Climate’s influence on topography encoded in stream network topology and geometry

Domain: chemistry
Published: 2026-03-03
Editorial outcome: minor_revision

Abstract
Stream networks express how Earth’s hydrologic cycle is embedded within its three-dimensional
topography. In a top-down view, a stream network’s morphology is often described by its
topological connectivity and branching geometry. Although these two characteristics are naturally
connected, they have mostly been studied independently, leaving their co-evolution poorly
understood. Here, we analyze the topology and geometry of 16,322 5th-order real-world stream
networks across the contiguous United States, showing how they are shaped by climate and the
evolution of Earth’s topography. We find that ~73% of these networks show topological self-
similarity in their branching patterns and that small tributaries join larger streams at systematically
wider angles. Our analysis further reveals that correlations between climate and network topology
observed in other studies are mainly mediated through the climate-dependence of networks'
geometric and topographic properties, such as their junction angles and channel slope ratios of
merging tributaries. These findings demonstrate the co-evolution of network geometry, topography,
and topology under the influence of landscape evolution driven by climatic forcing.

Introduction
Branching networks form striking patterns in many natural systems and are often characterized by
power-law scaling relations that suggest underlying universality1,2,3,4,5. Stream networks, in
particular, form tree-like structures that collect water, sediment, and solutes from the landscape
and deliver them to larger water bodies downstream6,7. Horton8 and Strahler9 introduced a
hierarchical ordering scheme (Fig. 1) that has been widely applied to network studies in geoscience
and related disciplines10,11,12,13,14. Unfortunately, it provides only limited insight into network
topology because it does not describe how streams of different orders are interconnected. However,
the connectivity between small and large rivers is crucial for flood propagation11, riverine
biodiversity15, and the understanding of transport processes16,17,18. Headwater streams, for example,
are more dynamically linked to their surrounding hillslopes and groundwater systems19,20 and
therefore serve as hotspots for channel erosion and biogeochemical activity13,21. Here, we analyze
the relationships between stream network topology and geometry, and explore how climate
influences these properties through the networks’ embedding in Earth's three-dimensional
topography.

To quantify stream network topology (the connectivity between streams of different orders),
Tokunaga22,23 expanded the Horton-Strahler ordering scheme by introducing the concept of side
branches (streams of order ω entering streams of higher order ω’, with order differences k=′−,
k>0), and bifurcations (streams of the same order merging at a junction, with order difference k=0;
see Fig. 1a). By assuming scale invariance for the number of streams of order ω entering streams
of order ω+k, a scaling relation can be derived that depends solely on the order differences k, rather
than on the network’s absolute order:
T = ack-1 (1)
k
Here, T represents the average number of side-branches whose order is k lower than the streams
k
they flow into, a is Tokunaga’s constant, and c is known as the Tokunaga ratio (see also Methods).
Stream networks that satisfy Equation (1) are called Tokunaga self-similar networks23. Tokunaga
parameter c measures the relative frequency of stream junctions that have different contrasts in
stream order between their tributaries, covering both small- and large-scale features of the
network24 and thus serving as a scale-invariant metric of the network’s topology (Supplementary
Text S1 and Fig. S1). As illustrated in Fig. 1b, larger values of parameter c imply a greater
abundance of low-order channels joining high-order streams, resulting in a more ‘feathered’
network. While parameter a varies only slightly across different networks, parameter c is sensitive
to climatic influences24. Yet, estimates of this climatic sensitivity vary with the area thresholds
used to extract topographic flow paths24, and whether such climatic sensitivity persists at the
continental scale remains unresolved.

Previous research on stream network topology has mainly focused on determining whether
principles such as topological randomness25 or optimality6,14,26 can generate realistic-looking
network configurations27,28,29,30. However, these statistical methods have largely ignored the
topographic controls that actively shape network topology7,31. Three-dimensional topography
results from the interaction between tectonic uplift and climate-driven erosion32,33,34,35, through
which landscapes evolve highly dissected, multi-scale drainage networks (Fig. 1b)7,36. As a result,
the branching stream networks embedded within a landscape reflect the relative dominance of
different forcings, each of which leaves a distinct imprint on how channels initiate, grow, and
connect across scales7,34,36. Laboratory experiments, computational simulations of landscape
evolution, and analyses of topographic flow paths from digital elevation data suggest that climate
may affect a network’s overall topology24,37,38,39. Testing these findings in a natural system requires
stream networks mapped at high resolution across a wide range of climatic conditions. Here we
analyze stream networks from the high-resolution National Hydrographic Dataset40 (NHDPlus-
HR), which is extensively ground-checked and provides the best available continental-scale
mapped stream networks41. This allows us to re-examine classic questions about how much real-
world stream networks exhibit self-similar scaling, and how topography and climate influence
their topology24,25,27,28,29,30,38,42.

While network topology describes the connectivity of streams of different orders, it does not
capture the network’s geometry—namely, the length of segments5 and the angles between
them8,43,44,45,46,47,48,49,50,51,52. A key geometric measure of branched stream networks is the angle
between pairs of upstream tributaries, which may indicate different erosion processes in humid
and dry climates44,47,48,51,52, and also influence basins shapes53,54. While stream branching angles
are only weakly correlated with the average slopes of the two tributaries47, they are more strongly
correlated with the contrast in slopes at the confluence49. According to Horton’s geometric model8,
branching angles depend on the ratio between the slopes of the shallower stream and the steeper
one (the slope ratio SR). The planform structure of stream networks has also been shown to be
related to the channel concavity exponent55, which relates the downstream change in channel slope
to drainage area. Despite these insights, it remains unclear how climatically mediated landscape
dissection influences the branching geometry of stream networks at side-branches and bifurcations,
as well as network topology.

To better understand how the planform geometry and topological connectivity of stream networks
are embedded in three-dimensional landscapes, we first test Tokunaga self-similarity in 16,322 5th-
order real-world stream networks across the contiguous United States using the high-resolution
National Hydrographic Dataset40. We then analyze relationships among Tokunaga parameter c,
bifurcation and side-branching angles, slope ratios, and climatic aridity. This information allows
us to develop a conceptual framework that explains how climate influences network topology
through its impact on topography and network geometry.

Results
Test of stream network self-similarity
Because Tokunaga parameter c assumes topological self-similarity23,24, we limit our analysis to
Tokunaga self-similar networks. Of the 16,332 5th-order stream networks from the NHDPlus-HR
dataset, 73% (11,946) pass the Tokunaga self-similarity criteria of ref. 24 (see Supplementary Text
S2 and Fig. S2). To determine whether the proportion of Tokunaga self-similar networks is affected
by external factors like lithology, climate, or topography, we grouped these networks based on the
underlying lithology type, mean aridity index (A̅̅̅I ), network-averaged channel slope (𝑆̅ ), and
network-averaged slope ratio (S̅̅̅R̅; see Methods). Here, slope ratio is defined as the ratio of the
gentler to the steeper slope in each pair of upstream tributaries and therefore ranges from 0 to 1
(see Methods). S̅̅̅R̅ values closer to 1 indicate smaller contrasts in slopes between pairs of
tributaries. The proportion of Tokunaga self-similar networks shows only minor variation across
different lithology types and channel slopes (see Methods and Supplementary Figs. S3a, c), and
the percentage of Tokunaga self-similar networks in arid climates (A̅̅̅I ≤ 0.22) is only slightly lower
(66.6%) than in more humid ones (73.3-75.2%; see Supplementary Fig. S3b). The proportion of
Tokunaga self-similar networks decreases slightly, from 77.1% to 62.2%, as slope ratios increase,
suggesting that Tokunaga self-similar networks are moderately more prevalent in more dissected
landscapes with greater contrasts in channel slopes (smaller slope ratios; Supplementary Fig. S3d).
The 11,946 5th-order Tokunaga self-similar networks have drainage areas with 20th, 50th, and 80th
percentiles of 21 km2, 90 km2, and 297 km2, respectively. To explore how varying stream network
scales could affect our results, we also repeated our main analysis on the 3,454 6th-order stream
networks in the contiguous US, resulting in similar conclusions (Supplementary Text S3 and Table
S1).

Spatial patterns of stream network side-branching
Stream network branching patterns result from the evolution of the landscape they are embedded
in, and thus can be used to infer climatic and tectonic factors that shape the landscape7,32,33,36. To
compare regional patterns of Tokunaga parameter c with patterns of climatic aridity, channel slope,
slope ratio, we spatially aggregated these network attributes into 893 equally sized hexagons, each
with an area of 10,000 km2 (Figs. 2a-d; see Methods). Each hexagon contains, on average, thirteen
5th-order Tokunaga self-similar networks. Less feathered networks (dark colors in Fig. 2a) are more
prevalent in arid regions (dark colors in Fig. 2b). Individual hexagons with less feathered networks
are found along coastlines and in the glaciated upper Midwest (Fig. 2a), presumably reflecting
local geomorphic controls42. The binned scatterplot in Fig. 2e shows a slight tendency for
Tokunaga parameter c to increase with A̅̅̅I (see Methods; higher A̅̅̅I values indicate more humid
conditions), with the raw data exhibiting a weak but statistically significant rank correlation
(ρ=0.12, p<0.0001). Note that all Spearman rank correlations in this study are calculated based on
the raw data, and binning was only used for visualization.

Notable similarities in the spatial patterns of Tokunaga parameter c and slope ratios are observed
across the US, with basins having slope ratios closer to 1 (dark color in Fig. 2c) generally
corresponding to small values of parameter c (dark color in Fig. 2a). This indicates that basins with
smaller contrasts in channel slopes tend to have less feathered networks (ρ=-0.25, p<0.0001; Fig.
2f). By contrast, there is only a weak (ρ=0.06), although still statistically significant, spatial
correspondence between Tokunaga parameter c (Fig. 2a) and network-averaged channel slope
(Figs. 2d, g).

Interrelations of stream network topology and planform geometry
The planform configuration of stream networks is characterized not only by their topology but also
by their branching geometry, which is quantified here by the angles formed at each junction.
To explore whether junction angles differ between bifurcations (where tributaries of equal order meet)
and side-branches (formed by tributaries of different orders), we split our dataset into its 876,903
bifurcation angles and 1,956,624 side-branching angles. We then examined how these angles vary
with aridity index, mean channel slope, and Tokunaga parameter c.

Network-averaged side-branching angles systematically widen with increasing degrees of side-
branching as quantified by Tokunaga parameter c (ρ=0.25, p<0.0001; diamonds in Fig. 3a). By
contrast, network-averaged bifurcation angles vary only weakly with parameter c (ρ=0.01; circles
in Fig. 3a). The average of all junction angles (bifurcations plus side-branches) follows the general
trend of the side-branching angles (ρ=0.20, p<0.0001; triangles in Fig. 3a), because they make up
over two-thirds of all network junction angles (Fig. 3b). Both bifurcation angles and side-
branching angles tend to be wider in humid landscapes than in arid ones47,48, 49,50,51 (Figs. 4a,c),
while steep channel slopes lead to narrower angles47,52 (Figs. 4b,d). Similar patterns are seen when
network-averaged differences in Horton-Strahler order are used as an alternative measure of
network topology (see Supplementary Text S1 and Fig. S4).

Why are side-branching angles wider than bifurcation angles, and why do they vary more
systematically with Tokunaga parameter c? As Fig. 3b shows, junctions with larger differences k
in Horton-Strahler orders are more common in networks with higher Tokunaga parameter c values.
Junctions with larger order differences k, in turn, have larger contrasts in the drainage areas and
slopes of their tributaries (as reflected in slope ratios farther below 1; Fig. 3c). This directly implies
greater contrasts in channel slopes at side-branching junctions (k>0) than at bifurcation junctions
(k=0), and greater contrasts in drainage area (and thus channel slope50) in networks with greater
degrees of side-branching (as measured by higher values of Tokunaga parameter c). Pairs of
tributaries with larger differences in order tend to have larger differences between their upstream
slopes (i.e., smaller slope ratios SR) as a direct consequence of the power-law relationship between
drainage area and channel slope56, combined with Horton’s exponential relationship between order
and drainage area8. Consistent with Horton’s steepest-descent geometric model8, tributaries with
larger order differences k – and thus larger differences in their drainage areas and slopes – have
wider average junction angles (Fig. 3d). This observation leads directly to the expectation that
side-branching angles should be wider than bifurcation angles, and should be wider in networks
with greater degrees of side-branching (larger values of Tokunaga parameter c).

Slope ratios, and their corresponding junction angles, are topographic expressions of landscape
dissection. A valley's high-order main stream will carry a relatively large discharge and therefore
adjust toward a relatively low equilibrium channel gradient34, whereas its side slopes will remain
steep unless the streams draining those slopes have sufficient drainage areas (and thus discharges)
to incise them7. Thus more feathered networks, whose tributary junctions will tend to have larger
order differences k and greater contrasts in drainage areas and channel slopes, will also tend to
have wider average junction angles. From this perspective, slope ratios and junction angles are not
only a direct consequence of local erosion asymmetry, but also a broader result of side-branch
formation, which ultimately sets a stream network's topology and geometry.

We further analyzed the empirical cumulative distribution functions of the network-averaged
bifurcation angles and side-branching angles for different parameter c classes (Fig. 5). Mean
bifurcation angles (circles in Fig. 5a) tend to center around 50º independent of c, whereas mean
side-branching angles (circles in Fig. 5b) range from 65º to 72º and increase systematically with c.
As parameter c increases, the curves in Fig. 5b also become steeper, reflecting narrower
distributions of network-averaged side-branching angles. The patterns in Fig. 5 imply that
processes associated with the creation of low-order side-branches, such as lateral erosion57 may
produce junction geometries that differ greatly from those generated by bifurcation.

Drivers of stream network topology and geometry
To account for confounding effects that Spearman rank correlations cannot detect, we used partial
rank correlation statistics (Fig. 6) to quantify interdependencies between stream network topology
(i.e., Tokunaga parameter c), side-branching geometry (i.e., network-averaged side-branching
angles), and climatic and topographic drivers (i.e., climatic aridity A̅̅̅I, mean channel slope 𝑆̅, and
mean slope ratios S̅̅̅R̅). Analyzing these interdependencies is necessary because climate patterns
may be associated with topographic dissection and therefore influence network topology only
indirectly.

Prior studies have hinted at possible climatic influences on stream network topology. For example,
ref. 24 reported correlations between Tokunaga parameter c and precipitation or storm frequency
across 408 stream networks extracted from digital elevation models in the United States. However,
these relationships weakened or disappeared when coarser channel initiation thresholds (i.e.,
drainage area ≥0.3 km2) were used24, raising the question of whether climatic signatures persist in
real-world network topology. Our partial correlation analysis (Fig. 6) indicates that climatic aridity
has only a weak direct influence on parameter c (ρpartial=-0.06), but stronger relationships with
average channel slope (ρpartial=0.28), slope ratio (ρpartial=-0.32), and mean side-branching angle
(ρpartial=0.22). These variables, in turn, are correlated with parameter c. This is consistent with the
concept that climatic aridity affects channel incision, which in turn controls landscape dissection7,
thereby setting Tokunaga parameter c, channel slopes and slope ratios, which ultimately impact
side-branching angles. After accounting for climate aridity, slope ratio, and mean side-branching
angle, mean channel slope becomes a stronger predictor of Tokunaga parameter c (increasing from
an overall correlation of ρ=0.06 to a partial correlation of ρpartial=0.19). This suggests that channel
slope exerts a more substantial direct influence on parameter c than climatic aridity does (and that
this influence is masked in the correlations reported in ref. 24 and shown in Fig. 2g). These
relationships suggest that the observed Spearman correlation between climatic aridity and
Tokunaga parameter c (Fig. 2e) is primarily mediated through climate effects on topography and
network geometry (Fig. 6) rather than through a direct impact of climate on network topology.

Stream networks delineate the pathways along which surface water aggregates, and their shapes
and structures mirror the landscape’s development. Where erosional efficiency is high relative to
diffusive smoothing, a branching instability7 triggers the growth of steep, low-order tributaries
with small drainage areas (Fig. 1b). Viewed through this lens, Tokunaga parameter c expresses the
prevalence of this side-branching instability: networks in more strongly dissected terrain exhibit
higher c values and their junctions exhibit correspondingly stronger contrasts in stream orders,
drainage areas (Supplementary Table S2), and channel slopes (Fig. 6). The prevalence of low-order
side branches, which tend to run down valley walls perpendicular to the main stream8,43 (Fig. 1b),
influences the statistics of network-averaged junction angles50 and explains the strong partial
correlation between network-averaged slope ratios and side-branching angles (ρpartial=-0.47; Fig.
6). However, the effect of average channel slope on side-branching angles is weaker (ρpartial=-0.06).
Thus, these side-branching angles are more sensitive to how erosion creates contrasts in slope
between pairs of tributaries than to the corresponding average channel slopes (Fig. 6). In wetter
climates, more effective fluvial incision produce s stream junctions with greater contrasts in
channel slopes (slope ratios farther below 1; ρpartial=-0.32). When topographic effects are factored
out by partial rank regression, we find a substantial direct correlation between climatic aridity and
side-branching angles (ρpartial=0.22).

Considered together, our observations suggest a conceptual model (Fig. 7) in which climatic aridity
may shape both basin topography (i.e., mean channel slope and slope ratios) and network geometry
(i.e., side-branching angles), thereby indirectly influencing network topology (as quantified by
Tokunaga parameter c). In wetter climates, pairs of tributaries are less likely to share a common
slope and orientation, resulting in bigger slope differences and wider junction angles49. This
observation suggests that the dependence of slope ratios on aridity may partly reflect topological
differences in stream networks between arid and humid environments, as noted by ref. 24 and this
study (Figs. 2, 7). Our findings thus illustrate how topography, network topology, and network
geometry represent co-evolving fingerprints of climatic influences on drainage basin evolution.

Methods
Metric of climate
The aridity index (AI) is the ratio of precipitation to potential evapotranspiration and is widely
used as an indicator of climatic wetness (higher AI values indicate more humid climates). We
obtain AI values from the Global Aridity Index and Potential Evapotranspiration (ET0) Climate
Database, which provides 30-year (1970-2000) climate normals at a resolution of 30 arc-seconds58.
We expect that the broad spatial patterns of aridity in this 30-year record also reflect long-term
spatial patterns, despite shifts in the average climate, barring large-scale reorganization of
atmospheric circulation (such that, for example, relatively arid sites have generally remained
relatively arid over time59).

Stream networks from NHDPlus-HR
The National Hydrographic Dataset Plus High Resolution (NHDPlus-HR) is a scalable geospatial
hydrography framework built from the high-resolution (1:24,000-scale or better) National
Hydrography Dataset, the nationally complete Watershed Boundary Dataset, and a 1/3-arc-second
(10-m) digital elevation model across the United States40.

We remove segments labeled “Coastline” from the NHDPlus-HR database, and extract the main
flowpath of braided rivers by removing flowlines with divergence flag=2, yielding networks that
have only one downstream segment at each junction. The order Ω of a network is defined by the
order of its most downstream segment, namely the segment that terminates at a lake or ocean, or
that merges with another stream of order Ω or higher. Given the terminal segment, we then identify
the upstream network using the 'FromNode' and 'ToNode' attributes in the NHDPlus-HR dataset.
This approach allows us to delineate the whole network upstream of any channel with a given
Horton-Strahler order. The NHDPlus-HR dataset, however, also includes canals, connectors, and
pipelines, which are sometimes relevant to the network's connectivity and therefore cannot be
removed easily. Networks where the channel slope is uniformly equal to 0.00001 due to the
dataset’s slope cutoff are excluded. To mitigate the impact of artificial channels, if more than 10%
of a network consists of artificial flowlines (i.e., canals and pipelines with Fcodes of 42800-42817,
42820-42824, 33600, 33601, or 33603), the entire network is discarded. The 10% threshold
removes networks with pervasive human disturbance while retaining basins whose artificial
channels are limited and spatially localized. Using a threshold of 5% or 20% instead of 10% yields
similar results (Supplementary Tables S3-S4).

The NHDPlus-HR dataset assigns attributes such as Horton-Strahler order and slope values to
individual river flowlines. One or more of these flowlines make up each stream segment in the
network, that is, each segment connecting a junction or channel head to the next junction
downstream (Supplementary Fig. S5). To calculate the slope of each segment, we exclude any
flowlines lacking slope data (~0.1% of all the flowlines in 11,946 5th-order networks analyzed in
the main text) and then calculate the length -weighted slope for each segment using the remaining
flowlines. The slope ratio (SR) at any junction between two stream segments is defined as the ratio
of the gentler slope to the steeper slope in each pair of upstream tributaries (which therefore ranges
from 0 to 1), so smaller SR values represent larger differences in slopes of the incoming tributaries.
SR is then averaged over all junctions in each network to yield the network-averaged slope ratio
S̅̅̅R̅, which is used in the main analysis. To obtain the hexagon-averaged values shown in Fig. 2,
we extracted Aridity Index values for the midpoint of each flowline from the Global Aridity Index
and Potential Evapotranspiration (ET0) Climate Database58. Given that the Tokunaga parameter c
is a network attribute, all midpoints within the same stream network are assigned identical values
of c. Likewise, all midpoints within the same network share the same network-averaged slope ratio
S̅̅̅R̅. Finally, we calculated the median of each variable across all midpoints within each hexagon.

The lithology type of each stream network was determined from the global lithology map dataset
from ref. 60. Lithology types were extracted for the midpoint of each flowline, and the lithology
type covering more than 50% of the flowlines in each network was identified as the dominant
lithology. Networks in which no single lithology type exceeded 50% coverage were classified as
having mixed lithology. 121 networks with mixed or missing lithology data (~0.7% of all networks)
were excluded from the lithology analysis.

Calculation of Tokunaga parameters
Tokunaga's ordering system extended Horton’s ordering by introducing the concept of side-
branching using the Horton-Strahler orders of the two joining tributaries at a junction22,23. The
Tokunaga side-branching ratio
T = Nω,ω+k / Nω+k (1 ≤ k ≤ Ω−ω) (2)
ω,ω+k
is the number N of streams in a network with order ω flowing into streams with Horton-
ω,ω+k
Strahler order ω+k, divided by the number of streams N with order ω+k. Here, Ω is the highest
ω+k
order in the network. In self-similar networks, the side-branching ratio T is independent of the
ω,ω+k
order ω and depends only on the increase in order k23,24, satisfying Equation (1). In Equation (1),
a represents the mean number of streams of order ω flowing into streams of order ω+1, and c
denotes how this side-branching ratio grows with increasing contrasts k between the orders of main
streams and their tributaries. Tokunaga parameter c thus reflects the degree of lower-order side-
branching, with higher c values indicating larger average differences between the orders of side
branches and the main streams that they flow into.

To estimate Tokunaga parameter c, we follow the method outlined by ref. 24. First, we calculate
the side-branching ratio T as
k
T = 1/nk ∑Ω-k i=1 N i,i+k (3)
where nk = ∑Ω i=k+1 Ni is the number of streams of order larger than k. In some cases, Tk can be zero
because the network does not contain two tributaries whose difference in Horton-Strahler order is
k. In these cases, the Tokunaga coefficients cannot be reliably determined, so we discard the entire
network.

We then estimate c from linear regression of the log transform of Equation (1),
log10 Tk = (k-1) log10 c + log10 a (4)
using weighted least squares with weights wk based on the number of branches,
wk = √ ∑Ω-k i=1 ∑l=1 Ni+k (5)
The weighted least squares method yields a smaller variance for the Tokunaga parameters than
that obtained with unweighted least squares24. As suggested by ref. 24, statistics for the highest-
order rivers of each network are excluded in the Tokunaga parameter calculation to minimize the
influence of finite-size effects.

Stream network branching geometry
We characterize network geometry using the branching angles between pairs of incoming
tributaries, averaged over all junctions. To calculate the branching angles, we use a conformal
projection (Lambert conformal cone 102004) to map stream networks from NHDPlus-HR.
Adopting the approach described in ref. 47, we converted all river segments to a sequence of
discretization points. Then we fitted a straight line through the points of each river segment using
orthogonal regression. This method allows us to characterize the average orientations of the
tributary valleys and the angles between them47. Our analysis encompasses a total of 2,833,527
junctions in 11,946 5th-order Tokunaga self-similar stream networks, and 2,209,988 junctions in
2,417 6th-order Tokunaga self-similar networks.

Scatterplot binning
In our binned scatterplots (Figs. 2e-g, 3a, and 4a-d), the first and last bins comprise x-axis values
smaller than the 1st percentile and larger than the 99th percentile, respectively. The remaining bins
are equally spaced between these percentiles. The error bars indicate the standard error of the mean
for each bin, where these are larger than the plotting symbols. Note that this binning procedure
retains most of the variability along the horizontal axes but averages out much of the variability
along the vertical axes.

Peer review rounds
[{"round": 1, "reviewer_comments": {"reviewer_1": "23 September 2025\nReview of “Climate’s influence on topography encoded in stream network topology and geometry”\nIn the submitted manuscript, the authors use a recent hi-resolution dataset of stream networks across the USA to identify\nhow climate affects stream network topology and network geometry. Specifically, they identify that increases in the\nbranching angle of river networks is accommodated through increases in the branching angles of “side branches”, not\nbifurcation branches. The results presented here show that, in self-similar networks, the angle of side branches records\nvariation in both the slope ratio of streams at confluence, and the aridity index of a landscape.\nOverall, I believe this manuscript represents a significant contribution to the scientific community and its potential impact to a\ndiverse cross-disciplinary audience justifies its publication in a high impact journal such as Nature Communications. I do\nhave some comments regarding the methodology, clarity of text, and discussion points which I outline below.\nMajor Comment: Adding mechanistic explanations of the results\nThe largest shortcoming of the manuscript is its lack of mechanistic explanation for the observed results and correlations.\nNumerous times the authors stated (or implied) that one measured quantity drove another based on a correlation, without\nproviding a reasonable mechanism to explain it (i.e., there is correlation, but no causation). For example, L198-201 argues\nslope ratios may influence side branching and thus topological connectivity, as well as branching geometry. While I agree\nwith the authors’ findings that these network characteristics and metrics are correlated, a mechanistic explanation\nsignificantly strengthens the argument that one drives another. I will not go through every example of this in the manuscript,\nbut other instances of this can be seen in L271-274, L309-312 and L315-317. Addressing this will provide support for the\nauthors’ argument, starting in L76, that physical processes are considered in this contribution.\nMinor Comments\nManuscript structure:\nThe following is a suggestion which the authors can ignore if they choose: I think this manuscript would be easier to read\n(and thus more impactful) without using or minimizing the use of self-similarity and Takunaga’s parameter c. After reading\nthe manuscript, I believe the only benefit of including Takunaga’s parameter c is to show that increases in the average side\nbranching angle are a result of actual branching angles increasing and not a result of basins with inordinate amounts of\nlarge delta HS confluences (i.e., there are two ways to increase the average side branching angle in a basin: have more\nlarge delta HS confluences relative to small delta HS confluences, or increase the branching angle of confluences).\nHowever, this same point, I think, could also be made in a different way which I believe will be more intuitive for most\nreaders and will not take away the scientific rigor of the approach. Instead of using Takunaga’s parameter c as the x axis in\nFigure 3, I think these results could be broken up by delta HS values or potentially normalized by the average delta HS\nwithin the basin. This approach would clearly show the reader that increase in the average side-branching angles correlated\nwith Aridity Index or average slope are a result of actual angles of the confluences increasing. If the authors feel that\nTakunaga’s parameter c is still better, perhaps an alternative is to show both? One of the metrics could be shown in the\nsupplement if space a concern.\nMethods:\n• Why was 10% of the network consisting of artificial channels chosen as a threshold cutoff? While a sensitivity analysis\nwould be helpful to show the influence of artificial channels on the results, I recognize this requires significant effort. If a\nsensitivity analysis is not performed in a future submission, it would be helpful to provide justification for the 10% cutoff\nthreshold.\n• More information about the lack of slope information connected with certain stream segments would be helpful for the\nreader. How many stream segments lack slope information? Is there a spatial trend to the lack of slope information? Similar\nto the previous comments, how does this impact the results?\nLine and Figure Comments\n• Line 52-56: It appears the variable k, may represent two things. Text on line 52 implies k may be the order of the tributary,\nwhile Lines 58-59 clearly define k as the difference in Strahler stream orders. Can you please clarify this text?\n• Line 84-86: How are channel heads identified if a threshold drainage area is not used?\n• Line 87-90: I would suggest either softening this language or describing the exact question that is answered here in more\ndetail. Many workers have done substantial work on this topic, and many questions are left. Please give citations for the\nlong-standing questions as well.\n• Line 96: Please ensure at least one of these citations is appropriate support for the topology and geometry argument in this\nsentence. From my recollection the cited references mainly discuss the morphologic characteristics, but I could be wrong.\n• Line 121: More information would be helpful to let the reader know why a two-step approach is necessary here. It is unclear\nhow a river can be self-similar but not meet Takunaga’s scaling criteria.\n• Line 131: Although the slope ratio is well described in the methods, SR is a major component of this story and, for the\nreader to understand the results described here, a better main text explanation of SR would be helpful.\n• Line 144-146: If c is kept in the manuscript, I suggest moving this description of c to earlier in the text. The variable is\nreferred to frequently and a description such as this helps readers to conceptualize the variable.\n• Line 152: Can you provide a citation?\n• Line 180-182: I suggest moving this description of side branching earlier. It will help the reader understand the arguments\npresented before this point.\n• Line 320: I do not believe the analysis provided in this manuscript provides support for this statement. If the authors would\nlike to argue that side-branching angles are not controlled by tectonics, a more robust analysis of this is required. I would\nsuggest removing the text “overall rates of uplift and” and change steepness to slope. The word steepness suggests the\nnormalized metric, channels steepness, was used in this analysis.\n• Figure 3: Having the same symbols in panel b represent something different than they do in panels c-f is confusing for the\nreader. Please change.", "reviewer_2": "I co-reviewed this manuscript with one of the reviewers who provided the listed reports. This is part of the Nature\nCommunications initiative to facilitate training in peer review and to provide appropriate recognition for Early Career\nResearchers who co-review manuscripts.", "reviewer_3": "REVIEW – NCOMMS-25-68072\nThis manuscript sets out a compelling data-driven argument for how climatic signature is expressed in river network\ntopology – not directly, but through mediating conditions of basin topography and network geometry.\nThe analysis draws upon a collectively extensive body of work that has explored each of these contributing components –\ntopography, network geometry, and network topology – respectively in relation to climatic forcing without quite disentangling\nthe nature of their inter-relationship. This contribution gets closer to that aim, leveraging both a high-resolution dataset of\nchannel networks for the contiguous USA, and a clever application of partial rank correlation statistics to unpack subtle but\nsignificant indirect links through which climatic forcing is imbued in network topology.\nMy remarks on this manuscript are relatively minor, but pertain to the narrative. I hope my comments might help the authors\nclarify their message that much more, for their readers' benefit.\nThe first sentence of the final paragraph (L327–329) presents the clearest summary framing (problem and findings) in the\nmanuscript – so much so that I think it should get worked into the introduction. To me, the introductory paragraphs dive too\nquickly into how topology and topography are quantified, and there are some intermediate punchlines (e.g., L88–89) that are\nconfusing. (I understand that the NHDPlus-HR dataset allows previously inaccessible insight into self-similarity in real river\nnetworks, and therefore robust application of Tokunaga ordering. The authors should absolutely point this out – but as\nwritten it diverts the reader from the larger aim; it's an important finding, but also a means to an end.)\nI wonder if the authors might shift the paragraph at L106 up to be the second paragraph (inset at L49). The paragraph on\nTokunaga ordering (L49) could introduce the Results section at L117. For continuity, I would also put the paragraph at L141\nabove the section break, to be the final paragraph of the first Results section – that is, insert after L139. Similarly, the\nparagraph on topography (L91) sets up the Results section at L147, and could serve as the opening paragraph there.\nI really enjoyed the synthesis section from L252 onward, and I think it's one of the strengths of this manuscript. In that vein, I\nencourage the authors, when they re-read this work with fresh eyes, to do their best to make each paragraph a ratchet that\nmoves the reader inexorably forward. (Put another way, be on the lookout for recursions in the text.)\nI look forward to seeing this work in print – congratulations to the authors on a fine analysis.", "reviewer_4": "This paper looks at relationships between networks topology, channel gradients, lithology and climate. The paper shows\nthat gradients are more highly correlated with a metric called the Tokunaga ratio than they are with climate. I have a number\nof questions related to the analysis but overall I think this is a very interesting paper and shows something new. One of the\nmost interesting aspects of this work is that the Tokunaga ratio is correlated with the side branching angle and not the\nbifurcation angle, suggesting that the process of adding smaller links leads to different channel geometry than bifurcation. To\nme this has interesting implications for network growth, has never been shown before, and somehow the authors have not\ndeemed it important enough to mention in the abstract. I would change that.\nI think the choice of using 5th order basins vs 6th or 7th order could be clearer. On the other end of the size spectrum, I think\na comment about how many 5th order basins cross big physiographic divides might be in order (that is, does the basin size\nlead to many basins crossing from steep mountains into gentle basins). The reason for a comment on this is the somewhat\nstrange pattern in the slope map (see comment below).\nOverall I think this is a very interesting contribution, raises some new questions about network topology, and I would\ncharacterise most of my comments as cosmetic.\nLined comments\nLine 64: You later say that you cannot reproduce this result (or at least you think climate is of secondary importance). The\nway this is written seems (to me at least) that you are taking this result as a given, when in fact there is only one paper that\nsays this and that your work does not support it.\nFigure 1: A this point in the paper omega` is not defined. It should be somewhere (perhaps above equation 1). Also the\nlabelling is inconsistent (are you labelling nodes or edges, and if one or the other why aren’t all of them labelled?).\nLine 81-90: The novelty of this paper (and I think it is quite novel) is the analysis. It is not the underlying data. These lines\nhave many problems and are not necessary for the manuscript.\nThe report cited here has been superseded by a 2025 report (Moore et al., 2025). It does not really explain how channel\nheads are found in the NHDPlus HR dataset. It does explain the many corrections needed to be made to the underlying\nNHD data because once the lidar was collected it emerged that many of the channels mapped on USGS quads were not\nactually in the right place (see page 60 of the report). So the NHDPlus HR is already corrected by topographic data. The\nauthors then say that other datasets use a threshold drainage area, which leads to inconsistent channel networks. But as the\nreport from Terziotti and Archuleta (2020) makes clear, the NHD is also inconsistent (from their page 16):\n“The original NHD was digitized from individual 7.5-minute quadrangle map sheets that were compiled at different times, by\nmany individuals, using varied sources; therefore, some areas of the country have hydrography that is represented at\ndifferent densities. These discrepancies are due to differing source material or standards and procedures and are not due to\ndifferences in geomorphology or hydrologic conditions.”\nThis report goes on to explain how these differences in channel heads would be fixed, and advocates for a variety of\nmethods for repositioning channel heads. They will insert “additional features” (including new channel heads)\n“● if there is clear evidence of the feature in the elevation data source,\n● if there is clear evidence of the feature using an appropriate ancillary data source,\n● if a method has given good results for delineation of stream channels or other features, and it is quality assured using the\nelevation data and other high-quality ancillary datasets”\nSo the overall impression is that the NHDPlus HR is hand curated in some way that is not reproducible and is just as\nsusceptible to bias as an algorithmically-derived channel network. The user guide of Moore et al (2025) doesn’t explain how\nthis is done so we are left to guess (unlike networks that use a threshold drainage network and the threshold drainage area\nis reported). I have a strong suspicion the results using a threshold extraction or a more advanced channel head finding\nalgorithm on the NDEP lidar data would result in outcomes indistinguishable from those reported here, NHDPlus HR is as\ngood a network as any (and if you think hand curation is better, it might be better), and I don’t think there needs to be any\nmodification to the analysis. But this paragraph makes misleading statements and needs to go. Just say “The channel\nnetwork used was the NHDPlus HR dataset”.\nMoore, R.B., McKay, L.D., Rea, A.H., Bondelid, T.R., Price, C.V., Dewald, T.G., Hayes, L., 2025. User’s guide for the\nNational Hydrography Dataset Plus High Resolution (NHDPlus HR) (No. 2025–5031), Scientific Investigations Report. U.S.\nGeological Survey. https://doi.org/10.3133/sir20255031\nTerziotti, S., Archuleta, C.-A., 2020. Elevation-derived hydrography acquisition specifications (No. 11-B11), Techniques and\nMethods. U.S. Geological Survey. https://doi.org/10.3133/tm11B11\nLine 108: Why 5th order? In 5th order channels, when you do the regression to calculate c you are only fitting 4 points. Do\nyour results change with 6th order basins, for example?\nLine 120-122: The explanation of the ANOVA test is missing from the methods. I don’t think it will change the result, but why\nwas a non-parametric test not chosen for this step? Zanardo et al have an entire paragraph about the drawbacks of the\nANOVA (paragraph 31 in their paper) and I never understood why they didn’t use a non-parametric test.\nLine 130-132: Climate varies over a longer wavelength (loosely defined) than lithology. That is, in a 5th order channel\nnetwork you are unlikely to have a large variation in the aridity index, but you could have several rock types with very\ndifferent properties. The rock hardness is quite strongly correlated to the various slope metrics. The lithology is assigned of\n50% of the underlying rocks are the same in a catchment, but harder lithologies in the headwaters and softer lithologies\ndownstream will have quite a different effect, I imagine, on topology than vice versa. Some comment on this would be\nwelcome.\nLine 130-131 and Line 371-373: I find it counterintuitive to select a slope ratio, which is a metric specifically designed to test\ndifferences in gradients in streams of different order, in such a way that a larger value represents a smaller variation in\nchannel gradients. Surely this metric should be chosen so a higher slope ratio represents a larger variation in channel\ngradients.\nLines 143-149: Can you please report the distribution of sizes of the basins. How many are in each 10,000km^2 hex?\nLine 152: You mention here clustering of more feathered networks in specific geomorphic settings, and then say this\n“presumably reflects geological controls”. If you think it is glaciers causing the changing topology then you are implying it is\n*not* a geological control.\nFigure 2f: I presume, because you are using NHDPlus, the more arid catchments have a lower drainage density. The slope\nratio between two parts of a drainage network depends on the ratio of drainage area raised to the power of the concavity\nindex. We know there is a climate control on the concavity index. Is the signal in panel f controlled by this or by the difference\nin area ratios because of the changing drainage densities?\nFigure 2d: I am puzzled by the slope map. The southern tip of the Appalachians appears to have the similar gradients to the\nmost tectonically active parts of the west coast. This makes me a bit concerned that the size of the hex squares is introducing\nsome bias (i.e., if the hex square is centred on a hilly region, vs a very mountainous region that have half the square on a low\nrelief area (easy to do in, say, southern California), you might get a result not really reflective of the true gradients of the\nchannels. This fear would be mitigated by some analysis of the basin sizes.\nLine 186-187: This sentence implies that the 72 degree result is general, and that it has been observed in seepage\nnetworks, when in fact the 72 degree result is based specifically on a model including seepage. Do you have a reference for\nthe 72 degrees resulting from a process other than seepage?\nLine 195: The relationship between slope ratios and delta HS is controlled by the area ratio, so I don’t see what the work\n“also” is doing in this sentence.\nLine 284: Add “the” at the beginning of this sentence.\nLine 199: Can you explain how the degree of landscape dissection is reflected in the slope ratio? Are you trying to make the\npoint that a more feathered network has greater area ratios at tributaries?\nLine 227: Again, the 72 degrees is the theoretical prediction only for stream sapping.\nLine 239-240: “tend to reflect distinct erosion mechanisms”. Reference 53 proposed a very specific erosion model and then\nwent to one of the very few places on Earth where the model could be applied to real topography (Apalachicola is as close\nto a pile of noncohesive sand as it is possible to get in a natural landscape). And since many of the authors of this paper\nwere also authors of reference 47, they should know that they did not compile erosion mechanisms, but rather speculated on\nthis based on climate regimes. Soften this statement.\nLine 264: Replace the word “these” with “their” to make it clear this is a result form the zanardo et al paper."}, "author_response": ""}, {"round": 2, "reviewer_comments": {"reviewer_1": "8 February 2026\nSecond Review of “Climate’s influence on topography encoded in stream network topology and\ngeometry”\nI have now read through the revised version of this manuscript, including the supplement and\nresponse to reviewer comments. I believe the revised manuscript represents an improvement upon\nthe original submission, and I am satisfied with the author responses to my previous comments\n(and corresponding changes to the text). Overall, I think this is an interesting contribution that can\nbe published as is. At this point, I only have a few very minor comments that I have listed below,\nand which the authors can choose to take or leave as they see fit. I’d like to thank the authors for\ntheir thorough response to my previous comments, and for sharing their exciting science.\nMinor comments:\nL214-223: Parts of this explanation were a bit hard for me to follow and I had to take my time with\nit. Here’s how I think about it (which I think may be a bit more intuitive than the text in the\nmanuscript). Side-branches need to have higher contrasts in slopes (lower SR) than bifurcations\ndue to the scaling of slope with drainage area. This dictates that side-branching angles should\ngenerally be wider than bifurcation angles, since a wider angle minimizes the portion of the main\nvalley along which the side branch flows. Consider a thought experiment where a side branch\ncomes in with a tiny (let’s say 1 degree) junction angle with the main stem. In this case, both the\nside branch and the main stem must be flowing along the central valley axis. Thus, the topography\nwould need to be really strange for the side branch to have a steeper slope than the main stem. But,\nif the side branch doesn’t have a steep slope, there’s likely not enough discharge (for that low\ndrainage area of the side branch) to move the imposed sediment load. In contrast, if the side branch\ncomes in at a 90-degree junction angle, there is no overlap between the side branch and the main\nvalley axis, allowing a low SR. Aspects of this come up in L238-247, but even then, I don’t feel\nlike those lines fully explain this concept.\nFig. 4: In Fig. 4, red colors correspond to high AI, which is a humid climate. I (and I think most\nother people?) tend to think of red as warm/arid. It might help to flip the color scheme for 4a and\n4c and make red the low AI (arid) color and make the high AI (humid) bin a cooler color (blue?).\nWhile I found the authors analyses to be robust, one thing that struct me, especially with Figure 7,\nis that drainage density isn’t discussed in the manuscript. Doesn’t the increase in Tokunaga\nparameter c with AI (higher c in more humid climate) imply an increase in drainage density (i.e.,\nhigher drainage density in more humid climate)? If so, this seems at odds with studies showing\ndrainage density decreases with increases in mean annual precipitation (e.g., Chadwick et al, 2013).\nThis could be worth a few lines of discussion in the manuscript.\nChadwick, Oliver A., Josh J. Roering, Arjun M. Heimsath, Shaun R. Levick, Gregory P. Asner,\nand Lesego Khomo. 2013. “Shaping Post-Orogenic Landscapes by Climate and Chemical\nWeathering.” Geology 41 (11): 1171–74.", "reviewer_3": "Thanks to the authors for their considered and substantive revisions to this submission. I have no\nfurther comments, and am happy to see this work advance.", "reviewer_4": "I am satisfied with the authors’ responses to my previous comments. However they have added\nsome text in response to another reviewer that I don’t agree with (and mis-represent the findings\nfrom one of my papers). However this is easily corrected and constitute minor revisions.\nLine 62: Insert “The” before Tokunaga. Same on line 126.\nLine 133-134: Say which channels are being compared the SR here (not just in methods).\nLines 159-162: Consider making a comparison to reference 24 here.\nLine 220-231: Reference 50 has a long discussion of these effects so I am surprised that paper is not cited here.\nLine 252: Reference 50 showed that the junction angles were a function of the area ratio, which could have a large range in\n“side-branching” channels. Lumping all side branching channels seems like a good way to hide interesting behaviour.\nLine 254-256: I don’t agree with these statements, and it mis-cites our paper. Lateral erosion does not produce low-order\nside branches. In the case of very large area ratios, where the larger channel meanders, there is a greater probability that a\nside tributary will intersect with a meander apex. Here is the text from our paper (reference 50):\nThe complex hydrodynamics of river confluences and associated sedimentation and erosion (e.g., ref. (69) and references\ntherein) may plausibly promote the lateral migration of network junctions in the direction of the smaller tributary, causing the\nlarger river to form a bend, with the tributary joining at the outside apex. This explanation seems unlikely for two reasons.\nFirst, our junction angle measurements reflect the network-scale structure rather than the functional scale of confluence\nhydrodynamics. Second, it seems inconceivable that the paths of very large channels could be meaningfully impacted by\nchannels orders of magnitude smaller.\nWhat appears as the “deflection” of large rivers by minor tributaries may alternatively be interpreted as minor tributaries\npreferentially joining large rivers at the outside apex of large bends. In other words, the location of the junction may be\ninfluenced by the location of the bend, rather than vice-versa. This interpretation is supported by the observation that\ndeveloping tributaries nucleate at the outside apex of bends when tidal channel networks form (70)."}, "author_response": "Response: We appreciate the reviewer’s positive assessment of our work. We have carefully\nconsidered the minor comments provided and addressed them where appropriate, as detailed in the\nresponses.\nResponse: We understand the reviewer's thought experiment, but we are cautious about basing the\ndiscussion on it, since its application to low-gradient landscapes seems unclear to us. We did add,\nat line 186 of the revised manuscript, the point that large differences in stream order imply large\ncontrasts in both drainage area and slope. This was already mentioned at line 227 of previous\nversion (now at line 196 of the revised manuscript) but now we mention it both places.\nResponse: We thank the reviewer for this helpful suggestion. We have revised Fig. 4 to use dark\nblue for more humid conditions and light blue for more arid conditions, improving accessibility\nfor color-blind readers. Notably, different symbols are also used to distinguish aridity classes.\nResponse: A larger value of Tokunaga parameter c means that low-order streams are more likely\nto join higher-order streams (big order differences k) than they are to join other low-order streams\n(small order differences k). A larger value of Tokunaga parameter c does not mean that there are\nmore low-order streams overall; that is set by the bifurcation ratio instead. Nor does Tokunaga\nparameter c determine the relative lengths of lower order streams, which instead is set by the length\nratio. Thus changes in drainage density will be determined by the joint effects of the bifurcation\nratio and the length ratio, not by Tokunaga parameter c. Note, this does not mean that there cannot\nbe an indirect correlation between topological and geometric characteristics of channel networks.\nResponse: We thank the reviewer for their careful review and positive assessment of our revised\nmanuscript.\nResponse: We thank the reviewer for their careful reading and for their positive assessment of our\nprevious responses. We apologize for misrepresenting the findings from the reviewer’s work. We\nhave revised the relevant text.\nResponse: One of our native English speakers (James Kirchner) holds that the definite article \"the\"\nhere would be misleading and confusing because there is no other \"parameter c\" under discussion.\nUsing the definite article, as in \"the Tokunaga parameter c\", will lead readers to ask themselves,\n\"as compared to which other parameter c?\", for which they will not find an answer because there\nis none. This can of course be revisited if the copyeditor believes a definite article is needed here.\nPlease note that line 62 and line 126 in the previous version now correspond to lines 62 and 116\nin the revised manuscript.\nResponse: We thank the reviewer for this helpful suggestion. The original sentence at Lines 133-\n134 said “Here, slope ratio is defined as the ratio of the gentler to the steeper slope and therefore\nranges from 0 to 1 (see Methods).” We have now revised it to “Here, slope ratio is defined as the\nratio of the gentler to the steeper slope in each pair of upstream tributaries and therefore ranges\nfrom 0 to 1 (see Methods).” Please see Lines 123-125 in the revised manuscript.\nResponse: We did not add a comparison to ref. 24 in Lines 159–162 (now Lines 150-153 in the\nrevised manuscript); instead, the manuscript already addressed this comparison in detail later in\nthe “Drivers of stream topology and geometry” section, where it fits more naturally with the\nanalysis. Please see Lines 227-248 in the revised manuscript: “Prior studies have hinted at possible\nclimatic influences on stream network topology. For example, ref. 24 reported correlations\nbetween Tokunaga parameter c and precipitation or storm frequency across 408 stream networks\nextracted from digital elevation models in the United States. However, these relationships\nweakened or disappeared when coarser channel initiation thresholds (i.e., drainage area ≥0.3\nkm2) were used24, raising the question of whether climatic signatures persist in real-world\nnetwork topology. Our partial correlation analysis (Fig. 6) indicates that climatic aridity has only\na weak direct influence on parameter c (ρ =-0.06), but stronger relationships with average\npartial\nchannel slope (ρ =0.28), slope ratio (ρ =-0.32), and mean side-branching angle\npartial partial\n(ρ =0.22). These variables, in turn, are correlated with parameter c. This is consistent with the\npartial\nconcept that climatic aridity affects channel incision, which in turn controls landscape dissection7,\nthereby setting Tokunaga parameter c, channel slopes and slope ratios, which ultimately impact\nside-branching angles. After accounting for climate aridity, slope ratio, and mean side-branching\nangle, mean channel slope becomes a stronger predictor of Tokunaga parameter c (increasing\nfrom an overall correlation of ρ=0.06 to a partial correlation of ρ =0.19). This suggests that\npartial\nchannel slope exerts a more substantial direct influence on parameter c than climatic aridity does\n(and that this influence is masked in the correlations reported in ref. 24 and shown in Fig. 2g).\nThese relationships suggest that the observed Spearman correlation between climatic aridity and\nTokunaga parameter c (Fig. 2e) is primarily mediated through climate effects on topography and\nnetwork geometry (Fig. 6) rather than through a direct impact of climate on network topology.”\nResponse: We agree and have added the citation to the respective sentence. Please note that lines\n220–231 in the previous version now correspond to lines 187–199 in the revised manuscript; the\nspecific addition can be found at line 189 of the revised manuscript.\nResponse: Figure 5 and the associated discussion (lines 249–255 in the previous version, now\nlines 210–218 in the revised manuscript) refer to distributions of branching angles and how those\ndistributions change with Tokunaga parameter c. By definition, distributions involve lumping\nchannels together (otherwise there is no distribution). Of course there will also be reasons for the\nvariations that one will see if one looks at individual branching angles within these distributions,\nbut that is not the point of Figure 5. Figure 3 and associated discussion (Lines 182-199 in the\nrevised manuscript) provide more details on side branches with varying Horton-Strahler order\ndifferences. We have modified line 189 in the revised manuscript to say, \"This directly implies\ngreater contrasts in channel slopes at side-branching junctions (k>0) than at bifurcation junctions\n(k=0), and greater contrasts in drainage area (and thus channel slope50) contrasts in networks\nwith greater degrees of side-branching (as measured by higher values of Tokunaga parameter c).\"\nResponse: We thank the reviewer for pointing this out. We apologize for misrepresenting reference\n50 in Lines 254-256 (now Lines 216-218 in the revised manuscript) and we have removed the\ncitation accordingly. Please see Lines 216-218 in the revised manuscript."}]

Decision letter