the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 06 Mar 2026
Unified Patterns of Topological Structure of Hydrological Characteristics in Global River Networks
Abstract. Unravelling the coupling between river network structure and hydrological fluxes is essential for understanding basin-scale dynamics. While traditional ordering methods describe macro-scale patterns, they often obscure local functional variations. This study quantifies the universal hydrological patterns of global river networks by integrating the classical Horton–Strahler framework with a hierarchical pyramid decomposition technique. Leveraging the global HydroATLAS dataset, we analysed 228 representative basins spanning diverse hydro-climatic regimes. We extracted rigorously defined network attributes and hydrological fluxes to examine the scaling behaviours of fundamental structural components, defined here as basic units. Our results reveal a striking topological invariance in hydrological characteristics across both varying spatial scales and distinct geographic regions. Specifically, the runoff and discharge ratios of these basic units maintain robust statistical consistency regardless of basin size or climatic conditions ranging from humid to arid. This suggests that network topology functions as a dominant physical control, effectively acting as a low-pass filter that dampens high-frequency climatic variability to produce unified global scaling laws. These findings advance the theoretical understanding of fractal river networks. Furthermore, they open new avenues for prospective research, including the integration of these physics-informed topological priors into next-generation Earth system models to improve discharge predictions and water resource modelling in ungauged basins.
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Status: open (extended)
- RC1: 'Comment on egusphere-2026-1128', Anonymous Referee #1, 26 May 2026 reply
Data sets
Global hydro-environmental sub-basin and river reach characteristics at high spatial resolution S. Linke et al. https://doi.org/10.1038/s41597-019-0300-6
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- 1
In the manuscript, the authors investigate the existence of universal hydrological scaling laws in global river networks by analysing 228 basins form HydroATLAS and combining Horton-Strahler ordering with a hierarchical pyramid decomposition framework. The authors show that runoff and discharge rations exhibit scale-invariant statistical behaviour across climates and basin sizes, suggesting that river network topology acts as a dominant control on hydrological dynamics and filters climatic variability.
The manuscript addresses an interesting question using a large global dataset and generally sound analytical methods. Although the presentation is comprehensive and well structured, the interpretation occasionally overstates the universality and physical significance of the reported scaling relationships. My two major comments are:
1) I found the manuscript a bit dense, with 14 figures (4 of which in the discussion, which really break the flow of thoughts). I would consider moving some of the less important figures in the Supporting Info, only citing the result in the main text when applicable.
2) More care needs to be given to the interpretation of the results and consequent discussion. Being a global dataset, HydroATLAS does a great job at capturing global larger-scale patterns. However, the interpretation of "headwaters" that define first order streams requires much attention. In my experience, real first and second order rivers are mostly missing, and this could affect the interpretation of the results. Even more importantly, I think much more care needs to be given to the interpretation of the provided mean annual runoff and discharge for each river. Being derived from a global model, this inevitably misses local heterogeneity and enhances the cross-scale structure, as defined by the structure of the model itself. Often in these cases the provided values should be interpreted as an order or magnitude estimate, more than an actual mean annual runoff. Therefore, the findings of these papers need to be put in this perspective, care taken when projecting these results back to physical processes, and these limitations need to be acknowledged in the discussion.
The manuscript would benefit from a more rigorous assessment of uncertainty and sensitivity to HydroATLAS preprocessing choices.
ADDITIONAL COMMENTS:
The physical interpretation that topology acts as a “low-pass filter” remains largely conceptual and is not directly demonstrated.
Additional validation against observed gauged river data, synthetic benchmark networks, or independent hydrological products would strengthen confidence that the identified patterns are not artefacts of the chosen decomposition scheme or HydroATLAS topology. I know this would be a lot of work, but at least it should be acknowledged in the paper and deferred to a future work.
It will be more informative to change Table 2 into a figure. It will be nice to have a global map showing the basins (maybe using different color for each region). This would give an indication also of the size variability of the basins around the globe. The data in the current table could be shown as a bar plot if you feel it's useful.
The sentence in lines 135-138 needs some restructuring, as the grammar is missing something. Also, point (4) is a consequence, rather than a rule.
Line 159: I think RMS should actually be in mm/year, since it's annual runoff, therefore cumulative runoff should be m3/year.
Line 166: hypothesis should be reported in the final part of the intro
Figure 2: I am not sure what is the added value of this figure as compared with Figure 3 (which I find more intuitive). Consider removing it and use Figure 3 in the explanations.
Line 234: What is specifically the characteristic length? Is this analysis done for each decomposition level (i.e. Strahler order), or are you combining all units with same length together? Also, since length is a continuous variable, it is highly improbable to have two units with exactly the same length. Did you use length classes (e.g., from 0 to 100m, from 100 to 200m etc)?
Caption of Figure 4: "to enable cross-basin comparison", since cross-scale is within the single basin
Is figure 4c and d the same as Figure 4 but in semilog space? If so, consider joining the two figures.
Line 303: what's an iterator and an iteration in this case? Please use consistent terminology and/or an example to clarify.
Caption of Figure 7: please give a specific definition of variability range (e.g. 3 standard deviations).
Figure 9, but in all the paper too: I feel like reporting median values rather than mean ones would be more informative, since most of the indicators show some skewness in the distribution, and it's evident also here.
Figure 9: in many cases it seems that there is a well-defined range and some outliers. Can you identify the outliers in the map and discuss what could cause this deviation?
Appendices: this is the guide text; remove it if no appendices are used.
Code availability: it is highly suggested to share the code in a public repository, too.