Application of hydrological models to streamflow estimation at ungauged transboundary Himalayan River basin, Nepal

Precipitation plays a vital role in streamflow contribution at the Himalayan River basins (Raghunath 2006). The flow regime is more pronounced in the summer season due to the high precipitation amounts and temperature response on snow melting discharge in the high mountains. The rainfall characteristics are very important for watershed management in the central Himalayas. The precipitation trend in monsoon seasons is increasing in the middle mountain of the western and central high Himalayan region and it is also increasing in the low land areas in pre-monsoon seasons in the central Himalayan region (Karki et al. 2017; Shrestha et al. 2019). Spatial and temporal patterns of precipitation characteristics in the catchment area affect downstream discharges (Dhital & Kayastha 2013). The changing pattern of precipitation affects mountainous communities and downstream agriculture, hydropower, and ecosystems (Shrestha et al. 2016; Khanal et al. 2021). The changing of glacier coverage and glacier melt runoff significantly impact water resource availability in the Himalayan River basins. The glacier ice volume is reducing by 18–12%, resulting in the runoff variation in the Himalayan River basin (Singh et al. 2021).

The river basin is formed by connecting with one or more sub-basins. The river discharge continuously changes from upstream to downstream and is also difficult to predict accurately. The prediction of runoff is a main challenge due to the heterogeneous topography of mountainous catchments (Zhang & Han 2017). The average precipitation, slope, channel length, and elevations are the main parameters to estimate discharge at ungauged catchments (WECS/DHM 1990; DHM 2004; Li et al. 2019). The transfer of the flow simulation from the gauge station to the ungauged site is carried out by different approaches. Regionalization of parameters by nearest neighbors, donor technique, and regional averaging using hydrological simulation by multiple modeling approaches have been used in past studies (Gao et al. 2018; Razavi & Coulibaly 2016; Van Liew & Mittelstet 2018). Hydrological modeling is considered as a realistic alternative option for streamflow data prediction and calibration at ungauged sites (Bergstrom 2006). In addition, parameter regionalization by hydrological simulation could predict discharge at ungauged streams (Kim & Kaluarachchi 2008). Any hydrological models are independent to ungauged simulation for discharge estimation (Swain & Patra 2017).

The hydrological model serves as a valuable tool in water resource management in the river basins and is highly applicable to estimating the runoff from a catchment corresponding to rainfall and routing the runoff downstream through a river network (Bhadra et al. 2010). Hydrological simulation by a fully distributed hydrological model is applicable for flow forecasting in scarce and data-inaccessible mountain areas (Terink et al. 2015; Kayastha et al. 2020). Hydrological models mimic the streamflow as runoff components with appropriate performance (Gao et al. 2018). Further, the physically based hydrological model could predict real-time river flow with ice breakup in cold regions (Rokaya et al. 2020). Furthermore, hydrological models could simulate the future possible hydrological response and state of the catchments (Pechlivanidis et al. 2011). Hydrological models are categorized into lumped, semi-distributed, and distributed based on physically based and conceptual aspects (Cunderlik 2003). In the Himalayan regions, Spatial Process in HYdrology (SPHY), HBV, Hydrologic Engineering Centre (HEC) series, SWAT, MIKE SHE, SRM, GDM, J2000, etc., models have been successfully employed to evaluate future discharge projection, the cryospheric study, water balance estimation, inundation mapping, etc.

Streamflow information has great importance for planning and designing water resource projects, early warning systems, dry season water management, climate foresight, and inventory of power potentiality on local as well as regional scales. The spatial and temporal coverage of river flow discharge data at a desired site is usually unavailable. Gauging stations installed across the basins are limited and are also not viable according to the norms and criteria of the World Meteorological Organization (WMO 2008). Further, in-situ observations are limited due to the loss of gauging stations and the lack of continuous monitoring (Wongchuig-Correa et al. 2020). The availability of water from upstream to downstream in mountainous regions is continuously changing due to climate change and other anthropogenic factors (Dhital et al. 2013; Adhikari et al. 2022). Climate change has been reported to directly affect river discharge and create challenges in managing hydraulic structure and water resources projects (Khadka et al. 2014; Bajracharya et al. 2018; Dhital et al. 2023). Therefore, accurate hydrological predictions and information for the future water supply are very important (Lutz et al. 2016). Furthermore, design discharge data is crucial, and transposing hydrological information at ungauged river basins is a significant task for water resource management (Seibert & Beven 2009; Waseem et al. 2015).

The prediction of river discharge at ungauged sites is very limited in mountain regions. These regions also have continuous data record gaps at gauged stations due to inaccessible terrain. Few past studies have been conducted at ungauged sites in the mountain river basins of Nepal. For example, Budhathoki et al. (2023a) examined the applicability of the hydrological model in the Himalayan River basin to simulate ungauged discharge. Similarly, Panthi et al. (2021) regionalized a flow duration curve to estimate streamflow data in data-scarce regions in the central Himalayan regions. The continuous flow estimation at the desired site is still a challenge in the Himalayan region. Thus, by using the multi-modeling approach, simulation at gauged to gauged stations first and then gauged stations to ungauged sites is a novel approach for ungauged simulation. In this context, this study aims (i) to simulate and calibrate streamflow on gauged stations using multiple models and (ii) to estimate streamflow at neighboring ungauged sites using the multi-modeling approach. This study will be helpful for data gap filling in gauged stations and for continuous discharge estimation at ungauged sites in transboundary mountain river basins.

The SPHY, HBV, and HEC Hydrologic Modelling System (HMS) models utilize two types of data layers, static (rasterized) and dynamic (hydrometeorological) datasets. These datasets include a land use/land cover (LULC) map, a soil map, a digital elevation model (DEM), and meteorological parameters such as precipitation, average temperature, minimum temperature, maximum temperature, evapotranspiration, and discharge. The Globecover (2009) was used for land use classification, and these datasets can be accessed from http://due.esrin.esa.int/page_globcover.php and are available as an open source. Shuttle Radar Topographic Mission (SRTM) 3 arc seconds hydrologically conditioned is used for the DEM and can be accessed from http://hydrosheds.cr.usgs.gov/. The glaciers inventory outlines, Randolph Glacier Inventory (RGI 6.0) South Asia East is also used, which is provided by Consortium (2017). The Department of Hydrology and Meteorology (DHM), Government of Nepal provides the ground station datasets for dynamic observations, including precipitation, temperature, and discharge. The daily rainfall data records had a 2.64% gap filled by the normal ratio method, while the daily temperature data records had a 0.55% gap filled by the temperature lapse rate method. Evapotranspiration datasets were prepared by the Blaney Criddle method using the mean monthly temperature of the Jiri station (Budhathoki et al. 2023b).

The SPHY, HBV-light, and HEC HMS models are widely implemented in the Himalayan River basins. These diverse models were selected to represent the diversity in terms of process representation and spatial resolutions. SPHY and HBV-light models have glacier modules. The selected hydrological models were set up with input static and dynamic datasets in the TRB. The details of the model setup are described in the following subsections.

The SPHY model has a dynamic glacier module that operates on a fully distributed hydrological concept. It enables simulation of hydrology at large scales ranging from basins and sub-basins to regional scales. This model has been successfully applied in the high-mountain Asia upstream river basin (Terink et al. 2015). The SPHY model simulates precipitation in the form of rainfall or snowfall, depending on the threshold temperature. In general, it can be used on a daily basis, generating total runoff for each grid cell. Additionally, several outlets within the delineated basin can be created at desired locations to estimate daily flow in the absence of continuous records. The meteorological stations and outlets are created in respective locations in delineated watersheds of cloned DEM. The locations of meteorological stations require a bilinear interpolation method for rainfall interpolation. Outlets of each sub-basin are mandatory to place and must be located on the river network. The SPHY model simulates the total runoff from each cell from the desired outlet of the basin. Each and every runoff should route downstream using a simple recession coefficient. The accuflux function of the SPHY model determines flow accumulation for total discharge in locations of outlet in the river network. Further, the SPHY model can simulate runoff using satellite datasets, gridded data products, and station data in PC Raster format. For the TRB, the SPHY model was set up with three outlets: Busti station (ID 647), Rasnalu station (ID 650), and an ungauged site at Benighat.

The HBV is a conceptual model that combines physical processes and basin structure to simulate streamflow using temperature and precipitation data as inputs (Vormoor et al. 2018). The lumped parameter modeling approach optimizes precipitation-runoff model parameters to generate streamflow. The model evaluates the combination of precipitation, climate, and land use data by using normal and extreme rainfall, snow melt simulation, and soil–water relationship to assess basin response on water balance, flow regimes, flood peaks and volume, and sediment yields. The HBV-light version, as described by Seibert & Vis (2012), includes rainfall in snow routine, soil–moisture response, and routing routine process to parameterization, including lakes and glaciers. The area, elevation, and aspect data are needed to model glaciated and non-glaciated regions. Further, this model can simulate discharge at vegetation and non-vegetation zones by elevation and orientation at a desired site within the basin area. In this study, the HBV model was set up with 13 elevation zones at Busti gauging station and 14 elevation zones at Benighat with a 500 m elevation interval of catchment setting. The temperature and precipitation require correction factors as height increment Precipitation Correction Altitude (PCALT) 10%/100 m and Temperature Correction Altitude (TCALT) −0.0065/m (Gao et al. 2022; Budhathoki et al. 2023b).

The generated streamflow of a one-time step is distributed on different time steps, which is the MAXBAS free parameter that determines the base in an equilateral triangular weighting function.

The HEC HMS, developed by the US Army Corps of Engineers, is a rainfall-runoff model that enables hydrological simulation in both gauged and ungauged catchments. This hydrological modeling system is designed to simulate the watershed-scale hydrologic process. The Clark Unit Hydrograph, employed by HEC HMS, allows for continuous simulation to transfer simulated flow to ungauged catchments. This hydrograph is utilized to estimate the basin lag time and continuous runoff coefficient. The simulation of the parameters for this model includes the sub-basins (10), junctions (9), reaches (10), sinks (1), simple canopy, deficit and constant, simple surface, constantly monthly baseflow, wet and dry evapotranspiration period, and Clark UH.

Three different models, including SPHY, HBV-light, and HEC HMS were used to estimate streamflow data at the ungauged site of Benighat. The TRB, which is a snow–glacier-fed river, includes several tributaries, with Khimti being the major rain-fed tributary. We employed both static datasets, such as LULC, DEM, and RGI 6, and dynamic datasets, such as ground station daily time series data of precipitation, mean temperature, maximum temperature, and minimum temperature to simulate the hydrological models. The simulated discharge was calibrated manually or through a trial-and-error approach using observed discharge data from the Busti discharge station and the Rasnalu discharge station between 2004 and 2008 for all models except for the SPHY model, which was calibrated at the Rasnalu discharge station in Khimtikhola and validated at the Busti discharge station in TRB, and vice versa. The model performance was evaluated using continuous streamflow without discrepancy between high flow and low flow. The evaluation of model performance was carried out using the Nash–Sutcliffe efficiency (NSE) as the objective function (Nash & Sutcliffe 1970), while the simulated discharge was assessed based on statistical parameters such as the coefficient of determination (R²) and the volume difference, which was evaluated using PBias.

The HEC HMS model was calibrated using observed discharge data from 2004 to 2008 at the Busti discharge station in the TRB. It was then validated using data from 2011 to 2012. During calibration, the HEC HMS model performed well at the Busti station, with NSE of 0.78, R² of simulated and observed discharge was 0.79, and a simulated volume bias with observed discharge (PBias) that was biased by −2%. During validation, the model again performed well at the Busti station, a model efficiency NSE was 0.77, the R² of simulated and observed discharge was 0.78, and the PBias was 0.26% (Table 1). The calibrated parameters of HEC HMS are quantified in Supplementary Table S3.

The HBV model was applied to the Busti station, and its model efficiency was found with NSE as 0.77, while the R² of observed and simulated discharge was 0.77. The simulated discharge biases with observed discharge (PBias) exhibited a slight bias of −3%. The HBV model was also validated using the same calibrated parameters and values, and it showed an improved performance with model efficiency NSE of 0.82 and R² of observed and simulated discharge of 0.87 and the simulated volume difference PBias by −21%. The model's performance during the validation period was better than during the calibration period (Table 1). The peak flow was underestimated due to the rating estimation by the DHM, instantaneous flow record, and cascading flooding types in Himalayan catchments. Due to extreme precipitation events and physical obstructions in the upstream sites, river discharge is not uniformly continuous and regular. The calibrated parameters are quantified in Supplementary Table S4.

Based on calibration and validation, the comparison of statistical indexes is shown in Table 1. The HBV model performed better than SPHY and HEC HMS in the TRB (Figure 3). The model performance was evaluated using continuous streamflow of discharge stations. These models simulated continuous streamflow based on dynamic input data and static data at gauged and ungauged sites. These models are not accountable and could not simulate cascading hazards; flow from check dam operation of hydropower and river-stream blocked flow. River discharge is contributed from glacier–snow melt, baseflow, and rainfall runoff. Generally, hydrological models simulate discharge based on the rainfall-runoff relation. Precipitation is the principal factor of river discharge. Low flow simulation showed less deviation, but high flow simulation showed more biases compared with low flow simulation (Figure 3). The deviation of high flow simulation caused impacts on overall model performance. The model performance mainly depends on the types of model structure and parameters (Ouyang et al. 2014; Nonki et al. 2021). All these models can be used for simulation in the Himalayan River basins. The SPHY model is a spatially distributed model with a glacier module; the HBV model is a conceptual semi-distributed model with dynamic glacier simulation; and HEC HMS is a semi-distributed model with snow melt simulation. Generally, physically based distributed models are more reliable than conceptual and lumped modeling systems (Tran et al. 2018; Dhital et al. 2021). Similarly, our result showed the HBV and HEC HMS models performed better than the SPHY model in all statistics (Table 1). Lumped models in most cases exhibit better performances than physically based models due to the holistic modeling framework in lumped model development (Das et al. 2008). These results further confirmed the long-standing suspicion on the ‘physics’ of the traditional so-called physically based models (Beven & Germann 2013; Gao et al. 2023). The hydrological models also encountered uncertainties from input datasets, model structure, and parameters (Song et al. 2015; Moges et al. 2021). Further, meteorological forcing plays a vital role in the performance of hydrological models that may cause uncertainty in hydrological modeling (Budhathoki et al. 2022).

Runoff estimation improved at ungauged sites using combined methods rather than individual methods (Oudin et al. 2008). The consistency to more reliable simulation over the entire basin was ensemble simulated streamflow. The average discharge at Benighat using SPHY, HEC HMS, and HBV models was ensembled by using a deterministic averaging process, the annual average discharge was found as 175.03 m³/s (Figure 4(c)), the monthly average maximum discharge was found as 526.97 m³/s in August and minimum discharge was found as 36.82 m³/s in February (Figure 4(b)). The streamflow simulation at an ungauged site was two multi-modeling approaches adopted in this study; the streamflow simulation from the gauged station to the gauged station supposed when ungauged, and adopted gauged station to the ungauged site by using calibrated models within the basin from the headwater donor catchment to the downstream receiver basin. The streamflow estimation at ungauged sites using multi-models and ensemble approach is usually more reliable than model simulation merely dependent on the individual catchment.

The SPHY, HBV, and HEC HMS models all performed differently based on their respective characteristics. The SPHY model, which was calibrated and validated, continuously transferred streamflow from the upstream catchments of Busti and Rasnalu to the downstream catchment of Benighat. In contrast, the HBV and HEC HMS models transposed streamflow from Busti to Benighat. It should be noted that Benighat is the receiver of the TRB, with Busti serving as the head donor catchment. Both Busti and Rasnalu are donor catchments to Benighat. The SPHY model's daily flow simulation at Benighat utilized two approaches in its spatial distributed modeling system; one simulating flow from the Busti station and the other simulating flow from the Rasnalu station. The daily streamflow simulations from Busti and Rasnalu at Benighat were closely aligned and exhibited perfectly correlated streamflow at Benighat. The HBV model's simulation of daily, monthly, and annual streamflow was higher than that of other models. The HEC HMS model simulated peak daily discharge than the other models during high flow seasons. These three models' simulation results indicated a greater amount of streamflow at Benighat than the summation of the discharge from the upstream gauging stations of Busti and Rasnalu. As a result, the discharge downstream is greater than upstream due to the contribution of the stream network to runoff. The upstream donor catchments, Busti and Rasnalu, flow into the downstream receiver basin at Benighat, which serves as the final outlet of the TRB. Each model could not simulate a similar flow due to their different parameterization in the models (Myers et al. 2021), which is also revealed by this study. The process of parameterization is independent of model variants (Refsgaard 1997). Hydrological models are independent of streamflow simulation at the ungauged site. Thus, all methods of ungauged streamflow could not simulate similar discharge (Van Liew & Mittelstet 2018). Further, the performance of the hydrological models varied based on their features and the characteristics of the catchments (Refsgaard 1997; Pechlivanidis et al. 2011). The hydrological models could be applied without calibration in the absence of observations; well-performed calibrated models should work within range and out of range in both gauged and ungauged basins (Bergstrom 2006).

This research contributes to ungauged data records estimation in the Himalayan River basin. These results will be helpful to hydropower promoters and hydraulic designers. Furthermore, this study will enhance hydropower and hydraulic structure designs across the river in mountainous river basins.

Hydrological information at ungauged basins is very important for water resource management. In this study, the ungauged discharge is estimated in daily, monthly, and annual time steps from upstream to downstream. The comparison of fully distributed and semi-distributed hydrological models, i.e. SPHY, HBV, and HEC HMS, is a robust method to estimate the discharge at ungauged sites. HBV-light and HEC HMS models showed better performance in comparison to the SPHY model in this study. In the overall comparison of NSE, coefficient of determination, and volume differences of hydrological models' simulation, the coefficient of determination showed almost similar performance. The SPHY model indicated the highly correlated estimation of ungauged discharge transferred from two different gauged stations due to the spatially distributed features of the model but it performed better at the Rasnalu gauge station than the Busti gauge station. The annual ensembled discharge of Benighat was estimated as 175.03 m³/s. The deviation between predicted flow mostly appeared in high flow periods. The low flow simulation is better than the high flow. The comparative estimation using different models is a better discharge estimation than the individual method at ungauged discharge estimation by continuous simulation at the transboundary Himalayan River basin. Future studies at ungauged sites may enhance hydrological simulation capability by using satellite and reanalysis data.

We would like to thank SPHY, HEC HMS, and HBV model developer, and the first author is supported by the University Grants Commission Ph.D. fellowship (Award no. S&T 15-076/77). Two anonymous reviewers and the editor Dr. Prabin Rokaya are also greatly acknowledged for their comments, corrections, and suggestions to improve the quality of the manuscript.

Data cannot be made publicly available; readers should contact the corresponding author for details.

The authors declare there is no conflict.