An automatic-differentiation framework for time-lapse electrical resistivity tomography inversion of hydrologic dynamics

Time-lapse electrical resistivity tomography (TL-ERT) provides spatially distributed information on subsurface hydrologic changes. However, inversion of long monitoring sequences is computationally demanding. Modifying the data misfit, regularization, model parameterization, or petrophysical transformation may also require new gradient derivations and separate implementations. Here, we present AD-TLERT, a unified, GPU-accelerated framework for time-lapse ERT inversion based on automatic differentiation. The framework integrates model parameterization, differentiable petrophysical transformations, forward modeling, data misfit, regularization and auxiliary constraints into a single computational chain. Alternative inversion formulations can therefore reuse the same PDE derivative implementation without re-deriving the complete ERT sensitivity for each case. Comparisons with pyGIMLi showed close agreement in the forward responses, gradients, and recovered resistivity models. Under the tested configuration, AD-TLERT achieved an approximately 51-fold speedup. Synthetic experiments showed that inversion choices affect the amplitude, geometry, and temporal behavior of recovered anomalies. By propagating gradients through the embedded petrophysical relationship, AD-TLERT enabled direct water-content inversion and yielded more accurate estimates than post-inversion conversion for the tested model. A field application further demonstrated how ERT, temperature, and soil-moisture observations can be combined to image snowmelt-driven hillslope wetting. AD-TLERT provides an efficient and flexible framework for time-lapse ERT inversion and hydrologic interpretation.

HydroAgent: Formalizing Forecaster Expertise into Skill-Orchestrated Flood Forecasting Workflows

Operational flood forecasting depends on tacit forecaster expertise that is difficult to formalize, audit, and transfer. Although artificial intelligence methods have advanced flood prediction and model-error correction, most existing studies have not explicitly represented the tacit expert rules, review checkpoints, and workflow constraints that connect model outputs to operational warning decisions. To address this issue, we propose HydroAgent, a skill-orchestrated agent framework that embeds Large Language Models (LLMs) into a model-driven flood forecasting workflow, where each skill encodes explicit rules to bound LLM reasoning. We validated its effectiveness using five state-of-the-art LLMs in the South Yamhill River basin. Our results demonstrate that prior judgment captures observed peak flow and flood volume within 5% tolerance in 10 and 11 out of 14 events, with 5-fold cross-validation over 129 events yielding Pearson correlations of 0.62 and 0.84. Building on a high-baseline scheme library (average KGE 0.890), the guided scheme selection further improves KGE by 0.023-0.154, with simulated peak flow and flood volume falling within the prior judgment ranges for 14 and 13 out of 14 events. All five tested LLMs successfully execute the HydroAgent workflow with comparable judgment accuracy (40%-80%), while showing moderate performance variation and substantial cost differences. HydroAgent does not aim to replace human forecasters; instead, it translates their tacit expertise into an auditable and reproducible workflow, streamlining analytical steps and supporting more informed decision-making. This skill-orchestrated paradigm demonstrates how explicit rule boundaries can guide language model reasoning to complement physically based simulation in next-generation flood forecasting.

Context-Aware Concept Distillation for Trustworthy Flood Prediction

Effective flood risk management relies on accurate forecasting, yet the "black box" nature of stateof-the-art Deep Learning models creates a barrier to trust and accountability in high-stakes public safety decisions. While existing Explainable AI (XAI) methods offer local attributions, they fail to provide the verifiable, operationally meaningful causal narratives required by disaster response authorities. To address this societal challenge, we propose Context-Aware Concept Distillation (CACD), a framework developed in collaboration with domain experts to distill opaque LSTMs into interpretable, hydrology-aware surrogate models. We introduce an unsupervised pipeline to discover a "Hydrological Language" and a Residual Hypernetwork that dynamically modulates these concepts based on static basin characteristics. Evaluated on 5,203 basins globally, our model achieves high fidelity (Median NSE 0.70), significantly outperforming black-box baselines (e.g., Multi Layer Perceptrons) on unseen future data. By demonstrating that human-interpretable concepts are sufficient to reconstruct flood dynamics, this work balances AI accuracy with the transparency required for responsible environmental decision-making.

Transformer-based Diffusion models for Hydrological Time Series Probabilistic Imputation and Forecasting

The modeling of hydrometeorological time series with limited observations is a key challenge in the monitoring of hydro-systems and water resources, as well as for flood or drought risk assessment. Due to the high variability of the underlying processes and the sparsity of available measurements, traditional statistical approaches often struggle to accurately represent their dynamics. In this context, recent advances in deep learning offer a promising direction for improving the representation and generation of complex temporal processes sampled at several observation sites. This study investigates the application of transformer-based diffusion models to the simulation and reconstruction of hydrological time series. The proposed framework is applied to the joint modeling of water quantity and quality at six sites spread across three adjacent headwater catchments located in North-East France on a limestone plateau covered by forests and field crops. The model is calibrated and validated using available observational data, which has been quality controlled and corrected for sensor drift and malfunction through collaborative efforts by LNE metrology expertise and Andra monthly quality control over more than 15 years. Its performance is compared with several established baseline approaches commonly used for time series modeling. Quantitative evaluation metrics are employed to assess the ability of the proposed method to reproduce key temporal characteristics of the observed signals in two settings: the imputation of incomplete time series and the forecasting of upcoming hydrological conditions. Results support the effectiveness of the transformer-based approach and highlight its capacity to capture and simulate the complex patterns present in hydrological data. In particular, the results indicate that diffusion models can efficiently sample realistic time series distributions under observation settings with variable missing data for both forecasting and imputation.

Joint distribution of upstream runoff governs downstream river-discharge prediction uncertainty in distributed ML models

Uncertainty quantification of hydrological predictions is necessary to inform operational decisions. Recent generative machine-learning methods have advanced probabilistic streamflow prediction, but have remained confined to lumped models that predict a basin outlet directly. At the same time, deterministic LSTM runoff models are increasingly applied at grid or catchment scale and routed through river networks to produce spatially continuous, physically consistent discharge fields. This technical note argues that moving probabilistic prediction from lumped to distributed models introduces a specific new requirement: the joint distribution of upstream runoff generation must be sampled jointly. In lumped inference, the model predicts the outlet distribution directly and can modulate spread from basin attributes. In distributed inference, downstream discharge is obtained by routing many upstream runoff predictions, so independent local sampling averages uncertainty away. Using Japan as a case study, we train two probabilistic basin-scale runoff LSTMs and route their runoff through a Hayami routing scheme. Randomly matching upstream ensemble members produces severely under-dispersed downstream ensembles, whereas a simple quantile matching strategy restores much of the spread of the direct basin-scale reference. The shift from lumped to distributed probabilistic hydrology therefore requires explicit attention to the spatial joint structure of runoff uncertainty.

Extreme Adaptive Transformer for Time Series Forecasting

Time series forecasting remains challenging when the underlying data contain rare but critical extreme events. This issue is particularly important in hydrologic forecasting, where streamflow distributions are often highly skewed and extreme peaks can have substantial impacts on flood monitoring, water resource management, and early warning systems. Although Transformer-based forecasting models have achieved strong performance by modeling long-range temporal dependencies, they typically treat all time points uniformly and may therefore underrepresent rare extreme patterns. In this paper, we propose the Extreme-Adaptive Transformer (Exformer), a forecasting framework designed to explicitly model temporal dependencies involving both normal and extreme events. Exformer introduces an extreme-adaptive attention mechanism composed of three sparse components: Local, Stride, and Extreme. The Local and Stride components capture short-term and periodic temporal dependencies, respectively, while the Extreme component selectively models event-aware dependencies between normal and extreme streamflow patterns. Experiments on four real-world hydrologic streamflow datasets show that Exformer achieves superior 3-day forecasting performance compared with state-of-the-art baselines. Our findings demonstrate that explicitly incorporating extreme-aware attention improves the forecasting capacity of Transformer models on imbalanced time series with rare but consequential events.

Reconstructing GRACE Terrestrial Water Storage with Spatio-Temporal Graph Neural Networks: An Application to South America

Terrestrial water storage (TWS) integrates snow, soil moisture, surface water, and groundwater and is a key indicator of how climate variability and human activity reshape the global water cycle. The GRACE and GRACE-FO satellite missions provide the only direct, globally consistent observations of TWS change, but their record only begins in 2002 which is too short for many climate-scale analyses. We present a deep learning application that reconstructs monthly GRACE-like TWS anomalies (TWSA) back to 1940 by learning the relationship between daily ERA5 meteorological forcing (precipitation, evapotranspiration, runoff) and monthly GRACE observations. In contrast to prior reconstruction approaches based on grid-cell-wise regression, CNNs, or LSTMs, we adapt a multi-variate time series graph neural network (MTGNN) architecture, which was originally developed for mobility and traffic forecasting on urban sensor networks to this satellite-geodesy task. Spatial dependencies are encoded in a static, interpretable hybrid adjacency matrix that combines geodesic proximity with lagged correlations of climatic time series, capturing both local hydrological coupling and large-scale teleconnections. The reconstruction achieves a grid-cell Pearson correlation of 0.69, a basin-mean correlation of 0.94, and a near-zero bias, and it reproduces the spatial fingerprints of the 2015/16 El Niño and 2020/21 La Niña events. A systematic comparison with established reconstruction approaches (GTWS-MLrec, RM-REC, GRAiCE) shows that the graph-based model is statistically competitive at basin scale, reaching a correlation within 0.025 of the best baseline while using only roughly half to a tenth of the predictors the other models require and revealing characteristic weaknesses in arid regions in all models. The complete implementation is publicly available at github.com/hcu-cml/MTGNN-TWS-Reconstruction-GRACE

INDEQS: Informed Neural controlled Differential EQuationS

Neural Controlled Differential Equations (NCDE) provide a powerful continuous-time framework for forecasting time series, but standard graph-based extensions typically learn spatial structure purely from data, even in settings where a directed graph structure is known a priori. We introduce Informed Neural controlled Differential EQuationS (INDEQS), a graph-based NCDE forecasting method that incorporates prior knowledge of a directed graph at distinct architectural positions. INDEQS separates inner mixing of hidden states across graph nodes from outer mixing between vector field and control, and offers both a lightweight graph-constrained variant and a more expressive variant, learning additional graph connections from data via adaptive graph convolutions. To systematically study when graph informedness is beneficial in forecasting, we devise a continuous advection simulation on directed graphs, yielding synthetic spatio-temporal datasets with known ground-truth flow structure. We then evaluate INDEQS on two real-world tasks: river discharge forecasting on a hydrological network and traffic flow prediction on PeMS08. Across these synthetic and real-world benchmarks, outer informedness consistently improves mean absolute error over an uninformed NCDE with comparable parameter count, particularly on larger graphs, while inner informedness offers a more parameter-efficient alternative when strict adherence to a known adjacency is desired. A comparison of discrete convolutional and continuous-time decoders further shows that continuous decoders yield better accuracy and greater temporal flexibility on real-world tasks. An implementation of INDEQS and the advection simulation is available at https://github.com/Mitchi1/indeqs.

Learned Response-Field Inertia Operator for HEC-RAS 2D Water-Surface Elevation Prediction

This article presents a cross-dataset evaluation of learned native-cell surrogate models for solver-consistent water-surface elevation (WSE) prediction in HEC-RAS 2D. To avoid raster remapping error and information-access confounding, surrogates are evaluated directly on the original nonuniform computational cells under an explicit policy that separates static project inputs, current hydraulic state, project-input forcing, calibration-derived quantities, and future solver-output targets. We introduce the Learned Response-Field Inertia Operator (LRFIO), a no-forcing, increment-based learned surrogate that calibrates an inertial response operator from solved HEC-RAS trajectories and deploys the retained operator through closed-form native-cell rollout. LRFIO evaluates a base-case-first response hierarchy consisting of persistence, global calibrated inertia, and segmented response-field inertia. Segmentation, residual correction, and neuralized inertia are treated as learnable modeling choices, with added complexity retained only when validation evidence justifies its cost. Evaluated across four diverse HEC-RAS 2D benchmarks, LRFIO retains different response structures for different domains, demonstrating adaptive learned complexity. The selector audit shows controlled complexity with a maximum validation regret of 4.30%. During deployment, retained rollout times range from 0.003 s to 0.242 s, and the Beaver Bayou measured-solve comparison gives an estimated 2.75 x 10^4 horizon-normalized speedup over HEC-RAS. These results indicate that the current native-cell increment is a strong solver-conditioned predictive scaffold and that added response-field, neural, or spatial complexity should be retained only when empirically justified.

Physics-Informed Machine Learning for Short-Term Flood Prediction

Accurate flood forecasting is essential for mitigating disaster risks and protecting communities. However, purely data-driven machine learning models often struggle in data-scarce environments and may violate fundamental hydrological principles. Standard Long Short-Term Memory (LSTM) networks can generate physically inconsistent predictions, particularly when extrapolating to extreme weather conditions. To address these limitations, we propose a Physics-Informed Machine Learning (PIML) framework that incorporates hydrological knowledge directly into the loss function of an LSTM model. Specifically, a Trend Alignment constraint penalizes directional inconsistencies between precipitation and discharge trends, improving model robustness without requiring complex hydrodynamic equations. This regularization encourages the model to learn physically plausible hydrograph behavior, even with limited training data, while enhancing reliability during peak flood events. Experimental results show that the proposed physics-informed model outperforms a standard LSTM baseline in data-scarce settings, increasing the Nash-Sutcliffe Efficiency (NSE) from 0.20 to 0.23 when trained on only 5% of the available data. Additional stress tests under simulated extreme climate scenarios demonstrate that the baseline model exhibits unstable behavior, whereas the physics-informed model maintains directional consistency and physical plausibility. Although accurately predicting extreme peak magnitudes remains challenging with limited data, the proposed approach substantially reduces unphysical fluctuations common in purely data-driven models. These findings demonstrate that simple physical constraints can significantly improve the reliability of deep learning models for real-time flood forecasting, offering a practical solution for ungauged basins and evolving climate conditions.

Evaluating Transformer and LSTM Frameworks for Prediction in Ungauged Basins

Watershed networks exhibit convergent topologies in which multiple tributaries merge into downstream channels,integrating diverse upstream hydrological processes. In ungauged basins, the absence of direct observations increases uncertainty and limits the ability to anticipate extreme events. This study evaluates whether an encoder-only Transformer provides an advantage over an LSTM for upstream streamflow inference under limited hydrologic information, using retrospective simulations from the NOAA National Water Model (NWM). Across both upstream-only and combined configurations, the LSTM showed stronger overall performance than the Transformer model across the two configurations. Incorporating downstream information further boosted performance for all models, increasing median NNSE by more than 60%. Rather than treating this as a leaderboard-style comparison, we interpret the experiments as a test of architectural inductive bias for hydrologic sequence inference. The results indicate that recurrent memory remains better aligned with this upstream reconstruction task than an encoder-only Transformer, while downstream hydrologic context provides a strong auxiliary constraint that substantially improves prediction skill across architectures