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Towards Learning Universal, Regional, and Local Hydrological Behaviors via Machine-Learning Applied to Large-Sample Datasets
Frederik Kratzert, Daniel Klotz, Guy Shalev, Günter Klambauer, Sepp Hochreiter, Grey Nearing
TL;DR
The paper addresses the longstanding challenge of modeling rainfall-runoff behavior across multiple basins with one model. It develops an Entity-Aware-LSTM that embeds catchment information and reports that a single universal model can learn regional and local hydrological behaviors while outperforming locally and regionally calibrated models.
Problem
A longstanding Hydrological Sciences problem is how to use one model, or one set of models, across basins using observable catchment characteristics.
Method
The paper adapts LSTMs with a static embedding layer, allowing the model to learn catchment similarities and predict in basins absent from training data.
Results
A single universal deep learning model learned both regional and local hydrological behaviors, with the EA-LSTM outperforming locally and regionally calibrated models.
Takeaways & Limitations
The results demonstrate that one universal deep learning model can learn hydrological behavior across basins rather than requiring separate basin-specific models.
Takeaways & Limitations
Catchment attributes may change over time across vegetation, topography, pedology, and climate, motivating future strategies to address this changing reality.
Abstract
from arXiv · showhide
Regional rainfall-runoff modeling is an old but still mostly out-standing problem in Hydrological Sciences. The problem currently is that traditional hydrological models degrade significantly in performance when calibrated for multiple basins together instead of for a single basin alone. In this paper, we propose a novel, data-driven approach using Long Short-Term Memory networks (LSTMs), and demonstrate that under a 'big data' paradigm, this is not necessarily the case. By training a single LSTM model on 531 basins from the CAMELS data set using meteorological time series data and static catchment attributes, we were able to significantly improve performance compared to a set of several different hydrological benchmark models. Our proposed approach not only significantly outperforms hydrological models that were calibrated regionally but also achieves better performance than hydrological models that were calibrated for each basin individually. Furthermore, we propose an adaption to the standard LSTM architecture, which we call an Entity-Aware-LSTM (EA-LSTM), that allows for learning, and embedding as a feature layer in a deep learning model, catchment similarities. We show that this learned catchment similarity corresponds well with what we would expect from prior hydrological understanding.
1 Introduction
Regional rainfall-runoff modeling seeks one model that transfers hydrologic information across catchments while representing their differing behaviors. The paper proposes a data-driven LSTM approach using large-sample data and catchment attributes, including an Entity-Aware-LSTM that learns catchment similarities.
- Regional modeling must extrapolate hydrologic information between areas while accounting for differences in catchment characteristics and rainfall-runoff behavior.
- Data-driven regional methods learn mappings from catchment attributes and meteorological inputs directly to streamflow, rather than deriving parameters for a predefined hydrological model.
- Traditional hydrological models often perform best when calibrated separately for each catchment, motivating approaches that transfer knowledge across diverse training data.
- The study trains an LSTM-based regional model on multiple basins using meteorological forcing data and ancillary catchment attributes, and evaluates it in a gauged setting.
- The proposed Entity-Aware-LSTM lets catchment attributes control the utilized state-space components, sharing network parts across similar basins while differentiating dissimilar behaviors.
- The learned embedding maps catchment attributes into a high-dimensional space where catchments with similar rainfall-runoff behavior can be grouped for data-driven similarity analysis.
2.1 A Brief Overview of the Long Short-Term Memory network
LSTMs are recurrent networks whose gated memory cells support long-term information storage and make them suitable for dynamical watershed processes. The paper contrasts the standard cell with the proposed EA-LSTM architecture.
- LSTMs use dedicated memory cells and gated information flow to learn long-term dependencies between inputs and outputs.
- In rainfall-runoff modeling, LSTM memory can represent processes such as snow accumulation and melt that operate over relatively long timescales.
- At each time step, the LSTM forward pass uses the network input and previous hidden and cell states to update its gates and cell state.
- The forget gate can delete stored states, while the input gate and cell update add new information to selected cells.
- Figure 1 compares the standard LSTM cell with the proposed Entity-Aware-LSTM cell.
2.2 A New Type of Recurrent Network: The Entity-Aware-LSTM
The EA-LSTM conditions dynamic rainfall-runoff processing on static catchment characteristics while explicitly separating their roles. Its static input gate provides an embedding that can represent catchment similarities and differences learned from rainfall-runoff data.
- Design rationale: Unlike appending static features at every time step, the EA-LSTM makes the network’s use of catchment attributes directly inspectable.The alternative of repeating static features through the sequence does not allow direct inspection of what the LSTM learns from them.
- Architecture: The proposed EA-LSTM explicitly processes static catchment characteristics and dynamic meteorological inputs separately within the architecture.Static features condition the mapping from meteorological time series to streamflow.
- Architecture: Static features control the input gate, while dynamic and recurrent inputs govern information written, deleted, and exposed by the LSTM memory.The static input gate remains constant over time; the remaining LSTM components operate across time steps.
- Entity awareness: The EA-LSTM differentiates similar dynamical behaviors that vary between individual watersheds.The architecture is named Entity-Aware-LSTM because it explicitly distinguishes entity-specific rainfall-runoff processes.
- Entity awareness: Its static input gate acts as an embedding layer whose learned values allow catchments to share some network components while retaining distinct components.The embedding can represent complex interactions among catchment characteristics and is informed by rainfall-runoff data from all training catchments.
2.3 Objective Function: A Smooth Joint NSE
The paper uses a basin-averaged NSE objective to balance training across catchments with different discharge magnitudes. A constant variance term stabilizes the objective for very low-flow-variance basins.
- Stabilization: The objective is formulated for regression tasks such as runoff prediction, where mean-squared error is a common alternative.NSE has an interpretable range of (-∞, 1).
- Objective design: Across multiple basins, MSE and NSE are not linearly related because observation means and variances differ between basins.For single-basin optimization, the two objectives typically yield the same optimum parameter values.
- Objective design: MSE generally produces smaller errors for low-discharge arid basins than for high-discharge humid basins, creating unequal basin weighting.This motivates an objective normalized by basin-specific discharge variability.
- Objective design: The basin-averaged Nash-Sutcliffe Efficiency (NSE*) averages each basin’s NSE so large humid basins do not dominate training.The objective is designed to avoid poor performance on small, arid basins.
- Stabilization: Adding ϵ = 0.1 to the denominator prevents the loss from diverging to negative infinity for catchments with very low flow variance.The loss uses the variance of observations in its denominator.
2.4 The NCAR CAMELS Dataset
The study uses a 531-basin subset of CAMELS, a 671-basin dataset spanning diverse basin sizes, geologies, and ecoclimatologies. Inputs combine daily meteorological forcings with 27 static catchment characteristics.
- Study use: The study benchmarks the EA-LSTM and assesses whether it learns meaningful catchment similarities.The dataset and input design support both hydrological simulation and similarity-learning evaluation.
- Dataset: CAMELS contains data for 671 basins curated by NCAR, spanning 4 to 25 000 km2 with relatively low anthropogenic impacts.The basins cover a range of geologies and ecoclimatologies.
- Dataset: The experiments use a subselection of 531 CAMELS basins chosen partly to avoid uncertainty from discrepancies in basin-area calculations.The selected basins also have catchment areas smaller than 2000 km2.
- Inputs: Dynamic inputs are daily basin-averaged Maurer forcings: cumulative precipitation, minimum and maximum air temperature, short-wave radiation, and vapor pressure.These variables provide the time-dependent meteorological inputs.
- Inputs: The model uses 27 static CAMELS catchment characteristics derived from remotely sensed or CONUS-wide data products.The attributes include climatic and vegetation indices, soil properties, and topographical properties.
2.5 Benchmark models
The EA-LSTM is evaluated against existing hydrological model runs on the same CAMELS catchments and time periods. Benchmarks include individually calibrated models and regionally calibrated models sharing one parameter set across basins.
- Benchmark design: The first study component benchmarks the EA-LSTM against several high-quality hydrological models to assess whether it produces reasonable simulations.The benchmark runs were collected from previous studies rather than generated by the authors.
- Benchmark design: The authors use existing model runs to avoid calibrating the benchmarks in a way that might favor their own model.The benchmark models were run by other groups.
- Benchmark design: All benchmark models use the same daily Maurer forcings and were calibrated and validated over the same time periods as the EA-LSTM.This aligns the principal input and evaluation periods across model comparisons.
- Benchmark groups: Individually calibrated benchmarks include SAC-SMA, VIC, FUSE2, mHM, and HBV.HBV provides lower and upper benchmarks based on uncalibrated and calibrated ensembles, respectively.
- Benchmark groups: Regionally calibrated benchmarks use one parameter set for all basins and include VIC and mHM calibrations.These models represent the regional-calibration comparison group.
2.6 Experimental Setup
The study evaluates single regional LSTM and EA-LSTM models across all basins, compares configurations and metrics, and probes embedding robustness, sensitivity, and hydrological similarity.
- Model training and evaluation: A single parameter set was trained on calibration data from all basins and evaluated on validation data from all basins.
- Model configurations: The experiments compared LSTMs without static inputs, LSTMs with concatenated static inputs, and EA-LSTMs with static attributes entering a dedicated input gate.
- Model configurations: Six model/training configurations were trained with eight random seeds each, producing ensembles from mean predictions and 48 trained LSTM-type models overall.
- Performance evaluation: Evaluation used multiple metrics targeting high-flows, low-flows, overall performance, bias sensitivity, consistency, reliability, accuracy, and precision.
- Robustness and feature ranking: Robustness was assessed by adding Gaussian noise at 10 standard deviations to catchment attributes, with 265500 evaluations of each trained EA-LSTM.
- Robustness and feature ranking: Morris sensitivity analysis used analytically available neural-network gradients, averaging absolute daily gradients to derive basin- and feature-level global sensitivity.
3 Results
Across 531 basins, LSTM models using catchment attributes and basin-average NSE* achieved strong regional rainfall-runoff performance, outperforming calibrated hydrological benchmarks. Catchment attributes improved low-performing basins and enabled the model to distinguish basin-specific behaviors, while learned embeddings added interpretability with only a small performance cost.
- LSTM modeling approaches: Catchment attributes improved overall model performance and provided information that helped distinguish different catchment-specific rainfall-runoff behaviors.The authors interpret this information as sufficient for high-quality regional modeling competitive with lumped models calibrated separately for each basin.
- LSTM modeling approaches: The EA-LSTM and LSTM with static features differed significantly but only slightly, with effect size d = 0.055.The embedding layer adds interpretability for understanding catchment similarity, while the authors report a small performance sacrifice likely associated with additional tunable parameters.
- Model benchmarking: The EA-LSTM significantly outperformed all benchmark models in overall NSE, including basin-calibrated models.Its ensemble mean had mean NSE 0.67 ± 0.006 and median NSE 0.71 ± 0.004, compared with VIC mean 0.17 and mHM mean 0.44.
- Robustness and feature ranking: Performance degraded smoothly as noise increased in static inputs, indicating the LSTM learned a smooth representation rather than memorizing each basin exactly.Static features were especially helpful for basins at the lower end of the NSE spectrum, where hydrological behaviors were under-represented in training data.
4 Discussion and Conclusion
The paper presents EA-LSTM as a single regional rainfall-runoff model that incorporates catchment similarities while learning regionally consistent and location-specific behaviors. It reports strong benchmark performance and discusses interpretability, parameter-transfer advantages, and limitations from treating catchment attributes as static.
- EA-LSTM achieved state-of-the-art results, outperforming multiple locally and regionally calibrated models, including models calibrated separately for individual catchments.
- The model uses a static embedding layer to connect catchment characteristics with site-specific dynamics while learning from combined data across catchments.
- The embedding layer offered interpretability into how the model differentiates complex catchment-specific behaviors, while achieving similar performance to a conventional LSTM.
- EA-LSTM learns a single model from large catchment datasets while explicitly incorporating local catchment similarities and differences.
- Deep learning jointly learns time-series and spatial relationships, sidestepping problems associated with estimating and transferring hydrologic model parameters.
- Treating catchment attributes as static is a strong assumption because vegetation, topography, pedology, and climate may change across timescales.
- Future work could develop dynamic embedding layers using time-dependent observables from climate models or remote sensing.
- The results indicate that CAMELS catchment attributes contain enough information to distinguish diverse rainfall-runoff behaviors to a meaningful degree.
Appendix A: Full list of the used CAMELS Catchment Characteristics
Appendix A lists the CAMELS catchment characteristics used in the experiments, including soil composition, carbonate-area fraction, and surface permeability.
- The appendix identifies the source and organization of the catchment-attribute table used in the experiments.
- The listed soil characteristics include fractions of sand, silt, and clay.
- Additional characteristics include the fraction of catchment area characterized as carbonate and log10 surface permeability.
Appendix B: Hyperparameter tuning
Appendix B describes grid-search hyperparameter tuning with four-fold basin splits and selection by the highest median NSE across configurations.
- The hyperparameter search varied hidden or cell states, dropout rate, input-sequence length, and the number of stacked LSTM layers.
- The candidate number of stacked LSTM layers was 1 or 2.
- Four-fold cross-validation split basins into training and independent test sets for each parameter combination.
- The final configuration maximized median NSE over all tested parameter configurations.
- The selected input sequence length was 270.
- The final configuration used one stacked LSTM layer.