Performance evaluation of a physically informed ANN machine learning model for short-term and extended-range streamflow prediction in the Himalayan Catchment

Performance evaluation of a physically informed ANN machine learning model for short-term and extended-range streamflow prediction in the Himalayan Catchment | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Performance evaluation of a physically informed ANN machine learning model for short-term and extended-range streamflow prediction in the Himalayan Catchment Bhanu Sharma, Narendra Kumar Goel This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7001048/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract Accurate streamflow prediction is vital for effective reservoir operation, flood forecasting, and water resource planning, particularly in snow and glacier-fed Himalayan catchments. Existing studies reveal that physically based models (PBMs) often face challenges such as parameter uncertainty, scale mismatches, and the need for extensive calibration. In contrast, data-driven models (DDMs) depend heavily on large datasets and lack integration of physical processes. Addressing these limitations, this study presents a Physically Informed Artificial Neural Network (PIANN) framework that integrates climatic, remote sensing, and hydrological inputs for streamflow prediction at daily and ten-daily time scales in the Tehri Catchment, Indian Himalayas. Two model configurations were evaluated: (i) a four-variable model including rainfall (R t ), temperature (T t ), snow cover area (SCA t ), and previous discharge (Q t-1 ), and (ii) a three-variable model excluding Q t-1 . The short-term (daily) model with four variables achieved high accuracy (NSE = 0.957, R² = 0.955 in calibration; NSE = 0.939, R² = 0.940 in validation), but in three variable model, accuracy is reduced (NSE = 0.837, R² = 0.845 in calibration; NSE = 0.734, R² = 0.753 in validation). The ten-daily model also attained high performance (NSE = 0.969, R² = 0.973 in calibration; NSE = 0.954, R² = 0.966 in validation). Excluding Q t-1 reduced model accuracy, underscoring its importance in maintaining flow memory and baseflow continuity. The model consistently captured low- and high-flow events, exhibiting physical plausibility and generalisation across extreme hydrological conditions. Error model analysis showed minimal change in prediction accuracy, indicating the robustness of the original PIANN outputs. This study demonstrates the strength of integrating physical understanding into ANN frameworks, offering a scalable and reliable tool for streamflow prediction in complex, data-scarce mountainous regions. Hydrology Machine Learning Physically informed Artificial Neural Network Streamflow Prediction Himalayan Catchment Error model Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Figure 8 Figure 9 Figure 10 Figure 11 1 Introduction Streamflow prediction at different temporal scales, such as hours, days, weeks, months, and other temporal scales, is essentially required to operate water resources efficiently (Yaseen et al., 2017). The accurate and reliable streamflow prediction helps the water authorities to use the water optimally for power generation, agricultural use, domestic use, maintaining environmental flows, and flood mitigation (Moradkhani et al., 2004). Hydrologists across the world proposed new and effective methods to predict streamflow. Physically based models (PBM) and data-driven Models (DDM) are two prominent traditional approaches for streamflow prediction (Mosavi, Ozturk, & Chau, 2018). The first approach uses mathematical relationships to understand the sub-processes of the hydrological cycle. The parameters for these models are non-linear, time-invariant, and deterministic (Hsu et al., 1995). Such a concept does not reflect the stochastic characteristics of the Rainfall–Runoff (R–R) process (Kitanidis & Bras, 1980a, b; Duan et al., 1992, 1993; Sorooshian et al., 1993; Yapo et al., 1996; Hsu et al., 1995). The data-driven models (DDMs) trained on historical data and enables to discover and generalize the relationship between different variables. These models are frequently used where non-linear modelling is required, less reliance on physical understanding more recent hydrological applications in non - linearity modelling, less reliance on physical understanding, and possibility of data integration (Shrestha, Bardossy, & Zehe, 2005). Physically based models (PBMs) face several challenges in streamflow prediction, primarily due to their reliance on extensive spatially distributed data, such as soil, land use, topography, and meteorological inputs, which are often unavailable or unreliable in data-scarce regions like the Himalayas (Beven, 2001; Hrachowitz et al., 2013). Its high parameterisation complexity leads to equifinality, where multiple parameter sets produce similar outputs, undermining model reliability (Beven & Freer, 2001). Additionally, the computational burden associated with high-resolution simulations limits their applicability for large-scale or real-time forecasting (Refsgaard & Storm, 1995). PBMs also encounter scale-transfer issues, as physically derived equations may not remain valid when applied beyond their original spatial or temporal domain (Singh & Woolhiser, 2002). Furthermore, uncertainty is amplified by model structure simplifications, especially in snow- and glacier-dominated catchments (Clark et al., 2011). Although these models produced reasonable results, their linearity meant they were ineffective at modelling complex hydrological processes. Researchers acknowledged that streamflow is affected by several interacting factors such as precipitation, temperature, soil moisture, and land-use change with time-varying relationships (Nayak et al., 2005; Mensah et al., 2022). To overcome the limitations of traditional physical-based models, researchers turned towards the non-linear data-driven models such as Artificial Neural Networks (ANNs), Support Vector Regression (SVR), K-nearest Neighbours (KNN), etc., which offer greater flexibility in capturing the nonlinearities of hydrological processes (Dibike & Solomatine, 2001; Brath, Montanari, & Toth, 2002; Liong & Sivapragasam, 2002). In order to further improve the accuracy of data-driven models in streamflow prediction, researchers have developed several data pre-processing techniques such as Singular Spectrum Analysis (SSA), Wavelet Transform (WT), and Particle Swarm Optimisation (PSO) to improve the quality (Maier et al., 2010; Dawson & Wilby, 2001; Wu et al., 2009; Partal & Kisi, 2007; Sivapragasam et al., 2001; Chau, 2006). These approaches contribute to better-quality data in DDMs, leading to improved pattern recognition and enhanced hydrological forecasting (Tiwari & Chatterjee, 2011; Maheswaran & Khosa, 2012). In the latter stage, DDMs were integrated with complementary techniques such as wavelet transforms, fuzzy logic, optimisation algorithms, or statistical resampling to enhance prediction accuracy and robustness. These hybrid models effectively capture nonlinear relationships, handle non-stationary data, and reduce uncertainty, making them well-suited for complex environmental and hydrological modelling tasks (Tiwari & Chatterjee, 2011; Maheswaran & Khosa, 2012; Kasiviswanathan et al., 2016; Zhang et al., 2018; Mohammadi et al., 2020). Ensemble learning approaches have also significantly enhanced the performance of DDMs by integrating them with other machine learning models and optimisation algorithms (Kişi & Shiri, 2011). In such frameworks, DDMs are combined with the same categories of models like Support Vector Machines (SVM) and Random Forests (RF) and optimised using algorithms such as Particle Swarm Optimisation (PSO), Differential Evolution (DE), and Genetic Algorithms (GA) (Mosavi et al., 2018; Abrahart et al., 2012; Noori et al., 2010; Shortridge et al., 2016; Malik et al., 2021). Quantifying the uncertainty associated with ensemble machine learning models significantly enhances the reliability and robustness of hydrologic forecasting by accounting for model diversity and data variability (Sharma et al., 2018; Kasiviswanathan et al., 2016). In the subsequent development, temporal memory and sequence models were integrated with DDMs to enhance the ability to model time-dependent and sequential patterns in hydrological and environmental systems. These models include architectures such as Recurrent Neural Networks (RNNs), Long Short-Term Memory (LSTM) networks, and Gated Recurrent Units (GRUs), which are specifically designed to retain and utilise temporal dependencies in data (Shen et al., 2020; Jamali et al., 2018; Mosavi et al., 2018). These sequence models incorporate memory elements that enable learning from past states, making them highly effective for streamflow prediction, rainfall-runoff modelling, and climate-driven time series forecasting. The integration of such temporal memory structures with DDMs has been shown to significantly improve model performance, especially under conditions of nonlinearity and temporal autocorrelation (Kratzert et al., 2018; Feng et al., 2020; Chattopadhyay et al., 2020). These models have proven particularly useful when dealing with long lead-time forecasts or highly variable inputs such as precipitation, snowmelt, and evapotranspiration (Hu et al., 2018; Dehghani et al., 2023; Natel de Moura, Seibert, & Detzel, 2022). The review of existing studies highlights that traditional DDMs rely heavily on large datasets and lack physicality aspects. PBMs often suffer from parameter uncertainty, scale mismatch, and require extensive calibration (Shen, 2018). To overcome these limitations, the researchers developed physically informed machine learning models (PIML). PIML embed physical rules directly into the learning process, ensuring physically plausible predictions that enhance reliability and interpretability (Karpatne et al., 2017; Karniadakis et al., 2021). Integrating Physical processes with machine learning models bridges the gap between physical processes and data-driven machine learning approaches. PIML also mitigates bias in traditional hydrological models, enhancing overall prediction accuracy. It also leads to faster computing, more performant simulations, and more robust and actionable predictions (Zhu et al., 2019; Jia et al., 2021). With increasing climate variability and extreme weather events, hydrologic systems exhibit non-stationary behaviour. PI-ANNs, by combining physical laws and adaptive learning, better handle non-stationary conditions and improve extrapolation to unseen climate scenarios (Willard et al., 2020). PIML incorporates physical constraints , which guide the learning process toward physically plausible solutions even outside the training domain (Mushtaq et al., 2024; Bhasme et al., 2022; Lu et al., 2021; Parisouj et al., 2022; Deng et al., 2024; Zhang, 2024). PIML models have been adopted for rainfall-runoff modelling in temperate and data-rich regions in few studies (Kratzert et al., 2019; Feng et al., 2020), but their application in topographically complex, data-scarce basins such as the Indian Himalayas remains sparse. The Indian Himalayan catchments present unique challenges due to high spatial heterogeneity, steep terrain, snow–glacier dynamics, and limited gauging infrastructure. The present study addresses this gap by developing a physically informed Artificial Neural Network (PI-ANN) framework for a snow-fed catchment for a multiscale temporal framework (short-term and extended-range). In most studies, the basic input variable, such as rainfall, neglects critical factors like temperature, snow cover area, and travel time from different elevation zones to the outlet of a catchment (Yang et al., 2021; Mushtaq et al., 2024). The present study analyses streamflow prediction accuracy of a physically informed ANN model considering the combination of climate variables (Rainfall, Temperature), remote sensing-derived data (Snow cover area), and a hydrological dataset. The study also addresses a critical gap in using the IMD gridded meteorological dataset (Rainfall and Temperature) in streamflow prediction in an Indian Himalayan catchment (Bhagirathi Catchment), which is limited. A custom transfer function was used to model the hydrological response from each catchment zone to the catchment outlet. The study advances the understanding of hydrological processes in the Himalayan region and contributes to more accurate predictions for effective water resources management. By incorporating these physically meaningful variables, the PIANN framework captures the spatiotemporal variability of catchment hydrological responses. 2 Study Area and Data 2.1 Study Area Tehri Dam catchment (Bhagirathi River catchment) 7,293 km² ( Fig. 1 ), encompassing mountainous terrain that includes several snow-covered peaks and glaciers having an area of 2042 km² (Agarwal et al., 2019). Tehri dam's gross and live storage capacities are 3540 MCM and 2615 MCM, respectively. It plays a crucial role in hydroelectric power generation, irrigation, and drinking water supply for northern India. Tehri dam is located at the confluence of the Bhagirathi and Bhilangana Rivers in Uttarakhand, India. Tehri Dam is an earthen rockfill dam that is 260.5 meters (839.50 meters above MSL) high and has an installed capacity of 1000 MW. Commissioned in 2006, the dam provides irrigation water to Uttar Pradesh and Uttarakhand and also provides drinking water to almost seven million people in these two states. Its flood management system consists of three chute spillways (5500 cumecs), two left bank shaft spillways (3650 cumecs) and two ungated spillways (3850 cumecs) to pass the Probable Maximum Flood (PMF) of 15,540 cumecs. The MFL (maximum flood level) of the dam is at 839.50 meters, while FRL (full reservoir level) is at 830 meters. 2.2 Data The present study utilised multiple hydro-meteorological and remote sensing datasets to develop and evaluate the Physically-Informed Artificial Neural Network (PIANN) model for streamflow prediction over the Tehri Dam catchment. Gridded daily rainfall data at a spatial resolution of 0.25° × 0.25° were downloaded from the India Meteorological Department (IMD) from 2006–2020 (Pai et al., 2014). This dataset was produced with the help of a dense network of rain gauge stations and interpolated using an objective analysis method, providing spatial coherence and reliability for regional-scale hydrological modelling. Daily temperature data at a relatively coarse spatial resolution of 1.0° × 1.0° were also obtained from IMD for the same period (Srivastava et al., 2009). The temperature database is based on quality-controlled stations, provide important inputs in a catchment for snowmelt and evapotranspiration. Moreover, snow cover area (SCA) was derived from the MODIS Terra daily SCA climate modelling coverage products with 500 m spatial resolution. The MODIS snow data were analysed, and the snow cover extent were derived for the catchment by GIS techniques. Streamflow data at Tehri Dam, which reflects the sum of upstream catchment runoff response, were obtained from Tehri Hydro Development Corporation India Ltd. (THDCIL) for the period 2006–2020. This dataset served as the target variable for model calibration and validation. 3 Methodology 3.1 PI-ANN Model for Short-term (Daily) Streamflow Prediction The methodology ( Fig. 2 ) begins with data processing, where the catchment is divided into 10 zones for rainfall zoning and five zones for temperature through DEM-based delineation. Rainfall and temperature data are clipped to the extent of each catchment zone, and zonal statistics are performed to obtain representative input values. Snow cover data is extracted to complement hydroclimatic variability. The effective rainfall is calculated using the SCS-CN method, which incorporates land use and soil characteristics and helps represent infiltration-excess runoff more realistically. Lagged streamflow variable is also included as predictors to account for catchment memory effects and autoregressive properties of streamflow systems. These pre-processed and engineered variables are then used to train separate ANN models for each zone, consisting of an input layer (to take climate and spatial variables), a hidden layer with non-linear activation (to capture complex relationships), and an output layer producing predicted discharge. Two modelling scenarios are considered: Case 1 uses rainfall, temperature, snow cover area, and the previous day's discharge as inputs, enhancing model memory and performance; Case 2 excludes the previous day's discharge, relying only on rainfall, temperature, and snow cover area. A custom transfer function based on the Muskingum routing method is then applied to simulate the translation and attenuation of flow between upstream and downstream zones, ensuring hydrological consistency across space. The model is calibrated for the year 2006-2016 and validated over the period 2017–2020, ensuring temporal robustness. To further refine prediction quality, an autoregressive error model is used to correct residuals between observed and simulated streamflow, thereby improving the calibrated and validated output. The final model is evaluated using several widely accepted hydrological performance metrics such as Nash–Sutcliffe Efficiency (NSE), coefficient of determination (R²), Root Mean Square Error (RMSE), Mean Absolute Error (MAE), PBIAS, LogNSE, and Skill Score. These allow multi-dimensional assessment of model accuracy, consistency, and bias. One of the key advantages of this methodology lies in its physical interpretability due to the integration of snow cover area and effective rainfall; its spatial representativeness via catchment zoning; and its flexibility and robustness due to the use of lagged discharge and error correction techniques. Moreover, the incorporation of Muskingum routing introduces a hydrologically sound transfer function that respects the flow dynamics within a basin. This framework bridges the gap between physically based and data-driven models, offering a powerful tool for short-term streamflow forecasting, especially in data-scarce or complex terrains such as the Himalayan or snow-fed basins. 3.2 PI-ANN for Extended (10 daily) Streamflow Prediction (ESP) The methodology ( Fig. 3 ) integrates multisource datasets comprising gridded daily rainfall (0.25° × 0.25°) and temperature (1.0° × 1.0°) from the India Meteorological Department (IMD), snow cover area from MODIS satellite products, and observed ten-daily streamflow data. The catchment was divided into ten rainfall zones and five temperature zones through GIS-based overlay and zonal statistics. Effective rainfall was estimated using the Soil Conservation Service-Curve Number (SCS-CN) method, and hydrological memory was incorporated by including lagged discharge as a feature. Two PIANN model configurations were tested: Case 1 included climate variables (10 daily rainfall, 10 daily average temperature), remote sensing input (10-day snow cover), and the previous 10 daily streamflow to capture autoregressive dynamics, while Case 2 used only climate (10 daily rainfall, 10 daily average temperature) and remote sensing (10 day snow cover) variables as inputs. Subsequently, a custom transfer function based on the Muskingum routing method was used to propagate discharge from upstream to downstream zones, ensuring physical flow continuity. Model calibration was conducted from 2006-2016, and validation was performed over 2017–2020. Model performance was assessed by NSE and R 2 . The results were post-processed with an autoregressive error model and several accuracy indices such as NSE, LogNSE, R², RMSE, Skill Score, PBIAS, and MAE. This hybrid approach has resulted in a strong, interpretable, and spatially explicit tool for 10 daily streamflow prediction in data-sparse and snow‐influenced mountainous basins. 4 Results and Discussions 4.1 Short-term Streamflow Prediction using PI-ANN Model 4.1.1 Four variable model (Q t-1 , R t , T t , SCA t ) During the calibration period , the model achieved a high NSE of 0.957 and an R 2 value of 0.955 , indicating an excellent match between observed and predicted discharge ( Fig. 4 ). The hydrograph shows that the model accurately captures both the timing and magnitude of peak flows as well as baseflow conditions , highlighting the model’s ability to replicate intra-annual and inter-annual variability. In extreme flow years (e.g., 2013–2014) the predicted peaks well reproduce the observed ones showing the model ability in generalising non-linear hydrological responses. The model performed well also in the validation period, NSE = 0.939, R 2 = 0.940 ( Fig. 5 ). It means that the model predictions are so close to the observed flows, even in the independent validation phase, suggesting the good generalisation capability and not overfitting, an important property of reliable streamflow models (Zhang, 2024; Deng et al., 2024). A significant improvement in the model performance was due to the incorporation of the discharge at the previous time step as an input variable, serving as a memory term (Adamowski & Karapataki, 2010; Mosavi et al., 2018; Ni et al., 2020). This autoregressive input helps the model identify delayed runoff, storage effects, and baseflow contributions that are not purely dependent on the meteorological inputs (Bhasme et al., 2022; Lu et al., 2021). Especially during base flow, the new input increases continuity and decreases the fluctuations of the predicted discharge, leading to more accurate results for both the dry and wet seasons. The findings also suggest that the model is capable to perform very well in low-flow periods, remaining near to the observed values without any over-prediction which is frequent issue in ML-based models (Zahmatkesh, Karamouz, & Nazif, 2015; Sit & Demir, 2019). In the same way, the model also simulates relatively extreme flow events successfully, where sudden peaks are close to observed peaks, this suggests that inclusion of physically meaningful variables (especially rainfall and temperature) allows the network to learn and simulate unexpected hydrological responses (Parisouj et al., 2022). 4.1.2 Three variable model (R t , T t , SCA t ) The performance during the calibration period yielded a NSE of 0.837 and a R 2 of 0.845 ( Fig. 6 ) , indicating a reasonably good fit between observed and predicted streamflow. However, during the validation period model performance dropped, with NSE and R 2 values declining to 0.734 and 0.753 , respectively ( Fig. 7 ). These results suggest that while the model can capture general flow patterns, its ability to generalize across time is moderate , and the accuracy is average compared to more robust configurations that include hydrological memory. A noticeable limitation in this model is the lag in peak timing , where the model consistently delays the occurrence of peak flows compared to observed streamflow. This time lag may be attributed to the absence of previous time step discharge as an input. In hydrological systems, past flow values carry important memory about soil saturation, baseflow, and delayed runoff, which rainfall and temperature alone cannot explain (Lu et al., 2021; Bhasme et al., 2022). The mismatch of peak magnitudes further indicates that the model struggles to learn rapid, nonlinear runoff generation mechanisms, particularly during extreme rainfall or snowmelt events. In low-flow conditions , the model tends to underpredict , which can be attributed to the lack of temporal continuity in the inputs. Without the memory provided by lagged streamflow, the model cannot accurately account for groundwater contributions or baseflow recession curves. During high-flow periods , such as monsoonal peak floods, the model shows inconsistent performance , either underestimating or delaying peaks . This is particularly evident in snow-dominated catchments, where the timing and volume of meltwater depend not only on temperature and snow cover but also on accumulated storage from prior days, which the current model setup lacks. Without Q t-1 , the model has to infer the influence of antecedent conditions indirectly, leading to greater uncertainty in predictions, especially during transitional periods (e.g., shifts between wet and dry seasons). Without Q t-1 , the model becomes highly dependent on rainfall, temperature, and snow cover data. Any inaccuracies or uncertainties in these inputs are amplified in the prediction, resulting in less reliable outcomes. In the context of daily streamflow prediction using a physically informed ANN model , the results not only demonstrate high predictive accuracy but also reflect strong physical consistency and hydrological plausibility . The model successfully replicates seasonal streamflow dynamics characteristic of a snow and glacier-fed Himalayan catchment , where flow peaks are dominantly driven by a combination of monsoonal rainfall and snowmelt contributions. The predicted hydrographs align well with the observed timing and magnitude of flow events, particularly capturing the gradual rise during the pre-monsoon snowmelt season and sharp peaks during monsoon rainfall, thus adhering to the natural hydrological cycle . This alignment underscores the model's ability to simulate physically meaningful streamflow responses , not just statistical fitting. From a spatial and climatic context , the incorporation of snow cover area (SCA t ) and temperature (T t ) as inputs enhances the model's capability in cold and complex terrains like the Himalayas. These inputs are especially critical in regions where snowmelt substantially contributes to river discharge, and their inclusion enables the PIANN to better capture seasonal lags and flow magnitude variations . The model performance indicates that factors such as previous discharge (Q t-1 ) and snow cover area (SCA t ) are determinants. Q t-1 would help to preserve a certain temporal continuity and flow memory, while SCA t better represents remote sensing related dynamics that are important in these river basins. Temperature has a double effect by conditioning snowmelt rates and evapotranspiration and rainfalls directly induce runoff events, therefore the union of these four variables is physically and statistically significant. Nevertheless, some uncertainties and limitations should also be noted. The use of gridded or remotely sensed data (e.g., SCA t from MODIS) carries potential errors by way of cloud contamination, resolution, or misclassification. Furthermore, while the ANN can model the nonlinear relations on the other hand, its black-box type reduces the interpretative and extrapolatory abilities especially under the extreme or a non-stationary climate context. There may also be scale differences between forcing data and the catchment's hydrological response, that could influence the prediction accuracy in certain events. 4.2 Extended (Ten Daily) Streamflow Prediction Using PIANN Model 4.2.1 Four variable Model (Q t-1 , R t , T t , SCA t ) The model achieved a NSE of 0.969 and a R² of 0.973 during the calibration period ( Fig. 8 ) , indicating excellent agreement between observed and predicted streamflow values. The hydrograph comparison shows that the predicted flows closely match the observed hydrographs, capturing both peak and low-flow events effectively. Notably, the model successfully replicates the seasonal variability, especially during the monsoon season, demonstrating its sensitivity to the climatic inputs. The scatter plot confirms signifying minimal bias in prediction. In the validation period , the model maintains a high prediction performance with an NSE of 0.954 and R² of 0.966 , which confirms the model's generalizability and robustness ( Fig. 9 ). The hydrograph comparison again reveals that the model adequately captures the magnitude, timing, and pattern of flow peaks. The scatter plot continues to show a strong correlation between observed and simulated flows, reaffirming the predictive skill of the model. The high NSE and R² values in both calibration and validation phases indicate that the model effectively leverages the selected predictors to capture the underlying hydrological processes governing streamflow in the Himalayan catchment. The inclusion of snow cover area (SCA t ) appears particularly valuable for this snow-glacier-fed basin, contributing to better simulation of spring-summer flows driven by snowmelt. Similarly, previous discharge (Q t-1 ) contributes to preserving temporal continuity in flow dynamics, enhancing the model’s memory and improving lagged predictions. Overall, the model performs well across a 10-daily temporal resolution, which is suitable for extended-range water resource planning and hydrological applications such as reservoir operation and flood forecasting in data-scarce, mountainous regions. 4.2.2 Three variable model (R t , T t , SCA t ) The model accuracy is slightly reduced in comparison to the four-variable model that included previous discharge (Q t-1 ). During the calibration period , the model achieved a NSE of 0.901 and an R² of 0.914 , indicating very good agreement between observed and predicted streamflow. The model effectively captures the seasonal flow dynamics, particularly the rise and recession patterns associated with snowmelt in spring and monsoon rainfall in summer. The performance is slightly lower than the four-variable case, likely due to the absence of Q t-1 , which serves as a memory component capturing baseflow persistence and flow continuity. Interestingly, in the validation period , the model maintains and even slightly improves performance with an NSE of 0.915 and R² of 0.921 . This indicates good generalization capability and model robustness under varying hydro-meteorological conditions, despite the reduced input dimensionality. The slight increase in validation accuracy may be attributed to the dominant influence of snow and rainfall in those years, where lagged memory may have played a lesser role compared to the physical drivers. The results also support the physical consistency of the model. The inclusion of SCA t and temperature allows the model to simulate snowmelt-driven contributions, while rainfall serves as a direct runoff driver. This three-variable setup still enables the ANN to reflect seasonal hydrologic behavior typical of snow-dominated Himalayan catchments—i.e., snowmelt-induced flow in pre-monsoon and high-flow peaks during monsoon months. From a spatial and climatic perspective , this configuration is highly relevant for glacier-fed basins where snow and temperature are key hydrological drivers. The use of a 10-daily temporal resolution remains appropriate, balancing responsiveness to climatic inputs and smoothing out short-term fluctuations. However, the absence of Q t-1 slightly limits the model’s ability to simulate flow memory and autocorrelation , especially during dry periods or in capturing recession limbs of hydrographs. This underscores the importance of lagged discharge as a performance-enhancing variable , particularly in PIANN models that benefit from temporal dependencies. Overall, the three-variable model still performs well, making it suitable for applications like streamflow forecasting , climate change impact assessment , and water resource management in data-scarce regions. Its simplicity offers computational efficiency and interpretability while maintaining strong predictive accuracy rooted in physically meaningful inputs. This setup may be particularly useful when discharge observations are missing, or unreliable but climate and remote sensing data are available. The physically informed ANN model produced streamflow predictions that are physically consistent and hydrologically realistic at a 10-daily temporal resolution. The model successfully captured the seasonal hydrological cycle, with high flows coinciding with monsoon rainfall and snowmelt periods, and low flows during the dry winter season. This alignment reflects an appropriate simulation of snowmelt-induced discharge peaks during late spring and early summer , and rainfall-driven peaks during the monsoon months, indicating that the model’s outputs conform to the known hydrological behavior of Himalayan catchments. Given the glacier-fed and snow-dominated characteristics of the study basin , the inclusion of temperature (T t ) and snow cover area (SCA t ) as inputs significantly enhanced model responsiveness to snow accumulation and melt processes. The 10-daily time step proved optimal in balancing temporal detail with data availability, effectively smoothing short-term fluctuations while still capturing seasonal dynamics. The model’s sensitivity to physical inputs was evident, with previous discharge (Q t-1 ) and SCA t emerging as dominant predictors. Q t-1 included a memory term essential for maintaining flow continuity, whereas SCA t reproduced the timing and amplitude of snowmelt-driven flows more accurately. Rainfall (R t ) and temperature (T t ) were further climatic forcing required to capture the dynamics for rain and meltwater contributions. However, some uncertainties are expected despite the strong statistical performance due to possible errors associated with the satellite-sensed SCAt and the gridded climatic inputs. Furthermore, the black-box nature of the ANN prevents its interpretability and can hinder extrapolation under new climate or land cover situations. Nevertheless, the results affirm the model’s applicability for extended-range prediction, flood and drought monitoring, and reservoir operation planning . Furthermore, the model architecture—being physically informed—offers a promising foundation for future climate change impact studies , especially when driven by downscaled projections from CMIP6-based SSP scenarios. Finally, this ANN framework could be integrated with conceptual or process-based hydrological models to develop hybrid tools that combine data-driven flexibility with physical realism, suitable for complex mountainous basins under changing hydro-climatic regimes. Using PIANN for Extended Range (Ten-Daily), Streamflow Prediction benefits flood susceptibility assessment, flood risk potential evaluation, and watershed management strategies. The ability to predict changes in streamflow over 10 days improves reservoir operations, irrigation planning, and flood early warning systems. Extended-range prediction in the context of the Tehri Dam is significant for optimizing hydropower generation, water supply, and flood control. 4.3 Error Model 4.3.1 Error model for daily and extended range streamflow prediction model Error models play a crucial role in improving the reliability of streamflow predictions by accounting for the temporal dependency often observed in model residuals. In streamflow modelling, residuals are rarely purely random; instead, they frequently exhibit autocorrelation due to unmodelled processes, input data errors, or model structure limitations (Beven, 2001; Klemeš, 1986). Ignoring this autocorrelation can lead to biased parameter estimation and overconfident predictions. Auto regressive error models, explicitly capture these dependencies, enabling more accurate representation of uncertainty. By incorporating the memory effect of past errors, these models help refine both short-term and extended range predictions. This is particularly important in flood forecasting and water resources management, where prediction accuracy is critical. Overall, it provides a more robust framework for streamflow prediction under uncertainty. Table 1 AR Error model results for daily streamflow prediction model Performance Parameters Observed and Predicted Discharge Series After Error Model Implication Calibration Validation Calibration Validation AR (2) Coefficient (a 1 ) - - 0.68 0.68 AR (2) Coefficient (b 1 ) - - -0.23 -0.23 NSE 0.957 0.9402 0.958 0.901 R 2 0.9577 0.9405 0.9748 0.946 LogNSE 0.921 0.9038 0.923 0.880 Skill Score 0.957 0.941 0.959 0.948 RMSE 59.977 61.899 59.315 79.47 PBIAS -0.0030 -0.71 -0.0086 -0.394 MAE 32.75 33.205 32.470 40.923 Table 1 presents the performance evaluation matrix of a daily streamflow prediction model before and after applying an Autoregressive (AR) error model. The AR (2) model coefficients are 0.68 and -0.23, respectively, indicating a significant temporal correlation in the residuals. After the AR model application, slight improvements are observed in the calibration phase for NSE (from 0.957 to 0.958), R² (from 0.9577 to 0.9748), and Skill Score (from 0.957 to 0.959), showing that the error model enhances the model's ability to capture streamflow variability but to a very low extent. However, during the validation phase, the NSE and LogNSE values slightly decline, suggesting reduced generalization. RMSE and MAE increase noticeably in validation (RMSE from 61.899 to 79.47 and MAE from 33.205 to 40.923), highlighting potential overfitting. Although PBIAS remains low across all cases, the larger prediction error during validation suggests that the AR model may be too closely fitted to the calibration data. The overall results emphasize that while autoregressive error modelling improves the model fit during calibration, careful validation is essential to ensure robustness. It also reflects the importance of handling residual autocorrelation to improve model credibility. Therefore, combining AR models with prediction techniques helps to improve validation performance but to a very low extent. Table 2 AR error Model results for ten daily streamflow prediction model Performance Parameters Observed and Predicted Discharge Series After Error Model Implication Calibration Validation Calibration Validation AR (2) Coefficient (a 1 ) - - 0.0482 0.0482 AR (2) Coefficient (b 1 ) - - 0.0494 0.0494 NSE 0.974 0.964 0.973 0.963 R 2 0.9846 0.9812 0.9847 0.9809 LogNSE 0.967 0.948 0.968 0.951 Skill Score 0.973 0.9658 0.9771 0.9693 RMSE 44.299 45.293 44.184 45.829 PBIAS 0.2 2.7 0.018 2.4 MAE 26.548 29.329 26.264 29.415 Table 2 presents performance metrics for ten-daily (ANN) streamflow predictions before and after applying an Autoregressive (AR) error model. The AR (2) model coefficients are 0.0494 and 0.0482, indicating mild but notable temporal autocorrelation in the residuals, validating the need for an autoregressive correction. During calibration, performance remains nearly identical before and after applying the AR model. NSE slightly drops from 0.974 to 0.973, while R² remains stable at around 0.9846–0.9847. Metrics such as LogNSE, Skill Score, RMSE, and MAE also show only marginal changes, suggesting that the original model already had a strong fit. In the validation phase, similar trends are observed. The NSE shows a negligible decrease from 0.964 to 0.963, and R² slightly improves from 0.9812 to 0.9809, indicating the autoregressive model maintains the strength of the original model’s performance. RMSE and MAE slightly increase, from 45.293 to 45.829 and 29.329 to 29.415, respectively, but remain within acceptable bounds. Importantly, PBIAS decreases from 2.7 to 2.4 after error modelling, reflecting a reduction in systematic bias. The error analysis indicates that the inclusion of the error model has a negligible impact on the overall predictive accuracy, suggesting that the model's performance remains largely unaffected by its application. 5 Conclusion This study developed and evaluated a Physically Informed Artificial Neural Network (PIANN) model for streamflow prediction at daily and ten-daily timescales in a snow and glacier-fed Himalayan catchment. The results demonstrated that the inclusion of physically meaningful processes in combination with the data driven machine learning models. The analysis shows the effectiveness and robustness in multi temporal streamflow prediction. The study also explains the importance of choosing right variables for a model. PI-ANNs represent a shift toward theory-guided data science , a paradigm that supports scientific discovery by blending observations, physical theory, and machine learning (Karpatne et al., 2017). A critical finding of this research is the pivotal role of the previous discharge (Q t-1 ) as a memory component. Its inclusion allowed the model to capture delayed runoff processes, maintain baseflow continuity, and improve peak timing. These are the key aspects that are often inadequately represented in conventional data-driven models. The SCA t variable further contributed to improved simulation of snowmelt-driven flows, particularly during pre-monsoon and transitional seasons, enhancing the model's responsiveness over remote sensing data. The three-variable model, although physically consistent, exhibited limitations in peak timing and low-flow accuracy. The absence of Q t-1 forces the model to rely solely on climatic and remote sensing variables, due to which the model does not fully capture the persistence and lag effects inherent in river flow patterns. This omission leads to a loss of temporal dependencies, but reasonable accuracy of three variable model suggests the usage for streamflow prediction in an ungauged catchment or when the flow data is missing data for some period. PIANN model performed well at reproducing the seasonal and inter-annual variations of flow, which indicate a good consistency between the model and the underlying hydrological processes. The inclusion of physically meaningful predictors can improve model robustness more under low-flow periods and extreme hydrological conditions (Kratzert et al., 2019; Shen & Lawson, 2021; Zahmatkesh et al., 2015). The study also has its own limitations. The use of satellite-based snow cover data and gridded climate inputs could potentially introduce uncertainties related to misclassification and resolution mismatch. Additionally, the ANN model’s black-box nature limits physical interpretability, particularly under non-stationary conditions. Future work should focus on coupling the PIANN approach with conceptual or process-based hydrological models to improve interpretability and extrapolation under climate change scenarios. Integrating downscaled CMIP6-based projections will further enhance its application in long-term water resource planning and disaster risk reduction in data-scarce, climate-sensitive mountainous regions. PIANN proves to be a robust tool for streamflow prediction, when used with the relevant input data. The study contributes to advancing machine learning applications in hydrology, emphasizing the need for accurate and reliable predictions for sustainable water management. Declarations DATA AVAILABILITY STATEMENT The relevant information of data is included in the paper. The observed discharge data cannot be shared due to confidentiality issues. CONFLICT OF INTEREST The authors declare there is no conflict. ACKNOWLEDGEMENT The Authors have acknowledged THDCIL for providing data for the study. We would also like to thank the post-doctoral fellows of International Centre of Excellence for Dams (ICED) for proofreading the manuscript for clarity, language and appropriate presentation of the work. References Abrahart, R.J., Anctil, F., Coulibaly, P., Dawson, C.W., Mount, N.J., See, L.M., Shamseldin, A.Y., Solomatine, D.P., Toth, E. and Wilby, R.L., 2012. Two decades of anarchy? Emerging themes and outstanding challenges for neural network river forecasting. Progress in Physical Geography , 36 (4), pp.480-513. Adamowski, J., & Sun, K. (2010). 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-7001048","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":477886060,"identity":"76dba6c9-aec2-4ea1-bf97-7452c11bf74c","order_by":0,"name":"Bhanu Sharma","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA40lEQVRIie3OMQuCQBTA8Setgo222Fe4EAoh+ixPhFosgqZoSKe+gh/D6aLt4gaXi1Zbgj5CuNiWWdZ22hZ0/8EHx/vhA1CpfjACejktUnwYvl5ZE2I/CX5B3LgcKFmtGhiHfbb0R5OtiRq75GcwNkzjcwlxopnXOVBvuovwcdgCTIHAI9lhqU46IW1N47QkxWUpANdl5CjsW0jXE1KRbi1hfr/4C8c3IXXEify+E9KkF4tLwHCMek+4gZQMDGGfQrrqksTj13yIlpVwnsnIp7YbPEaxrAWNAIDBGi6qVCrV33UHAHlSQMwCQTAAAAAASUVORK5CYII=","orcid":"https://orcid.org/0000-0002-2825-4761","institution":"Indian Institute of Technology Roorkee, Roorkee","correspondingAuthor":true,"prefix":"","firstName":"Bhanu","middleName":"","lastName":"Sharma","suffix":""},{"id":477886260,"identity":"4f8e1088-b994-4c71-addd-ab22b13bc677","order_by":1,"name":"Narendra Kumar Goel","email":"","orcid":"https://orcid.org/0000-0002-8196-4738","institution":"Indian Institute of Technology Roorkee, Roorkee","correspondingAuthor":false,"prefix":"","firstName":"Narendra","middleName":"Kumar","lastName":"Goel","suffix":""}],"badges":[],"createdAt":"2025-06-29 06:51:24","currentVersionCode":1,"declarations":{"humanSubjects":true,"vertebrateSubjects":false,"conflictsOfInterestStatement":false,"humanSubjectEthicalGuidelines":true,"humanSubjectConsent":true,"humanSubjectClinicalTrial":false,"humanSubjectCaseReport":false,"vertebrateSubjectEthicalGuidelines":false},"doi":"10.21203/rs.3.rs-7001048/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-7001048/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":85918088,"identity":"ff8f714d-1735-4415-bbef-1e0324a72bac","added_by":"auto","created_at":"2025-07-03 07:19:49","extension":"jpeg","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":163903,"visible":true,"origin":"","legend":"\u003cp\u003eTehri catchment location map\u003c/p\u003e","description":"","filename":"image1.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-7001048/v1/cb52a97c213992cdf29c0e6b.jpeg"},{"id":85917738,"identity":"7c54c155-5657-4093-874a-21e96aaf76bd","added_by":"auto","created_at":"2025-07-03 07:11:49","extension":"jpeg","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":533979,"visible":true,"origin":"","legend":"\u003cp\u003eMethodology for short-term streamflow prediction using PIANN Model\u003c/p\u003e","description":"","filename":"image2.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-7001048/v1/a3d43121388e5d639d294c4c.jpeg"},{"id":85917736,"identity":"e62d84be-0dbc-44b1-af45-7cfcebcffc3d","added_by":"auto","created_at":"2025-07-03 07:11:49","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":152059,"visible":true,"origin":"","legend":"\u003cp\u003eMethodology for Extended Range Streamflow Prediction using PIANN Model\u003c/p\u003e","description":"","filename":"image3.png","url":"https://assets-eu.researchsquare.com/files/rs-7001048/v1/005c465714ea6e3ce050119e.png"},{"id":85918090,"identity":"6de96784-c0f0-4c7b-9f72-6d2015f18fa3","added_by":"auto","created_at":"2025-07-03 07:19:49","extension":"jpeg","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":121826,"visible":true,"origin":"","legend":"\u003cp\u003eObserved \u0026amp; predicted discharge with scatter plot for the calibration period.\u003c/p\u003e","description":"","filename":"image4.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-7001048/v1/6cbc463668420472833186ba.jpeg"},{"id":85918091,"identity":"1d7362f6-f380-42f2-91db-b7cce5477fdd","added_by":"auto","created_at":"2025-07-03 07:19:49","extension":"jpeg","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":128011,"visible":true,"origin":"","legend":"\u003cp\u003eObserved \u0026amp; predicted discharge with Scatter plot for the Validation period\u003c/p\u003e","description":"","filename":"image5.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-7001048/v1/0e69ea0df66cc0eb6467bdfe.jpeg"},{"id":85919348,"identity":"f3b805ed-033f-4f0f-a868-62c3ca312eb8","added_by":"auto","created_at":"2025-07-03 07:35:49","extension":"jpeg","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":119621,"visible":true,"origin":"","legend":"\u003cp\u003eObserved and predicted discharge with a Scatter plot for the calibration period\u003c/p\u003e","description":"","filename":"image6.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-7001048/v1/ac584cf3cf084298dfe22e04.jpeg"},{"id":85918093,"identity":"7abee375-8ac1-4a13-8d71-c93ce5c19f68","added_by":"auto","created_at":"2025-07-03 07:19:49","extension":"jpeg","order_by":7,"title":"Figure 7","display":"","copyAsset":false,"role":"figure","size":141231,"visible":true,"origin":"","legend":"\u003cp\u003eObserved and predicted discharge with scatter plot for the validation period\u003c/p\u003e","description":"","filename":"image7.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-7001048/v1/ef06950cc1227b0072eb67dd.jpeg"},{"id":85917742,"identity":"9e0a5563-f416-4066-bae2-7dfb0ab18bd2","added_by":"auto","created_at":"2025-07-03 07:11:49","extension":"jpeg","order_by":8,"title":"Figure 8","display":"","copyAsset":false,"role":"figure","size":129541,"visible":true,"origin":"","legend":"\u003cp\u003eObserved and predicted discharge with Scatter plot for the calibration period\u003c/p\u003e","description":"","filename":"image8.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-7001048/v1/28fb055f282f75be70b47505.jpeg"},{"id":85919160,"identity":"d761987b-aeb1-496e-ba38-05f258160c36","added_by":"auto","created_at":"2025-07-03 07:27:49","extension":"jpeg","order_by":9,"title":"Figure 9","display":"","copyAsset":false,"role":"figure","size":122186,"visible":true,"origin":"","legend":"\u003cp\u003eObserved \u0026amp; Predicted discharge with scatter plot for the validation period\u003c/p\u003e","description":"","filename":"image9.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-7001048/v1/040d3e7b821d4f388f699950.jpeg"},{"id":85917746,"identity":"ff292b22-42fb-407e-9453-250048c2b96a","added_by":"auto","created_at":"2025-07-03 07:11:49","extension":"jpeg","order_by":10,"title":"Figure 10","display":"","copyAsset":false,"role":"figure","size":151217,"visible":true,"origin":"","legend":"\u003cp\u003eObserved and predicted discharge with a scatter plot for the Calibration period\u003c/p\u003e","description":"","filename":"image10.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-7001048/v1/5f4a61b8cc8fbbee6a02331f.jpeg"},{"id":85917744,"identity":"42cff6ab-703c-49cc-a8fb-c41da08f459f","added_by":"auto","created_at":"2025-07-03 07:11:49","extension":"jpeg","order_by":11,"title":"Figure 11","display":"","copyAsset":false,"role":"figure","size":121096,"visible":true,"origin":"","legend":"\u003cp\u003eObserved \u0026amp; and predicted discharge with Scatter plot for the Validation period\u003c/p\u003e","description":"","filename":"image11.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-7001048/v1/bd66b8f291a5068e9fc8cb1e.jpeg"},{"id":85920303,"identity":"3f69d905-d990-47f0-a7f9-3875c6dec682","added_by":"auto","created_at":"2025-07-03 07:43:55","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":3594318,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-7001048/v1/119b675b-b498-4468-9c00-548df2d9f9b0.pdf"}],"financialInterests":"The authors declare no competing interests.","formattedTitle":"\u003cp\u003e\u003cstrong\u003ePerformance evaluation of a physically informed ANN machine learning model for short-term and extended-range streamflow prediction in the Himalayan Catchment\u003c/strong\u003e\u003c/p\u003e","fulltext":[{"header":"1 Introduction","content":"\u003cp\u003eStreamflow prediction at different temporal scales, such as hours, days, weeks, months, and other temporal scales, is essentially required to operate water resources efficiently (Yaseen et al., 2017). The accurate and reliable streamflow prediction helps the water authorities to use the water optimally for power generation, agricultural use, domestic use, maintaining environmental flows, and flood mitigation (Moradkhani et al., 2004). Hydrologists across the world proposed new and effective methods to predict streamflow. Physically based models (PBM) and data-driven Models (DDM) are two prominent traditional approaches for streamflow prediction (Mosavi, Ozturk, \u0026amp; Chau, 2018). The first approach uses mathematical relationships to understand the sub-processes of the hydrological cycle. The parameters for these models are non-linear, time-invariant, and deterministic (Hsu et al., 1995). Such a concept does not reflect the stochastic characteristics of the Rainfall\u0026ndash;Runoff (R\u0026ndash;R) process (Kitanidis\u0026ensp;\u0026amp; Bras, 1980a, b; Duan et al., 1992, 1993; Sorooshian et al., 1993; Yapo et al., 1996; Hsu et al., 1995). The data-driven models (DDMs) trained on historical data and enables to\u0026ensp;discover and generalize the relationship between different variables. These models are frequently used where non-linear modelling is required, less reliance on physical understanding more recent hydrological applications in\u0026ensp;non - linearity modelling, less reliance on physical understanding, and possibility of data integration (Shrestha, Bardossy, \u0026amp; Zehe, 2005).\u003c/p\u003e\n\u003cp\u003ePhysically based models (PBMs) face several challenges in streamflow prediction, primarily due to their reliance on extensive spatially distributed data, such as soil, land use, topography, and meteorological inputs, which are often unavailable or unreliable in data-scarce regions like the Himalayas (Beven, 2001; Hrachowitz et al., 2013). Its high parameterisation complexity leads to equifinality, where multiple parameter sets produce similar outputs, undermining model reliability (Beven \u0026amp; Freer, 2001). Additionally, the computational burden associated with high-resolution simulations limits their applicability for large-scale or real-time forecasting (Refsgaard \u0026amp; Storm, 1995). PBMs also encounter scale-transfer issues, as physically derived equations may not remain valid when applied beyond their original spatial or temporal domain (Singh \u0026amp; Woolhiser, 2002). Furthermore, uncertainty is amplified by model structure simplifications, especially in snow- and glacier-dominated catchments (Clark et al., 2011). Although these models produced reasonable results, their\u0026ensp;linearity meant they were ineffective at modelling complex hydrological processes. Researchers acknowledged that streamflow is affected by several interacting factors such as\u0026ensp;precipitation, temperature, soil moisture, and land-use change with time-varying relationships (Nayak et al., 2005; Mensah et al., 2022). To overcome the limitations of traditional physical-based models, researchers turned towards the non-linear data-driven models such as Artificial Neural Networks (ANNs), Support Vector Regression (SVR), K-nearest Neighbours (KNN), etc., which offer greater flexibility in capturing the nonlinearities of hydrological processes (Dibike \u0026amp; Solomatine, 2001; Brath, Montanari, \u0026amp; Toth, 2002; Liong \u0026amp; Sivapragasam, 2002).\u003c/p\u003e\n\u003cp\u003eIn order to further improve the accuracy of data-driven models in streamflow prediction, researchers have developed\u0026ensp;several data pre-processing techniques such as Singular Spectrum Analysis (SSA), Wavelet Transform (WT), and Particle Swarm Optimisation (PSO) to improve the quality (Maier et al., 2010; Dawson \u0026amp; Wilby, 2001; Wu et al., 2009; Partal \u0026amp; Kisi, 2007; Sivapragasam et al., 2001; Chau, 2006). These approaches contribute to better-quality data in DDMs, leading\u0026ensp;to improved pattern recognition and enhanced hydrological forecasting (Tiwari \u0026amp; Chatterjee, 2011; Maheswaran \u0026amp; Khosa, 2012). In the latter stage, DDMs were integrated with complementary techniques such as wavelet transforms, fuzzy logic, optimisation algorithms, or statistical resampling to enhance prediction accuracy and robustness. These hybrid models effectively capture nonlinear relationships, handle non-stationary data, and reduce uncertainty, making them well-suited for complex environmental and hydrological modelling tasks (Tiwari \u0026amp; Chatterjee, 2011; Maheswaran \u0026amp; Khosa, 2012; Kasiviswanathan et al., 2016; Zhang et al., 2018; Mohammadi et al., 2020). Ensemble learning approaches have also significantly enhanced the performance of DDMs by integrating them with other machine learning models and optimisation algorithms (Kişi \u0026amp; Shiri, 2011). In such frameworks, DDMs are combined with the same categories of models like Support Vector Machines (SVM) and Random Forests (RF) and optimised using algorithms such as Particle Swarm Optimisation (PSO), Differential Evolution (DE), and Genetic Algorithms (GA) (Mosavi et al., 2018; Abrahart et al., 2012; Noori et al., 2010; Shortridge et al., 2016; Malik et al., 2021). Quantifying the uncertainty associated with ensemble machine learning models significantly enhances the reliability and robustness of hydrologic forecasting by accounting for model diversity and data variability (Sharma et al., 2018; Kasiviswanathan et al., 2016).\u003c/p\u003e\n\u003cp\u003eIn the subsequent development, temporal memory and sequence models were integrated with DDMs to enhance the ability to model time-dependent and sequential patterns in hydrological and environmental systems. These models include architectures such as Recurrent Neural Networks (RNNs), Long Short-Term Memory (LSTM) networks, and Gated Recurrent Units (GRUs), which are specifically designed to retain and utilise temporal dependencies in data (Shen et al., 2020; Jamali et al., 2018; Mosavi et al., 2018). These sequence models incorporate memory elements that enable learning from past states, making them highly effective for streamflow prediction, rainfall-runoff modelling, and climate-driven time series forecasting. The integration of such temporal memory structures with DDMs has been shown to significantly improve model performance, especially under conditions of nonlinearity and temporal autocorrelation (Kratzert et al., 2018; Feng et al., 2020; Chattopadhyay et al., 2020). These models have proven particularly useful when dealing with long lead-time forecasts or highly variable inputs such as precipitation, snowmelt, and evapotranspiration (Hu et al., 2018; Dehghani et al., 2023; Natel de Moura, Seibert, \u0026amp; Detzel, 2022).\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eThe review of existing studies highlights that traditional DDMs rely heavily on large datasets and lack physicality aspects. PBMs often suffer from parameter uncertainty, scale mismatch, and require extensive calibration (Shen, 2018). To overcome these limitations, the researchers developed physically informed machine learning models (PIML). PIML embed physical rules directly into the learning process, ensuring physically plausible predictions that enhance reliability and interpretability (Karpatne et al., 2017; Karniadakis et al., 2021). Integrating Physical processes with machine learning models bridges the gap between physical processes and data-driven machine learning approaches. PIML\u0026ensp;also mitigates bias in traditional hydrological models, enhancing overall prediction accuracy. It also leads to faster computing, more performant simulations, and more robust and\u0026ensp;actionable predictions (Zhu et al., 2019; Jia et al., 2021). With increasing climate variability and extreme weather events, hydrologic systems exhibit non-stationary behaviour. PI-ANNs, by combining physical laws and adaptive learning, better handle non-stationary conditions and improve extrapolation to unseen climate scenarios (Willard et al., 2020). PIML incorporates \u003cstrong\u003ephysical constraints\u003c/strong\u003e, which guide the learning process toward physically plausible solutions even outside the training domain (Mushtaq et al., 2024; Bhasme et al., 2022; Lu et al., 2021; Parisouj et al., 2022; Deng et al., 2024; Zhang, 2024).\u003c/p\u003e\n\u003cp\u003ePIML models have been adopted for rainfall-runoff modelling in temperate and data-rich regions in few studies (Kratzert et al., 2019; Feng et al., 2020), but their application in topographically complex, data-scarce basins such as the Indian Himalayas remains sparse. The \u003cstrong\u003eIndian Himalayan catchments\u003c/strong\u003e present unique challenges due to high spatial heterogeneity, steep terrain, snow\u0026ndash;glacier dynamics, and limited gauging infrastructure. The present study addresses this gap by developing a physically informed Artificial Neural Network (PI-ANN) framework for a snow-fed catchment for a multiscale temporal framework (short-term and extended-range). In most studies, the basic input variable, such as rainfall, neglects critical factors like temperature, snow cover area, and travel time from different elevation zones to the outlet of a catchment (Yang et al., 2021; Mushtaq et al., 2024). The present study analyses streamflow prediction accuracy of a physically informed ANN model considering the combination of climate variables (Rainfall, Temperature), remote sensing-derived data (Snow cover area), and a hydrological dataset. The study also addresses a critical gap in using the IMD gridded meteorological dataset (Rainfall and Temperature) in streamflow prediction in an Indian Himalayan catchment (Bhagirathi Catchment), which is limited. A custom transfer function was used to model the hydrological response from each catchment zone to the catchment outlet. The study advances the understanding of hydrological processes in the Himalayan region and contributes to more accurate predictions for effective water resources management. By incorporating these physically meaningful variables, the PIANN framework captures the spatiotemporal variability of catchment hydrological responses.\u0026nbsp;\u003c/p\u003e"},{"header":"2\tStudy Area and Data","content":"\u003ch2\u003e2.1 Study Area\u003c/h2\u003e\n\u003cp\u003eTehri Dam catchment (Bhagirathi River catchment) 7,293 km\u0026sup2; (\u003cstrong\u003eFig. 1\u003c/strong\u003e), encompassing mountainous terrain that includes several snow-covered peaks and glaciers having an area of 2042 km\u0026sup2; (Agarwal et al., 2019). Tehri dam\u0026apos;s gross and live storage capacities are 3540 MCM and 2615 MCM, respectively. It plays a crucial role in hydroelectric power generation, irrigation, and drinking water supply for northern India. Tehri dam is located at the confluence of the Bhagirathi and Bhilangana Rivers in\u0026ensp;Uttarakhand, India. Tehri Dam is an earthen rockfill dam that is 260.5 meters (839.50 meters above MSL) high and has an installed capacity of\u0026ensp;1000 MW. Commissioned in 2006, the dam provides irrigation water to Uttar Pradesh and Uttarakhand and also\u0026ensp;provides drinking water to almost seven million people in these two states.\u0026nbsp;Its flood management system\u0026ensp;consists of three chute spillways (5500 cumecs), two left bank shaft spillways (3650 cumecs) and two ungated spillways (3850 cumecs) to pass the Probable Maximum Flood (PMF) of 15,540 cumecs.\u0026nbsp;The MFL (maximum flood level) of the dam is at 839.50 meters, while FRL (full reservoir level) is at 830\u0026ensp;meters.\u003c/p\u003e\n\u003ch2\u003e2.2 Data\u003c/h2\u003e\n\u003cp\u003eThe present study utilised multiple hydro-meteorological and remote sensing datasets to develop and evaluate the Physically-Informed Artificial Neural Network (PIANN) model for streamflow prediction over the Tehri Dam catchment. Gridded daily rainfall data at a spatial resolution of 0.25\u0026deg; \u0026times; 0.25\u0026deg; were downloaded from\u0026ensp;the India Meteorological Department (IMD) from 2006\u0026ndash;2020 (Pai et al., 2014). This dataset was produced with the help of a dense network of rain gauge stations and interpolated using an objective analysis method, providing spatial coherence and reliability for\u0026ensp;regional-scale hydrological modelling. Daily temperature data at a relatively coarse spatial resolution of 1.0\u0026deg; \u0026times; 1.0\u0026deg; were also obtained from\u0026ensp;IMD for the same period (Srivastava et al., 2009). The temperature database is based on quality-controlled stations, provide important inputs in a catchment for\u0026ensp;snowmelt and evapotranspiration. Moreover, snow cover area (SCA)\u0026ensp;was derived from the MODIS Terra daily SCA climate modelling coverage products with 500 m spatial resolution. The MODIS snow data were analysed, and the snow cover extent were derived for the catchment by GIS\u0026ensp;techniques. Streamflow data at Tehri Dam, which reflects the sum of upstream catchment runoff response, were obtained from Tehri Hydro Development\u0026ensp;Corporation India Ltd. (THDCIL) for the period 2006\u0026ndash;2020. This dataset served as the target variable for model calibration and validation.\u003c/p\u003e"},{"header":"3\tMethodology","content":"\u003ch2\u003e3.1 PI-ANN Model for Short-term (Daily) Streamflow Prediction\u003c/h2\u003e\n\u003cp\u003eThe methodology (\u003cstrong\u003eFig. 2\u003c/strong\u003e)\u003cstrong\u003e\u0026nbsp;\u003c/strong\u003ebegins with data processing, where the catchment is divided into 10 zones for rainfall zoning and five zones for temperature through DEM-based delineation. Rainfall and temperature data are clipped to the extent of each catchment zone, and zonal statistics are performed to obtain representative input values. Snow cover data is extracted to complement hydroclimatic variability. The effective rainfall is calculated using the SCS-CN method, which incorporates land use and soil characteristics and helps represent infiltration-excess runoff more realistically. Lagged streamflow variable is also included as predictors to account for catchment memory effects and autoregressive properties of streamflow systems. These pre-processed and engineered variables are then used to train separate ANN models for each zone, consisting of an input layer (to take climate and spatial variables), a hidden layer with non-linear activation (to capture complex relationships), and an output layer producing predicted discharge. Two modelling scenarios are considered: Case 1 uses rainfall, temperature, snow cover area, and the previous day\u0026apos;s discharge as inputs, enhancing model memory and performance; Case 2 excludes the previous day\u0026apos;s discharge, relying only on rainfall, temperature, and snow cover area. A custom transfer function based on the Muskingum routing method is then applied to simulate the translation and attenuation of flow between upstream and downstream zones, ensuring hydrological consistency across space. The model is calibrated for the year 2006-2016 and validated over the period 2017\u0026ndash;2020, ensuring temporal robustness.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eTo further refine prediction quality, an autoregressive error model is used to correct residuals between observed and simulated streamflow, thereby improving the calibrated and validated output. The final model is evaluated using several widely accepted hydrological performance metrics such as Nash\u0026ndash;Sutcliffe Efficiency (NSE), coefficient of determination (R\u0026sup2;), Root Mean Square Error (RMSE), Mean Absolute Error (MAE), PBIAS, LogNSE, and Skill Score. These allow multi-dimensional assessment of model accuracy, consistency, and bias. One of the key advantages of this methodology lies in its physical interpretability due to the integration of snow cover area and effective rainfall; its spatial representativeness via catchment zoning; and its flexibility and robustness due to the use of lagged discharge and error correction techniques. Moreover, the incorporation of Muskingum routing introduces a hydrologically sound transfer function that respects the flow dynamics within a basin. This framework bridges the gap between physically based and data-driven models, offering a powerful tool for short-term streamflow forecasting, especially in data-scarce or complex terrains such as the Himalayan or snow-fed basins.\u0026nbsp;\u003c/p\u003e\n\u003ch2\u003e3.2 \u0026nbsp;PI-ANN for Extended (10 daily) Streamflow Prediction (ESP)\u003c/h2\u003e\n\u003cp\u003eThe methodology \u003cstrong\u003e(\u003c/strong\u003e\u003cstrong\u003eFig. 3\u003c/strong\u003e\u003cstrong\u003e)\u003c/strong\u003e integrates multisource datasets comprising gridded daily rainfall (0.25\u0026deg; \u0026times; 0.25\u0026deg;) and temperature (1.0\u0026deg; \u0026times; 1.0\u0026deg;) from the India Meteorological Department (IMD), snow cover area from MODIS satellite products, and observed ten-daily streamflow data. The catchment was divided into ten rainfall zones and five temperature zones through GIS-based overlay and zonal statistics. Effective rainfall was estimated using the Soil Conservation Service-Curve Number (SCS-CN) method, and hydrological memory was incorporated by including lagged discharge as a feature. Two PIANN model configurations were tested: Case 1 included climate variables (10 daily rainfall, 10 daily average temperature), remote sensing input (10-day snow cover), and the previous 10 daily streamflow to capture autoregressive dynamics, while Case 2 used only climate (10 daily rainfall, 10 daily average temperature) and remote sensing (10 day snow cover) variables as inputs. Subsequently, a custom transfer function based on the Muskingum routing method was used to propagate discharge from upstream to downstream zones, ensuring physical flow continuity. Model calibration was conducted from 2006-2016, and validation was performed over 2017\u0026ndash;2020. Model performance was\u0026ensp;assessed by NSE and R\u003csup\u003e2\u003c/sup\u003e. The results were post-processed with an autoregressive error model and several accuracy indices such as NSE,\u0026ensp;LogNSE, R\u0026sup2;, RMSE, Skill Score, PBIAS, and MAE. This hybrid approach has resulted in a strong, interpretable, and\u0026ensp;spatially explicit tool for 10 daily streamflow prediction in data-sparse and snow‐influenced mountainous basins.\u003c/p\u003e"},{"header":"4 Results and Discussions","content":"\u003ch2\u003e4.1 Short-term Streamflow Prediction using PI-ANN Model\u0026nbsp;\u003c/h2\u003e\n\u003cp\u003e\u003cstrong\u003e4.1.1 Four variable model (Q\u003csub\u003et-1\u003c/sub\u003e, R\u003csub\u003et\u003c/sub\u003e, T\u003csub\u003et\u003c/sub\u003e, SCA\u003csub\u003et\u003c/sub\u003e)\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eDuring the \u003cstrong\u003ecalibration period\u003c/strong\u003e, the model achieved a high NSE of 0.957 and an R\u003csup\u003e2\u003c/sup\u003e value of \u003cstrong\u003e0.955\u003c/strong\u003e, indicating an excellent match between observed and predicted discharge (\u003cstrong\u003eFig. 4\u003c/strong\u003e). The hydrograph shows that the model accurately captures both the \u003cstrong\u003etiming and magnitude of peak flows\u003c/strong\u003e as well as \u003cstrong\u003ebaseflow conditions\u003c/strong\u003e, highlighting the model\u0026rsquo;s ability to replicate intra-annual and inter-annual variability. In extreme flow years (e.g., 2013\u0026ndash;2014) the predicted peaks well reproduce the\u0026ensp;observed ones showing the model ability in generalising non-linear hydrological responses. The model performed well also\u0026ensp;in the validation period, NSE = 0.939, R\u003csup\u003e2\u003c/sup\u003e = 0.940 (\u003cstrong\u003eFig. 5\u003c/strong\u003e). It means that the model predictions are so close to the observed flows, even in the independent validation phase, suggesting the good generalisation capability and not overfitting, an important property of reliable\u0026ensp;streamflow models (Zhang, 2024; Deng et al., 2024). A significant improvement in the model performance was due to the incorporation of the discharge at the previous time step as an input variable, serving as a memory term (Adamowski \u0026amp; Karapataki, 2010; Mosavi et al., 2018; Ni et al., 2020). This autoregressive input helps the model identify delayed runoff, storage effects, and baseflow contributions\u0026ensp;that are not purely dependent on the meteorological inputs (Bhasme et al., 2022; Lu et al., 2021). Especially during base flow, the new input increases continuity and decreases the fluctuations\u0026ensp;of the predicted discharge, leading to more accurate results for both the dry and wet seasons. The findings also suggest that the model is capable to perform very well in low-flow periods, remaining near to the observed values without any over-prediction which is frequent issue\u0026ensp;in ML-based models (Zahmatkesh, Karamouz, \u0026amp; Nazif, 2015; Sit \u0026amp; Demir, 2019). In the same way, the model also simulates relatively extreme flow events successfully, where sudden peaks are close to observed peaks, this suggests that inclusion of physically meaningful variables (especially rainfall and temperature) allows the network to learn\u0026ensp;and simulate unexpected hydrological responses (Parisouj et al., 2022).\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003e4.1.2 Three variable model (R\u003csub\u003et\u003c/sub\u003e, T\u003csub\u003et\u003c/sub\u003e, SCA\u003csub\u003et\u003c/sub\u003e)\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe performance during the \u003cstrong\u003ecalibration period\u0026nbsp;\u003c/strong\u003eyielded a NSE of \u003cstrong\u003e0.837\u003c/strong\u003e and a R\u003csup\u003e2\u003c/sup\u003e of \u003cstrong\u003e0.845 (\u003c/strong\u003e\u003cstrong\u003eFig. 6\u003c/strong\u003e\u003cstrong\u003e)\u003c/strong\u003e, indicating a reasonably good fit between observed and predicted streamflow. However, during the \u003cstrong\u003evalidation period\u0026nbsp;\u003c/strong\u003emodel performance dropped, with NSE and R\u003csup\u003e2\u003c/sup\u003e values declining to \u003cstrong\u003e0.734\u003c/strong\u003e and \u003cstrong\u003e0.753\u003c/strong\u003e, respectively (\u003cstrong\u003eFig. 7\u003c/strong\u003e). These results suggest that while the model can capture general flow patterns, its ability to generalize across time is \u003cstrong\u003emoderate\u003c/strong\u003e, and the \u003cstrong\u003eaccuracy is average\u003c/strong\u003e compared to more robust configurations that include hydrological memory. A noticeable limitation in this model is the \u003cstrong\u003elag in peak timing\u003c/strong\u003e, where the model consistently \u003cstrong\u003edelays the occurrence of peak flows\u003c/strong\u003e compared to observed streamflow. This time lag may be attributed to the absence of \u003cstrong\u003eprevious time step discharge\u003c/strong\u003e as an input. In hydrological systems, past flow values carry important memory about soil saturation, baseflow, and delayed runoff, which rainfall and temperature alone cannot explain (Lu et al., 2021; Bhasme et al., 2022). The \u003cstrong\u003emismatch of peak magnitudes\u003c/strong\u003e further indicates that the model struggles to learn rapid, nonlinear runoff generation mechanisms, particularly during extreme rainfall or snowmelt events. In \u003cstrong\u003elow-flow conditions\u003c/strong\u003e, the model tends to \u003cstrong\u003eunderpredict\u003c/strong\u003e, which can be attributed to the lack of temporal continuity in the inputs. Without the memory provided by lagged streamflow, the model cannot accurately account for \u003cstrong\u003egroundwater contributions\u003c/strong\u003e or \u003cstrong\u003ebaseflow recession\u003c/strong\u003e curves. During \u003cstrong\u003ehigh-flow periods\u003c/strong\u003e, such as monsoonal peak floods, the model shows \u003cstrong\u003einconsistent performance\u003c/strong\u003e, either \u003cstrong\u003eunderestimating or delaying peaks\u003c/strong\u003e. This is particularly evident in snow-dominated catchments, where the \u003cstrong\u003etiming and volume of meltwater\u003c/strong\u003e depend not only on temperature and snow cover but also on accumulated storage from prior days, which the current model setup lacks. Without Q\u003csub\u003et-1\u003c/sub\u003e, the model has to infer the influence of antecedent conditions indirectly, leading to greater uncertainty in predictions, especially during transitional periods (e.g., shifts between wet and dry seasons).\u003c/p\u003e\n\u003cp\u003eWithout Q\u003csub\u003et-1\u003c/sub\u003e, the model becomes highly dependent on rainfall, temperature, and snow cover data. Any inaccuracies or uncertainties in these inputs are amplified in the prediction, resulting in less reliable outcomes. \u0026nbsp;\u003c/p\u003e\n\u003cp\u003eIn the context of daily streamflow prediction using a \u003cstrong\u003ephysically informed ANN model\u003c/strong\u003e, the results not only demonstrate high predictive accuracy but also reflect strong \u003cstrong\u003ephysical consistency and hydrological plausibility\u003c/strong\u003e. The model successfully replicates seasonal streamflow dynamics characteristic of a \u003cstrong\u003esnow and glacier-fed Himalayan catchment\u003c/strong\u003e, where flow peaks are dominantly driven by a combination of monsoonal rainfall and snowmelt contributions. The predicted hydrographs align well with the observed timing and magnitude of flow events, particularly capturing the gradual rise during the pre-monsoon snowmelt season and sharp peaks during monsoon rainfall, thus adhering to the \u003cstrong\u003enatural hydrological cycle\u003c/strong\u003e\u003cstrong\u003e.\u003c/strong\u003e This alignment underscores the model\u0026apos;s ability to simulate \u003cstrong\u003ephysically meaningful streamflow responses\u003c/strong\u003e, not just statistical fitting.\u003c/p\u003e\n\u003cp\u003eFrom a \u003cstrong\u003espatial and climatic context\u003c/strong\u003e, the incorporation of snow cover area (SCA\u003csub\u003et\u003c/sub\u003e) and temperature (T\u003csub\u003et\u003c/sub\u003e) as inputs enhances the model\u0026apos;s capability in cold and complex terrains like the Himalayas. These inputs are especially critical in regions where snowmelt substantially contributes to river discharge, and their inclusion enables the PIANN to better capture \u003cstrong\u003eseasonal lags and flow magnitude variations\u003c/strong\u003e.\u003c/p\u003e\n\u003cp\u003eThe\u0026ensp;model performance indicates that factors such as previous discharge (Q\u003csub\u003et-1\u003c/sub\u003e) and snow cover area (SCA\u003csub\u003et\u003c/sub\u003e) are determinants. Q\u003csub\u003et-1\u003c/sub\u003e would help to preserve a certain temporal continuity and flow memory, while SCA\u003csub\u003et\u003c/sub\u003e better represents\u0026ensp;remote sensing related dynamics that are important in these river basins. Temperature has a double effect by conditioning snowmelt rates and evapotranspiration and rainfalls directly induce runoff events, therefore the union of these four variables is physically\u0026ensp;and statistically significant.\u003c/p\u003e\n\u003cp\u003eNevertheless, some uncertainties and limitations should also be\u0026ensp;noted. The use of gridded or remotely sensed data (e.g., SCA\u003csub\u003et\u003c/sub\u003e from MODIS) carries potential errors by way\u0026ensp;of cloud contamination, resolution, or misclassification. Furthermore, while the ANN can model the nonlinear relations on the other hand, its black-box\u0026ensp;type reduces the interpretative and extrapolatory abilities especially under the extreme or a non-stationary climate context. There may also be scale differences between forcing data and the catchment\u0026apos;s hydrological response, that could influence the prediction\u0026ensp;accuracy in certain events.\u003c/p\u003e\n\u003ch2\u003e4.2 Extended (Ten Daily) Streamflow Prediction Using PIANN Model\u003c/h2\u003e\n\u003cp\u003e\u003cstrong\u003e4.2.1 Four variable Model (Q\u003csub\u003et-1\u003c/sub\u003e, R\u003csub\u003et\u003c/sub\u003e, T\u003csub\u003et\u003c/sub\u003e, SCA\u003csub\u003et\u003c/sub\u003e)\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe model achieved a \u003cstrong\u003eNSE of 0.969\u003c/strong\u003e\u003cstrong\u003e\u0026nbsp;\u003c/strong\u003eand a\u003cstrong\u003e\u0026nbsp;\u003cstrong\u003eR\u0026sup2; of 0.973\u0026nbsp;\u003c/strong\u003e\u003c/strong\u003eduring the \u003cstrong\u003ecalibration period (\u003c/strong\u003e\u003cstrong\u003eFig. 8\u003c/strong\u003e\u003cstrong\u003e)\u003c/strong\u003e\u003cstrong\u003e,\u003c/strong\u003e indicating excellent agreement between observed and predicted streamflow values. The hydrograph comparison shows that the predicted flows closely match the observed hydrographs, capturing both peak and low-flow events effectively. Notably, the model successfully replicates the seasonal variability, especially during the monsoon season, demonstrating its sensitivity to the climatic inputs. The scatter plot confirms signifying minimal bias in prediction. In the \u003cstrong\u003evalidation period\u003c/strong\u003e, the model maintains a high prediction performance with an \u003cstrong\u003eNSE of 0.954\u003c/strong\u003e and \u003cstrong\u003eR\u0026sup2; of 0.966\u003c/strong\u003e, which confirms the model\u0026apos;s generalizability and robustness (\u003cstrong\u003eFig. 9\u003c/strong\u003e). The hydrograph comparison again reveals that the model adequately captures the magnitude, timing, and pattern of flow peaks. The scatter plot continues to show a strong correlation between observed and simulated flows, reaffirming the predictive skill of the model.\u003c/p\u003e\n\u003cp\u003eThe high NSE and R\u0026sup2; values in both calibration and validation phases indicate that the model effectively leverages the selected predictors to capture the underlying hydrological processes governing streamflow in the Himalayan catchment. The inclusion of snow cover area (SCA\u003csub\u003et\u003c/sub\u003e) appears particularly valuable for this snow-glacier-fed basin, contributing to better simulation of spring-summer flows driven by snowmelt. Similarly, previous discharge (Q\u003csub\u003et-1\u003c/sub\u003e) contributes to preserving temporal continuity in flow dynamics, enhancing the model\u0026rsquo;s memory and improving lagged predictions. Overall, the model performs well across a 10-daily temporal resolution, which is suitable for extended-range water resource planning and hydrological applications such as reservoir operation and flood forecasting in data-scarce, mountainous regions.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003e4.2.2 Three\u0026nbsp;\u003c/strong\u003e\u003cstrong\u003evariable model (R\u003csub\u003et\u003c/sub\u003e, T\u003csub\u003et\u003c/sub\u003e, SCA\u003csub\u003et\u003c/sub\u003e)\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe model accuracy is slightly reduced in comparison to the four-variable model that included previous discharge (Q\u003csub\u003et-1\u003c/sub\u003e). During the \u003cstrong\u003ecalibration period\u003c/strong\u003e, the model achieved a \u003cstrong\u003eNSE of 0.901\u003c/strong\u003e and an \u003cstrong\u003eR\u0026sup2; of 0.914\u003c/strong\u003e, indicating very good agreement between observed and predicted streamflow. The model effectively captures the seasonal flow dynamics, particularly the rise and recession patterns associated with snowmelt in spring and monsoon rainfall in summer. The performance is slightly lower than the four-variable case, likely due to the absence of Q\u003csub\u003et-1\u003c/sub\u003e, which serves as a memory component capturing baseflow persistence and flow continuity. Interestingly, in the \u003cstrong\u003evalidation period\u003c/strong\u003e, the model maintains and even slightly improves performance with an \u003cstrong\u003eNSE of 0.915\u003c/strong\u003e\u003cstrong\u003e\u0026nbsp;\u003c/strong\u003eand\u003cstrong\u003e\u0026nbsp;\u003cstrong\u003eR\u0026sup2; of 0.921\u003c/strong\u003e\u003c/strong\u003e. This indicates good generalization capability and model robustness under varying hydro-meteorological conditions, despite the reduced input dimensionality.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eThe slight increase in validation accuracy may be attributed to the dominant influence of snow and rainfall in those years, where lagged memory may have played a lesser role compared to the physical drivers. The results also support the \u003cstrong\u003ephysical consistency\u003c/strong\u003e of the model. The inclusion of SCA\u003csub\u003et\u003c/sub\u003e and temperature allows the model to simulate snowmelt-driven contributions, while rainfall serves as a direct runoff driver. This three-variable setup still enables the ANN to reflect \u003cstrong\u003eseasonal hydrologic behavior\u003c/strong\u003e typical of snow-dominated Himalayan catchments\u0026mdash;i.e., snowmelt-induced flow in pre-monsoon and high-flow peaks during monsoon months. From a \u003cstrong\u003espatial and climatic perspective\u003c/strong\u003e, this configuration is highly relevant for glacier-fed basins where snow and temperature are key hydrological drivers. The use of a \u003cstrong\u003e10-daily temporal resolution\u003c/strong\u003e remains appropriate, balancing responsiveness to climatic inputs and smoothing out short-term fluctuations. However, the absence of Q\u003csub\u003et-1\u003c/sub\u003e slightly limits the model\u0026rsquo;s ability to simulate \u003cstrong\u003eflow memory and autocorrelation\u003c/strong\u003e, especially during dry periods or in capturing recession limbs of hydrographs. This underscores the importance of \u003cstrong\u003elagged discharge as a performance-enhancing variable\u003c/strong\u003e, particularly in PIANN models that benefit from temporal dependencies. Overall, the three-variable model still performs well, making it suitable for applications like \u003cstrong\u003estreamflow forecasting\u003c/strong\u003e\u003cstrong\u003e, \u003cstrong\u003eclimate change impact assessment\u003c/strong\u003e\u003c/strong\u003e, and\u003cstrong\u003e\u0026nbsp;\u003cstrong\u003ewater resource management\u003c/strong\u003e\u003c/strong\u003e in data-scarce regions. Its simplicity offers \u003cstrong\u003ecomputational efficiency\u003c/strong\u003e\u003cstrong\u003e\u0026nbsp;\u003c/strong\u003eand interpretability while maintaining \u003cstrong\u003estrong predictive accuracy\u003c/strong\u003e rooted in physically meaningful inputs.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eThis setup may be particularly useful when discharge observations are missing, or unreliable but climate and remote sensing data are available. The physically informed ANN model produced streamflow predictions that are \u003cstrong\u003ephysically consistent and hydrologically realistic\u003c/strong\u003e at a 10-daily temporal resolution. The model successfully captured the seasonal hydrological cycle, with high flows coinciding with monsoon rainfall and snowmelt periods, and low flows during the dry winter season. This alignment reflects an appropriate simulation of \u003cstrong\u003esnowmelt-induced discharge peaks during late spring and early summer\u003c/strong\u003e, and rainfall-driven peaks during the monsoon months, indicating that the model\u0026rsquo;s outputs conform to the known hydrological behavior of Himalayan catchments. Given the \u003cstrong\u003eglacier-fed and snow-dominated characteristics of the study basin\u003c/strong\u003e\u003cstrong\u003e,\u003c/strong\u003e the inclusion of \u003cstrong\u003etemperature (T\u003csub\u003et\u003c/sub\u003e)\u003c/strong\u003e and \u003cstrong\u003esnow cover area (SCA\u003csub\u003et\u003c/sub\u003e)\u003c/strong\u003e as inputs significantly enhanced model responsiveness to snow accumulation and melt processes. The 10-daily time step proved optimal in balancing temporal detail with data availability, effectively smoothing short-term fluctuations while still capturing seasonal dynamics.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eThe model\u0026rsquo;s \u003cstrong\u003esensitivity to physical inputs\u003c/strong\u003e\u003cstrong\u003e\u0026nbsp;\u003c/strong\u003ewas evident, with \u003cstrong\u003eprevious discharge (Q\u003csub\u003et-1\u003c/sub\u003e)\u003c/strong\u003e and \u003cstrong\u003eSCA\u003csub\u003et\u003c/sub\u003e\u003c/strong\u003e\u003cstrong\u003e\u0026nbsp;\u003c/strong\u003eemerging as dominant predictors. Q\u003csub\u003et-1\u003c/sub\u003e included a memory term essential for maintaining flow continuity, whereas SCA\u003csub\u003et\u003c/sub\u003e reproduced the timing\u0026ensp;and amplitude of snowmelt-driven flows more accurately. Rainfall (R\u003csub\u003et\u003c/sub\u003e) and temperature (T\u003csub\u003et\u003c/sub\u003e)\u0026ensp;were further climatic forcing required to capture the dynamics for rain and meltwater contributions. However, some uncertainties are expected despite the strong statistical performance due to possible errors associated with\u0026ensp;the satellite-sensed SCAt and the gridded climatic inputs. Furthermore, the\u0026ensp;black-box nature of the ANN prevents its interpretability and can hinder extrapolation under new climate or land cover situations.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eNevertheless, the results affirm the model\u0026rsquo;s applicability for \u003cstrong\u003eextended-range prediction, flood and drought monitoring, and reservoir operation planning\u003c/strong\u003e. Furthermore, the model architecture\u0026mdash;being physically informed\u0026mdash;offers a promising foundation for future \u003cstrong\u003eclimate change impact studies\u003c/strong\u003e, especially when driven by downscaled projections from CMIP6-based SSP scenarios. Finally, this ANN framework could be integrated with \u003cstrong\u003econceptual or process-based hydrological models\u003c/strong\u003e to develop hybrid tools that combine data-driven flexibility with physical realism, suitable for complex mountainous basins under changing hydro-climatic regimes. Using PIANN for Extended Range (Ten-Daily), Streamflow Prediction benefits flood susceptibility assessment, flood risk potential evaluation, and watershed management strategies. The ability\u0026ensp;to predict changes in streamflow over 10 days improves reservoir operations, irrigation planning, and flood early warning systems. Extended-range prediction in the context of the Tehri Dam is significant for optimizing hydropower generation, water supply, and flood control.\u0026nbsp;\u003c/p\u003e\n\u003ch2\u003e4.3 Error Model\u003c/h2\u003e\n\u003cp\u003e\u003cstrong\u003e4.3.1 Error model for daily and extended range streamflow prediction model\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eError models play a crucial role in improving the reliability of streamflow predictions by accounting for the temporal dependency often observed in model residuals. In streamflow modelling, residuals are rarely purely random; instead, they frequently exhibit autocorrelation due to unmodelled processes, input data errors, or model structure limitations (Beven, 2001; Kleme\u0026scaron;, 1986). Ignoring this autocorrelation can lead to biased parameter estimation and overconfident predictions. Auto regressive error models, explicitly capture these dependencies, enabling more accurate representation of uncertainty. By incorporating the memory effect of past errors, these models help refine both short-term and extended range predictions. This is particularly important in flood forecasting and water resources management, where prediction accuracy is critical. Overall, it provides a more robust framework for streamflow prediction under uncertainty.\u003c/p\u003e\n\u003cp\u003eTable 1 AR Error model results for daily streamflow prediction model\u003c/p\u003e\n\u003cdiv align=\"\"\u003e\n \u003ctable border=\"0\" cellspacing=\"0\" cellpadding=\"0\" width=\"532\"\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd rowspan=\"2\" style=\"width: 157px;\"\u003e\n \u003cp\u003e\u003cstrong\u003ePerformance Parameters\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd colspan=\"2\" style=\"width: 195px;\"\u003e\n \u003cp\u003e\u003cstrong\u003eObserved and Predicted Discharge Series\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd colspan=\"2\" style=\"width: 180px;\"\u003e\n \u003cp\u003e\u003cstrong\u003eAfter Error Model Implication\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd style=\"width: 100px;\"\u003e\n \u003cp\u003e\u003cstrong\u003eCalibration\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 94px;\"\u003e\n \u003cp\u003e\u003cstrong\u003eValidation\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 93px;\"\u003e\n \u003cp\u003e\u003cstrong\u003eCalibration\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 87px;\"\u003e\n \u003cp\u003e\u003cstrong\u003eValidation\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"bottom\" style=\"width: 157px;\"\u003e\n \u003cp\u003e\u003cstrong\u003eAR (2) Coefficient (a\u003csub\u003e1\u003c/sub\u003e)\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"bottom\" style=\"width: 100px;\"\u003e\n \u003cp\u003e-\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"bottom\" style=\"width: 94px;\"\u003e\n \u003cp\u003e-\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"bottom\" style=\"width: 93px;\"\u003e\n \u003cp\u003e0.68\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"bottom\" style=\"width: 87px;\"\u003e\n \u003cp\u003e0.68\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"bottom\" style=\"width: 157px;\"\u003e\n \u003cp\u003e\u003cstrong\u003eAR (2) Coefficient (b\u003csub\u003e1\u003c/sub\u003e)\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"bottom\" style=\"width: 100px;\"\u003e\n \u003cp\u003e-\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"bottom\" style=\"width: 94px;\"\u003e\n \u003cp\u003e-\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"bottom\" style=\"width: 93px;\"\u003e\n \u003cp\u003e-0.23\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"bottom\" style=\"width: 87px;\"\u003e\n \u003cp\u003e-0.23\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"bottom\" style=\"width: 157px;\"\u003e\n \u003cp\u003e\u003cstrong\u003eNSE\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"bottom\" style=\"width: 100px;\"\u003e\n \u003cp\u003e0.957\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"bottom\" style=\"width: 94px;\"\u003e\n \u003cp\u003e0.9402\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"bottom\" style=\"width: 93px;\"\u003e\n \u003cp\u003e0.958\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"bottom\" style=\"width: 87px;\"\u003e\n \u003cp\u003e0.901\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"bottom\" style=\"width: 157px;\"\u003e\n \u003cp\u003e\u003cstrong\u003eR\u003csup\u003e2\u003c/sup\u003e\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"bottom\" style=\"width: 100px;\"\u003e\n \u003cp\u003e0.9577\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"bottom\" style=\"width: 94px;\"\u003e\n \u003cp\u003e0.9405\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"bottom\" style=\"width: 93px;\"\u003e\n \u003cp\u003e0.9748\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"bottom\" style=\"width: 87px;\"\u003e\n \u003cp\u003e0.946\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"bottom\" style=\"width: 157px;\"\u003e\n \u003cp\u003e\u003cstrong\u003eLogNSE\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"bottom\" style=\"width: 100px;\"\u003e\n \u003cp\u003e0.921\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"bottom\" style=\"width: 94px;\"\u003e\n \u003cp\u003e0.9038\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"bottom\" style=\"width: 93px;\"\u003e\n \u003cp\u003e0.923\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"bottom\" style=\"width: 87px;\"\u003e\n \u003cp\u003e0.880\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"bottom\" style=\"width: 157px;\"\u003e\n \u003cp\u003e\u003cstrong\u003eSkill Score\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"bottom\" style=\"width: 100px;\"\u003e\n \u003cp\u003e0.957\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"bottom\" style=\"width: 94px;\"\u003e\n \u003cp\u003e0.941\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"bottom\" style=\"width: 93px;\"\u003e\n \u003cp\u003e0.959\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"bottom\" style=\"width: 87px;\"\u003e\n \u003cp\u003e0.948\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"bottom\" style=\"width: 157px;\"\u003e\n \u003cp\u003e\u003cstrong\u003eRMSE\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"bottom\" style=\"width: 100px;\"\u003e\n \u003cp\u003e59.977\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"bottom\" style=\"width: 94px;\"\u003e\n \u003cp\u003e61.899\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"bottom\" style=\"width: 93px;\"\u003e\n \u003cp\u003e59.315\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"bottom\" style=\"width: 87px;\"\u003e\n \u003cp\u003e79.47\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"bottom\" style=\"width: 157px;\"\u003e\n \u003cp\u003e\u003cstrong\u003ePBIAS\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"bottom\" style=\"width: 100px;\"\u003e\n \u003cp\u003e-0.0030\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"bottom\" style=\"width: 94px;\"\u003e\n \u003cp\u003e-0.71\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"bottom\" style=\"width: 93px;\"\u003e\n \u003cp\u003e-0.0086\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"bottom\" style=\"width: 87px;\"\u003e\n \u003cp\u003e-0.394\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"bottom\" style=\"width: 157px;\"\u003e\n \u003cp\u003e\u003cstrong\u003eMAE\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"bottom\" style=\"width: 100px;\"\u003e\n \u003cp\u003e32.75\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"bottom\" style=\"width: 94px;\"\u003e\n \u003cp\u003e33.205\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"bottom\" style=\"width: 93px;\"\u003e\n \u003cp\u003e32.470\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"bottom\" style=\"width: 87px;\"\u003e\n \u003cp\u003e40.923\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n \u003c/table\u003e\n\u003c/div\u003e\n\u003cp\u003e\u003cstrong\u003eTable 1\u003c/strong\u003e\u003cstrong\u003e\u0026nbsp;\u003c/strong\u003epresents the performance evaluation matrix of a daily streamflow prediction model before and after applying an Autoregressive (AR) error model. The AR (2) model coefficients are 0.68 and -0.23, respectively, indicating a significant temporal correlation in the residuals. After the AR model application, slight improvements are observed in the calibration phase for NSE (from 0.957 to 0.958), R\u0026sup2; (from 0.9577 to 0.9748), and Skill Score (from 0.957 to 0.959), showing that the error model enhances the model\u0026apos;s ability to capture streamflow variability but to a very low extent. However, during the validation phase, the NSE and LogNSE values slightly decline, suggesting reduced generalization. RMSE and MAE increase noticeably in validation (RMSE from 61.899 to 79.47 and MAE from 33.205 to 40.923), highlighting potential overfitting. Although PBIAS remains low across all cases, the larger prediction error during validation suggests that the AR model may be too closely fitted to the calibration data. The overall results emphasize that while autoregressive error modelling improves the model fit during calibration, careful validation is essential to ensure robustness. It also reflects the importance of handling residual autocorrelation to improve model credibility. Therefore, combining AR models with prediction techniques helps to improve validation performance but to a very low extent.\u003c/p\u003e\n\u003cp\u003eTable 2 AR error Model results for ten daily streamflow prediction model\u003c/p\u003e\n\u003cdiv align=\"\"\u003e\n \u003ctable border=\"0\" cellspacing=\"0\" cellpadding=\"0\" width=\"567\"\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd rowspan=\"2\" style=\"width: 157px;\"\u003e\n \u003cp\u003e\u003cstrong\u003ePerformance Parameters\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd colspan=\"2\" style=\"width: 230px;\"\u003e\n \u003cp\u003e\u003cstrong\u003eObserved and Predicted Discharge Series\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd colspan=\"2\" style=\"width: 180px;\"\u003e\n \u003cp\u003e\u003cstrong\u003eAfter Error Model Implication\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd style=\"width: 100px;\"\u003e\n \u003cp\u003e\u003cstrong\u003eCalibration\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 130px;\"\u003e\n \u003cp\u003e\u003cstrong\u003eValidation\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 93px;\"\u003e\n \u003cp\u003e\u003cstrong\u003eCalibration\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 87px;\"\u003e\n \u003cp\u003e\u003cstrong\u003eValidation\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd style=\"width: 157px;\"\u003e\n \u003cp\u003e\u003cstrong\u003eAR (2) Coefficient (a\u003csub\u003e1\u003c/sub\u003e)\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 100px;\"\u003e\n \u003cp\u003e-\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 130px;\"\u003e\n \u003cp\u003e-\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 93px;\"\u003e\n \u003cp\u003e0.0482\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 87px;\"\u003e\n \u003cp\u003e0.0482\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd style=\"width: 157px;\"\u003e\n \u003cp\u003e\u003cstrong\u003eAR (2) Coefficient (b\u003csub\u003e1\u003c/sub\u003e)\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 100px;\"\u003e\n \u003cp\u003e-\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 130px;\"\u003e\n \u003cp\u003e-\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 93px;\"\u003e\n \u003cp\u003e0.0494\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 87px;\"\u003e\n \u003cp\u003e0.0494\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd style=\"width: 157px;\"\u003e\n \u003cp\u003e\u003cstrong\u003eNSE\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 100px;\"\u003e\n \u003cp\u003e0.974\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 130px;\"\u003e\n \u003cp\u003e0.964\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 93px;\"\u003e\n \u003cp\u003e0.973\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 87px;\"\u003e\n \u003cp\u003e0.963\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd style=\"width: 157px;\"\u003e\n \u003cp\u003e\u003cstrong\u003eR\u003csup\u003e2\u003c/sup\u003e\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 100px;\"\u003e\n \u003cp\u003e0.9846\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 130px;\"\u003e\n \u003cp\u003e0.9812\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 93px;\"\u003e\n \u003cp\u003e0.9847\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 87px;\"\u003e\n \u003cp\u003e0.9809\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd style=\"width: 157px;\"\u003e\n \u003cp\u003e\u003cstrong\u003eLogNSE\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 100px;\"\u003e\n \u003cp\u003e0.967\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 130px;\"\u003e\n \u003cp\u003e0.948\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 93px;\"\u003e\n \u003cp\u003e0.968\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 87px;\"\u003e\n \u003cp\u003e0.951\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd style=\"width: 157px;\"\u003e\n \u003cp\u003e\u003cstrong\u003eSkill Score\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 100px;\"\u003e\n \u003cp\u003e0.973\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 130px;\"\u003e\n \u003cp\u003e0.9658\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 93px;\"\u003e\n \u003cp\u003e0.9771\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 87px;\"\u003e\n \u003cp\u003e0.9693\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd style=\"width: 157px;\"\u003e\n \u003cp\u003e\u003cstrong\u003eRMSE\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 100px;\"\u003e\n \u003cp\u003e44.299\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 130px;\"\u003e\n \u003cp\u003e45.293\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 93px;\"\u003e\n \u003cp\u003e44.184\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 87px;\"\u003e\n \u003cp\u003e45.829\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd style=\"width: 157px;\"\u003e\n \u003cp\u003e\u003cstrong\u003ePBIAS\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 100px;\"\u003e\n \u003cp\u003e0.2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 130px;\"\u003e\n \u003cp\u003e\u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp;2.7\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 93px;\"\u003e\n \u003cp\u003e0.018\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 87px;\"\u003e\n \u003cp\u003e2.4\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd style=\"width: 157px;\"\u003e\n \u003cp\u003e\u003cstrong\u003eMAE\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 100px;\"\u003e\n \u003cp\u003e26.548\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 130px;\"\u003e\n \u003cp\u003e29.329\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 93px;\"\u003e\n \u003cp\u003e26.264\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 87px;\"\u003e\n \u003cp\u003e29.415\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n \u003c/table\u003e\n\u003c/div\u003e\n\u003cp\u003e\u003cstrong\u003eTable 2\u003c/strong\u003e\u003cstrong\u003e\u0026nbsp;\u003c/strong\u003epresents performance metrics for ten-daily (ANN) streamflow predictions before and after applying an Autoregressive (AR) error model. The AR (2) model coefficients are 0.0494 and 0.0482, indicating mild but notable temporal autocorrelation in the residuals, validating the need for an autoregressive correction. During calibration, performance remains nearly identical before and after applying the AR model. NSE slightly drops from 0.974 to 0.973, while R\u0026sup2; remains stable at around 0.9846\u0026ndash;0.9847. Metrics such as LogNSE, Skill Score, RMSE, and MAE also show only marginal changes, suggesting that the original model already had a strong fit. In the validation phase, similar trends are observed. The NSE shows a negligible decrease from 0.964 to 0.963, and R\u0026sup2; slightly improves from 0.9812 to 0.9809, indicating the autoregressive model maintains the strength of the original model\u0026rsquo;s performance. RMSE and MAE slightly increase, from 45.293 to 45.829 and 29.329 to 29.415, respectively, but remain within acceptable bounds. Importantly, PBIAS decreases from 2.7 to 2.4 after error modelling, reflecting a reduction in systematic bias. The error analysis indicates that the inclusion of the error model has a negligible impact on the overall predictive accuracy, suggesting that the model\u0026apos;s performance remains largely unaffected by its application.\u0026nbsp;\u003c/p\u003e"},{"header":"5 Conclusion","content":"\u003cp\u003eThis study developed and evaluated a Physically Informed Artificial Neural Network (PIANN) model for streamflow prediction at daily and ten-daily timescales in a snow and glacier-fed Himalayan catchment. The results demonstrated that the inclusion of physically meaningful processes in combination with the data driven machine learning models. The analysis shows the effectiveness and robustness in multi temporal streamflow prediction. The study also explains the importance of choosing right variables for a model.\u0026nbsp;PI-ANNs represent a shift toward \u003cstrong\u003etheory-guided data science\u003c/strong\u003e, a paradigm that supports scientific discovery by blending observations, physical theory, and machine learning (Karpatne et al., 2017).\u003c/p\u003e\n\u003cp\u003eA critical finding of this research is the pivotal role of the previous discharge (Q\u003csub\u003et-1\u003c/sub\u003e) as a memory component. Its inclusion allowed the model to capture delayed runoff processes, maintain baseflow continuity, and improve peak timing. These are the key aspects that are often inadequately represented in conventional data-driven models. The SCA\u003csub\u003et\u0026nbsp;\u003c/sub\u003evariable further contributed to improved simulation of snowmelt-driven flows, particularly during pre-monsoon and transitional seasons, enhancing the model\u0026apos;s responsiveness over remote sensing data. The three-variable model, although physically consistent, exhibited limitations in peak timing and low-flow accuracy. The absence of Q\u003csub\u003et-1\u0026nbsp;\u003c/sub\u003eforces the model to rely solely on climatic and remote sensing variables, due to which the model does not fully capture the persistence and lag effects inherent in river flow patterns. This omission leads to a loss of temporal dependencies, but reasonable accuracy of three variable model suggests the usage for streamflow prediction in an ungauged catchment or when the flow data is missing data for some period.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003ePIANN model performed well at reproducing the seasonal and inter-annual\u0026ensp;variations of flow, which indicate a good consistency between the model and the underlying hydrological processes. The inclusion of physically meaningful predictors can improve\u0026ensp;model robustness more under low-flow periods and extreme hydrological conditions (Kratzert et al., 2019; Shen \u0026amp; Lawson, 2021; Zahmatkesh et al., 2015). The\u0026ensp;study also has its own limitations. The use of satellite-based snow cover data and gridded climate inputs could potentially introduce uncertainties related\u0026ensp;to misclassification and resolution mismatch. Additionally, the ANN model\u0026rsquo;s black-box nature limits physical interpretability, particularly under non-stationary conditions. Future work should focus on coupling the PIANN approach with conceptual or process-based hydrological models to improve interpretability and extrapolation under climate change scenarios. Integrating downscaled CMIP6-based projections will further enhance its application in long-term water resource planning and disaster risk reduction in data-scarce, climate-sensitive mountainous regions. PIANN proves to be a robust tool for streamflow prediction, when used with the relevant input data. The study contributes to advancing machine learning applications in hydrology, emphasizing the need for accurate and reliable predictions for sustainable water management.\u0026nbsp;\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003e\u003cstrong\u003eDATA AVAILABILITY STATEMENT\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe relevant information of data is included in the paper. The observed discharge data cannot be shared due to confidentiality issues.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eCONFLICT OF INTEREST\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe authors declare there is no conflict.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eACKNOWLEDGEMENT\u0026nbsp;\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe Authors have acknowledged THDCIL for providing data for the study. We would also like to thank the post-doctoral fellows of International Centre of Excellence for Dams (ICED) for proofreading the manuscript for clarity, language and appropriate presentation of the work. \u0026nbsp;\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\n \u003cli\u003eAbrahart, R.J., Anctil, F., Coulibaly, P., Dawson, C.W., Mount, N.J., See, L.M., Shamseldin, A.Y., Solomatine, D.P., Toth, E. and Wilby, R.L., 2012. Two decades of anarchy? Emerging themes and outstanding challenges for neural network river forecasting. \u003cem\u003eProgress in Physical Geography\u003c/em\u003e, \u003cem\u003e36\u003c/em\u003e(4), pp.480-513.\u003c/li\u003e\n \u003cli\u003eAdamowski, J., \u0026amp; Sun, K. (2010). 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Journal of Computational Physics, 394, pp.56-81.\u003c/li\u003e\n\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":true,"highlight":"","institution":"Indian Institute of Technology Roorkee","isAcceptedByJournal":false,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"Machine Learning, Physically informed Artificial Neural Network, Streamflow Prediction, Himalayan Catchment, Error model","lastPublishedDoi":"10.21203/rs.3.rs-7001048/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-7001048/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003e\u003cem\u003eAccurate streamflow prediction is vital for effective reservoir operation, flood forecasting, and water resource planning, particularly in snow and glacier-fed Himalayan catchments. Existing studies reveal that physically based models (PBMs) often face challenges such as parameter uncertainty, scale mismatches, and the need for extensive calibration. In contrast, data-driven models (DDMs) depend heavily on large datasets and lack integration of physical processes. Addressing these limitations, this study presents a Physically Informed Artificial Neural Network (PIANN) framework that integrates climatic, remote sensing, and hydrological inputs for streamflow prediction at daily and ten-daily time scales in the Tehri Catchment, Indian Himalayas. Two model configurations were evaluated: (i) a four-variable model including rainfall (R\u003c/em\u003e\u003csub\u003e\u003cem\u003et\u003c/em\u003e\u003c/sub\u003e\u003cem\u003e), temperature (T\u003c/em\u003e\u003csub\u003e\u003cem\u003et\u003c/em\u003e\u003c/sub\u003e\u003cem\u003e), snow cover area (SCA\u003c/em\u003e\u003csub\u003e\u003cem\u003et\u003c/em\u003e\u003c/sub\u003e\u003cem\u003e), and previous discharge (Q\u003c/em\u003e\u003csub\u003e\u003cem\u003et-1\u003c/em\u003e\u003c/sub\u003e\u003cem\u003e), and (ii) a three-variable model excluding Q\u003c/em\u003e\u003csub\u003e\u003cem\u003et-1\u003c/em\u003e\u003c/sub\u003e\u003cem\u003e. The short-term (daily) model with four variables achieved high accuracy (NSE = 0.957, R² = 0.955 in calibration; NSE = 0.939, R² = 0.940 in validation), but in three variable model, accuracy is reduced (NSE = 0.837, R² = 0.845 in calibration; NSE = 0.734, R² = 0.753 in validation). The ten-daily model also attained high performance (NSE = 0.969, R² = 0.973 in calibration; NSE = 0.954, R² = 0.966 in validation). Excluding Q\u003c/em\u003e\u003csub\u003e\u003cem\u003et-1\u003c/em\u003e\u003c/sub\u003e\u003cem\u003e reduced model accuracy, underscoring its importance in maintaining flow memory and baseflow continuity. The model consistently captured low- and high-flow events, exhibiting physical plausibility and generalisation across extreme hydrological conditions. Error model analysis showed minimal change in prediction accuracy, indicating the robustness of the original PIANN outputs. This study demonstrates the strength of integrating physical understanding into ANN frameworks, offering a scalable and reliable tool for streamflow prediction in complex, data-scarce mountainous regions.\u003c/em\u003e\u003c/p\u003e","manuscriptTitle":"Performance evaluation of a physically informed ANN machine learning model for short-term and extended-range streamflow prediction in the Himalayan Catchment","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-07-03 07:11:45","doi":"10.21203/rs.3.rs-7001048/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"07df811e-791a-4f32-a1ce-9dac88c15442","owner":[],"postedDate":"July 3rd, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[{"id":50740934,"name":"Hydrology"}],"tags":[],"updatedAt":"2025-07-03T07:11:45+00:00","versionOfRecord":[],"versionCreatedAt":"2025-07-03 07:11:45","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-7001048","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-7001048","identity":"rs-7001048","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}