**2. Data and methods**

#### **2.1 Data used**

In this study, we analyze daily summer (JJAS) and winter (DJF) precipitation extremes using various fine resolution multi-source gridded datasets including a gauge-based, a satellite dataset, a recently released regional reanalysis as well as a global reanalysis over WH (29°N-37.5°N and 72.5°E-80.5°E, see **Figure 1a**) within the time period 1979–2020. We have used India Meteorological Department's (IMD) daily rainfall data available at 0.25° 0.25°, interpolated from 6955 rain gauge stations throughout the Indian subcontinent [51]. However, comparatively less stations are available over WH. We have also used, Integrated MultisatellitE Retrievals (V3) for Global Precipitation Measurement (GPM-IMERG), a merged high-resolution satellite product. Precipitation estimates are produced using Day-1 IMERG algorithm through intercalibration, merging, and interpolation of microwave and infrared records from GPM satellite constellation with gauge-based observations [52]. The regional reanalysis-IMDAA, is a recently released high resolution (12 km) product over the South Asian domain, generated by National Centre for Medium Range Weather Forecasting in collaboration with UK Met Office and IMD using a unified atmospheric model and the four-dimensional variational (4D-Var) data assimilation technique [53]. The dataset provides advantages in better representation of orographic features owing to its high spatial resolution [1, 2, 54]. Finally, we have also utilized the

*Hydrological Extremes in Western Himalayas-Trends and Their Physical Factors DOI: http://dx.doi.org/10.5772/intechopen.109445*

#### **Figure 1.**

*(a) Elevation (in meters) of Western Himalayan region. Subplots (b) represent annual distribution of liquid (blue line) and solid (red line) precipitation and (c) indicates same as (b) in terms of precipitation fraction over WH during 1979–2020.*

state-of-the-art global reanalysis ERA5, developed by European Centre for Medium-Range Weather Forecasts [55] available at a resolution of 0.25° 0.25°. Further, daily values of different meteorological variables, including air temperature, specific humidity, vorticity, three-dimensional wind components, etc. at various pressure levels from ERA5 have also been considered.

#### **2.2 Methodology**

#### *2.2.1 Identification of precipitation extremes*

Keeping in mind the complexity of the study region and high spatio-temporal variability of precipitation over the regime, we have identified extreme precipitation thresholds at each grid point using percentile approach. This helps in describing intensity of extreme precipitation without having a stringent threshold for such varying terrains. Extremes are considered when the daily precipitation amount from the entire time series of precipitation exceeds the 95th percentile threshold at a particular grid point. The accumulated precipitation exceeding these thresholds have the potential to expedite floods in the downstream regions and affect the agricultural crops sown in the region during summer and winter seasons. Thus, we have chosen the 95th percentile as the threshold for our study for identifying EPEs.

#### *2.2.2 Trends for intensity and frequency of EPEs*

WH is known to be a complex and topographically heterogeneous regime. A wide discrepancy in precipitation patterns is observed among different datasets over this region [1]. Thus, we focus on analyzing precipitation extremes in various datasets to understand how different datasets depict precipitation extremes over the region. Datasets from different sources have been selected on the basis of the availability of long-term (20 years) daily precipitation records, and having a relatively finer resolution. Considering that the selected datasets are generated with different input data and dissimilar developmental methods, the presence of any similar signals are strong

indicators of real situation [1, 56]. Collaterally, we also explore the fidelity of the newly developed high resolution IMDAA reanalysis in representing WH precipitation extremes during the summer and winter season. IMDAA's high resolution offers significant potential in better resolution of orography [1, 2, 54], thus, a relatively better depiction of precipitation extremes is a key possibility. IMDAA's potential in the representation of climatological winter and summer precipitation characteristics over WH has been described thoroughly by [1, 2], respectively. The present study provides additional characterization of precipitation extremes in IMDAA.

Here, we investigate the intensity and frequency of EPEs in the respective datasets for summer and winter seasons after performing a bilinear interpolation to a common spatial resolution of 0.25° 0.25° for a fair comparison purpose. Further, a common period 2000–2020 has also been considered for extreme precipitation intensity and frequency trend analysis to understand how EPEs are changing in the recent decades. Spatial trends at decadal scale for intensity and frequency of EPEs are calculated at each grid point from the daily time series of precipitation. The magnitude of trend to the whole seasonal extreme precipitation at individual grid points is computed using a non-parametric Mann-Kendall Test [57, 58]. This is a rank-based method and widely used in hydrometeorological data studies [59]. Temporal trends for the frequency of EPEs are the seasonal average of the total number of grid points on each day that satisfies the EPE criteria specified earlier.

#### *2.2.3 Trends for dynamical and thermodynamic variables*

In addition, the climatological trends of key atmospheric thermodynamic variables such as air temperature and specific humidity at different pressure levels and hydrometeors in the total atmospheric column are investigated as these parameters strongly influence the extreme precipitation over any region. We further estimated climatological temporal trends for different derived variables such as moist static energy (MSE), vertically integrated moisture transport (VIMT), eady growth rate (EGR) and eddy kinetic energy (EKE) over WH to explore the impact of synoptic signatures associated with summer and winter precipitation extremes during the period 1979– 2020.

### **3. Results and discussion**

#### **3.1 Distribution of liquid and solid precipitation over WH**

The study area includes highly rugged mountains and comparatively gentler foothills as well as surrounding plain regions of Punjab and Haryana (see **Figure 1a**). WH experiences precipitation in different seasons through different weather systems. Moreover, the effect of regional orography as well as seasonal variations is predominant in the distribution of liquid and solid precipitation over different sub-regimes of WH (e.g. [3]). The intra-annual cycle of climatological mean precipitation averaged over the WH region from ERA5 reanalysis (**Figure 1b**) shows dominant contributions of liquid form of precipitation (rainfall) during summer season (JJAS) whereas solid precipitation (snowfall) is observed to be the primary form of precipitation during winter months (DJF). This implies that a large fraction (about 61% or more) of the received total precipitation during the DJF months comes from frozen hydrometeors (**Figure 1c**). The maximum precipitation over WH is received during the month of

#### *Hydrological Extremes in Western Himalayas-Trends and Their Physical Factors DOI: http://dx.doi.org/10.5772/intechopen.109445*

July followed by August (**Figure 1b**), of which rainfall contributes almost 95% and 94% respectively (**Figure 1c**). During DJF months, highest amounts of total precipitation are observed during February followed by January and December, respectively. Similar results were reported for winter precipitation amounts at sub-seasonal scale by [1, 54].

Looking into the segregated precipitation fractions, December observes almost 68% of total monthly precipitation in solid form and the rest 32% as rainfall. Approximately 65% and 61% of the total monthly precipitation during January and February respectively are observed as snowfall. Although the individual fractions of monthly solid precipitation are lesser for February compared to December, it is significant to note that the total monthly precipitation observed during February is nearly more than double compared to December, implying that total snowfall amounts observed in February are higher.

### **3.2 Extreme precipitation intensity, frequency and trends**

#### *3.2.1 Summer season*

We have examined spatiotemporal changes in the intensity and frequency of precipitation extremes over the WH using the daily gridded precipitation data (IMD), satellite-based data (IMERG), IMDAA regional reanalysis and global reanalysis ERA5. **Figure 2** shows the precipitation intensity exceeding the 95th percentile at each grid point for the summer monsoon and trends in the intensity and frequency of EPEs. The distribution of grid-wise precipitation intensity exhibits heterogeneity in precipitation amounts over the WH (**Figure 2a**–**d**). However, the Himalayan foothill belt shows the highest precipitation intensity of EPEs. All datasets show that the spatial distribution of precipitation intensity over the WH is characterized by low precipitation at higher altitudes (the northern part of the WH) and high precipitation over low-altitude regions, albeit with varying magnitudes. Satellite-based data (IMERG) and reanalysis dataset (IMDAA) overestimates the precipitation intensity as compared to the daily gridded precipitation (IMD), specifically over the Himalayan foothills. Although the

#### **Figure 2.**

*Precipitation intensity (> 95th percentile) and trends in intensity and frequency of EPEs for the summer season. Set of plots (a-d) represents intensity climatology, (e-h) shows intensity trend (per decade), and (i-l) represents frequency trend (events per decade) of EPEs for IMD, IMERG, IMDAA, and ERA5 respectively. Subplots (m, n) represent the area averaged time series in intensity and frequency of EPEs for entire duration (1979–2020) in dotted line and recent decades (2000–2020) in solid line.*

datasets show heterogeneity in spatial distribution of long-term trends of extreme precipitation intensity, specific hotspots in the Himalayas show significant increasing trends (up to 12 mm day<sup>1</sup> per decade; **Figure 2e**–**h**). In addition to the increasing intensity of EPEs, these same hotspots have been observed for the increasing frequency of EPEs in Himachal Pradesh, Uttarakhand, and Jammu and Kashmir (**Figure 2i**–**l**). However, relatively mixed trends for frequency of EPEs over different regions of WH is clearly visible. The northern part of the study region is an exception in terms of opposite grid wise trends of frequency and intensity of extremes. To have a more elaborate understanding, we have further investigated the temporal trends of precipitation extremes (both intensity and frequency) through an area-averaged timeseries of EPEs at seasonal scale in different gridded datasets (**Figure 2m**–**n**). The timeseries of intensity of daily precipitation extremes shows an increasing trend for all datasets in the long-term as well as recent decades (**Figure 2m**). In addition, all datasets agree on the long-term rise in frequency of EPEs over the region as well as during recent decades, exception being only IMD which shows negative trend in recent decades (**Figure 2n**).

### *3.2.2 Winter season*

The geographical distribution of multi-year seasonal winter precipitation extremes' intensity and decadal trends in each dataset (after re-gridding) during 1979–2020 as per the duration of data availability for each dataset have been presented in **Figure 3**. Looking into the climatology of extreme precipitation intensity (> 95th percentile), considerable heterogeneity in extreme precipitation amounts as well as patterns are observed among different datasets, highlighting the role played by complex regional topographical variations. However, the highest precipitation amounts are observed along the western Himalayan foothills in all datasets (**Figure 3a**–**d**). The spatial extent of precipitation is maximum with high intensity over J&K, followed by HP and UK, respectively. This is due to the fact that vigor of WDs decreases as they move from J&K along WH towards central Himalayas [60]. Daily extreme

#### **Figure 3.**

*Precipitation intensity (> 95th percentile) and trends in intensity and frequency of EPEs for the winter season. Set of plots (a-d) represents intensity climatology, (e-h) shows intensity trend (per decade), and (i-l) represents frequency trend (events per decade) of EPEs for IMD, IMERG, IMDAA, and ERA5 respectively. Subplots (m, n) represent the area averaged time series in intensity and frequency of EPEs for entire duration (1979–2020) in dotted line and recent decades (2000–2020) in solid line.*

precipitation amounts are found to be reaching beyond 50 mm day<sup>1</sup> in IMDAA. Although it becomes important to note here that, like any reanalysis product IMDAA too, has been found to overestimate regional precipitation amounts [1].

The spatial variations of long-term trends per in extreme precipitation intensity although exhibit considerable heterogeneity, however, significant (confidence level = 0.95) increasing trends (up to 3.5 mm day<sup>1</sup> per decade) over some parts of HP, UK, JK and Ladakh can be observed (**Figure 3e**–**h**). Moreover, the trends in IMERG are very intense and highly significant, implying the strengthening of extreme precipitation intensities in the recent decades. Along with extreme precipitation intensity, the frequency of occurrence of such extreme events at different grid locations also seems to be on the rise over some parts of JK, northern part of HP and some parts of Punjab (**Figure 3i**–**l**). Again, IMERG shows highly significant rising trends of extreme precipitation intensity over most regions of WH.

Further, we have investigated the trends for area-averaged precipitation extremes at seasonal scale in different re-gridded datasets over the entire study domain (**Figure 3m**–**n**). All datasets including IMDAA clearly indicate that precipitation extremes are not only becoming frequent but are also intensifying over time, exception being IMD which shows a decreasing trend. Although it is important to note that none of the trends pass the significance test.

IMDAA and ERA5 show that precipitation intensity of extremes has increased by almost 16% and 23% respectively from 1979 to 2020 (**Figure 3m**). The magnitude of increase in intensity observed in IMERG from 2000 to 2020 is about 23.5%. In terms of rise in frequency of EPEs, IMDAA shows an increase of about 14 events (grid wise) per day seasonally over the domain since 1979 (**Figure 3n**). ERA5 agrees well on the enhancing frequency too but shows a slightly lesser increase of about 8 events per day. However, the rise is much sharper in the recent decades observed in IMERG satellite data which shows an increase over approximately 32 events per day in the region. The findings highlight the fact that extreme precipitation conditions are strengthening recently. The obtained results are in compliance with individual station-based trends over WH reported in some studies [40, 41] as well as other studies based on gridded observations and satellite datasets [14, 33], thus indicating a rise in precipitation extremes. Considering that the precipitation extremes are on a rise over the region, it becomes critical to understand the possible causes for these enhancements through trends for various dynamics and regional atmospheric conditions contributing to rise in precipitation extremes over WH.

#### **3.3 Trends for different dynamic and thermodynamic controls related to EPEs**

Any changes in weather and climate extremes are generally related to local exchanges in heat, moisture, and other thermodynamic quantities as well as dynamic changes. Although dynamic and thermodynamic processes in the atmosphere are interlinked, it is important to separately investigate their roles for variations in climate extremes (e.g. [61]). The thermodynamic controls of precipitation extremes are associated with an enhancement in the atmospheric moisture content, the most basic assumption being that precipitation extremes portray a tendency to rise in a warming climate, as per Clausius–Clapeyron relationship [62, 63]. Several studies propose the direct link for amplification of extremes over the WH region with increasing temperatures as well as atmospheric moisture content during both summer and winter seasons (e.g. [14, 64, 65]). Changes in the thermodynamic signatures significantly contribute to variations in precipitation patterns.

#### *3.3.1 Summer season*

In order to understand the variability of precipitation and the underlying factors might be contributing to the rise of extreme precipitation over the WH during summer monsoon season, seasonal trends of various atmospheric parameters, including hydrometeors, have been investigated. Interannual variations of tropospheric air temperatures at different levels and their trends for long-term as well as recent decades are shown in **Figure 4a**–**b**. The results show that the upper level (200 hPa) and mid-tropospheric (500 hPa) temperatures are significantly increasing, and in recent decades this increase is much sharper, which indicates the warming in the upper levels of troposphere over the WH (**Figure 4a**).

However, the seasonal trends at the lower level (850 hPa) and near-surface (1000 hPa) show a relative cooling trend in the long term (1979–2020), whereas the recent decades show warming at these near surface levels (**Figure 4b**). It is well known that global warming and related changes in the atmosphere above the WH generate EPEs, flash floods, cloud bursts, river flooding, landslides etc. [23, 66]. The overall result suggests that the increased precipitation intensity and frequency over the WH are directly associated with warming. Additionally, we have investigated the climatology of specific humidity at upper-level and low levels over the study region (**Figure 4c**–**d**). It has been observed that the specific humidity shows an increasing trend during the summer monsoon even though it is not significant at upper level but mid-tropospheric and lower-tropospheric specific humidity exhibits significantly increasing trends that is indicative of possibility of increased evaporation which can consequently contribute to increased precipitation, thus supporting the rise in precipitation intensity and frequency trends over the WH.

The interannual variability of cloud hydrometeors, total column of snow water, total column ice water, total column liquid water, and total column rain water in the long-term (1979–2020; dotted pink line) and recent decades (2000–2020; black line)

#### **Figure 4.**

*Time series of the temperature (a-b) and specific humidity (c-d). Total column variables (e) snow water, (f) ice water, (g) liquid water, and (h) rainwater. Subplot (i) represents vertical velocity at 500 hPa, and (j) represents moisture flux convergence, (k) represents moist static energy, and (l) represents vertically integrated moisture transport using ERA5 reanalysis data during 1979–2020 for summer (JJAS) season. Dotted line represents the trend in entire duration and solid line indicate recent decades.*

#### *Hydrological Extremes in Western Himalayas-Trends and Their Physical Factors DOI: http://dx.doi.org/10.5772/intechopen.109445*

are shown in **Figure 4e**–**h**. Several studies have found that changes in cloud microphysical properties can have an effect on the simulated mesoscale dynamics of extreme events (e.g. [31, 67]). All the hydrometeors exhibit increasing yet insignificant long-term trends except for total column liquid water, which shows a significantly increasing trend (**Figure 4g**). It is worth noting that all four hydrometeors reveal comparatively sharper increasing trends in recent decades when compared to the entire study period. Studies report that the presence of atmospheric aerosols potentially assists an alteration of these cloud properties leading to more precipitation under favorable atmospheric conditions (e.g. [68]). This could be a possible explanation for the role of natural as well as anthropogenic forcings to increasing levels of precipitation extremes. Although a clear justification of these possibilities is beyond the scope of this study.

We further investigate extreme precipitation events by examining the underlying changes in other related dynamical and thermodynamic parameters whose characteristics provide crucial information about atmospheric conditions, which is important in the case of extreme precipitation events. Generally, the variations in dynamical components are caused by changes in vertical motion, whereas variations in atmospheric water vapor lead to changes in thermodynamic components [69]. **Figure 4i** displays a decreasing trend of 500 hPa vertical velocity (Pa s�<sup>1</sup> ) over the study domain, indicating a rise in convection over the WH which can favor cloud formation. This rising motion causes supersaturation, which is the primary cause of cloud droplet nucleation, condensation of water vapor into liquid water droplets and eventually precipitation [70, 71]. Therefore, increasing strength of vertical velocity over time is closely related and has far-reaching implications for vertical water, mass transport, and extreme precipitation.

Our study further investigates the roles of variability in atmospheric moisture transport over the topographic regimes of WH in case they show any contribution towards the rise of summer extreme precipitation. To accomplish this, we have investigated the trends for vertically integrated moisture flux convergence (VIMFC) and vertically integrated moisture transport (VIMT) over WH during the ISM which are given by,

$$\text{VIMFC} = -\frac{1}{g} \int\_{p \le vq^f}^{p \land p} \left( \frac{duq}{d\mathfrak{x}} + \frac{dvq}{d\mathfrak{y}} \right) dP \tag{1}$$

$$\text{VIMT} = \frac{1}{g} \int\_{300\text{ kPa}}^{1000\text{ kPa}} qV \,dP\tag{2}$$

where, *q* is specific humidity, *V* is the horizontal velocity, and *dP* denotes the vertical incremental change in pressure.

Observed increasing seasonal trends in VIMFC (**Figure 4j**) directly characterize the behavior of EPEs and provide a favorable condition for increasing trends of EPEs in the WH. The region receives moisture directly from the Arabian Sea through southwesterlies and Bay of Bengal from north-easterlies [11] during southwest monsoon. Increasing levels of VIMT observed in **Figure 4l** explains that more moisture is getting transported to the region over the time. Further, our study notes that VIMT shows a significantly increasing and comparatively sharper trend over the WH during the recent decades, which constitutes enhanced seasonal moisture transport and, thus

more precipitation. MSE is the one of the most important thermodynamic parameters, defined as the total sum of an air parcel's internal and gravitational potential energy.

$$\text{MSE} = \text{CpT} + \text{gz} + \text{L}\_{v}q \tag{3}$$

where, *CP* is the specific heat capacity at constant pressure, *T* is the air temperature, *g* is the gravitational acceleration, *z* is the geopotential height, *Lv* is the latent heat of vaporization, and *q* is the specific humidity. The MSE at 500 hPa shows a significantly increasing trend, which reveals a higher atmospheric instability during the summer monsoon season **Figure 4k**. When the MSE is imported from the surrounding environment, it destabilizes the atmosphere by heating and humidifying it, resulting in deep convective precipitation [72, 73].

#### *3.3.2 Winter season*

The examination of area-averaged wintertime trends for mean air temperatures and specific humidity at different tropospheric levels (200 hPa, 500 hPa, 850 hPa and 1000 hPa) over the study region in ERA5 reanalysis are presented in **Figure 5a**–**d**. The trends indicate an increase in the air temperatures at all considered levels in the troposphere indicating that both lower and upper atmospheric temperatures are on a rise in western Himalayas, a clear indication of global warming effects. At the same time, atmospheric water vapor concentrations seem to be on a significant rise specifically in the upper and lower tropospheric levels. Conclusively, we can infer that changes observed in these regional thermodynamic variables are crucial and contributing to rising trends for precipitation extremes over the region. However, no discernible trend in middle troposphere vertical velocity has been observed over the region.

Further, we aimed to understand if there is any role of dynamical signatures of the atmosphere in influencing the rise in precipitation extremes over WH. We have focused on the variability associated with transient activity of westerly troughs

#### **Figure 5.**

*Time series of the temperature (a-d), specific humidity (e-h), frequency of vortices (i), vertical velocity (500 hPa, j), eddy kinetic energy (k), brunt–Väisälä frequency (l), meridional moisture flux convergence (m), vertically integrated moisture transport (n), eady growth rate (o), and vertical shear (p) during 1979–2020 for winter (DJF) season in ERA5 reanalysis.*

#### *Hydrological Extremes in Western Himalayas-Trends and Their Physical Factors DOI: http://dx.doi.org/10.5772/intechopen.109445*

(vortices) over WH. Our analysis considers total counts of cyclonic (relative) vorticity in each winter season to measure the activity of troughs over WH. The occurrences of vorticity (500 hPa) exceeding 1.5 standard deviation at individual grid points over WH for each winter season has been counted and the trends have been observed (**Figure 5i**). An increase in the frequency count of vortices over the region is found, which indicates that the formation of these troughs is becoming more frequent in the recent decades. Such conditions can lead to development of deep convection in the presence of enough moisture and thus can create favorable conditions for heavy precipitation. Moreover, moisture flux convergence plays an important role in inducing heavy precipitation through the deepening of such vortices, thus, we also investigated the trends for vertically integrated meridional moisture flux convergence over the region. **Figure 5m** shows the time-series for moisture convergence associated with meridional � *<sup>∂</sup>vq ∂y* winds, area-weighted over WH.

The results reveal a slight increasing trend, though insignificant, in moisture flux convergence associated with meridional winds. Moisture transport from the Arabian Sea into WH during winter has been designated as a crucial moisture input source during extremes (see [34]). As our findings suggest an enhancement in both transient activity of westerly troughs and moisture flux convergence, it can be concluded that variability in dynamic responses of the atmosphere in conjunction with thermodynamic variations might be a major contributing factor for increasing trends of extreme precipitation over the region. Mediterranean, Caspian, Red and Arabian seas are primary contributors for eastward moisture advection towards WH leading to moisture availability for precipitation [74, 75]. Here, we have tried to investigate the trends for winter seasonal moisture supply over WH (**Figure 5n**) through time series for VIMT which reveals a clear increasing trend in the moisture transport over WH through the years. This implies that with more moisture available over the region, conducive conditions for development and sustenance of heavy precipitation events can be created.

WDs, termed as immature baroclinic waves [76], develop and intensify primarily through atmospheric baroclinic instability, known to be generated by the meridional gradient of temperature and vertical shear of the background subtropical westerly flow [14]. Strong upper-atmospheric baroclinicity is generally observed in the locality of the subtropical jet during winter season [77]. The baroclinic processes partially influence the vertical velocities in the region majorly through a coupling between the background westerly flow (jet), WDs, and the orography and, thus leads to precipitation over WH [56]. The baroclinic instability in the atmosphere can be measured through maximum Eady growth rate (EGR) which follows the maximum growth rates to configure the Eady problem [78, 79] and is given as:

$$
\sigma\_E = 0.3098 \frac{|f| |\frac{\partial U(x)}{\partial x}|}{N} \tag{4}
$$

where, *f* is the Coriolis parameter, *U z*ð Þ is the vertical profile for zonal component of wind, *z* is the vertical coordinate and, *N* refers to the Brunt–Väisälä/buoyancy frequency defined by,

$$N^2 = \frac{\text{g}}{\theta} \frac{\partial \theta}{\partial \mathbf{z}}\tag{5}$$

where, *g* is the acceleration due to gravity, and *θ* is the potential temperature. The buoyancy frequency represents atmospheric static stability. We have calculated EGR

between two levels (200 minus 850 hPa) and further looked into its long-term trends (**Figure 5o**).

It is evident that the trends for EGR are increasing with high statistical significance. This highlights the fact that baroclinic instability is on a rise in the atmosphere over WH. A more baroclinically unstable atmosphere favors an intensification of WDs and can lead to heavy precipitation [13, 14, 41, 76, 80] have reported enhanced baroclinicity over WH during the recent decades and suggested the potential role of zonally asymmetric changes in the wintertime circulation caused by the elevation dependent climate warming signal. Further, we tried to investigate whether this enhancement in the regional baroclinicity, and consequently EPEs, is contributed through changes in the vertical shear of zonal wind (**Figure 5p**) or static stability (buoyancy frequency; **Figure 5l**). The results revealed that there has been an increase in the vertical shear over the period in WH and at the same time static stability of the region is observing a decreasing trend, meaning a more unstable atmosphere to intensify WDs. Further, it is clear that changes in both vertical shear and static stability are responsible for enhancing the regional baroclinicity and thus increase precipitation extremes over the region.

Various studies suggest that higher kinetic energy in the atmosphere in response to jet helps in the growth and intensification of WDs due to their baroclinic nature [13, 81]. The dynamical variations over WH are largely characterized by high frequency transient eddies in the atmosphere, which result from the conversion of the available potential energy into kinetic energy through baroclinic instability [82–84]. Therefore, we have investigated the trends for upper tropospheric (200 hPa) eddy kinetic energy (EKE) in ERA5 to understand the role of localized impacts of westerly flow and consequent energy exchange processes in the atmosphere for fueling the rise of precipitation extremes. EKE is defined as the kinetic energy associated with the time-varying component of the horizontal velocity field.

$$\text{EKE} = \frac{1}{2} \left( \mu'^2 + \nu'^2 \right) \tag{6}$$

$$
\overline{u} = \overline{u} + u'\tag{7}
$$

$$
v = \overline{v} + v'\tag{8}$$

here, *u* and *v* are horizontal velocity components, *u*<sup>0</sup> and *v*<sup>0</sup> denote time-varying velocity components whereas, *u* and *v* represent the time mean velocity components. A bandpass filter of 2–10 days has been applied to the anomalies of horizontal velocity fields to filter out the mesoscale transient eddies and their trends have been looked into. The findings reveal that EKE over the region has been increasing significantly (**Figure 5k**) which provides preferable conditions for intensifying WDs over WH and thus can contribute to heavy precipitation over the region.

### **4. Summary and conclusion**

The projected rise in precipitation extremes under the warming climate is a key matter of concern. This study investigates the spatiotemporal variations and trends for intensity and frequency of precipitation extremes over the western Himalayan region during summer and winter monsoon seasons. Furthermore, the potential dynamical and thermodynamic controls of precipitation have been explored to understand their
