Streamflow forecasting is crucial for water resource management and risk mitigation. While deep learning models have achieved strong predictive performance, they often overlook underlying physical processes, limiting interpretability and generalization. Recent causal learning approaches address these issues by integrating domain knowledge, yet they typically rely on fixed causal graphs that fail to adapt to data. We propose CauStream, a unified framework for causal spatiotemporal streamflow forecasting. CauSTream jointly learns (i) a runoff causal graph among meteorological forcings and (ii) a routing graph capturing dynamic dependencies across stations. We further establish identifiability conditions for these causal structures under a nonparametric setting. We evaluate CauSTream on three major U.S. river basins across three forecasting horizons. The model consistently outperforms prior state-of-the-art methods, with performance gaps widening at longer forecast windows, indicating stronger generalization to unseen conditions. Beyond forecasting, CauSTream also learns causal graphs that capture relationships among hydrological factors and stations. The inferred structures align closely with established domain knowledge, offering interpretable insights into watershed dynamics. CauSTream offers a principled foundation for causal spatiotemporal modeling, with the potential to extend to a wide range of scientific and environmental applications.
Deep Dive into CauSTream: Causal Spatio-Temporal Representation Learning for Streamflow Forecasting.
Streamflow forecasting is crucial for water resource management and risk mitigation. While deep learning models have achieved strong predictive performance, they often overlook underlying physical processes, limiting interpretability and generalization. Recent causal learning approaches address these issues by integrating domain knowledge, yet they typically rely on fixed causal graphs that fail to adapt to data. We propose CauStream, a unified framework for causal spatiotemporal streamflow forecasting. CauSTream jointly learns (i) a runoff causal graph among meteorological forcings and (ii) a routing graph capturing dynamic dependencies across stations. We further establish identifiability conditions for these causal structures under a nonparametric setting. We evaluate CauSTream on three major U.S. river basins across three forecasting horizons. The model consistently outperforms prior state-of-the-art methods, with performance gaps widening at longer forecast windows, indicating str
Accurate streamflow forecasting is critical for water resource management, supporting applications from flood control to hydropower scheduling and ecosystem preservation. Process-based models such as VIC-CMF [1], [2] simulate streamflow through a two-stage mechanism: meteorological forcings (e.g., precipitation, temperature) generate surface and subsurface runoff, which is then routed through river networks to produce downstream streamflow. While grounded in physical principles, these models require extensive basinspecific calibration and are infeasible to deploy in regions with limited data. In the past decade, deep learning models such as ConvLSTM [3] and Spatio-Temporal Graph Convolutional Networks (STGCN) [4] have shown strong predictive performance [5]. However, these models often behave as "black boxes," offering limited interpretability and reduced robustness under distribution shifts.
A recent promising direction is the causal machine learning model, where a directed acyclic graph (DAG) encodes causal knowledge to guide model learning. For instance, Causal Streamflow Forecasting (CSF) [6] utilizes a river flow network as the causal graph, improving prediction accuracy. However, such approaches depend on a pre-defined causal graph, instead of learning it from data. Recent advances in nonlinear causal discovery show that such causal structures can be identified from observational data under mild assumptions [7], opening the door to end-to-end models that jointly perform causal discovery and prediction.
We introduce CauSTream, a framework for Causal SpatioTemporal stream forecasting. CauSTream is a general causal learning framework that integrates causal discovery with multi-step streamflow prediction. Inspired by processbased hydrological models, it learns two causal graphs: (i) an instantaneous DAG (G F ) that captures dependencies among meteorological forcings, and (ii) a spatiotemporal routing DAG (G Q ) that governs runoff routing. The learned causal graphs provide both physical interpretability and improved generalization in streamflow forecasting.
CauSTream is implemented in two variants designed for efficiency and adaptability: 1) CauSTream-Shared, which learns a single global runoff function suitable for relatively homogeneous catchments; 2) CauSTream-Local, which uses a hypernetwork [8] to capture station-specific heterogeneity, analogous to calibration in hydrological models.
We evaluate CauSTream on three large U.S. river basins (Brazos, Colorado, and Upper Mississippi). The empirical results demonstrate substantial improvements over conventional forecasting methods, affirming the capability of our causal framework to effectively model complex hydrological processes. Thus, our work contributes significantly to advancing streamflow prediction methodologies and providing robust, interpretable insights into hydrological dynamics across diverse geographic contexts.
Our contributions are as follows:
• We propose CauSTream, a novel end-to-end framework that, to our knowledge, is the first to unify causal dis-arXiv:2512.16046v1 [cs.LG] 18 Dec 2025 covery and multi-step-ahead forecasting for streamflow prediction; • We demonstrate state-of-the-art forecasting performance on three large-scale, hydrologically diverse U.S. river basins (Brazos, Colorado, and Upper Mississippi), consistently outperforming strong baselines, particularly on long-range horizons; • We show that our model learns interpretable causal graphs for both meteorological forcings (G F ) and streamflow routing (G Q ) that align with established hydrological principles and domain knowledge, and • We validate that the model’s internal runoff embedding is aligned with the runoff simulated by the hydrological model.
Process-based hydrologic models. The Variably Infiltration Capacity (VIC) model [1] is a widely used large-scale distributed model that assumes (i) universal governing equations for hydrologic processes and (ii) independent treatment of each grid with locally calibrated parameters. While this structure enables flexibility, it introduces bias by neglecting crossgrid interactions. In coupled modeling frameworks, runoff is the sole output passed from VIC to the Catchment-based Macro-scale Floodplain (CaMa-Flood) model [2], which performs river routing to estimate streamflow (Fig. 1). This VIC-runoff-CaMa-Flood configuration has become a standard approach and has demonstrated high fidelity in prior studies [9]. However, despite its accuracy, process-based models demand extensive calibration and detailed geophysical inputs, making them time-consuming and difficult to apply at scale or for real-time forecasting.
Causal-guided machine learning models. Machine learning methods such as Convolutional Neural Networks, Bayesian Neural Networks, Graph Neural Networks, and Conv-LSTM networks have demonstrated strong predictive performance in hydrologic forecasting [3], [5], [10], [11]. However, purely data-driven methods often fai
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