Precipitation Scaling in Extreme Rainfall Events and the Implications for Future Indian Monsoon: Analysis of High‐Resolution Global Climate Model Simulations

The increase in water holding capacity of the atmosphere with temperature, given by the Clausius‐Clapeyron (CC) relationship, describes the changes in extreme rainfall intensities at warmer atmospheric states. We study the characteristics of extreme rainfall events (EREs) during the Indian summer monsoon season with respect to thermodynamic changes and precipitation‐scaling over the Indian subcontinent and its homogeneous rainfall zones. We utilize outputs from a present‐day climate simulation and a time‐slice future climate change projection experiments of a high‐resolution global climate model. Large changes are seen for very EREs (vEREs) which suggests their sensitivity to warmer temperatures. In future, the altered radiative forcing will heat up the upper atmosphere, stabilize it and offset the effect of increasing humidity on precipitation intensity. Our analysis also suggests that more convective clouds and the interplay of increased moisture content and circulation will result in future changes in EREs.

• The scaling of precipitation with warming using climate simulations can give information on the regional changes of extreme rainfall events • Very extreme rainfall events will increase and become highly sensitive to warming in future • Warmer atmosphere favors more convective clouds and a stronger interplay of dynamic-thermodynamic factors

Supporting Information:
Supporting Information may be found in the online version of this article.
among other factors, can lead to deficiencies in the simulation of the characteristics of precipitation extremes (Wilcox & Donner, 2007).The convective organization is another factor that can induce dynamic changes in extreme precipitation.Studies have identified an increased frequency of such regimes (Tselioudis et al., 2010) under warming.The projected enhancement in EREs can be attributed to the increasing atmospheric moisture content in a warming climate, which may approximately follow the CC equation to the first order (O' Gorman & Muller, 2010).Changes in the temperature lapse rate, vertical wind and temperature anomaly when the EREs occur can, in turn, influence the intensity of ERE (O'Gorman & Schneider, 2009;Sugiyama et al., 2010).So, the regional changes in extreme precipitation can be composed of a thermodynamic component representing changes in water vapor/precipitation and a dynamic component representing changes in vertical motion (Allen & Ingram, 2002;O'Gorman, 2015;Trenberth, 1999).
Although studies have documented how well regional precipitation intensity and surface air temperature scale, studies for the Indian region are still scarce.Mukherjee et al. (2018), using simulations of coarse resolution CMIP5 models, showed super-CC scaling between extreme precipitation and dew point temperature over south and central India on a daily timescale, while a sub-CC over north India.The scaling of daily extreme precipitation and extreme streamflow to rising temperature was observed to differ by Ghausi and Ghosh (2020).A lack of studies that use high-resolution simulations poses a challenge in understanding the CC precipitation scaling and the relative importance of dynamic and thermodynamic processes associated with the EREs of the Indian summer monsoon (ISM).Yoshimura et al., 2015), which considers convective updrafts with minimum and maximum entrainment/ detrainment rates calculated as individual plumes similar to the Tiedtke convection scheme (Tiedtke, 1989).This scheme also considers multiple convective updrafts with different heights, as in the Arakawa Schubert scheme (Arakawa & Schubert, 1974), by representing them as continuous convective updrafts between minimum and maximum turbulent entrainment/detrainment rates.In addition, the model also simulates the observed long-term trend of rainfall, especially the reduction over Western Ghats (Rajendran et al., 2012).Thus, the significance of our study is that the characteristics of extremes are analyzed using more reliable simulations/projections.
We investigate the changes in the precipitation scaling and thermodynamic characteristics of EREs during the ISM season over India and its homogeneous rainfall zones (Parthasarathy et al., 1995).Understanding the detailed mechanism for the difference in response over different regions is not a major objective of the present study because this aspect can be analyzed as a future work.Section 2 describes the model, simulations, data sets and methodology adopted for defining the extreme indices.Ours is not a case study; we identify a composite of extreme events based on an objectively defined threshold.Section 3 discusses our results on precipitation scaling in EREs under the present and future warming scenario.Further, we quantify the future changes in EREs and the role of different mechanisms.Section 4 gives a discussion and conclusion of the results.

Model, Simulations and Data Sets
A very high-resolution GCM of the MRI, Japan, at a horizontal resolution of T L 959 (∼20-km) having Yoshimura Scheme (referred to as MRI AGCM3.2 by Mizuta et al., 2012) is used.Here, we assess the characteristics of EREs under the present-day  and future RCP8.5 (2079-2099) scenarios, using corresponding 20-km resolution simulations for which extensive validation has been done over the past decade (Mizuta & Endo, 2020;Rajendran & Kitoh, 2008;Rajendran et al., 2013).The simulations are done for all the months of 21 years, but the analysis focuses on the ISM season (June-September, hereafter referred to as JJAS).We use India Meteorological Department (IMD) gridded rainfall observed over India at 0.25° resolution (Pai et al., 2014) over the 1983-2003 period for validation.Figure 1j validates the JJAS rainfall climatology from the present-day simulation of MRI AGCM3.2 against the observed climatology from IMD data set (Figure 1k).We find an excellent agreement in the mean distribution of ISM rainfall.Importantly, the model captures the fine features of mean rainfall along the Western Ghats and northeast and high rainfall along the monsoon trough, which is a challenge for coarse-resolution GCMs (Rajendran et al., 2022).

Extreme Rainfall Indices
Two extreme indices, R95p (representing Extreme Rainfall Events, EREs) and R99p (representing very Extreme Rainfall Events, vEREs), corresponding to 95th and 99th percentiles of rainy days in JJAS, respectively, are calculated for the present-day and future scenarios.For estimating the indices over India and its homogeneous zones, corresponding thresholds are identified from the first 10 years of the present-day simulation (1983)(1984)(1985)(1986)(1987)(1988)(1989)(1990)(1991)(1992), which gives the control statistics of the extremes at these thresholds.For examining the projected changes in frequency and intensity of EREs over the homogeneous precipitation zones, we have adapted six extreme rainfall thresholds, viz.95th, 99th, 99.7th, 99.9th, 99.95th, and 99.97th percentiles normalized by respective changes in temperature.These percentile thresholds are obtained from the daily rainfall area averaged over the specific region of interest.As there are few dry days during JJAS in the simulations, excluding dry days from the study has no discernible qualitative impact on the results.

Precipitation Scaling in EREs and vEREs
The daily and 6-hourly R99p and R95p variations for the present-day and RCP8.5 scenarios are checked with surface air temperature (T a ). Figure 1a shows the changes for vERE (R99p daily), where the intensity gradually increases with T a up to a certain threshold where it peaks and later decreases.The variation is sharper in future scenario, along with an increase in the peak intensity of EREs.The shift in the peak with increased temperatures is more conspicuous for R99p and relatively moderate for R95p (Figures S1, S2, and S3 in Supporting Information S1).R99p intensities show a super-CC scaling for both daily and 6-hourly precipitation, whereas the future scenario shows a much higher scaling compared to the present-day, as evident for daily rainfall values.The variation of R95p shows that compared to R99p, a near-CC scaling is followed for both daily and 6-hourly precipitation.Our analysis reveals that at lower temperatures (up to 10-15 o C in Figure 1a), the rainfall extremes follow a near-CC scaling, beyond which the scaling follows a super-CC scaling as temperature increases.This continues up to 28 o C in Figure 1a, after which the scaling falls to negative CC scaling, as found by Ghausi et al. (2022) due to radiative cooling by clouds.The regional behavior of the simulated future EREs and vEREs from the context of their dependence on local temperature is then checked by analyzing the scaling of the intensity of EREs over homogeneous precipitation zones of India, viz., central northeast, hilly regions of the northeast (hilly regions-1), northern hilly regions (hilly regions-2), northeast, northwest, peninsular and west-central as well as over the Western Ghats.From the simulated daily and 6-hourly rainfall extremes for the present-day and future scenarios for R99p and R95p, we find several zones show a negative scaling, especially central northeast, northwest and west-central.A near-CC scaling is seen over hilly regions-1 and northeast.The hilly regions-2 characterizes near-CC scaling for lower temperatures and super-CC scaling for higher temperatures.A negative scaling at lower temperatures and near-CC scaling at higher temperatures are seen for the peninsular region.Although the scaling remains more or less unchanged, the variation is often sharper with (a) a warmer threshold and higher intensity for the future scenario compared to the present-day and (b) for R99p compared to R95p.

Quantification of Future Changes in Extremes
Quantification of future changes in EREs is essential when it comes to planning adaptation and mitigation strategies.The contribution of extreme events to the season's total precipitation in terms of EREs (R95p) and vEREs (R99p) is quantified.The change in the percentage of ISM rainfall falling on days that are wetter than the 99th and 95th percentiles of the base period threshold is shown in Figure S4 in Supporting Information S1.The change is uniform over the whole of India with around 10% increase, except for a few pockets over north-central and peninsular regions, which show an increase of about 20% and a relatively higher occurrence of very wet days (R99p) compared to wet days (R95p).The Western Ghats shows a slightly negative value, which was also established by Varghese et al. (2020).
Next, we estimated the change in the intensity of EREs and vEREs between present-day and future scenario (Figure 2).The changes are normalized by the corresponding change in temperature between the two climate scenarios.For vEREs, daily extremes are more intense than 6-hourly extremes, especially over the peninsular region and parts of north India, with an increase of 25% per degree.The majority of the area shows an increase in extreme events with very few pockets indicating a slight future decrease in vEREs.Although the wet extremes corresponding to the 95th percentile project an overall increase, the rate of change is lesser compared to the 99th percentile, suggesting that vEREs are prone to undergo more significant changes compared to EREs.Also, there is only an insignificant difference between the relative changes for the daily and 6-hourly events, suggesting that vEREs contribute mainly to the extreme events and their greater sensitivity to temperature changes.Consistently, the corresponding change in mean rainfall normalized by change in temperature shows a marked increase over the peninsular region and a decrease over the Western Ghats (Figure S5 in Supporting Information S1).
We examined how well the model simulates rainfall intensities at different percentiles over India and over its homogeneous zones for present-day simulation and future projection (Figure 3a).The model shows marked fidelity in capturing the variation in the intensity of precipitation at different percentile values for the Indian land region.There are slight biases in the simulation of the present-day rainfall over hilly regions-1, hilly regions-2 and the northeast, which are largely non-monsoonal in rainfall characteristics, as pointed out by Gadgil et al. (2019).Large increases in the projected intensity of future monsoon rainfall are seen as the extremeness of rainfall goes very high for all the regions except hilly regions-2, with maximum increase projected for hilly regions-1 and northeast India.The rainfall distribution for Western Ghats shows a marked decrease in future for lower percentiles, which increases for higher percentile thresholds.
We found significant changes for R99p compared to R95p (Figure 3a).Since percentiles greater than R99p represented stronger extreme events (Myhre et al., 2019), we estimated the normalized changes in the intensity and frequency of EREs/vEREs based on six levels of extremeness at very small intervals defined by 95th, 99th, 99.7th, 99.9th, 99.95th and 99.97th percentiles for different regions.There is a steady increase in both the intensity and frequency of extreme precipitation from R95p to R99.95p (stabilizing thereafter) in overall regions (Figure 3b).
Northeast and peninsular regions show a much higher change in intensity compared to frequency, whereas the whole of India has a near-equal change.Over Western Ghats, the 95th percentile shows a decreasing trend which is consistent with the already existing trend of rainfall along with increase for other higher percentiles.A striking feature in the projected future change is that the changes are magnified as the extremeness level increases, indicating maximum change in the tail region of the probability density function.Sarkar and Maity (2022) reported an increase in frequency more than intensity for annual extreme precipitation.In contrast, our analysis suggests that during ISM, future changes in intensity are much larger than frequency, suggesting that EREs in the future JJAS period may be caused by convective clouds.This can be further explained by looking into the dynamics of atmospheric instability, such as the vertical velocity or ascent.

Extreme Events and the Role of Convective Organization
Climate model projections indicate a relatively rapid temperature change, given the increase in absolute humidity and its potential to cause significant warming.Investigation of our model's ability to correctly estimate the relative humidity can enable us to look further into whether it will yield any useful results concerning the thermodynamic state of the atmosphere in future.The daily minimum and maximum relative humidity and their respective changes under the future scenario show only marginal differences from the present day to the future, indicating that they are not so sensitive to changes in climate (Figure S6 in Supporting Information S1).The comparability of the relative humidity for the present and future suggests that the actual moisture amount in the atmosphere must have increased on par with temperature.Indeed, there is a linear increase in the simulated near-surface specific humidity and precipitable water with temperature (Figure S7 in Supporting Information S1).
Wang et al. ( 2020) laid down the processes by which radiative forcing determines the future changes in a monsoon system, with changes in specific humidity being the primary factor.This is confirmed by our analysis (Figure 4).Interestingly, although the change is uniform throughout the monsoon region, the precipitation patterns are not.This is because of the interplay with dynamic aspects.Due to altered radiative forcing, the upper atmosphere gets heated, stabilizing the atmosphere and ultimately offsetting the effect of increasing humidity on the precipitation intensity.This can be gleaned from the vertical profiles of pressure velocity and cloud water content in Figure 4. Contrasting results are found concerning cloud cover and cloud water content.The cloud cover is reduced, whereas a slight increase in cloud water content is seen in future.This suggests that the clouds will be more convective in future, which supports extreme rainfall.A latitudinally uniform decrease of cloud water content at 500 hPa is likely due to the tendency to lift up the level of maximum cloud water content in the future.
The convective organization can induce dynamic changes in extreme precipitation (e.g., Pendergrass, 2020).The degree and extent of any such convective organization can affect the tropospheric state through their interaction with atmospheric temperature, humidity and circulation.The intensity of extreme precipitation can sometimes go beyond the thermodynamic scaling, indicating the dominance of such convective aggregations.As a result of global warming, studies have identified an increased frequency of such regimes (e.g., Tselioudis et al., 2010).However, in our cases where the extreme precipitation has exceeded the thermodynamic scaling (e.g., Figure 1), we find that the upward vertical velocity does not increase much relatively, except for a few positive regions (Figure 4 and Figure S7 in Supporting Information S1).This invariably suggests that more than the convective aggregations, it is the interplay of increased large-scale atmospheric moisture content and the circulation or the moisture convergence which are responsible for the changes in the extreme events.Varghese et al. (2020) have already shown that the vertically integrated moisture transport contributes to the increase in mean rainfall.The moisture convergence is largely offset by the decreasing zonal velocity during the projected summer monsoon over India.

Discussion and Conclusions
The current study of analyzing present-day and future projection outputs from the MRI model, focuses on examining the characteristics of extreme precipitation events during summer monsoon over India in the context of global warming.The changes in scaling rates of extreme rainfall over India, its seven homogeneous zones and Western Ghats show that 95th and 99th percentile precipitation intensities clearly shift in the peak temperature from the present-day to future RCP8.5 scenario, suggesting that vEREs will intensify further.The 6-hourly and daily R99p show a super-CC scaling for the present-day and much higher scaling for the future scenario, whereas R95p shows near-CC scaling.Over the homogeneous zones and Western Ghats, varied responses are seen.The scaling rates can vary largely for short-duration events as they result from individual storm cells that climate models do not accurately simulate.Here, we have considered the CC scaling hypothesis to interpret changing rainfall intensities as a response to increasing temperatures.Any other additional/complementary governing mechanism responsible for this relationship must be explored for clarity.
The relative change in the contribution of extreme events to seasonal rainfall shows an increase throughout the Indian land region and more intensified change for R99p compared to R95p.The normalized change of summer monsoon extreme precipitation shows a much larger change for daily extremes than sub-daily extremes with intensification over peninsular regions and parts of north India (∼25%/ O C).The rate of change is also much intensified for R99p, suggesting larger changes for vEREs, thus contributing largely to the total extreme rainfall and their greater sensitivity to temperature.Our analysis of normalized changes in intensity and frequency of extreme events with six levels of extremeness over various zones of India suggests that the EREs in the future may be caused by convective clouds.In other words, monsoon season is expected to have short and intense bursts of convective rain leading to EREs, but drier conditions for most days.
The change in specific humidity is uniform throughout the monsoon region, whereas the precipitation patterns aren't because of the interplay with dynamic factors.The altered radiative forcing heats up the upper atmosphere thereby stabilizing the atmosphere that ultimately offsets the effect of increasing humidity on the precipitation intensity.This is supported by the lack of pronounced change in the vertical pressure velocity over most of India.Conversely, there will be reduction in cloud cover along with pronounced increase in cloud water content, suggesting more convective clouds in future, which again supports future increase in extreme rainfall.More convective aggregations and interplay of increased moisture content with circulation will result in future changes in extreme rainfall events.
As already mentioned, the effect of convective organization on extreme precipitation is sensitive to model parameterizations and is often poorly represented in global models (Pendergrass, 2020).With the Yoshimura convection scheme, we have confidence in our results of the projection of extremes.A word of caution is appropriate because all EREs are not always associated with extreme convection.Again, a mere large water-holding capacity of the atmospheric column will not sustain rainfall.An associated optimum weather condition is also required so that water from one region is effectively transported to another, thus enhancing condensation and rainfall.It is thus necessary to quantify the dynamic players as well while quantifying the changes in extreme precipitation events.As a future work, the mechanisms responsible for the projected changes in rainfall intensities and their scaling with temperature over different zones can be done by incorporating a detailed analysis of atmospheric instability.

Figure 1 .
Figure 1.Variation of daily R99p to surface air temperature (°C) for (a) Indian land region and over seven homogeneous rainfall zones of India, namely, (b) central northeast, (c) hilly regions-1, (d) hilly regions-2, (e) northeast, (f) northwest (g) peninsular and (h) west-central India and (i) Western Ghats.Green and purple scatters correspond to present-day and future RCP8.5 scenarios, respectively.Green and purple solid lines show their respective non-parametric fitting using LOWESS smoothing.Black dotted lines illustrate CC scaling (7%/°C) for reference.(j) Climatological JJAS mean rainfall simulation from MRI AGCM3.2 20-km presentday simulation and (k) IMD observation.The homogeneous rainfall zones are demarcated inside (j) and Western Ghats in (k).The pattern correlation (PCC) and root-mean-square-error (RMSE) are written on the bottom-right and bottom-left of (k), respectively.

Figure 2 .
Figure 2. The normalized change in extreme rainfall intensity as percentage of the present-day base period value under future warming scenario for R99p (top panels) and R95p (bottom panels).The left panel shows the relative change of extreme rainfall normalized by the rise in temperature (in %/°C) of 6-hourly rainfall and the right panel shows the same for daily rainfall.

Figure 3 .
Figure 3. (a) The intensity of rainfall during June to September (JJAS) of the simulation period, against different percentiles for the whole of India, seven homogeneous precipitation zones of India and Western Ghats.The rainfall distribution from IMD observation (black), present-day simulation (blue) and future projection under RCP8.5 scenario (orange) are shown.(b) The projected changes in the frequency and intensity of rainfall for different levels of extremeness in EREs and vEREs over the regions mentioned in (a).The changes are normalized by the respective changes in surface air temperature (%/°C).

Figure 4 .
Figure 4. Vertical profiles of zonally averaged (strictly over the Indian land region as shown in Figure 1j) projected future changes in JJAS of (a) specific humidity, (b) vertical pressure velocity, (c) cloud cover, (d) cloud water content and (e) relative humidity.