We present Latent Diffeomorphic Dynamic Mode Decomposition (LDDMD), a new data reduction approach for the analysis of non-linear systems that combines the interpretability of Dynamic Mode Decomposition (DMD) with the predictive power of Recurrent Neural Networks (RNNs). Notably, LDDMD maintains simplicity, which enhances interpretability, while effectively modeling and learning complex non-linear systems with memory, enabling accurate predictions. This is exemplified by its successful application in streamflow prediction.

Data assimilation (DA) enables hydrologic models to update their internal states using near-real-time observations for more accurate forecasts. With deep neural networks like long short-term memory (LSTM), using either lagged observations as inputs (called "data integration") or variational DA has shown success in improving forecasts. However, it is unclear which methods are performant or optimal for physics-informed machine learning ("differentiable") models, which represent only a small amount of physically-meaningful states while using deep networks to supply parameters or missing processes. Here we developed variational DA methods for differentiable models, including optimizing adjusters for just precipitation data, just model internal hydrological states, or both. Our results demonstrated that differentiable streamflow models using the CAMELS dataset can benefit strongly and equivalently from variational DA as LSTM, with one-day lead time median Nash-Sutcliffe efficiency (NSE) elevated from 0.75 to 0.82. The resulting forecast matched or outperformed LSTM with DA in the eastern, northwestern, and central Great Plains regions of the conterminous United States. Both precipitation and state adjusters were needed to achieve these results, with the latter being substantially more effective on its own, and the former adding moderate benefits for high flows. Our DA framework does not need systematic training data and could serve as a practical DA scheme for whole river networks.

This study explores the efficacy of a Transformer model for 120-hour streamflow prediction across 125 diverse locations in Iowa, US. Utilizing data from the preceding 72 hours, including precipitation, evapotranspiration, and discharge values, we developed a generalized model to predict future streamflow. Our approach contrasts with traditional methods that typically rely on location-specific models. We benchmarked the Transformer model's performance against three deep learning models (LSTM, GRU, and Seq2Seq) and the Persistence approach, employing Nash-Sutcliffe Efficiency (NSE), Kling-Gupta Efficiency (KGE), Pearson's r, and Normalized Root Mean Square Error (NRMSE) as metrics. The study reveals the Transformer model's superior performance, maintaining higher median NSE and KGE scores and exhibiting the lowest NRMSE values. This indicates its capability to accurately simulate and predict streamflow, adapting effectively to varying hydrological conditions and geographical variances. Our findings underscore the Transformer model's potential as an advanced tool in hydrological modeling, offering significant improvements over traditional and contemporary approaches.

Predicting the spatiotemporal variation in streamflow along with uncertainty quantification enables decision-making for sustainable management of scarce water resources. Process-based hydrological models (aka physics-based models) are based on physical laws, but using simplifying assumptions which can lead to poor accuracy. Data-driven approaches offer a powerful alternative, but they require large amount of training data and tend to produce predictions that are inconsistent with physical laws. This paper studies a constrained reasoning and learning (CRL) approach where physical laws represented as logical constraints are integrated as a layer in the deep neural network. To address small data setting, we develop a theoretically-grounded training approach to improve the generalization accuracy of deep models. For uncertainty quantification, we combine the synergistic strengths of Gaussian processes (GPs) and deep temporal models (i.e., deep models for time-series forecasting) by passing the learned latent representation as input to a standard distance-based kernel. Experiments on multiple real-world datasets demonstrate the effectiveness of both CRL and GP with deep kernel approaches over strong baseline methods.

Highlights A CNN-LSTM model was developed for time series forecasting of streamflow in Nebraska by combining CNN for spatial data and LSTM for sequence data. A substantial improvement was observed for 66% of the basins for this model compared to the standalone LSTM. This superior performance was achieved just by using gridded precipitation and 2-m temperature as exogenous inputs. Abstract Significant strides have been made in advancing streamflow predictions, notably with the introduction of cutting-edge machine-learning models. Predominantly, Long Short-Term Memories (LSTMs) and Convolution Neural Networks (CNNs) have been widely employed in this domain. While LSTMs are applicable in both rainfall-runoff and time series settings, CNN-LSTMs have primarily been utilized in rainfall-runoff scenarios.

Over the past few decades, the hydrology community has witnessed notable advancements in streamflow prediction, particularly with the introduction of cutting-edge machine-learning algorithms. Recurrent neural networks, especially Long Short-Term Memory (LSTM) networks, have become popular due to their capacity to create precise forecasts and realistically mimic the system dynamics. Attention-based models, such as Transformers, can learn from the entire data sequence concurrently, a feature that LSTM does not have. This work tests the hypothesis that combining recurrence with attention can improve streamflow prediction. We set up the Temporal Fusion Transformer (TFT) architecture, a model that combines both of these aspects and has never been applied in hydrology before. We compare the performance of LSTM, Transformers, and TFT over 2,610 globally distributed catchments from the recently available Caravan dataset. Our results demonstrate that TFT indeed exceeds the performance benchmark set by the LSTM and Transformers for streamflow prediction. Additionally, being an explainable AI method, TFT helps in gaining insights into the streamflow generation processes.

Streamflow forecasts are critical to guide water resource management, mitigate drought and flood effects, and develop climate-smart infrastructure and governance. Many global regions, however, have limited streamflow observations to guide evidence-based management strategies. In this paper, we propose an attention-based domain adaptation streamflow forecaster for data-sparse regions. Our approach leverages the hydrological characteristics of a data-rich source domain to induce effective 24hr lead-time streamflow prediction in a data-constrained target domain. Specifically, we employ a deep-learning framework leveraging domain adaptation techniques to simultaneously train streamflow predictions and discern between both domains using an adversarial method. Experiments against baseline cross-domain forecasting models show improved performance for 24hr lead-time streamflow forecasting.

Skillful streamflow forecasts can inform decisions in various areas of water policy and management. We integrate numerical weather prediction ensembles, distributed hydrological model and machine learning to generate ensemble streamflow forecasts at medium-range lead times (1 - 7 days). We demonstrate a case study for machine learning applications in postprocessing ensemble streamflow forecasts in the Upper Susquehanna River basin in the eastern United States. Our results show that the machine learning postprocessor can improve streamflow forecasts relative to low complexity forecasts (e.g., climatological and temporal persistence) as well as standalone hydrometeorological modeling and neural network. The relative gain in forecast skill from postprocessor is generally higher at medium-range timescales compared to shorter lead times; high flows compared to low-moderate flows, and warm-season compared to cool ones. Overall, our results highlight the benefits of machine learning in many aspects for improving both the skill and reliability of streamflow forecasts.

While long short-term memory (LSTM) models have demonstrated stellar performance with streamflow predictions, there are major risks in applying these models in contiguous regions with no gauges, or predictions in ungauged regions (PUR) problems. However, softer data such as the flow duration curve (FDC) may be already available from nearby stations, or may become available. Here we demonstrate that sparse FDC data can be migrated and assimilated by an LSTM-based network, via an encoder. A stringent region-based holdout test showed a median Kling-Gupta efficiency (KGE) of 0.62 for a US dataset, substantially higher than previous state-of-the-art global-scale ungauged basin tests. The baseline model without FDC was already competitive (median KGE 0.56), but integrating FDCs had substantial value. Because of the inaccurate representation of inputs, the baseline models might sometimes produce catastrophic results. However, model generalizability was further meaningfully improved by compiling an ensemble based on models with different input selections.

In recent years, the paradigms of data-driven science have become essential components of physical sciences, particularly in geophysical disciplines such as climatology. The field of hydrology is one of these disciplines where machine learning and data-driven models have attracted significant attention. This offers significant potential for data scientists' contributions to hydrologic research. As in every interdisciplinary research effort, an initial mutual understanding of the domain is key to successful work later on. In this work, we focus on the element of hydrologic rainfall--runoff models and their application to forecast floods and predict streamflow, the volume of water flowing in a river. This guide aims to help interested data scientists gain an understanding of the problem, the hydrologic concepts involved, and the details that come up along the way. We have captured lessons that we have learned while "coming up to speed" on streamflow prediction and hope that our experiences will be useful to the community.