| 26 Oct 2026
Beyond instantaneous runoff generation: large-sample evaluation of temporal forcing kernels in mGRHyMoLAP
Abstract. Conceptual rainfall–runoff models retain antecedent information through dynamic states, but differ in whether individual runoff-generation contributions are distributed over subsequent time steps. GRHyMoLAP represents antecedent influence through its production store and recession dynamics, yet applies its additive runoff-generation forcing instantaneously. We introduce mGRHyMoLAP, which replaces this instantaneous application with a normalized temporal convolution while retaining the original storage and recession structure. We represent different temporal convolution shapes by comparing a flexible discrete kernel with parsimonious exponential and log-normal kernels and testing them out of sample across 623 CAMELS-GB catchments against the original GRHyMoLAP and GR4J. The log-normal formulation improves NSE in 93.1% and KGE in 90.7% of catchments relative to GRHyMoLAP and outperforms GR4J in 68.1% and 72.6%, respectively. Beyond aggregate performance, mGRHyMoLAP maintains similar agreement during non-increasing-flow periods while more consistently reproducing the observed direction of daily flow increases. Extending the kernel from current-day forcing only to include one antecedent day captures most of the performance gain, with little further median improvement for longer memory windows. A non-zero kernel peak occurs in 42.9% of catchments, indicating a substantial contribution of antecedent runoff-generation forcing; 96.6% of these catchments peak at a lag of one day. All catchments with a non-zero lag peak improve relative to GRHyMoLAP, with a median NSE increase of 0.067, compared with improvements in 87.9% and a median increase of 0.010 among catchments with a lag-0 peak. Simulated performance is robust across calibration choices, whereas detailed kernel moments and tails are less identifiable, supporting peak lag as the primary diagnostic while cautioning against interpreting the calibrated kernel as a direct estimate of physical travel-time distributions. Non-zero peak lags are associated with larger catchments, longer high-flow durations, lower mean precipitation, higher aridity, and greater cropland fractions. These results demonstrate that temporal redistribution of runoff-generation forcing can improve GRHyMoLAP predictions and provide a useful model-based diagnostic of where such additional temporal flexibility is beneficial.
Dear Authors,
I have carefully evaluated the submitted manuscript and it was definitely an enjoyable read. The study addresses a very interesting limitation of the GRHyMoLAP model, and its evaluation across 623 CAMELS-GB catchments provides a substantial empirical basis for assessing the proposed extension. However, some weaknesses remain concerning the hydrological interpretation of the temporal kernels, the experimental design, and the identifiability of the inferred memory characteristics. But I believe they can easily be addressed without substantial additions.
Lines 55-73: The distinction between delayed runoff generation and conventional flow routing requires stronger justification. Since GRHyMoLAP lacks the explicit routing structure present in GR4J, the improved performance may primarily reflect compensation for this structural omission rather than a distinct runoff-generation mechanism.
Lines 140-156: The normalization of kernel weights preserves the cumulative forcing signal but does not necessarily ensure water-balance consistency in the nonlinear runoff equation. Redistributing the product of percolation and effective precipitation may modify simulated runoff volumes through interactions with the recession term. The authors should examine whether the extension alters cumulative runoff, runoff coefficients, or water-balance residuals relative to GRHyMoLAP. Clarification of how non-negative discharge is maintained under the explicit Euler scheme would also strengthen the physical and numerical interpretation.
Lines 187-205: The log-normal kernel is discretized by evaluating its density at shifted integer lags rather than integrating probability over daily intervals. This choice influences the relative weights assigned to lag 0 and lag 1, which becomes particularly important given that nearly all non-zero kernel peaks occur at one day. The authors should assess whether the inferred peak-lag classifications remain stable under interval-integrated weights or alternative discretization conventions. Otherwise, part of the identified temporal structure could reflect the discretization scheme rather than catchment response.
Lines 265-280: The calibration strategies differ between model formulations, particularly in optimization algorithms, initial parameter sets, and parameter dimensionality. This complicates attribution of performance differences to kernel structure alone, especially when the log-normal kernel only marginally outperforms the much more flexible explicit kernel. Although the expanded-search experiment is useful, comparable convergence diagnostics and computational search budgets across the formulations would better establish whether these small differences reflect model structure or optimization efficiency. The initialization of production storage and discharge states, and the adequacy of the 15-day exclusion period for model spin-up, also require clarification.
Lines 314-327: The use of daily precipitation forcing introduces uncertainty into the interpretation of the inferred one-day memory. Errors in precipitation timing or temporal aggregation may be absorbed by the calibrated kernel, making it difficult to distinguish actual catchment response delays from forcing-related errors. This issue is particularly relevant because allowing only one antecedent day produces nearly the entire performance improvement. Sensitivity experiments involving shifted precipitation inputs or alternative forcing datasets would help assess this ambiguity. The implications of precipitation uncertainty for parameter inference could also be discussed in relation to DOI: 10.1016/j.ejrh.2025.102957.
Lines 345-360: The statistical comparisons emphasize highly significant Wilcoxon tests, although the median differences between the log-normal and explicit kernels are only 0.0012 for NSE and 0.0006 for KGE. These differences have limited practical significance despite their small p-values. Additionally, spatial dependence and potentially nested catchments in CAMELS-GB may weaken the independence assumption underlying catchment-level inference. Reporting confidence intervals obtained through spatially grouped resampling, together with the distributions of paired performance differences, would provide a more informative assessment of the practical advantage of each formulation.
Lines 395-414: The analysis of flow-change direction offers an interesting diagnostic, but its interpretation needs qualification. Under zero effective precipitation, GRHyMoLAP cannot generate a positive discharge increment by construction, making its zero agreement for observed rising flows a mathematical consequence of the model equation. The improvement therefore does not independently establish the physical relevance of the proposed memory mechanism. Furthermore, the difference between mGRHyMoLAP and GR4J under these conditions is modest (0.340 versus 0.329). Event-based assessments of rising-limb timing, peak displacement, and discharge-change magnitude would better establish whether the new formulation improves hydrological dynamics beyond reproducing the correct sign.
Lines 441-475: The sensitivity analyses provide useful evidence that peak-lag classification is relatively stable, while the strong relationship between kernel-tail mass and recession loss indicates substantial parameter compensation. Nevertheless, stability of the largest kernel weight does not necessarily imply that the peak timing is identifiable, particularly when weights at adjacent lags are nearly equal. The authors should examine the separation between the two largest weights and the associated calibration-objective sensitivity. Constraining recession parameters or comparing near-equivalent parameter sets would help determine whether the inferred peak lag represents a distinguishable model characteristic rather than one of several compensating solutions.
Lines 483-527: The relationship between positive peak memory lags and larger performance improvements deserves a more independent assessment. Catchments are classified using parameters estimated by the same extended model whose benefit is subsequently evaluated, introducing potential dependence between the grouping criterion and the reported improvement. Similarly, the univariate comparisons in Table 6 do not distinguish the individual contributions of catchment area, precipitation, aridity, slope, and cropland fraction, which may be strongly correlated. A multivariate analysis accounting for spatial dependence and covariate interactions would help determine which attributes retain explanatory value. The scale dependence of runoff response also warrants consideration when interpreting these relationships (DOI: 10.1016/j.jaridenv.2021.104590).