Skip to main content

Thank you for visiting You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

Aridity is expressed in river topography globally

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.

This is a preview of subscription content, access via your institution

Relevant articles

Open Access articles citing this article.

Access options

Buy article

Get time limited or full article access on ReadCube.


All prices are NET prices.

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

Change history


  1. Tucker, G. E. & Slingerland, R. Drainage basin responses to climate change. Wat. Resour. Res. 33, 2031–2047 (1997).

    ADS  Article  Google Scholar 

  2. Ferrier, K. L., Huppert, K. L. & Perron, J. T. Climatic control of bedrock river incision. Nature 496, 206–209 (2013).

    ADS  CAS  Article  Google Scholar 

  3. Perron, J. T., Richardson, P. W., Ferrier, K. L. & Lapôtre, M. The root of branching river networks. Nature 492, 100–103 (2012).

    ADS  CAS  Article  Google Scholar 

  4. Wolman, M. G. & Gerson, R. Relative scales of time and effectiveness of climate in watershed geomorphology. Earth Surf. Processes 3, 189–208 (1978).

    Article  Google Scholar 

  5. Roe, G. H., Montgomery, D. R. & Hallet, B. Effects of orographic precipitation variations on the concavity of steady-state river profiles. Geology 30, 143–146 (2002).

    ADS  Article  Google Scholar 

  6. Han, J., Gasparini, N. M., Johnson, J. P. & Murphy, B. P. Modeling the influence of rainfall gradients on discharge, bedrock erodibility, and river profile evolution, with application to the Big Island, Hawai’i. J. Geophys. Res. Earth Surf. 119, 1418–1440 (2014).

    ADS  Article  Google Scholar 

  7. Zaprowski, B. J., Pazzaglia, F. J. & Evenson, E. B. Climatic influences on profile concavity and river incision. J. Geophys. Res. Earth Surf. 110, (2005).

  8. Sólyom, P. B. & Tucker, G. E. Effect of limited storm duration on landscape evolution, drainage basin geometry, and hydrograph shapes. J. Geophys. Res. Earth Surf. 109, (2004).

  9. Collins, D. & Bras, R. Climatic and ecological controls of equilibrium drainage density, relief, and channel concavity in dry lands. Wat. Resour. Res. 46, (2010).

  10. Harel, M.-A., Mudd, S. & Attal, M. Global analysis of the stream power law parameters based on worldwide 10Be denudation rates. Geomorphology 268, 184–196 (2016).

    ADS  Article  Google Scholar 

  11. Hack, J. T. Studies Of Longitudinal Stream Profiles In Virginia And Maryland. Report 294B (US Government Printing Office, 1957).

  12. Phillips, J. D. & Lutz, J. D. Profile convexities in bedrock and alluvial streams. Geomorphology 102, 554–566 (2008).

    ADS  Article  Google Scholar 

  13. Leopold, L. B. & Wolman, M. G. Fluvial Processes in Geomorphology (General Publishing, 1964).

  14. Snow, R. S. & Slingerland, R. L. Mathematical modeling of graded river profiles. J. Geol. 95, 15–33 (1987).

    ADS  Article  Google Scholar 

  15. Vogel, J. Evidence of past climatic change in the Namib Desert. Palaeogeogr. Palaeoclimatol. Palaeoecol. 70, 355–366 (1989).

    Article  Google Scholar 

  16. Singer, M. B. & Michaelides, K. How is topographic simplicity maintained in ephemeral dryland channels? Geology 42, 1091–1094 (2014).

    ADS  Article  Google Scholar 

  17. Michaelides, K., Hollings, R., Singer, M. B., Nichols, M. H. & Nearing, M. A. Spatial and temporal analysis of hillslope–channel coupling and implications for the longitudinal profile in a dryland basin. Earth Surf. Process. Landf. 43, 1608–1621 (2018).

    ADS  Article  Google Scholar 

  18. Whipple, K. X. & Tucker, G. E. Dynamics of the stream-power river incision model: implications for height limits of mountain ranges, landscape response timescales, and research needs. J. Geophys. Res. Solid Earth 104, 17661–17674 (1999).

    Article  Google Scholar 

  19. Tucker, G. E. & Bras, R. L. Hillslope processes, drainage density, and landscape morphology. Wat. Resour. Res. 34, 2751–2764 (1998).

    ADS  Article  Google Scholar 

  20. Wickert, A. D. How should we estimate river discharge from drainage area? In AGU Fall Meeting Abstract EP21D–2294 (AGU, 2018).

  21. Lague, D., Hovius, N. & Davy, P. Discharge, discharge variability, and the bedrock channel profile. J. Geophys. Res. Earth Surf. 110, (2005).

  22. Knighton, A. & Nanson, G. Distinctiveness, diversity and uniqueness in arid zone river systems. In Arid Zone Geomorphology: Process, Form and Change in Drylands 2nd edn, 185–203 (John Wiley & Sons, 1997).

  23. Yair, A., Sharon, D. & Lavee, H. An instrumented watershed for the study of partial area contribution of runoff in the arid zone. Z. Geomorphol. 29, 71–82 (1978).

    Google Scholar 

  24. Jaeger, K. L., Sutfin, N. A., Tooth, S., Michaelides, K. & Singer, M. Geomorphology and sediment regimes of intermittent rivers and ephemeral streams. In Intermittent Rivers and Ephemeral Streams 21–49 (Elsevier, 2017).

  25. Fan, Y., Li, H. & Miguez-Macho, G. Global patterns of groundwater table depth. Science 339, 940–943 (2013).

    ADS  CAS  Article  Google Scholar 

  26. Farr, T. G. et al. The shuttle radar topography mission. Rev. Geophys. 45, (2007).

  27. Clubb, F. J., Mudd, S. M., Milodowski, D. T., Grieve, S. W. D., & Hurst, M. D. LSDChannelExtraction version v1.0, (2017).

  28. Peel, M. C., Finlayson, B. L. & McMahon, T. A. Updated world map of the Köppen-Geiger climate classification. Hydrol. Earth Syst. Sci. Discuss. 4, 439–473 (2007).

    ADS  Google Scholar 

  29. Trabucco, A. & Zomer, R. J. Global Aridity and PET Database (CGIAR Consortium for Spatial Information, 2009).

  30. Slingerland, R., Harbaugh, J. W. & Furlong, K. Simulation Clastic Sedimentary Basins: Physical Fundamentals and Computer Programs for Creating Dynamic Systems (Prentice Hall, 1994).

  31. Seybold, H., Rothman, D. H. & Kirchner, J. W. Climate’s watermark in the geometry of stream networks. Geophys. Res. Lett. 44, 2272–2280 (2017).

    ADS  Article  Google Scholar 

  32. Bonnet, S. Shrinking and splitting of drainage basins in orogenic landscapes from the migration of the main drainage divide. Nat. Geosci. 2, 766–771 (2009).

    ADS  CAS  Article  Google Scholar 

  33. Molnar, P., Anderson, R. S., Kier, G. & Rose, J. Relationships among probability distributions of stream discharges in floods, climate, bed load transport, and river incision. J. Geophys. Res. Earth Surf. 111, (2006).

  34. Wang, L. & Liu, H. An efficient method for identifying and filling surface depressions in digital elevation models for hydrologic analysis and modelling. Int. J. Geogr. Inf. Sci. 20, 193–213 (2006).

    CAS  Article  Google Scholar 

  35. Braun, J. & Willett, S. D. A very efficient O(n), implicit and parallel method to solve the stream power equation governing fluvial incision and landscape evolution. Geomorphology 180, 170–179 (2013).

    ADS  Article  Google Scholar 

  36. Grieve, S. W., Mudd, S. M., Milodowski, D. T., Clubb, F. J. & Furbish, D. J. How does grid-resolution modulate the topographic expression of geomorphic processes? Earth Surf. Dyn. 4, 627–653 (2016).

    ADS  Article  Google Scholar 

  37. Montgomery, D. R. & Dietrich, W. E. Where do channels begin? Nature 336, 232–234 (1988).

    ADS  Article  Google Scholar 

  38. Tarboton, D. G., Bras, R. L. & Rodriguez-Iturbe, I. On the extraction of channel networks from digital elevation data. Hydrol. Processes 5, 81–100 (1991).

    ADS  Article  Google Scholar 

  39. Al-Masrahy, M. A. & Mountney, N. P. A classification scheme for fluvial–aeolian system interaction in desert-margin settings. Aeolian Res. 17, 67–88 (2015).

    ADS  Article  Google Scholar 

  40. Flint, J. J. Stream gradient as a function of order, magnitude, and discharge. Wat. Resour. Res. 10, 969–973 (1974).

    ADS  Article  Google Scholar 

  41. Royden, L. H., Clark, M. K. & Whipple, K. X. Evolution of river elevation profiles by bedrock incision: analytical solutions for transient river profiles related to changing uplift and precipitation rates. Eos 81, Fall Meeting Suppl. Abstract T62F-09 (AGU, 2000).

  42. Yang, C. T. Incipient motion and sediment transport. J. Hydraul. Div. 99, 1679–1704 (1973).

    Article  Google Scholar 

Download references


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.

Ethics declarations

Competing interests

The authors declare no competing interests.

Additional information

Publisher’s note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

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

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

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

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI:

Further reading


By submitting a comment you agree to abide by our Terms and Community Guidelines. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate.


Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing