Steady state erosion of critical Coulomb wedges with applications to ...

JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 109, B01411, doi:10.1029/2002JB002284, 2004 

Steady state erosion of critical Coulomb wedges with 

applications to Taiwan and the Himalaya 

G. E. Hilley 1 and M. R. Strecker 

Institut für Geowissenschaften, Universität Potsdam, Potsdam, Germany 

Received 1 November 2002; revised 14 July 2003; accepted 2 October 2003; published 23 January 2004. 

[1] Orogenic structure appears to be partially controlled by the addition to and removal of 

material from the mountain belt by tectonic accretion and geomorphic erosion, 

respectively. We developed a coupled erosion-deformation model for orogenic wedges 

that are in erosional steady state and deform at their Coulomb failure limit. Erosional 

steady state is reached when all material introduced into the wedge is removed by erosion that is 

limited by the rate at which rivers erode through bedrock. We found that the 

ultimate form of a wedge is controlled by the wedge mechanical properties, sole-out depth 

of the basal decollement, erosional exponents, basin geometry, and the ratio of the added 

material flux to the erosional constant. As this latter ratio is increased, wedge width 

and surface slopes increase. We applied these models to the Taiwan and Himalayan 

orogenic wedges and found that despite a higher flux of material entering the former, the 

inferred ratio was larger for the latter. Calculated values for the erodibility of each wedge 

showed at least an order of magnitude lower value for the Himalaya relative to Taiwan. 

These values are consistent with the lower precipitation regime in the Himalaya relative to 

Taiwan and the exposure of crystalline rocks within the Himalayan orogenic wedge. 

Independently determined rock erodibility estimates are consistent with the accretionary 

wedge sediments and metasediments and the crystalline and high-grade metamorphic 

rocks exposed within Taiwan and the Himalaya, respectively. Therefore differences in 

rock type and climate apparently lead to key differences in the erosion and hence orogenic 

structure of these two mountain belts. INDEX TERMS: 1824 Hydrology: Geomorphology (1625); 

8110 Tectonophysics: Continental tectonics—general (0905); 8020 Structural Geology: Mechanics; 8102 

Tectonophysics: Continental contractional orogenic belts; 8107 Tectonophysics: Continental neotectonics; 

KEYWORDS: critical Coulomb wedge, fluvial bedrock incision, Himalaya, Taiwan 

Citation: Hilley, G. E., and M. R. Strecker (2004), Steady state erosion of critical Coulomb wedges with applications to Taiwan and 

the Himalaya, J. Geophys. Res., 109, B01411, doi:10.1029/2002JB002284. 

1. Introduction 

[2] Many recent studies [e.g., Dahlen and Suppe, 1988; 

Dahlen and Barr, 1989; Barr and Dahlen, 1989; Beaumont 

et al., 1992; Willett and Beaumont, 1994; Willett, 1999; 

Horton, 1999; Beaumont et al., 2001; Willett and Brandon, 

2002] show that erosional processes exert an important 

control on the structure of orogens. Specifically, the construction 

of high topography creates gravitational body 

forces that may favor the migration of deformation to 

lower-elevation areas [e.g., Willett and Beaumont, 1994; 

Royden, 1996]. Where erosional processes are efficient 

relative to tectonic accretion, material is transported from 

the interior to the exterior of an orogen, reducing the 

topography and gravitational load. In this case, deformation 

and orogenic structure may be focused in a relatively small 

area [Willett, 1999]. However, where erosional processes are 

1 Now at Department of Earth and Planetary Sciences, University of 

California, Berkeley, California, USA. 

Copyright 2004 by the American Geophysical Union. 

0148-0227/04/2002JB002284$09.00 

inefficient, accreted material is stored in the orogen’s 

interior, resulting in the continual migration of deformation 

toward its margins [e.g., Royden, 1996]. 

[3] The relationship between topographic slope and the 

triangular geometry of an orogenic wedge was first explored 

by considering brittle, cohesionless orogenic wedges that 

deform at their Coulomb failure limit [Davis et al., 1983; 

Dahlen, 1984]. In addition, Dahlen and Suppe [1988] and 

Dahlen and Barr [1989] recognized that erosion may act to 

modify the deformation within such wedges and their 

geometries by removing material from their interiors. As 

this removal occurs, two effects are seen: (1) the wedge 

grows in width until all of the material accreted to the toe of 

the orogen is removed by erosional processes acting along 

its surface, and (2) the orogenic wedge adjusts its internal 

kinematics to accommodate the local variations in erosion 

rates [Dahlen and Barr, 1989]. In these studies, two simple 

erosion laws were prescribed in which a uniform erosion 

rate was specified to erode the entire width of the orogen, 

and this erosion rate was allowed to vary as a function of 

elevation [Dahlen and Barr, 1989]. Recently, a series of 

geodynamic modeling studies have revisited these interac- 

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B01411 HILLEY AND STRECKER: STEADY STATE EROSION OF CRITICAL COULOMB WEDGES 

tions between surface processes and tectonics by considering 

more complicated rheological conditions [e.g., Willett, 

1999; Beaumont et al., 2001]. The results have been 

quantitatively compared to the Taiwanese orogenic wedge 

[e.g., Dahlen and Barr, 1989] and qualitatively compared to 

the Southern Alps of New Zealand and the Olympic 

Mountains in Washington State, USA, for example [Willett, 

1999]. These studies highlight the importance of erosional 

processes in determining tectonic deformation patterns and 

thermochronologic age distributions [Willett and Brandon, 

2002]. However, the simple treatment of erosion in these 

studies may hamper quantitative tests of these models that 

relate the orogen’s geometry directly to rock erodibility or 

climatic conditions. For example, Dahlen and Barr [1989] 

found that erosion rates inferred for Taiwan based on its 

geometry were consistent with those inferred by fission 

track studies of this island. However, these quantities cannot 

be related directly to landscape attributes such as rock 

erodibility and climate, and so for example, cannot be used 

to predict the effect of the exposure of different rock types 

within the wedge on its geometry. Likewise, the treatment 

of erosion as a simple power law in which the erosion rate is 

linearly proportional to orogen slope and catchment area 

[e.g., Willett, 1999] neglects a more complex power law 

dependence on these factors that appears to be required by 

detailed field studies of bedrock channels [e.g., Howard and 

Kerby, 1983; Whipple et al., 1999; Whipple and Tucker, 

1999; Sklar and Dietrich, 1998, 2001]. Because these 

geodynamic models have shown that exhumation patterns 

and orogenic forms are sensitive to spatial variations in 

erosional power within the orogen, properly characterizing 

the relations between channel slope and catchment area are 

essential to make quantitative comparisons between tectonically 

active mountain belts and process-based models. 

Instead of these simple erosional models, many workers 

have endorsed fluvial bedrock incision as the rate-limiting 

erosion process in orogens [e.g., Whipple et al., 1999]. 

Studies that relate the rate of erosion in bedrock channels to 

channel slope and catchment area suggest that erosion may 

not be linearly proportional to channel slope and catchment 

area [e.g., Howard and Kerby, 1983; Sklar and Dietrich, 

1998] and may vary depending on the processes that act to 

erode the channel bed [Whipple et al., 2000]. 

[4] In this study, we constructed a coupled model of 

bedrock fluvial incision and topographic loading of the crust. 

This approach allows us to directly examine dependence of 

wedge geometry on factors such as the types of rocks exposed 

in the orogen and the climatic conditions acting to erode the 

wedge. We used the critical Coulomb wedge (CCW) theory 

[Davis et al., 1983; Dahlen et al., 1984; Dahlen, 1984] and 

simple models of mass accretion in an orogenic wedge to 

constrain the relationship between deformation and topography. 

We focused on the condition in which all material 

accreted to the orogen by tectonic processes is removed by 

erosion (hereafter referred to as a steady state orogen). We 

found that the orogenic wedge geometry is related to the ratio 

of the mass flux of tectonically accreted material and the 

bedrock incision erosion constant. As this ratio increases, 

orogenic width increases. This steady state coupled erosiondeformation 

model is applied to Taiwan and the Himalaya, 

which are interpreted to be in tectonic and erosional steady 

state [Suppe, 1981; Hodges, 2000; Hodges et al., 2001]. 

2of17 

B01411 

Good agreement was found between the inferred values of 

the erosional constants, the rock types exposed in each 

orogen, and independently determined values of erodibilities 

of similar rocks [Stock and Montgomery, 1999]. Interestingly, 

while the tectonic accretion of material to the Taiwan 

orogenic wedge is significantly larger than along the Himalaya, 

easily eroded accretionary complex sediments and 

abundant precipitation result in a narrower orogen than the 

dryer Himalaya, which comprises rocks of lower erodibility. 

2. Model Formulation 

[5] We combine the CCW model [Davis et al., 1983; 

Dahlen, 1984] with models of tectonic accretion of material 

[DeCelles and DeCelles, 2001] and erosion by bedrock 

incision [e.g., Howard and Kerby, 1983; Seidl and Dietrich, 

1992]. This work examines a subset of conditions whose 

complete formulation is presented by Hilley et al. [2003]. 

We model the relationship between topography and deformation 

by assuming that the orogenic wedge is approximately 

triangular in cross section, a situation that arises in 

cohesionless wedges that deform at their Coulomb failure 

limit [e.g., Davis et al., 1983; Dahlen, 1984] (Figure 1). In 

this case, the decollement is planar until it reaches the its 

sole-out depth (D in Figure 1). Under these conditions, the 

width is related to the basal fault dip of the wedge (b) and D. 

Likewise, the surface slope (a) of the orogenic wedge 

remains constant along its width. Convergence may be 

accommodated by introduction of material into the back 

of the wedge (left side in Figure 1), incorporation of 

foreland material into the front of the wedge, and/or stable 

sliding of the wedge over the foreland. The mass added to 

the wedge from the first two of these mechanisms may be 

removed from the wedge by erosion or may induce a change 

in the cross-sectional area of the wedge. Therefore the 

wedge geometry (as gauged by its cross-sectional area) is 

controlled by the rates of addition of mass to and removal of 

mass by material accretion and erosion, respectively. 

[6] First, we relate the surface slope to the decollement 

geometry using the critical Coulomb wedge (CCW) theory 

[Davis et al., 1983; Dahlen et al., 1984; Dahlen, 1984]. In 

this formulation, lithostatic loading increases with surface 

slope and fault dip. The theory predicts that an orogenic 

wedge is in mechanical equilibrium when the resolved 

tractions along the fault surface are equal to the failure limit 

along the surface as defined by the Coulomb Failure Criterion 

[Davis et al., 1983; Dahlen, 1984]. The relationship 

between the surface slope (a) and fault dip (b) at this critical 

condition is expressed most simply as [Dahlen, 1984] 

a þ b ¼ y b y o; ð1Þ 

where y b and y o is the angle between the base and surface 

of the wedge and the maximum principle compressive 

stress, respectively. For subaerial orogenic wedges, y b and 

y o depend on the friction of the wedge (m) and the fault 

plane (m b), the Hubbert-Rubey fluid pressure ratio within the 

orogenic wedge (l) and along its basal decollement (l b), 

and a. Complete expressions for these parameters are given 

by Dahlen [1984]. 

[7] We show an example of the relationship between a 

and b in Figure 2 [Davis et al., 1983; Dahlen, 1984], when m


Figure 1. Schematic model depiction. Orogenic wedge has mechanical properties, m, mb, l, and lb, 

converges with the foreland and its rear at velocity, vf and vr, respectively, accretes a thickness Tf and Tr of 

material from the foreland and rear, respectively, into the wedge, soles out at depth D, and is eroded 

according to the erosional parameters K, ka, h, m, and n. Figure modified after Hilley et al. [2003]. 

and m b are fixed to 1.1 and 0.85, respectively. Solid lines in 

Figure 2 show combinations of a and b that lead to critically 

deforming wedges for different l and l b. Measured a, b 

relations for Taiwan and the Himalaya are shown for 

reference. Generally, an inverse relationship between the 

surface slope and basal decollement angle is observed when 

a wedge is at its failure limit. Therefore, as the fault dip 

steepens, the surface slopes must shallow to maintain a 

wedge that deforms at its critical limit. Importantly, wedges 

that are in mechanical and erosional equilibrium will plot 

along one of these lines, given m, m b, l, and l b. As the pore 

pressure ratios within the wedge and along its base increase 

(l and l b), or the basal decollement friction decreases (m b), 

this reduces the ability of the wedge to support a large 

topographic load and the surface slope must shallow, all else 

being equal [Davis et al., 1983]. 

[8] The erosional component of our model considers the 

material fluxes entering and leaving the wedge from tectonic 

accretion and erosional removal of material, respectively. 

If the density of material does not change as material 

is accreted to the wedge, the material flux entering the 

wedge is equal to the product of the convergence velocity 

(v) and the thickness of accreted material (T) relative to and 

entering the front and rear of the wedge, respectively 

[DeCelles and DeCelles, 2001]: 

vT ¼ vf Tf þ vrTr: ð2Þ 

where vf and Tf and vr and Tr are the wedge convergence 

velocities relative to and thicknesses of accreted material of 

the foreland and rear of the wedge, respectively. 

[9] This tectonically accreted material is at least partially 

removed by erosion. Following the work of others [Whipple 

et al., 1999; Whipple and Tucker, 1999, 2002; Whipple, 

2001], we consider the relief traversing the orogenic wedge 

to be limited by the rate of fluvial incision into bedrock. This 

rate is thought to be a power function of the channel slope 

(S), the catchment area (A, a proxy for discharge [Howard et 

al., 1994]), and a constant (K) that represents the effects of 


B01411 

rock erodibility and climate [Howard and Kerby, 1983; 

Howard et al., 1994; Stock and Montgomery, 1999]: 

dz 

¼ KA 

dtb 

m S n : ð3Þ 

Here the power law exponents (m, n) may partially 

encapsulate the processes acting to erode the channel bed 

[Whipple et al., 2000]. In particular, hydraulic lifting of 

blocks from the channel may tend to favor low values of m 

and n, while processes such as cavitation may result in 

higher values [Whipple et al., 2000]. To express A in terms 

Figure 2. Relationship between orogenic wedge surface 

slope (a) and wedge decollement angle (b) when wedge is 

at its Coulomb failure limit. Model lines show expected 

relations when m = 1.1 and mb = 0.85. An inverse 

relationship between b and a is observed when b is small. 

The a-b relations and their uncertainties are plotted for the 

Taiwan and Himalayan orogenic wedges. Figure modified 

after Davis et al. [1983].


of the downstream profile position (x), we relate the source 

area to the upstream profile length [Hack, 1957]: 

A ¼ kax h ; ð4Þ 

where ka and h are constants that depend on the catchment 

geometry. As h increases, larger amounts of source area are 

collected for a given downstream distance than when h is 

low. Therefore increases in h result in more square geometry 

basins than low values of h. By combining equations (3) 

and (4), we express the rate of change of the channel 

elevation in terms of the downstream profile distance, x: 

dz 

¼ Kk 

dtb 

m a xhmS n : ð5Þ 

[10] By assuming that wedges grow in their mechanically 

critical state according to equation (1), accrete material 

according to equation (2), and erode by fluvial bedrock 

incision (equation (5)), Hilley et al. [2003] derive an 

expression for the temporal rate of change of the basal 

decollement angle as a function of the erosional and 

mechanical parameters of the wedge: 

db 

dt ¼ 

Figure 3. Contoured base 10 logarithm values of vT/K, highlighting the effect of changing k a for 

different values of m and n. Mechanical stability lines for a wedge in which m = 1.1; m b = 0.85; and l = 

l b = 0, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 0.97 are shown for reference (lines are the same as in Figure 2). 

D2 tan a 

sin b cos b þ D2 cot2 bgðÞ b 

2 cos2 f ðÞ b 

D2 csc2 b 

2 

vT KkahmD hmþ1 ð Þcot hmþ1 ð ÞbSn hm þ 1 

; ð6Þ 

where f(b) and g(b) are functions that relate the value and 

temporal rate of change of a as a function of b [Dahlen, 

1984; Hilley et al., 2003]. 

[11] In this paper, we consider the special condition in 

which all material entering the wedge from tectonic accretion 

is removed by erosion and, hence, its cross section 

remains invariant with time. Under these circumstances, db/ 

dt = 0 and the first term on the right-hand side of 

equation (6) may be eliminated. Rearranging this equation 

and letting S =tana, we cast the ratio of the material flux of 

accreted material and the erosion constant (vT/K) as a 

function of the erosional parameters of the wedge: 

vT 

K 

¼ khm 

a Dhmþ1 cothmþ1 b tann a 

: ð7Þ 

hm þ 1 

1 


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Equation (7) requires that for a given set of (a, b) pairs and for 

erosional and basin geometry constants, there is a single 

value of vT/K that will lead to a wedge in which erosion is 

sufficient to remove all accreted material. Values of vT/K 

larger and smaller than this result in growing and shrinking 

wedges, respectively. Wedges in mechanical and erosional 

steady state must satisfy the two conditions imposed by 

equations (1) and (7), respectively. Therefore, for wedges in 

which the basal sole-out depth is constant (i.e., don’t grow 

self-similarly) a unique combination of a and b exist that 

allow wedges to be in both mechanical and erosional steady 

state. This pair can be determined graphically by locating the 

intersection of the CCW functions (equation (1) and Figure 1) 

and those derived from equation (7). While many orogenic 

wedges may adjust to changes in erosion by deepening their 

wedge sole-out depth, we first consider the case of fixed D 

and then determine the effects of changing D on the required 

vT/K ratio that produces wedges in which accretion is 

balanced by erosion. 

3. Model Results 

[12] We explored the relationship between erosional 

parameters and steady state orogenic wedge geometries 

using equation (7). We varied the free parameters in our 

model (ka, h, and D), and computed vT/K values for all a, b 

pairs between the range 0° a, b 25° that were required 

to maintain a steady state erosional wedge. In each case, we 

fixed two of the three free parameters to constant default 

values while varying the other over a full range of their 

potential values. Default values for the parameters are ka =5, 

h = 1.6, and D = 20 km. In addition, a full range of power 

law bedrock incision exponents were explored (1/3 m 

5/4, 2/3 n 5/2) [e.g., Whipple et al., 2000]. For 

reference in each of the plots that follow, we show the 

mechanical stability lines computed in Figure 2 (m = 1.1; 

mb = 0.85; l = lb = 0, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 0.97). 

However, our results may easily extrapolated to other 

mechanical wedge conditions by superposing the appropriate 

mechanical stability limits and finding the intersection 

between these functions and those presented. 

3.1. Variation in ka 

[13] Figure 3 shows the effect of changing ka on the steady 

state erosional geometry of the wedge. In Figures 3–5 values


Figure 4. Contoured base 10 logarithm values of vT/K, highlighting the effect of changing h for 



of the base 10 logarithm of vT/K are contoured for each 

value of the changing parameter. For example, dashed lines 

in Figure 3, first column, show the isolines of vT/K 

between 10 6 and 10 9 when ka =2,h = 1.6, D = 20 km, 

and m = 1/3, n = 2/3. Increases in vT/K represent greater 

convergence velocities, larger thickness of accreted material, 

and/or smaller K due to exposure of less erodible rock 

types and/or lowered erosional capacity due to reduced 

precipitation. 

[14] In all models with fixed D, higher values of vT/K lead 

to orogenic wedges with higher surface slopes and lower 

wedge decollement angles. These low-angle decollements 

lead to wider orogenic wedges if D is held constant. Figure 3 

indicates that for similar values of vT/K, large ka values result 

in steeper stable decollements and shallower surface slopes 

than small values. In these and all subsequent models, as m 

and n increase, larger values of vT/K are required to produce 

similar a, b combinations. This results from the fact that as 

erosional exponents increase, the erosion rate increases for 

fixed values of the catchment area and local slope of the 

channel at each point. Therefore the amount of material 

accreted to the wedge must increase or the erosional efficiency 

must decrease to maintain a constant topographic 

form. Both of these factors lead to the increase in vT/K for 

constant a, b when the exponents are increased. 

3.2. Variation in h 

[15] We show the effect of changing h on the vT/K values 

for a range of (a, b) pairs in Figure 4. Previous studies 

suggest that this value varies over a narrow range between 

1.67 and 1.92 [Hack, 1957; Maritan et al., 1999; Rigon et 

al., 1996]. We consider a conservative range of h between 

1.3 and 1.9 in our models. As with ka, high values of 

h require lower values of vT/K for fixed values of a and b 

to maintain the wedge in an erosional steady state. For the 

range in h explored, the variation of vT/K for fixed a, b pairs 

is larger than for the range in ka that was modeled. Increasing 

m and n require larger values of vT/K to produce a topographic 

form similar to their lower valued counterparts. 

3.3. Variation in D 

[16] The effects of changing D are shown in Figure 5. We 

chose values for the sole-out depth of 5, 10, and 20 km, 

representing movement along a plastically deforming weak 

decollement [e.g., Stocklin, 1968], the depth to the brittleplastic 

transition in areas of high to moderate heat flow 

[Brace and Kohlstedt, 1980], and the depth to the brittleplastic 

transition when heat flow is low. As D increases, the 

absolute size of the steady state wedge increases, allowing 

greater storage of material in the wedge as material is 

accreted and eroded from its extremes. This results in high 

Figure 5. Contoured base 10 logarithm values of vT/K, highlighting the effect of changing D for 




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Figure 6. Simplified geologic map of Taiwan. Westward underthrusting of the Eurasian Plate (EP) 

beneath the Philippine Sea Plate (PSP) at 70–82 mm/yr has resulted in the formation of a west vergent 

fold-and-thrust belt that is actively accreting material of the EP. Geology compiled from Suppe [1987] 

and maps of Taiwan Geological Survey. Structures based on work by Suppe [1987] and Davis et al. 

[1983] and geologic map relations. 

b and lower a values when D is large. As in other models, 

as m and n increase, so must the values of vT/K to maintain 

constant (a, b) relations within the wedge. 

4. Application to Taiwan and the Himalaya 

4.1. Tectonics, Geology, Topography, and Climate 

of the Taiwan and Himalayan Orogenic Wedges 

[17] Numerous studies within the Taiwan and Himalayan 

orogens constrain the tectonics, geology, topography, climate, 

and mechanical properties of these two wedges. 

Below, we review each of these aspects to deduce appro- 


B01411 

priate inputs to our steady state erosion-deformation wedge 

model. 

4.1.1. Taiwan 

[18] The island of Taiwan lies between the Philippine Sea 

Plate (PSP) and the Eurasian Plate (EP) in eastern Asia 

(Figure 6). North and eastward directed subduction thrusts 

the PSP beneath the EP and the EP beneath the PSP, along 

E-W and N-S trending subduction margins, within the 

northern, and central and southern parts of the island, 

respectively. Therefore the northern section of the island 

records a shift in subduction polarity at a triple junction that 

is migrating southward with time [Suppe, 1987]. For the


Figure 7. Taiwanese wedge geometries considered in this study. For simplicity, we only consider 

forewedge erosion in this study and treat the potential contribution of erosion from the retrowedge as an 

additional material flux leaving the wedge. Cross section modified after Davis et al. [1983, and references 

therein]. 

purposes of this study, we will only consider the effects of 

westward directed overthrusting of the PSP onto the EP that 

is the dominant plate tectonic regime throughout most of the 

island, while neglecting the potential complications that 

arise from the southward migration of the shift in subduction 

polarity with time. Measurements of the convergence 

between the EP and PSP vary between 70 mm/yr [Seno, 

1977; Minster and Jordan, 1979; Ranken et al., 1984; Seno 

et al., 1993] and 82 mm/yr [Yu et al., 1997], directed NW- 

SE. The onset of underthrusting varies depending on the 

location along the island. In the north, stratigraphic studies 

indicate that the arc-continent collision began 4 Ma, 

whereas it appears to be beginning presently at the southernmost 

tip of the island [Suppe, 1987]. 

[19] Underthrusting of the EP beneath the PSP throughout 

the majority of the island leads to uplift and exhumation 

of the subduction accretionary prism and volcanic arc to the 

east. The geology of this area is well constrained by both 

surface and subsurface geologic and petroleum exploration 

studies [e.g., Suppe, 1981, 1984, and references therein]. 

The salient geologic features of the island for this study are, 

from west to east, are as follows: 

[20] 1. Cenozoic clastic sediments and metasediments 

constitute the bulk of the exposed rocks in western and 

central Taiwan (exposed area 60–70 km wide from NW- 

SE). These deposits record the deformation, uplift, erosion, 

and deposition around the EP-PSP accretionary wedge 

complex. Neogene units comprise 5 to 6 km thick unmetamorphosed 

to weakly metamorphosed sediments, whereas 

Paleogene sediments at their lowest structural level consist 

of greenschist grade slates and phyllites [Suppe et al., 1976]. 

[21] 2. A pre-Oligocene unconformity separates these 

sediments from pre-Cenozoic quartzites and slates within 

the Hsuehshan Range and Central Mountains in eastern 

Taiwan (exposed area 10–20 km wide from NW-SE) that 

constitute the basement of this area, which are often 

exposed by NNE striking backthrusts. 

[22] 3. In the easternmost sector of the island, west 

verging reverse faults juxtapose ophiolitic fragments and 

arc remnant material with the basement of the 10-km-wide 

Coastal Range. These rocks likely represent sections of 

South China Sea crust and the Luzon volcanic arc, which 

formed above, and in response to the subduction of the EP 

beneath the PSP [Suppe et al., 1981]. 

[23] Geologic units and their relationships indicate several 

important properties of this orogen. First, sediments 


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exposed in western Taiwan constitute a westward migrating 

orogenic wedge that is composed of sediments from the EP 

and incorporates material by underplating of EP sediments. 

Second, this westward verging wedge (prowedge) is mirrored 

by an eastward verging orogenic wedge (retrowedge) 

whose basal decollement is apparently the backthrust of a 

larger, westward verging structure. Global Positioning System 

velocities [Yu et al., 1997] in this area indicate that 

material that is accreted to the westward verging wedge is 

eroded from the prowedge and may be transported through 

the drainage and structural divide into the eastward verging 

retrowedge. Third, exposed rocks generally become more 

structurally competent, and presumably more difficult to 

erode, to the SE. The Cenozoic clastic sediments constitute 

most of the width of the westward verging orogenic wedge, 

with only limited exposure of pre-Cenozoic crystalline 

rocks along the topographic crest of the wedge in a zone 

not exceeding 20 km in width. 

[24] The topography of Taiwan reflects the present high 

denudation and precipitation regimes. The width and height 

of the mountain belt grow steadily from south to north for 

120 km [Suppe, 1987] from the southern tip of the island. 

North of this point, the mountain belt is consistently 90 km 

wide and appears to be in a flux steady state in which all 

material accreted to the westward verging orogenic wedge is 

removed by erosion [Suppe, 1981; Deffontaines et al., 1994; 

Willett and Brandon, 2002]. Peak elevations within the 

Central Range exceed 4 km [Suppe, 1987], while surface 

slopes along the westward flanks of the island range from 

2.6°–3.2° [Davis et al., 1983; Suppe, 1980, 1981]. The 

cross-sectional geometry typical of the Taiwanese orogenic 

wedge is shown in Figure 7. The topographic crest of 

Taiwan is located along the eastern section of the island 

where the metamorphic rocks are exposed. This NE-SW 

topographic asymmetry may be explained by the rapid 

eastward advection of material through the forewedge 

[Willett et al., 2001], or alternatively, the exposure of lowerodibility 

crystalline rocks along the eastern margin of the 

orogen, which leads to the migration of the drainage divide 

to areas where these rocks are exposed. Currently, up to 

4 m/yr of precipitation falls on the island. High exhumation 

rates produced by the high rock uplift, high precipitation, 

and low rock erodibility conditions are documented at 

decadal, Holocene, and 1 Myr timescales by suspended and 

dissolved stream load measurements [Li, 1975], uplifted 

Holocene reefs and marine terraces [Peng et al., 1977], and


Figure 8. Geologic map of the Himalaya. Ongoing collision of India with respect to Asia has produced 

15.5–19.5 mm/yr of convergence between the two. The orogenic wedge is constituted by, from northeast to 

southwest, ophiolites and sutures, metamorphosed sedimentary rocks from the Tethys basin, high-grade 

metamorphic rocks of the High Himalayan Crystalline, lower-grade metamorphic rocks of the Lesser 

Himalaya, and sedimentary foreland deposits of the Subhimalaya. Various volcanic and crystalline rocks 

are included within these units. Geology and structures simplified after Hodges et al. [2000, and references 

therein]. 

apatite, sphene, and zircon fission track thermochronology 

[Liu, 1982], respectively. Exhumation rates over these timescales 

are 5–6, 5, and 5–9 mm/yr, respectively. 

4.1.2. Himalayan Orogenic Wedge 

[25] Northward translation of India with respect to Eurasia 

and the resulting continental collision has produced one of 

the most spectacular active mountain belts on Earth [e.g., 

Molnar and Tapponnier, 1975]. This collision has been 

ongoing since 50 Ma [Rowley, 1996; Searle et al., 1997; 

Ratschbacher et al., 1994] and has resulted in a total of 1800 

and as much as 2750 km of relative displacement between 

India and Eurasia in the western and eastern Himalaya, 

respectively [Dewey et al., 1989]. Global Positioning System 

(GPS) reoccupations of sites across the Himalaya indicate 

that the current rate of convergence is 17.5 ± 2 mm/yr [Bilham 

et al., 1997], and most of the resulting interseismic contraction 

is concentrated in the northern parts of the Himalaya 

[Jackson and Bilham, 1994; Bilham et al., 1997]. However, 

studies of uplifted and warped Quaternary terraces along the 

southern margin of the Nepalese Himalaya record similar 

deformation rates [Lave and Avouac, 2000]. Therefore, while 

high interseismic strain may accumulate within the core of the 

Himalaya, it is apparently released primarily along its southern 

margin. This continued contraction within the Himalaya 

has produced an orogenic wedge 250 km in width, from 

northeast to southwest [DeCelles and DeCelles, 2001]. 


B01411 

[26] The geology of the Himalayan orogenic wedge is 

shown in Figure 8. The regional geology reflects the progressive 

incorporation of material into and exhumation of the 

wedge from northeast to southwest. The major lithotectonic 

units exposed in the wedge are, from northeast to southwest: 

[27] 1. Ophiolites and crystalline batholiths represent the 

suture between the Indo-Eurasian plates and the eroded 

remnants of the volcanic arc that formed behind the 

northward directed subduction [Dewey and Bird, 1970; 

Tapponnier et al., 1981]. 

[28] 2. These rocks are thrust onto a thick section of 

sedimentary rocks that represent the deposition of material 

into the Tethys basin prior to collision [S¸engör et al., 1988; 

Gaetani and Garzanti, 1991]. 

[29] 3. A series of high-grade metamorphic rocks are 

juxtaposed with these metasediments by a low-angle normal 

fault within the orogen’s interior [e.g., Caby et al., 1983; 

Burg et al., 1984; Burchfiel et al., 1992; Searle, 1986; 

Herren, 1987; Valdiya, 1989]. These rocks are bounded to 

the southwest by a north dipping low-angle thrust system 

[e.g., Hodges, 2000] and comprise a fault-bounded wedge 

whose structural thickness varies along strike between 3.5 

and 11.7 km. 

[30] 4. The high-grade metamorphic rocks supersede 

weakly to moderately metamorphosed clastic sediments of 

the Lesser Himalaya 8 to 10 km thick, and form a series of


Figure 9. Two modeled Himalayan wedge geometries considered in this study. Model 1 assumes a 

simple wedge geometry originally calculated by Davis et al. [1983] and recently used by DeCelles and 

DeCelles [2001]. Model 2 assumes a crustal-scale ramp beneath the High Himalaya [e.g., Cattin and 

Avouac, 2000, and references therein], allowing the wedge to penetrate to a depth of 40 km. 

fold-and-thrust nappes [e.g., Schelling, 1992; Hodges, 

2000]. 

[31] 5. Rocks at the periphery of the orogen belong to the 

Subhimalaya and consist of Tertiary siltstones and sandstones, 

and lower Miocene to Pleistocene clastic sediments 

that represent the deposition of material in front of the 

advancing orogenic wedge [e.g., Burbank et al., 1997; 

DeCelles et al., 1998]. 

[32] These structures are bounded by a set of thrust faults 

that daylight intermittently, resulting in both faulting and 

folding at the surface [Nakata, 1989; Yeats et al., 1992]. 

Important for this study, the lithologies exposed within the 

orogenic wedge consist of a large fraction of crystalline and 

metamorphic rocks (Figure 8). The structural competency of 

these rocks generally decreases to the southwest; however, 

the areal extent of each rock type indicates that the weakly 

metamorphosed sediments and uplifted foreland rocks of 

the Lesser Himalaya and Subhimalaya, respectively, constitute 

a small fraction of the wedge relative to the crystalline 

and metasedimentary rocks to the northeast. 

[33] The long-lived Indo-Eurasian collision has produced 

a mountain belt 250 km wide with elevations in excess of 

8 km. Two end-member models exist for the geometry of the 

Himalayan orogenic wedge. The first geometry explored 

(hereafter referred to as model 1) assumes a simple wedge 

geometry (Figure 9). In this model, surface slopes of the 

orogenic wedge range from 3.5°–4.5°, while basal decollement 

dips range between 2° and 3° [Ohta and Akiba, 1973; 

Seeber et al., 1981; Schelling, 1992; DeCelles et al., 1998]. 


B01411 

More recent structural and geophysical studies indicate that 

this simple wedge geometry may not completely characterize 

the geometry of the deforming wedge. Data synthesized 

by Cattin and Avouac [2000] suggest the presence of a 

crustal-scale ramp under the High Himalaya (this model 

hereafter referred to as model 2), with an average decollement 

dip between 10° and 12° (Figure 9). We also recalculated 

the average surface slope in this case by considering the 

mean topography between the front of the wedge and the 

rigid backstop of the Tibetan Plateau. In this case, average 

surface slopes are between 1° and 2° for the entire wedge. In 

addition, the internally drained Tibetan Plateau lies northeast 

of the externally drained Himalaya; therefore, the orogen 

consists of only a forewedge whose eroded material is 

deposited directly into the Himalayan foreland to the southwest. 

Precipitation along the range front averages between 1 

and 3 m/yr and decreases to the northeast due to the presence 

of high topography. On the basis of a synthesis of the 

geologic history, calculations of the distribution of potential 

energy gradients in Asia, and topographic analyses, Hodges 

[2000] and Hodges et al. [2001] speculated that the 

Himalayan orogenic wedge is in a quasi-steady state in 

which material introduced into the wedge by tectonic 

accretion is removed by erosion or tectonic exhumation. 

4.2. Model Parameters 

[34] To interpret the topography and structural geometries 

of the Taiwan and Himalayan orogenic wedges in terms of 

our coupled erosion-deformation model, basin hydrologic


Figure 10. Basin area and channel length relationships for (left) Taiwan and (right) the Himalaya. 

Regression of these data constrain h and ka to be 1.7 and 4.9 and 1.65 and 9.4, in Taiwan and the 

Himalaya, respectively. Data computed using Hydro1K digital elevation model. 

parameters (ka and h), the accretionary material flux (vT), 

and the mechanical properties of the wedge (mb, m, lb, and l) 

must be constrained. We directly constrained h and ka using 

topographic analyses of the western slopes of the Taiwan 

orogenic wedge (Figure 10, left). We used the Hydro1K 1 

km topographic data set to define the basin area and channel 

length relationships encapsulated in ka and h. We solved for 

these parameters using a brute force approach in which rootmean-square 

(RMS) misfit values between observed and 

predicted (equation (4)) basin area-channel lengths were 

calculated for different combinations of ka and h to find 

those values that produced the lowest RMS values. Best fit 

values for the steady state section of the Taiwan orogenic 

wedge were h = 1.7, ka = 4.9. The accretionary material flux 

(vT) entering the Taiwan wedge was constrained by Suppe 

[1981], who indicated that a flux of 500 m 2 /yr of eroded 

rocks is incorporated into the orogenic wedge by frontal 

accretion. To account for the removal of material from the 

retrowedge, we use relative GPS velocities to estimate a 

conservative range of the material flux that travels through 

and is eroded from the retrowedge. This flux was then 

subtracted from the total accreted flux to determine that 

eroded from the forewedge. Our calculations indicate that 

between 276 and 333 m 2 /yr is eroded from the forewedge 

(Appendix A). Regional cross sections from Davis et al. 

[1983]; Suppe [1980, 1981] indicate that the depth to the 

base of the wedge is 11.5 km. The mechanical properties 

of the westward verging orogenic wedge have been constrained 

by formation tests and sonic log measurements 

during petroleum exploration [Suppe and Wittke, 1977; 

Suppe et al., 1981; Davis et al., 1983]. Using these 

measurements, Davis et al. [1983] estimate the Hubbert- 

Rubey fluid pressure ratios within the wedge and along the 

basal decollement to be l = l b = 0.675 ± 0.05. Finally, an 

analysis of the surface and basal decollement slopes in this 

wedge yield a wedge internal friction of m = 1.1 when the 

friction along the basal decollement is assumed to obey 

Byerlee’s friction law (m b =0.85[Byerlee, 1978; Dahlen, 

1984]). 

10 of 17 

B01411 

[35] Within the Himalayan orogenic wedge, analyses of 

the basin area to channel length relations were conducted 

in the manner described above. The current relationships 

along the Himalayan mountain belt produce best fit h and ka 

values of 1.65 and 9.4, respectively (Figure 10, right). The 

accretionary material flux entering the Himalayan orogenic 

wedge probably constitutes several components. First, 

7 km of foreland material is accreted to the front of the 

orogenic wedge [DeCelles and DeCelles, 2001] at a rate 

between 15.5 and 19.5 mm/yr [Bilham et al., 1997]. Therefore 

the cross-sectional material flux due to frontal accretion 

is between 109 and 137 m 2 /yr. In addition, Hodges [2000] 

and Hodges et al. [2001] explain the contemporaneous 

movement of normal and reverse faults bounding the northern 

and southern margins of the Higher Himalayan crystalline 

rocks, respectively, by the extrusion of lower Tibetan 

crust southward into the Himalaya. Extensional movement 

along the top of this potentially extruded section commenced 

in the Miocene ( 15 Ma) and has produced a minimum of 

40 km of displacement [Hodges, 2000, and references 

therein]. Finally, the structural thickness of the extruded 

section is between 3.5 and 11.7 km perpendicular to the 

transport direction of material. Therefore we estimate that a 

flux of 31 m 2 /yr may be added to the Himalayan orogenic 

wedge through the extrusion of Tibetan lower crust. Because 

this extrusion remains controversial, we add this material 

flux to the maximum estimate of the material flux into the 

wedge. Consequently, a conservative bound on vT entering 

the Himalayan orogenic wedge that accounts for the full 

range of tectonic models of deformation within the wedge is 

between 109 and 168 m 2 /yr. We calculated vT/K values for 

the two end-member geometries discussed above (model 1 

and model 2). For the model 1 wedge geometry, we followed 

DeCelles and DeCelles [2001] by calculating the depth to 

the basal decollement beneath the surface trace of the 

drainage divide by extrapolating the average 6° decollement 

dip across the 250 km width of the orogen, yielding 

D = 13 km. For model 2, we simplified the crustal ramp 

structure as a planar, triangular wedge with an average basal


Figure 11. Observed (gray boxes) and predicted a, b relationships for the Taiwan orogenic wedge. 

Solid lines show mechanical stability limits computed by Davis et al. [1983] and Dahlen [1984]. Dotted 

lines contour base 10 logarithm of vT/K that is required to produce an orogenic wedge in which all 

tectonically accreted material is erosionally removed from the wedge. 

decollement dip that reflected the average observed by Cattin 

and Avouac [2000]. The mechanical properties of the Himalayan 

orogenic wedge are not as well defined as those in 

Taiwan. However, the wedge geometry of the Himalaya 

imply that if l = l b, m b = 0.85 according to Byerlee’s friction 

law, and m = 1.1, l b =0.76[Davis et al., 1983]. 

4.3. Results 

[36] We show the results of the application of our model to 

the Taiwan and Himalayan orogenic wedges in Figures 11 

and 12, respectively. In Figures 11 and 12, dotted lines are 

the contoured base 10 logarithm value of vT/K and solid 

lines are the mechanical stability limits of the orogenic 

wedges. Figures 11 and 12 show the effect of changing m 

and n on values of vT/K required to produce the different 

(a, b) pairs. In general, higher vT/K values are required to 

produce the a, b relations observed in the Himalaya relative 

to the Taiwan orogenic wedge. For the Taiwan wedge, base 

10 logarithm values of vT/K between 7.1–7.4, 7.3–7.5, and 

13.3–13.7 are required when m = 1/3, n = 2/3, m = 0.4, 

Figure 12. Observed (gray boxes) and predicted a, b relationships for the Himalayan orogenic wedge. 

Solid lines show mechanical stability limits computed by Davis et al. [1983] and Dahlen [1984]. Dotted 

lines contour base 10 logarithm of vT/K that is required to produce an orogenic wedge in which all 

tectonically accreted material is erosionally removed from the wedge. (top) Wedge parameters defined 

originally by Davis et al. [1983] and utilized by DeCelles and DeCelles [2001]. (bottom) Crustal ramp 

model summarized by Cattin and Avouac [2000]. 


B01411


Table 1. Inferred vT/K and K Values for Taiwan and Himalayan Orogenic Wedge 

m = 1/3, n =2/3 m = 0.4, n =1 m = 5/4, n =5/2 

Minimum Maximum Minimum 

Taiwan 

Maximum Minimum Maximum 

vT/K 1.4 10 7 

2.1 10 7 

2.0 10 7 

3.3 10 7 

1.8 10 13 

5.1 10 13 

K 1.3 10 5 

2.4 10 5 

8.3 10 6 

1.6 10 5 

5.4 10 12 

1.7 10 11 

vT/K 5.1 10 7 

K 6.2 10 7 

vT/K 2.9 10 7 

K 2.0 10 6 

n = 1, and m = 5/4, n = 5/2, respectively. In the Himalaya, 

the base 10 logarithms of this value range between 7.7–8.5, 

7.9–8.6, and 14.7–15.8 when m = 1/3, n = 2/3, m = 0.4, 

n = 1, and m = 5/4, n = 5/2, respectively. Interestingly, the 

effects of the deeper wedge sole-out depths implied by the 

model 2 wedge geometry were roughly offset by the steeper 

basal decollement geometry. This resulted in similar vT/K 

values for model 1 and model 2 wedges, despite their 

disparate geometries. While the poorly constrained mechanical 

properties of the Himalayan orogenic wedge may cause 

shifts in the solid lines in Figure 12, the geomorphic 

isolines are solely the product of the geometry of the 

wedge. Therefore this fundamental observation of high 

and low values of vT/K required to produce the Himalayan 

and Taiwan orogenic wedges does not change with changing 

wedge mechanical properties. 

[37] Table 1 shows the range in vT/K values required to 

produce the geometry of each wedge when they are in 

erosional steady state. In general, vT/K increases with 

increasing m and n. Using the constraints on vT described 

above, we calculated a range of K values required to produce 

steady state geometries for Taiwan and the Himalaya. 

Because vT is significantly larger for Taiwan, larger K values 

are necessary to produce vT/K values that are less than those 

observed in the Himalaya. Inferred mean K values for 

Taiwan are 1.9 10 5 ,1.2 10 5 , and 1.2 10 11 when 

m = 1/3, n = 2/3, m = 0.4, n = 1, and m = 5/4, n = 5/2, 

respectively. Mean K values from Himalaya model 1 are 

2.0 10 6 ,1.1 10 6 , and 2.1 10 13 when m = 1/3, n = 

2/3, m = 0.4, n = 1, and m = 5/4, n = 5/2, respectively. Mean 

K values for the Himalaya model 2 geometry are 3.9 10 6 , 

2.8 10 6 , and 2.26 10 12 when m = 1/3, n = 2/3, m = 0.4, 

n = 1, and m = 5/4, n = 5/2, respectively. 

5. Discussion 

1.8 10 8 

3.3 10 6 

5.5 10 7 

5.8 10 6 

[38] Our models highlight the important role of changing 

tectonic rates and erosional processes in controlling deformation 

in actively deforming, externally drained orogens. 

First, rock type erodibility and precipitation may exert 

strong controls on the orogenic structure. When rocks are 

difficult to erode and/or precipitation is low, larger wedges 

must be built in order to produce surface slopes that are 

sufficient to remove material introduced by accretion. 

Second, as the accreted material flux (vT) increases, so does 

the size of the wedge, as steeper wedge slopes are required 

to evacuate this larger input of material. Therefore wedges 

Himalaya Model 1 

9.0 10 7 

2.9 10 7 

Himalaya Model 2 

3.9 10 7 

1.2 10 6 


3.7 10 8 

1.9 10 6 

9.0 10 7 

4.3 10 6 

4.2 10 14 

1.6 10 14 

5.2 10 13 

3.3 10 13 

B01411 

6.6 10 15 

4.0 10 13 

3.3 10 14 

3.2 10 12 

subjected to low precipitation that expose low-erodibility 

rocks should be wider than their high precipitation, high 

erodibility counterparts, if all other properties are fixed. This 

phenomenon was identified by Dahlen and Barr [1989] in 

Taiwan; however, because the erosion rate is specified 

directly in their models, it is not possible to attribute this rate 

to specific factors such as the exposed rock type and to 

validate consistency between these landscape and climatic 

parameters and those measured elsewhere by independent 

means. In addition, this observation has been made in the 

Bolivian Andes [Horton, 1999], where narrow and wide 

portions of the orogen are associated with high and low 

precipitation, respectively. In addition, Schlunegger and 

Simpson [2002] suggested that the lateral growth of the Alps 

is related to the exposure of less erodible rocks in their core. 

Both observations and conditions in the Himalaya and 

Taiwan are consistent with the basic conclusion of our model 

that reduced erodibility (either by rock type exposure or 

climate) or increased material input to the wedge leads to 

wider orogenic wedges. 

[39] Our analysis of Taiwan and the Himalaya highlight 

the important role of the exposure of different rock types in 

the orogenic wedge on its structure. The material input into 

the Taiwan orogenic wedge is significantly larger than that 

entering the Himalaya (500 m 2 /yr versus 110–170 m 2 /yr). 

However, the inferred values of vT/K are far lower for 

Taiwan than the Himalaya. This leads to lower inferred K 

values in the Himalaya relative to Taiwan. This is qualitatively 

consistent with the observations that the Himalaya 

receives lower average precipitation than Taiwan [World 

Meteorological Organization, 1981] and exposes crystalline 

and high-grade metamorphic rocks, rather than the accretionary 

wedge sediments present in Taiwan. Interestingly, 

the only systematic study that inferred rock type erodibilities 

for a variety of lithologies determined best fit power 

law exponents m = 0.4 and n = 1, and K values to be 

between 4.8 10 5 –4.7 10 4 and 4.4 10 –7 –1.1 

10 6 for volcaniclastics and mudstones, and granitoid and 

metasedimentary rocks, respectively [Stock and Montgomery, 

1999]. When similar power law exponents are used in 

our models, these values quantitatively agree with our 

estimates of 8.3 10 6 –1.6 10 5 and 2.9 10 7 – 

1.9 10 6 determined for Taiwan and the Himalaya, 

respectively. We conjecture that the K value in Taiwan is, 

and should be, lower than that inferred for volcaniclastics 

and mudstones, due to the exposure of lightly metamorphosed 

rocks within the prowedge. K values inferred for the


Himalaya agree well with those determined for similar 

metasedimentary and crystalline rocks. However, while 

the Taiwan wedge appears to be in a steady state form, 

the Himalayan orogenic wedge may not have reached the 

steady state postulated by Hodges [2000] and Hodges et al. 

[2001]. The fact that this orogenic wedge is growing into 

the foreland at 3 mm/yr [DeCelles and DeCelles, 2001] 

argues that the wedge is not yet in steady state, although it 

may be close to this condition [Hilley et al., 2003]. In this 

case, estimated K values are maximum estimates. In any 

case, even substantial decreases in K would be broadly 

consistent with independent estimates for these rock types 

being eroded in an arid climate. These adjustments do not 

change the qualitative conclusion that the dryer climate and 

exposure of crystalline rocks in the core of the Himalayan 

wedge may lead to a vastly different orogenic geometry 

than that observed in Taiwan. 

[40] It is worth pointing out that the Taiwanese orogenic 

wedge appears to be growing in a self-similar manner in 

which the fault angle and surface slope remain fixed with 

time and the decollement flattening depth increases as 

material is accreted to the wedge [e.g., Davis et al., 

1983]. In these cases, the temporal evolution of the wedge 

may not be well characterized by equation (6), as this 

formulation assumes that the wedge grows by a reduction 

in the decollement angle rather than a deepening of the soleout 

depth. However, our steady state parameterization 

(equation (7)) allows us to generalize this equation to 

wedges that grow by any combination of decollement 

flattening and self-similar growth. In this case, the steady 

state geometry of the wedge is not influenced by how the 

wedge grows, but instead depends only on the three 

independent variables that capture the geometry of the 

wedge (a, b, and D). Therefore, while the application of 

the temporal growth of these wedges must be taken with 

care when wedges grow self-similarly, our steady state 

results should be insensitive to the way in which the wedge 

grows into its steady state geometry. However, complimentary 

formulations applying the bedrock power law incision 

model to the growth of orogenic wedges that grow selfsimilarly 

have been produced (K. X. Whipple and B. J. 

Meade, Dynamic coupling between erosion, rock uplift, and 

strain partitioning in two-sided, frictional orogenic wedges 

at steady state: An approximate analytical solution, submitted 

to Journal of Geophysical Research, 2003, hereinafter 

referred to as Whipple and Meade, submitted manuscript, 

2003). By combining our model results with these studies, a 

full range of wedge development by both decollement 

flattening (this work and Hilley et al. [2003]) and self-similar 

growth (Whipple and Meade, submitted manuscript, 2003) 

can be explored and applied to a wide range of orogens. 

[41] Our findings and those of others [e.g., Davis et al., 

1983; Dahlen, 1984; Hilley et al., 2003] allow the temporal 

development of orogenic wedges whose decollement soleout 

depth remains fixed to be represented graphically 

(Figure 13). Triangular orogenic wedges at any time in 

their developmental history plot as a point on this a, b 

diagram. First, the works of Davis et al. [1983] and Dahlen 

[1984] define the stability lines of a brittle-elastically 

deforming triangular orogenic wedge that is at its Coulomb 

failure limit (Figure 13, A, solid lines). This theory predicts 

the possible wedge geometries for a set of mechanical 


B01411 

Figure 13. Schematic graphical depiction of the development 

of orogenic wedges. Solid lines (A) show stability 

limits calculated by Davis et al. [1983] and Dahlen [1984]. 

Arrows on these lines (B) show transient wedge development 

when it grows in its critical state, as formulated in 

Hilley et al. [2003]. Dashed lines (C) show condition under 

which wedge is in erosional equilibrium. Intersection of 

these lines with mechanical stability lines (solid circles) 

indicate an orogen’s geometry when it is in mechanical and 

erosional steady state. 

parameters; however, it provides no information as to the 

specific location on these lines an orogenic wedge will plot. 

Second, Hilley et al. [2003] developed a transient coupled 

erosional-tectonic wedge development model that shows the 

direction and rate at which points move along these lines 

(Figure 13, B, arrows on solid line), given the mechanical 

properties, erosional parameters, and initial geometry of the 

wedge. In the simple case of a wedge with no surface 

topography, the wedge geometry will initially plot at the 

point labeled (1). As material is added to the wedge, 

the surface topography steepens, accelerating erosional


processes (2). This acceleration in erosion reduces the rate 

at which the wedge widens with time. This particular model 

assumes that wedges grow in their mechanically critical 

state. However, other models [e.g., Willett, 1992] may be 

used to estimate the path of points within this diagram when 

the wedge does not grow in its critical condition. In these 

cases, the trajectory of points may deviate from the mechanical 

stability lines [Davis et al., 1983; Dahlen et al., 

1984; Willett, 1992]. In the case that the wedge grows selfsimilarly 

(‘‘self-similar growth’’; fixed alpha and beta) and 

in its mechanically critical state, the point representing the 

wedge geometry will not move from a single point on this 

diagram. Instead, increases in the depth to the basal decollement 

with time causes the vT/K base 10 logarithm contours 

to rotate counterclockwise in Figure 13 until the erosional 

flux balances the tectonic accretion rate. Finally, the wedge 

geometry will approach its steady state form (3) in which 

erosion is sufficient to remove all material accreted to the 

wedge. This study shows the ultimate form of the wedge 

when it is in its erosional steady state form (Figure 13, C, 

dashed lines). When the wedge is in mechanical and 

erosional steady state, the orogenic wedge geometry plots 

at the intersection of the vT/K contour and the mechanical 

stability line appropriate for a specific orogenic wedge 

(Figure 13, solid circles). Using these diagrams, the development 

and ultimate geometry of orogenic wedges that gain 

material by accretion and lose material by bedrock fluvial 

incision may be understood. 

[42] Finally, it is important to acknowledge the assumptions 

of our estimated values of vT and our model formulations. 

For the Taiwanese orogenic wedge, vT was 

estimated by Suppe [1981] to be 500 m 2 /yr based on 

balanced cross sections that sample accretion over several 

million years. However, in the Himalaya, wedge accretion 

rates were based on geodetic measurements and the thickness 

of accreted foreland material and the potential lower 

crustal Tibetan channel (Appendix A). While the geodetic 

rates may only sample instantaneous accretion rates, no 

further information exists regarding the material fluxes 

entering the Himalayan wedge. In addition, the application 

of geodetic rates to wedge accretion rates over longer 

timescales has been successfully employed previously 

[e.g., DeCelles and DeCelles, 2001]. 

[43] For simplicity, the formulations of Davis et al. [1983] 

and Dahlen [1984] assume that the wedge has a simple 

triangular cross section and deforms brittle-elastically at the 

Coulomb failure limit of the wedge. In real orogens, plastic 

deformation within the wedge and deviations in this simple 

geometry may confound the simple relationships presented. 

In addition, we neglect isostasy in our analysis and assume 

that heterogeneities in mechanical and erosional properties 

within the wedge may be represented by average, homogeneous 

values. Isostasy may increase the decollement angle 

and reduce the surface slope to maintain the inverse relationship 

predicted between fault dip and surface slope [Davis et 

al., 1983]. Both isostasy and heterogeneity within orogens 

are important factors, and so their incorporation into our 

models provides a fruitful direction of future research. 

However, as shown by Davis et al. [1983], Dahlen [1984], 

and DeCelles and DeCelles [2001], simple wedge models 

apparently capture the first-order features of the structures of 

many orogens. 


B01411 

[44] In addition, it is important to note that all terms 

related to the mechanical properties of the wedge have 

vanished from our formulation (equation (7)), as long as 

we assume that the wedge maintains a triangular cross 

section. More complex rheologies may lead to the violation 

of this geometry [e.g., Willett, 1999]; however, where an 

approximately triangular wedge geometry can be demonstrated, 

our model can be employed. Therefore, because we 

estimate the geometry of the wedge a priori, the steady state 

geometry is independent of the rheological properties, and 

isostatic adjustments should be encapsulated within the 

derived estimates of vT/K, allowing us to discard many of 

the mechanical and isostatic processes and parameters that 

may be difficult to constrain by field data. 

[45] Two of the largest uncertainties in our analysis 

include the assumption of mechanical and erosional steady 

state, and the broad application of the bedrock power law 

incision model to an entire orogen. First, few wedges likely 

exist that are in this steady state condition, and the Taiwan 

orogen is probably the best example of this phenomenon 

[Suppe, 1981]. Because this steady state condition is likely 

the exception to the rule, the direct applicability of our 

models to other orogens may be limited. However, our 

results provide important information about the state toward 

which mountain belts tend to evolve. In many areas of the 

world and ancient orogens, information on steady state 

behavior does not exist. However, as this study and those 

of others [e.g., Willett, 1999; Hilley et al., 2003] have 

shown, erosion may nevertheless exert important controls 

on deformation within and topographic form of many 

orogens. Our results provide a valuable heuristic guide for 

interpreting changes in orogenic structure with respect to 

these erosional factors in settings where tectonic and erosional 

rates may not be available. 

[46] Second, we assume that the rate-limiting process in 

orogenic wedges is bedrock fluvial incision [Whipple et al., 

1999]. Other erosional processes may be important in 

denuding the orogenic wedge; however, many of these 

other processes (e.g., glacial transport) are less well understood 

than bedrock erosion. Instead of including less well 

constrained processes, we followed the approach of many 

[e.g., Whipple et al., 1999; Whipple and Tucker, 1999; 

Kirby and Whipple, 2001; Whipple and Tucker, 2002] by 

using the power law as our rate-limiting orogen-scale 

erosion process. However, there are several important 

limitations of the bedrock power law incision model that 

warrant discussion. The erodibility parameter (K) may be 

influenced by rock type [Stock and Montgomery, 1999], the 

distribution of fractures within the bedrock [e.g., Whipple et 

al., 2000], allometric changes within the channel, the 

relations between catchment area and effective discharge 

in the channel [Whipple and Tucker, 1999; Sklar and 

Dietrich, 1998], the power law exponents [Sklar and 

Dietrich, 1998], and sediment input from hillslopes [Sklar 

and Dietrich, 1998, 2001; Whipple and Tucker, 2002]. 

Many of the factors that control the value of K remain only 

qualitatively or poorly understood, limiting the predictive 

capability of the bedrock incision model. As an example, 

Sklar and Dietrich [1998, 2001] found that sediment input 

from hillslopes may exert a strong control on the rate of 

bedrock incision, and this sediment input may be modulated 

by the effects of climate and uplift rate [Montgomery and


Dietrich, 1994; Fernandes and Dietrich, 1997; Whipple and 

Tucker, 2002]. Also, incision rates may be related to the 

amount of excess transport capacity that these bedrock 

channels may contain after sediment has been transported 

(the ‘‘over-capacity’’ model of Kooi and Beaumont [1994]). 

However, we do not consider these models because they 

tend to predict unrealistic stream profile geometries relative 

to those observed in nature [Whipple and Tucker, 2002]. 

Stock and Montgomery [1999] analyzed a series of bedrock 

channels in different parts of the world that were cut into 

various types of bedrock and found that the primary 

controlling factor of K appeared to be lithology. The 

consistency between our inferred K values and those estimated 

for similar rock types indicates that while there are a 

plethora of factors included in K, temporal averaging over 

the timescales applicable to orogen-scale development may 

fold many of these factors into a bulk lithology factor in 

which specific and perhaps covarying erosional mechanisms 

may be captured by a single effective rock type. 

Therefore, while our formulations presented will change 

with greater understanding of these erosional processes, the 

heuristic results of our analysis may be unaffected. 

6. Conclusions 

[47] We developed a coupled erosion-deformation model 

that is used to understand how deformation within and 

erosion of an orogenic wedge are linked. The model 

assumes that the wedge (1) has a triangular cross section, 

(2) gains mass either from underplating of foreland sediments 

or injection of material into the back of the wedge, 

(3) looses mass removed by erosional processes whose rates 

are limited by fluvial bedrock incision, (4) is in a steady 

state form in which all material that is tectonically introduced 

into the wedge is removed by erosion, and (5) is at its 

Coulomb failure limit. Under these assumptions, the morphology 

of the steady state wedge is controlled by its 

mechanical properties (m, mb, l, lb), the basin hydrologic 

parameters (ka and h), the erosional exponents (m and n), 

the sole-out depth of the basal decollement (D), and the 

ratio of the flux of tectonically added material to the 

erosional constant (vT/K). 

[48] In general, increasing values of vT/K produce steady 

state orogenic wedges that are wider than their low vT/K 

counterparts. Increases in this parameter may result from 

increasing material flux introduced into the wedge, the 

exposure of less-erodible rock types within the wedge, 

and/or decreased erosional power due to reduced precipitation 

and runoff. Our results highlight the role of erosion, and 

by inference, the importance of climate and rock type 

exposure in determining orogenic structure. While a steady 

state condition may not be satisfied in most orogens, our 

analysis provides important heuristic results that may be 

used to interpret both active and ancient orogens in terms of 

the accretion and erosion of material from the wedge where 

information about the controlling processes and their rates 

may be unavailable or erased. 

[49] We applied these models to the Taiwan and Himalayan 

orogenic wedges, which may be in tectonic and erosional 

steady state. In the case of Taiwan, previous work has 

found that erosion rates inferred from fission track analyses 

are consistent with those required to explain wedge steady 


B01411 

state geometry [Dahlen and Barr, 1989]. However, these 

studies do not allow direct comparison of the inferred rock 

resistance to fluvial bedrock incision with those exposed 

within the island. Our analysis demonstrates that large values 

of vT/K are required to explain the structural and topographic 

relations in the Himalaya relative to Taiwan. However, 

independent estimates of the material flux entering the 

Himalaya relative to Taiwan are substantially lower and 

require an order of magnitude smaller K acting to erode this 

wedge. This reduced K value in the Himalaya is consistent 

with the lower precipitation and exposure of less erodible 

rock types within this wedge relative to Taiwan. Our 

calculated K values are consistent with those determined 

independently for similar rock types. Therefore differences 

in rock type and climate apparently lead to key differences in 

the erosion, and hence, structure of these two mountain belts. 

Appendix A: Estimation of Material Leaving 

Retrowedge in Taiwan 

[50] To calculate the range of material fluxes eroded from 

Taiwan’s eastward verging retrowedge, we calculated the 

velocity of the Luzon arc remnants relative to the prowedge 

and retrowedge drainage divide using Global Positioning 

System measurements [Yu et al., 1997] to determine the 

velocity of material moving out of the wedge at its eastern 

boundary. We found that material moves out of the wedge’s 

eastern boundary at a horizontal velocity of 36–48 mm/yr. 

We assumed a maximum rock uplift rate of 10 mm/yr 

throughout the retrowedge. This value was chosen as a 

conservative maximum estimate of rock uplift rates, and so 

a reduction in this value slightly reduces the material flux 

leaving the retrowedge and increases that eroded from the 

prowedge. Using these values, we determined the velocity 

component perpendicular to the wedge surface and integrated 

this velocity along its length. By assuming that all material 

moving through the orogenic system is removed by erosion, 

leaving the cross-sectional geometry of the orogen unchanged, 

these calculations indicate that between 168 and 

224 m 2 /yr of material moves through the surface slope of the 

retrowedge. By assuming that all material moving through 

the orogenic system is removed by erosion, we equated 

erosional removal with this amount. The total estimated 

accreted material flux was estimated to be 500 m 2 /yr; 

therefore between 276 and 333 m 2 /yr is removed from the 

prowedge before reaching the boundary between the prowedges 

and retrowedges. This estimate is consistent with 

fluxes calculated from GPS-derived decollement slip rates 

beneath the western portion of the island [Hsu et al., 2003]. 

[51] Acknowledgments. G.H. acknowledges support from the 

Alexander von Humboldt Foundation and the DAAD IQN program for 

support of his research at Potsdam. M.S. acknowledges support by the 

German Research Council (DFG) grant STR 373/-3. Also, G.H. thanks 

Vince Matthews for introducing him to the critical Coulomb wedge and 

astutely suggesting its utility in understanding orogen-scale tectonic and 

landscape development. We gratefully acknowledge Edward Sobel for 

commentaryonanearlydraftofthismanuscript.Inaddition,FritzSchlunegger, 

Terence Barr, and Jean Braun all provided valuable reviews that improved 

the manuscript. Finally, we would like to acknowledge comments on the 

manuscript by Roland Bürgmann that improved our analyses. 

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