| 25 Aug 2026
Simulating Subsurface Stormflow Across Catchments: Parameter Estimation and Uncertainties
Abstract. Subsurface Stormflow (SSF) is an important runoff-generation process, especially in temperate and mountainous regions. It can play a substantial role in catchment-scale flood generation and nutrient or contaminant transport. Due to process heterogeneity and subsurface occurrence, it is difficult to be quantified in the field. Since hydrological models are often calibrated using only discharge data at the catchment outlet, SSF-relevant parameters are often affected by equifinality, leading to large uncertainties in simulated SSF. In this study, we used the widely used bucket-type HBV model to analyse simulated SSF uncertainty across four catchments. We performed Monte Carlo simulations with 1,000,000 parameter sets and selected the top 5 % as behavioural. We subsequently analysed SSF parameter sensitivity in a regional sensitivity analysis and SSF simulation uncertainty in a GLUE-type approach. We examined whether more information on SSF is hidden in specific discharge conditions using a parameter-estimation approach based on percentiles of the flow-duration curve. In addition, we investigated simulated SSF uncertainty by disentangling simulated SSF volume and occurrence uncertainties. We found that there are high uncertainties in simulated SSF volume and occurrence across all catchments, with mostly low sensitivity of SSF-relevant parameters. We further found that SSF parameter identifiability could be improved by percentile parameter estimation, and more so in snow-insensitive catchments than in snow-dominated catchments. However, SSF simulation uncertainty still remained high. In the SSF uncertainty decomposition we could show that SSF occurrence uncertainty contributes a substantial part to total SSF simulation uncertainty. This study therefore emphasises the need to include SSF data into model calibration to ensure a realistic simulation of SSF and thereby achieve better process representation in lumped hydrological models and thus yield more robust prediction models. Our findings suggest that SSF proxy data indicating SSF occurrence in the catchment might already help to reduce SSF simulation uncertainty.
Competing interests: At least one of the (co-)authors is a member of the editorial board of Hydrology and Earth System Sciences.
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General comments:
Subsurface stormflow (SSF) plays a critical role in hillslope runoff generation, flood formation, as well as nutrient and contaminant transport. Therefore, investigating the capability of lumped hydrological models to represent SSF carries clear scientific relevance, and the present study addresses a meaningful research topic. The most important finding of this paper is that substantial simulated uncertainty in SSF persists even when applying the proposed percentile parameter‑estimation approach.
While hillslope hydrological processes are complex and heterogeneous, catchment‑scale rainfall‑runoff responses often exhibit a certain degree of “simplicity” that can be represented with only a few parameters. Accordingly, whether a detailed representation of subsurface stormflow (SSF) processes is necessary for catchment‑scale simulation deserves further discussion and testing (McDonnell, 2003 & 2013; Ameli et al., 2015). This raises a core scientific question: for hydrological models applied at relatively large catchment scales, SSF may exert only minor influences on runoff simulation, particularly for flood processes. What really needs to be clarified is the scientific value of quantifying SSF: what new insights can it bring to our understanding of catchment‑scale runoff generation and routing? Which stages and subunits of runoff simulation can it improve?
Although many statements in this manuscript are consistent with existing knowledge, the paper fails to address the above‑mentioned core scientific question, which constitutes a critical shortcoming of this work. If the authors keep the current technical framework, I suggest refocusing the core analyses to answer the following questions: can lumped hydrological models such as HBV reproduce SSF‑related processes at the catchment scale? Which phases of runoff are dominated by SSF? Or is SSF intrinsically unimportant for catchment‑scale hydrological simulation?
The authors propose and adopt a percentile parameter-estimation approach. In my view, however, global calibration does not delete high-/low-flow information; it merely assigns implicit weights to different flow segments through the objective function. The authors' statement of "information loss" is not rigorous enough—the information still exists, but its contribution is diluted in the global objective function rather than disappearing. Regarding the percentile parameter-estimation approach, the authors still need to provide an in-depth justification of its relationship with global calibration, and in particular to further demonstrate whether it has the ability to supplement new information.
An important finding of this study is the generally large simulated uncertainty in SSF across all catchments. One plausible explanation is that SSF may simply play a negligible role in catchment‑scale runoff simulation. I do not deny the importance of SSF in runoff generation and source partitioning, especially in humid regions. Nevertheless, such understanding originates from the perspective of water‑particle transport for water‑source separation, rather than flood‑wave propagation dynamics — the very target simulated by conventional hydrological models. Moreover, extensive modelling experience suggests that SSF generation and transformation are mostly restricted to hillslopes at the 100‑m scale, and its contribution to whole‑catchment flood‑wave propagation tends to be small, thus having limited impacts on overall hydrological simulation. The authors are recommended to comprehensively re‑evaluate the positioning of this research topic.
In addition, the writing of the paper is not sufficiently developed. For example, the methods are not adequately explained, and the figures, in combination with the relevant text, still need further improvement, making the paper difficult to follow.
Specific comments:
Lines 22-26: There is an important reason that may directly lead to the uncertainty in SSF simulation: SSF may simply not matter for catchment-scale runoff simulation. For catchment-scale runoff simulation, compared with channel flood routing, is the short-term hydrological storage on hillslopes and the resulting SSF really so important for the overall runoff evolution of the catchment? Then the question is: what exactly does SSF control in the rainfall–runoff response—be it a feature of the hydrograph or of the flow-duration curve (FDC)?
Lines 34-36: This statement appears to be correct, but it does not get to the heart of this paper, namely, what exactly SSF determines in terms of response characteristics at the catchment scale—something that can be revealed from the hydrograph or the FDC as the lumped outcome of the runoff response of the catchment's individual sub-units.
Lines 43-45: The point conveyed by this statement actually corresponds to the questions I raised above, namely, whether it is truly necessary and important to characterize SSF processes in catchment scale simulations of flood events.
Lines 48-51: It is true that they can reflect some sensitive and controlling processes, but the problem is that, due to the existence of equifinality, through analyses based on such models we are basically unable to state with certainty which factors play a crucial role under specific conditions. As stated by Beven (2006), “The equifinality thesis is intended to focus attention on the fact that there are many acceptable representations that cannot be easily rejected...”
Lines 54-55: This statement hits the nail on the head: since it cannot clearly represent this process, the SSF characteristics reflected by its parameters are inevitably ambiguous, which makes the conclusions of papers based on it highly questionable.
Lines 59-63: There are many factors that lead to equifinality, such as the inadequate representation of processes by the model and the resulting ambiguity in parameter meaning, as mentioned above. Therefore, attributing equifinality solely to observations here is somewhat misleading.
Line 67: Then, can the HBV model you adopted actually support the research results you aim to achieve? From the above discussion, it seems that it cannot?!
Lines 80-81: The key issue is: without observations, how can you prove that your improved model is correct?
Lines 87-88: This challenge can arise from multiple aspects, including how to obtain high-resolution soil thickness, soil structure, and hydraulic parameters, how to quantitatively and mathematically describe the SSF process based on vegetation–soil conditions, and so on.
Lines 91-94: Why was FDC information adopted without the necessary justification beforehand? Is it to consider high, medium, and low flow information from multiple perspectives? There is also a possibility: if this process is not important in flood generation, then its uncertainty, i.e., equifinality, may also be relatively large. As for HBV, as you also mentioned, in the study by Hughes and Farinosi (2021), due to differences in topography, soil thickness, etc. across hillslopes, the proportion and pathways of interflow may exhibit considerable spatial variability. So why was a lumped hydrological model adopted here?
Lines 106-107: ‘First, we examined whether more information on SSF is hidden in specific discharge conditions using a parameter-estimation approach based on percentiles of the flow-duration curve’. There is bound to be information that remains hidden, because not every discharge stage contains an SSF component, and the flow pathways by which SSF reaches the river differ—for example, some SSF enters the channel directly, while some is first converted to overland flow and then reaches the river. In my view, it is very difficult to identify these different pathways and response patterns using only discharge data at the catchment outlet.
Lines 111-115: These fragments of the discharge time series are most likely non-continuous within each flood event—they are fragmented pieces of data. As we know, what the model simulates is a continuous process. So how can the comparison be made?
Line124: The reviewer feels that the flowchart in Figure 1 is too crude, and the logical connections between its parts are lacking. For example, it does not present the percentile parameter estimation method very well—is "11 sets of top 5% behavioural parameter sets" equivalent to "selection of most promising percentiles" in the figure? What is regional sensitivity analysis?
Line 135: Does TT correspond to PTT in the equations (1) and Figure (2)?
Lines 159-164: As the authors themselves mention, SSF should by no means be reflected only in Q0; it should also be reflected in Q1, and even in Q2. Therefore, I suggest further improving the experimental methodology based on this more scientifically sound understanding.
Lines 176-179: procedures for parameter sets and sampling are repetitive with the earlier description in this section.
Lines 197-198: The reviewer suggests providing a more detailed description of the random parameter set method, as it constitutes a critical step in the methodology of this paper.
Line 303: What is a lower benchmark for model performance?
Lines 327-330: Does this imply that there are too‑few flood events in the Black Forest (BF) catchment compared with SL, or does it point to other underlying mechanisms?
Lines 367-369: Suggest conducting supplementary statistical analyses, since the above‑mentioned findings can hardly be clearly identified merely from the current figure.
Lines 386-387: What is the meaning of ‘with the Sauerland also being the only catchment where SSF volume uncertainty does not entail zero at all times’?
Lines 389-390: It is suggested to add the fraction of snowfall relative to total precipitation for the Ore Mountains (OM) catchment. In addition, is the plotted hydrological year 2005‑2006 a drought year? Judging from this year, the low‑season hydrograph of the catchment is flat, indicating that total runoff fluctuations induced by interflow and baseflow are very small. This matches the authors’ statement of a high SSF activation threshold. Nevertheless, one question arises: does this catchment possess relatively thick weathered regolith or periglacial cover beds, such that a substantial amount of deep subsurface runoff is routed via deeper flow‑paths and does not eventually discharge at the catchment outlet? The authors are recommended to add runoff coefficients of all catchments to Table 2.
Lines 394-395: Why?
Lines 401-402: I do not fully understand the rationale behind the authors’ decomposition into occurrence‑related uncertainty and volume‑related uncertainty. These two components essentially represent different facets of one single problem, which is distinct from attribution analyses of runoff change, where precipitation, temperature and land‑surface conditions act as independent driving factors that each contribute to runoff variations.
Lines 428-429: This comment is rather vague and unconvincing as an explanation for inter‑catchment differences in KGE values.
Lines 459-465: From my perspective, this so‑called percentile parameter‑estimation approach is merely a way to emphasize either flood peaks or low‑flow processes. Such information is still retained and may be diluted in conventional global calibration. I therefore disagree with the claim that this information is lost.
Lines 482-485: The schemes for the main analysis and the additional analysis should be illustrated in Figures 1 and 2.
Lines 491-500: Is the low sensitivity of SSF‑related parameters attributable to the fact that this process is not important for simulating flood‑wave propagation at the catchment scale?
Lines 501-504: As the authors state in this paragraph, their results do not provide strong evidence that SSF is important, and the percentile parameter‑estimation method remains to be further tested.
Lines 515-518: The authors’ description appears inconsistent with the results shown in Figure 5. Please check and verify whether there is a contradiction.
Lines 525-526: I would like to emphasize again that the primary reason why SSF appears less important in HBV simulations may be that this process is not critical for the simulation of flood‑wave propagation at the catchment scale. Isotope‑based observations reveal water source composition from the perspective of water particle transport, rather than the evolution of hydrological dynamics in terms of flood‑wave propagation, which is what current hydrological models aim to simulate.
Lines 556-557: What does the finding that SSF occurrence uncertainty contributes substantially to the total simulated SSF uncertainty imply? Is this a problem inherent to the model itself?
Lines 560-569: This paragraph largely reiterates existing findings and conclusions from previous literature, and we suggest its removal.
Lines 570-581: This paragraph is logically sound. However, as outlook statements for this study, it should be moved to the Conclusions section.
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