rainfall events, additional investigation that considers a larger number of torrential rainfall events is required.
Our results indicated that the extremely heavy precipitations (> 50 mm h−1) shows an increase in intensity with temperature up to certain degree, which was not found for the light to moderate precipitation cases. Previous studies mostly consider the light precipitations cases (> 0.1 mm). Further we found that the rate of change of extreme precipitations with temperature is higher together with higher moisture availability in future climate, implying more intensified rainfall. So our discussion is twofold: (1) Why CC scaling is not prominent with light precipitation cases, and (2) Why the rate of change of extreme precipitations is higher in future climate.
5.1 CC scaling is not prominent with light precipitation casesWe found that the intensities of the extremes (99th percentile) of light to moderate precipitations do not vary significantly for the temperatures below 23°C, but decrease with higher temperatures in the present climate. Previous studies over Japan and other regions with a threshold of 0.5–1 mm d−1 also show a decrease in precipitation intensity at higher temperatures (Hardwick et al. 2010; Utsumi et al. 2011; Nayak and Dairaku 2016; Prein et al. 2017; Nayak et al. 2018; Nayak 2018). A decrease in precipitation at higher temperatures during June-August was also reported over Europe (Berg et al. 2009).
However, we found that the amount of extremely heavy precipitations during July 2017 and July 2018 events increases with temperature in both climates (present-day and future). We have shown that our result can be explained in terms of the CC equation, which states that with the increase in temperature the water vapor content is increased. This response seems to be different from the findings in light to moderate precipitation cases. For example, the previous studies such as Berg et al. (2009) examined precipitation intensity of greater than 0.5 mm d−1 to 1 mm d−1, while we have focused on extreme precipitation intensity of greater than 50 mm h−1. We consider that the difference is due to the difference in the environmental conditions. Specifically, the cases chosen here are the extremely heavy rainfall events that occurred in the wettest season in Japan, i.e., the Baiu season. Under such moist conditions, water vapor content is generally large. Therefore, the reason for the increase in the extremely heavy precipitation amount with temperate is considered to be associated with the availability of water vapor which is sufficiently higher during the extremely heavy precipitations (Dairaku and Emori 2006; Lenderink and Meijgaard 2008, 2010).
On the other hand, the water vapor availability during light and moderate rainfall events does not sufficiently increase with temperature (Berg et al. 2009). Moreover, the moisture will not increase endlessly with temperature if there is less moisture available in the atmosphere (Westra et al. 2014). These could be some possible reasons for decreasing the precipitation intensities at higher temperatures. The results of precipitation analysis, which is linked to the atmospheric water vapor, also show a decreasing tendency at higher temperatures (Fig. 7b). To understand the underlying mechanisms, we analyzed the specific humidity and relative humidity at the surface (2-m level) (Figs. 9a, b), mean relative humidity averaged at the levels of 850 hPa and 500 hPa (Fig. 9c), temperature lapse rate (TLR) between 850 hPa and 500 hPa (Fig. 10), and convective available potential energy (CAPE) (Fig. 11) for all the categorized rainfall cases during July 2017 and July 2018 events. TLR here is one of the environmental parameters useful to diagnose the intensity of convection (Takemi 2007, 2010). We found that both specific humidity and relative humidity at the surface are declined at higher temperatures during the light precipitation cases (Fig. 9). This indicates less moisture supply for saturation at higher temperatures for the light precipitations. From Fig. 10, it is seen that in the present climate the TLR between 850 hPa and 500 hPa slightly decreases with temperature up to ∼ 21°C but shows an increasing tendency at higher temperatures. This tendency can also be seen for the PGW climate, but the magnitude of TLR in the PGW climate is lower than that in the present climate case, and therefore the impact of the lower TLR (which indicates that the atmosphere is more stable) appears more clearly in the PGW climate (Takemi 2007, 2010).
The 99th percentile of (a) specific humidity at a height of 2 m, (b) relative humidity at a height of 2 m and (c) mean relative humidity (RH) with 850 hPa and 500 hPa as a function of temperature during the extreme precipitations.
The 99th percentile of TLR between 850 hPa and 500 hPa as a function of temperature during the extreme precipitations.
The 99th percentile of CAPE as a function of temperature during the extreme precipitations.
The change in CAPE with temperature is shown in Fig. 11. Although there is no significant change in CAPE at higher temperatures for the light precipitations in the present climate, the CAPE values increase with temperature, reaching the highest range for all the rainfall categories in the PGW climate. Because CAPE is an integrated quantity in the vertical, the value of CAPE becomes larger when the temperature and water vapor at the surface are higher. In the present case, because of the very high temperature in the PGW climate, CAPE does generally become larger. However, the extreme precipitations at the higher temperatures decrease, despite CAPE is larger and TLR is higher. At the higher temperatures, precipitable water vapor content decreases (Fig. 7b). Therefore, because of the less availability of moisture in the troposphere, precipitation intensity decreases at the higher temperatures.
In this way, generally low TLR with insufficient moisture at higher temperature will lead to suppress convection development and hence decrease the precipitation intensities at higher temperatures. Conversely, the specific humidity, precipitable water, and CAPE during moderate and extremely heavy rainfall events continued to increase with temperature, and keep on relative humidity 100 %, they cause heavy precipitations.
5.2 The rate of change of extreme precipitations is higher in future climateWe further found that the extremely heavy precipitations (> 50 mm h−1) follow CC scaling up to a certain temperature and then exhibit sub-CC scaling in present climate as well as future climate. The sub-CC scaling behavior of precipitation extremes are also highlighted in multitude of studies over different regions across the globe (e.g., Lenderink and Meijgaard 2010; Mishra et al. 2012; Westra et al. 2014; Nayak and Takemi 2019a). However, we found that the rate of change of precipitation is higher for heavier precipitations in present climate and projected to further increase in future warming climate. In addition to this, the intensities of extreme precipitations are increased by ∼ 20 mm h−1 in future warming climate. This indicates that the extremely heavy precipitations in future warming climate will be more intense and may cause local flooding and landslides. This may cause major challenges for the societal livelihood systems in future warming climate. The rate of change of extreme precipitations and intensity of the extremely heavy precipitations in future climate could be attributed to the increase in atmospheric water vapor under warmer climate (Fig. 7b). It is also noticed that the specific humidity at surface during the extremely heavy precipitations is increased in future warming climate (Fig. 9a) and the temperature during these precipitation cases is increased by 4°C (Fig. 6b). This may lead to increase the moisture availability in future warming climate and keep on saturating the moisture for another 4°C. Our results of relative humidity justify this (Fig. 9b). Mean relative humidity between 850 hPa and 500 hPa also shows a higher moisture saturation tendency in the troposphere in future warming climate (Fig. 9c). Similarly, the CAPE during the extreme precipitations is significantly increased in future warming climate, indicating more potential energy available for convection to form intense precipitation. Agard and Emanuel (2017) also highlighted higher CAPE linked to temperature may increase severe continental convection in warmer climates.
This study explores CC scaling of extremely heavy precipitations associated with the torrential rainfall events occurred during July 5–6, 2017 and July 5–8, 2018 over Kyushu and Shikoku Islands of Japan, respectively in present-day climate and with pseudo global warming (PGW) conditions by use WRF model at 1-km grid resolution. We found that the frequency and intensity of extremely heavy precipitations associated with the two events are increased in future warming climate which may cause major challenges for the society. The peak intensity of the extremely heavy precipitations corresponds to ∼ 140 mm h−1 at 25°C in present climate, which is projected to be ∼ 160 mm h−1 at 27°C in future warming climate. The 99th percentile of extremely heavy precipitations follow CC scaling for the temperatures up to 22°C in present-day climate, and up to 24°C in future warming climate. The rate of change of all extremely heavy precipitations in future warming climate are expected to increase by ∼ 0.5 % °C−1 plus that of in present-day climate (∼ 3 % °C−1 in present climate and ∼ 3.5 % °C−1 in future). Overall analysis suggests that the extremely heavy precipitations in future warming climate will be more intense and may cause local flooding and landslides and CC scaling of extreme precipitations exists up to certain temperature over western parts of Japan. It should be pointed out that our analysis is a first step to explore CC scaling on two torrential rainfall events as a case study. We would like to further consider more number of similar torrential rainfall events to provide more precise results.
The comments by anonymous reviewers are greatly aknowledged in improving the original manuscript. This study is supported by the TOUGOU Program, funded by the Ministry of Education, Culture, Sports, Science, and Technology, Government of Japan. Japan Meteorological Agency (JMA) and National Aeronautics and Space Administration (NASA) are acknowledged for providing the Automated Meteorological Data Acquisition System (AMeDAS) data and MERRA-2 Reanalysis data (https://gmao.gsfc.nasa.gov/reanalysis) respectively.
