Traditional equation-driven hydrological models often struggle to accurately predict streamflow in challenging regional Earth systems like the Tibetan Plateau, while hybrid and existing algorithm-driven models face difficulties in interpreting hydrological behaviors. This work introduces HydroTrace, an algorithm-driven, data-agnostic model that substantially outperforms these approaches, achieving a Nash-Sutcliffe Efficiency of 98% and demonstrating strong generalization on unseen data. Moreover, HydroTrace leverages advanced attention mechanisms to capture spatial-temporal variations and feature-specific impacts, enabling the quantification and spatial resolution of streamflow partitioning as well as the interpretation of hydrological behaviors such as glacier-snow-streamflow interactions and monsoon dynamics. Additionally, a large language model (LLM)-based application allows users to easily understand and apply HydroTrace's insights for practical purposes. These advancements position HydroTrace as a transformative tool in hydrological and broader Earth system modeling, offering enhanced prediction accuracy and interpretability.

Managing resources effectively in uncertain demand, variable availability, and complex governance policies is a significant challenge. This paper presents a paradigmatic framework for addressing these issues in water management scenarios by integrating advanced physical modelling, remote sensing techniques, and Artificial Intelligence algorithms. The proposed approach accurately predicts water availability, estimates demand, and optimizes resource allocation on both short- and long-term basis, combining a comprehensive hydrological model, agronomic crop models for precise demand estimation, and Mixed-Integer Linear Programming for efficient resource distribution. In the study case of the Segura Hydrographic Basin, the approach successfully allocated approximately 642 million cubic meters ($hm^3$) of water over six months, minimizing the deficit to 9.7% of the total estimated demand. The methodology demonstrated significant environmental benefits, reducing CO2 emissions while optimizing resource distribution. This robust solution supports informed decision-making processes, ensuring sustainable water management across diverse contexts. The generalizability of this approach allows its adaptation to other basins, contributing to improved governance and policy implementation on a broader scale. Ultimately, the methodology has been validated and integrated into the operational water management practices in the Segura Hydrographic Basin in Spain.

The application of process-based and data-driven hydrological models is crucial in modern hydrological research, especially for predicting key water cycle variables such as runoff, evapotranspiration (ET), and soil moisture. These models provide a scientific basis for water resource management, flood forecasting, and ecological protection. Process-based models simulate the physical mechanisms of watershed hydrological processes, while data-driven models leverage large datasets and advanced machine learning algorithms. This paper reviewed and compared methods for assessing and enhancing the extrapolability of both model types, discussing their prospects and limitations. Key strategies include the use of leave-one-out cross-validation and similarity-based methods to evaluate model performance in ungauged regions. Deep learning, transfer learning, and domain adaptation techniques are also promising in their potential to improve model predictions in data-sparse and extreme conditions. Interdisciplinary collaboration and continuous algorithmic advancements are also important to strengthen the global applicability and reliability of hydrological models.

The application of Machine Learning (ML) to hydrologic modeling is fledgling. Its applicability to capture the dependencies on watersheds to forecast better within a short period is fascinating. One of the key reasons to adopt ML algorithms over physics-based models is its computational efficiency advantage and flexibility to work with various data sets. The diverse applications, particularly in emergency response and expanding over a large scale, demand the hydrological model in a short time and make researchers adopt data-driven modeling approaches unhesitatingly. In this work, in the era of ML and deep learning (DL), how it can help to improve the overall run time of physics-based model and potential constraints that should be addressed while modeling. This paper covers the opportunities and challenges of adopting ML for hydrological modeling and subsequently how it can help to improve the simulation time of physics-based models and future works that should be addressed.

Current hydrological modeling methods combine data-driven Machine Learning (ML) algorithms and traditional physics-based models to address their respective limitations incorrect parameter estimates from rigid physics-based models and the neglect of physical process constraints by ML algorithms. Despite the accuracy of ML in outcome prediction, the integration of scientific knowledge is crucial for reliable predictions. This study introduces a Physics Informed Machine Learning (PIML) model, which merges the process understanding of conceptual hydrological models with the predictive efficiency of ML algorithms. Applied to the Anandapur sub-catchment, the PIML model demonstrates superior performance in forecasting monthly streamflow and actual evapotranspiration over both standalone conceptual models and ML algorithms, ensuring physical consistency of the outputs. This study replicates the methodologies of Bhasme, P., Vagadiya, J., & Bhatia, U. (2022) from their pivotal work on Physics Informed Machine Learning for hydrological processes, utilizing their shared code and datasets to further explore the predictive capabilities in hydrological modeling.

Estimating spatially distributed hydrological parameters in ungauged catchments poses a challenging regionalization problem and requires imposing spatial constraints given the sparsity of discharge data. A possible approach is to search for a transfer function that quantitatively relates physical descriptors to conceptual model parameters. This paper introduces a Hybrid Data Assimilation and Parameter Regionalization (HDA-PR) approach incorporating learnable regionalization mappings, based on either multivariate regressions or neural networks, into a differentiable hydrological model. It enables the exploitation of heterogeneous datasets across extensive spatio-temporal computational domains within a high-dimensional regionalization context, using accurate adjoint-based gradients. The inverse problem is tackled with a multi-gauge calibration cost function accounting for information from multiple observation sites. HDA-PR was tested on high-resolution, hourly and kilometric regional modeling of two flash-flood-prone areas located in the South of France. In both study areas, the median Nash-Sutcliffe efficiency (NSE) scores ranged from 0.52 to 0.78 at pseudo-ungauged sites over calibration and validation periods. These results highlight a strong regionalization performance of HDA-PR, improving NSE by up to 0.57 compared to the baseline model calibrated with lumped parameters, and achieving a performance comparable to the reference solution obtained with local uniform calibration (median NSE from 0.59 to 0.79). Multiple evaluation metrics based on flood-oriented hydrological signatures are also employed to assess the accuracy and robustness of the approach. The regionalization method is amenable to state-parameter correction from multi-source data over a range of time scales needed for operational data assimilation, and it is adaptable to other differentiable geophysical models.

Regionalization (MPR) method, combining descriptors upscaling Regardless of the improvements made in hydrological and pre-regionalization function in form of multilinear forward models and available data, hydrological calibration regressions, implemented within a spatially distributed remains a challenging ill-posed inverse problem faced with multiscale hydrological model (mHm), has been proposed the equifinality (Beven, 2001) of feasible solutions. Most by Samaniego et al. (2010), and later applied to other gridded calibration approaches aim to estimate spatially uniform model hydrological models in several applicative studies (e.g., parameters for a single gauged catchment, resulting in piecewise Mizukami et al. (2017); Beck et al. (2020)). In all the constant discontinuous parameters fields for adjacent above studies, state of the art optimization algorithms are catchments. Moreover, these calibrated parameter are not used, especially Shuffle Complex Evolution algorithm (SCE) transferable to ungauged locations, which represents the majority (Duan et al., 1992) in Mizukami et al. (2017) or Distributed of the global land surface (Fekete & Vörösmarty, 2007; Evolutionary Algorithms (DEAP) (Fortin et al., 2012) in Beck Hannah et al., 2011).

Current modeling approaches for hydrological modeling often rely on either physics-based or data-science methods, including Machine Learning (ML) algorithms. While physics-based models tend to rigid structure resulting in unrealistic parameter values in certain instances, ML algorithms establish the input-output relationship while ignoring the constraints imposed by well-known physical processes. While there is a notion that the physics model enables better process understanding and ML algorithms exhibit better predictive skills, scientific knowledge that does not add to predictive ability may be deceptive. Hence, there is a need for a hybrid modeling approach to couple ML algorithms and physics-based models in a synergistic manner. Here we develop a Physics Informed Machine Learning (PIML) model that combines the process understanding of conceptual hydrological model with predictive abilities of state-of-the-art ML models. We apply the proposed model to predict the monthly time series of the target (streamflow) and intermediate variables (actual evapotranspiration) in the Narmada river basin in India. Our results show the capability of the PIML model to outperform a purely conceptual model ($abcd$ model) and ML algorithms while ensuring the physical consistency in outputs validated through water balance analysis. The systematic approach for combining conceptual model structure with ML algorithms could be used to improve the predictive accuracy of crucial hydrological processes important for flood risk assessment.

Regional rainfall-runoff modeling is an old but still mostly outstanding problem in Hydrological Sciences. The problem currently is that traditional hydrological models degrade significantly in performance when calibrated for multiple basins together instead of for a single basin alone. In this paper, we propose a novel, data-driven approach using Long Short-Term Memory networks (LSTMs), and demonstrate that under a'big data' paradigm, this is not necessarily the case. By training a single LSTM model on 531 basins from the CAMELS data set using meteorological time series data and static catchment attributes, we were able to significantly improve performance compared to a set of several different hydrological benchmark models. Our proposed approach not only significantly outperforms hydrological models that were calibrated regionally but also achieves better performance than hydrological models that were calibrated for each basin individually. Furthermore, we propose an adaption to the standard LSTM architecture, which we call an Entity-A ware-LSTM (EA-LSTM), that allows for learning, and embedding as a feature layer in a deep learning model, catchment similarities. We show that this learned catchment similarity corresponds well with what we would expect from prior hydrological understanding. 1 Introduction A longstanding problem in the Hydrological Sciences is about how to use one model, or one set of models, to provide spatially continuous hydrological simulations across large areas (e.g., regional, continental, global). This is the so-called regional modeling problem, and the central challenge is about how to extrapolate hydrologic information from one area to another - e.g., from gauged to ungauged watersheds, from instrumented to non-instrumented hillslopes, from areas with flux towers to areas without, etc. (Blöschl and Sivapalan, 1995). Often this is done using ancillary data (e.g.