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Journal ArticleDOI

Aridity is expressed in river topography globally.

26 Sep 2019-Nature (Nature Research)-Vol. 573, Iss: 7775, pp 573-577

TL;DR: A global dataset of river longitudinal profiles is presented and it is shown that river profiles become straighter with increasing aridity and numerical modelling suggests that this can be explained by rainfall–runoff regimes in different climate zones.

AbstractIt 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.

Topics: Drainage basin (58%), Streamflow (52%), Hydrology (agriculture) (51%)

Summary (2 min read)


  • Having confirmation from two climatic indices (K-G and AI), which are computed in distinct ways (e.g., AI represents the balance between PET and P), gives us confidence that the authors have captured real climate influences on long profile development.
  • This was performed using an algorithm 34 which minimizes the topographic change required to ensure all DEM cells flow to the DEM base level.
  • This is the channel that was extracted in their analysis for this area and which is included in GLoPro.
  • Given their source in SRTM data, the extracted profiles represent the water surface profile for perennial rivers and the bed topography profile for ephemeral rivers.

Normalized Concavity Index (NCI).

  • The authors define the endpoints of the longitudinal profile (L0, E0) and (Ln, En) where L is distance downstream, E is elevation, and where the subscripts 0 and n indicate the most upstream and downstream points, respectively.
  • Then, at each measured point along the profile, the vertical offset between the river profile and the fitted straight line is calculated as EL -YL.
  • The authors then calculate the median value of all offsets, normalized by the total topographic relief along the profile (E0 -En) to enable comparison across scales (Extended Data Fig. 1b ).

NCI = median[(EL-YL)/(E0-En)]

  • (1) There have been previous concavity indices developed in the literature, such as Stream Concavity Index (SCI) 7 , Concavity Index (θ) 40 , and Chi (χ) transformation 41 .
  • SCI, for example, calculates the area between channel elevation and the straight line connecting the endpoints of channel, similar to NCI.
  • SCI is sensitive to local variations along the profile (e.g., knickpoints) and requires smoothing.
  • Since their goal was to explore conditions where the relationship between area and channel discharge are weak for complete river profiles, the authors opted for a different metric.

as an example).

  • The river extraction methods and concavity calculation result in an internally consistent NCI dataset.
  • The impact of channel head location on NCI is minimal because only the longest river of each basin or sub-basin was analyzed (not smaller tributaries).
  • The authors confirmed that NCI for extracted rivers in GLoPro are not correlated with key river metrics, such as river length, gradient, relief, or basin area (Extended Data Fig. 4 ).
  • Therefore, the authors were confident in using it to compare rivers of different sizes and across climate zones.

2. riverid:

  • The unique name given to each river record in GLoPro.
  • Comprises the K-G climate zone that the river is within and a unique alphanumeric string.
  • Used to identify the associated data for the river recorded in rivers.

SELECT elevation, length FROM profiles WHERE riverid like 'Aw_75_river_72';

  • Note that due to the size of the profiles table, queries can take a few minutes to complete.
  • To learn more about using SQL databases in a research context, the authors recommend the training materials provided by Software Carpentry:

Kernel density estimation (KDE).

  • In several figures in the paper, the authors present plots generated based on kernel density estimation (KDE).
  • Statistical differences of the NCI distributions were analyzed using the Kolmogorov-Smirnov test (K-S test) between distribution pairs across climate zones.
  • K-S test is a nonparametric test for checking whether two continuous, one-dimensional data samples, X1 and X2, come from the same distribution.
  • The authors simulated variations in downstream discharge and their impact on long profile evolution.
  • Since other model parameters can also affect long profile concavities, the authors conducted sensitivity analyses to discharge (Qmax), median grain size , tectonic uplift, and base level change.

Calculation of α values from real rivers.

  • To develop a real-world understanding of α and its variation in different climate zones, the authors downloaded multidecadal mean daily streamflow data for rivers from the US Geological Survey's National Water Information System (
  • For each main K-G climate zone, the authors selected 5 rivers, spanning a range of river lengths, with at least three gauging stations along the same river (a total of 20 rivers), ensuring via Google Earth satellite imagery that there are no obvious anthropogenic factors that could influence the downstream variation in discharge.
  • Then the authors extracted α for each power law fit from equation (3) (Extended Data Table 2 ).
  • The exponent for arid channels is closest to zero for small floods and increases slightly for higher flood recurrence intervals.
  • The analysis of α values was not exhaustive.

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Citation for final published version:
Chen, Shiuan-An, Michaelides, Katerina, Grieve, Stuart W. D. and Singer, Michael Bliss 2019.
Aridity is expressed in river topography globally. Nature 573 , pp. 573-577. 10.1038/s41586-019-
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Aridity is expressed in river topography globally 1
Shiuan-An Chen
*, Katerina Michaelides
, Stuart W. D. Grieve
and Michael Bliss Singer
School of Geographical Sciences, University of Bristol, Bristol, BS8 1SS, UK.
Earth Research Institute, 5
University of California Santa Barbara, Santa Barbara, California 91306, USA.
University College 6
London, London, WC1E 6BT, UK.
School of Earth and Ocean Sciences, Cardiff University, Cardiff, CF10 7
3AT, UK.
Water Research Institute, Cardiff University, Cardiff, CF10 3AX, UK. 8
*e-mail: 9
It has long been suggested that climate shapes land surface topography, through interactions between 11
rainfall, runoff, and erosion in drainage basins
. The longitudinal profile of a river (elevation versus 12
distance downstream) is a key morphological attribute that reflects the history of drainage basin 13
evolution, so its form should be diagnostic of the regional expression of climate and its interaction with 14
the land surface
. However, both detecting climatic signatures in longitudinal profiles and 15
deciphering the climatic mechanisms of their development have been challenging due to the lack of 16
relevant data across the globe, and due to the variable effects of tectonics, lithology, land-surface 17
properties, and humans
. Here we present a global dataset of river longitudinal profiles (n = 18
333,502), and use it to explore differences in overall profile shape (concavity) across climate zones. 19
We show that river profiles are systematically straighter with increasing aridity. Through simple 20
numerical modeling, we demonstrate that these global patterns in longitudinal profile shape can be 21
explained by hydrological controls that reflect rainfall-runoff regimes in different climate zones. The 22
most important of these is the downstream rate-of-change in streamflow independent of drainage 23
basin area. Our results illustrate that river topography inherits a signature of aridity, suggesting that 24
climate is a first-order control on drainage basin evolution. 25

Conventional theory presents river longitudinal profiles (long profiles) as having a generally concave-up 26
shape, with knickpoints and other fluctuations expressing the interactions of several independent variables: 27
climate, tectonics, lithology, and human impacts
. This characteristic shape of long profiles has been 28
interpreted to arise due to downstream flow increase with drainage area, which erodes the riverbed, 29
transports sediment from upstream to downstream, and produces fining profiles in bed material grain 30
. However, there are long profiles with overall concavity much closer to zero (straighter) than the 31
typical concave-up profile shape
, yet there is limited understanding of the global distribution of long 32
profile concavities and their relation to climate. Stream power incision theory states that channel erosion is 33
intrinsically tied to an assumed relationship between river discharge (Q) and drainage area (Q~A
). Based 34
on this theory, an expression has been derived that links supply-limited river long profile concavity to the 35
exponent c
, illustrating that profiles will be concave up for c > 0, straight for c = 0, and convex for c < 0, 36
and a similar dependency of profile concavity on the Q-A relationship has been derived for 37
transport-limited fluvial systems
. Previous work has largely emphasized long profile concavity for cases 38
where c > 0, despite evidence that c in many river basins, especially in drylands, may vary flood to flood 39
between negative, zero, and positive values
. Of particular interest here is to ascertain whether the 40
climatic expression within river channel hydrology may be a first-order control on long profile shape, and 41
whether its climatic signature is preserved across the globe. 42
A river experiences a cascade: from climate to hydrology to erosion, which evolves its long profile. 43
Therefore, the climatic expression within streamflow should be a first-order control on long profile shape
. 44
Numerical analysis of profile shape responses to a distribution of flow events above the threshold for 45
bedrock incision has demonstrated part of this dependency
. However, there is limited global evidence 46
of how the hydrologic expression of climate affects long profiles, across a wide range of climate zones. 47
Climate determines the precipitation regime within a region. In turn, the precipitation regime controls the 48
rate and frequency of water supply to the land surface, a proportion of which generates runoff over drainage 49
basins, subject to losses by infiltration and evapotranspiration. Flow in rivers occurs when runoff reaches 50

the channel, with notable baseflow contributions from groundwater and subsurface drainage in humid 51
regions and potential for prolonged periods of no flow in arid channels. The flow of water within a river is 52
a key driver of landscape evolution, through the corresponding downstream force exerted on the stream bed, 53
the associated channel erosion, and the expression of local river incision at each elevation position along 54
the long profile. Therefore, we propose that the climate-streamflow relationship exerts a strong control on 55
long profiles. 56
Cimate is expressed differently in the downstream rate-of-change in streamflow between arid and humid 57
endmember rivers. In arid climates, streamflow tends to decrease downstream in all but extreme floods
for two main reasons: 1) Low annual rainfall, limited areal coverage of rainstorms, and short duration of 59
rainfall events generates partial area runoff
. This results in a small proportion of basin tributaries 60
contributing streamflow to the mainstem for limited periods of time. 2) Rivers are typically ephemeral (no 61
permanent flow)
, so channels lose water through dry, porous beds (transmission losses
) because water 62
tables are well below the channel
. Thus, the commonly assumed power law relationship between 63
streamflow and drainage area (with positive exponent c) breaks down
such that the long-term average 64
value of c may be negative, positive, or zero. In contrast, humid channels have perennial flow (all year 65
round), supported by baseflow from groundwater, and they accumulate flow from adjoining tributaries, 66
producing downstream increases in discharge
(positive c). We intuit that there is a spectrum of prevailing 67
downstream changes in streamflow across the globe based on the regional expression of climate within 68
discharge regimes (e.g., dryland hydrology, mountain front orography
), rather than simply on drainage 69
basin area. Given the obvious link between streamflow and riverbed erosion, we hypothesize that climatic 70
signatures are imprinted within river long profiles, superimposed upon other exogenous controls. In other 71
words, we expect a great deal of scatter typical of environmental data, but we hypothesize that climate will 72
reveal itself as a first-order control on long profile shape. 73
To test this hypothesis, we produced a new and unprecedented database of Global Longitudinal Profiles
(GLoPro) of rivers between 60°N and 56°S (Fig.1) extracted from NASA’s 30-m Shuttle Radar 75

Topography Mission Digital Elevation Model (SRTM-DEM)
. The profiles were extracted using 76
, software with advanced capabilities in topographic analysis, employing a conservative 77
threshold for upstream drainage area and an algorithm of downstream flow accumulation, both of which 78
reduce the likelihood of Type 1 errors (Methods). For each profile we computed the Normalized Concavity 79
Index (NCI), a metric computed based solely on profile geometry (Methods; Extended Data Fig.1) that 80
allows for standardized comparisons of river profile shapes across the globe. The NCI is negative if the 81
profile is concave-up, zero if the profile is straight, and positive if the profile is convex-up. 82
We categorized each profile in GLoPro using the Köppen-Geiger (K-G) climate classification
and the 83
quantitative Aridity Index (AI = Precipitation/Potential Evapotranspiration)
, to investigate relationships 84
between climate and river long profile shape and to test whether the expression of aridity is detectable in 85
NCI. K-G is based on temperature and precipitation thresholds, emphasizing vegetation response to climate. 86
AI is a scale that represents the balance between precipitation and evaporative demand, and it declines with 87
aridity. Here we addressed the null hypothesis that there are no differences in NCI between climate 88
categories. We did not censor GLoPro for any other natural or anthropogenic factors, and it includes both 89
bedrock and alluvial rivers. We do not make any assumptions about whether the profiles are steady-state 90
(equilibrium) or transient, but we assumed that climate categories in K-G and AI have not changed 91
significantly over the timescales of long profile development (Methods). 92
The global distribution of NCI values does not suggest any strong geographic biases, although there are 93
clear concentrations of convex (Southern Siberia), concave (SE Asia), and nearly straight (Arabian 94
peninsula) rivers (Fig.1). NCI distributions of different climate classes (Fig.2a) overlap and display great 95
breadth, reflecting the large sample size and the many interacting independent variables (climate, tectonics, 96
lithology, and human factors) that affect drainage basin development. Nevertheless, statistically significant 97
differences between distributions are evident (Extended Data Fig.5). Comparing the four main K-G climate 98
zones, all NCI distributions are negatively skewed, revealing that river long profiles are generally 99
concave-up (Fig.2a). However, compared to the other three main climate zones (Tropical, Temperate, and 100

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