Introduction

Melting from snow and glaciers is an important surface water component. It significantly impacts various aspects of hydrology, including water supply, erosion and flood control (National Research Council 2012). Melting processes in the Himalayan basins involve seasonal snow, perennial snow melting and glacier melting, particularly at high elevations. Snow and glaciers play a vital role in the basins’ hydrology by modulating the volume and timing of runoff. Changes in meteorological parameters can have profound effects on the melting of snow and glaciers. It helps in understanding the hydrological processes in the region in the context of global warming (Bookhagen and Burbank 2010). The melt water generated provides a natural storage buffer for precipitation that accumulates as snow in winter and contributes substantially to late summer flows when water demand is highest (Comeau et al. 2009). The glacier melt component of streamflow in five major Southeast Asian rivers significantly supports the food supply of nearly 60 million people (Immerzeel et al. 2010).

Himalayan glaciers provide around 8.6 × 106 m3 of water annually to 1.3 billion people (Bolch et al. 2012). The three major rivers—the Indus, the Ganga and the Brahmaputra—significantly influence India’s water resources. They collectively provide close to 50% (320 km3) of the total country’s utilizable surface water resources (690 km3) (Srivastava 2012). These rivers originated from the Cryosphere system of the Himalayas. Perhaps billions of people solely depend on these rivers for irrigation, ingestion and hydropower needs (Singh and Jain 2002; Kesarwani et al. 2015; Arora et al. 2016). Because of these reasons, hydrological studies in the Cryosphere regime of the Himalayas have gained much attention. There is a growing concern regarding the impact of climate change and global warming on the health of the Gangotri Glacier and the Ganga River (Singh et al. 2005; Arora et al. 2008, 2010). It is essential to study the hydrological system of the Himalayan Cryosphere in a comprehensive way using observational methods, geospatial techniques and numerical modelling so that prediction of future water supplies from these glacierized catchments in the downstream area can be performed precisely.

The monsoon and melting of snow and glaciers dominate the hydrological regime of the Himalayan basins. Understanding the relevance of the contribution of glaciers to runoff makes it an essential tool for knowing the impact of climate change on water resources, flooding and drought in glacier-fed basins. Most hydrological processes occurring in the glacierized regime are complex, and it is not easy to understand them in detail as several physical phenomena are followed to generate meltwater streamflow (Bergstrôm 1995; Arora et al. 2014). Therefore, a model or abstraction is needed to understand their behaviour. Hydrological models are essential tools for quantifying and predicting hydrological processes, and melt models should be involved in hydrological simulation over the cryosphere. Four distinct methods are employed to analyse runoff components from various sources, such as rainfall, snowmelt and glacier melting. These methods include: the water balance analysis (Thayyen et al. 2005; Kumar et al. 2007), glacier degradation from observation or modelling as a contribution to runoff (Kotliakov 1996; Kaser et al. 2010), isotopic investigations (Dahlke et al. 2014) and hydrological modelling (Hagg et al. 2007; Naz et al. 2014). The selection of the appropriate method hinges on specific study area characteristics, data availability and research objectives. Researchers often use these methods to obtain comprehensive insights into the complex dynamics of runoff in diverse environmental settings.

Melt models can be broadly classified into two main categories: energy balance models and temperature-index models (Hock 2003). Energy balance models rely on solid physical mechanisms (Pomeroy et al. 2007). However, they often face limitations in application, particularly in mountainous basins like the Tibetan Plateau (TP), where data availability is a challenge (Zhao et al. 2015). The derivation of parameters for energy balance models proves challenging over such terrains, making them less suitable for large basins. In contrast, temperature-index models simplify melting processes by utilizing the empirical relationship between temperature and melt rates. These models have lower data requirements, contributing to their widespread use (Carenzo et al. 2009; Gao et al. 2012; Hock 2003; Pellicciotti et al. 2005; Zhang et al. 2012; Zhao et al. 2015). Many studies (Butt and Bilal 2011; Ali et al. 2017; Muhammad et al. 2017) have employed the snowmelt runoff model (SRM), designed for runoff simulation in snow-dominant basins. However, the accuracy of the SRM is compromised when applied to partly glacier-fed bays, where the model neglects the contribution of glacier melt. Traditional hydrological models like the SWAT (Soil and Water Assessment Tool) and HEC-HMS (Hydrologic Engineering Center’s Hydrologic Modelling System) face limitations in accurately simulating the impacts of climate change and land use alterations on hydrological systems (Arnold and Fohrer 2005; Fleming and Neary 2004).

Various methods have been employed in the development of hydrological models to represent snow processes and ice melting better (Bergström 1976; Shrestha et al. 2012; Wrede et al. 2013). These models primarily rely on meteorological data, satellite information on snow cover and climate scenarios to investigate the implications of climate change on glaciers (Khadka et al. 2014; Jasper et al. 2004). Among the commonly utilized models, the snowmelt runoff model (SRM) (Khadka et al. 2014; Immerzeel et al. 2009) and the HBV model (Mayr et al. 2013; Hagg et al. 2006; Akhtar et al. 2008) hold widespread use. GIS-based modelling of snow accumulation and melt processes is an efficient method to understand hydrological processes (Pyankov et al. 2018). It has been observed that remote sensing and GIS applications are helpful in estimating the necessary input parameters, such as rainfall, water bodies, snow cover and soil moisture (Thakur et al. 2017). The hydrological processes related to rainfall runoff and snowmelt runoff can be further computed using hydrological modelling by incorporating remote sensing inputs. This coupled approach can improve the understanding of hydrology, as it aids in visualizing the results of the hydrological method within the geospatial domain (Singh et al. 2021). In the previous study conducted over the Gangotri Glacier, the GIS domain was also incorporated into the SNOWMOD model to compute glacier melt runoff (Salim and Pandey 2021). In the previous study conducted over the Gangotri Glacier, the GIS domain was also incorporated into the SNOWMOD model to compute glacier melt runoff (Salim and Pandey 2021). It has been observed that remote sensing and GIS applications are helpful in estimating parameters such as rainfall, water bodies, snow cover and soil moisture (Thakur et al. 2017). The hydrological processes related to evapotranspiration, infiltration, interception, soil wetness and runoff (rainfall runoff and snowmelt runoff) can further be computed using hydrological modelling incorporating remote sensing inputs. This coupled approach can improve the understanding of hydrology, as it aids in visualizing the results of the hydrological method within the geospatial domain (Singh et al. 2021). GIS-based modelling of snow accumulation and melt processes is an efficient method to understand hydrological processes (Pyankov et al. 2018).

Furthermore, recent advancement in computational techniques, use of artificial intelligence and machine learning (AI-ML) have demonstrated significant performance in hydrological models for simulating river basin streamflow (Kim et al. 2021). In larger river basins, the integration of AI-ML techniques into hydrological modelling also proved invaluable for understanding the influence of climate drivers on evolving hydrological complexities (Ji et al. 2021). This approach offers a more effective means of understanding and predicting changes in water flow dynamics, forecasting potential floods or droughts and managing surface and subsurface water resources (Long et al. 2024). However, AI-ML-based hydrological models have certain limitations related to prediction, classification, learning rates process, over-fitting problems and regression capabilities when used for short-term runoff simulation (Mohammadi 2021). One major challenge is the integration and interpretability of long short-term memory (LSTM) networks, within hydrological modelling. While LSTM models demonstrate superior predictive capabilities in streamflow and other hydrological processes, their complex architecture often limits interpretability, impeding scientific insights and hypothesis testing. Enhancing the interpretability of these ML models remains a priority to ensure they contribute to expanding hydrological knowledge effectively (Fluente et al. 2024). Another critical area of research is the improvement of data assimilation techniques. These techniques help to reduce uncertainties in model predictions by integrating observational data with model outputs. Ensemble-based methods, such as the ensemble Kalman filter, have shown promise in enhancing the accuracy of hydrological predictions (Evensen et al. 2022). However, challenges remain in assimilating measurements across different compartments of the hydrological cycle and improving the joint update of model states and parameters (Camporese and Girotto 2022). The INTENSE project, for instance, uses observations and models to understand subdaily rainfall extremes, which are crucial for managing flood risks (Blenkinsop et al. 2018). Addressing the research gaps in hydrological modelling involves improving the integration of surface and subsurface processes, enhancing data assimilation techniques and focussing on the performance of models under extreme conditions. These advancements are essential for better water resource management and for mitigating the impacts of climate change on hydrological systems. Reducing computational complexity is also necessary to reduce the computational demands of integrated hydrological models, making them more accessible for large-scale applications (De la Fuente et al. 2024).

However, considerable advancements have been achieved in comprehending the role of snow and ice melt in influencing streamflow in the Himalayas through the application of degree-day or simple ablation models, as evidenced by studies conducted by Immerzeel et al. (2010, 2012), along with the work of Racoviteanu et al. (2013). To study all the glaciers and associated streamflow in the Himalayas, using ground survey methods and instrumental techniques is not possible due to rough terrain and harsh climatic conditions. The most preferable and convenient way (both economically and physically) to solve such complex problems is using a combination of observational, geospatial and numerical modelling studies. The utilization of a fully distributed, physically based glacier model that accounts for factors such as mass balance, subglacial drainage and ice flow dynamics faces challenges related to substantial data requirements and computational expenses, particularly when integrated into a comprehensive glacio-hydrological model covering both glacierized and non-glacierized segments of a catchment. In this study, the HBV model has been used to simulate the runoff from the glacier-dominated basin. The HBV-Light model simulates all glacierized headwater catchments separately at the hydrological mesoscale. This semi-distributed conceptual hydrological model integrates routines for snow and glaciers. The modelling approach is designed to efficiently represent long-term glacier changes and the evolution of streamflow, ensuring a robust simulation of hydrological processes in glacierized headwater catchments.

Understanding snow and glacier melt dynamics in the Himalayan rivers is crucial for managing water resources, especially in a changing climate. A new snow distribution approach was implemented in a model, specifically for the accumulation areas of glaciers. This approach aims to simulate snow accumulation over multiple years at high altitudes. This type of modelling is likely employed to understand better or predict the behaviour of glaciers and their response to changing environmental conditions, such as climate change. This study can serve the runoff simulation in glacierized regions and estimate the contribution from different components in the runoff. Monitoring and research efforts are ongoing to assess the impact of climate change on these water sources and to develop strategies for sustainable water management in the region.

Study area

The Gangotri Glacier, situated between latitudes 30° 43′ N–31° 01′ N and longitudes 79° 00′ E–79° 17′ E, is the second-largest glacier in the Indian Himalayas (Fig. 1). This glacier is located in the Uttarkashi district of Uttarakhand state and is classified as a Valley type of glacier. It covers the headwater region of the Bhagirathi River basin (5O 131 06). Though it is commonly known as Gangotri Glacier rather than a singular entity, the Gangotri Glacier is a complex network comprising numerous large and small glaciers known as the Gangotri Glacier System (Fig. 1). This large glacier is vital as the source of the Bhagirathi River, a prominent tributary of the Ganges River. This system comprises three major glacier tributaries, namely, Chaturangi Glacier (length 22.45 km; area 67.70 km2), Raktvarn Glacier (length 15.90 km; area 55.30 km2) and Kirti Glacier (length 11.05 km; area 33.14 km2) with main Gangotri Glacier (length 30.20 km; area 86.32 km2) as trunk part of the system. Apart from these three significant glaciers, the other tributary glaciers draining directly into the Gangotri Glacier system are Swachand, Maindi and Ghanohim. The total catchment area of the Gangotri Glacier study basin up to the discharge gauging site at Bhojbasa is about 556 km2, out of which nearly 286 km2 is glacierized. The elevation of the study basin ranges between 3800 and 7000 m.

Fig. 1
figure 1

Location of Gangotri Glacier, Bhagirathi River Basin, Garhwal Himalaya, Uttarakhand. The hydro-meteorological observatory was established near Bhojbasa (~ 3800 m a.s.l.) about 3 km downstream to the snout of Gangotri Glacier

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The general climate of the glacier catchment is humid–temperate in summer and dry–cold in winter. The area receives major precipitation during the winter (October–April) from western disturbance, and from Indian summer monsoon during summers (June–September). The average seasonal rainfall (summer) in this region is around 260 mm, with average mean temperature of 9.4 °C. The mean season total evaporation in this region was estimated 640.8 mm (Singh et al. 2005). From 1965 to 2015, the frontal recession of the glacier was ~ 889.4 ± 23.2 m with an average rate of 17.9 ± 0.5 m a−1 (Bhattacharya et al. 2016). The mass loss of Gangotri and its tributary glaciers was observed to be 0.19 ± 0.12 m w.e. a−1 from 1968 to 2014 (Bhattacharya et al. 2016). Past hydrological observations during the ablation seasons (May–October) of 1999–2000 to 2002–2003 hydrological years suggested that the mean discharge of streamflow varied from 8 to 194 m3 s−1 reaches to its highest value in July and then starts reducing (Singh et al. 2006).

The Gangotri Group of glaciers systems significantly contributes to the Bhagirathi River through snow and glacier melt. With growing demands for freshwater to sustain irrigation, drinking water supplies, urbanization, industrial development and hydroelectric power generation in the country, conducting comprehensive hydrological studies on the Gangotri Glacier system becomes imperative.

Methodology

Glacier area–altitude distribution

To interpolate the meteorological parameters from meteorological observatory (3800 m a.s.l.) to upper accumulation zone (7000 m a.s.l.) of the Gangotri Glacier, total glacier area was divided into sixteen elevation zones (E1 to E16) following hypsometric approach having difference of 200 m a.s.l. (Fig. 2). Advanced Spaceborne Thermal Emission and Reflection Radiometer (ASTER) Global Digital Elevation Model Version 2 (GDEM V2) (spatial resolution 30 m) was used for extracting the elevation information from the catchment area. The total catchment area (556.23 km2) was further divided into glacierized (240.03 km2) and non-glacierized (316.19 km2) zones.

Fig. 2
figure 2

Area–altitude distribution of glacierized and non-glacierized area at different elevation bands (E1–E16) for the Gangotri Glacier

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Hydro-meteorological measurement

A standard hydro-meteorological observatory (30 m × 30 m) was established at Bhojbasa site (altitude: 3800 m a.s.l., latitudes: 30° 56′ 59″ N, longitude: 79° 03′ 2.25″ E) about 3 km downstream to the snout of Gangotri Glacier for the collection of hydro-meteorological data during the six consecutive ablation seasons (May–October), starting from 2013–14 to 2018–19 hydrological year (Singh et al. 2005). This observatory is equipped with ordinary rain gauge, maximum and minimum thermometers, dry and wet bulb thermometers, hygrograph, evaporimeter, cup-counter anemometer, wind vane and sunshine recorder (Fig. 3). These instruments are calibrated each year as per the standards and guidelines suggested by Indian Meteorological Department (IMD) for the optimum results and to maintain the accuracy in measurements. Indian Standard timings (0830, 1130, 1430 and 1730) for hydro-meteorological data collection are used according to the practice followed by the IMD. The hydro-meteorological records, viz. near-surface air temperature (T), evaporation (E), rainfall (P) and meltwater discharge (Qobs), were used for the present study.

Fig. 3
figure 3

Hydro-meteorological observatory (3800 m a.s.l.) established at Bhojbasa, Gangotri Glacier catchment, Central Himalaya, India

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Furthermore, climate records (2013–14 to 2018–19) of daily near-surface air temperature (T in °C d−1), precipitation (P in mm d−1) and evaporation (E in mm d−1) available from the World Climate Research Programme (WCRP)-CORDEX (Coordinated Regional climate Downscaling Experiment) dataset for South Asia region (Taylor et al. 2012; Sanjay et al. 2017) were also for the study area to model the catchment’s streamflow throughout the year.

Qobs measurement was carried out using water level data at the Bhojbasa gauging site (3800 m a.sl.) during the ablation season. To channelized all the meltwater and achieving the laminar streamflow as far as possible, the gauging site was made along the banks of the stream with the use of stone walls and sandbags. Also, the large boulders transported by the stream were removed periodically from the channel area to maintain the accuracy in discharge measurement. Standard velocity-area method was used to estimate the meltwater discharge of the Gangotri Glacier (Thayyen et al. 2005). The cross section of the meltwater stream was measured using a graduated staff, and a manual stage was placed to read the water level. Surface velocity of the meltwater stream was measured by using float method (Thayyen et al. 2005). The meltwater discharge was calculated using standard area-velocity method –

$$Q_{{{\text{obs}}}} = \, A \, \times \, V_{{\text{m}}}$$

where Qobs is the observed discharge (m3 s−1), A is the cross-sectional area of the stream (m2), Vm is the mean velocity of the stream (m s−1). The mean velocity (Vm = C × Vs) is calculated here using the constant for mountain streams (C = 0.85) and the surface velocity of the stream (Vs = D (fix distance in m)/Td [float travel time (s) to cover the fix distance].

Hydrological modelling

The HBV model is a semi-distributed conceptual precipitation–runoff model that has been under continuous development in Scandinavia since the 1970s. Initially conceptualized by the Swedish Meteorological and Hydrological Institute (SMHI) in the early 1970s, the model has undergone several modifications to create various versions (Bergström 1976; Ehret et al. 2008; Wrede et al. 2013). Widely adopted as a standard tool for catchments with significant snow presence, the HBV model requires daily temperature, precipitation and potential evaporation time series as input data. The model comprises four primary routines designed to simulate hydrological processes within a catchment: snow/glacier routine, soil moisture routine, response routine and streamflow routing routine (Fig. 4).

  1. 1.

    Snow/glacier routine: this routine model accumulation and melting of snow and ice, utilizing a degree-day method for calculating melting.

  2. 2.

    Soil moisture routine: this routine addresses soil moisture dynamics within the catchment, incorporating evapotranspiration calculations on the basis of field capacity and permanent wilting point.

  3. 3.

    Response routine: simulating runoff generation, this routine has two nonlinear parallel reservoirs each representing direct discharge and groundwater response. The distribution of soil saturation across different locations controls the response, with a nonlinear distribution function describing this relationship.

  4. 4.

    Streamflow routing routine: this routine simulates the routing of streamflow within the catchment.

  5. 5.

    Model efficiency: the efficiency of the model was computed using three statistical indices: (1) Kling–Gupta efficiency (KGE), which measures goodness-of-fit; (2) root mean square error (RMSE), which measures the difference between observations and simulations; and (3) Nash–Sutcliffe efficiency (NSE), which measures the predictive power of hydrological models.

Fig. 4
figure 4

Mechanism of HBV model

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Kling–Gupta efficiency (KGE)

A goodness-of-fit indicator, Kling–Gupta efficiency (KGE) was used to compute the model performance (Gupta and Kling 2011)—

$${\text{KGE}} = 1 - \sqrt {(r - 1)^{2} + (\alpha - 1)^{2} + (\beta - 1)^{2} }$$

where \(r\) is the Pearson correlation coefficient, α is variability of prediction errors, β is a bias term. α is the ratio of standard deviation of simulated streamflow (\(\sigma_{{{\text{sim}}}}\)) and standard deviation of observed streamflow (\(\sigma_{{{\text{obs}}}}\)), and can be computed as –

$$\alpha = \frac{{\sigma_{{{\text{sim}}}} }}{{\sigma_{{{\text{obs}}}} }}$$

whereas, \(\beta\) is the ratio of mean of the simulated streamflow and mean of the observed streamflow.

$$\beta = \frac{{\overline{Q}_{{{\text{sim}}}} }}{{\overline{Q}_{{{\text{obs}}}} }}$$

If, KGE = 1, it is a perfect fit between the observed and simulated discharge, consequently model performs well.

Root mean square error (RMSE)

The RMSE is a measure of the differences between predicted or modelled values and observed values (Willmott and Matsuura 2005). It is calculated as:

$${\text{RMSE}} = \sqrt {\frac{1}{n}\sum\nolimits_{i = 1}^{n} {\left( {O_{i} - P_{i} } \right)^{2} } }$$

where Oi is observed value, Pi is predicted or modelled value and n is number of observations. RMSE lower values indicate better model performance.

Nash–Sutcliffe efficiency (NSE)

The Nash–Sutcliffe efficiency (also known as the Nash–Sutcliffe model efficiency coefficient) is used to assess the predictive power of hydrological models (Nash and Sutcliffe 1970). It is calculated as:

$${\text{NSE}} = 1 - \frac{{\mathop \sum \nolimits_{i = 1}^{n} \left( {O_{i} - P_{i} } \right)^{2} }}{{\mathop \sum \nolimits_{i = 1}^{n} \left( {O_{i} - \overline{O}} \right)^{2} }}$$

where Oi is observed value, Pi is predicted or modelled value, O̅ is mean observed values and n is number of observations. NSE values range from (−) infinity to 1. An NSE value of 1 indicates a perfect match between predicted and observed values. An NSE value of 0 indicates that the model predictions are as accurate as the mean of the observed data, whereas negative values indicate that the observed mean is a better predictor than the model.

The HBV model is widely used for simulating the hydrological processes in a catchment area, while it is a powerful and popular tool in hydrology, it has several limitations and constraints. Accurate input data, such as precipitation, temperature and evapotranspiration, are crucial. In regions with sparse meteorological stations, the quality of the model output can be compromised. The model requires historical discharge data for calibration. In ungauged or poorly gauged basins, reliable calibration is challenging. The model’s performance is sensitive to its parameters, which need careful calibration. Parameter uncertainty can affect the reliability of the model outputs (Lindström et al. 1997). The HBV model typically uses daily or subdaily time steps. This might not be sufficient to capture very short-term hydrological phenomena or rapid changes in catchment response. Effective use of the HBV model requires expertise in hydrology, particularly in calibration and validation processes. The model’s results depend heavily on the user’s judgment and experience (Wagener et al. 2004; Seibert 2005). Despite these limitations, the HBV model remains a valuable tool in hydrology due to its relatively simple structure, flexibility and the balance it strikes between complexity and ease of use. Moreover, the inclusion of a glacier routine is the recent improvements to the HBV-Light software; a user-friendly and free available version of the HBV model includes the addition of a glacier evolution approach. This addition enables the simulation of glacier mass balance, extending the model’s capabilities to address catchments with glacierized areas.

The streamflow of the Gangotri Glacier was modelled during the hydrological years of 2013–14 to 2018–19 using HBV model. The model used the meteorological parameters (daily observed air temperature, precipitation and evaporation) and Gangotri Glacier catchment area (glacierized and non-glacierized) as input parameters for operating the submodel routines. During the simulation, the entire ablation season (May–October) in each observation year is divided into three subcategories—(1) pre-monsoon (May–June), (2) monsoon (July–August–September) and (3) post-monsoon (October), to achieve the maximum accuracy. Simulations were performed separately for each subcategory period so that seasonal weather inferences could be included. Initially, the model is calibrated using the dataset of three consecutive hydrological years 2013–14 to 2015–16, and further validated for hydrological years of 2016–17 to 2018–19. For the streamflow simulation, variable parameters, such as threshold temperature, degree-day factor, snowfall correction factor, refreezing coefficient, water holding capacity, glacier correction factor, slope correction factor, maximum soil moisture storage, soil moisture value above which actual evapotranspiration (AET) reaches potential transpiration (PET) and parameter that determines the relative contribution to runoff from rain or snowmelt, were used and their corresponding values are detailed in Table 1.

Table 1 Major parameters and their average values used for streamflow simulation
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To measure the sensitivity of the model, a Monte Carlo simulation was employed. In this approach, model parameters were set within a specified range, and the parameter values were computed. It was found that the most sensitive parameters were CFSlope, CFGlacier and CFMAX. Variations in these parameters drastically changed the output, resulting in the model simulating higher melt than observed. Along with that variation in CFGlacier resulted higher contribution of glacier melt for the region. Based on this approach, the major parameters and their average values used for streamflow simulation were determined (Table 1).

Results and discussion

Hydro-meteorological observation

During the ablation seasons of 2013–14 to 2018–19 hydrological years, a notable trend was observed in near-surface air temperature. Initially, it exhibited an increasing pattern until July, after which it gradually decreased (Fig. 5). In the study area, the average near-surface air temperature ranged between 8.7 and 10.5 °C throughout the observation periods (Table 2). Based on the records, 2018–19 was the warmest among the ablation seasons. Analysis of average evaporation rates indicated lower levels during rainy days and higher rates during dry periods, with values ranging between 2.8 and 4.2 mm (Fig. 5 and Table 2).

Fig. 5
figure 5

Time series of meteorological data–mean air temperature (T in °C d−1), total evaporation (E in mm d−1), total rainfall (P in mm d−1) and observed streamflow (Qobs in mm d−1) collected during the ablation seasons of hydrological year 2013–14 (25 May–14 October), 2014–15 (13 May–09 October), 2015–16 (17 May–30 September), 2016–17 (20 May–30 September), 2017–18 (21 May–30 September) and 2018–19 (04 June–30 September) at hydro-meteorological observatory, Bhojbasa (3800 m a.s.l.), Gangotri Glacier catchment, Central Himalaya (Uttarakhand), India

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Table 2 Calculated mean monthly air temperature (T), evaporation (E), total precipitation (P) and meltwater discharge (Qobs) and from the observed records available for the ablation seasons of 2013–14 to 2018–19
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Furthermore, glacier valley experienced low precipitation (rainfall) during the summer months, and maximum precipitation was observed between July and August months. In the valley, total seasonal precipitation varied between 187.80 and 317.30 mm, reaching highest in 2017–18 and lowest in 2018–19 hydrological years (Fig. 5 and Table 2). In the valley, streamflow variations were significantly affected by snow glacier melt and monsoonal precipitation (Fig. 5 and Table 2). Streamflow records indicated a consistent increase from May onwards, reaching peak levels in mid-July or the first week of August before gradually declining. However, there was irregularity in the streamflow pattern during the observed period. The average monthly flow ranged between 7.5 and 11.7 mm d−1.

Streamflow modelling

In the pre-monsoon period (May–June), the glacier catchment is majorly covered with winter residual snow, and due to the high albedo effect, almost 80–90% of insolation gets reflected back to the atmosphere, which is the critical energy portion responsible for snow/ice melt. This will result in less melting of snow/glaciers and ineffectively developed meltwater channels over the glacier surface. Considering this natural phenomenon, low values of CFMAX (5.4), CFGlacier (2.2), KGmin (0.015) and PERC (5.0) are adopted in pre-monsoon months to generate the meltwater streamflow. However, precipitation occurs more frequently in the monsoon months (July–August–September) due to the influence of the Indian Summer Monsoon over the Central Himalayas. Summer precipitation increases the melting of overlying snow very fast, and consequently, the glacier surface is exposed, and glacier channels develop. The exposed glacier surface comes directly in contact with sunlight, and increased input energy causes a rapid surface melting rate. Therefore, higher values of CFMAX (7.2), CFGlacier (2.4), KGmin (0.1) and PERC (7.0) are adopted for the model to be performed well in the monsoon season. The assumed conditions increased the melting of snow/glaciers within the catchment boundary, resulting in more meltwater discharge in streamflow. For the post-monsoon season (October), observed streamflow is low compared to the monsoon months and high related to the pre-monsoon season (Fig. 6). The main reason is that precipitation events are generally minor during this period, reducing the contribution of rain to the streamflow. Additionally, the absence of snow cover over the glacier surface in the ablation zone area and moderate temperature triggered the surface melting. Keeping account of the post-monsoon weather conditions, the melting parameters CFMAX, CFGlacier, KGmin and PERC are set to be 6.2, 2.4, 0.1 and 4.0, respectively, for the simulation of streamflow in this period. It is observed that the model either underestimates or overestimates the streamflow due to the constant outflow coefficient (K1, K2) when abrupt changes in meteorological parameters occur. The degree-day factor (CFMAX) values varied between 3.1 and 9.2 because of high precipitation and temperature. KGmin (0.015–0.10), which controls the outflow from the glacier surface, is lower for May due to poor flow channel and increases up to the end of October. PERC (1.0–8.0), which controls the amount of water to the lower ground, was higher for the monsoon season, where ample water was available for percolation and common for the dry season.

Fig. 6
figure 6

Daily observed and simulated Gangotri Glacier streamflow (mm d−1) during the ablation seasons of 2013–14, 2014–15, 2015–16, 2016–17, 2017–18 and 2018–19 hydrological years

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A Monte Carlo simulation was performed to identify abnormal values or noise in the datasets used for hydrological modelling. This simulation estimated model parameters more accurately by considering a range of possible values and calculating their statistical significance. Abnormal values or noise were addressed by generating multiple simulations and averaging the results, which helped to smooth out noise and highlight the underlying trends. Outliers were identified by comparing the simulated dataset with the observed dataset and were treated separately, either using robust statistics or removing them manually to minimize their impact. By introducing controlled noise and abnormal values into the dataset through simulations, the robustness of the HBV model was tested. This approach helped identify the model’s sensitivity to such variations. The challenges posed by anomalies were better understood and managed by iteratively refining the dataset through simulations, leading to improved model accuracy and reliability.

The performance of the model was assessed using Kling–Gupta efficiency (KGE) method (Gupta and Kling 2011). During the calibration (2013–14 to 2015–16) and validation periods (2016–17 to 2018–19), KGE values varied from 0.85 to 0.95, with an average of 0.90 representing model performed well for all the studied years except for some months, where abrupt changes in the contrasting weather parameters (precipitation and temperature) were recorded (Table 3). Statistical analysis was also performed to assess the proportion of variation for simulated streamflow (Qsim) against observed streamflow (Qobs) using coefficient of determination (R2) method. R2 values ranged between 0.88 and 0.93, with average value of 0.91 representing best fit and low proportion of variation for Qsim. RMSE values range from 1.6 to 2.2; the range of RMSE values considered good or bad is highly context-dependent. Generally, lower RMSE values indicate better model performance, but what constitutes a good RMSE can vary widely across different fields and applications, here the average RMSE value is 1.9. Similarly, NSE value 1 indicates a perfect match between predicted and observed values, here it ranged from 0.83 to 0.90 which states good fit, average NSE value is 0.89 (Table 3).

Table 3 Summary of statistical analysis used for model performance during the calibration and validation periods
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The average contribution of rainfall, snowmelt and glacier melt to total streamflow was calculated for all the studied years (Fig. 7). Snowmelt (QS) contribution depends mainly on the previous winter’s snowfall amount and the valley’s temperature. QS was higher than glacier melt and rainfall runoff, and varied between 1.16 and 2.73 mm d−1, with average contribution of 2.06 mm d−1 (55.5%). QS was highest for the hydrological years of 2013–14 (61.7%), 2014–15 (63.2%), 2016–17 (52.1%), 2017–18 (48.3%) and 2018–19 (67.5%) due to residual high winter snowfall. The contribution of the glacier melt (QG) varied from 0.56 (16.3%) to 1.72 (42.9%) mm d−1. The average contribution of QG was 1.1 mm d−1 (29.7%). Glacier melt contribution (1.72 mm d−1/42.9%) was the maximum for 2015–16 hydrological year due to higher average temperature and less precipitation, while it was less for 2014–15 (16.3%). Variation in the contribution of rainfall to total streamflow was irregular as it depends on the seasonal rainfall amount. The contribution of rainfall was between 0.32 (7.2%) and 0.71 (20.6%), and the average contribution for the entire duration of the study was 0.53 (14.7%). The Gangotri Glacier Valley received high precipitation (rainfall) amounts in the ablation seasons of 2014–15 (263.2 mm), 2015–16 (195.70 mm) and 2017–18 (317.3 mm). Therefore, the contribution of rain (~ 17.9%) was higher for these years.

Fig. 7
figure 7

Average contribution of streamflow components (%) to total streamflow during the hydrological year (01 November–31 October of the following year): 2013–14 to 2018–19. QR represents rainfall contribution (%), QS represents snowmelt contribution (%) and QG represents glacier melt contribution (%)

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Conclusions

This study collected hydro-meteorological data of the Gangotri Glacier Valley at the Bhojbasa meteorological observatory (~ 3800 m a.s.l.) during the ablation seasons (May–October) of hydrological year 2013–14 to 2018–19. The analysed hydro-meteorological records were further used for streamflow modelling purposes. A semi-distributed conceptual hydrological model known as HBV is utilized for streamflow modelling. Initially, the model is calibrated using the available in situ meteorological variables (air temperature, precipitation and evaporation) of 2013–14 to 2015–16 and catchment parameters (degree-day factor, glacier correction factor, glacier outflow coefficient percolation, glacierized and non-glacierized area). Further, the model is validated for the ablation seasons of 2016–17 to 2018–19 using the in situ hydro-meteorological dataset of the corresponding year and average submodel conditions based on the calibrated dataset. To achieve the maximum accuracy level, model simulations were performed for the pre-monsoon (May–June), monsoon (July, August, September) and post-monsoon (October) seasons separately so that seasonal weather inferences can be included well. The simulated streamflow is compared with observed values using different statistical techniques (Kling–Gupta efficiency, coefficients of efficiency and determination, RMSE and NSE) to compute the model efficiency. Results of the study suggested that the snowmelt contribution ranged between 1.2 (40.4%) and 2.7 (67.5%) mm d−1, glacier melt contribution varied between 0.6 (16.3%) to 1.7 (42.9%) mm d−1 per day and rainfall contribution ranged from 0.3 (7.2%) to 0.7 mm d−1 (20.6%) per day. These percentages indicate the proportion of each water source to the total daily runoff. It is evident that generally snow melt is the dominant contributor, followed by glacier melt, while rainfall has a relatively smaller contribution. Results suggest that the simulated streamflow is in close agreement with observed records, which indicates that all important processes are moderately included in the streamflow modelling for the Gangotri Glacier Valley. Further research in hydro-meteorological analysis and streamflow modelling in glacierized regions like the Gangotri Glacier Valley is crucial for effective water resource management, especially amidst climate change.

However, the HBV model has certain limitation in simulating hourly streamflow patterns as it is very sensitive to quick precipitation–runoff processes (high streamflow) (Parra et al. 2018). The model is complex and requires greater number of parameters which needs more computational resources at calibration stages and the model’s limitations in simulating hourly streamflow were also noted. The presence of glaciers significantly influences hydrology in glacierized areas, and understanding these effects is crucial for various reasons. However, these effects need to be better understood due to imperfect tools and data scarcity. Improved data collection, advanced modelling techniques and ongoing research are essential for enhancing our understanding of the intricate relationships between glaciers and hydrology in glacierized regions. This knowledge is crucial for making informed decisions related to water resource management and adapting to ongoing environmental changes. Future research should focus on enhanced data collection, advanced modelling techniques, understanding climate change impacts, interdisciplinary approaches and developing adaptive water management strategies to ensure sustainable water resources.