Geomorphic constraints on landscape sensitivity to climate in tectonically active areas

Geomorphology xxx (2013) xxx–xxx

GEOMOR-04463; No of Pages 16

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Geomorphology

j ourna l homepage: www.e lsev ie r .com/ locate /geomorph

Geomorphic constraints on landscape sensitivity to climate in tectonically active areas

Mitch D'Arcy ⁎, Alexander C. WhittakerDepartment of Earth Science and Engineering, Imperial College London, SW7 2AZ, United Kingdom

⁎ Corresponding author. Tel.: +44 20 7594 7491; fax: +E-mail address: [email protected] (M. D

0169-555X/$ – see front matter © 2013 Elsevier B.V. All rhttp://dx.doi.org/10.1016/j.geomorph.2013.08.019

Please cite this article as: D'Arcy, M.,WhittaGeomorphology (2013), http://dx.doi.org/

a b s t r a c t
a r t i c l e i n f o
Article history:Received 2 May 2013Received in revised form 5 August 2013Accepted 15 August 2013Available online xxxx

Keywords:RiversLong profileChannel steepnessClimatic geomorphologyPrecipitation rateUplift rate

The geomorphology of fluvial landscapes is known to record information about uplift rate, spatial patterns offaulting, and tectonic history. Data is far less available when addressing the sensitivity of common geomorpho-logical metrics, such as channel steepness, to climatic boundary conditions. We test the relationship betweenchannel steepness and precipitation rate by measuring a large number of channels in different mountainousareas. These regions exhibit a tenfold variation in precipitation rate between them (~100–1000 mm y−1) buthave similar uplift rates, allowing the tectonic variable to be controlled. By accounting for the orographic couplingof rainfall with uplifted topography, we find that channel steepness is significantly suppressed by higher precip-itation rates in a measurable way that conforms to simple stream power erosion laws and empirical constraintson their parameters. We demonstrate this using modern and estimated glacial precipitation rates; and climateemerges as an important, quantifiable control on channel geometry. These findings help to explain why highlyvariablemeasurements of channel steepness are reported fromdifferent locations and provide important empir-ical constraints on how climate shapes tectonically active landscapes.

© 2013 Elsevier B.V. All rights reserved.

1. Introduction

1.1. Background

The geomorphology of the landscape represents the balance be-tween processes creating and destroying topographic relief. Over geo-logic time, topography is produced by tectonic forces through thetime-integrated effects of surface and rock uplift, subsidence, and crust-al deformation (e.g., Whipple, 2004; Wobus et al., 2006; Allen, 2008;Whittaker and Boulton, 2012). The resulting relief is significantly mod-ified by erosion: a process that is strongly controlled by climate. Theform and evolution of a landscape is therefore determined by severalfundamental controls, including tectonics, erosion, climate, lithology,and pre-existing geomorphology (Cowie et al., 2008; DiBiase andWhipple, 2011; Kirby and Whipple, 2012; Whittaker, 2012).

In principle, inverting the landscape for these boundary conditionsin a quantitative way should be possible using theoretical, empirical,or modelling approaches (e.g., Kirby et al., 2003; Wobus et al., 2006;Attal et al., 2008; Tucker, 2009; Miller et al., 2012). This would enableus to convert geomorphological measurements into empirical informa-tion about uplift rates, spatial patterns of faulting, and landscape sensi-tivity to future climate change, among other useful insights (Whittaker,2012). Deciphering the underlying equations that govern geomorphicform raises the prospect of using the landscape as a rich information

44 20 7594 7444.'Arcy).

ights reserved.

ker, A.C., Geomorphic constr10.1016/j.geomorph.2013.08

archive about how tectonics, climate, and surface processes haveevolved through time (Wobus et al., 2006; Allen, 2008; Whittakeret al., 2008; Kirby andWhipple, 2012). To achieve this goal, we need re-liable measurements of landscape form that can be compared in timeand space. A good example is the longitudinal geometry of river chan-nels (e.g., Tucker and Whipple, 2002). Rivers are widespread, easilymeasured, and known to be patently sensitive to their tectonic and cli-matic boundary conditions (Whipple and Tucker, 1999; Snyder et al.,2000; Whittaker et al., 2008; DiBiase and Whipple, 2011; Whittaker,2012). Stream power erosion laws describing channel geometry havebeen successfully applied to a range of tectonically active fluvial land-scapes, and the way rivers transmit tectonic signals to the landscapehas already been partially quantified (e.g., Tucker and Whipple, 2002;Whipple and Tucker, 2002; Crosby and Whipple, 2006; Whittakeret al., 2007a,b, 2008; DiBiase et al., 2010; Miller et al., 2012; amongstmany). However, much less is known about how climate controls land-scape form, and this remains a major challenge for geomorphologists(Wobus et al., 2010; Champagnac et al., 2012; Whittaker, 2012). Theaim of this paper is to introduce climate into a common stream powererosion law and to test how well this approach fits real landscapes.

1.2. Previous work

As the longitudinal form of rivers responds to tectonic and erosionaldriving forces, it can capture the balance between processes creatingand destroying topography (e.g., Whipple and Tucker, 1999; Kirby andWhipple, 2012). At a basic level, this balance can be described

aints on landscape sensitivity to climate in tectonically active areas,.019

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2 M. D'Arcy, A.C. Whittaker / Geomorphology xxx (2013) xxx–xxx

geometrically. A starting point is a steady-state equation where the rateof change of elevation, dz / dt, is zero if the local rock uplift rate, U, isequal to the local erosion rate, E (e.g., Whipple and Tucker, 2002):

dzdt

¼ U−E: ð1Þ

The erosion rate in turn depends on other factors; and for fluvial sys-tems it is often expressed as a stream power erosion law (Howard,1994; Whipple and Tucker, 1999):

E ¼ KAmSn ð2Þ

where K is a dimensionless erodibility coefficient that encapsulates li-thology, climate, and transport processes; A is the drainage area raisedto the power of an empirical constant m; and S is the local channelslope raised to the power of an empirical constant n (Hack, 1957;Seidl and Dietrich, 1992; Whipple and Tucker, 1999; Tucker andWhipple, 2002). Drainage area is typically taken as a proxy for discharge(Wobus et al., 2006). Given that discharge must also be a function ofprecipitation rate, P, averaged over a geomorphically relevant periodof time, this can be incorporated into a stream power erosion law thathas been used to describe varied landscapes (e.g., Whittaker et al.,2008; Whittaker and Boulton, 2012):

dzdt

¼ U−K PAð ÞmSn: ð3Þ

Assuming that uplift rate is counterbalanced by an equal erosionrate, i.e., the landscape is in ‘topographic steady state’, dz / dt inEq. (3) is zero and the right-hand side can be rearranged to find thelocal slope S:

S ¼ UPmK

� �1n � A−m

n : ð4Þ

The exponent m/n is often represented by θ, the concavity index(Whipple and Tucker, 1999). The constant of proportionality betweenlocal slope and drainage area in Eq. (4) is termed the ‘channel steepnessindex’, ks, i.e.,

ks ¼U

PmK

� �1n

: ð5Þ

Channel steepness is explicitly sensitive to rock uplift rate, U, and toprecipitation rate, P (Wobus et al., 2006; Kirby and Whipple, 2012).Measuring ks from a log–log plot of channel slope against upstreamcatchment area is simple, and it is usually normalised to a reference con-cavity index, θref (Kirby and Whipple, 2012; Whittaker, 2012). Its unitsdepend on the choice of this (dimensionless) concavity, e.g., m0.9 forθref = 0.45. Normalisation facilitates ksn comparisons between differentrivers, locations, and studies (Kirby and Whipple, 2012), and if individ-ualmeasurements of θ do not deviate widely from the local mean value,the effect of normalisation on ks primarily reflects the scatter of the log–log plot (Snyder et al., 2000).

A significant quantity of research in the last 10 years has investigat-ed the links between uplift and ksnwhere climate (precipitation) gradi-ents have either been neglected or assumed to be unimportant relativeto the tectonic driver (c.f. Kirby et al., 2003; Boulton and Whittaker,2009; Bookhagen and Strecker, 2012) These studies have successfullyrevealed a positive correlation between U and ksn, albeit with somecomplexities in postulated functional form (e.g., Snyder et al., 2000;Kirby and Whipple, 2001; Ouimet et al., 2009; DiBiase et al., 2010). Insome areas this correlation appears to be strongly linear (e.g., Lagueand Davy, 2003), in others it appears sublinear (e.g., DiBiase et al.,2010), while in some places it has apparent linearity until a thresholduplift rate above which significant nonlinearity is observed. For example,

Please cite this article as: D'Arcy, M.,Whittaker, A.C., Geomorphic constrGeomorphology (2013), http://dx.doi.org/10.1016/j.geomorph.2013.08

in northern and southern Italy, Cyr et al. (2010) observed a threshold ofnonlinearity at ~1 mm y−1 mean catchment uplift rate. More data isneeded to shed further light on this relationship; we provide some inthis study. Nevertheless, stream profile analysis is often compatible withindependent erosion rate measurements (Ouimet et al., 2009; DiBiaseet al., 2010) and has been used both to identify transient responses to tec-tonic change and to deduce rock uplift rates across a landscape (Kirbyet al., 2003; Harkins et al., 2007; Whittaker et al., 2007b, 2008). Otherwork has shown that indices such as ksn can capture fine spatial detailsin uplift rate. For example, in eastern Idaho, USA, Densmore et al.(2007) observed that channels near active normal fault tips arecharacterised by gentler slopes, while those nearer to the faults' along-strike centres are steeper and less concave.

Other workers have found that channel geometry is also sensitive toerosion rate, the other half of Eq. (1) (e.g., Finnegan et al., 2005;Whittaker et al., 2007a; Ouimet et al., 2009; DiBiase et al., 2010). Of par-ticular relevance is a reviewof six different regional studies byKirby andWhipple (2012) and references therein, which demonstrates a logarith-mic (sublinear) scaling between normalised channel steepness andmeasured erosion rates for catchments in tectonically active ranges. Inaddition, channel steepness depends on a set of ‘erodibility’ variables in-cluding bedrock lithology and climate. This is likely why awide range ofks values have been reported from different locations when tectonicsalone is considered to be the primary variable (Whittaker, 2012). Oneexample that highlights this problem is a comparison of Boulton andWhittaker (2009) and Snyder et al. (2000). Boulton and Whittaker(2009) studied channels in southern Turkey where uplift rate hasbeen well-constrained at 0.45 mm y−1, and using θref = 0.5 they mea-sure ksn averaging 230 m and up to a maximum of 485 m. In contrast,Snyder et al. (2000) measured channels in northern California with up-lift rates of 0.5 mm y−1 and ksn values b 60 m0.86 (the authors use aslightly lower reference concavity, θref = 0.43). This large difference inksn, despite equivalent uplift rates, cannot be explained by small differ-ences in θref. Both areas drain mixed sedimentary bedrock, so it is alsounlikely to reflect lithological differences alone. The discrepancy maybe partially climatic in origin: while the Turkish catchments receive~800–900 mm y−1 rainfall, the California catchments receive signifi-cantly more at ~1500–1800 mm y−1 (Hijmans et al., 2005).

That a higher precipitation rate would correlate with reduced ksvalues (uplift rate being constant) is clear within Eqs. (4) and (5). How-ever, little empirical work has directly tested the relationship betweenchannel steepness and precipitation rate. A global investigation byChampagnac et al. (2012) used digital elevation models (DEMs) to ex-amine 69 mountain ranges and compared their gross geomorphologywith tectonic and climatic variables. From a broad perspective, theyfound that the size and shape of mountainous landscapes is partly con-trolled by latitudinal variations in climate. This invites more detailedwork examining the direct effects of climate on longitudinal channelform. Recently, Bookhagen and Strecker (2012) found that channels inthe Argentinian Andes tend to have higher slopes where the precipita-tion rate is lower. They also found cosmogenic nuclide erosion rates de-creasing by an order of magnitude in response to local aridification,following a wetter period 25–40 ka ago. Their data suggest that evenin a tectonically active area, rainfall rate is an important control onriver long profiles and that this control can be quantified. However todate, no precipitation signal has been explicitly extracted from ksn datagathered in disparate study areas, suggesting that there is some wayto go before we have a complete understanding of how channel steep-ness records climatic and tectonic boundary conditions together.

However, theoretical studies have already emphasised the influenceof precipitation rate on channel form (Sólyom and Tucker, 2004;Wobuset al., 2006, 2010; DiBiase andWhipple, 2011). For instance, DiBiase andWhipple (2011) used a numerical model calibrated with erosion rateconstraints from the SanGabrielMountains in California to demonstratethat the relationship between erosion rate and channel steepness is con-trolled by river discharge and, furthermore, can be strongly nonlinearized



3M. D'Arcy, A.C. Whittaker / Geomorphology xxx (2013) xxx–xxx

by the variability of discharge through time. This raises questions aboutthe importance of low frequency but high magnitude storm events onlandscape evolution because parameters like storminess are notoriouslydifficult to reconstruct as a geological time series (DiBiase and Whipple,2011; Whittaker, 2012).

Amajor issue with all of the studies highlighted above is that climat-ic variables (especially precipitation rate) and tectonic variables (suchas rock uplift rate) are normally coupled in one or both directions(Champagnac et al., 2012). Inmany locations, precipitation rate increaseswith altitude, while high elevation and relief are often correlated withhigh uplift rates (Roe et al., 2002). Consequently, ksn will embody thecombined effects of uplift and precipitation together (Bookhagen andStrecker, 2012). Breaking this coupled circle is a major challenge. A sec-ond challenge lies in addressing the variability of climate through time.This is important because modern climate averages are constrainedwith a high spatial and temporal fidelity, while palaeoclimate data andreconstructions are far more limited, particularly further back into thegeologic past. So while many studies addressing the interactions be-tween tectonics and climate have exploited modern records for neces-sary reasons (Champagnac et al., 2012), these records cannot trulyrepresent an integration of climate across many glacial–interglacial cy-cles. This raises uncomfortable questions regarding the use of modernclimate averages to explain landscapes with a response timescale thatmay be on the order of 105 or 106 years (Snyder et al., 2000; Whittakeret al., 2007a,b;Whittaker and Boulton, 2012), andwe consider the impli-cations of this for our data.

Here, we begin to address the important question of how climatecontrols landscape morphology. We provide new constraints abouthow precipitation rate controls channel steepness index in six carefullyselected landscapes where the uplift rate variable can be controlled. Weattempt to generalise our observations in order to assess the extent thatmodern day landscapes record climatic differences within well-knowngeomorphic indices like ksn. We note that ‘climate’ embodies a rangeof characteristic variables, so we concentrate on precipitation rate as alogical starting point because this data is widely available asmodern re-cords and can be (partially) reconstructed for the geologic past(Section 3.2). Other variables that may count, such as storminess orrainfall intensity (c.f. DiBiase andWhipple, 2011), remain extremely dif-ficult to reconstruct into the geologic past.

2. Sensitivity of ksn to uplift and precipitation rates

If the simple assumptions laid out in Eqs. (1–5) are valid, then chan-nel steepness, Eq. (5), should be positively correlated with uplift rate, U,and linearly proportional to it for the case of any specific stream powermodel in which n = 1 andm = 0.5 (Fig. 1A). In contrast, ksn should beinversely proportional to precipitation rate, P, raised to the powerm [c.f.Eq. (5)], which would imply that ksn ~ P−0.5 for an identical specificstream powermodel (Fig. 1B). So, if we select a value of K that gives ‘re-alistic’ estimates of channel steepness index for reasonable uplift andprecipitation rate inputs (i.e., ksn = 200 m0.9 for U = 1 mm y−1 and

Constant Uplif

Cha

nnel

ste

epne

ss

Uplift rate

Constant Precipitation

Precipita

BAk ~ Us

Fig. 1. Expected relationships between channel steepness, uplift, and precipitation rate. (A) Ch(B) Channel steepness decreases with precipitation rate, following a power law relationship whecoupling precipitation rate with uplift rate: channel steepness sublinearly increases with precipita


P = 500 mm y−1), we can generate simple relationships for ksn againsta range of uplift rates for varying P (black curves, Fig. 2A), and for ksnagainst a precipitation rate for varying U (black curves, Fig. 2B). In prin-ciple, these relationships are easily identified for areas with uniform li-thology where U and P are independent variables, and this is indeedthe standard approach for deducing rock uplift rates from variations inchannel steepness index (e.g., Wobus et al., 2006; Whittaker, 2012).However, as we point out above, climate and tectonics are rarelydecoupled. Even for a simple orographic precipitation case, in whichrainfall rate is linearly proportional to uplift rate (driven for instanceby the generation of relief: see insets, Fig. 2A and B), the functionalform of the relationship between channel steepness and uplift ratewould effectively scale as ksn ~ U0.5 because of the implicit dependenceof P on U (red lines, Fig. 2A). Consequently, enhanced precipitation ‘actsto limit’ the steepening of channel gradients as topography is uplifted.Moreover, the precise shape of the ksn–U curves would be controlledby the magnitude and rate of change of P with respect to U (red lines,Fig. 2A).

In a similarway, a linear relationship betweenU and P is theoretical-ly capable of producing a complex relationship between channel steep-ness index and local precipitation rates (red lines, Fig. 2B). For a K valueagain selected to produce a realistic ksn = 200 m0.9 for U = 1 mm y−1

and P = 500 mm y−1, if uplift rates are low (i.e., 0.2 mm y−1) and pre-cipitation rates are low (i.e., b200 mm y−1), a linear increase in UwithP (here with a gradient of 2 × 10−3) produces a slow rise of channelsteepness index with precipitation rate, which necessarily approxi-mates ksn ~ P−0.5 (c.f. Eq. (5)). In contrast, if baseline uplift rates arerelatively high (i.e., N1.5 mm y−1) for low precipitation rates, thesame rate of increase of Uwith P produces a decline in ksn with increas-ing precipitation. In this case, we would observe the steepness index ofhigh uplift rate landscapes becoming relatively insensitive to thesemea-sures of ‘tectonics’ or ‘climate’ at realistic precipitation rates above~400 mm y−1. Intermediate uplift rates (~1 mm y−1) produce a situa-tion in which ksn falls with an initial increase in precipitation rate, aswetter landscapes require lower slopes to balance the imposed upliftfield, but then increases for higher precipitation rates. This is simply be-cause the implicit increase in uplift rate for wetter conditions starts todominate over the precipitation signal. Therefore, for any initial upliftrate (Fig. 2C), whether ksn decreases (scenarios 1–2), increases (scenar-ios 5–9), or stays the same (scenarios 3–4) with respect to precipitationrate depends on the magnitude and rate of increase of P relative to U(Fig. 2C) (c.f. Eq. (5)). Although K and initial conditions make a signifi-cant difference, in general terms for a specific stream power modelwherem = 0.5 and n = 1 andU ~ Pa, if a N 0.5, then ksnwill (eventual-ly) increasewith precipitation rate; if a b 0.5 then ksnwill decreasewithprecipitation rate; and if a ~ 0.5, ksn is relatively insensitive to tectonicsand climate. Ifm varies in the stream power erosion law, then the prin-ciples involved are the same (i.e., if a N m, ksn will increase with precip-itation rate), although the details will differ.

This analysis suggests that to quantify the sensitivity of landscapes toa climate parameter such as precipitation rate, one approach is to plot

Orographic Couplingt

tion rate

C

Precipitation rate

k ~ s1P m k ~ s

UP m

m = 0.3

m = 0.5 m = 0.3

m = 0.5

annel steepness increases linearly with uplift rate (assuming constant precipitation rate).re P is raised to the exponent m (assuming constant uplift). (C) The effect of orographicallytion rate (behaving as an uplift rate proxy), following a power law with exponentm.



Precipitation rate, P (mm/y)

0 200 400 600 800 10000

1

2

3

4

0 200 400 600 800 10000

200

400

600

800

1000

1200

1400

1600


Upl

ift r

ate,

U (

mm

/y)

Ui =2.0


0 200 400 600 800 10000

1

2

3

4

5

0 200 400 600 800 10000

200

400

600

800

1000

1200


Upl

ift r

ate,

U (

mm

/y)

k sn

(m)

k sn

(m)

k sn

(m)

0.0 0.5 1.0 1.5 2.00

500

1000

1500

2000

2500

0.0 0.5 1.0 1.5 2.00

200

400

600

800

Uplift rate, U (mm/y)

Uplift rate, U (mm/y)

Pre

cipi

tatio

n ra

te, P

(m

m/y

)

A

B

C

Fig. 2. (A) Sensitivity of ksn on uplift rate,U, for constant precipitation rate, P, (black lines) andvarying P that also depends on U (red lines), assuming that ksn ~ U. Inset shows dependenceof U and P used to reconstruct red lines. (B) ksn against P for constant U in the case thatksn ~ U/Pm, withm = 0.5 (black lines). Red lines show ksn against P for varying precipita-tion rates that are correlated with varying U (inset). (C) ksn against P for a set uplift rate(0.2 mm y−1) (black line). Red lines show functional form of ksn against P for varyingintensities of the relationship betweenU and P. (For interpretation of the references to col-our in this figure legend, the reader is referred to the web version of this article.)


the variation of ksn with P and extract the ‘true’ dependence of channelsteepness on precipitation rate by accounting for the component of thetrend that is explained by a variation in tectonic rates. We take this ap-proach by combining theory with empirical data. It is important toremember that channel steepness index is a necessary simplification(c.f. Wobus et al., 2006), and the landscape response to climate or tec-tonicswill not be fully captured by a singlemetric. In the following anal-yses, we assume that uplift, climate, and erodibility are constant acrossthe many catchments we evaluate; and we do not consider alternativeclimate variables such as temperature change or storm size. Therefore,ksn only approximates how landscape form is related to its primary


controls. At this stage, such a generalisation is needed to gain firstorder insights that can be extended into future work.

3. Study areas

To test for a precipitation control on channel steepness, we comparethe six mountainous areas summarised in Table 1 and located on thecentral maps in Fig. 3. These areas occupy a range of climatic zonesand have a large number of frontal catchments,making them ideal loca-tions for this type of analysis. Four of the regions have time-averagedcatchment uplift rates of ~1 mm y−1 (this is a maximum rate, as it de-cays to zero approaching individual fault tips). These are the westernCordillera of the Peruvian Andes; the southern Sierra Nevada and adja-cent ranges in eastern California, USA; the Sierra de San Pedro Mártir ofnorthern Baja California,Mexico; and theAspromontemassif in southernCalabria, Italy. Two additional areas are selected that have much lowercatchment uplift rates (b0.3 mm y−1 to negligible): the Beaverhead,Lemhi, and Lost River ranges of central Idaho, USA; and the Sinai HighMountains on the southern Sinai Peninsula, Egypt. With these locations,we can compare the effects of precipitation rate on longitudinal channelgeometry in tectonically active areas where uplift rate is reasonablycontrolled.

3.1. Geologic and climatic settings

Each study area has at least 60mountain front catchments that drainsubstantial relief, exiting to either an alluvial plain with an axial river orto the sea (in the cases of Italy and Peru). See the Supplementary infor-mation in Appendix A for detailed maps. The study areas occupy differ-ent tectonic settings, but in each case constraints are available on thecatchment uplift rates relative to base level. Mostly, this is equivalentto the vertical displacement rates on range-bounding normal faults,documented for the Pleistocene–Holocene period. The exception isPeru, where we examine coastal catchments from an active continentalmargin. Here, uplift rate is relative to average sea level and determinedby the thrust belt generating relief. In our study area, uplift rates of0.5–1.0 mm y−1 (representative of the last 400 ka) have been wellconstrained using marine terraces dated with cosmogenic radionu-clides (Pedoja et al., 2006; Saillard et al., 2011).

In Fig. 3, we have inset detailed maps of each study area, displayingthe spatial distribution ofmean annual precipitation rate, averaged overrecent decades. These illustrate the climatic gradients in and be-tween the six regions. The Peruvian catchments are dry, on averagereceiving b400 mm rainfall y−1 owing to their location along thewestern Cordillera (Kummerow et al., 1998). We only select westward-draining channels, as these are driest. These bedrock-channelled riversdrain Cretaceous volcaniclastics and some volcanic lithologies aroundthe headwaters (Gonzalez and Pfiffner, 2012). The significant relief ofthe catchments — in some cases approaching 6000 m from headwatersto mouth — has been built by the subduction of the Nazca plate, withat least half the uplift of the western Cordillera having occurred in thelast 25 Ma (Gregory-Wodzicki, 2000). We restrict our study to thePeruvian segment of the Andes not only because catchment uplifthas been well-constrained but also because volcanoes are generallyabsent (Gonzalez and Pfiffner, 2012) and do not complicate land-scape evolution.

The Californian catchments lie in the east California shear zone anddrain into four main valleys at the western edge of the basin andrange: Owens Valley, Panamint Valley, Fish Lake Valley, and Death Val-ley. These probably formed by several phases of extensional breakup ofa Miocene plateau, and the rate of extension has changed through time(Phillips, 2008). For this reason we adopt only recent (Pleistocene–Holocene) constraints on the relative catchment uplift rates. Like Peru,these reach an upper rate of ~1 mm y−1 (see a review by Jayko, 2009,and references therein). This study area includes the eastward-drainingpart of the southern Sierra Nevada, along with smaller neighbouring



Table 1The main tectonic, climatic, and lithological properties of the six study areas.

Study area Number ofchannels studied

Recent normal component of slip rate(mm y−1)

Mean annual precipitation rate(mm y−1)

Estimated LGM rainfall Major bedrock lithology

Faster uplift rates (up to ~1 mm y−1)Southern Sierra Nevada, White-Inyo, Panamint, Silver Peak andFuneral Mountains, California/Nevada, USA

295 0.5–1.0 mm y−1 at the centres of mostrange-bounding normal faults (USGS, 2006;Jayko, 2009). Fish Lake Valley Fault andPanamint Valley Fault are slightly slower at~0.35 mm y−1 (Reheis and Sawyer, 1997;Vogel et al., 2002).

Above 1000 mm y−1 high in the SierraNevada, causing a rain shadow on the otherranges that rarely exceeds 500 mm y−1. Aslow as 100 mm y−1 in low-lying catchments(Danskin, 1988; Daly et al., 2008).

Wetter: estimates range from 1.5 to 4.0times modern annual rainfall rates(Thompson et al., 1999; McDonaldet al., 2003; Kessler et al., 2006). Thepenultimate glaciation may have beeneven more severe (Quade et al., 2003).

Mostly granodiorites, smaller outcrops ofmafic igneous, metamorphic, andcarbonate units (USGS, 2006).

Sierra de San Pedro Mártir, BajaCalifornia, Mexico

62 Slip rate on the San Pedro Mártir Fault is notexplicitly reported, but there has been 5 kmdisplacement in≤11 Ma, so the long-termnormal slip rate must be at least 0.45 mm y−1

(Lee et al., 1996). Dixon et al. (2002) estimate ahorizontal extension rate of 2.8 ± 1.4 mm y−1,which if multiplied by tan(60°) = ~0.9 ±0.4 mm y−1 for an Andersonian normal fault.

200–600 mm y−1 (TRMM — see Kummerowet al., 1998; Hijmans et al., 2005).

Dated pollen and stratigraphic recordssuggest a wetter glacial climate(Holmgren et al., 2011), and avegetation record from packratmiddens indicates that around the endof the glacial period rainfall rates wereat least 2.0 timesmodern rates (Rhode,2002).

Predominantly tonalites and granodiorites(O'Connor and Chase, 1989).

Coastal catchments of westernCordillera, Peruvian Andes

120 Dated marine terraces indicate catchmentuplift rates of 0.2–0.5 mm y−1 in the north ofthe study area (Pedoja et al., 2006) increasingto 0.4–0.9 mm y−1 in the south (Saillard et al.,2011).

≤400 mm y−1 for most catchments(TRMM — see Kummerow et al., 1998).

Wetter as pluvial lakes existed similarto California; however, the magnitudeof change has not been quantified(Hillyer et al., 2009; Kanner et al.,2012).

Dominant volcaniclastic sediments andrecent (Pliocene) sediments. SomePalaeogene–Neogene volcanics (Gonzalezand Pfiffner, 2012).

Aspromonte Mountains, Calabria,Italy

94 0.8–1.0 mm y−1 (Olivetti et al., 2012).Detailed constraints are provided by Ferrantiet al. (2006) and Antonioli et al. (2006, 2009).

Averaging ~850 mm y−1 (Hijmans et al.,2005).

Some vegetation and sediment supplydata suggests a wetter glacial period(Le Pera and Sorriso-Valvo, 2000;Massari et al., 2007). However, pollenrecords in Sicily indicate a more aridLGM (e.g., Incarbona et al., 2010 andreferences therein). PMIP II 21 ka syn-thesis suggests that the LGM was drierby amodest b100 mm y−1 (Braconnotet al., 2007).

Gneisses, quartzites, and othermetamorphics, turbidites, and recentsediments (Atzori et al., 1983).

Slower uplift rates (b0.3 mm y−1)Beaverhead, Lost River and LemhiMountains, Idaho, USA

203 0.1–0.3 mm y−1 at the centres of range-bounding faults (Foster et al., 2008).

400–800 mm y−1 (Daly et al., 2008). Similar to modern rainfall rates,however, the ranges were glaciated(Johnson et al., 2007).

Carbonates, metasediments, andquartzites (Foster et al., 2008).

Sinai High Mountains, SinaiPeninsula, Egypt

72 Fault blocks formed during the Oligocene–Miocene opening of the Suez Rift and havesince been abandoned (Sharp et al., 2000).During formation, slip rates were low at0.1–0.2 mm y−1 (Kohn and Eyal, 1981).

Very dry, ≤50 mm y−1 (TRMM — seeKummerow et al., 1998; Hijmans et al., 2005).

Wetter, probably ~200 mm y−1 (Issarand Bruins, 1983; Issar et al., 2012).

Mostly granitoids, but some smalloutcrops of various metamorphics andsediments (Eyal et al., 1980).

5M.D

'Arcy,A

.C.Whittaker

/Geom

orphologyxxx

(2013)xxx–xxx

Pleasecite

thisarticle

as:D'Arcy,M

.,Whittaker,A

.C.,Geom

orphicconstraints

onlandscape

sensitivityto

climate

intectonically

activeareas,

Geom

orphology(2013),h

ttp://dx.doi.org/10.1016/j.geomorph

.2013.08.019


Sinai Peninsula, Egypt

Aspromonte, Calabria, Italy

Western Cordillera, Andes, Peru

California, USA

Baja California, Mexico

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Fig. 3.Continental-scalemaps locating the six study areas (centre). Thosewith catchments uplifting at about 1 mm y−1 relative to base level are (i) easternCalifornia, USA (southern SierraNevada andnearby ranges); (ii) the Sierra de San PedroMártir, northern Baja California,Mexico; (iii) thewestern Cordillera of the Peruvian Andes; and (iv) theAspromonte, Calabria, Italy.Two additional study areas are selected with minimal rates of catchment uplift: (v) the Beaverhead, Lemhi, and Lost River ranges of Idaho, USA; and (vi) the southern ranges of the SinaiPeninsula, Egypt. See Table 1 for location summaries. Inset maps around the edge display the detailed mean annual precipitation (MAP) rate gradients (averaged over recent decades, inmm y−1) within each study area. Catchments are outlined in black. MAP has been scaled differently to display rainfall gradientsmost clearly in each area. See the text for details about thedata sources. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)


ranges bordering the valleys (see supplementary information). Theirfrontal catchments receive a tenfold range of precipitation rates betweenthem, from ~100 mm y−1 bordering Death Valley to ~1000 mm y−1 inthe high Sierra Nevada (Danskin, 1988; Daly et al., 2008).

The Sierra de San Pedro Mártir in northern Baja California, Mexico,also experiences an intermediate range of precipitation rates from ~200to 600 mm y−1 (Kummerow et al., 1998; Hijmans et al., 2005). All ofthe catchments we measure are eastward-draining and bound by the(normal) San Pedro Mártir Fault. The dip-slip rate on this fault is not ex-plicitly reported, but 5 km of displacement has occurred in b11 Ma, so


the long-term slip rate must be a minimum of 0.45 mm y−1 (Lee et al.,1996). Dixon et al. (2002) estimated a modern horizontal extension rateof 2.8 ± 1.4 mm y−1, which is supported by a regional tectonic model.Assuming Andersonian geometry, wemultiply this by tan (60°) to obtaina throw rate estimate of 0.9 ± 0.4 mm y−1. In both the Californian andMexican study areas the dominant bedrock lithology is granodiorite, buta variety of metamorphic, igneous, and sedimentary lithologies do cropout also (O'Connor and Chase, 1989; USGS, 2006).

The catchments of the Aspromonte in Calabria, Italy, receive themost rainfall of the four Umax ~ 1 mm y−1 areas. Mean precipitation




rate is 800–900 mm y−1 owing to the mid-latitude location in theMediterranean, and the catchments drain mixed metamorphics andsediments (Atzori et al., 1983). The Pleistocene–Holocene uplift rateof the Calabrian arc is 0.8 to 1.0 mm y−1 (Olivetti et al., 2012), and spa-tially detailed constraints are provided by Ferranti et al. (2006) andAntonioli et al. (2006, 2009).

Two additional areas are studied that have undergone comparativelyless tectonic activity in the Pleistocene–Holocene. The Sinai High Moun-tains on the Egyptian Sinai Peninsula are extremely arid, with precipita-tion averaging just 50 mm y−1 (Kummerow et al., 1998; Hijmans et al.,2005). The rivers predominantly drain granitoid basement, but amixtureofmetamorphic and sedimentary rocks are also present (Eyal et al., 1980).Today, tectonic activity on the range-bounding faults is small, with mostdeformation having taken place in the Oligocene and Miocene (Sharpet al., 2000). Much ‘wetter’ are the catchments in the Idaho, USA studyarea with precipitation averaging 400–800 mm y−1 (Daly et al., 2008).These catchments have also undergone little Pleistocene–Holocenetectonic uplift with range-bounding faults slipping at a maximum ofonly 0.1 to 0.3 mm y−1 in the centres, decaying to zero at fault tips(Densmore et al., 2007; Foster et al., 2008). The Idaho catchments liealong the Beaverhead, Lemhi, and Lost River ranges and include thoseinvestigated by Densmore et al. (2007).

3.2. Palaeoclimate constraints

Given the likelihood that the geomorphological response time to atectonic–climatic perturbation may exceed 104 or even 105 years(Snyder et al., 2000; Armitage et al., 2011; Whittaker and Boulton,2012), one should consider the effects of glacial–interglacial climatechanges on time-averaged precipitation rates. Modern climate normsare well-constrained, but they represent the interglacial end-memberof a cyclic climate. We therefore consider precipitation rate differencesat the Last Glacial Maximum (LGM) and explore the implications ofthis for our analysis.

With respect to glacial palaeoclimate, the California study area is themost researched. It was measurably wetter during recent glacialperiods, and lake-highstand data suggest that LGM precipitation ratescould have been up to four times modern rates (Anderson and Wells,2003). However most estimations agree on ~1.5–2.0 times modernrates (Thompson et al., 1999; McDonald et al., 2003; Kessler et al.,2006). With a modern mean rate of ~450 mm y−1 in the study area,this equates to LGM rates of between ~700 and 900 mm y−1. Slightlymoremodest are the findings of the PMIP II project (PaleoclimateModel-ing Intercomparison Project), a synthesis of climate simulations. Theseestimate a California climate at 21 ka with ~150 to 300 mm y−1 morerainfall than present (see Braconnot et al. (2007), for project details),equating to 600 to 750 mm y−1. For our purposes, we adopt a mid-range estimate of LGM precipitation rate of 750 mm y−1 for California,satisfying empirical data and climate simulations.

Multiple lines of evidence suggest that thewestern Cordillera in Perubecame arid 10 to 15 Ma ago and that the current dry climate has beenestablished for a long period of time (Gregory-Wodzicki, 2000). The cli-mate waswetter during glacial maxima as indicated by the existence ofpluvial lakes, but the magnitude of the rainfall rate change is not yetknown empirically (Hillyer et al., 2009; Kanner et al., 2012). Howeverthese pluvial lakes were similar to those in California at the LGM,which were themselves sustained by an estimated increase in precipita-tion rate of ~300 mm y−1 (see above). Syntheses of LGM climatemodelssuggest an increase of 100–200 mm y−1 for the Peruvian study area com-pared to present (PMIP II project, see Braconnot et al., 2007). We there-fore adopt an estimate of +200 mm y−1 precipitation at the LGM. Themodern mean rate for this study area is ~150 mm y−1 (Hijmans et al.,2005) so this corresponds to ~350 mm y−1.

In northern Baja California, a vegetation record from packrat mid-dens indicates that around the end of the glacial period rainfall rateswere at least 2 times modern rates (Rhode, 2002). However Holmgren


et al. (2011) examined part of the northern Sierra de San Pedro Mártirand found that, while precipitation rates might have been slightlyhigher, the difference was minimal enough not to cause a significantvegetation response. These findings are in disagreement with a studyby Spelz et al. (2008) who found no sedimentological evidence thatthe glacial climatewas anywetter than at present. Syntheses of coupledatmospheric–oceanic general climatemodels like the PMIP II project in-dicate that at the LGM northern Baja California was receiving 100 to200 mm y−1 more rainfall than at present. The modern average rateis ~410 mm y−1 (Hijmans et al., 2005), so we adopt an LGM rate of550 mm y−1 as a balanced estimate. This is a fair compromise betweenthe vegetation records of Rhode (2002) and Holmgren et al. (2011) andthe PMIP II findings.

Limited evidence from vegetation and sediment supply data indicatesthat the LGM climate was wetter in the Aspromonte of southern Italy(e.g., Le Pera and Sorriso-Valvo, 2000; Massari et al., 2007). Howeverpollen records from neighbouring Sicily indicate a more arid LGM(e.g., Incarbona et al., 2010, and references therein), which agrees notonly with data from elsewhere in Italy (e.g., Giraudi, 1989) but alsowith the PMIP II synthesis, which predicts the LGM was ~100 mm y−1

drier (Braconnot et al., 2007). We therefore assume that LGM precipita-tion rates were lower on average by ~100 mm y−1, taking the modernmean of ~850 mm y−1 (Hijmans et al., 2005) down to ~750 mm y−1.The LGM precipitation rates in the Idaho area were probably slightlylower than today (Meyer et al., 2004; Johnson et al., 2007) and the SinaiPeninsula in Egypt was probably wetter by around 200 mm y−1 (Issarand Bruins, 1983; Issar et al., 2012).

For our study areas, these are all helpful constraints. However,unavoidable uncertainties in reconstructing past climates mean thatthese are first-order estimations. Together, they show that the differ-ence in precipitation rates from the LGM to the present day is on theorder of 100–300 mm y−1.While not negligible, it is less than the annu-al rates themselves and the variation between study areas.

4. Materials and methods

We analyse ASTER digital elevation models (DEMs) to extract a de-tailed stream network of channels draining catchments in each studyarea. The ASTER DEMs have a spatial resolution of ~30 m, and we onlyconsider catchments with a drainage area of N10 km2. Aerial imagery,theDEMs, geologicalmaps, and slopemaps are used together to identifythe points where mountain catchment channels cross the mountainfronts and exit onto an alluvial plain (or the ocean in the cases of Peruand Italy). Upstream of these points, we extract and mask the water-sheds using the DEMs. In total, 846 channels aremeasured in this study.

To extract longitudinal channel profiles, we use the ‘Stream Profiler’methodology of Whipple et al. (2007). Profiles are measured from thehighest tributary in each catchment following a central path down tothe mouth. Where the main channel forks, each channel is extractedseparately. Channel concavity, θ, is taken as the gradient of a plot of log-slope against log-drainage area, and the normalised channel steepnessindex, ksn, is calculated as the intercept using Eq. (5) and a reference con-cavity of 0.45. Normalising the channel steepness is a useful way of com-paring different catchments and areas, but it also means that our datadoes not capture the effects of varying concavity, e.g., along fault strikes(Densmore et al., 2007). As the purpose of this study is to investigatethe precipitation control on channel steepness by comparingmany differ-ent channels and locations, we choose to normalise ks and overlook con-cavity variance arising from small-scale effects.

We display characteristic longitudinal profiles for each study area inFig. 4, to illustrate our data. This shows two sets of channels: (i) theme-dian channels (sorted by ksn) for each study area (in black), which aretherefore representative of each location. We also show (ii) typicalchannels with ksn = 130 m0.9 (in red). Examples of this steepnessoccur in all six regions, so these plots allow the study areas to be com-pared with each other. The longitudinal profiles and the log–log plots



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Please cite this article as: D'Arcy, M.,Whittaker, A.C., Geomorphic constraints on landscape sensitivity to climate in tectonically active areas,Geomorphology (2013), http://dx.doi.org/10.1016/j.geomorph.2013.08.019



of slope against upstream drainage area are shown.We note that on thefew occasions where glacially eroded, flat reaches were observed at theheadwaters in the upper channel profiles, we did not include those sec-tions in ourmeasurements. This is tominimise the effects of glacial ero-sion in our data.

For eachwatershed extracted, themean elevation,mean annual pre-cipitation, and total relief (defined as the difference in elevation fromthe headwaters to the mouth of the catchment) were calculated usingzonal statistics tools in ArcGIS 10.0. Mean annual precipitation was cal-culated from the best data set available for each location. In the UnitedStates, this is the PRISMmodel (Daly et al., 2008), and in Baja Californiaand Italy we use the global WorldClim model (Hijmans et al., 2005).These are both based on multi decadal precipitation averages (from1971 to 2000 for PRISM, and from 1950 to 2000 forWorldClim) collect-ed from a large number of terrestrial climate stations. These measure-ments are treated as point data, and a precipitation rate model isinterpolated between them, in both cases with a spatial resolution of30 arc sec (~1 km). For the Sinai High Mountains and the PeruvianAndes, annual precipitation rate averages (for the period 1997 onward)are available from the Tropical Rainfall Measuring Mission (TRMM) (seeKummerow et al. (1998), for a description of methods), and we selectthis as the best data source for these study areas. We have used TRMMproduct 2B31, which has a spatial resolution of around 5 km2 and climatenorms averaged from 1997 to present. Given that the mean catchmentsizes in the Peru and Sinai study areas are 1490 and190 km2, respectively,this spatial resolution is more than sufficient for characterising precipita-tion rate. We have selected the TRMM data over theWorldClimmodel inthese areas because the latter is based on surface weather station data,which is not very extensive in these regions. The TRMM satellite data istherefore much more reliable for these locations. One drawback of thesatellite data is that it could underestimate the annual contribution ofsnowfall to the precipitation budget. We make the assumption that thisis not a significant issue in Egypt and the most arid part of western Peru.

The PRISM, WorldClim, and TRMM precipitation averages werecompared in areas where they overlap geographically, and they are allin close agreement. The uncertainty arising from the differences be-tween the models is much smaller than the differences in precipitationrate within and between the six study areas. We compare our channelsteepness data with precipitation rates using the statistical packageOrigin 8.6. We fit our data with linear regressions or allometric powerlaws of the form y = axb consistently throughout the study.

5. Results

5.1. Channel steepness variation with precipitation rate

Fig. 5 shows ksn varying with mean annual precipitation rate for thesix study areas. Each data point represents one catchment, and thegraphs share the same axis ranges to ease comparison. Best-fit allometricpower laws of the form

ksn ¼ aPb ð6Þ

have been fitted to the data (solid red lines), where P is the mean annualprecipitation rate. The standard errors on the coefficient a and exponent bhave also been calculated. On each graph, this statistical fit has then beenduplicated with the same value of constant a, but with b varying at 0.1intervals, producing the dotted grey lines. These curves help to visualisethe upper and lower bounds of the exponent b between which the datasets lie.

Fig. 4. Representative longitudinal profiles (top graphs) and log–log plots of channel slope agashown. In black are the channels with median ksn values for each region, which are therefo130 m0.9; examples of this steepness occur in all six data sets. These are not necessarily aversame channel steepness. (For interpretation of the references to colour in this figure legend, th


In general terms, channel steepness increases sublinearly with pre-cipitation rate rather than decreasing as onemight simplistically expect(Figs. 1B, 2B). Of the study areaswith catchments uplifting at ~1 mm y−1

(Fig. 5A), the channels in Peru exhibit the highest ksn values reachingwellabove 300 m0.9 in the upper quartile. This study area is also the driest,with most catchments receiving b250 mm y−1 precipitation. The beststatistical fit is a strongly sublinear power law,withmost catchments fall-ing within the limits of b = 0.2 to 0.3, with a heavyweighting of the datatoward the dry extreme.

The channels in California and Mexico have lower ksn values thanthose in Peru, rarely exceeding 300 m0.9 and 200 m0.9 respectively.They are also wetter, mostly occupying the range of P ~ 200 to600 mm y−1. The California data spans the widest range of precipitationrates of all the areas, and the best statistical fit is a power lawwith an ex-ponent b ~ 0.6. In the case of Baja California, most of the channels fall be-tween the bounds of b = 0.6 and 0.9. The Italian channels have lower ksnvalues still, averaging only ~100 m0.9, and these catchments also receivethe highest precipitation rates of 800–900 mm y−1. They display very lit-tle variation in rainfall, and we exploit this later.

Despite the four areas sharing similar maximum uplift rates of~1 mm y−1, between them exists at least a threefold variation in ksnacross precipitation rates from b200 to ~900 mm y−1. Upper-quartileksn values clearly decline from Peru, through the two California areas,to Italy, which follows the trend of increasing precipitation rate.

In the two study areas with low uplift rates (Fig. 5B), channel steep-ness also increases as themean annual precipitation rate rises. The veryarid catchments in Egypt occupy an extremely narrow precipitationrange, yet they still show evidence of a slightly sublinear increase inksn with precipitation rate, where b = 0.76 ± 0.12. The wetter Idahocatchments span amuchwider precipitation range, with the best statis-tical fit being a power law with b = 0.62 ± 0.09. This data covers thebroadest range of precipitation rates of all areas besides California(~250 to 950 mm y−1); and it also suggests that ksn scales with Psublinearly. Nevertheless, in contrast to the faster-uplift study areas,the total range of ksn (~20–200 m0.9) is similar for the Egyptian andIdaho catchments in spite of their different climates.

The graphs in Fig. 5 exhibit scatter about the power law trends fitted,although this is significantly smaller than the differences between thestudy areas. We attribute this scatter to a combination of effects arisingfrom lithological variations, fault distribution and interactions, andother uncontrolled variables like differences in hydraulic geometryand perhaps vegetation dynamics affecting erosion. In Section 5.3, wewill introduce an averaging approach that aims to accommodate thisscatter.

5.2. Coupling of orographic precipitation, relief, and tectonics

The data in Fig. 5 shows a general sublinear increase of normalisedsteepness index with mean annual precipitation rather than a decrease(c.f. Fig. 1B). An obvious way to explain this trend is that channels withgreater precipitation are also thosewith higher local elevations or relief.The sublinear increase of ksnwith P could therefore bemasking a tecton-ic uplift trend (e.g., Fig. 2B, C) because we know that in general, higherrates of recent tectonic uplift are correlated with higher elevation, Z,and relief (c.f. Ahnert, 1970; Pinet and Souriau, 1988; Tippett andKamp, 1995; BurbankandAnderson, 2001). In fact, plots of precipitationrate against catchment elevation above local base level (Fig. 6) demon-strate unambiguously that greater rainfall directly correlateswith great-er elevations in all study areas, although the precise gradient variesbecause of location, latitude, and topographic constraints. In each case,the best statistical fit is a linear increase in P with mean catchment

inst upstream drainage area (bottom graphs) for the six study areas. Two sets of data arere average channels representative for each study area. In red are channels with ksn =age channel profiles, but allow the study areas to be compared with each other for thee reader is referred to the web version of this article.)



(A)

(B)

Peruvian Andes, western Cordillera

k ~ 89 (±13)P0.21(±0.03)sn

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California, USA

Baja California, Mexico Aspromonte, Italy

Sinai Peninsula, Egypt Idaho, USA

k ~ 1.3 (±1.4)P0.78(±0.19)sn

k ~ 9.1 (±3.3)P 0.76(±0.12)sn

k ~ 1.7 (±0.9)P0.62(±0.09)sn

m ~ 0.2

m ~ 0.25 m ~ 0.4

Fig. 5. Variation in normalised channel steepness index (θref = 0.45)withMAP rate for (A) the four study areaswithUmax ~ 1 mm y−1 and (B) the two study areas with lower uplift ratesof b0.3 mm y−1. The solid lines are allometric power laws fitted to each plot, with the form y = axb. The dotted lines show similar curveswith the same value of a, but with P raised to 0.1intervals of b. Channel steepness increaseswith precipitation rate, sublinearly, for all areas apart fromAspromonte, Italy,where the catchments occupy a narrow range of P. Values ofm areestimated, assuming that the exponent of the best-fit power law is equal to (1 − m). The two study areas with the broadest ranges of P (California and Idaho) give estimates of m around0.4. The slower uplifting study areas have lower ksn values. Of the graphs in (A), the highest ksn values are found in the driest area (Peru) and decline through California andMexico to thelowest values in the wettest area (Italy). (For interpretation of the references to colour in this figure, the reader is referred to the web version of this article.)


elevation; allometric power laws of the form P = aZd also give d valuesaround 1 but have similar or lower R2 values.

This orographic coupling of elevation with both uplift rate andprecipitation rate complicates any attempt to extract either signal


geomorphologically as outlined in Section 2. However, we can usethe Italian (south Calabria) study area to break this coupling circlebecause these coastal catchments lack the apparent orographic signalthat is inherent to the other areas. This difference can be observed clearly



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Fig. 6. The relationship between precipitation rate and mean catchment elevation.Elevation is adjusted to be above base level in each location. Calabria has uniformlylow-lying and wet catchments. In the other five areas, precipitation rate increasesorographically with elevation, and the best statistical fit is a linear trend in each location.These trends are annotated with their R2 values.


in Fig. 6. The Italian catchments have mean elevations of b1000 m, withprecipitation rate narrowly clustered around 850 mm y−1. Not onlydoes it lack a pronounced orographic signal, but southern Calabria alsohas Pleistocene–Holocene uplift rate estimates that are constrained witha high spatial resolution (Antonioli et al., 2006, Ferranti et al., 2006;Antonioli et al., 2009). Alongside uniform rainfall, this allows us to explorehow ksn varies with uplift rate alone, i.e., test the schematic graph inFig. 1A. We have taken local uplift rate constraints reported by Antonioliet al. (2006, 2009) and Ferranti et al. (2006), and calculated the averageksn values of the catchments in the immediate vicinity of each (Fig. 7).Seventy-seven channels and sixteen uplift constraints were used to esti-mate how mean ksn values vary with U, and the error bars reflect ±1σstandard deviation of the data. The best statistical fit is a linear trendthat intersects the origin. The trend is not sufficient to disprove a sublinearksn-uplift (or erosion) relationship in other areas, as has been suggested in

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Fig. 7. Mean values of normalised channel steepness index (θref = 0.45) plotted againstmean catchment uplift rate in Aspromonte, Italy. Uplift rate estimates were taken fromAntonioli et al. (2006, 2009) and Ferranti et al. (2006), and the error bars show the ±1σuncertainty in the data set. The Italian study area is an ideal location to explorethis relationship as it occupies a very narrow range of P (~800–900 mm y−1) with noorographic trend (see Figs. 4 and 5). A linear trend offers a good fit to the data and inter-sects the origin.


some studies (Tucker, 2004; DiBiase and Whipple, 2011; Kirby andWhipple, 2012), although we note these studies do not tend to accountfor orographic rainfall effects.

5.3. Extracting a precipitation signal?

The data above demonstrate that to successfully evaluate the truedependence of landscape on climatewe need to tease apart the compet-ing roles of tectonics and precipitation. To do this, we adopt two com-plementary methods. The first uses data within each study area toestimate the true scaling of ksn and precipitation if the coupling betweenuplift and ksn is known (above). The second uses comparisons betweenareas to pull out statistical differences between regionswith similar up-lift rates but different precipitation rates, for themodern day and for thegeologic past.

5.3.1. Comparison within field sitesThe linear ksn ~ U scaling suggested by the southern Calabrian data

(Fig. 7), in the known absence of orographic precipitation, implies thatthe exponent n in Eq. (5) for ksn is approximately equal to 1. Manydata sets also demonstrate the linear scaling between topographicelevation and the uplift rate generating it (Ahnert, 1970; Pinet andSouriau, 1988; Tippett and Kamp, 1995; Burbank and Anderson,2001). Consequently, to first order the effective precipitation rate expo-nent b, Eq. (6) must be related to the true precipitation exponent m[Eq. (5)], as b = 1 / d − m. For each graph in Fig. 5, correspondingvalues of m have been estimated where d ~ 1 as argued above (c.f.Fig. 6). The California data provides the most accurate estimate of m,as these data points span the broadest range of precipitation rateswith thewetter catchments needed to clearly show sublinearity. Almostall of this data falls between the limits of b = 0.5 and 0.7, therebyconstraining estimates of m to between 0.3 and 0.5. This indicatesthat, all other things being equal, channel steepness is inversely propor-tional to the square root of precipitation. Similar findings are obtainedfor Idaho in the USA at lower maximum uplift rates. This is compatiblewith the empirical findings of other workers (e.g., Sklar and Dietrich,1998; Stock and Montgomery, 1999; Wobus et al., 2006) and newwork by Ferrier et al. (2013) who recovered b = 0.5 to 0.6 using a bed-rock river analysis on the Hawaiian island of Kaua'i. In contrast, data forthe more arid Sinai, Baja California, and Peru are most consistent withlower values where m ~ 0.2, which would suggest these more aridcatchments may be relatively insensitive to precipitation gradientsin time or space, at least for the range of mean annual precipitationrates considered here. We take this opportunity to comment on thePeruvian data: the scatter andweighting of the data to the arid extrememean that this particular estimate ofm and the constant a are quite un-certain. This dataset becomesmuchmore useful in comparisonwith theother three Umax ~ 1 mm y−1 locations as we now discuss.

5.3.2. Comparison between field sitesOur field sites have mean annual rainfalls from b100 to almost

1000 mm y−1. To compare the landscapes as awhole, we calculated ar-ithmeticmean values of ksn and P for each of the study areas to enable usto compare the relatively large data sets statistically (Fig. 8A). However,we chose to restrict our averaging to the upper quartile of channelsteepness in each study area for several reasons. First, the precipitationsignal is most pronounced where the uplift rates are highest, preciselybecause of the orographic coupling deduced above, so it is in this do-main that (i) our data is most sensitive and (ii) our signal is less likelyto be affected by other factors that may affect the signal-to-noise ratiosuch as lithology changes (c.f. Section 6, below). Secondly, this allowsus to more effectively compare channels with similar Umax ~ 1 mm y−1,e.g., by excluding less steep channels sitting at fault tips or betweenfault strands. Thirdly, Fig. 5 shows us that steeper channels aremore likelyto capture any precipitation effect; in Fig. 5A, the differences between thefour Umax ~ 1 mm y−1 areas is most apparent when comparing the



0 200 400 600 800 10000

100

200

300

400

0 200 400 600 800 10000

100

200

300

400

n=52n=19

n=24n=16

n=76

Faster uplif Slower uplif

n=32 ~

R2 = 0.96

(A)

Modern precipitation ratesLGM precipitation rates

(B)

)

M )

ksn1

P0.53 (±0.08)

Fig. 8. (A) Mean normalised channel steepness index (θref = 0.45) plotted against meanannual precipitation rate, for the upper quartile of channels (selected by ksn) in each area.The annotation gives the number of channels that are included in each average, and theerror bars show ±1σ uncertainty (one standard deviation). For the two areas with slowercatchment uplift (open squares), ksn averages ~125 m0.9 regardless of P. For the areas withfaster Umax ~ 1 mm y−1, ksn averages more than double this in Peru (P b 200 mm y−1),declining as precipitation rate increases. This relationship can be approximated with apower law of ksn ~ 1 / Pm where m is an expected value of ~0.5. The average ksn reaches acomparable value to the low uplift areas when P ~ 800 mm y−1. (B) The ~1 mm y−1 upliftdata only, comparing modern precipitation rates (black circles) with estimates of LGMprecipitation rates (red stars). (For interpretation of the references to colour in this figurelegend, the reader is referred to the web version of this article.)


steepest channels. This is because each area has points where U decays tozero, so ksn similarly decays to lowvalues in places.We need to isolate thesteeper, most sensitive channels.

The number of measurements included in each data point is anno-tated on Fig. 8A. Error bars reflect ±1σ standard deviation withineach set of channels, hence the greater error on the Peru point. For theUmax ~ 1 mm y−1 areas (black circles), mean ksn decreases from Peru,through the California examples, to Italy as the mean precipitationrate increases. The best fit to the data is an inverse power law whereksn ~ P−0.53 ± 0.08. This result compares well with the analysis for indi-vidual catchments in Fig. 5, with the ‘expected’ value of m derivedfrom theory (Sklar and Dietrich, 1998; Wobus et al., 2006) and is invery good agreement with the empirical findings of others (Stock andMontgomery, 1999; Snyder et al., 2000; Ferrier et al., 2013).We empha-sise that the two- to threefold decrease in mean ksn (from ~320 m0.9 inarid Peru to ~110 m0.9 in wetter Italy) over a precipitation range from~100 to N800 mm y−1 cannot be explained by uplift rate differences.However, for the two areas with catchment uplift rates below0.3 mm y−1 (open red squares), mean upper quartile ksn averages


~120 m0.9 in both areas despite the difference in rainfall rates. In thesetwo cases, the absolute range and magnitude of ksn values is small.

In Fig. 8B,we plot ksn as a function of P reconstructed for the last glacialmaximumusing the data discussed in Section3.2 to evaluate the likely cli-mate ranges these catchments have been exposed to. We only focus onthe four U ~ 1 mm y−1 areas as these clearly capture the precipitationsignal. The red stars represent the precipitation rate of each area, shiftedto the predicted LGM position (c.f. Section 3.2). This is only a first-orderinsight because the uncertainties on LGM climate are large (and also dif-ficult to meaningfully quantify, so we have omitted error bars). Nonethe-less, a general decline in ksnwith precipitation rate is observed, suggestingthat channel steepness declines with precipitation rate whether or notLGM or modern data are used. In reality, these precipitation rates formthe two end-members of glacial–interglacial conditions. Geomorphicresponse timescales are currently a topic of intense debate (Armitageet al., 2011; Castelltort et al., 2012; Whittaker and Boulton, 2012)but catchment response times are likely to cover at least one glacial–interglacial cycle. Averaged over this period, effective precipitation ratesprobably lie somewhere between the data sets in Fig. 8B. Accounting forpalaeoclimate variabilitymay alter the estimate ofm slightly, but it is sec-ondary to the finding that precipitation rate measurably suppresses thesteepening of channels in response to uplift.

5.4. The importance of relief

Relief is the integrated product of uplift and erosion, both of whichare moderated by tectonic and climatic boundary conditions. Conse-quently, any geomorphic index that captures the fundamental controlson landscape morphology should potentially scale with relief. For ourstudy areas, we test the scaling of normalised channel steepness indexwith mean catchment relief using the whole data set, comprising sixstudy areas and 846 channel measurements in total (Fig. 9). We mea-sure catchment relief as the vertical difference in elevation, betweenthe highest and lowest points in a catchment. The result is strikingbecause (i) this suggests that ksn is linearly proportional to catchmentrelief with a gradient of ~7%; and (ii) the graph shows that the data allcollapse together on a similar trend. In otherwords, for an order ofmag-nitude range in precipitation rate (~100 to 1000 mm y−1) and upliftrate (~0.1 to ~1 mm y−1) and despite possible differences in bedrockerodibility, the relationship between channel steepness and relief is al-most identical in these six areas. Channel steepness indices are there-fore extremely efficient predictors of catchment relief and vice versa.Importantly, this indicates that for these regions, topographic reliefand channel geometry are responding in similar ways to boundary con-ditions and probably with a similar response time.

6. Discussion

6.1. Decoupling tectonics and climate?

Our data highlight the fact that tectonic and climatic variables playimportant roles in determining channel steepness, but it also empha-sises how difficult they are to deconvolve. In simple plots such asFig. 5, ksn increases with precipitation when theory suggests it shoulddecline. We attribute this to an orographic coupling of precipitationrate and tectonic uplift; so in order to constrain the precipitation–ksnsignal, we need to remove the uplift signal. This is a complicated taskprimarily because many areas of the world do not have robust con-straints on the rate of rock or surface uplift. Moreover, we still do notknow the ‘typical’ response timescale over which tectonic–climaticboundary conditions ought to be averaged (e.g., Whittaker andBoulton, 2012). Fortunately, in our four ‘faster uplift’ study areas,existing work has constrained Umax at ~1 mm y−1, determinedusing a range of methods and representative of the recent ~1 Ma(see Table 1 for references). We have chosen uplift rate estimates aver-aged over the Pleistocene–Holocene period because this corresponds



0 1000 2000 3000 4000 5000 60000

100

200

300

400

500

R2 = 0.91

Catchment relief (m)


Peruvian Andes California, USA Baja California, Mexico Calabria, Italy

Wet

ter

U U

k = 0.07 R sn

k = 0.10 R sn

k = 0.04 R sn

Fig. 9. Normalised channel steepness index (θref = 0.45) plotted against total catchmentrelief (R, the elevation difference between the highest and lowest points). Channel steepnessincreases linearly with relief, in a very similar way for all six study areas, across gradients inclimate and in tectonics.


with current best estimates of the geomorphic response times of fluviallandscapes: between 105–6 years (Snyder et al., 2000; Whittaker et al.,2007a,b; Armitage et al., 2011; Whittaker and Boulton, 2012). Theseareas also have different climates and are, therefore, some of the bestlandscapes for testing climatic ideas using stream profile analysis. We in-vestigated the dependency of ksn on average precipitation rate in twocomplementary ways. Initially, we deduced the orographic covarianceof uplift and precipitation (Fig. 6); we showed that the ksn–U relationshipcan also be treated as linear for our purposes (Fig. 7). Consequently, thesignificant sublinearity of the ksn–precipitation relationships in the vari-ous study areas (Fig. 5) suggests that precipitation does have a reducingeffect on ksn. However, the effect of the orographic coupling with upliftrate is such that precipitation ‘acts to limit’ the increase in ksn with uplift.In other words, precipitation rate is acting as a proxy for the uplift signalbut transforming it simultaneously, producing a composite signal. For thetwo areas that receive a substantial range of precipitation rates (Californiaand Idaho), we extract values of m around 0.4 ± 0.1 (Eq. (5)), in agree-ment with published constraints (Sklar and Dietrich, 1998; Stock andMontgomery, 1999; Snyder et al., 2000; Wobus et al., 2006; Ferrieret al., 2013). All of the study areas provide evidence for sublinearity inFig. 5, other than the Aspromonte which is used to decouple uplift andprecipitation. The second approach we take to characterising the precipi-tation dependence of ksn is to draw a comparison between the four areasuplifting at ~1 mm y−1 so that the tectonic variable is largely controlled.Averaging the steepest quartile of channels in each area, to represent thelandscape as a whole, produces a power law decline in ksn with modernmean annual precipitation rate (Fig. 8), which also reveals an expectedvalue of m around 0.5. A comparison with LGM rates indicates that ksnalso declines as palaeoprecipitation rate increases.

We also find that ksn scales linearly with catchment relief in a near-identical fashion for our study areas despite differences in uplift rate,precipitation rate, and erodibility. Fig. 9 is highly encouraging becauseit suggests that ksn does intrinsically quantify the time-integrated equi-librium between uplift and erosion.

A key concern in any study of this type is whether mean annual pre-cipitation rate is the best way of quantifying a ‘climate’, which evidentlycan be (and is) characterised by a range of variables (e.g., Champagnacet al., 2012; Whittaker, 2012). Mean annual precipitation is a variableexplored in the majority of advanced landscape evolution models(e.g., Carretier and Lucazeau, 2005; Armitage et al., 2011; Allen et al.,


2013), but others clearly matter too, such as the magnitude–frequencydistribution of storm size and maximum rainfall rates, the seasonal dis-tribution of precipitation, and the effects of temperature on landscapeevolution transmitted by vegetation dynamics, glaciation, and the spa-tial distribution of rainfall (Sólyom and Tucker, 2004; Istanbulluogluand Bras, 2005; Anders et al., 2008; Wobus et al., 2010; Wulf et al.,2010; DiBiase and Whipple, 2011; Egholm et al., 2012). Such effectsmay be complicated further by erosion thresholds (Molnar, 2001). Thetwo big questions we must answer are (i) which climatic data closelyscales with the geomorphically effective channel discharge? and (ii)which climatic or landscape variables can we realistically measure inspace and also back in time (c.f. Whittaker, 2012)? In principle, meanannual precipitation is directly related to effective discharge andhence landscape form, so a good way to address this debate is arguablyto test the first-order relationship between geomorphological data andmean precipitation rate, as we have done here, before moving on toother variables. We also exploit one of the main advantages of usingsuch data: it is possible (to an extent) to reconstruct these rates forthe past. Other parameters like maximum storm size, rainfall intensity,or vegetation density remain very challenging to reconstruct over 105

to 106 year periods in reliable detail. This is clearly an issue that needsto be addressed by future work.

6.2. Lithological effects and other study limitations

It is worth commenting on the effects of bedrock lithology in ourfindings. We have not controlled the lithology variable between orwithin our study areas (see Table 1); and there are necessarily a rangeof sedimentary, metamorphic, and igneous bedrocks exposed in thecatchments for any global-scale investigation such as ours. Nonetheless,we can make a very important observation: the steepest channels werefound in the Peruvian data, and these catchments predominantly drainvolcaniclastic sediments and other recent Pliocene sediments, withmore resistant Palaeogene–Neogene volcanic rocks only cropping outnear the catchment headwaters (Gonzalez and Pfiffner, 2012). In con-trast, the Italian catchments with the lowest ksn measurements for thesame uplift rate largely drain highly resistant gneisses, quartzites, andother metamorphics of the Aspromonte massif (Atzori et al., 1983).The Peruvian catchmentsmay indeed have themost erodible lithologiesof all the areas, yet have the steepest channels with the greatest reliefand the highest headwaters. Therefore, while rock erodibility obviouslyadds scatter to the data, we donot consider that lithology explains awaythe relationships between uplift rate, precipitation rate, relief, and chan-nel steepness deduced here. Similarly, we suggest that lithological dif-ferences do not explain why the Sinai and Idaho data sets have similarranges and magnitudes of ksn: both have a range of sedimentary, meta-morphic, and igneous lithologies. Channel steepness is more likely to below in these areas simply because the uplift rate is very low.

We have also not directly addressed glaciation effects in our data. Aspreviously mentioned, we have excluded from our measurements anyobvious glacially eroded plateaus in the upper reaches of channels tominimise the effects of glacial erosion. However, glaciers did occupythe headwaters of some of the 846 catchmentswemeasured here, and ef-fects arising from this perhaps contribute to some of the unexplainedscatter on our plots. Future studies may benefit from isolating the glacia-tion variable alone to elucidate its controls on channel geometry in loca-tions where other climatic and tectonic variables are controlled.

This is a broad-scale study encompassing nearly 850 channels in sixstudy areas around the globe. If each of these were examined in closespatial detail, the precise fluvial erosion process, the positions of indi-vidual faults, and/or lithological boundaries probably play a role in de-termining ksn in individual catchments. We emphasise that the focusof this studywas to derivefirst-order regional trends using a statisticallylarge data set, rather than attempting to quantify everything know-able about individual catchments. This applies through time as wellas across space: we have used uplift rate averages over the most likely




geomorphologically relevant timescale according to recent research, andwe have assumed that modern topography captures the integrated uplifthistory averaged over this timescale. However, future studies could ex-plore variations in boundary conditions averaged over different timeperiods.

7. Conclusions

In this paper we demonstrate that longitudinal channel profiles aresensitive to mean annual precipitation rate in tectonically active land-scapes. We find that channel steepness increases with precipitationrate sublinearly, but in a way that can be explained by the orographiccoupling of precipitation and recent topographic uplift. While greaterrainfall has a reducing effect on channel steepness, this couplingmeans it acts as a proxy for the uplift signal whilst also modulating it.Put another way: precipitation rate limits the amount that channelscan steepen in response to tectonic uplift. This effect can be detectedin the sublinearity of the relationship between normalised channelsteepness and precipitation rate from individual study areas and alsoby comparing the steepest, most sensitive channels from different re-gions that share equivalent uplift rates.

Our twin approaches to characterising the ksn–P relationship arecomplementary and give similar results to each other, to existingtheoretical work (Sklar and Dietrich, 1998; Wobus et al., 2006)and to localised empirical studies (Stock and Montgomery, 1999;Snyder et al., 2000; Ferrier et al., 2013). We therefore argue thatchannel steepness in arid locations like western Peru is measurablyhigher by combination of significant uplift rates and a dry climateand that channel steepness declines when either uplift rate slowsor precipitation rate rises. When comparing multiple locations,channel steepness cannot be explained by either tectonics or cli-mate alone; both must be considered together. We also demonstratethat ksn scales with catchment relief in a linear, similar way for allour study areas, despite their differences in climatic, tectonic, andlithological boundary conditions. This is an encouraging testamentto how intrinsically linked channel steepness is to the balance be-tween uplift and erosion.

To our knowledge, this is the first time a clear precipitation rate sig-nal has been empirically extracted from ksn data representing differentlandscapes where the effects of tectonic uplift have been largely con-trolled, in keeping with theoretical considerations. The results are sig-nificant because they demonstrate that climate and palaeoclimaticrainfall averages play an important but often neglected role in deter-mining the geomorphic form of the landscape in nonglaciated terrain.A key challenge for future studies is to quantify climatic controlson upland catchments more widely, including magnitude–frequencydistribution of storminess, associated vegetation dynamics, and channelerosion thresholds. Of course, this needs to be characterised across arange of landscape metrics including hillslope angles and curvatures,not just ksn (c.f. Abbühl et al., 2011; Bookhagen and Strecker, 2012;DiBiase et al., 2012; Hurst et al., 2012). To answer these questionsfully, workers therefore need to tackle the outstanding ‘big-ticket’question in quantitative geomorphology—what is the characteristicresponse time of landscapes to climatic or tectonic perturbations(c.f. Jerolmack and Paola, 2010; Aguilar et al., 2011; Armitage et al.,2011, 2013)?

Acknowledgements

D'Arcy was supported by an Imperial College Janet Watson bursaryand Whittaker was supported by funding from the Royal Society. Wethank Sebastian Erhardt for his technical help with GIS. We thankBodo Bookhagen and an anonymous reviewer for their detailed com-ments which greatly improved the manuscript.


Appendix A. Supplementary data

Detailedmaps of the study areas can be foundonline at http://dx.doi.org/10.1016/j.geomorph.2013.08.019.

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Geomorphic constraints on landscape sensitivity to climate in tectonically active areas