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The study investigates trends and teleconnections of extreme precipitation events in the Upper Indus Basin (UIB) within the Indian region, part of the crucial geo-ecological Hindu Kush Himalayan Mountain system. Utilizing high-resolution (10km) HAR data from 2002 to 2013, we analyzed 11 indices established by the Expert Team on Climate Change Detection and Indices (ETCCDI) to observe variations in extreme precipitation at the monthly, seasonal, and annual scales. Results show an increase in dry and wet extreme precipitation frequency and intensity, increased monsoon precipitation, and a shift of winter precipitation, increasing continuous dry days. Using APHRODITE daily (0.25°) data from 1952 to 2014, continuous wavelet transform and wavelet coherence analysis indicate significant periodicities and correlations with large-scale climate anomalies such as El Niño-Southern Oscillation (ENSO) and North Atlantic Oscillation (NAO). Wavelet coherence analysis reveals that monthly extreme precipitation events significantly correlate with ENSO at 3-5 years periodicity, while annual extremes show significant coherence with NAO at 8-10 years and over 16 years periodicities. The study highlights the impact of global climate change on regional precipitation and the need for adaptive water management policies to mitigate flood risks during the rainy season and address water scarcity in the dry season.

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  • In this study, the trend analysis of extreme precipitation indices is done with high spatial resolution dataset.

  • Teleconnections of the indices with various climatic oscillations were identified using the wavelet transform method.

extreme indices, periodicity, teleconnection, trend analysis, wavelet analysis
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The Fifth Assessment Report (AR5) of the Intergovernmental Panel on Climate Change (IPCC) indicated that the earth's land and global average ocean temperature increased by 0.85 °C from 1880 to 2012 (IPCC 2014). This warming enhances atmosphere's moisture holding capacity that can change the frequency and intensity of the precipitation. Carbon emissions from agricultural, livestock, and industrial sectors are the main reason for extreme weather and global warming (Abbas et al. 2022a, 2022c; Elahi et al. 2024). Consequently, extreme precipitation intensity and frequency continuously increase in most parts of the world (Mei et al. 2018). Extreme precipitation events that include both high and low precipitation events will occur more frequently, as indicated by different climate model simulations (Allan & Soden 2008; Gupta et al. 2020).

Global and regional level studies indicate a change in intensity and frequency of extreme events, but these changes' characteristics differ with the study area scale (Fan et al. 2012; Ul Hasson et al. 2017). Understanding the variability and trends of extreme precipitation events is crucial for managing water resources and mitigating related risks. The Upper Indus Basin (UIB), which shares boundaries with six countries, is a crucial water source for India and Pakistan but facing significant challenges due to climate changes. The UIB's complex topography and varying altitude influence precipitation patterns within the basin and that demands a detailed study of extreme events in the region as suggested by Orr et al. (2022).

Many researchers have noticed mixed results in precipitation characteristics in the UIB after the 1950s (Malla & Arya 2023). Latif et al. (2018) analyzed variability, identified a trend, and assessed changes in annual and seasonal variability in the precipitation for the four-time series over the UIB. Bhutiyani et al. (2010) checked the trend from 1866 to 2006 and found no trend in winter precipitation and a significant increasing trend for monsoon precipitation; they also observed the influence of the North Atlantic Oscillation (NAO) in winter precipitation. Rizwan et al. (2019)) concluded an increasing trend in annual precipitation but a decreasing trend in rainy days. However, these studies often focused on the mean and total precipitation, neglecting the extreme events. In early winter, Sabin et al. (2020) found a decreasing snowfall trend in the Hindukush Himalayan mountains. Therefore, it is essential to check the variation of the extreme event on a smaller time scale with high spatial resolution data available for understanding the full impact of climate change.

The primary motivation for this study stems from the lack of comprehensive analyses on the temporal variability and teleconnections of extreme precipitation events in the UIB, particularly in the Indian region. Previous studies have mostly focused on the mean precipitation for annual and seasonal analyses with less attention on the frequency and intensity of extreme events. With these gaps, this paper has objectives for the study area to (1) firstly identify the trend of extreme precipitation at various temporal scales, (2) find the periodicity of the extreme and their coherence with the large-scale climate anomalies, and (3) assess the implications of these trends for regional water resource management.

State and variation of the extreme precipitation identification are done with the 11 indices established by the Expert Team for Climate Change Detection Indices (ETCCDI) that are used as a significant source around the globe (López-Moreno et al. 2010; Fan et al. 2012). The indices capture various aspects of extreme precipitation including frequency, intensity, and duration, offering a comprehensive understanding of changes in the UIB. There are four major categories of ETCCDI: absolute, threshold, duration, and percentiles analyzed on three temporal scales of monthly, seasonal, and annual. These index's trend significance is identified with the Mann-Kendall (MK) test, and the magnitude of this trend is checked with Sen's slope method (Mann 1945; Sen 1968). The published research categorizes extreme daily precipitation based on frequency, intensity, and amount (You et al. 2011; Madsen et al. 2014). The selection of mostly percentile thresholds in place of a fixed threshold is that the space distribution is evenly and meaningful compared with the fixed threshold (Zhang et al. 2011). Cloud bursts and flash floods are extreme events that the Indian Himalayan Region has faced in the recent past (Malla & Arya 2024; Mishra et al. 2019).

More attention is paid to the study to find the possible driving factor responsible for the changes in extreme precipitation. The study done in the past reveals that large-scale atmospheric circulation patterns are appropriate for the study of hydroclimatic records, such as the NAO, El Niño-Southern Oscillation (ENSO), and the Pacific Decadal Oscillation (PDO) (Wagesho et al. 2013). However, the specific impacts of these teleconnections on extreme precipitation in the UIB are not well understood. Many studies attempted to find the teleconnection between precipitation extremes and anomalies better to understand the underlying mechanism of extremes in regional precipitation (Ananthakrishnan & Soman 1989; Dimri et al. 2004; Han et al. 2021). Most of the methods used in the UIB use correlation coefficients between extreme and anomalies, but we should consider the characteristic of non-linearity to know about the influence of teleconnections, and for multiscale relationships, various timescales should be known (Nalley et al. 2019). There are various tools to analyze the multiscale response; after work on wavelet transform by Torrence & Compo (1998) and their update by Grinsted et al. (2004) wavelet transform became the most common tool to analyze the multiscale response (Torrence & Compo 1998; Grinsted et al. 2004; Sharma & Goyal 2020).

This paper aims to comprehensively analyze the trend in extreme precipitation and their possible driving factors, such as large-scale climate anomalies ENSO and NAO. In the paper, we have used advanced analytic techniques and the available high-resolution dataset, which is essential for spatial variability in complex terrain. The research findings are intended to inform regional water resource management policies and enhance community resilience to climate-related hazards. Additionally, we aim to contribute to a deeper understanding of the interactions between climate anomalies and extreme precipitation events.

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Study area

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Hindukush, Karakoram, and the Himalayas (HKH) range of mountains are called our planet's ‘third pole’ (Latif et al. 2018; Jiang et al. 2019). This HKH terrain consists of the glacier, which provides water downstream of the relative basin for agriculture, power production, and drinking water. The Indus River originates 5,166 m from MSL in the Kailash range of mountains. Then, the river approaches Tibet through Lima La pass, which is on the westward slope of Kailash. The Indus River basin consists of the mountainous terrain of the Ladakh range, Karakoram Mountain, the north and Zanskar range, and the Greater Himalayan range until it reaches Hindu Kush Mountain. Major tributaries of the river are Jhelum, Sutlej, and Chenab. The Indus basin river feeds over 300 million people in India and Pakistan (Widmann et al. 2019). The UIB ranges from western Tibet and the Ladakh region of Kashmir to the foothills of the Himalayas. Figure 1 shows the map of the UIB part of our study area lies at the geographical range of longitude 31–37° E and latitude 72–82° N, and the elevation from mean sea level varies from 944 to 8,533 m. The total area considered in the study is 1,33,248 km2, approximately 745 km in length and 200 km in width. The study area's average rainfall is around 850 mm annually, with a high spatial variation of 300 mm to 3,000 mm annually.
Figure 1
Indian part of UIB showing the elevation.
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Indian part of UIB showing the elevation.

Figure 1
Indian part of UIB showing the elevation.
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Indian part of UIB showing the elevation.

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Materials

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High Asian Refined (HAR) data is the analysis data used to decadal study climate variability and atmosphere-related processes on the Tibetan plateau (Maussion et al. 2011, 2014). The data used for the trend analysis was downloaded from the TU Berlin website with a high resolution of 10 km × 10 km gridded daily precipitation data (Index of /HAR/V1/ (tu-berlin.de)), and the period of the data is from 2002 to 2013. However, it is essential to acknowledge its limitation of relatively short period restricts its ability to capture long-term trends. Despite the limitation, our selection criteria for HAR data were based on high resolution (10 km × 10 km) specifically suited for mountainous reasons. Additionally, previous studies have shown HAR data reasonable correspondence with most in situ measurements in the UIB (Pritchard et al. 2019).

Asian Precipitation Highly Resolved Observational Data Integration Towards Evaluation (APHRODITE) is a long-term continental-scale daily product that prepares precipitation data by the dense network of rain gauge data. It includes the Asia region in the south and southeast, the Himalayas, and the mountain region in the Middle East and is also majorly used in the periodicity analysis (Irannezhad et al. 2022). This study uses 0.25° × 0.25° resolution gridded data for the period 1952–2014. APHRODITE data has limitations in terms of relatively low spatial availability, but the availability for the long term makes the data suitable for the study of the periodicity and frequency analysis in the study area.

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Selection of precipitation indices

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The Expert Team on Climate Change Detection and Indices (ETCCDI) has selected 11 indices to observe extreme precipitation intensity duration and frequency variations. The list is available in Supplementary Annexure 1. In the study, there are five categories of indices: (i) percentile-based indices (R95p, R99p), (ii) indices that are absolute and represent maximum and minimum values within a month, season, and year (Rx1day, Rx5day), (iii) indices based on threshold values as the number of the days when precipitation exceeds specific depths in a year (R10, R20, R25), (iv) indices based on the duration that represents a period when excessive cold, warmth, dryness, or wetness or in case of growing season period, length of mildness (CDD, CWD), and (v) total precipitation (PRCPTOT) and the intensity index (SDII) are other general indices. These indices are defined and guided by the World Meteorological Organization (WMO) (Data 2009).

Climate indices

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The effects of climate anomalies (i.e., ENSO and NAO) on extreme precipitation in the UIB region impact Himalayan precipitation. For the ENSO indices, the intensity measurement on sea surface temperature anomaly in the Niño3.4 region, and the indices are named the Niño3.4 index. In the North Atlantic region, NAO is the dominant mode of changing the winter climate variability (Emori & Brown 2005). NAO is measured by the difference in normalizing sea level pressure between the low polar center and high subtropical centers; Greenland is the center and the other center of opposite signs 35° and 40° N in central latitude in the North Atlantic. The Niño3.4 and NAO are available from the National Oceanic and Atmospheric Administration (http://www.ersl.noaa.gov/psd).

Trend analysis

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When it comes to examining climatic variables for trends, the application of linear tendency estimation techniques has been prevalent. Alongside the commonly used least-squares methods, the MK method is prominently employed in this study to determine the statistical significance of trends within extreme indices. Furthermore, the magnitude of these trends is evaluated using Sen's slope. A significance level of 0.05 is adopted to ascertain the significance of precipitation trends. Specifically, the slope and significance of trends are computed for the 1,332 grid cells within the study area. To capture spatial variation, the inverse distance weighting (IDW) interpolation technique is employed. While various interpolation techniques are employed globally for such data, IDW has proven to be the most effective technique for the intricate and expansive system of the UIB. As such, IDW is selected for generating accurate spatial maps within the study area.

Wavelet analysis

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Continuous wavelet analysis

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The continuous wavelet transform (CWT) helps extract the dominant frequencies in the hydrological time series (Mei et al. 2018). CWT examines extreme precipitation and climate anomalies in the current work to know their dominant mode of variability. CWT is applied for the APHRODITE gridded data falling in the study area to reveal the time series' variability and temporal evolution for each periodicity. It produces a wavelet spectrum with two dimensions by decomposing it into various continuous scales. Torrence & Compo (1998), Song et al. (2020), and Grinsted et al. (2004) have detailed the method.

Wavelet coherence

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Generally, for two discrete time series, X (n = 1 … , N) and Y (n = 1, … , N), we use the cross-wavelet transform to identify the cross-power of two-time series:
(1)
where WX (s,t) is CWT of X series and WY* (s,t) is complex conjugation.

The cross-wavelet analysis is helpful for detecting phase spectrum but may give misleading results to the two non-normalized spectrums of the wavelet.

After that, it measures the intensity of two different time series covariance with frequency wavelet coherence. It reveals the correlation between climate anomalies of large scale and hydrologic series, which are as follows:
(2)
(3)
where is the measure of coherence between response variable y and the predictor x; Ry,x (s,t)∗ is the conjugation of Ry,x (s,t); R2(s,t) is the square wavelet coherence between y and x; and S is the smoothing operator.

To balance the difference between significance and desired time–frequency features done by a smoothing operator. Significant wavelet coherence identification by the significance test based on red noise with the Monte Carlo method, which performs with the help of the MATLAB toolbox developed by Grinsted et al. (2004) and Song et al. (2020). This work is also represented the same for the above section.

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Spatiotemporal changes of precipitation extremes

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Understanding average precipitation at different locations in the study area is essential. Figure 2 shows the spatial variation of average daily precipitation, with a mean of 2.36 mm/day. Precipitation varies from less than 1 mm to over 9 mm/day. The East part of the Karakoram range, with lower elevation, has more precipitation, while the upper part, in the east, has lower daily precipitation. As the study area has higher spatial precipitation variability, it is better to know the monthly precipitation distribution. For that analysis, the box plot diagram is plotted on a daily scale for all months, which gives an idea of precipitation distribution throughout the year. The four consecutive months of monsoon, June, July, August, and September, have the highest amount of precipitation. In January and February, the amount of precipitation is less than during the Monsoon period, but the outliers represent the rarity of extreme precipitation. In comparison, dry day events can be seen from October to December.
Figure 2
(a) Box plot diagram for the precipitation of every month and (b) spatial variation in average precipitation in mm/day increasing from green to red.
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(a) Box plot diagram for the precipitation of every month and (b) spatial variation in average precipitation in mm/day increasing from green to red.

Figure 2
(a) Box plot diagram for the precipitation of every month and (b) spatial variation in average precipitation in mm/day increasing from green to red.
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(a) Box plot diagram for the precipitation of every month and (b) spatial variation in average precipitation in mm/day increasing from green to red.

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Based on the length of period

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Precipitation extremes can involve excess or lack of precipitation. This section defines the maximum length for continuous events in a year. Days with more than 1 mm of precipitation are wet days; less is dry days. Continuous wet days (CWD) and continuous dry days (CDD) are analyzed. Figure 3 shows Sen's slope (days/year), where blue indicates increasing trends and red indicates decreasing trends at a 95% significance level. MK test results show 272 grids with significant increasing trends and two with decreasing trends for CWD. Most parts of the study area show an increasing trend in CWD. In contrast, 137 grids show a significant increasing trend for CDD, with no grids showing a decreasing trend, based on the absolute percentile value.
Figure 3
CDD and CWD spatial variation of Sen's slope with the red color indicating a decreasing trend and the blue color indicating an increasing trend and a 95% confidence level significant trend is indicated by the upward and downward arrow of opposite color.
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CDD and CWD spatial variation of Sen's slope with the red color indicating a decreasing trend and the blue color indicating an increasing trend and a 95% confidence level significant trend is indicated by the upward and downward arrow of opposite color.

Figure 3
CDD and CWD spatial variation of Sen's slope with the red color indicating a decreasing trend and the blue color indicating an increasing trend and a 95% confidence level significant trend is indicated by the upward and downward arrow of opposite color.
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CDD and CWD spatial variation of Sen's slope with the red color indicating a decreasing trend and the blue color indicating an increasing trend and a 95% confidence level significant trend is indicated by the upward and downward arrow of opposite color.

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Other seasons are divided into post-monsoon (October–November), fall (December–February), and pre-monsoon (March–May). Extreme precipitation events mostly occur in the fall. Figure 4 shows that December has a significant decreasing trend for Rx1day and Rx5day values, while February shows an increasing trend. January shows no significant trends. December's decreasing trend in the upper study area and February's increasing trend indicate a shift in early winter precipitation, based on the absolute maximum value.
Figure 4
R95p and R99p spatial variation of Sen's slope with the red color indicating a decreasing trend and the blue color showing an increasing trend and a 95% confidence level significant trend is indicated by the upward and downward arrow of opposite color.
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R95p and R99p spatial variation of Sen's slope with the red color indicating a decreasing trend and the blue color showing an increasing trend and a 95% confidence level significant trend is indicated by the upward and downward arrow of opposite color.

Figure 4
R95p and R99p spatial variation of Sen's slope with the red color indicating a decreasing trend and the blue color showing an increasing trend and a 95% confidence level significant trend is indicated by the upward and downward arrow of opposite color.
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R95p and R99p spatial variation of Sen's slope with the red color indicating a decreasing trend and the blue color showing an increasing trend and a 95% confidence level significant trend is indicated by the upward and downward arrow of opposite color.

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JJAS (monsoon) months trend analysis

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Rx1day and Rx5day indices show maximum precipitation in 1 day and consecutive 5 days, respectively. Previous indices are considered yearly; to check the change in the different seasons, Rx1day and Rx5day are helpful. We are considering monthly extreme for monsoon months. All monsoon months show increasing trends, but the intensity varies. June, July, August, and September have 43, 181, 225, and 17 grids with significant increasing trends, respectively (Table 1). The seasonal 1-day and 5-day maximum precipitation indicate that extreme events are spread throughout the season. Continuous 5-day maximum precipitation increases more rapidly than the 1-day maximum precipitation. The high average precipitation zone in the North-West and low average precipitation in the southeast have the most significant increasing trend. From Figure 5, it can be interpreted that July and August have the most precipitation and the most area of a significant increasing trend for both indices.
Table 1

Indices with their significant trend grids number out of 1,332 and their initial value of trend line as intercept and average Sen's slope

IndexPositive countNegative countInterceptSlope
R10 250 1 21.91 0.699 
R20 144 5 6.71 0.33 
R25 119 4 3.89 0.21 
R95p 266 0 305.86 8.38 
R99p 138 0 110.43 2.98 
CDD 137 0 53.16 1.87 
CWD 272 2 19.22 0.82 
PRCPTOT 364 0 705.94 23.68 
SDII 228 1 6.39 0.106 
Rx1Jan 0 1 14.95 −0.63 
Rx1Feb 42 0 7.89 2.01 
Rx1Mar 0 73 8.90 −0.42 
Rx1Apr 8 25 9.44 −0.04 
Rx1May 96 2 9.94 0.34 
Rx1Jun 43 3 15.13 0.2 
Rx1Jul 181 3 19.14 0.59 
Rx1Aug 225 0 16.04 0.96 
Rx1Sep 17 1 16.76 0.125 
Rx1Oct 23 1 7.03 −0.01 
Rx1Nov 0 3 2.32 −0.06 
Rx1Dec 0 318 8.42 −0.69 
Rx1DJF 0 0 20.12 0.535 
Rx1MAM 7 136 20.35 −0.33 
Rx1JJAS 114 1 27.97 0.6686 
Rx1ON 9 1 8.89 −0.15 
Rx5Jan 0 10 32.88 −1.8 
Rx5Feb 18 0 22.49 2.27 
Rx5Mar 0 52 13.48 −0.55 
Rx5Apr 10 32 15.66 −0.06 
Rx5May 30 22 24.45 0.32 
Rx5Jun 61 1 15.13 1.14 
Rx5Jul 327 0 48.34 1.95 
Rx5Aug 275 0 44.57 2.35 
Rx5Sep 31 0 41.72 0.83 
Rx5Oct 7 12 17.37 −0.11 
Rx5Nov 0 2 3.33 −0.04 
Rx5Dec 0 295 12.22 −0.81 
Rx5DJF 0 0 36.83 0.78 
Rx5MAM 18 158 35.90 −0.28 
Rx5JJAS 275 0 63.22 2.1 
Rx5ON 7 12 17.37 −0.11 
IndexPositive countNegative countInterceptSlope
R10 250 1 21.91 0.699 
R20 144 5 6.71 0.33 
R25 119 4 3.89 0.21 
R95p 266 0 305.86 8.38 
R99p 138 0 110.43 2.98 
CDD 137 0 53.16 1.87 
CWD 272 2 19.22 0.82 
PRCPTOT 364 0 705.94 23.68 
SDII 228 1 6.39 0.106 
Rx1Jan 0 1 14.95 −0.63 
Rx1Feb 42 0 7.89 2.01 
Rx1Mar 0 73 8.90 −0.42 
Rx1Apr 8 25 9.44 −0.04 
Rx1May 96 2 9.94 0.34 
Rx1Jun 43 3 15.13 0.2 
Rx1Jul 181 3 19.14 0.59 
Rx1Aug 225 0 16.04 0.96 
Rx1Sep 17 1 16.76 0.125 
Rx1Oct 23 1 7.03 −0.01 
Rx1Nov 0 3 2.32 −0.06 
Rx1Dec 0 318 8.42 −0.69 
Rx1DJF 0 0 20.12 0.535 
Rx1MAM 7 136 20.35 −0.33 
Rx1JJAS 114 1 27.97 0.6686 
Rx1ON 9 1 8.89 −0.15 
Rx5Jan 0 10 32.88 −1.8 
Rx5Feb 18 0 22.49 2.27 
Rx5Mar 0 52 13.48 −0.55 
Rx5Apr 10 32 15.66 −0.06 
Rx5May 30 22 24.45 0.32 
Rx5Jun 61 1 15.13 1.14 
Rx5Jul 327 0 48.34 1.95 
Rx5Aug 275 0 44.57 2.35 
Rx5Sep 31 0 41.72 0.83 
Rx5Oct 7 12 17.37 −0.11 
Rx5Nov 0 2 3.33 −0.04 
Rx5Dec 0 295 12.22 −0.81 
Rx5DJF 0 0 36.83 0.78 
Rx5MAM 18 158 35.90 −0.28 
Rx5JJAS 275 0 63.22 2.1 
Rx5ON 7 12 17.37 −0.11 
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Figure 5
Sen's slope of 1-day and consecutive 5-day maximum precipitation for JJAS months and individual months of JJAS. The blue color indicates an increasing pattern and the red color as a decreasing pattern. Significant changes are indicated by the upward and downward arrow of opposite color.
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Sen's slope of 1-day and consecutive 5-day maximum precipitation for JJAS months and individual months of JJAS. The blue color indicates an increasing pattern and the red color as a decreasing pattern. Significant changes are indicated by the upward and downward arrow of opposite color.

Figure 5
Sen's slope of 1-day and consecutive 5-day maximum precipitation for JJAS months and individual months of JJAS. The blue color indicates an increasing pattern and the red color as a decreasing pattern. Significant changes are indicated by the upward and downward arrow of opposite color.
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Sen's slope of 1-day and consecutive 5-day maximum precipitation for JJAS months and individual months of JJAS. The blue color indicates an increasing pattern and the red color as a decreasing pattern. Significant changes are indicated by the upward and downward arrow of opposite color.

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Winter (monsoon) months trend analysis

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In other seasons, we have divided the remaining year into three seasons: post-monsoon, fall, and pre-monsoon. Post-monsoon consists of October and November; fall months are December, January, and February; and pre-monsoon is March, April, and May. In non-monsoon months, major extreme precipitation events occur in the fall season. Figure 6 shows there is a major deviation in the monthly scale and the seasonal scale. The 3 months in the season show the different trends for the extreme events of 1-day and continuous 5-day maximum precipitation. During December, for most of the grids, there is a significant decreasing trend for the Rx1day and Rx5day values; whereas, during February same indices show an increasing trend for most of the grids, and January has no trends in extreme precipitation for most grids and decreasing trends for some grids. While all the months of the seasons have different directions of detected change, the entire season shows no significant trend for all the grid. In December, the spatial variation shows a significantly decreasing trend in the upper boundary side of the study area. Overall, no change in the season, along with a decreasing trend during December and an increasing trend during February, indicate some extent of the shift in the early winter precipitation.
Figure 6
Sen's slope of 1-day and consecutive 5-day maximum precipitation for DJF months and individual months of DJF. The blue color indicates an increasing pattern and the red color as a decreasing pattern. Significant changes are indicated by the upward and downward arrow of opposite color.
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Sen's slope of 1-day and consecutive 5-day maximum precipitation for DJF months and individual months of DJF. The blue color indicates an increasing pattern and the red color as a decreasing pattern. Significant changes are indicated by the upward and downward arrow of opposite color.

Figure 6
Sen's slope of 1-day and consecutive 5-day maximum precipitation for DJF months and individual months of DJF. The blue color indicates an increasing pattern and the red color as a decreasing pattern. Significant changes are indicated by the upward and downward arrow of opposite color.
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Sen's slope of 1-day and consecutive 5-day maximum precipitation for DJF months and individual months of DJF. The blue color indicates an increasing pattern and the red color as a decreasing pattern. Significant changes are indicated by the upward and downward arrow of opposite color.

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Based on the absolute threshold value

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Defining extreme events by fixed thresholds (10, 20, and 25 mm) shows significant increasing trends. About 20% of the grid shows a significant increasing trend for heavy precipitation days. Only one grid shows a significant negative trend for R10. Very heavy precipitation days show significant increases for most grids, with 144 grids showing significant increasing trends. The 25 mm threshold increases in most parts of the basin, with 119 grids showing a significant increasing trend. Figure 7 shows significant increasing trends in all indices, with R10mm having the highest increase.
Figure 7
R10mm, R20mm, and R25mm spatial variation of Sen's slope with the red color indicating a decreasing trend and the blue color indicating an increasing trend and a 95% confidence level significant trend is indicated by the upward and downward arrow of opposite color.
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R10mm, R20mm, and R25mm spatial variation of Sen's slope with the red color indicating a decreasing trend and the blue color indicating an increasing trend and a 95% confidence level significant trend is indicated by the upward and downward arrow of opposite color.

Figure 7
R10mm, R20mm, and R25mm spatial variation of Sen's slope with the red color indicating a decreasing trend and the blue color indicating an increasing trend and a 95% confidence level significant trend is indicated by the upward and downward arrow of opposite color.
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R10mm, R20mm, and R25mm spatial variation of Sen's slope with the red color indicating a decreasing trend and the blue color indicating an increasing trend and a 95% confidence level significant trend is indicated by the upward and downward arrow of opposite color.

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Based on other general value

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Besides the indices mentioned above, it is also important to check the precipitation trend for the total depth of precipitation on wet days and the average precipitation intensity on wet days. Figure 8 shows the spatial distribution of Sen's slope for the different indices. The upper part of the basin gets higher intensity for a significant increasing trend. A total of 364 grids are a significantly increasing trend out of 1,332 grids for the PRCPTOT indices. The trend line shows an increasing pattern starting from 706 mm with a 23.68 mm/year rate. SDII indices also have an overall increasing trend starting from 6.39 mm/day and increasing by 0.1 mm/day/year. SDII indices are significantly increasing in the 228 grids, and one grid has a significant decreasing trend. Figure 8 shows the spatial variation of the trend of the PRCPTOT and SDII indices in different locations, suggesting some common areas for both. Still, many grid locations have only indices that have a significant trend.
Figure 8
PRCPTOT and SDII spatial variation of Sen's slope with the red color indicating a decreasing trend and the blue color indicating an increasing trend and a 95% confidence level significant trend is indicated by the upward and downward arrow of opposite color.
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PRCPTOT and SDII spatial variation of Sen's slope with the red color indicating a decreasing trend and the blue color indicating an increasing trend and a 95% confidence level significant trend is indicated by the upward and downward arrow of opposite color.

Figure 8
PRCPTOT and SDII spatial variation of Sen's slope with the red color indicating a decreasing trend and the blue color indicating an increasing trend and a 95% confidence level significant trend is indicated by the upward and downward arrow of opposite color.
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PRCPTOT and SDII spatial variation of Sen's slope with the red color indicating a decreasing trend and the blue color indicating an increasing trend and a 95% confidence level significant trend is indicated by the upward and downward arrow of opposite color.

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Wavelet power spectrum of precipitation extremes and climate indices

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Continuous wavelet distribution explains the relationship between extreme precipitation and climate anomalies. For the analysis of data, first, we calculated the standardized series. The difference from the mean in the original series is divided by the original series's variance. The monthly series of Rx1day monthly generates from the extreme monthly indices Rx1day. Similarly, the Rx5day monthly series is standardized and named Rx5day monthly. Rx1day yearly and Rx5day yearly are considered the extreme annual indices. To better understand yearly periodicity, R95p yearly and R99p yearly are two more indices based on percentile. The standardized 1-day (Rx1day monthly) and 5-day (Rx5day monthly) precipitation anomalies are estimated by subtracting the mean values from the Rx1day and Rx5day monthly original series and then dividing by the standard deviation for each grid. The same technique also standardizes climate anomalies. APHRODITE data are at the resolution of 0.25° × 0.25°. Climate anomalies are available every month.

CWT gives the multiscale variation of precipitation extremes and climate anomalies. In Figure 9, the thick black counter enclosing the regions gives significant wavelet power in time–frequency space with a significance level of 5% with a white noise process. The apparent periodicity of 0.5–1.5 years is available for the Rx1day monthly. The first decade of the 21st century showed a periodicity of 3.5–4.5 years. A significant trend is more after the 1980s is present in the spectrum. Nearly 7–10 years periodic band has a positive coefficient for the whole period, but that is not significant at 95% confidence. The apparent periodicity of 0.5–1.5 years is present. Similar to the Rx1day monthly, the Rx5day monthly in the first decade of the 21st century showing periodicity of 3.5–4.5 years is not significant. The significant trend is that more after the 1980s is available in the spectrum. Nearly 7–10 years periodic band has a positive coefficient for the whole period, but that is not significant at 95% confidence. Moreover, the value of the coefficient is less than the Rx1day monthly. The final takeaway is that no periodicity for the more extended period exists for the extreme event. ENSO periodicity is present at 1–5 years; significant periodicity is also present. The ENSO periodicity exists throughout the period but breaks from 1998 to 2002. For NAO, most periodicity is available at 0.5–1 year. For the yearly variation, the precipitation indices chosen for the annual change in the extremes are Rx1day yearly and Rx5day yearly, R95p and R99p. Rx1day yearly shows the periodicity of 0.6–1 year and 3.5–4.5 years is significant at different times. After 2000, the periodicity of 4 years is dominant. Similar results are available for the Rx5day yearly; before 2000, the periodicity with significance is more for Rx1day yearly than Rx5day yearly. R95p, which represents the precipitation amount for the day having more than 95% days, is shown 2–6 years periodicity. The CWT result of the R99p indices shows a similar periodicity pattern as it is available in R95p. At the annual scale of extreme events, no permanent periodicity is dominant for any of the indices.
Figure 9
Continuous Morlet wavelet spectrum of monthly and yearly precipitation extremes over and climate anomalies for the period 1952–2014. The thick black contours depict the 95% confidence level of local power relative to white noise.
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Continuous Morlet wavelet spectrum of monthly and yearly precipitation extremes over and climate anomalies for the period 1952–2014. The thick black contours depict the 95% confidence level of local power relative to white noise.

Figure 9
Continuous Morlet wavelet spectrum of monthly and yearly precipitation extremes over and climate anomalies for the period 1952–2014. The thick black contours depict the 95% confidence level of local power relative to white noise.
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Continuous Morlet wavelet spectrum of monthly and yearly precipitation extremes over and climate anomalies for the period 1952–2014. The thick black contours depict the 95% confidence level of local power relative to white noise.

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Wavelet coherence between precipitation extremes and climate indices

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Figure 10 shows the wavelet coherence between regional precipitation and the climate indices. The arrow indicates the phase difference between precipitation extremes and climate indices. The phase depends on the direction of the arrow for the series are in phase, the arrow points toward right whereas the left arrow indicates antiphase. While the arrow pointing upward tells, one series leads the other by 90° and the opposite for the arrow pointing downwards. The black contour shows the significance at a 5% significance level by the Monte Carlo experiments. Figure 10 indicates that the coherence of Rx1day monthly and ENSO is significant for 3–5 years periodicity. In Rx5day monthly and ENSO, coherence is positive in phase coherence for the 3–5 years. Some other periods are there for Rx1day monthly where significant coherence is present, but the time interval for the same is less. 1.5–2 years periodicity having the most time significant coherence is present. The result of coherence between Rx5day monthly and ENSO shows a similar pattern as the Rx1day was showing. NAO and monthly indices, Rx1day monthly and Rx5day monthly, show reasonable coherence of periodicity of less than a year in a staggered way. The 2.5 to 4 years correlation periodicity is significant, but the phase present is mostly antiphase. Figure 10 shows the coherence of Rx1day yearly and ENSO. Some periods exist for Rx1day yearly where insignificant coherence is present, but the time interval for the same is high. Four to six years periodicity have the most time little coherence is observed, the phase is in phase for the ENSO and Rx1day yearly other coherence is available for the periodicity less than 6 months. When we compare the coherence of ENSO with Rx1day yearly and Rx5day yearly for the same period, the periodicity is different in the two precipitation indices. However, the yearly coherence of Rx1day yearly and NAO is good for 8–47 years at a 12 years periodicity. The coherence is significant for the same period. Both the series are in the same phase. At the same time, the periodicity with the Rx5day yearly is statistically insignificant at 95% confidence. According to the above discussion, the monthly scale of extreme indices has significant coherence with ENSO, but at the interdecadal level, NAO is more significant.
Figure 10
Wavelet coherence (WTC) spectra between the monthly and yearly precipitation extremes and ENSO and NAO. Significant coherence at α = 5% are enclosed inside the thick black contour lines.
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Wavelet coherence (WTC) spectra between the monthly and yearly precipitation extremes and ENSO and NAO. Significant coherence at α = 5% are enclosed inside the thick black contour lines.

Figure 10
Wavelet coherence (WTC) spectra between the monthly and yearly precipitation extremes and ENSO and NAO. Significant coherence at α = 5% are enclosed inside the thick black contour lines.
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Wavelet coherence (WTC) spectra between the monthly and yearly precipitation extremes and ENSO and NAO. Significant coherence at α = 5% are enclosed inside the thick black contour lines.

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This study provides a comprehensive analysis of the trends and teleconnections of extreme precipitation events in the UIB within the Indian region, part of the critical geo-ecological Hindu Kush Himalayan Mountain system. The extreme is defined based on percentile value, threshold value, a specific amount of precipitation, and maximum precipitation in the period 2001–2013 using HAR high-resolution (10 km × 10 km) precipitation data. The result of the monthly, seasonal, and annual trends indicates an increase in the frequency and intensity of both dry and wet extreme precipitation events, an increase in monsoon precipitation, a shift in winter precipitation, and an increase in CDD.

Using APHRODITE daily (0.25° × 0.25°) data from 1952 to 2014, we employed CWT and wavelet coherence analysis to identify significant periodicities and correlations with large-scale climate anomalies such as the ENSO and NAO. The results of indices periodicity show that percentile-based extremes have more significant periodicities than absolute indices. The coherence of monthly indices is better with the ENSO at a periodicity of 3–5 years. In comparison, coherence of the yearly extreme is significant with NAO with 8–10 years periodicity and more than 16 years periodicity. ENSO and NAO both affect the extreme precipitation in the UIB.

Our findings show an increase in CDD and increased rainfall during the monsoon period, with a decreasing pattern in early monsoon and early winter monsoon. This leads to floods in the rainy season and hydrological drought due to water scarcity in the pre-monsoon and early monsoon months. It is recommended to increase storage capacity to utilize water during the dry periods. The findings highlight the impact of global climate change on regional precipitation patterns in the UIB and underscore the necessity for adaptive water management policies. These policies are crucial for mitigating flood risks during the rainy season and addressing water scarcity during the dry season.

The findings suggest that the trends and patterns of extreme precipitation events and the influence of teleconnections point to a shift in precipitation extremes in the future. This underscores the need for future research focusing on global climate change and large atmospheric circulation (Ullah et al. 2023; Wijeratne et al. 2023). Earlier studies have shown that comparable patterns observed across various South Asian regions have been linked to climate change (Sarwar et al. 2022; Waseem et al. 2022; Rinzin et al. 2024). Consequently, there is a scope for comprehensive regional studies that utilize the latest CMIP6 dataset to extend the analysis using the ETCCDI that earlier researchers have highlighted (Abbas et al. 2022b, 2023). This approach would enhance our understanding of climate dynamics and inform future climate resilience strategies.

In summary, this study not only identifies significant trends in extreme precipitation events in the UIB but also provides a deeper understanding of the underlying mechanisms driven by large-scale climate anomalies. The insights gained from this research are essential for guiding policy decisions and improving the resilience of communities dependent on the water resources of the UIB.

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The authors declare that no funds, grants, or other support were received during the preparation of this manuscript.

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A.K.: conceptualization, methodology, writing – original draft, writing – review and editing, data curation, investigation, validation, visualization, and formal analysis. M.K.M.: methodology, validation, formal analysis, review and editing, and conceptualization. D.S.A.: investigation, validation, formal analysis, supervision, writing – review and editing, conceptualization, and methodology.

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All relevant data are included in the paper or its Supplementary Information.

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The authors declare there is no conflict.

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