the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 04 Mar 2026
Beyond Runoff Coefficient: Revealing Global Patterns of Process Connectivity in Runoff Generation through Intensity Integration
Abstract. Climate change and human activities have profoundly altered the connectivity of runoff generation (i.e., the transformation process from precipitation to runoff). It is critical to understand this connectivity for climate change adaptation and water-related risk management. However, the runoff coefficient (RC), as the most common connectivity indicator, only describes the ratio of precipitation transformed into runoff, failing to characterize the rate of the transformation. Here we develop a novel framework to assess process connectivity in runoff generation through intensity integration. The RC and runoff intensity (RI) are adopted to represent the transformation ratio and rate from precipitation to runoff, respectively, and a composite metric runoff efficiency (RE), calculated as the product of RC and RI, is proposed to capture both dimensions. Applying this framework to 6,603 catchments globally over 1950–2020, we quantify the spatial patterns of process connectivity, diagnose their influencing factors, and examine their long-term trends and event-scale responses to precipitation intensity. According to their multi-year average values, we find a relatively high RC and RI in wet and dry areas, respectively. Interpretable machine learning further reveals that climatic attributes primarily control the process connectivity globally. The results of long-term trends show that the hotspots of increasing process connectivity are South America and central North America, which are typically associated with a higher flood risk. Event-scale results indicate a high sensitivity of precipitation intensity on RE in dry climate zones. These findings not only enhance our understanding of runoff generation processes under the changing environment, but also offer valuable insights into adaptive water resources management.
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RC1: 'Comment on egusphere-2026-1006', Anonymous Referee #1, 30 Mar 2026
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The comment was uploaded in the form of a supplement: https://egusphere.copernicus.org/preprints/2026/egusphere-2026-1006/egusphere-2026-1006-RC1-supplement.pdfReplyCitation: https://doi.org/
10.5194/egusphere-2026-1006-RC1 -
RC2: 'Comment on egusphere-2026-1006', Anonymous Referee #2, 03 Apr 2026
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Liang et al. assess rainfall-runoff relationships at the global scale by introducing a composite metric “runoff efficiency” (RE), defined as the product of runoff coefficient (RC) and runoff intensity (RI). They find that while the three indicators differ in magnitude across different regions, they are primarily controlled by climate attributes at the global scale. In addition, the authors implement a power law relation between RE and precipitation intensity, with its parameters varying for different climates. While the proposed approach is quite interesting, I would like to raise some critical points and general comments for the authors to consider before proceeding with the manuscript’s publication process.
Major comments
- I do not fully understand the reason for setting up a hydrological model as described in section 3.1.1., especially since the simulations obtained with the model are not used later on in the analysis? The parametrization of the model introduces additional uncertainty, and I do not believe that its use can be justified only to exclude catchments with a KGE < 0.5. The data described in section 3 has additionally been quality-checked as indicated by the authors, so why not focus on these data and, if necessary, interpolate between the gaps (maybe set a lower threshold of, e.g., 5 days to reduce interpolation time span)
- While the idea of introducing a metric “RE” that reflects runoff intensity (RI) and transformation depth (RC) is interesting, I do not agree with the implications the authors attribute to RE. As far as I understand, a higher RE does not automatically imply “a larger fraction that is transformed to runoff with a faster rate for a given precipitation input” (L153). RC can be large while RI can be small, and the other way around, both resulting in the same RE. In the revised version of the manuscript, I would encourage the authors to explicitly explain these characteristics (and thus possible implications) of RE.
- Based on their analysis of catchment attributes influencing the above-mentioned metrics of RC, RI, and RE, the authors find that climate attributes exert strong influence on all metrics. Given the large, inherent climate gradients in global datasets, these gradients may overwrite differences in physical catchment properties, e.g., in terms of soil types or geology. This is especially relevant since many field-based studies emphasize the importance of catchment properties in runoff processes (e.g., Tromp-van Meerveld & McDonnell, 2006). I would recommend to at least discuss this issue in the revised version of the manuscript, including appropriate references of both large-scale and field-based studies.
- In my view, the authors usages of the terms “process connectivity” and “flood risk” may be misleading. With regard to the first term, “connectivity” can occur at different spatial scales. At the catchment scale, it may refer to the hillslope-riparian connectivity of different flow paths leading to the catchment’s outlet. In that sense, I do not see how the authors’ suggested metrics reflect hydrological connectivity; for example, a large RC does not automatically imply fully established connectivity within a catchment - one would need additional information (e.g., spatially distributed soil moisture measurement) to support this hypothesis. With regard to the second term, I do not see how “flood risk” can be quantified by simply looking at the runoff metrics. The authors are encouraged to revise (or omit) the use of the two terms in the revised manuscript.
- While results obtained in snow-dominated regions are still described in the results section, they are almost entirely omitted in the discussion section. For a complete picture, it would be beneficial to include these results into the discussion as well. On the other hand, other parts of the discussion (e.g., L 414-431) are excessively long and may be shortened.
Line by line comments
L 15-21: I would recommend to start with a summary of both long-term and event-based analysis for the different regions (wet, dry, snow), followed by the implications of the findings to conclude the abstract.
L 34-37: The authors may want to consider deleting this sentence, as I do not see how this is relevant to the present study.
L 44-46: Runoff coefficients have been analyzed on larger scales as well, e.g., Merz & Blöschl, 2009, Tarasova et al., 2018, Zheng et al., 2023
L 60-62: Merge sentences
L 75: This sentence is rather unspecific. In the previous sentences, the authors describe their analysis steps, but the aim(s) of the paper need to be stated more specifically.
L 86: Should be “2.1 Quantification […]”?
L 96: Specifying that the model is applicable to snow-dominated catchments seems unnecessary.
L 134: Is the threshold of 0.1 mm d-1 set for all catchments globally? If so, it should be indicated somewhere.
L 207: In the data section, the temporal resolution of the data should be indicated.
L 288: Are the trends described in this section statistically significant? This information should be added somewhere, either in the text or in Figure 5.
L 295- 298: The terms related to the “transformation rate” seem to have been mixed up here? Please check again.
L 329-330: Here, it would be good to shortly repeat the meaning of parameter m in a more physically interpretable context (e.g., move sentence from L 335).
L 360-361: I do not fully understand this sentence. What exactly does “transfer of the temporal characteristics of precipitation” mean?
L 402-408: These sentences rather read like the first sentences of a conclusion. The authors may want to consider removing this part.
L 447: The conclusions section rather reads like a summary of the results. What do the authors actually conclude based on their findings?
Technical comments
- The font sizes in almost all figures are too small and hard to read, especially the ones showing the global maps. It would be beneficial to adapt this in the revised version of the manuscript.
- Table 2: It would be interesting to transform this table into a figure (for the supplement) of, e.g., boxplots per regions, where each catchment can actually be represented as a point.
References
Merz, R., & Blöschl, G. (2009). A regional analysis of event runoff coefficients with respect to climate and catchment characteristics in Austria. Water Resources Research, 45(1).
Tarasova, L., Basso, S., Zink, M., & Merz, R. (2018). Exploring controls on rainfall‐runoff events: 1. Time series‐based event separation and temporal dynamics of event runoff response in Germany. Water Resources Research, 54(10), 7711-7732.
Tromp-van Meerveld, H. J., & McDonnell, J. J. (2006). On the interrelations between topography, soil depth, soil moisture, transpiration rates and species distribution at the hillslope scale. Advances in water resources, 29(2), 293-310.
Zheng, Y., Coxon, G., Woods, R., Li, J., & Feng, P. (2023). Controls on the spatial and temporal patterns of rainfall‐runoff event characteristics—A large sample of catchments across Great Britain. Water Resources Research, 59(6), e2022WR033226.
Citation: https://doi.org/10.5194/egusphere-2026-1006-RC2 -
RC3: 'Comment on egusphere-2026-1006', Anonymous Referee #3, 03 Apr 2026
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Beyond Runoff Coefficient: Revealing Global Patterns of Process Connectivity in Runoff Generation through Intensity Integration (Liang et al.,)
The manuscript Liang et al., discusses the connectivity processes describing runoff generation. Authors propose a new composite runoff efficiency integrating runoff coefficient and runoff intensity and have examined more than 6000 catchment globally over 1950-2020 to quantify the spatial-temporal patterns and characteristics. A machine learning based analysis has also been incorporated which reveals that climate attributes primarily control the runoff processes. Further hotspots of process connectivity has been identified with their further implications. The study is timely and comprehensive and can be crucial in providing new insights into global runoff generation process and can be utilised in relevant applications of the same. However, there are several avenues where authors need to clarify and possibly modify before publication.
- The authors need to built up on the foundation of why process connectivity is relevant for the arguments provided in paragraph one in the introduction section. The authors have mentioned hydrological connectivity L 25-28¸ and then process connectivity in L 39 however, more clarity and connection on why this is important need to be provided.
- In the literature review, it has been mentioned that majority of existing research concentrates on small scale catchments and some examples of UK, Austria and Italy etc have been cited. Reasoning behind the focus on small scale catchments and limitations related to attempting diverse regions globally need to be discussed in further details (not just limiting to L64-66).
- Relating to previous comment…RC for diverse global regions is itself sensitive to many factors, given runoff intensity has also been added, the authors really need to clarify 1. Why runoff intensity is crucial here? 2. Why this is important in a global context in terms of both hydrological processes and implications,3. L75 outlines very vaguely about how the proposed framework is helpful. Authors need to elaborate here.
- Overall methodology seems to be fragmented and proper explanations are needed behind selection of the approaches and later combining them. For e.g. a very simplistic representation of rainfall-runoff model has been considered (Fig1b), this is fine for a small scale study, however for such large number of diverse catchments, I wonder what limitations might arise because of this and if they need to be clarified or discussed. Some sort of sensitivity/uncertainty analysis is highly recommended at least demonstrating these.
- Authors also need to elaborate the methofology described in Fig1. There are several steps, for e.g. derived quikflow from insitu streamflow vs quickflow simulation from other hydro-met data, pugging into hydrological model?
- In Section 3.1.2. there are several points which need more explanations and disclaimers, e.g. to what extent , presence of noise has been addressed in order to define a runoff event, the quickflow might not be reaching 0 in humid catchments or in the cases where model/data’s structural influences overtake. This might lead of splitting or separation of one event into multiple and vice-versa. Similar comment can be made for the threshold of 0.1 mm/day. Further, since the response of rainfall to runoff is not linear therefore, the centroid might not fall withing the lag window as suggested, for e.g. for long rainfall events…what impact such events can lead to, needs to be discussed.
- Direct multiplication of RC*RI might be sensitive to very small values of t_R and P, what precautions have been taken to address these?
- L218 The catchments have been selected into wet, dry and snow. May be, the authors can also display the distribution of catchments according to sizes. May be a histogram will help, later dependence of results on the size of catchments can also be checked. Did the authors also check the presence of reservoirs, dams.. or such structures..in the catchments, they can be critical in influencing the results
- L295 confusing statement… “trends of the transformation rate (i.e., runoff coefficient) and the transformation rate (i.e., runoff intensity) …” please rephrase.
- Figure 5,6,7 are too small to be analysed. Please resize/reorganize in the revised version.
- L365“…climatic indicators control the process connectivity at global scale…”, although authors mention some results Fig 5. and arguments . I feel this is too broad statement to be made here. A more suitable approach would be to discuss in detail, how the factors were selected and how they sufficiently represent climatic controls. May be a region-wise characterisation would help.
- Similarly, L370, the jump to flood risk is not understood. Please clarify what is meant by floods and flood risks here… for e.g. an overflowing river in amazon might be called flooded but does it also necessarily represent risk?
Citation: https://doi.org/10.5194/egusphere-2026-1006-RC3
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