| 05 Aug 2026
Climate and human organization decouple geometric and functional scaling in river networks
Abstract. Scaling laws are widely regarded as fundamental organizing principles of river networks, however, whether different scaling relationships emerge from common or distinct mechanisms remains unresolved. Using 41,677 rivers across China, we show that geometric and functional scaling exhibit fundamentally different sensitivities to climatic and anthropogenic forcing. The classical Hack’s law relationship between river length and drainage area remains remarkably stable across river hierarchies, climatic gradients, and major basins, indicating a highly conserved geometric organization of river networks. In contrast, runoff-efficiency scaling varies systematically with precipitation, transitioning from strongly negative exponents in arid regions to near-zero values in humid environments. This climatic dependence is associated with hydrological connectivity: river-network structure suppresses runoff efficiency, whereas lake systems enhance the scaling efficiency of runoff generation and transport across basin sizes. Furthermore, administrative fragmentation weakens natural geometric scaling while generating apparent functional scaling relationships absent in intact drainage systems. These findings reveal a fundamental asymmetry in river-network organization: geometric scaling remains highly conserved, whereas functional scaling is strongly shaped by climate, connectivity, and human spatial partitioning. Our results suggest that the organizing principles governing river systems are not fixed properties of natural landscapes, but emergent behaviors continually reshaped by climate variability, hydrological connectivity, and human modification.
This study examines how geometric and functional scaling in Chinese river networks respond to climate, hydrological connectivity, and administrative fragmentation. Using 41,677 river records, the authors claim that Hack’s law is relatively stable across environmental gradients, whereas runoff-efficiency scaling varies strongly with precipitation, lake density, and network structure.
The idea could be interesting, but I identified several major issues in the applied methods that defeat the scientific validity of the manuscript and require reworking. The most important are about the dataset and the whole statistical framework of the analysis. I suggest the authors deeply rework the manuscript, starting from the methods, before resubmitting the paper.
MAJOR COMMENTS
More information about the dataset is required (section 2.1).
- How has it been built, and when was it last updated? What models were used to build and characterize the river network (later on you mention zero or negative L and A, so it seems not to be a DTM-based extraction)? Is there any validation to the resulting L and A values?
- What is the spatial resolution of L and A?
- How can you trust the data if they report negative values of L and A?
- What is the smallest river size it reliably includes? Usually, these datasets miss all the smallest rivers (e.g., with mean flow less than 2 m3/s). This is an inevitable limitation for practical reasons, but we need to know.
- It would be nice to also have a map to accompany this description
- What about P and R? It seems you did not use the ones from the presented dataset (L77), so where did you get them from? If you use long term averages, how do you account for regime changes when new water management structures are built during that period?
I really can't make any sense of the (seemingly arbitrarily) defined river-level scaling index (section 2.3). What does i represent? Also, hi seem to have a similar form to eq. (4) but neglecting the scaling coefficient c. As a consequence, points laying on the line represented by eq. (4) will have a higher hi the lower Ai they have. What would this tell you about climatic influences on geometric scaling?
Also the runoff efficiency scaling (section 2.4) seems an arbitrary definition. Did you find it from literature (if so, it needs citations). Or did you choose it yourself? If so, why? Why do you expect runoff efficiency to grow as a power-law of contributing area? R/P is roughly bound between 0 and 1, while a power-law is not by nature. How do you account for that? If this is a model you chose, did you test different ones and compare them? It also feels like you are trying to hide the fact that this is not a good model choice: fig 2c reports RP vs A plots only in a conceptual representation, and fig 3a shows almost 1 order of magnitude of resituals (on the variable RP, which should vary between 0 and 1). Fig 4c and d actually show that there's no real trend in RP vs A. This whole analysis on RP should be completely removed from the manuscript.
Then, in section 2.5 you perform a multiple log regression for R/P, which is a direct extension of the one in 2.4 but you present it as "network structure" analysis instead of climatic. The whole methods need a structural rethinking; right now they are a number of disconnected statistical exercices that don't connect with each other.
You always refer to climate and climatic conditions but really are only looking at precipitation amount. The reality is that similar precipitation amounts can occur in very different climates (thing about seasonal distribution, potential evapotranspiration, rain/snow distribution). Consider either rephrasing the whole manuscript or splitting your rivers by actual climatic areas.
Also I cannot understand how the methods in section 2.6 could make sense. Administrative units are arbitrary regions defined by humans. Why should they relate to any type of scaling between river length and contributing area? For sure you'll find that longer/larger rivers tend to span more administrative units, therefore have a larger n. Also, the fact of partitioning length and area equally among administrative fragments (eq. 10 and 11) does not make any sense. What could you possibly explain from this analysis?
The writing is very dry particularly in the methods section: single lines of text seemingly disconnected from each other, all in a separate line.
The statistical framework used to assess how Hack exponent h varies with precipitation, lake density, and other variables needs reconsideration. The manuscript estimates the h-A and R/P-A scaling separately after stratifying by one variable at a time and then relates the resulting beta values to that same variable. This does not account for correlations among precipitation, lake density, river level, administrative fragmentation, and basin area, so the observed variation cannot be uniquely attributed to the variable used for stratification. A more appropriate approach would be to first define a common statistical model for L as a function of A and all the relevant predictors, including predictor interactions and non-linearity where the hypothesis concerns changes in the scaling exponent, and then assess parameter variation and uncertainty using an appropriate validation/resampling framework. The non-independence introduced by the strongly overlapping moving windows should also be considered.
I am not reviewing the results, discussion and conclusions at this stage as I don't believe they are meaningful given the methods used.
MINOR COMMENTS
I would specify in the title and text that these results refer mostly to China. This is because I have a strong feeling that they are very dependent on the specific dataset that has been used (in terms of data resolution/quality/bias).
- L12: 41677 rivers reaches or measurement points?
- L75: what is river level? Is it Strahler order?
- L77: are L and A local values (e.g. the current river reach) or accumulated upstream?
- L83: what does a river-record represent? A monitoring station, river reach, or what?
- L83-87: how many records in total and how many were removed for each reason? Where they uniformly distributed across China or is there some regional bias? Can we safely assume the remaining data is ok, or is there an inherent bias in P, R, A and L?
- L85: how did you identify artificial channels from the rest?
- L88: what units are R and P? Are they volumes, depths, mean annual flows?
- L88: also, where did you get R and P data from?
- L108: this seems an arbitrary definition with no reason or explanation behind it?
- L112: why not RP instead of R/P?
- L137: moving window framework as in section 2.4, so you fit eq. 6 in sub-groups defined by DL?
- L153: there is no influence of administrative partitioning on hydrological scaling. At most there could be a correlation, but you wouldn't really catch anything useful with the methods you're applying here.
- L155: this is not what a sensitivity analysis is.
- L162: is this a single fit for all available rivers?
- L163: report this range
Figure 1:
- it seems that the very large majority of points have log10(A) < 2.5. This means that the fit is heavily influenced by the larger rivers, therefore h is not representative and R2 and p are artificially inflated.
- how did you generate panel c?
- you also need to report h uncertainty for each point.
- panel a is repeated in figure 4.