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Aridity is expressed in river topography globally

Matters Arising to this article was published on 21 December 2022

An Author Correction to this article was published on 04 August 2022

This article has been updated


It has long been suggested that climate shapes land surface topography through interactions between rainfall, runoff and erosion in drainage basins1,2,3,4. The longitudinal profile of a river (elevation versus distance downstream) is a key morphological attribute that reflects the history of drainage basin evolution, so its form should be diagnostic of the regional expression of climate and its interaction with the land surface5,6,7,8,9. However, both detecting climatic signatures in longitudinal profiles and deciphering the climatic mechanisms of their development have been challenging, owing to the lack of relevant global data and to the variable effects of tectonics, lithology, land surface properties and human activities10,11. Here we present a global dataset of 333,502 river longitudinal profiles, and use it to explore differences in overall profile shape (concavity) across climate zones. We show that river profiles are systematically straighter with increasing aridity. Through simple numerical modelling, we demonstrate that these global patterns in longitudinal profile shape can be explained by hydrological controls that reflect rainfall–runoff regimes in different climate zones. The most important of these is the downstream rate of change in streamflow, independent of the area of the drainage basin. Our results illustrate that river topography expresses a signature of aridity, suggesting that climate is a first-order control on the evolution of the drainage basin.

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Fig. 1: Global map of extracted river long profiles classified by NCI values.
Fig. 2: Effect of climate on NCI.
Fig. 3: Modelling river long profiles with various downstream rates of flow change.

Data availability

The datasets generated and analysed during the current study are available at

Code availability

The code for river long profile extraction (LSDTopoTools), including the code for calculating NCI, is available on GitHub ( The code for the LONGPRO model is available on the Community Surface Dynamics Modelling System ( The repository that contains all of the code is at

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M.B.S. was supported in part by the NSF (grants BCS-1660490 and EAR-1700555). We acknowledge the use of the UCL Legion High Performance Computing Facility (Legion@UCL), and associated support services, in the completion of this work. We thank R. Slingerland for sharing the code and providing advice on the LONGPRO model. We thank J. Willenbring for comments on an early version of the manuscript.

Author information

Authors and Affiliations



K.M. and M.B.S conceived the research and designed the study. S.W.D.G. extracted the river long profiles. S.-A.C. carried out the data analysis and model simulations. S.-A.C., K.M. and M.B.S. wrote the manuscript with contributions from S.W.D.G.

Corresponding authors

Correspondence to Shiuan-An Chen or Katerina Michaelides.

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Extended data figures and tables

Extended Data Fig. 1 Schematic of GLoPro river selection and NCI calculation.

a, For each drainage basin, we selected the longest river that does not cross between Köppen–Geiger sub-zones. The schematic drainage system shows the rivers above the threshold drainage area in red (Methods), which were extracted into the GLoPro database. Extracted rivers could include the mainstem river of a whole basin (left) and/or its sub-basins (right). The longest river on the right (blue line) was not extracted, since it crosses Köppen–Geiger climate sub-zones. b, The blue line is a measured or modelled river long profile, and the orange line is the straight line fitted through the profile endpoints. The offset (ELYL) is the difference in elevations between the river long profile (EL) and the straight line (YL) at each distance L. NCI is the median value of all offsets divided by topographic relief (E0En). NCI is negative when the profile is concave, zero when the profile is straight, and positive if the profile is convex.

Extended Data Fig. 2 Flow accumulation in The Grand Erg Oriental, Western Sahara.

a, The wider context of the area. b, Close-up of the red rectangle in panel a. c, Flow accumulation traces derived from LSDTopoTools. d, The extracted mainstem channel in the area representing the coalescence of flow traces into a dominant channel based on topography.

Extended Data Fig. 3 River long profiles and NCI values for Walnut Gulch extracted from DEMs of varying resolutions.

a, River long profiles extracted from SRTM and light detection and ranging (LiDAR) DEMs with different resolutions. b, Comparison of normalized offsets between river long profiles and the straight-line-fitted profile endpoints. Positive offsets indicate that the elevation of the river long profile is higher than the straight line, whereas negative values mean the elevation of the long profile is lower than the straight line. The red dashed line indicates zero NCI (straight profiles). The red solid line in each boxplot represents the median offset value, which we define as the NCI value. These profiles show that DEM resolution has a minimal influence on NCI.

Extended Data Fig. 4 Relationships between NCI and topographic metrics.

a, Relationship between NCI and river length; b, Relationship between NCI and river gradient; c, Relationship between NCI and river relief; and d, Relationship between NCI and drainage area. The density of points (number of rivers represented by each pixel) in the scatter plot is shown in the colour scales to the right of each panel. The results show no apparent relationship between NCI and any of these topographic metrics, suggesting that NCI is unbiased.

Extended Data Fig. 5 Statistical differences of NCI distributions between climate zones.

Graphical results of two-sample Kolmogorov–Smirnov (K-S) tests, which include the P values of NCI comparisons within the main Köppen–Geiger climate zones (a) and within the Aridity Index climate categories (b). The red box in panel a shows the comparisons involving the Arid zone, which all have smaller P values than other comparisons.

Extended Data Fig. 6 Modelled NCI values for river long profiles simulated by LONGPRO generated with different forcings for various α values.

a, NCI values for long profiles with various values of maximum discharge; b, NCI values for long profiles with various values of uniform median grain sizes of riverbed material; c, NCI values for long profiles with various values of tectonic uplift rates of the headwater; and d, NCI values for long profiles with various values of base level decline rates. All plots highlight the dominant effect of α on the river concavity. e, Long profile evolution with tectonic uplift (1 mm yr−1), in which the profiles are shown for the initial profile (dashed line, the same for all simulations), 2 yr, 5 yr, 10 yr, 15 yr, 20 yr, 30 yr and 500 yr. The final simulated profile for each is indicated as a dark black line. The NCI values of final profiles for each value of α are also shown. Profiles evolve rapidly to near-steady-state conditions for all simulations.

Extended Data Fig. 7 Calculation of α values from discharge data.

Power-law fits between median daily discharge (Q50) and L/Ln (see equation (3) in the Methods) for each discharge gauging station are shown for the selected rivers within the four main Köppen–Geiger climate zones in the USA (Extended Data Table 2). The colours and codes in brackets below each river name correspond to the Köppen–Geiger climate classification (Fig. 2).

Extended Data Fig. 8 Comparison of α and ephemerality for selected rivers between the main Köppen–Geiger climate zones in the USA.

a, α values for each selected river; b, Corresponding values of ephemerality. The order of rivers is consistent with the data in Extended Data Table 2. The colours correspond to the Köppen–Geiger climate classification (Fig. 2). Dotted lines indicate the median value for each main climate zone, showing that the Arid zone has a lower α and higher ephemerality compared to the others.

Extended Data Table 1 Summary data on the number of rivers and summary statistics of NCI by Köppen–Geiger (K-G) and Aridity Index climate classifications
Extended Data Table 2 Data on α and ephemerality (percentage of time with no flow, ‘Ephe.’) for twenty rivers spanning the four main Köppen–Geiger climate zones within the USA

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Chen, SA., Michaelides, K., Grieve, S.W.D. et al. Aridity is expressed in river topography globally. Nature 573, 573–577 (2019).

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