Introduction

Fresh water is one of the basic needs of living beings, and owing to certain anthropogenic activities, its sources are either getting contaminated or are being diminished. For instance, groundwater is getting contaminated with illegitimate discharge of industrial effluents, disposal of demolition waste has increased the inflow of sediments in surface water bodies (Lida et al. 2012), and emission of greenhouse gases (GHGs) is contributing to depleting the snow cover. Among these incidents, the decrease in snow cover area (SCA) has recently gained significant attention from the global scientific community due to the associated chain of drastic events, viz., climate change, floods, intensification of sediment load in tributaries, glacial lake outburst, and glacier retreat (Mishra et al. 2014; Kaab et al. 2015; Thapa et al. 2020). Globally, such events may further impact the livelihood of millions of populations every year. Therefore, it is imperative to study the changes in SCA in various regions of the world.

Snow cover dynamics are mainly influenced by variability in climatic stressors (CSs), i.e., precipitation and temperature (Shrestha and Aryal 2010; Snehmani et al. 2016). A small variation in these stressors, i.e., either temperature or precipitation may have negatively affected the hydrological regime of the snow cover area and glacierised basins. Azmat et al. (2016) have reported a significant change in temperature and precipitation over the Jhelum River basin of India during the last 50 years, which affects the SCA, high risk of floods, food insecurity, and shortage of drinking water over the basin. Meanwhile, along with precipitation and temperature, several studies have also been reported in mountainous glaciers, where the altitude of the region also contributes to the variations of SCA (Sharma et al. 2014; Kour et al. 2015; Tahir et al. 2015; Gurung et al. 2017; Muhammad et al. 2018; Singh et al. 2018). Hence, it can be presumed that the variation in the SCA could be most predominant in the Third Pole of the world. The SCA of the Himalayas has a considerable impact on the river basin and its hydrologic response behaviour. Snowmelt runoff is the foremost source of freshwater in South Asia and is required for domestic, drinking, agricultural, industrial, and hydropower sectors in downstream areas. A review of the literature has found it evident that the Himalayan region has detected both rising and declining trends in SCA with different altitudinal variations. Bookhagen and Burbank (2010) and Kour et al. (2016) have detected a rise in the SCA in the western Himalayan region due to the strong influence of winter westerlies in this region. However, Tahir et al. (2016) witnessed a constant or a slight rise in the SCA during the winter season. Conversely, Kaab et al. (2015) and Thapa et al. (2020) have reported a negative mass balance in the western Himalayan region’s SCA due to the constant warming of the winter season. These studies have demonstrated a significant association between the CSs, elevation, and SCA of a hydrological regime. However, studies focusing specifically on the Himalayas and its river basins are a challenging task owing to their large area, and therefore, further research is required to make a conclusive argument about them. Hence, it is essential to understand the association between the CSs, altitude, and the SCA in the Himalayan region.

In the Himalayan region, to find stations related to the snowfield observation dataset is a difficult task. The maximum observatory stations have been set up below 2200 m due to the rugged topography of the Himalayas region. Satellite-based climatic and snow cover data are useful for analysing spatiotemporal variability in CSs and SCA in ungauged or poorly gauged river basins in the Himalayas (Tahir et al. 2011). The National Aeronautics and Space Administration (NASA) launched the Moderate Resolution Imaging Spectroradiometer (MODIS) to monitor worldwide snow cover extents. The MODIS sensor can estimate snow cover with a wide range of spectral coverage at moderate spatial resolutions. Since the year 2000, a suite of MODIS products has been provided to the research community for a variety of applications related to the atmosphere, land, and ocean (Zhang et al. 2014; Wen et al. 2013; Joshi et al. 2013). According to Huang et al. (2017), monitoring snow cover variations with the MODIS snow product has been detected to have more advantages over ASTER and Landsat 8 (OLI) imagery due to direct and continuous snow cover estimates at fine temporal resolutions using the MODIS dataset. Furthermore, Gurung et al. (2017) have observed that the MODIS snow product is a reliable source of snow cover estimation in the Hindu-Kush Himalayas (HKH) region. Several studies have examined the accuracy of MODIS snow products in various parts of the world, including the HKH region, the Tibetan Plateau, etc., and found very significant results with an overall accuracy of 90% vis-à-vis in situ or high-resolution satellite datasets (Hall and Riggs 2007; Wang et al. 2007; Tahir et al. 2011; Wang et al. 2008; Parajka and Blöschl 2012; Mishra et al. 2014). To assess the validity of the MODIS snow product, researchers have compared the performance of MODIS images to ASTER images at both lower and higher elevations and found that the MODIS products are more reliable than the ASTER dataset (Tahir et al. 2011; Tekeli et al. 2005; Mishra et al. 2014).

Therefore, in this study, satellite-based precipitation, temperature, and SCA data have been used to fulfil the following objectives: to understand the variability of SCA at different elevation zones and its correlation with the CS parameters (precipitation and temperature) in the Parvati River Basin (PRB) of the western Himalayan region. The novelty of the study is to examine the behaviour of SCA at different altitude zones over the mountainous regions, which offers an opportunity to examine the snow cover dynamics on a watershed scale. Furthermore, the changing climate is adversely affecting the SCA variability at high-altitude river basins like the PRB in the north-western Himalayan region. Therefore, this study will be useful for planning, designing, installing, and operating small and large hydropower projects that have already been executed or are under construction and are being planned in the future over the PRB. Finally, this study will also be beneficial for environmentalists, climatologists, glaciologists, global and regional policymakers in setting legislation, and researchers in further designing the climatic models over high-elevation regions.

Study area

The PRB has been selected for this study, and its coordinates are between latitudes of 31° 40′ and 32° 15′ north and longitudes of 77° 10′ to 77° 55′ east. The PRB falls in the Kullu district of Himachal Pradesh in the western Himalayas region of India. The geographical position of the PRB is shown in Fig. 1. The total geographical area of the basin is about 1763 km2. It is an arc-shaped basin bounded by the middle Himalayan range in the south and the greater Himalayan range in the north. The Parvati River rises from the Mantalai glacier below the Pin Parvati pass in the western Himalayas and flows gradually through a curvature from north–north-west to west-south-west. The Mantalai glacier is situated in the PRB at an elevation of around 5200 m above mean sea level (amsl). The altitude of the basin ranges from 1100 to 6200 m (amsl). It is the major left-bank tributary of the Beas River and joins it at Bhuntar, about 10 km downstream of Kullu town. The upper parts of the basin are mostly covered with snow and 300 small and large glaciers (Fig. 1).

Fig. 1
figure 1

Location map of the Parvati River basin in Himachal Pradesh

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The climate of the PRB is largely sub-temperate in the lower reaches and temperate in the higher reaches. The basin’s climate is separated into four different seasons, i.e., winter (December to March), summer (April to June), monsoon (July to September), and post-monsoon (October to November). The basin remains cold between December to March. Both snowfall and heavy frost occur during this period due to north-westerly disturbances. The snowline is highly variable on account of temperature and elevation differences. It varies from 2000-m amsl during the winter season to around 5000-m amsl during the summer season. Like temperature, rainfall is highly variable in the PRB due to its topography and geographical location.

Data collection

This study is exclusively based on secondary sources of data. The data comprised different satellite products for the period of 2001–2017. The various datasets used in this study, along with their sources and a detailed description of their types, are given in Table 1. Furthermore, the location map of climatic data stations at different elevation zones has been shown in Fig. 2.

Table 1 Shows the parameters their types, sources and period used in the present study
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Fig. 2
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Map showing the location of climatic data taken from different elevation zones

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Methods

Snow cover monitoring

The MODIS data has been processed using the ERDAS and Arc GIS 10.0 software, which was further used to convert the geometric correction to project the geographical latitude–longitude projection Universal Transverse Mercator (UTM) Zone 43 with WGS84 and generate the Normalised Difference Snow Index (NDSI). The brief methodology adopted during this study has been shown in Fig. 3. This figure depicts a detailed description of the data used in the present study, with various methodological steps applied for the extraction of SCA using satellite data.

Fig. 3
figure 3

Flow chart showing the methodology adopted for mapping (extraction) of the snow cover

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Cloud cover removal

The estimation of SCA is difficult to determine in the Himalayan region due to the presence of mountain shadows and cloud cover in the same visible spectrum. Therefore, parametric algorithm classification is a challenging task in this region (Kulkarni et al. 2002). Several researchers have used different techniques to extract the cloud cover pixels from MODIS snow cover data (Gao et al. 2010; Parajka et al. 2010). The cloud filter is used to create the daily and 8-day composite snow cover data using MODIS swath products as basic inputs (Hall et al. 1995). In this study, February, July, August, and October are high cloud cover months. So, these months have been excluded from the analysis due to high cloud cover errors. In this study, around 136 MODIS cloud-free images have been processed to generate the long-term monthly SCA of the PRB.

Extraction of SCA map

The SCA data for the PRB has been generated using the ERDAS Imagine image processing and ArcGIS 10 software. Snow data are automatically created with the help of ERDAS Imagine using the NDSI algorithm to recognise the snow pixel (Hall et al. 1995). A snow pixel has been identified using the NDSI approach. This technique is effective for identifying snow and ice (Hall et al. 2002; Hall and Riggs 2007). The NDSI was used to determine the amount of typical reflectance to differentiate between snow’s visible and short-wave infrared reflectance (SWIR).

Snow is categorised by the NDSI using data from MODIS bands 4 (0.545–0.565 m) and 6 (1.628–1.652 m):

$$NDSI=\frac{Reflectance\mathit\;in\mathit\;band\;4\;\left(VISIBLE\right)-Reflectance\mathit\;in\mathit\;band\mathit\;6\;(SWIR)}{Reflectance\mathit\;in\mathit\;band\;4\;\left(VISIBLE\right)+Reflectance\mathit\;in\mathit\;band\mathit\;6\;(SWIR)}$$
(1)

This algorithm classifies a pixel as snow if the NDSI is larger than 0.40, near-infrared reflectance in band 2 is greater than 0.11, and near-infrared reflectance in band 4 is greater than 0.10. To meet the demands of different users, NASA offers a hierarchy of snow products based on MODIS observations. After using ≥ 0.1 as the NDSI value, some pixels of dense coniferous forests and water bodies are also categorised as snow. To counter these misclassified pixels, a finer NDSI threshold of 0.4 has been used, which meant that NDSI pixels equal to or greater than 0.4 were classified as snow pixels (Klein and Barnett 2003). So, keeping this in mind, PRB snow cover data is automatically created with the help of ERDAS Imagine using the NDSI algorithm to recognise the snow pixel. ArcGIS 10 has been utilised to categorise, reclassify, and adjust the automatic extraction of snow cover and snow-free areas in the PRB various elevation zones.

Statistical analysis

Simple linear regression

It is a parametric method and is most commonly used to detect a trend. The linear regression method has been widely used in the literature (Immerzeel et al. 2009; Gurung et al. 2011). The trend of SCA, temperature, and snowfall has been computed using the linear regression test at a 95% confidence level at the annual, seasonal, and monthly time scales. The p-value has been utilised in this study to detect the significance level of the observed patterns. To examine the short-term trend, linear regression has been applied to the average SCA, temperature, and snowfall over 17 years of data. The linear trend has been calculated by the least squares method as follows:

$$b=\frac{\sum_{i}^{n}{X}_{i}{t}_{i}-\frac{1}{n}\left(\sum_{i}^{n}{X}_{i}\right)\left(\sum_{i}^{n}{t}_{i}\right)}{\sum_{i}^{n}{{t}_{i}}^{2}-\frac{1}{n }{\left(\sum_{i}^{n}{t}_{i}\right)}^{2}}$$
(2)

where n is the number of study years, i is the serial number of the year (i = 1, …, n = 17), xi represents the SCA of each pixel for year I, t is corresponding time, b > 0 means upward trend in SCA, b = 0 means no trend, and b < 0 represents downward trend in SCA.

Kendall’s tau-β correlation (τ) analysis

Kendall’s tau (τ) has been widely used as a distribution-free measure of cross-correlation between two variables (Gurung et al. 2017). It has been previously shown that persistence in the two involved variables results in the inflation of the variance of τ. Kendall’s τ has been classically used to test the significance of cross-correlation between two variables when their distributions significantly deviate from the normal distribution. In that case, a significance test based on the distribution-free τ, which is a function of the ranks of the variates rather than their actual values, offers more power than other parametric tests such as the Pearson product-moment correlation coefficient. In this study, correlations between SCA, temperatures, and snowfall at different altitude zones have been analysed using Kendall’s tau-b correlation (τ). It evaluates the link between two variables similarly to Pearson’s (r) and Spearman’s (p)correlations.

Calculation of percent change

The percent change has been calculated with the help of a linear trend, as it corresponds to the median slope multiplied by the total period of length and divided by the total mean value. The percent change shows the rate of change of any variable over its historical time period. Here, the positive and negative values discourse about the significant increase or decrease of SCA over the basin. It can be calculated mathematically as:

$$\mathrm{Percent}\;\mathrm{change}=(\mathrm\beta\times\mathrm{length}\;\mathrm{of}\;\mathrm{year})/\mathrm{mean}\times100$$
(3)

where β is the Sen slope value an length of year denotes the study period. In this study, the percent change has been calculated to estimate the positive and negative change in SCA from its long-term mean record.

Results and discussion

It is important to analyse the variability of SCA at various altitude zones to understand the various components of the cryosphere. The variation in elevation has been increased with every 1000 m, whereas the snow cover durability has increased by about a month (Bilal et al. 2019). As a result, snow cover analysis at various elevations and aspect levels has been computed in this study.

Hypsometric analysis

The characteristics of hydrological and meteorological parameters in the Himalayan Mountains are directly linked to the altitude of a region. The PRB has been separated into five different elevation zones using ASTER DEM data, each with a 1000-m elevation difference. It helps us make more accurate estimations of snow cover and snow-free areas. Using a DEM of the study area, a GIS technique is utilised to generate the elevation map (Fig. 4) and prepare the elevation curve (Fig. 5). The tool has been customised using GIS techniques for automatic extraction of the area under various altitude zones. The summary table has been generated for future analysis of the hypsometric curve. The result obtained from the hypsometric curve has shown that the PRB area lies within the elevation range of 1100–6200 m (zones I–V). The maximum area has been detected at 39.12% in zone IV (4000–5000 m), followed by 22.89% in zone V (5000–6200 m), while the minimum area has been observed at 7.61% in zone I (1100–2000 m), 12.95% in zone II (2000–3000 m), and 17.44% in zone III (3000–4000 m) out of the total basin area from 2001 to 2017. The zonal analysis of SCA revealed that the maximum SCA has been observed in zone IV (33.83%), followed by zone V (22.58%), and the minimum SCA has been found in zone I (0.15%), zone II (1.6%), and 8.6% in zone III out of the total basin SCA (Fig. 5).

Fig. 4
figure 4

The delineated elevation map of the Parvati basin at 1000-m intervals

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Fig. 5
figure 5

Area-elevation curve and SCA under different elevation zones of the total area in the Parvati River basin

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The hypsometric curve reveals that the majority of the basin lies above 4000 m altitude, accounting for 62% (1093.11 km2) of the basin’s total area, and it covers approximately 56.41% SCA out of the total basin area. Overall analysis has revealed that about 85.46% of SCA has covered by zone IV and zone V out of the total basin SCA from 2001 to 2017. Meanwhile, the SCA and glaciers are found to be above the 4000 m altitude zone, and that is why the PRB is the most important basin for the study of the cryosphere and its melting contribution in hydro-meteorological studies.

Snow cover depletion

The ablation and accumulation behaviour of the SCA in the different elevation zones serves as an important input for estimating regional discharge for snow and glacier melting over the PRB. The SCA curves plotted for individual elevation zones for both accumulation (September to March) and ablation (March to September) have been revealed in Fig. 6. The snow cover accumulation and ablation periods clearly show a shift from 2001 to 2017. Furthermore, it has been revealed that the ablation period of the SCA has been increased in the middle and lower elevation zones (zones I, II, and III) because the accumulation pattern of the SCA has been found to be more variable in the lower and middle elevation zones.

Fig. 6
figure 6

Snow cover accumulation and ablation pattern over different elevation zones in the Parvati River basin

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Subsequently, the extent of the ablation period has increased by almost 1 month due to the greater melting of glacier and snow cover areas. It is a shift towards the early winter and spring season melting in the PRB, which may be due to the surface snow darkening due to the deposition of light-absorbing impurities, which can lower the albedo and accelerate SCA melting. Hence, snowmelt causes the underlying ice mass to be exposed to sunlight for a longer period, which causes glaciers retreat (Thind et al. 2021). The ablation happens through melting due to more direct solar radiation at lower and middle elevation zones. The summer temperatures may not rise above the freezing point in the higher altitude zones. So, ablation is mainly due to the sublimation process at higher elevations (snow gets converted to the vapour phase directly). Ablation and accumulation play a critical role in determining water balance, the seasonal budget, and the influence of climate changes on the cryosphere. These shifts will be caused by climate change and alterations in circulation patterns (Gurung et al. 2011). A large part of the Parvati basin has annual precipitation in the form of snow. Therefore, the study of ablation and accumulation is important in managing water resources in this region.

Annual analysis

Variability of SCA at different elevation zones

Over the PRB, the average annual SCA trend has been calculated in five elevation zones: zone I, which is between 1100 and 2000 m; zone II, which is between 2000 and 3000 m; zone III, which is between 3000 and 4000 m; zone IV, which is between 4000 and 5000 m; and zone V, which is between 5000 and 6200 m (Fig. 7). In zones II, III, and IV, a rising tendency in SCA has been found, while a slightly declining trend has been observed in zones I and V over the basin (Table 2). During the study period, it has been observed that there is a slightly decreasing or stable trend of SCA over higher altitudes (zone V) (Table 2) because of the inverse relationship of SCA with temperature and snowfall in high-altitude zones (Table 3). The rising trend in snowfall constantly feeds the high-altitude zones, while the rising trend in mean temperature increases melting losses, which results in a minor reduction in SCA at higher elevation zones. Similarly, researchers have observed that the higher altitude region has found a high warming rate in the Tibetan Plateau (Liu and Chen 2000), western Himalaya (Azmat et al. 2016; Singh et al. 2018; Muhammad et al. 2018), and Karakoram mountains (Tahir et al. 2015). The increased rate of warming at higher altitudes could be attributed to the increased rate of particle tendency in the atmosphere (Bollasina et al. 2011; Thind et al. 2021).

Fig. 7
figure 7

Annual mean variability and trends of snow cover area over different elevation zones in the Parvati River basin

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Table 2 Regression trend analysis of SCA, snowfall, and temperature of the Parvati River basin
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Table 3 Kendall tau correlation analysis between different parameters over different altitudinal zones in the Parvati River basin
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Barring zone III, all the elevation zones show a non-significant tendency in the SCA (Table 2). A significant increasing trend has been observed in zone III (3000 to 4000 m), with higher variability in SCA. It has found a significant increasing trend of snowfall in zone III, which indicates probable explanations for a significant rise in SCA in zone III. A significant positive relationship has been observed in SCA with snowfall in zones II and III over the PRB from 2001 to 2017 (Table 3). Solid precipitation in zone III has increased on an annual scale in the PRB region. Hence, the circulation system of westerlies may be the possible reason for the rising trend in snowfall over the basin (Tahir et al. 2016). In the lower elevation zone, a slight decreasing trend of SCA has been found due to the rising trend of temperature in this region. Lower and intermediate elevation zones may be more susceptible to changes in the SCA of PRB because of the higher temperatures and high coefficient variability, making it the snow-free area among the five elevation zones. As a result of these factors, it is especially vulnerable to precipitation transitions from snow to rain produced by a warmer environment. These elevation zones have a considerable impact on total basin snow cover patterns. Additionally, most of the glaciers predominate in the PRB’s higher elevation zones (Fig. 5), making it difficult to identify the variability in snow cover (particularly wet) due to different spectral signatures (Gupta et al. 2005).

SCA anomaly at different elevation zones

The SCA anomaly is the deviation of SCA from its long-term average value. The analysis reveals the highest anomaly of SCA has been found in zones III and IV due to more variability in temperature and precipitation. In contrast, fewer snow cover anomalies have been observed in the lower and higher elevation zones of I, II, and V from 2001 to 2017 (Fig. 8). In contrast, less variability is noticed in zones I and V from 2001 to 2017 in the PRB. In 2003 and 2016, the highest negative anomaly has been observed in zones III, IV, and V because the year 2016 has been found to be the warmest in India in the last 116 years, i.e., since 1901. IMD also reveals that India’s climate in 2016 was among the top five warmest years since 1901. The largest negative snow cover anomaly has been observed in zones I and V due to extreme warming in the particular elevation zones (Table 2). Zone V has been observed as a significant negative snow cover anomaly (Fig. 8) due to a significant negative relationship with snowfall and temperature from 2001 to 2017 (Table 3). It is also specifying that the ablation of snow cover is more than accumulation. These findings give an idea that the warming at higher altitudes is higher in the PRB. A similar study has revealed a high warming rate at high altitudes over the Tibetan Plateau (Liu and Chen 2000), western Himalayas (Azmat et al. 2016), and Karakoram mountains (Tahir et al. 2015). The increased rate of warming at higher altitudes can be attributed to rising concentrations of atmospheric aerosols (Bollasina et al. 2011; Thind et al. 2021). Surface snow darkening due to the accumulation of light-absorbing impurities can diminish the albedo rate and increase the SCA melting of an area. The early melting of surface snow uncovers the underneath ice mass of sunlight for extended periods, causing glaciers to retreat (Thind et al. 2021). This is the negative mass balance of SCA in zone V over the PRB from 2001 to 2017. The minimum number of negative snow cover anomalies has been noticed in zones II and III. In 2004, the largest positive snow cover anomaly occurred in zones I and II. However, during 2009 and 2013, the largest positive SCA anomaly occurred in the middle and higher elevation zones (zones III, IV, and V) over the PRB. From 2001 to 2017, a significant positive snow cover anomaly has been identified in zone III due to a significant positive relationship between SCA and snowfall (Table 3).

Fig. 8
figure 8

Snow covered area anomalies trends in different altitudinal zones over the Parvati River basin

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Seasonal analysis

SCA variability at different elevation zones

Seasonal analysis of SCA at various elevation zones in the PRB from 2001 to 2017 is presented in Table 4, and the curves of different seasons introduced during winter, summer, monsoon, and post-monsoon are shown in Fig. 9. The winter season analysis reveals the increasing trends of SCA in zones II, III, and IV. However, the winter SCA increasing trend is majorly due to a rise in winter snowfall, which has not been found significant in this study (Table 4). These results have been found to correspond with earlier studies by Hewitt (2005) and Archer and Fowler (2004). Furthermore, Ridley et al. (2013) have examined variations in the duration and magnitude of snowfall events using a regional climate model associated with meteorological patterns such as the westerlies and found a rise in the frequency of extreme events during the twenty-first century. However, a decreasing trend in SCA has been detected in zones I and V since a substantial negative relationship has been detected between SCA and temperature in zone V during the winter season (Table 5). It is depicted from the analysis that the ablation of snow cover is greater than the accumulation in zone V and vice versa in zone II during the winter season. It indicates that higher absorption of solar radiation leads to more melting patterns. Similarly, more mass loss from the snow cover surface in zone V during the winter season may be due to surface snow darkening induced by the accumulation of light-absorbing impurities, which can diminish its albedo and increase SCA melting (Thind et al. 2021).

Table 4 Zonal seasonal trend of SCA, snowfall and temperature in the Parvati River basin
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Fig. 9
figure 9

Zonal seasonal trend analysis of snow cover area in the Parvati River basin

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Table 5 Zonal seasonal Kendall tau correlation between SCA with temperature and SCA with snowfall in the Parvati River basin
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The summer season analysis reveals that the declining trends of SCA have been witnessed in lower elevation zones (zones I and II), and the increasing trend has been observed in the middle and higher elevation zones (zones III, IV, and V) over the PRB (Fig. 9). Noticeably, maximum snow melting has been observed during the summer seasons in low-altitude zones due to high temperatures. It also demonstrates that during the summer season, a strong negative relationship between SCA and temperature has been found in zones II, III, IV, and V (Table 5). The middle elevation zone (III) has observed a significant positive correlation between SCA and snowfall during the summer season. A rising trend in SCA has been perceived in higher elevations (zones IV and V) due to a significant increase in snowfall, and a decrease in temperature has been found in zones IV and V during the summer season (Table 5).

The monsoon season analysis has detected a substantial declining trend of SCA in different elevation zones I, IV, and V. This may be due to a significant negative relationship that has been observed between SCA and snowfall and temperature in these zones (Table 5). High temperatures enhance the snow melt, which further results in the reduction of SCA. Conversely, low temperatures result in a longer SCA. The significant increasing trend of snowfall and temperatures over the same period (2001–2017) suggested a possible cause for the SCA decline (Table 4) because the temperature has a greater influence on snowfall during the monsoon season as it enhances the snow melt over the time period. The snowfall continued to increase because the rising trend in mean temperature increased snowmelt losses, which have depicted a reduction of SCA throughout the monsoon season. It indicates that the ablation rate of snow covers is higher than the accumulation rate during the monsoon season in zones IV and V from 2001 to 2017. Surface snow darkens because of the accumulation of light-absorbing impurities, which reduces its albedo and accelerates SCA melting. The early melting of surface snow uncovers the underneath ice mass to sunlight for a longer period, resulting in glacier retreat (Thind et al. 2021). Seasonal trends in mean temperature and snowfall could aid in determining whether the meteorological elements contribute more to the variability pattern. The SCA decreased by the highest of 12.84% in zone IV during the monsoon season from 2001 to 2017. It also displays that the area covered by snow has been decreasing at an alarming rate in the higher elevation zones over the PRB during the monsoon season. The PRB’s cryosphere is suffering from a decreasing trend in SCA during the monsoon season. A non-significant declining trend has been observed in zones II and III during the study period. Interestingly, at all elevation zones, a declining tendency in SCA has been observed during monsoon season (Fig. 9).

Furthermore, during the post-monsoon season, a higher fluctuation in the extent of SCA has been observed at all elevation zones. In the lower and middle elevation zones I, II, and III, a rising tendency in the amount of snow cover has been noted throughout the post-monsoon season. The trend analysis has found that stable or slightly decreasing snow cover has been observed in the higher elevation zones IV and V from 2001 to 2017 (Fig. 9). The variability of SCA is higher in the post-monsoon and summer seasons in the PRB from 2001 to 2017. A positive relationship between SCA and temperature has been observed only in the post-monsoon season (Table 5). It may be due to higher SCA variability, snowfall, and temperature in the post-monsoon season over the PRB. The main cause of winter snow cover is westerly precipitation (mainly in solid form), while during the summer and monsoon seasons, the highest snow melting occurs due to high temperatures. As a result, measuring and mapping snow cover fluctuations at various elevations provides useful information for the climatology of the PRB.

Percent change in SCA at different elevation zones

The zonal seasonal percent change in SCA of the PRB has been depicted in Fig. 10. The maximum average negative percent change in SCA has been observed at − 34.66% during the monsoon season, which is maximum in the middle and higher altitude zones such as − 92.22% in zone III, − 68.31% in zone IV, and − 8.79% in zone V from 2001 to 2017. It is depicted that the permanent SCA and glacier also retreat during the monsoon season in higher-altitude regions of the basin. The minimum average positive percent change in SCA has been recorded at 5% during the summer season, while the maximum positive percent change has been found in zone III (32.54%), followed by zone IV (8.28%), and a negative percent change has been found in zone II (− 15.84%) during the study period. On the whole, in the post-monsoon and winter seasons, a substantial increase in SCA has been noticed. The maximum average positive change in SCA has been observed at 15.55% during the post-monsoon season, which is positive in all elevation zones, and the maximum positive change has been found in zone III (55.6%) and IV (21.88%) from 2001 to 2017. During the winter season, the lower and middle elevation zones (zone I, zone II, and zone III) have experienced a positive change in SCA, with 4.82%, 45.61%, and 16.32%, respectively. In the higher elevation zones, low positive growth of SCA has been noticed in zone IV from 2001 to 2017. It is revealed that the SCA increased in the lower and middle elevation zones due to strong westerly precipitation during the winter season. The average positive change in the SCA is 13% during the winter season from 2001 to 2017.

Fig. 10
figure 10

Zone-wise percent change in snow cover area over different seasons in the Parvati River basin from 2001 to 2017

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Overall analysis revealed that the maximum negative change has been found in zones III and IV during the monsoon season. The maximum average negative percent change of SCA has also been noticed in the monsoon season, and the maximum positive percent change has been witnessed in the post-monsoon and winter seasons in the middle and lower elevation zones. It has been found that the higher elevation zones have more negative change in the monsoon season, and the lower elevation zones have more positive change in the winter season. This demonstrates that the ablation rate of snow in zones IV and V is higher than the accumulation rate during the monsoon season. Noticeably, the amount of snow cover in higher elevation zones of the PRB region has been declining at an alarming rate during the monsoon season.

Glacial and leftover/perennial snow area

The conventional depletion curve (CDC), which is “the ratio of the SCA in a zone to the total area of that zone,” is used to determine glacial and leftover/perennial SCA. According to the CDC, the minimum SCA in zone V has been found to be nearly 98% over the last 17 years (2001–2017). Zone V has a total area of 403 km2, of which 98% is approximately 395 km2. The zone V has been found above 5000 m in elevation, and it is the most accumulated permanent snow and glacier cover area. According to Pfeffer et al. (2014), the glacier area has been assessed by the Randolph Glacier Inventory to be 2.9% of the catchment area. However, this study has depicted a watershed size of 1762 km2 and a glacier area of about 22.4%, which is larger than the glaciated area from the agreement, which is due to more than 60% area of the basin lying above 4000 m. These findings of our studies provide us with confidence that the assumptions we have taken to assess the change in the glacier-covered area are correct.

Conclusions

This study investigates the association between key climate stressors (CSs), i.e., temperature and precipitation, topography, and the variability of SCA at different elevation zones in the PRB from 2001 to 2017. For this study, the PRB has been classified into different elevation zones, i.e., from zone I to zone V, ranging from 1100 to 6200 amsl. The various satellite databases, such as MODIS, MEERA-2, and ASTER DEM V2, have been used to estimate the changes in the SCA and the CSs with changes in elevation and seasons. The results of the study reveal a slight decreasing or stable trend in zone V of the basin, because the SCA of this zone (higher elevation) has found a significant negative relationship with temperature and snowfall. However, the impact of temperature is greater than the impact of snowfall in this zone. On the other hand, the SCA indicates a significant increasing trend in zone III, with the higher variability of the SCA due to the offset effects of a significant increasing trend in winter snowfall. Furthermore, large events of negative anomalies have been noticed at higher elevations as compared to lower and medium elevation zones in the PRB region. The SCA anomaly trend has been identified with a substantial rise in zone III and a considerable reduction seen in zone V. The SCA accumulation and ablation analysis for each elevation zone reveals that the duration of the ablation period has been increased by about 1 month due to greater melting of glaciers and SCA in the PRB region during the study period.

Furthermore, the mean seasonal temperatures and snowfall play a significant role in deriving the SCA regime of the basin. The change in temperature and snowfall variables has a significant effect, specifically on high-altitude regions of the basin. The seasonal trend investigation of SCA has observed an increasing trend at the higher elevation zones (zones IV and V) during the summer season due to a significant rising trend in snowfall and a decreasing trend in temperature during the summer at higher elevation zones. A significant negative trend has been found at the higher elevation zones during the monsoon season due to SCA, which has detected a strong negative relationship with snowfall and temperature in zones IV and V. Interestingly, the results of the study indicated that the annual and seasonal SCA in the higher elevation zones of PRB has been declining at an alarming rate. These findings of this study will help in understanding the responses of seasonal snow cover to principal climatic variables (temperature and snowfall), agriculture, planning, management of water resources, and watershed managers. For future research, it is interesting to note that variations in snowfall and temperature can have major impacts on snow cover area and snow accumulation, which consequently influence the water availability in snowmelt-dominated river watersheds. However, due to the short time series data of SCA (2001–2017), this study claims the impact of climate variability rather than the impact of climate change on SCA variations. Further study is required at a sub-catchment level, using a longer time series of MODIS snow cover datasets for developing future scenarios.