rethinking low-temperature thermochronology data sampling strategies for quantification of...

8/6/2019 Rethinking Low-temperature Thermochronology Data Sampling Strategies for Quantification of Denudation and Reli

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Rethinking low-temperature thermochronology data sampling strategies forquantification of denudation and relief histories: A case study in the Frenchwestern Alps

Pierre G. Valla , Peter A. van der Beek, Jean Braun

Institut des Sciences de la Terre, Universit Joseph Fourier, CNRS, BP 53, F-38041 Grenoble, France

a b s t r a c ta r t i c l e i n f o

Article history:Received 10 December 2010

Received in revised form 29 April 2011

Accepted 2 May 2011

Available online 31 May 2011

Editor: T.M. Harrison

Keywords:

low-temperature thermochronology

numerical modeling

inversion

exhumation

relief development

sampling and modeling strategies

We assess the importance of thermochronometric data sampling and modeling strategies for correctlyestimating mountain belt exhumation. Thermochronological age-elevation profiles have been widely used to

infer orogenic exhumation histories; however, recent studies have shown that this sampling strategy may not

be the most pertinent for quantifying both denudation and relief history. Here, we investigate the ability of

combining different thermochronology data sampling schemes with numerical modeling to better constrain

denudation rates and relief changes. We produce synthetic thermochronology datasets for real Alpine

topography under a specific exhumation and relief scenario using the thermal-kinematic model Pecube. We

then adopt an inverse approach based on the Neighborhood Algorithm to quantitatively assess the resolution of

different thermochronology datasets collected following elevation profiles, long transects and valley bottom

sampling. We also test the effect of the modeling approach on denudation and relief predictions, in particular

the influence of the topographic grid resolution and of potential constraints on the geothermal gradient. Our

results show that sampling along a single elevation profile does not allow to quantitatively constrain both

denudation and relief histories. Numerical outputs clearly evidence tradeoffs that limit the capacity of

simultaneously resolving denudation rates and relief change. Quantitative predictions are only slightly

different when combining elevation profiles along different valleys, but are highly improved when using long

transects or valley-bottom samples combined with an elevation profi

le. The resolution with which reliefevolution can be predicted may be increased by a factor of 2 by using spatially distributed datasets. Results of

thermal parameter inversions suggest that the geothermal gradient may be better estimated using elevation

profiles or long-transect sampling rather than using valley bottom samples. Simulations with different model

topography resolutionsshow that degrading the resolution for computational efficiency may result ina loss of

quantitative information on denudation rates and relief history. In summary, we highlight that both

thermochronological sampling strategies and the choice of thermal parameters or model topography resolution

have a significant influence on predicted denudation and relief histories. Ideally,the samplingstrategy should be

designed using preliminary modeling of expected denudation and relief histories, and a sensitivity study on

assumed thermalparameters and model resolution should be performed whenmodeling the data. Although our

modelingis basedon a particular case study of reliefevolution in theFrench westernAlps,we believe that these

inferences have general relevance for thermochronological studies within mountain belts.

2011 Elsevier B.V. All rights reserved.

1. Introduction

Low-temperature thermochronology has been widely used to

quantify the exhumation history of mountain belts (e.g., Braun, 2005;

Gallagher et al., 1998; Reiners and Brandon, 2006). Numerous studies in

the last 20 yr or so have used apatite fission-track (AFT) (e.g., Fitzgerald

et al., 1995; Gallagher et al., 1998; Hurford, 1991) and (U-Th)/He (AHe)

(Ehlers and Farley, 2003; Farley, 2002) datato infer exhumation histories

in specific areas. Moreover, low-temperature thermochronology may

provide useful constraints for assessing paleo-topography and relief

development (e.g., Clark et al., 2005; House et al., 1998; Reiners, 2007).

The effect of steady-state topography on thermochronology data is well

understood (e.g., Mancktelow and Grasemann, 1997; Stwe et al., 1994).

However, potential effects of time-varying topography, leading to

spatially and temporally varying exhumation rates as well as a transient

thermal structure, are more difficult to assess (Braun, 2002a; Valla et al.,

2010).

Thermochronometric sampling strategies have often focused on

obtaining age-elevation profiles, i.e., datasets of AFT and/or AHe ages

collected along a steep elevation transect (e.g., Fitzgerald et al., 1995;

Earth and Planetary Science Letters 307 (2011) 309322

Corresponding author.

E-mail address: [email protected] (P.G. Valla).

0012-821X/$ see front matter 2011 Elsevier B.V. All rights reserved.

doi:10.1016/j.epsl.2011.05.003

Contents lists available at ScienceDirect

Earth and Planetary Science Letters

j o u r n a l h o m e p a g e : w w w . e l s e v i e r . c o m / l o c a t e / e p s l
http://dx.doi.org/10.1016/j.epsl.2011.05.003http://dx.doi.org/10.1016/j.epsl.2011.05.003http://dx.doi.org/10.1016/j.epsl.2011.05.003mailto:[email protected]://dx.doi.org/10.1016/j.epsl.2011.05.003http://www.sciencedirect.com/science/journal/0012821Xhttp://www.sciencedirect.com/science/journal/0012821Xhttp://dx.doi.org/10.1016/j.epsl.2011.05.003mailto:[email protected]://dx.doi.org/10.1016/j.epsl.2011.05.003


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Gallagher et al., 2005; Wagnerand Reimer, 1972). Thermochronologic

age-elevation relationships allow inferring apparent exhumation

rates over a specific time window and, in theory, do not require

knowledge of the geothermal gradient. One-dimensional consider-

ation of age-elevation relationships thus remains the most direct way

to interpret thermochronology data, either by simple linear regression

of the data (e.g., Fitzgerald et al., 1995; Wagner and Reimer, 1972) or

by using 1D thermal evolution models (e.g., Gallagher et al., 2005).

However, topographic effects on thermochronology data are noteasily extracted from age-elevation relationships (Braun, 2002a) and

recent modeling studies suggest that constraining mountain belt

paleo-relief from elevation profiles is difficult, even when combining

multiple thermochronometers (Valla et al., 2010; van der Beek et al.,

2010; Vernon et al., 2009).

Recent developments in numerical modeling offer tools for inter-

preting low-temperature thermochronology data, either considering

each sample individually (e.g., Ketcham, 2005) or exploiting the spatial

correlation between samples (Braun et al., 2006; Gallagher et al., 2005;

Stephenson et al., 2006a), to derive thermal histories and eventually

constrain bothdenudation and relief histories. Braun (2002b) proposed

an alternative approach to assess paleo-relief by sampling along a

horizontal transect and using the spatial coherence between the

topographic and thermochronological signals to determine both

regional denudation rate and relief change (Beucher et al., submitted

for publication; Herman et al., 2007, 2010a). However, the main

limitation of this spectral method is that it assumes a spatially and

temporally constant denudation history, and only provides an upper

bound on the timing of denudation or the age of relief change.

Numerical modeling offers the unique possibility to exploit dense

spatial datasets either with or without any specific spatial relationship

(Braun and van der Beek, 2004; Gallagher et al., 2005; Stephenson et al.,

2006a). In this study, we aim to assess under what sampling and

modeling conditionsquantitative constraintson the exhumationhistory

can be extracted from low-temperature thermochronology data. We

define different sampling strategies for a specific topography and test

whether each sampling schemepermits deriving both denudation rates

and relief history. Moreover, we assess to what extent the modeling

approach, especially the spatial resolution of the model grid or anyimposed constraint on the geothermal gradient, can bias predicted

denudation and relief histories. Our approach, although being specific

with respect to the study area and the relief scenario we simulated, has

been designed to more generally assess the potential influence of

specific sampling schemes for constraining orogen exhumation. Our

study thus follows an experimental design approach that has been

widely usedin geophysics(e.g.,Curtis, 2004a,b; Wood andCurtis, 2004),

although for computational simplicity we do not perform a complete

inverse analysis but rather a priori define specific 3D sampling schemes

that are traditionally used in thermochronological studies.

Several studies (Glotzbach et al., 2011; Valla et al., 2010; van der

Beek et al., 2010) have recently attempted to extract independent

information on denudation and relief development in the western

European Alps from thermochronology data. This was achieved bycombining the 3D thermal-kinematic model Pecube (Braun, 2003;

Braun et al., submitted for publication), which predicts thermal

histories and thermochronologicalages from an input denudation and

relief history, with an inversion scheme based on the Neighborhood

Algorithm (Sambridge, 1999a,b) to search the parameter space,

extract best-fitting scenarios from the data and derive quantitative

estimates for the parameters (rates, timing and relief ratio) describing

denudation and relief histories.

Weadopt a similarnumericalapproachas Valla et al.(2010); however,

their study specifically focused on the problem of interpreting age-

elevation profiles whereas here we consider various sampling strategies.

Moreover, instead of building a synthetic topography for inverse

modeling (Valla et al., 2010), we use real topography for predicting

synthetic thermochronology data (Fig. 1a). We focus on the Ecrins

Pelvoux massif (van der Beek et al., 2010), one of the External Crystalline

Massifs (ECMs) within the western European Alps (e.g., Dumont et al.,

2008). The Neogene exhumation history of the ECMs has been widely

studied in the last few years, leading to contrasting views regarding

timing and rates of exhumation, and the impact of Pliocene-Quaternary

climate change on late-stage exhumation (Glotzbach et al., 2008, 2010;

Reinecker et al., 2008; van der Beek et al., 2010; Vernon et al., 2009). Our

synthetic approach is motivated by recent predictions forthe exhumation

history of the Ecrins

Pelvoux massif from thermochronology datacollected along either an elevation profile (van der Beek et al., 2010) or

a long transect (Beucher et al., submitted for publication); both studies

providedpreciseconstraints ondenudationhistoriesbut could notresolve

relief evolution quantitatively. More generally, our study has been

motivated by several attempts to quantify both timing and magnitude

of topographicevolution in mountain belts using thermochronology (e.g.,

Braun, 2005; Ehlers and Farley, 2003; Reiners, 2007; Valla et al., 2010).

In the following, we first outline our modeling approach, present

the synthetic data used for the simulations and discuss the inverse

method. We then show inversion results and present to what extent

predictions of denudation rates, relief change and near-surface

thermal structure can be quantitatively determined by various

thermochronological sampling strategies. The potential effects of

varying the model gridresolution are reported in the Supplementary

data. We finally discuss the implications of our findings for

thermochronological sampling strategies to constrain regional

denudation rates and/or topographic evolution of mountain belts.

2. Modeling approach

2.1. Thermal-kinematic modeling and synthetic thermochronology data

The EcrinsPelvoux massif topography is characterized by a

dominant NorthSouth topographic wavelength of ~10 km (Figs. 1a

and 2a) organized around four major valleys (for details and locations

see van der Beek et al., 2010). The relief amplitude is ~3 km, with

summits around 4000 m and valley bottoms at ~1000 m (Fig. 1a). The

EcrinsPelvoux massif has been chosen for our study as it forms a

homogeneous area for the purpose of understanding Neogeneexhumation and relief development, i.e., no major active fault crosses

the massif and consequently its exhumation history can be assumed

to be spatiallyuniform (Delunel et al., 2010; van der Beek et al., 2010).

Based on this topography and an assumed exhumation history, we

predicted synthetic thermochronology data using the Pecube model

(Braun, 2003). Pecube is a 3D thermal-kinematic model that calculates

the thermal structure through time within an exhuming crustal block

and provides thermal histories for rock particles that end up at the

surface of the model, taking into account the effects of evolving

topography (see Valla et al., 2010; Braun et al., submitted for

publication for a detailed discussion). The Pecube finite-element

code permits defining exhumation/relief scenarios that are described

as discrete phases with an imposed regional denudation rate and

paleo-relief. Relief evolution is quantified using the relief ratio R: forR =0, the paleo-relief is a plateau at maximum elevation; for R= 1,

the paleo-relief is equal to present-day conditions; and for R=2, the

paleo-relief is twice as large as the present-day relief. Note that relief

increase operates through preferential valley incision in our model

(Fig. 2a); i.e., ridges remain at a constant elevation but valley bottoms

are lowered (see Valla et al., 2010; Braun et al., submitted for

publication for a complete description), as would be expected for

relief increase by glacial valley carving for instance. Isostatic rebound

in response to this erosional unloading is included. Thus, local

exhumation rates are the sum of: (1) the imposed regional

(background) exhumation; (2) local relief change through valley

incision; (3) spatially varying rock uplift induced by isostatic rebound.

Thermal, mechanical and kinematic parameters used in the forward

model are given in Table 1. The basal crustal temperature (Temp) and

310 P.G. Valla et al. / Earth and Planetary Science Letters 307 (2011) 309322


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the crustal heat production (H_prod; here normalized to heat capacity

and density) are fixed to produce a surface geothermal gradient of

~25 C km1.

Predicted thermal histories are then used to calculate different

thermochronometric ages. In this study, we focus on late-stage

exhumation histories and thus only compute low-temperature apatite

fission-track (AFT) and (U-Th)/He (AHe) ages, as well as mean

confined track lengths (MTL; see Valla et al., 2010). Thermal histories

are translated into AHe ages using a simple model for He production

diffusionejection (Farley, 2000); AFT ages are calculated using a

model forAFT annealing(Greenet al., 1989; Stephenson et al., 2006b).

We acknowledge that using these simple algorithms does not

completely reflect the complex annealing and diffusion processes

included in low-temperature thermochronology (Flowers et al., 2009;

Gautheron et al., 2009; Ketcham, 2005). However, as discussed in

Valla et al. (2010), we use the same forward models for AFT and AHe

600' 612' 624'

4448'

4500'

Longitude (E)

La

titude(N)

AHe age (Ma)3 5 7 9 11 13 15

c

600' 612' 624'

4448'

4500'

Longitude (E)

La

titude(N)

AFT age (Ma)3 5 7 9 11 13 15

b

4506

600

612

624

4500

4448500

900

1300

1700

2100

2500

2900

3300

3700

4100

Elevation(m)

Latitude(N)

Longitu

de(

E)

a

1_Profile

3_Profiles

Valleys

Transect

Profile + Valleys

VeneonVeneon

Bonn

e

Bonne

MontontPelvouxelvoux

Barre desarre desEcrinscrinsLa Meijea Meije

Severais

se

Sever

aisse

Rom

anche

Romanc

he

Fig. 1. a) 3D map view of the modeling area (90-m resolution SRTM DEM of the Ecrins Pelvoux massif, Western Alps, France) used to produce AFT and AHe ages maps (b, c). Names

of principal valleys and peaks are indicated for orientation. bc) Apatite fission-track (b) and (U-Th)/He (c) age map produced using Pecube (Braun, 2003; Table 1) and simulating a

scenario of 50% relief increase (Rinput=0.5) during the last 3 Ma (Tinput). The constant background denudation rate is 0.3 km Myr1 (E1input= E2input) and resulting maximum rate of

relief increase over the last 3 Ma is ~0.5 km Myr1 (see text for discussion). Sample locations for the 5 different sampling schemes are shown: (b) Sampling schemes 1_Profile

(yellow circles, based on van der Beek et al., 2010), 3_Profiles (black circles) and Valleys (white circles). (c) Sampling schemes Transect(red circles, partly based on Beucher et al.,

submitted for publication) and Profile+Valleys (yellow circles, partly based on van der Beek et al., 2010).

311P.G. Valla et al. / Earth and Planetary Science Letters 307 (2011) 309322


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age predictions when generating the synthetic data and resolving the

inverse problem; the results shown here are thus largely independent

of the specific age-prediction models.

To produce the synthetic datasets that we will use in the inversion,

wedefine a 2-phase exhumation scenario with steady-statedenudation

(0.3 km Myr1) over 15 Myr and a gradual 50% relief increase (R=0.5,

Fig. 2a) since 3 Ma (T=3 Ma). This scenario simulates moderate relief

increase (~1.5 km over the last 3 Myr, i.e., a maximum relief growth

rate of ~0.5 km Myr1) associated with a relatively low and constant

background denudation rate (0.3 km Myr1). Although this choicefor a

specific denudation and relief scenario renders our analysis somewhat

contextual, we focus on the type of scenario that has been inferred for

the western Alpine massifs (e.g., Glotzbach et al., 2011; van der Beek et

al., 2010; Vernon et al., 2009). Thermochronology data are predicted

following this input scenario on a very high-resolution grid (90-m,

Fig. 1b,c) to ensure that the numerical model properly resolves finite-

amplitude topography effects on the crustal thermal structure. AFT and

AHe age maps(Fig. 1b,c) show a significant age contrast between valley

bottoms (AFT ~7 Ma and AHe ~34 Ma) and ridges (AFT ~15 Ma and

AHe ~1213 Ma). Note that our synthetic AFT and AHe data are similarto measured thermochronological ages in the area (Beucher et al.,

submittedfor publication; van der Beek et al., 2010), suggestingthat the

imposed tectono-geomorphic scenario we define is reasonable.

We sampled both the AFT (and associated MTL) and AHe maps

following five different strategies: (1) a single elevation profile

(Fig. 1b, 1_Profile), partly based on sample locations reported by van

der Beek et al. (2010); (2) three elevation profiles sampling the three

main valleys of the massif (Figs. 1b and 3b, 3_Profiles); (3) valley

bottom samples along the major valleys (Figs. 1b and 3a, Valleys); (4)

an elevation profile combined with valley bottom samples (Figs. 1c

and 3c, Profile+Valleys); and finally (5) a long transect (partly based

on sample locations in Beucher et al., submitted for publication)

across the massif (Figs. 1c and 2, Transect). Each sampling scheme

includes exactly 20 samples for which AFT, AHe and MTL data are

1

2

3

4

Elevation(km)

Distance (km)

Age (Ma) MTL (m)

North South

a

Elevation(km)

Elevation(km)

0 5 10 15 20 25 30 35

4 6 80.5

1.5

2.5

3.5

10 11 12 13 140.5

1.5

2.5

3.5

cb

AFT

AHe

-1

-1

10 12 14

Fig. 2. a) Topographic cross-profile along the sampling scheme Transect(see Fig. 1b for location within the study area). Solid black and dashed red lines represent present-day and

paleo-topography (R =0.5, see text for discussion), respectively. Black circles show sample locations for the sampling scheme Transect, and arrows represent relief evolution along

the topographic profile (background denudation rate is 0.3 km Myr1). (b, c) Synthetic thermochronological ages versuselevation for Transectsamples, including AFT and AHe ages

(b) and mean fission-track length data (MTL, c). Apparent exhumation rates (AER) deduced from linear regression of elevation vs age (b) are 0.34 and 0.33 km Myr 1 for AHe and

AFT data, respectively (r=0.980.99). Note that the MTL pattern shows a normal correlation between MTL and elevation (c).

Table 1

Thermal, kinematic and elastic parameters used in Pecube. Crustal thickness, basal

temperature (Temp) and heat production parameter (H_prod) are set to obtain a

geothermal gradient of ~25 C km1 and a crustal heat production of ~7.5 CMyr1.

Poissonratio,Young's modulusand equivalentelasticthickness areusedfor calculatingthe

isostatic reboundin responseto relief change. Equivalent elasticthickness is set to a value

that simulates moderate isostatic rebound (Valla et al., 2010; van der Beek et al., 2010).

Parameter

(unit)

Inversions value

Crustal thickness (km) 40

Crustal density (kg m3) 2700

Sublithospheric mantle density (kg m3) 3200

Young's modulus (Pa) 1.1011

Poisson ratio 0.25

Equivalent elastic thickness (km) 25

Thermal diffusivity (km2 Myr1) 25

Basal crustal temperature (C) 600

Crustal heat production parameter 0.8

Sea-level temperature (C) 15

Atmospheric lapse rate (C km1) 6



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available. We thus compare the predictions of different sampling

strategies while maintaining identical dataset size. Figs. 2 and 3 show

synthetic AFT and AHe data plotted against elevation for the different

sampling schemes. All AFT and AHe age-elevation relationships suggest

nearly constant apparent exhumation rates (AER) of 0.330.39 and

0.330.47 km Myr1 (see Figs. 2 and 3, correlation coefficients

r0.950.99), respectively. The AER slightly overestimate the input

background denudation rate due to additional local exhumation

following relief growth (most strongly recorded by valley-bottomsamples, Fig. 3a).

2.2. Inverse thermal-kinematic modeling

For each sampling scheme, we run inversions to recover the four

parameters used to describe the imposed tectono-geomorphic

scenario, defining a range in which the inversion procedure will

search for each: (1) denudation rate of the first phase (E1: 0

2 km Myr1); (2) denudation rate of the second phase (E2: 0

2 km Myr1); (3) transition time (T: 0.514.5 Ma); and (4) relief

factor (R: 02). Each inverse simulation is run over 15 Myr. We run

inversions constrained by the full dataset (AFT+AHe+MTL) as well

as subsets of the input thermochronology data (AFT, AHe, AFT+AHe,

AFT+MTL, and AFT+AHe+MTL data) to test what combination of

thermochronometers is most useful to quantify relief and denudation

histories in different sampling schemes.

In a second set of inversions, we test the ability of the different

sampling schemes to constrain not only relief and denudation

histories, but also to retrieve the geothermal gradient (Temp and

H_prod parameters, Table 3). To achieve this, we run five additional

inverse simulations with the full dataset and 6 parameters to invert

(E1, E2, T, and R as described previously; Temp: 500800 C, and

H_prod: 03). We acknowledge that other thermo-physical parame-

ters such as diffusivity or thermal conductivity, as well as the surface

temperature history, are largely unknown and may also vary; butgiven the relatively homogenous lithology in our study area, we

suspect they will do so within much narrower limits than the thermal

parameters we test for and will therefore exert only a second-order

influence on model predictions. Finally, we test the influence of the

grid resolution on relief and denudation predictions (see Supplemen-

tary data for results and discussion).

To perform the inversions, we use the Neighborhood Algorithm

(NA) of Sambridge (1999a,b). NA is a two-stage numerical procedure

for non-linear inverse problems that allows efficient exploration of a

multidimensional parameter space to find best-fitting models (NA

sampling stage) as well as deriving estimates of posterior probability

distribution for inverted parameters from the ensemble of models run

during the sampling stage (NA appraisal stage).

The sampling stage iteratively explores the multi-dimensional

parameter space and progressively concentrates on regions where

parameter values minimize the misfit to the data. NA makes use of

1

2

3

4

1

2

3

4

4 6 8 14

4 6 8 10 12 14 4 6 8 14

1

2

3

4

Elevation(km)

Elevation(km)

Age (Ma) Age (Ma)

Elevatio

n(km)

Age (Ma)

a b

c Profile + Valleys

3_ProfilesValleys

AHe

AFTNorthCenterSouth

ProfileValleys

-1-1

-1

-1

-1

-1

10 12

10 12

Fig. 3. Synthetic thermochronology data (AFT and AHe ages) versus elevation for different sampling schemes; see Fig. 1 for sample locations. a) Synthetic data for the sampling

scheme Valleys. AER deduced from linear regression of elevation vs age are 0.47 and 0.39 km Myr 1 for AHe (white circles) and AFT (black circles) data, respectively (r=0.98). b)

Synthetic data for the sampling scheme 3_Profiles (individual profiles are represented by diamonds, squares and triangles, see Fig. 1b for locations). AER are 0.33 and 0.35 km Myr1

for AHe (white) and AFT (black) data, respectively (r=0.950.99). c) Synthetic data for the sampling scheme Profile+Valleys (profile and valleys samples are represented by

diamonds and circles, respectively). AER are 0.37 and 0.36 km Myr1

for AHe (white) and AFT (black) data, respectively ( r=0.98

0.99).



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simple geometrical concepts by dividing the entire parameter space

into a set ofn-dimensional Voronoi cells, which represent the nearest

neighborhood around each parameter combination. At each step, NA

samples a forward model centered on each Voronoi cell andcalculates

a misfit surface. Subsequent iterations make use of this misfit surface

to sample in regions of the parameter space where the misfit function

is minimized. The performance of the sampling stage is controlled by

tuning parameters determining the number of iterations, the number

of forward models generated at each iteration, and the number ofVoronoi cells to re-sample after each iteration. Varying these

parameters will make the NA method either more explorative of the

multi-dimensional parameter space, or more exploitative and faster in

converging toward potential misfit minima (Sambridge, 1999a).

Based on previous studies (Glotzbach et al., 2011; Valla et al., 2010),

we choose to run ~5000 models distributed in 35 iterations for each

inversion, with 50% of models re-sampled at each iteration.

In our approach, we use a weighted least-squares misfit function

for the NA appraisal stage:

=

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

N

i =1

M

j =1

i

j; modi

j;dat

2

ij2

vuuut 1

where Nisthe numberof datasets(13;AFT,AHe,AFT+ AHe,AFT+ MTL,

or AFT+AHe+MTL data), Mis the number of samples in each dataset

(20 samples in total for each sampling scheme), j,modi and j,dat

i are

predicted and observedvalues for AFT/AHeagesor MTLrespectively, and

ji is the uncertainty on the data. Here, we use constant synthetic

uncertainties (ji) of 0.5 Ma and 0.5 m for AFT/AHe ages and MTL,

respectively, to put an equal weight on all samples for misfit calculations

(Valla et al., 2010). The above approach allows us to quantitatively infer

the potential resolution ofperfect thermochronology data in resolving

tectono-geomorphicscenarios(and potentially thermalparameters). We

note, however, that adding random noise in the data could potentially

lead to different model sensitivity in constraining numerical parameters.

In the NA appraisal stage (Sambridge, 1999b), the model ensemblegenerated during the sampling stage is iteratively resampled to

provide optimal estimates in the form of marginal probability-density

functions (1D or 2D PDFs) of parameter values. For all parameters, we

assumea uniform prior distribution withineach parameterrange. The

posterior 1D (or 2D) PDFs are given based on the log-likelihood

function (ln(L)), following the equation:

ln L =0:5 2 =0:5 N

i =1

M

j =1

ij; modi

j;dat

2

ij2

0@

1A 2

3. Inversion results

We first present inversion results for each sampling scheme to

assess the effect of using various combinations of low-temperature

thermochronometers. We then compare the different sampling

schemes to discuss how best to predict denudation and relief

histories. Finally, we show modeling results for inverting the

geothermal gradient. We present inversion results as 1D marginal

posterior PDF's as well as 2D joint PDF's of parameter values and

discuss the reasons for the observed differences in the modeling

outputs (resolution and errors on parameter estimates, and potential

tradeoffs between model parameters) in the discussion section.

Optimal parameter values (mode of the 1D posterior PDF) and 1

uncertainties for the different sampling schemes and data combina-

tions are given in Table 2.

3.1. Sampling strategy

The first sampling scheme (1_Profile, Table 2) considers 20 samples

combined as a single elevation profile. Inversion results yield accurate

predictions for E1 (E1=0.230.28 km Myr1; E1input=0.3 km Myr

1) for

all input thermochronological datasets with uncertainties ~2040%

except when using AHe data alone. Estimates on E2 are less precise

(uncertainties ~3080%) andslightlyoverestimated whenusingAFTdata

alone or AFT+MTL data (E2 ~0.4 km Myr

1

; E2input=0.3 km Myr

1

).AHe data are required (alone or combined with AFT ages) to provide

accurate predictions for E2 (respectively E2=0.330.11 and 0.28

0.18 km Myr1). Adding MTL data, in contrast, does not improve

inversion predictions (Table 2). Timing predictions are underestimated

when using AFT alone, AFT+MTL or AFT+AHe+MTL data (T=1

1.4 Ma) and clearly overestimated for AHealone (T=12.2 Ma). Only the

AFT+ AHe inversion (T=2.8 Ma) gives predicted value of Tclose to the

input value of 3 Ma. However, in all cases uncertainties on Tpredictions

are very high (N100% for all inversions). Relief predictions are in

agreement with theinput value (Rinput=0.5)when using AHedata alone

or combined with AFT ages (R=0.530.58 and 0.63 0.55 respective-

ly). In contrast, using AFT ages alone or combined with MTL

measurements respectively under- (R=0.930.59) and over-predicts

(R=0.18 +0.93/0.18) relief increase. Combining both AFT and AHe

ages with MTL does not lead to an accurate estimate on R (R=1.08

0.55; i.e., between ~50% increasing and 50% decreasing topographic

relief).Moreover, as for Tpredictions, uncertainties on R are higher than

100% for all inversions. In summary, inverse simulations using

thermochronology data along a singleelevation profile provide accurate

estimates on denudation histories (E1 and E2) with moderate to high

uncertainties dependingon thedataset (~30 to 80%). In contrast, Tand R

estimates are not in agreement with input values and systematically

present uncertainties N100%. Best estimates are generally obtained

when using AHe ages alone or combined with AFT data; adding MTL

measurements does not improve denudation and relief predictions.

Sampling along three different elevation profiles (3_Profiles,

Table 2) provides similar predictions for E1, although the mean

uncertainty is slightly reduced (~2040%, except for AFT+AHe data

for which the uncertainty rises to 100%). E2 estimates are accurate forall inversions, but uncertainties remain quite high (~3080%). Similar

to the previous inversions, T is systematically under-predicted

(T=1.02.1 Ma) except for the AHe inversion (T=6.9 3.8 Ma);

uncertainties remain N100% for all inversions. Relief predictions are

much better than in the simulation using a single age-elevation

profile. All inversions predict relief increase (R =0.180.58), but the

inverse simulation combining all thermochronometric systems clearly

overestimates the R input value (R=0.18+ 0.30/0.18). Uncertainties

on R predictions are also reduced (~6590%, Table 2). As for a single

elevation profile, best estimates on E2 and R (recent exhumation

history) are provided using AHe data; however, for both Tand E1, most

accurate predictions are obtained when using the full dataset (AFT+

AHe+MTL data).

Sampling along valley bottoms (Valleys, Table 2) provides accuratepredictions for E1 and E2. Uncertainties on E1 are low (~320%) only

when using at least two thermochronometers, but are much higher

when using AFT or AHe data alone (~100200%). In contrast,

uncertainties on E2 are fairly constant, whatever the dataset used

(~4060%). Similarly, constraints on Tare very poor using AFT or AHe

data alone (T=11.9 +2.6/5.1 and 6.63.0 Ma, respectively) and

are improved when combining thermochronometers (best estimate

T=3.5 2.3 Ma for AFT+ AHe+MTL data). Uncertainties on T are

high and variable depending on the dataset used: N100% for all

inversions except for thefull dataset. Finally, relief increase is strongly

overestimated when using AFTor AHe data alone (R =0.030.08) and

predictions are not precise (uncertainties ~100%); however, combin-

ing the thermochronometers provides more accurate values of R and

reduced uncertainties (R=0.33

0.48 and uncertainties ~ 50%). In



7/14

summary, this specific sampling scheme provides reasonably accurate

and precise estimates of denudation history (E1 and E2) and accurate

but not very well resolved predictions for T and R; however this

requires combining at least two different thermochronometers (best

estimates for the full AFT+ AHe+ MTL dataset).

Combining valley bottom samples with an elevation profile(Profile+Valleys, Table 2) provides accurate and precise predictions

for both E1 and E2 (E1=0.230.28 0.010.12 km Myr1 and

E2=0.230.33 0.110.14 km Myr1). T estimates are similar for

allinversions andmostly under-predict thetiming of change(T=0.7

3.8 Ma); uncertainties on Tare around or above 100%. Similarly to the

Valleys sampling scheme, relief change R is strongly overestimated

when using AFT or AHe data alone (R =0.03 +0.55/0.03).

Combining thermochronometers still over-predicts relief change

(R =0.280.38) but uncertainties on R are reduced to ~50%.

Combining valley bottom samples with an elevation profile thus

provides reasonably precise and accurate estimates on E1, E2 and Tfor

nearly all thermochronometer combinations, even though best

estimates on inverted parameters, especially on relief change, are

obtained when using two or more thermochronometers.

The last inversion simulates sampling along a transect across the

massif (Transect, Table 2). This sampling scheme leads to accurate

estimates ofE1 withuncertainties around1040%(except forAFT+ AHe

data, for which the uncertainty rises to ~100%); however, E2 is slightly

over-predicted for AHe, AFT+ AHe and AFT+ MTL datasets (E2

~0.4 km Myr1

, associated uncertainties ~60%). The timing parameteris also not well resolved (T=0.76.3 Ma) with prediction uncertainties

of 100200%. Finally, relief estimates are quite accurate (R=0.180.58)

but associated uncertainties are between 75 and 130%. In summary,

sampling a long transect provides accurate predictions on denudation

rates (E1 and E2), however, timing is not well constrained and relief

estimates are accurate but associatedwith highuncertainties.Moreover,

our inversions results show thatin this sampling configuration, using at

least two thermochronometers strongly improves predictions on

denudation rates and relief evolution.

To better explore the potential differences between the sampling

strategies, Fig. 4 presents 1D marginal PDFs of inverted parameters

(E1, E2, Tand R) for each sampling strategy (using the full dataset). All

sampling schemes provide accurate predictions for E1 (Fig. 4a), even

though more precise estimates (uncertaintiesb

10%) are obtained

Table 2

Output estimates after the NA appraisal stage for inputparameters E1, E2, Tand R (see text fordescriptionand discussion). Thesecond line reports parameterranges andinputvalues

to calculate the synthetic thermochronology data (Fig. 1b,c). Optimal parameter values and associated uncertainties (mode 1of the 1D posterior PDF) are given in the following

lines for various sampling schemes and different input thermochronology datasets. Best parameter estimates (and associated input thermochronology dataset) are also reported as

percentage errors and uncertainties compared to input values (%Input).

Parameter (unit) E 1 (km Myr1) E2 (km Myr

1) T (Ma) R

Range/input 02/0.3 02/0.3 0.514.5/3 02/0.5

1_Profile

AFT 0.28 0.13 0.38 0.26 1.4 + 5.3/0.9 0.93 0.59

AHe 0.28 0.23 0.33 0.11 12.2 + 2.3/5.2 0.53 0.58AFT+AHe 0.28 0.06 0.28 0.18 2.8 + 3.9/2.3 0.63 0.55

AFT+MTL 0.23 0.1 0.43 0.24 1.0 + 8/0.5 0.18 +0.93/0.18

AFT+AHe+MTL 0.28 0.06 0.28 0.27 1.0 + 6.4/0.6 1.08 0.55

Best estimate (%Input) 7% 20% +10% 37% 7% 130% +6% 116%

Data AFT + AHe AHe AFT + AHe AHe

3_Profiles

AFT 0.28 0.12 0.28 0.21 2.1 + 5.5/1.6 0.38 0.41

AHe 0.23 0.1 0.28 0.13 6.9 3.8 0.53 0.32

AFT+AHe 0.28 0.3 0.28 0.14 1.0 + 3.9/0.5 0.58 0.29

AFT+MTL 0.28 0.08 0.33 0.19 1.4 + 5.9/0.9 0.58 0.40

AFT+AHe+MTL 0.28 0.05 0.28 0.15 1.7 + 3.8/1.2 0.18 +0.30/0.18

Best estimate (%Input) 7% 17% 7% 43% 43%127% +6% 64%

Data AFT + AHe + MTL AHe AFT + AHe + MTL AHe

Valleys

AFT 0.33 0.29 0.28 0.11 11.9 + 2.6/

5.1 0.08 + 0.37/

0.08AHe 0.33+0.56/0.33 0.23 0.12 6.6 3.0 0.03 + 0.50/0.03

AFT+AHe 0.28 0.05 0.23 0.11 0.7 + 4.8/0.2 0.48 0.25

AFT+MTL 0.28 0.06 0.33 0.10 2.1 + 5.3/1.6 0.33 0.21

AFT+AHe+MTL 0.28 0.01 0.28 0.11 3.5 2.3 0.38 0.22

Best Estimate (%Input) 7%3% 7%37% 17%77% 4%50%

Data AFT + AHe + MTL AFT + AHe+ MTL AFT + AHe + MTL AFT + AHe

Profile+Valleys

AFT 0.23 0.12 0.28 0.13 3.8 + 5.0/3.3 0.03 +0.55/0.03

AHe 0.23 0.11 0.28 0.14 2.8 + 3.7/2.3 0.03 +0.56/0.03

AFT+AHe 0.28 0.04 0.28 0.14 0.7 + 3.6/0.2 0.38 0.24

AFT+MTL 0.28 0.08 0.33 0.12 1.0 + 6.5/0.5 0.28 0.23

AFT+AHe+MTL 0.28 0.01 0.23 0.11 2.1 + 2.6/1.6 0.28 0.21

Best Estimate (%Input) 7%3% 7% 47% 30%87% 24% 48%

Data AFT + AHe + MTL AFT + AHe AFT + AHe + MTL AFT + AHe

Transect

AFT 0.23 0.12 0.28 0.17 2.1 + 7.0/1.6 0.18 + 0.44/0.18AHe 0.28 0.15 0.43 0.18 1.7 + 6.4/1.2 0.48 + 0.65/0.48

AFT+AHe 0.28 0.32 0.43 0.22 1.0 + 3.4/0.5 0.58 0.39

AFT+MTL 0.28 0.07 0.43 0.21 6.3 3.8 0.38 0.62

AFT+AHe+MTL 0.28 0.03 0.28 0.2 0.7 + 4.71/0.2 0.48 0.37

Best estimate (%Input) 7% 10% 7% 57% 67%113% 4%74%

Data AFT + AHe + MTL AFT AFT + AHe AFT + AHe + MTL



8/14

when sampling a transect, valley bottoms or an elevation profile

combined with valley bottoms; uncertainties from sampling along

elevationprofiles aretwiceas high. TheaccuracyofE2 estimates is also

similar for all sampling schemes, with only the resolution differing

(Fig. 4b); lowest uncertainties on E2 predictions are obtained when

sampling along valley bottoms (~40% for Valleys and Profile+Valleys),

the 3_Profiles sampling scheme yields an uncertainty of ~50% while

the Transect and 1_Profile sampling strategies yield uncertainties of

~70

90%. Fig. 4c confi

rms that timing of change (T) is the leastresolved parameter, with uncertainties of 8090% for the Valleys and

Profile+Valleys sampling schemes, and uncertainties N100% for the

other schemes. Finally, the predicted R (Fig. 4d) is reasonably accurate

(slightly overestimated) for the 3_Profiles, Valleys and Profile+Valleys

sampling schemes and is associated with uncertainties of ~5060%.

Transect sampling also leads to an accurate estimate for R but the

associated uncertainty is high (~ 75%) whereas 1_Profile does not

provide any constraint on R (i.e., it predicts either 50% increasing or

decreasing topographic relief).

3.2. Modeling approach

In all previous inverse simulations, our modeling approach assumed

the geothermal gradient was known. We now present results inverting

for both denudation/relief histories (E1, E2, T and R) and thermal

parameters (Temp and H_prod). We run inversions for allfive sampling

schemes and use the full (AFT+AHe+MTL) dataset to compare

output predictions with previous outcomes (Table 3). Basal temper-

ature (Temp) is slightly under-predicted for most sampling schemes

(Temp ~520565 C; Tempinput=600 C), except for 3_Profiles sampling

that leads to an overestimate (Temp=714 80 C). Associated un-

certainties are low and similar for all inversions (~1116%, Table 3).

Constraints on the crustal heat production parameter (H_prod,

Table 3) are less tight. The Profile+Valleys, 1_Profile and 3_Profiles

sampling strategies lead to accurate predictions (H_prod =0.56

0.94; H_prodinput=0.8) but estimated uncertainties are relativelyhigh (~80110%). Valleys sampling clearly does not resolve the heat-

production parameter (H_prod =0.04 +0.65/0.04) whereas best

predictions for H_prod are provided by the Transect inversion

(H_prod =1.16 0.44).

Predictions for E1 are slightly underestimated for the Transect,

3_Profiles and 1_Profile sampling schemes (E1=0.23 0.1 km Myr1)

and all results provide higher uncertainties on E1 (~30%) compared to

inversions that imposed the geothermal gradient (~320%). Tightest

constraints are placed on E1 using the Valleys and Profile+Valleys

sampling schemes. Results for E2 are variable with best predictions for

the3_Profiles inversion (E2=0.280.14 km Myr1). E2 is slightly over-

predictedin the Transectsamplingscheme(E2=0.430.21 km Myr1)

and under-predicted for Valleys and Profile+Valleys sampling schemes

(E2=0.230.19 km Myr1). However, uncertainties on E2 are very

similar to those obtained when imposing thegeothermal gradient (~50

100%). Timing predictions are all underestimated (T ~0.71.7 Ma) and

associated uncertainties are similar to those found during imposed

0 0.4 0.8 1.2 1.6 2

0.05

0.15

0.25

0.35

0

0.04

0.08

0.12

0.16

Probabi

lity

Probability

Probability

Probabi

lity

a

c

b

d

E1(km Myr-1) E

2(km Myr-1)

T(Ma) R

1_Profile3_ProfilesValleysProfile + valleysTransect

Sampling scheme:

2 6 10 14

0.01

0.03

0.05

0.07

0.09

0 2

0 20

0.02

0.04

0.06

0.08

0.1

0.4 0.8 1.2 1.6

0.4 0.8 1.2 1.6

Fig. 4. 1D posterior parameter PDF's obtained after the NA appraisal stage for the five different sampling schemes (AFT+AHe+MTL dataset): (a) denudation rate of the first

exhumation phase (E1); (b) denudation rate of the second exhumation phase (E2); (c) transition time between the two exhumation phases (T); and (d) relief factor between the

paleo-relief and the final relief (R). Each line defines an inversion experiment with a sampling scheme (see figure for color legend and Fig. 1 for sampling locations). Black stars

represent the input parameter values.



9/14

geothermal gradient inversions (~70230%). Moreover, best predictions

for Tare provided by the Valleys inversion (T=1.7 + 2.0/1.2 Ma), in

agreement with previous results. Finally, setting no constraint on the

geothermal gradient does not have any effect on relief evolution

predictions as R estimates are very close to values obtained with an

imposed geothermal gradient, and optimal predictions are obtained for

3_Profiles, Valleys and Profile+Valleys sampling schemes.

To summarize, numerical inversions without imposing constraints

on the geothermal gradient provide less accurate and precise

estimates for exhumation rates (E1 and E2), but output results for

timingand reliefchange (Tand R) areverycloseto thosefoundwith an

imposed geothermal gradient. Best estimates for thermal parameters

(H_prod and Temp) are given by Transectsampling, while inversions

including at least one elevation profile (Profile+Valleys, 1_Profile and3_Profiles) provide accurate estimates but associated with relatively

high uncertainties, and valley bottom sampling (Valleys) does not

resolve thermal parameters.

4. Discussion

4.1. Limits to the numerical modeling approach

Before interpreting our results, we should highlight potential

shortcomings associated with our numerical modeling approach.

First of all, the exhumation scenario we choose is fairly simple,

with only two exhumation phases, a constant and spatially uniform

regional denudation rate and a single episode of relief growth. This

choice could be considered specific and restrictive, although weconsciously chose uniform background exhumation within the study

area to focus on relief evolution. A similar inverse approach could,

however, be developed to specifically explore spatially varying

exhumation (e.g., Stephenson et al., 2006a). We have tested one

specific geothermal gradient that we also assume to be spatially

uniform, as we apply our inversions to a region of spatially relatively

homogeneous lithology. However, we note that localfluid circulations

along faults can induce large spatial variations in thermal gradient

(Whipp and Ehlers, 2007).

Despite several recent attempts (e.g., Ehlers et al., 2006; Glotzbach

et al., 2008, 2010; van der Beek et al., 2010; Vernon et al., 2009 ),

quantifying both timing and amplitude of topographic relief changes

in mountain belts using low-temperature thermochronology has

proven elusive, motivating the focus of our study on this specific

exhumation scenario. Although our study design might be somewhat

restrictive, we have consciously chosen quite a general synthetic

study regarding the exhumation history and the near-surface thermal

structure. The reliefevolution scenario should also be quite general, as

moderate relief increase since the mid-Pliocene is expected or has

been encountered in many mountain belts (e.g., Molnar and England,

1990; Zhang et al., 2001). We thus are confident that our inferences

regarding thermochronology sampling strategies for quantifying both

exhumation and relief histories, despite the above limitations, might

be of more general interest for studying at least the late-Neogene

exhumation history of mountain belts.

Second, the way we define relief changes in Pecube does not

capture the complexities of landscape evolution processes. Some

limitations include the constant planform drainage pattern assumedin our numerical approach, and a geometric approach to relief

development (Fig. 2a). An alternative approach would be to combine

Pecube with a landscape evolution model to fully simulate landscape

changes with surface process modeling (Herman et al., 2010b).

However, our synthetic approach allows us to address at first order

the effect of transient topography on thermochronology data and

their intrinsic resolution in quantitatively retrieving potential relief

changes.

We finally note that the different sampling scenarios explored

here, although they represent the most commonly used and simplest

ways to sample a given topography, might not be the most adequate

to independently quantify exhumation and relief histories, i.e., we do

not perform a complete experimental design study.

4.2. Parameter resolution and tradeoffs

Our numerical results show that some parameters(mainly Tand R,

Fig. 4) have been poorly constrained by the NA inversion. The lack of

convergence toward the input parameters may result from the poor

resolution of thermochronology data to constrain timing or relief

parameters (Valla et al., 2010), from some random elements, or from

potential tradeoffs between model parameters. To illustrate this

alternative explanation, Fig. 5 shows 2D scatter plots and PDFs for a

single elevation profile (1_Profile). There is no apparent tradeoff

between the initial and final denudation rates (E1 and E2, Fig. 5a), but

significant tradeoffs appear between the recent denudation rate ( E2)

and both the relief change (R, Fig. 5b) and the timing of change (T,

Table 3

Output estimates after the NA appraisal stage for input parameters E1, E2, T, R, Temp and H_prod. The second line reports parameter ranges and input values for the synthetic

thermochronology data (Fig. 1b,c). Optimal parameter values and associated uncertainties (mode 1) are given in the following lines for various sampling schemes (AFT+AHe+

MTL dataset). Inversion results are also reported as percentage errors and uncertainties compared to input values (%Input).

Pa ra meter (u ni t) E 1 (k m Myr1) E2 (km Myr 1) T (Ma) R Temp (C) H_prod

Range/input 02/0.3 02/0.3 0.514.5/3 02/0.5 500800/600 03/0.8

1_Profile

Mode1 0.23 0.1 0.33 0.29 0.7 + 3.1/0.2 1.08 0.52 549 + 98/49 0.64 + 0.82/0.64

%Input (23% 33%) (+10% 97%) (77% 103%) (+ 116% 104%) (9% 16%) (20%103%)

3_Profiles

Mode 1 0.23 0.1 0.28 0.14 0.7 + 6.9/0.3 0.48 0.27 714 80 0.94 0.66

%Input (23% 33%) (7% 47%) (77% 230%) (4% 54%) (+19% 13%) (+18% 83%)

Valleys

Mode 1 0.33 0.1 0.23 0.19 1.7 + 2.0/1.2 0.33 0.21 519 + 74/19 0.04 + 0.65/0.04

%Input (+10% 33%) (23% 63%) (43% 67%) (34% 42%) (14% 12%) (95%81%)

Profile+Valleys

Mode 1 0.28 0.1 0.23 0.19 0.7 + 5.1/0.3 0.48 0.26 534 + 95/34 0.56 + 0.85/0.56

%Input (7% 33%) (23% 63%) (77% 170%) (4% 52%) (11% 16%) (30%106%)

Transect

Mode 1 0.23 0.09 0.43 0.21 1.4 + 4.4/0.9 0.48 0.4 564 66 1.16 0.44

%Input (23% 30%) (+43% 70%) (53% 147%) (4% 80%) (6% 11%) (+ 45% 55%)



10/14

Fig. 5c). These tradeoffs may explain the relatively poor resolution

observed in the 1D marginal PDFs for these parameters ( Fig. 4c,d).

The potential parameters tradeoffs for the other sampling schemes

are shown in Figs. 6 and 7. Fig. 6 reveals that the tradeoff between E2and R is reduced for the 3_Profiles, Valleys, and Profile+Valleys

schemes (Fig. 6ac), but confirms their tendency to over-estimate the

relief increase. In contrast, there is an important tradeoff in the

Transect sampling scheme (Fig. 6d), which explains the high uncer-

tainties associated with R. Fig. 7 confi

rms that the timing parameterT is poorly constrained by our inverse approach; 2D scatter plots

reveal a significant tradeoff between E2 and T, even though the

covariance appears to be slightly reduced for sampling schemes

Valleys and Profile+Valleys (Fig. 7b,c). Interestingly, both Figs. 6 and 7

suggest that parameter tradeoffs, similar to 1D marginal PDFs, are

highly dependent on the sampling scheme and thus might also be

considered when designing sampling strategies.

4.3. Sampling strategy

Inversionresultsfor a singleelevation profile (1_Profile) show that,

although such a sampling approach allows accurately estimating

denudation rates, it does not constrain relief evolution satisfactorily

(uncertainties N100%, Table 2). This finding is similar to the

conclusion of Valla et al. (2010), who also performed a sensitivity

analysis and showed that relief evolution can only be precisely

predicted from thermochronological age-elevation profi

les if the rateof relief change is at least two to three times higher than the regional

background denudation rate. In our case, the regional denudation rate

is 0.3 km Myr1 and the relief scenario induces a maximum relief-

growth rate of ~0.5 km Myr1 for the last 3 Myr (i.e., ~60% higher

than the background denudation rate); under this configuration, our

inverse results are in good agreement with Valla et al. (2010). We

suggest that the inability of a single age-elevation profile to constrain

0 20 40 60 80 100

0

0.5

1

1.5

2

0 0.5 1 1.5 2

0

0.5

1

1.5

2

0 0.5 1 1.5 2

R

0 0.4 0.8 1.2 1.6 2

10

6

2

14

a b

c

E1(km Myr-1) E

2(km Myr-1)

E2(km Myr-1)

E2

(kmM

yr-

1)

T(Ma)

Fig. 5. Scatter plots (each dot represents a forward model color coded by its misfit value ) and 2D posterior marginal probability density functions with 1confidence contours

(black lines)for the sampling scheme 1_Profile: a)denudation rates of thefirst(E1) vsthesecond(E2) exhumation phases;b) denudation rate of thesecond exhumation phase (E2) vs

relief factor (R); and c) denudation rate of the second exhumation phase ( E2) vs transition time between the two exhumation phases ( T). Black stars represent the input parameter

values.



11/14


12/14

E2) and relief change (R); however, the uncertainties on these

parameters are higher than those obtained with Valleys and Profile+

Valleys sampling strategies, due to higher parameters tradeoffs (Figs. 6

and 7). These outcomes are consistent with recent analysis of AFT data

from a transect across the Pelvoux massif (Beucher et al., submitted for

publication): these data constrain exhumation rates well but provide

little insight into relief change. These differences appear to result from

the spatial configuration of the Transectsampling scheme. Although it

covers a larger area than the 1_Profile and 3_Profiles sampling schemes,

Transectdata only sampleone spatial direction(Fig. 2a) andmay notfully

record the 2D topographic perturbations of isotherms compared to data

that are spatially distributed along different valleys (Valleys or Profile+

Valleys sampling scheme). Combining a long transect with at least one

elevationprofile would have allowed to best capture both short and long

topographic wavelength effects on the thermal structure (Braun, 2002a,

b), simultaneously providing accurate and precise information on both

denudation and relief predictions.

4.4. Modeling approach

Inversionsfor which the thermal parameters are supposed unknown

lead to comparable accuracy but somewhat higher uncertainties for

2

6

10

14

0 0.4 0.8 1.2 1.6 20 0.4 0.8 1.2 1.6 2

00.4 0.8 1.2 1.6 2

00.4 0.8 1.2 1.6 2

2

6

10

14

2

6

10

14

2

6

10

14

a b

c d

3_Profiles Valleys

Profile+Valleys Transect

E2(km Myr-1)E

2(km Myr-1)

E2(km Myr-1) E

2(km Myr-1)

T(Ma)

T

(Ma)

T

(Ma)

T(Ma)

Fig. 7. Scatter plots (see Fig. 5 for legend) and 2D posterior marginal probability density functions with 1 confidence contours (black lines) of denudation rate of the secondexhumation phase (E2) vs transition time between the two exhumation phases (T) for different sampling schemes: a) 3_Profiles; b) Valleys; c) Profile+Valleys; and d) Transect. Black

stars represent the input parameter values.



13/14

denudation and relief predictions than when imposing a geothermal

gradient (Table 3). These differences in predicteduncertainties highlight

the classic problem of determining an appropriate dimensionality for a

numericalproblem,i.e.,the number of inverted parameters compared to

the intrinsic data resolution (see Gallagher et al., 2005, for a discussion

on this subject). Moreover, our results show that sampling along valley

bottoms does not allow resolving accurately the thermal parameters.

Sampling along elevation profiles helps constraining the geothermal

gradient, as suggested by Gallagher et al. (2005), pointing out that eventhough numerical modeling allows us to infer exhumation histories

from complex spatial sample distributions, age-elevation relationships

remain useful for interpreting thermochronology data. The ability of

age-elevation profiles to constrain both the exhumation history and

thermal parameters comes from the altitudinal distribution of samples;

the slope of the age-elevation relationship providing an estimate of the

apparent exhumation rate (e.g., Hurford, 1991), while the age-window

of the dataset may help to constrain the near-surface geothermal

gradient (Gallagher et al., 2005). Surprisingly, the Transect sampling

provided the best estimates on thermal parameters, which can be

explained by the simultaneous spatial and altitudinal data coverage

allowed by this sampling scheme(Fig.2a). It thusmightbe usednot only

for spectral analysis (Braun, 2002b) but also, like elevation profiles, to

constrain the geothermal gradient.

Finally, we have tested the effect of the grid resolution on the

predicted estimates of the various parameters. As reported in the

supplementary material section, we show that a minimum grid

spacing of 1 km (or ~1/10th of the valley spacing) is necessary to

properly resolve exhumation rates and relief change in the typical

mountainous terrain we have used here.

5. Conclusions

Our study was initially designed to determine to which extent

different sampling and modeling strategies could allow constraining

relief evolution from low-temperature thermochronology datasets.

Our results confirm the findings ofValla et al. (2010), who suggested

that age-elevation relationships do not resolve relief changes if these

do not induce an additional spatially variable exhumation rate that isat least two times higher than the regional background denudation

rate. Although our approach is slightly different from Valla et al.

(2010), we have shown here that age-elevation relationships do not

allow constraining relief changes. We have demonstrated that

spatially distributed sampling along a transect, several elevation

profiles or along valley bottoms, preferably combined with an

elevation profile, leads to better predictions of relief evolution. The

main drawback of only sampling along valley bottoms is the loss of

information on the near-surface thermal structure. However, using

higher-temperature thermochronometers may provide supplemen-

tary constraints on thermal parameters. Glotzbach et al. (2011)

recently used a dense thermochronology dataset combining both low-

and high-temperature thermochronometers along elevation profiles

and a tunnel transect to constrain both the near-surface thermalstructure and the exhumation history of the Mont-Blanc massif

(western European Alps). Their modeling results resolved a recent

relief increase whereas other recent studies using only data along a

single age-elevation profile were not able to resolve the recent relief

evolution (van der Beek et al., 2010; Vernon et al., 2009).

Based on synthetic data producedunder an imposed exhumation and

relief scenario, we have tested different sampling strategies to explore

how to best constrain denudation rates, timing and relief change. Our

results show that dense spatial sampling combining valley bottom

samples and elevation profiles, as well as long transects may help to

provide quantitative constraints on complex exhumation histories.

Moreover, we have highlighted that the modeling approach (choice of

thermalparametersor model resolution)potentiallyinfluencespredicted

denudation and relief histories. Although age-elevationprofiles may bea

useful and direct way to interpret thermochronology data, sampling

strategies should be rethought in the light of recent numerical modeling

developments. For a region where relief changeis expected to have been

minimal but the emphasis is on deciphering changes in denudation rate

through time, an appropriate sampling scheme would be using one or

several elevation profiles. However, when one has reason to believe that

exhumation rates may have been relatively constant (e.g., in stable

post-orogenic mountain belts) but the aim is to constrain the timing and

amount of relief change, our study would suggest a better choice is tosample valley bottoms, possibly combined with an elevation profile.

Therefore, ideallythesamplingstrategy should be designeda priori,using

preliminary modeling of expected denudation and relief histories and

preferably using multiple working hypotheses; and a sensitivitystudy on

assumed thermal parameters and model resolution should be performed

when modeling the data.

Acknowledgments

This study is supported by the INSU-CNRS through the European

Science Foundation Topo-Europe program 07-TOPO-EUROPE-FP-023Coupled climatic/tectonic forcing of European topography revealed

through thermochronometry (Thermo-Europe) and the Agence

Nationale de la Recherche project No. ANR-08-BLAN-0303-01 Erosionand Relief Development in the Western Alps. It forms part of PV's PhD

project at Universit Joseph Fourier, supported by the French Ministry

for Research and Higher Education. We thank Malcolm Sambridge and

two anonymous reviewers for insightful comments that helped to

improve the clarity of this manuscript. Computations were performed

on Brutus, the high performance computing facilitiesat ETH Zurich. The

codes are available at http://svn-geo.ethz.ch after registering at this

site.

Appendix A. Supplementary data

Supplementary data to this article can be found online at

doi:10.1016/j.epsl.2011.05.003.

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