Baseflow identification via explainable AI with Kolmogorov-Arnold networks

Hydrological models often involve constitutive laws that may not be optimal in every application. We propose to replace such laws with the Kolmogorov-Arnold networks (KANs), a class of neural networks designed to identify symbolic expressions. We demonstrate KAN's potential on the problem of baseflow identification, a notoriously challenging task plagued by significant uncertainty. KAN-derived functional dependencies of the baseflow components on the aridity index outperform their original counterparts. On a test set, they increase the Nash-Sutcliffe Efficiency (NSE) by 67%, decrease the root mean squared error by 30%, and increase the Kling-Gupta efficiency by 24%. This superior performance is achieved while reducing the number of fitting parameters from three to two. Next, we use data from 378 catchments across the continental United States to refine the water-balance equation at the mean-annual scale. The KAN-derived equations based on the refined water balance outperform both the current aridity index model, with up to a 105% increase in NSE, and the KAN-derived equations based on the original water balance. While the performance of our model and tree-based machine learning methods is similar, KANs offer the advantage of simplicity and transparency and require no specific software or computational tools. This case study focuses on the aridity index formulation, but the approach is flexible and transferable to other hydrological processes.

Reinforcement Learning for Sociohydrology

In this study, we discuss how reinforcement learning (RL) provides an effective and efficient framework for solving sociohydrology problems. The efficacy of RL for these types of problems is evident because of its ability to update policies in an iterative manner - something that is also foundational to sociohydrology, where we are interested in representing the co-evolution of human-water interactions. We present a simple case study to demonstrate the implementation of RL in a problem of runoff reduction through management decisions related to changes in land-use land-cover (LULC). We then discuss the benefits of RL for these types of problems and share our perspectives on the future research directions in this area.

A Parsimonious Setup for Streamflow Forecasting using CNN-LSTM

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. In this study, we extend the application of CNN-LSTMs to time series settings, leveraging lagged streamflow data in conjunction with precipitation and temperature data to predict streamflow. Our results show a substantial improvement in predictive performance in 21 out of 32 HUC8 basins in Nebraska, showcasing noteworthy increases in the Kling-Gupta Efficiency (KGE) values. These results highlight the effectiveness of CNN-LSTMs in time series settings, particularly for spatiotemporal hydrological modeling, for more accurate and robust streamflow predictions.

An Autoencoder-based Snow Drought Index

In several regions across the globe, snow has a significant impact on hydrology. The amounts of water that infiltrate the ground and flow as runoff are driven by the melting of snow. Therefore, it is crucial to study the magnitude and effect of snowmelt. Snow droughts, resulting from reduced snow storage, can drastically impact the water supplies in basins where snow predominates, such as in the western United States. Hence, it is important to detect the time and severity of snow droughts efficiently. We propose Snow Drought Response Index or SnoDRI, a novel indicator that could be used to identify and quantify snow drought occurrences. Our index is calculated using cutting-edge ML algorithms from various snow-related variables. The self-supervised learning of an autoencoder is combined with mutual information in the model. In this study, we use random forests for feature extraction for SnoDRI and assess the importance of each variable. We use reanalysis data (NLDAS-2) from 1981 to 2021 for the Pacific United States to study the efficacy of the new snow drought index. We evaluate the index by confirming the coincidence of its interpretation and the actual snow drought incidents.

Temporal Fusion Transformers for Streamflow Prediction: Value of Combining Attention with Recurrence

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.

Differentiable modeling to unify machine learning and physical models and advance Geosciences

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.