Source-linked AI summary
Differentiable, learnable, regionalized process-based models with physical outputs can approach state-of-the-art hydrologic prediction accuracy
Dapeng Feng, Jiangtao Liu, Kathryn Lawson, Chaopeng Shen
TL;DR
The paper examines differentiable, learnable process-based hydrologic models as an alternative to purely data-driven approaches. Using expert-selected model structure and dynamical parameterization, it reports strong performance and supports mechanistic questions through physical states and fluxes.
Problem
Purely data-driven models can achieve high performance, but their physical significance and evaluation of evapotranspiration remain limited.
Method
The framework uses expert-selected backbone structure and dynamical parameterization within differentiable programming.
Results
The evolved HBV model shows strong performance, and LSTM-like performance is not entirely necessary for high performance.
Takeaways & Limitations
Differentiable programming can support mechanistic questions while physical constraints allow models to output physical states and fluxes.
Takeaways & Limitations
The study notes a lack of evapotranspiration evaluation on CAMELS and warns that high performance may reduce physical significance.
Abstract
from arXiv · showhide
Predictions of hydrologic variables across the entire water cycle have significant value for water resource management as well as downstream applications such as ecosystem and water quality modeling. Recently, purely data-driven deep learning models like long short-term memory (LSTM) showed seemingly-insurmountable performance in modeling rainfall-runoff and other geoscientific variables, yet they cannot predict untrained physical variables and remain challenging to interpret. Here we show that differentiable, learnable, process-based models (called δ models here) can approach the performance level of LSTM for the intensively-observed variable (streamflow) with regionalized parameterization. We use a simple hydrologic model HBV as the backbone and use embedded neural networks, which can only be trained in a differentiable programming framework, to parameterize, enhance, or replace the process-based model modules. Without using an ensemble or post-processor, δ models can obtain a median Nash Sutcliffe efficiency of 0.732 for 671 basins across the USA for the Daymet forcing dataset, compared to 0.748 from a state-of-the-art LSTM model with the same setup. For another forcing dataset, the difference is even smaller: 0.715 vs. 0.722. Meanwhile, the resulting learnable process-based models can output a full set of untrained variables, e.g., soil and groundwater storage, snowpack, evapotranspiration, and baseflow, and later be constrained by their observations. Both simulated evapotranspiration and fraction of discharge from baseflow agreed decently with alternative estimates. The general framework can work with models with various process complexity and opens up the path for learning physics from big data.
2. Methods and datasets
The study evolves the time-discrete HBV process-based model with differentiable parameter learning and neural-network modifications, then trains and evaluates it regionally against an LSTM benchmark.
- Model formulation: Only the discrete formulation is demonstrated, and all HBV-based simulations include a routing module that converts runoff into final streamflow.The routing module uses a gamma-function unit hydrograph and convolves it with runoff.
- Model backbone: HBV provides the process-based backbone and simulates snow water equivalent, soil water, groundwater storage, evapotranspiration, quick flow, baseflow, and total streamflow.
- Regionalized parameterization: dPL estimates model parameters from static basin attributes and meteorological forcings, using static values or new daily values for dynamic parameters.The parameter-estimation network is trained jointly with the HBV model through a global loss across sites.
- Model modifications: The evolved models add or dynamically parameterize evapotranspiration terms, allow dynamic runoff-curve parameter βt, and optionally replace effective-rainfall calculations with a neural network.These modifications target vegetation effects, potential-ET errors, forcing-history effects, and alternative moisture-runoff relationships.
- Training objective: Training used a weighted loss combining RMSE on streamflow with RMSE on transformed streamflow to improve low-flow representation.The HBV-model loss used α = 0.25; the LSTM used RMSE on normalized transformed data.
3. Results and Discussion
The evolved differentiable HBV models approached LSTM streamflow performance while retaining process-based structure and producing interpretable internal hydrologic variables. Their learned dynamics improved flow behavior and yielded reasonable baseflow and evapotranspiration estimates, although added flexibility creates accuracy–interpretability trade-offs and unresolved component limitations.
- 3.1. Streamflow metrics.: Dynamical parameterization improved modeled flow dynamics across example basins, including flood peaks in east Texas and peak and baseflow estimation in a Rocky Mountain basin.
- 3.1. Streamflow metrics.: The evolved models approached LSTM performance without ensembles, narrowing the gap between process-based and purely data-driven prediction.
- 3.1. Streamflow metrics.: Median NSE reached 0.715 for the differentiable model with dynamical parameterization, versus 0.628 for regionalized HBV and 0.53 for mHm.
- 3.1. Streamflow metrics.: The learned runoff factor βt showed seasonal variation and storm-related spikes, while dynamic storage effects increased runoff after water accumulated over months.
- 3.3. Further discussion: Process granularity exposes streamflow sources and ET, enabling multiple observations to constrain modeled or previously unobserved hydrologic variables.
- 3.2. Comparisons of the baseflow index and ET: Simulated baseflow fraction correlated with Ladson et al. estimates, reaching R=0.745 for δ(γt, βt) and 0.729 for δ.
- 3.2. Comparisons of the baseflow index and ET: Even without ET training, differentiable models produced reasonable daily ET, with δ(γt, βt) improving correlation with MOD16-MT over original HBV.
- 3.3. Further discussion: Applying dynamical parameterization throughout the system can improve performance but may reduce physical significance; here its median NSE gain was minor, from 0.697 to 0.715.
4. Conclusion
The conclusion presents differentiable, learnable hydrologic models as a way to combine adaptive learning with physical constraints and interpretable outputs. Their performance approaches LSTM while retaining process states and fluxes and enabling mechanistic questions.
- Adaptive process-based modeling: The evolved HBV model shows that high performance does not require a purely data-driven architecture like LSTM.Its process-based structure retains physical constraints while incorporating learnable components.
- Complementarity: Pure deep-learning models remain valuable for gauging dataset information content and providing diagnostic signals.The conclusion presents this as complementary to the proposed differentiable models.
- Physical interpretability: Physical constraints from unchanged model components allow the models to output physical states and fluxes useful for downstream applications.The stated constraints include mass conservation, physical calculations, and interpretable physical outputs.
- Performance: Differentiable models and LSTM outperform traditional hydrologic models, while performance gaps are minor among alternatives with learnable components.The conclusion attributes this pattern to adaptive learning capacity.
- Training framework: Differentiable programming is required to train models with complex learnable functions because traditional optimization handles only limited parameter counts and numerical derivatives are expensive.The conclusion describes differentiable programming as a promising path for continued growth.
- Future research: The framework supports mechanistic questions and a new research direction because model equations and components can be learned or modified.The authors state that preliminary studies have only begun to explore this flexibility.
Appendix
The appendix summarizes the variables supplied to the parameter-learning neural network. Inputs include dynamic forcings and static catchment attributes describing climate, topography, land cover, soils, geology, and vegetation.
- Input variables: The parameter-learning neural network uses 3 dynamic forcings and 35 static attributes.The appendix table provides the input-variable summary.
- Forcings: Dynamic forcings include precipitation and potential evapotranspiration, both measured in mm/day.These variables are labeled P and Ep in the appendix.
- Climate attributes: Static climate attributes describe mean precipitation, mean PET, precipitation seasonality, snowfall fraction, and frequencies and durations of extreme precipitation or dry periods.The listed attributes include p_mean, pet_mean, p_seasonality, frac_snow, high_prec_freq, high_prec_dur, low_prec_freq, and low_prec_dur.
- Catchment attributes: Catchment descriptors include elevation, slope, area, forest fraction, vegetation indices, dominant land cover, and its spatial fraction.The vegetation inputs include maximum and seasonal difference measures for leaf area index and green vegetation fraction.
- Soil and geology: Soil and geological attributes include root depth, depths to bedrock and soil, porosity, hydraulic conductivity, water content, texture fractions, and geological classes.The geological inputs also include the fraction associated with the most common geological class.