| 07 Jul 2026
Differentiable Hybrid Hydrological Model for Short-Term Flood Forecasting with Future Meteorological Information
Abstract. Short-term flood forecasting is essential for flood control operation and risk warning in small- and medium-sized basins, yet its accuracy is constrained by rainfall uncertainty, hydrological model structural limitations, and watershed physical response characteristics. To address these challenges, this study developed a differentiable hybrid hydrological forecasting framework that coupled future meteorological information with physically representations of runoff generation, baseflow recession, flow concentration, and channel routing. A physics-informed neural architecture search (PINAS) routing scheme was further proposed and systematically compared with differentiable Muskingum routing and convolutional unit-hydrograph routing, while a purely data-driven LSTM model was used as the benchmark. The framework was evaluated in three representative watersheds in Hebei Province, China, namely the Shahe basin (2210 km2), Jumahe basin (1760 km2), and Liulin basin (57.4 km2), using rainfall–runoff observations from the flood seasons of 2000–2023 and radar-echo data from 2018–2023. Multi-lead flood forecasting experiments were conducted for lead times of 0.5–2.0 h. The results showed that the LSTM benchmark achieves high numerical accuracy in some high-peak flood events, but lacks explicit physical constraints. In contrast, the model with PINAS routing exhibited the most stable overall performance among the hybrid hydrological models, achieving a more balanced representation of flood-peak propagation, hydrograph smoothing, and recession preservation. The data-dependency analysis indicated that increasing the amount of training data improved forecasting stability, but model skill does not increase strictly monotonically with sample size, sample representativeness and flood-type coverage were also critical. SHAP interpretability analysis further revealed that forecasts in the Shahe and Jumahe basins were mainly controlled by radar echoes and their extrapolated features, whereas the small Liulin Basin was more strongly influenced by measured areal rainfall and gauge rainfall. These findings demonstrated that integrating physical constraints, differentiable runoff–routing structures, and future meteorological information can improve the stability, physical consistency, and hydrological interpretability of short-term flood forecasting in small- and medium-sized basins.
Dear Authors,
I have carefully evaluated the manuscript entitled “Differentiable Hybrid Hydrological Model for Short-Term Flood Forecasting with Future Meteorological Information.” The study addresses a scientifically relevant problem at the intersection of differentiable hydrological modelling, radar-based precipitation nowcasting, and operational flood forecasting. Its main strengths include the development of a modular hybrid architecture, the comparison of three differentiable routing formulations, the introduction of a physics-informed neural architecture search scheme, and testing across basins with markedly different drainage areas and response times. The combination of long-term rainfall-runoff records, recent radar observations, multi-lead forecasts, data-dependency experiments, and feature-attribution analyses gives the work potential significance for the emerging literature on physics-guided hydrological learning.
Despite these strengths, important weaknesses in the experimental design, description of the model, interpretation of physical consistency, and statistical evaluation currently limit the strength and reproducibility of the conclusions. I therefore recommend Major Revision.
Lines 75-107: The motivation for PINAS assumes that searchable routing architectures provide greater transferability and physical plausibility than manually specified operators, but the manuscript does not define what constitutes physical plausibility beyond non-negativity, approximate volume consistency, and smoothness. These constraints do not ensure realistic travel times, attenuation, causality at the river-network scale, or preservation of wave dynamics. The scientific question should therefore distinguish numerical constraints from hydrological process realism, and the evaluation should include learned travel times, reach-scale mass-balance residuals, kernel shapes, and stability outside the calibration events rather than inferring physical plausibility primarily from outlet hydrograph accuracy.
Lines 150-159: The event-selection and data-partitioning procedures are insufficiently documented and may introduce substantial selection and information-leakage biases. Selecting events only when they exhibit “distinct and complete” rising and recession phases can exclude poorly observed, compound, truncated, or operationally difficult floods, thereby yielding an optimistic assessment. The manuscript should report objective event thresholds, event separation rules, missing-data treatment, the number of radar-supported events actually used in training, validation, and testing, and whether splitting was chronological or event-wise. The stated data period ends in 2023, yet a 2024 Jumahe event is evaluated later, which must also be reconciled. All samples from a single event must remain within one partition because random division of overlapping 30 min sequences would leak nearly identical hydrograph and radar states across subsets.
Lines 153-155: Temporally interpolating rainfall-runoff records to 30 min resolution may create artificial timing information precisely where the study evaluates peak timing and short-lead predictability. The original resolutions of rainfall and discharge, interpolation methods, handling of accumulated rainfall, discharge-rating uncertainty, and temporal alignment between gauges, radar scans, and outlet flow are not provided. Linear interpolation of coarse discharge observations can smooth peaks, while interpolation of rainfall totals can alter intensity and antecedent wetness. The authors should document the native sampling frequencies and demonstrate that conclusions at 0.5-2 h lead times are not artifacts of temporal resampling.
Lines 191-222: The claimed spatial and physical representation of runoff generation is difficult to reconcile with assigning generated runoff to subbasins according only to area fractions. This formulation appears unable to represent spatial differences in rainfall, soils, land cover, antecedent moisture, or runoff coefficients, even though spatial radar information is central to the study. The SCS-CN implementation also lacks equations, parameter ranges, initialization, antecedent-moisture treatment, and an explanation of how an event-based cumulative formulation is applied recursively at 30 min resolution. Without these details, neither runoff volumes nor the attributed routing improvements can be independently reproduced, and errors assigned to routing may actually originate from an overly homogeneous runoff-generation module. The consequences of dynamic land-surface conditions for runoff attribution should also be discussed in relation to 10.5802/crgeos.179.
Lines 250-281: The PINAS procedure is not described at the level required to reproduce or assess the proposed methodological contribution. The manuscript should specify the number of layers, candidate kernel sizes and dilation factors, architecture parameters, relaxation or sampling method, search and retraining stages, validation criterion, complexity penalty, physical regularization formulas and weights, stopping rules, random seeds, and the final architecture selected for each basin or reach. It is also unclear whether architecture selection used any events subsequently included in testing. Because architecture search increases model-selection flexibility, comparing its best searched configuration with single fixed Muskingum and CNN-Unit configurations may confer an unfair advantage. Parameter counts, search costs, training times, repeated runs, and equivalently tuned baselines are needed to separate architectural benefit from greater optimization effort.
Lines 282-325: The residual forecasting head can potentially overwrite the hydrological prior, so the final prediction is not necessarily constrained by runoff generation, routing, or water balance despite the physical interpretation assigned to it. Non-negative output alone does not preserve mass, timing, recession dynamics, or the contribution of the physical core. The authors should quantify the magnitude of the residual relative to Q_phys evaluate physical-prior forecasts before correction, and report whether corrections systematically dominate during peaks or specific lead times. Ablations using the physical core alone, the forecasting head without Q_phys , and alternative correction constraints are essential to demonstrate that the final skill arises from meaningful hybridization rather than from an LSTM learning discharge while treating the physical simulation as an additional predictor.
Lines 333-368: Radar reflectivity is advected directly in dBZ space and supplied as future meteorological information, but the manuscript does not establish the hydrometeorological quality or independent value of these extrapolations. Details are needed on radar calibration, clutter and attenuation correction, beam blockage, scan interval, spatial resolution, gauge adjustment, missing echoes, PyrLK settings, and extrapolation verification. More importantly, no benchmark isolates the contribution of future information. Comparisons should include persistence of the latest echo, models without extrapolated radar, models with observed radar only, and, where possible, an upper-bound experiment using subsequently observed rainfall or radar. Otherwise, performance differences cannot be attributed specifically to meteorological foresight rather than to additional correlated predictors.
Lines 359-373 and 412-427: The training objective and evaluation design are internally unclear. Table 4 describes a quantile-based data loss, but the model is subsequently evaluated as a single deterministic forecast, and the quantile levels, weighting matrix, error function, regularization coefficients, ramp-up epoch, and hyperparameter-selection procedure are omitted. In addition, NSE and RMSE calculated over strongly autocorrelated time steps within only a few events do not provide independent evidence of superior generalization. Results should be aggregated across all withheld events, with event-level distributions and confidence intervals obtained from repeated training seeds or paired resampling. Peak-timing error should also be reported because much of the interpretation concerns phase displacement, yet the defined (T_p) variables are not used in the metrics.
Lines 396-402 and 480-527: The data-dependency experiment cannot presently support claims of sample efficiency because the method used to select the 25%, 50%, and 75% subsets is unspecified. Different fractions may contain different flood severities and types, making sample composition inseparable from sample quantity, as the authors themselves acknowledge. Nested subsets should be generated repeatedly using stratification by basin, peak magnitude, season, and hydrograph type, with identical independent test events and uncertainty across repetitions. A learning curve based on a single subset per fraction can produce non-monotonic behaviour simply through sampling variability or stochastic optimization and should not be interpreted as evidence that physical constraints alleviate data scarcity without direct comparison against the other models under the same reductions.
Lines 532-589: The SHAP results are interpreted too strongly as evidence that radar echoes or measured rainfall “control” basin forecasts and demonstrate the necessity of hydrometeorological fusion. These inputs are highly correlated across time and between gauge, areal-rainfall, observed-radar, and extrapolated-radar groups, under which SHAP attribution can be redistributed among redundant variables and depends on the background distribution and explainer. Summing absolute contributions also removes directionality and does not demonstrate hydrological causation or incremental predictive information. The authors should identify the SHAP algorithm and reference dataset, assess sensitivity to correlated-feature grouping, report signed and event-wise contributions, and corroborate the interpretation through input-ablation or permutation experiments. The basin-scale explanations should remain hypotheses unless supported by such predictive tests.