This research is part of a systematic study of scientific time series. In the last three years, hundreds of papers and over fifty new deep-learning models have been described for time series models. These mainly focus on the key aspect of time dependence, whereas in some scientific time series, the situation is more complex with multiple locations, each location having multiple observed and target time-dependent streams and multiple exogenous (known) properties that are either constant or time-dependent. Here, we analyze the hydrology time series using the CAMELS and Caravan global datasets on catchment rainfall and runoff. Together, these have up to 6 observed streams and up to 209 static parameters defined at each of about 8000 locations. This analysis is fully open source with a Jupyter Notebook running on Google Colab for both an LSTM-based analysis and the data engineering preprocessing. Our goal is to investigate the importance of exogenous data, which we look at using eight different choices on representative hydrology tasks. Increasing the exogenous information significantly improves the data representation, with the mean square error decreasing to 60% of its initial value in the largest dataset examined. We present the initial results of studies of other deep-learning neural network architectures where the approaches that can use the full observed and exogenous observations outperform less flexible methods, including Foundation models. Using the natural annual periodic exogenous time series produces the largest impact, but the static and other periodic exogenous streams are also important. Our analysis is intended to be valuable as an educational resource and benchmark.

Streamflow, vital for water resource management, is governed by complex hydrological systems involving intermediate processes driven by meteorological forces. While deep learning models have achieved state-of-the-art results of streamflow prediction, their end-to-end single-task learning approach often fails to capture the causal relationships within these systems. To address this, we propose Hierarchical Conditional Multi-Task Learning (HCMTL), a hierarchical approach that jointly models soil water and snowpack processes based on their causal connections to streamflow. HCMTL utilizes task embeddings to connect network modules, enhancing flexibility and expressiveness while capturing unobserved processes beyond soil water and snowpack. It also incorporates the Conditional Mini-Batch strategy to improve long time series modeling. We compare HCMTL with five baselines on a global dataset. HCMTL's superior performance across hundreds of drainage basins over extended periods shows that integrating domain-specific causal knowledge into deep learning enhances both prediction accuracy and interpretability. This is essential for advancing our understanding of complex hydrological systems and supporting efficient water resource management to mitigate natural disasters like droughts and floods.

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.

In recent years, climate extremes such as floods have created significant environmental and economic hazards for Australia, causing damage to the environment and economy and losses of human and animal lives. An efficient method of forecasting floods is crucial to limit this damage. Techniques for flood prediction are currently based on hydrological, and hydrodynamic (physically-based) numerical models. Machine learning methods that include deep learning offer certain advantages over conventional physically based approaches, including flexibility and accuracy. Deep learning methods have been promising for predicting small to medium-sized climate extreme events over a short time horizon; however, large flooding events present a critical challenge. We present an ensemble-based machine learning approach that addresses large-scale extreme flooding challenges using a switching mechanism motivated by extreme-value theory for long-short-term-memory (LSTM) deep learning models. We use a multivariate and multi-step time-series prediction approach to predict streamflow for multiple days ahead in the major catchments of Australia. The ensemble framework also employs static information to enrich the time-series information, allowing for regional modelling across catchments. Our results demonstrate enhanced prediction of streamflow extremes, with notable efficacy for large flooding scenarios in the selected Australian catchments. Through comparative analysis, our methodology underscores the potential for deep learning models to revolutionise flood forecasting across diverse regions.

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.

Process-Based Modeling (PBM) and Machine Learning (ML) are often perceived as distinct paradigms in the geosciences. Here we present differentiable geoscientific modeling as a powerful pathway toward dissolving the perceived barrier between them and ushering in a paradigm shift. For decades, PBM offered benefits in interpretability and physical consistency but struggled to efficiently leverage large datasets. ML methods, especially deep networks, presented strong predictive skills yet lacked the ability to answer specific scientific questions. While various methods have been proposed for ML-physics integration, an important underlying theme -- differentiable modeling -- is not sufficiently recognized. Here we outline the concepts, applicability, and significance of differentiable geoscientific modeling (DG). "Differentiable" refers to accurately and efficiently calculating gradients with respect to model variables, critically enabling the learning of high-dimensional unknown relationships. DG refers to a range of methods connecting varying amounts of prior knowledge to neural networks and training them together, capturing a different scope than physics-guided machine learning and emphasizing first principles. Preliminary evidence suggests DG offers better interpretability and causality than ML, improved generalizability and extrapolation capability, and strong potential for knowledge discovery, while approaching the performance of purely data-driven ML. DG models require less training data while scaling favorably in performance and efficiency with increasing amounts of data. With DG, geoscientists may be better able to frame and investigate questions, test hypotheses, and discover unrecognized linkages.

Accurate hydrological understanding and water cycle prediction are crucial for addressing scientific and societal challenges associated with the management of water resources, particularly under the dynamic influence of anthropogenic climate change. Existing reviews predominantly concentrate on the development of machine learning (ML) in this field, yet there is a clear distinction between hydrology and ML as separate paradigms. Here, we introduce physics-aware ML as a transformative approach to overcome the perceived barrier and revolutionize both fields. Specifically, we present a comprehensive review of the physics-aware ML methods, building a structured community (PaML) of existing methodologies that integrate prior physical knowledge or physics-based modeling into ML. We systematically analyze these PaML methodologies with respect to four aspects: physical data-guided ML, physics-informed ML, physics-embedded ML, and physics-aware hybrid learning. PaML facilitates ML-aided hypotheses, accelerating insights from big data and fostering scientific discoveries. We first conduct a systematic review of hydrology in PaML, including rainfall-runoff hydrological processes and hydrodynamic processes, and highlight the most promising and challenging directions for different objectives and PaML methods. Finally, a new PaML-based hydrology platform, termed HydroPML, is released as a foundation for hydrological applications. HydroPML enhances the explainability and causality of ML and lays the groundwork for the digital water cycle's realization. The HydroPML platform is publicly available at https://hydropml.github.io/.

In hydrology, modeling streamflow remains a challenging task due to the limited availability of basin characteristics information such as soil geology and geomorphology. These characteristics may be noisy due to measurement errors or may be missing altogether. To overcome this challenge, we propose a knowledge-guided, probabilistic inverse modeling method for recovering physical characteristics from streamflow and weather data, which are more readily available. We compare our framework with state-of-the-art inverse models for estimating river basin characteristics. We also show that these estimates offer improvement in streamflow modeling as opposed to using the original basin characteristic values. Our inverse model offers 3\% improvement in R$^2$ for the inverse model (basin characteristic estimation) and 6\% for the forward model (streamflow prediction). Our framework also offers improved explainability since it can quantify uncertainty in both the inverse and the forward model. Uncertainty quantification plays a pivotal role in improving the explainability of machine learning models by providing additional insights into the reliability and limitations of model predictions. In our analysis, we assess the quality of the uncertainty estimates. Compared to baseline uncertainty quantification methods, our framework offers 10\% improvement in the dispersion of epistemic uncertainty and 13\% improvement in coverage rate. This information can help stakeholders understand the level of uncertainty associated with the predictions and provide a more comprehensive view of the potential outcomes.

Prediction of dynamic environmental variables in unmonitored sites remains a long-standing challenge for water resources science. The majority of the world's freshwater resources have inadequate monitoring of critical environmental variables needed for management. Yet, the need to have widespread predictions of hydrological variables such as river flow and water quality has become increasingly urgent due to climate and land use change over the past decades, and their associated impacts on water resources. Modern machine learning methods increasingly outperform their process-based and empirical model counterparts for hydrologic time series prediction with their ability to extract information from large, diverse data sets. We review relevant state-of-the art applications of machine learning for streamflow, water quality, and other water resources prediction and discuss opportunities to improve the use of machine learning with emerging methods for incorporating watershed characteristics into deep learning models, transfer learning, and incorporating process knowledge into machine learning models. The analysis here suggests most prior efforts have been focused on deep learning learning frameworks built on many sites for predictions at daily time scales in the United States, but that comparisons between different classes of machine learning methods are few and inadequate. We identify several open questions for time series predictions in unmonitored sites that include incorporating dynamic inputs and site characteristics, mechanistic understanding and spatial context, and explainable AI techniques in modern machine learning frameworks.

You may have heard about the Supreme Court's recent ruling in Sackett v. EPA that the Clean Water Act does not permit the Environmental Protection Agency to regulate the use of wetlands that are not connected at the surface to lakes, rivers and streams. While there's been plenty of analysis of the significant legal flaws in the ruling--which will greatly restrict the ability of the EPA to protect not only wetlands but our entire fresh water system--less has been said about the science undergirding the case. The reality is this: The ruling takes no consideration whatsoever of the science of water. The court ruled that protection under the CWA only applies when wetlands have "a continuous surface connection to bodies that are'waters of the United States' in their own right, so that there is no clear demarcation between'waters' and wetlands." Justice Samuel Alito arrived at this distinction by parsing the wording of the Clean Water Act as passed by Congress in 1972 and amended in 2018--specifically the words "waters of the United States"--and the opinion makes much of this means of arriving at the decision.