Runoff thresholds as state-dependent connectivity transitions: A global synthesis across diverse catchments

Cui, Zhen; Tian, Fuqiang

doi:10.5194/egusphere-2026-1265

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https://doi.org/10.5194/egusphere-2026-1265

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12 Mar 2026

| 12 Mar 2026

Status: this preprint is open for discussion and under review for Hydrology and Earth System Sciences (HESS).

Runoff thresholds as state-dependent connectivity transitions: A global synthesis across diverse catchments

Zhen Cui and Fuqiang Tian

Abstract. Runoff threshold behavior is widely reported in event-based hydrological studies, but its interpretation and cross-catchment comparability remain unresolved due to variations in threshold metrics and values across climates, landscape structures, and observational focuses. This study synthesizes reported storm-runoff thresholds from experimental catchments worldwide by compiling the indicators used to detect nonlinearity, the dominant runoff generation mechanisms, their observed transition pathways under increasing wetness, and recurrent soil–geology fingerprints. Across mechanisms and climates, thresholds are identified using diverse (and often non-standardized) rainfall-based, state-based, and composite indicators. However, antecedent and within-event state variables (e.g., soil moisture, catchment storage, groundwater level) consistently provide better explanations for nonlinear runoff responses than rainfall metrics alone, indicating that threshold behavior is primarily controlled by the state of the catchment but is triggered by rainfall. Subsurface- and saturation-related mechanisms dominate the reported cases, particularly in humid environments. When mechanism shifts are explicitly documented, responses show a strong directional organization with increasing wetness, typically evolving from infiltration-excess overland flow to saturation-excess overland flow, and then to subsurface or groundwater-dominated pathways. Soil–geology network analysis further reveals that each dominant mechanism is associated with recurring combinations of soil depth, texture, permeability contrasts, lithology, and geological structure, forming structural fingerprints that regulate connectivity development. Overall, runoff thresholds are best understood as markers of hydrologic connectivity transitions within structurally constrained landscapes, rather than fixed rainfall exceedances. We propose a connectivity-based conceptual framework linking rainfall forcing, evolving states, structural controls, and mechanism transitions to support cross-catchment comparison, guide future observations, and improve the representation of nonlinear runoff responses in hydrological models.

Received: 06 Mar 2026 – Discussion started: 12 Mar 2026

Competing interests: At least one of the (co-)authors is a member of the editorial board of Hydrology and Earth System Sciences.

Publisher's note: Copernicus Publications remains neutral with regard to jurisdictional claims made in the text, published maps, institutional affiliations, or any other geographical representation in this paper. While Copernicus Publications makes every effort to include appropriate place names, the final responsibility lies with the authors. Views expressed in the text are those of the authors and do not necessarily reflect the views of the publisher.

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Zhen Cui and Fuqiang Tian

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RC1:
'Comment on egusphere-2026-1265', Anonymous Referee #1, 12 Apr 2026 reply
This is a really interesting paper reviewing threshold behaviors and runoff generation mechanisms for many catchments around the world and linking them to catchment properties. The analysis, and in particular the figures, are very insightful. However, the text is not always very clear and precise and the conclusions seem to go beyond the scope of the study. Below, I will give 3 examples, but there are more instances in the manuscript. These may seem like nuances, but they are important differences, especially in the abstract and conclusions:
There is a persistent mix-up in the text on the presence of a threshold (based on data) and the interpretation of either a hydrological process or connectivity. This distinction needs to be made much more carefully and clearly throughout the text. For some suggestions, see the annotated pdf.

On L425 it is said that “A key finding is that rainfall alone is insufficient to explain nonlinear runoff responses”. And on L586 “Across climates and landscapes, antecedent state variables consistently provide stronger explanatory power for nonlinear runoff responses than rainfall-based descriptors”. While these statements may be true, this study didn’t test nor compare the explanatory power of rainfall and other factors in explaining the threshold response for different datasets. Thus, this is not a finding of this review and someone who only reads the abstract and conclusions may get the wrong impression of the manuscript and its findings based on the quoted sentences. A key finding of this review is that few studies use rainfall alone to explain nonlinear runoff responses and that more studies used antecedent state variables. It is likely that more people report thresholds with antecedent wetness conditions because they perform better, but it may also be because they do this to compare their results with other published results (there are indeed cases where both rainfall and rainfall plus storage explain almost the same amount of variation in the data). Furthermore, the choice of a certain explanatory variable to describe the threshold may depend on the type of data that are available (only rainfall, soil moisture, or also groundwater levels) – which is not really discussed in the manuscript.

L579 – 582 and elsewhere in the manuscript “Our findings demonstrate that runoff thresholds are not fixed hydrologic constants, but emergent properties resulting from the interactions between rainfall forcing, evolving catchment states, and relatively stable structural constraints”. I agree with the later part of the sentence but why would the threshold not be a constant or emergent property for a specific catchment? Again, the study didn’t test if it is constant or if thresholds have changed over time or seasonally, so these types of statements seem to be too broad and beyond the scope of the study. Of course, it is not a constant for all catchments, but no one would expect that.

Important review papers on threshold responses, like Ross et al (https://agupubs.onlinelibrary.wiley.com/doi/full/10.1029/2020WR027498), Ali et al. (https://onlinelibrary.wiley.com/doi/10.1002/hyp.10527) and McDonnell et al (https://agupubs.onlinelibrary.wiley.com/doi/full/10.1029/2020WR027514) are not mentioned or discussed and there is no discussion on how this study complements these previous studies in the introduction, nor any comparison of similar findings or mention of discrepancies in the discussion. Similarly, the recent review papers highlighting the variation in runoff processes, such as Penna (https://www.nature.com/articles/s44221-025-00547-z) and McMillan et al (https://www.nature.com/articles/s44221-025-00407-w and https://onlinelibrary.wiley.com/doi/full/10.1002/hyp.14537) should be highlighted and discussed. That other reviews are available doesn’t mean that this work is not useful. Instead, it should be made clear how this review complements the previous reviews (i.e., the global scale and the linkage to runoff generation processes and catchment characteristics in this review) and where findings are different.
Finally, it is unclear what the difference is between antecedent soil moisture condition, antecedent soil moisture, and soil water content. Are these not all referring to the same thing? And what is the difference between coupled soil-groundwater, storage state, and storage? It will be very useful to define these terms more clearly in the methods sections where the annotations are also described. Even if there are small differences in these terms perhaps, they can still be grouped so that Figure 2 contains fewer terms?
Specific comments:
Methods and results: It is not clear if percentages are given per catchment or per study. The search terms probably led to multiple studies for some catchments and some studies that report results for multiple catchments. How were these treated in the statistics?

Methods L140: how many "hits" did your search terms get? Did you screen all of them? Or is the 200 a selection? To what time period did you limit your search?

Methods: Information on what software and packages were used to create the different diagrams and do the analyses needs to be added.

Figure 2: This is a really nice figure but spell out the acronyms in the caption. Also it would be useful to include a table (or figure) with the % of studies that used what metric (and possibly then split this also by runoff mechanism).

Section 3.3 and elsewhere – it is important to clearly state that studies that found a certain dominant runoff generation mechanism mainly took place in a certain climate - not that the runoff mechanism does not also have to be dominant in that climate. This is important as we know that research catchments are not representative of the entire land surface (as shown in Figure 4b by the dominance of forested catchments and an exclusion of catchments in croplands or (sub)urban areas, even though these cover a large part of the global land surface). This may seem like a nuance but is in my opinion an important one. See specific suggestions in the annotated pdf.

Section 3.3 (and 3.5) is interesting and very nice, but these results are not discussed in the discussion at all. How do these results compare to the recent studies of McMillan et al and Penna?

Figure 8: I understand the reason for the inclusion, but shallow groundwater is not a geological structure.

L456: What is meant with “perform”? This is not a model study where one can compare simulations and observations, nor are the “performance” of different metrics in explaining the thresholds tested. Instead, the review shows that some metrics are less frequently used (possibly because they describe the data less well, or because the data were not available, or simply because the use of other metrics makes comparisons with the literature easier).

L469-472: There are some non-intuitive results here that need to be explained or discussed better. Why would coarse material (which generally has a high conductivity) lead to HOF? Why would a limited storage capacity lead to HOF, rather than SOF? Why would low conductivity soils lead to SOF (via near surface saturation) but not also to HOF due to the low conductivity? This requires some discussion (and perhaps even some speculation).

Figure 9: I like the figure and think that it could be very useful for discussions and teaching. However, I don’t understand the y-axis and it is not explained in the text. Why is connectivity considered to be higher for groundwater flow than for subsurface stormflow and why would it be higher for SSF than OF? What is this based on and what is the evidence for that? And what is the arrow for soil depth supposed to reflect? Explain better in the caption.

Discussion: The discussion is long and at times extends beyond the topic and findings of the review and analyses. Try to shorten it and to stay closer to the core results of the manuscript.

General comments on the text: Several blocks of text are given at two locations in the manuscript (i.e., copied at two places). Please remove the duplicates (see annotated pdf). Other parts of text are not necessary as they should be part of the captions and can be removed (see annotated pdf for suggestions).

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Citation: https://doi.org/10.5194/egusphere-2026-1265-RC1
RC2: 'Comment on egusphere-2026-1265', Jintao Liu, 13 May 2026 reply

General comments:
This manuscript presents an ambitious synthesis of runoff threshold behavior across diverse catchments, offering a connectivity-based framework for understanding nonlinear rainfall-runoff responses. The authors have compiled an impressive dataset of 138 experimental catchments and conducted systematic analyses of threshold indicators, dominant runoff mechanisms, transition pathways, and soil-geology fingerprints. The central finding as stated by the authors—that runoff thresholds represent state-dependent hydrologic connectivity transitions rather than fixed rainfall exceedances—is conceptually valuable and advances the ongoing discourse on runoff generation processes.
However, I think the key finding of the paper is its clear demonstration that as catchments become wetter, the runoff generation zone progressively shifts from the soil surface or near-surface layers into the weathered bedrock layer. This indicates that, despite the dominant role of tectonic setting and lithology, climate still controls weathering and pedogenesis, thereby strongly influencing runoff generation. However, the paper still needs to further deepen our understanding of how climate, vegetation, soil, and rock weathering control runoff generation mechanisms across different catchments.
Therefore, the manuscript requires substantial revision to address several critical issues. The conceptual distinction between hydrologic connectivity across catchments (structural vs. functional connectivity) needs clearer articulation. The classification of dominant runoff mechanisms lacks operational clarity, and the methods section (Section 2) is insufficiently detailed for reproducibility. The interpretation of mechanism "transitions" within catchments versus across climatic gradients conflates fundamentally different processes, requiring separate treatment. Or I suggest that they only focus on the research of mechanism transitions across catchments. Additionally, the section of Data and Methods need a more detailed elaboration, and the presentation of results requires more transparent explanation of metrics and analytical procedures. The specific comments are presented following to guide the authors in strengthening the manuscript's conceptual framework, methodological rigor, and interpretive clarity.

Specific comments:
Lines 13-14: What is the recurrent soil geology combination? Does it refer to the repeated occurrence of similar soil geological and stratigraphic structures? From the following text, the author naturally believes that key band structures vary in different regions, thus forming structural fingerprints that regulate connectivity development. However, though readers are aware that they are different, and we want to know what characteristics the structures in different regions have, which can lead to different mechanisms of production flow connectivity.
Lines 33-40: The hydrological connectivity here includes both structural and functional connectivity. I suggest the author to delve deeper into the discussion of structural connectivity, i.e., how structural fingerprints of soil–geology combinations affect state-dependent connectivity which is functional connectivity from its literal meaning.
Lines 49-51: Traditionally, we also do not consider production flow to be linear, and the expression is not very rigorous.
Lines 62-63: In fact, hydrologic connectivity framework is proposed for explaining why similar storms generate different runoff responses due to different catchment state of connectivity. I do not think it is a good question in context. Rewrite this paragraph.
Lines 109-110: it is quite similar to above question. The readers may be more concerned about how much humidity increases in different climate basins can lead to abrupt changes in connectivity, resulting in so-called mechanism transitions. In addition, the language expression is not direct and difficult to understand. It is recommended to use simple language to express it.
Lines 104-112: In my opinion, none of these four questions are very clear and can be said to be expected. For example, for the second question, the answer is in a sense affirmative, but the transition of the runoff generation mechanism should also be different. In extremely arid and sparsely vegetated loess watersheds, the range of changes in runoff mechanisms may be limited despite increased humidity. In addition, the author uses the concept of mechanism transitions here, and I believe they should elaborate on what mechanism transitions are in the introduction? Traditionally, we believe that a location, such as a slope, has a fixed mechanism for runoff generation. If the slope does not produce runoff or is in the early stages of runoff generation, it is only due to differences in its internal hydrological connectivity that it is not suitable for runoff mechanism transitions. Personally, I think this is the case.
Lines 145-146: Studies focusing solely on linear rainfall-runoff relationships......, without event-scale threshold interpretation, were excluded. Why is there a linear relationship between precipitation and runoff in some watersheds, and shouldn't it all be nonlinear?
Lines 154-186: Though, according to the authors definition, i.e.，Classification reflects the mechanism that primarily controls stormflow during events exhibiting nonlinear or threshold behavior, however, for me, this classification definition is still very vague, not direct and clear enough. Hence, I strongly suggest that the authors present more clear definition and classification standard. Moreover, a conceptual diagram maybe needed to describe how HOF, SOF, SSF, GWF dominate or combine to shape stormflow of a headwater area.
Lines 218-245: What are the sensitivity tests (Line 243).
Section 2 Data and Methods is not detailed, and many methods were not provided. For instance, how do you obtain the result of figure 2 and the similar structural clusters (mentioned in section 2.5)? Moreover, the meaning of indicators (in figure 2), e.g., Pi and API, should be provided.
Lines 269-270: how many studies without specified threshold indicator?
Section 3.2 Frequency and proportional contribution of dominant runoff generation mechanisms is not important, and not recommended as a separate section, suggested to be included in section 3.1.
Line 302: how do you classify four aridity classes, i.e., humid, semi-humid, semi-arid, and arid? As it is not a standard pattern in Köppen climate classification, Provide the standards in section 2.
Figure 5 presents well that as the climate in the watershed becomes more humid, the runoff yielding interfaces gradually penetrate from the soil surface or surface layer to the weathered bedrock layer. This indicates that despite the dominant role of structure and rock lithology, climate still controls weathering and soil formation, thereby strongly affecting runoff. I suggest the author strengthen the discourse on this important discovery.
Line 343: Does node size refer to the bar height? And the rings represent the catchments where dominant mechanism remain unchanged?
In section 3.4, transitions of dominant runoff generation mechanisms with increasing soil wetness during rainstorm events and transitions across different catchments with increasing annual rainfall are quite different. I suggest the author to conduct relevant analyses separately. I can easily understand that as the humidity level increases, such as annual precipitation, the watershed runoff mechanism transitions from HOF to SOF. However, I don't understand why there is a similar transition within a watershed as rainfall events continue, HOF and SOF or SSF are essentially completely different mechanism of runoff generation, which is determined by vegetation-soils system. Hence, what is the underlying mechanism?
Line 384: what is Link thickness in figure 8? How do you calculate the frequency of repeated co-occurrence? Explain what co-occurrence is. Lack of necessary introduction makes it difficult for people to keep up with the author.
The results in Section 3.5 and figure 8 doesn't seem to be very convincing, for example, in small watersheds of limestone or granite, groundwater runoff can usually contribute to flood runoff processes, which seems to be missing from the author's analysis. In addition, the keywords listed in Figure 8d are not very accurate and cannot effectively represent the geological structure that affects runoff. It is recommended to merge Figure 8d and Figure 8c.
Lines 443-444: I totally agree that threshold are not fixed, catchment-invariant constant within each catchment. Many dynamic factors impact rainfall-runoff threshold, for instance rainfall intensity referring to Zhang et al. (2024). However, this factor has little impact on the threshold especially in humid climates, so the water storage capacity of a watershed is usually assumed to be a constant value, which explains why the water storage capacity parameter is set to a constant value in almost all hydrological models (e.g., the Xinanjiang model). While using the relationship curve of rainfall-runoff for determining the threshold and runoff, we always take storage state or antecedent rainfall into account. For example, the widely used method API is a Rainfall-Runoff Empirical Correlation Method.
Lines 447-448: I also totally agree that it is hydrologic connectivity that determines runoff generation. However, hydrologic connectivity including function and structure connectivity (Zhang et al., 2026) is quite difficult to be quantified. Hence, it is largely not a practical or directly available index.
Lines 456-457: in infiltration-excess-dominated systems, hydrologic connectivity determines runoff generation. However, what determines the former? It is soil-vegetation root systems (Gao et al., 2024). As mentioned above, hydrologic connectivity is difficult to quantify.
Lines 467-482. You must define what is SOF or SSF firstly in section 2. Otherwise, I could not figure out what the differences between SOF and SSF. As they are very close, and, in both conditions, overland flow will occur to shape flood discharge in creek channels.
Lines 504-505: we certainly know structural attributes, i.e., structural connectivity control connectivity and then threshold. However, the authors should provide more in-depth discussions about what (e.g., root biomass?) controls structural connectivity?
Lines 542-548: runoff mechanism transitions across catchments and within a catchment are totally different. The authors should provide discussions respectively.
Lines 549-556: things about rainfall have been mentioned repeatedly in the whole manuscript.
In figure 9, I agree that as wetness and connectivity increase, runoff mechanism could transit from HOF to GWF among different climates. However, subsurface flow could occur at very lower soil moisture level (SM<Field capacity), which could help explain why there are hockey stick rainfall-runoff curves in many catchments (Scaife and Band, 2017; Zhang et al., 2021). Moreover, in arid loess catchment, though with deep soils, HOF is the dominant runoff mechanism. In addition, SSF are easy to transit into SOF in the valley floors in steep humid hillslopes in the fields. Soil thickness or regolith thickness as well as vegetation root biomass may all control runoff mechanism transit. So, the conceptual framework still needs further review and revisions.
Reference:
Gao H,Hrachowitz M, Wang-Erlandsson L, Fenicia F, Xi Q, Xia J, Shao W, Sun GandSavenije H H G2024Rootzone in the Earth system Hydrol. Earth Syst. Sci. 28 4477–99
Scaife, C. I., Singh, N. K., Emanuel, R. E., Miniat, C. F., and Band, L. E.: Non‐linear quickflow response as indicators of
runoff generation mechanisms, Hydrological Processes, 34, 2949-2964, 2020. doi: 10.1002/hyp.13780.
Zhang, G., Cui, P., Gualtieri, C., Zhang, J., Ahmed Bazai, N., Zhang, Z., Wang, J., Tang, J., Chen, R., and Lei, M.: Stormflow generation in a humid forest watershed controlled by antecedent wetness and rainfall amounts, Journal of Hydrology, 603,
127107, 2021a. doi: https://doi.org/10.1016/j.jhydrol.2021.127107.
Zhang, J., Liu, J., Han, X., Shen, X., Liang, Z., & Wang, S. (2022). Variable storage behavior controlled by rainfall intensity and profile structure upon saturation excess overland flow generation. Journal of Hydrology, 610, 127860. https://doi.org/10.1016/j.jhydrol.2022.127860
Zhang, Y., Guo, L., Xu, H., Liu, H., Liu, J.,Sun, X., et al. (2026). Quantifyingsubsurface hydrological connectivity andits coupling with structural connectivity inheadwater catchments. Water ResourcesResearch, 62, e2025WR042599.

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Citation: https://doi.org/10.5194/egusphere-2026-1265-RC2

Zhen Cui and Fuqiang Tian

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Short summary

This study explores how storm runoff behavior varies across environments and identifies key factors driving these changes. We found that runoff thresholds depend on land state, such as soil moisture and groundwater levels, rather than just rainfall. A new framework is proposed to improve flood predictions and water management by focusing on landscape features, water storage, and flow paths.


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