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

Preprints

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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'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

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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