formation of internally drained contractional basins by...

Formation of internally drained contractional basins

by aridity-limited bedrock incision

Edward R. Sobel, George E. Hilley, and Manfred R. StreckerInstitut fur Geowissenschaften, Universitat Potsdam, Potsdam, Germany

Received 20 March 2002; revised 12 December 2002; accepted 13 March 2003; published 22 July 2003.

[1] Low internal relief, aridity, and internal drainage characterize the Puna-AltiplanoPlateau and the Tibetan Plateau and the Tarim basin. Structurally, these areas are reversefault bounded terrains with intervening wedge-top basins that store thick accumulations ofsediment for millions of years. Orographic barriers along the margins of these basinsare oriented normal to moisture bearing winds, resulting in regional aridity. Thecombination of this aridity, rapid shortening and uplift rates, and resistant exposedlithologies coincides with the location of these internally drained basins. We hypothesizethat these large, internally drained areas persist indefinitely when uplift overwhelms thefluvial systems and defeats the channel network. To test this hypothesis, we developedmodels of channel defeat to examine the threshold conditions required to fragment thechannel network. The results of these models suggest that low-erodibility rocks, moderateto high uplift rates, and low precipitation favor defeat of orogen-traversing channels. Mostcoupled tectonic-landscape development models prevent the development of internaldrainage and so may overestimate the voracity of erosion in regimes that favor internaldrainage, profoundly influencing predicted orogenic growth patterns. INDEX TERMS: 1815

Hydrology: Erosion and sedimentation; 1854 Hydrology: Precipitation (3354); 8102 Tectonophysics:

Continental contractional orogenic belts; 9320 Information Related to Geographic Region: Asia; KEYWORDS:

bedrock-incision, Puna-Altiplano Plateau, wedge top basin, Tarim basin, orographic barrier, Tibetan Plateau

Citation: Sobel, E. R., G. E. Hilley, and M. R. Strecker, Formation of internally drained contractional basins by aridity-limited

bedrock incision, J. Geophys. Res., 108(B7), 2344, doi:10.1029/2002JB001883, 2003.

1. Introduction

[2] Long-lasting, internally drained basins often consti-tute a first-order geomorphic feature of contractional tec-tonic settings. In some cases, these have apparently existedfor millions of years and store large sediment volumes [e.g.,Einsele and Hinderer, 1997; Metivier et al., 1998; Horton etal., 2002]. The Puna-Altiplano of the central Andes and theTibetan Plateau constitute the largest intraorogenic plateauson Earth and host a complex amalgamation of internallydrained basins and intervening ranges where the transitionfrom formerly open to closed drainage can be studied [e.g.,Isacks, 1988; Alonso et al., 1991; Alonso, 1992; Horton andDeCelles, 1997; Tapponnier and Molnar, 1979; Tapponnieret al., 2001]. Similarly, the Tarim basin of China comprisesseveral late Cenozoic contractile basins that have coalescedto form a single immense internally drained basin [e.g., Li etal., 1996]. Structurally, these regions are thrust or reversefault bounded terrains with intervening basins; the latter areoften wedge-top basins. Another unifying characteristic ofthese structural provinces is that orographic barriers alongtheir basin margins are oriented normal to moisture bearingwinds, resulting in pronounced regional aridity (Figure 1).

[3] Following the original hypothesis of Gilbert [1890],we propose that formation of internal drainage in contrac-tional regions results from the outpacing of incision bytectonic uplift, leading to fragmentation and defeat of theirfluvial systems, and subsequent coalescence of the resultinginternally drained basins. Whether rivers remain connectedto a constant base level in the foreland or are defeated infavor of internal drainage depends on interactions amongstream power, upstream deposition, sediment flux, bedrockresistance, uplift rate, and range width [e.g., Burbank et al.,1996; Whipple and Tucker, 1999]. Successive marginaluplifts can lead to or enhance aridification, thereby aidingthe formation or persistence of closed basins. The resultinginternally drained wedge-top basins can fill beyond thestructurally controlled topographic basin margins, permittingthe storage of significant quantities of sediment. Somelandscape development models [e.g., Willett, 1999] suggestthat such basins are transient features that are eventuallyreintegrated into the fluvial system, forcing the drainagenetwork to remain connected to an approximately constant,regional base level. However, the existence and persistenceof large basins over millions of years suggests that the fluvialsystems of the orogen have been disconnected from a steadybase level over similar timescales as the development of theorogen. These long-lasting internally drained basins in aridenvironments show that the orogen is far from a flux ortopographic steady state [e.g., Willett and Brandon, 2002];

JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 108, NO. B7, 2344, doi:10.1029/2002JB001883, 2003

Copyright 2003 by the American Geophysical Union.0148-0227/03/2002JB001883$09.00

ETG 6 - 1

thus, they offer an opportunity to test surface process modelsthat should reflect the evolution of orogenic features.[4] In the first part of this paper, we review the morphol-

ogy, climate, and geologic and tectonic history of theTibetan Plateau, the Tarim basin, and the Puna-AltiplanoPlateau. In particular, we highlight the timing of basinaridification and uplift at the basin margins, exposure ofdifferent rock types, and the onset of internal drainage. Weemphasize that it is unlikely that fluvial systems have beenintegrated with a regional, constant base level for millions

of years. As might be expected, high uplift rates andexposure of resistant lithologies coincide with arid environ-ments within the interior of these regions. Second, we useformulations of fluvial incision [Howard and Kerby, 1983;Whipple et al., 1999; Whipple and Tucker, 1999; Paola etal., 1992] to estimate the threshold conditions of uplift,climate, and rock erodibility that lead to defeat of the fluvialchannels and establishment of internal drainage. From thesemodels, we find that sustained moderate to high uplift rates,moderate to low rock erodibilities, and dry climates even-

ETG 6 - 2 SOBEL ET AL.: FORMATION OF INTERNALLY DRAINED BASINS

tually lead to the establishment of internal drainage. Finally,we extrapolate the theoretical and field-based modelingresults of others [e.g., Willett and Beaumont, 1994; Royden,1996; Willett, 1999; Horton, 1999; Schlunegger and Willett,1999] to suggest that the inability of fluvial systems toremove mass from uplifting, internally drained basins storesgravitational potential energy in the crust, favoring migra-tion of deformation to lower-elevation areas. This suggeststhat inefficient mass transfer by fluvial erosion may influ-ence the lateral growth of orogens.

2. Geology, Morphology, and Climate of theTibetan Plateau, Tarim Basin, andPuna-Altiplano Plateau

2.1. Northeastern Tibetan Plateau Margin

[5] The transpressive tectonic regime in northeast Tibethas resulted in crustal-scale thrusts propagating to thenortheast [Tapponnier et al., 1990]; the northern portion ofthis system uplifted the reverse and thrust-fault boundedblocks of the�700 km long Qilian Shan (Figures 2a and 2b).Northeast propagation of deformation and uplift are kine-matically linked to left-lateral strike-slip displacementsalong the Altyn Tagh fault [Tapponnier et al., 1990, 2001].Internally drained rhomboidal basins younging to the north-east have formed behind these rising tectonic barriers. Insome cases, these basins were filled to elevations of thepreviously formed Tibetan Plateau [Meyer et al., 1998]. Onthe basis of extrapolated Pliocene-Quaternary accumulationrates and isostatic compensation, Metivier et al. [1998]estimated that the surface of the largest basin on the plateauedge (Qaidam basin), could rise 2200 m to the level of theTibetan Plateau in about 9 million years. To test thishypothesis, we compared these accumulation rates to exhu-mation rates at the margins through a conservative massbalance, which assumes that horizontal shortening is uni-formly distributed along the transect but rock uplift relativeto the basin surface is restricted to outcropping basementranges underlain by faults. The conservative nature of thisbalance is emphasized by disregarding the possible contri-bution of sediment sourced from south of the crest of theKunlun Shan. We found a general agreement between thesolid mass volume being exhumed in basin-bounding rangesand being deposited in the basins [Metivier et al., 1998].Therefore, if the present tectonic and erosional regimepersists, the Qaidam basin could plausibly become indistin-guishable from the adjacent high plateau.

[6] The Qaidam basin is bounded by the Altyn Tagh,Qilian Shan, and Kunlun Shan ranges on its north, north-east, and southern margins, respectively. The latter rangeseparates the Tibetan Plateau from the Qaidam basin. Theranges are primarily composed of granitoids and Precam-brian-Triassic (meta)sediments [e.g., Li et al., 1991]. Ceno-zoic relief likely initiated in the Kunlun Shan, along thesouthern and western margin of the basin (Figure 2a).Potassium feldspar 40Ar/39Ar data indicate that significantexhumation began at circa 30 Ma [Mock et al., 1999] andapatite fission track data suggest that rapid exhumationcontinued into the early Miocene [Lewis, 1990; Jolivet etal., 2001]. We interpret the scarcity of young apatite fissiontrack ages to indicate slowing of exhumation rates since thattime; therefore, the southern margin of the Qaidam basinlikely formed in and has persisted without significanterosion since the early Miocene.[7] Transpression along the Altyn Tagh Fault system has

created a linear topographic barrier that hydrologically iso-lated the Qaidam basin from the Tarim basin (Figure 1a). Thefault apparently formed in part along a reactivated Paleo-zoic suture [Sobel and Arnaud, 1999]. Significant coolingalong thrust and strike-slip faults is documented by Oligo-cene to early Miocene apatite fission track ages [Sobel etal., 2001; Jolivet et al., 2001; Delville et al., 2001] andpotassium feldspar 40Ar/39Ar data [Cowgill et al., 2001].Diverging Oligocene and Miocene paleocurrent directionson either side of the Altyn Tagh range demonstrate that ithas been a positive topographic feature since this time[Hanson, 1999]. Sedimentary basin piercing points bound-ing the eastern and central portions of the fault suggest alate Oligocene-early Miocene initiation of slip [Yue et al.,2001].[8] The location and trend of the ranges comprising the

Qilian Shan is likely controlled by reactivated Paleozoicstructures [e.g., Meyer et al., 1998]. Shortening and upliftalong these laterally extensive structures provides few or nooutlets for the fluvial networks draining the area. Extrapo-lation of studies along the northern margin of the rangeimplies that the Qilian Shan has been largely constructedsince the late Miocene [Meyer et al., 1998]. However,apatite fission track data show that the southern andnorthern range fronts experienced early Miocene exhuma-tion [Jolivet et al., 2001; George et al., 2001]. In addition,deposition of northwardly derived coarse conglomerates inthe southern range is magnetostratigraphically dated as circa21 Ma, and likely records initiation of thrusting in the South

Figure 1. (opposite) Contoured annual precipitation (thin black lines) [WMO, 1975, 1981] superposed on local reliefderived from GTOPO30 data for the eastern portion of (a) Tibet, (b) the central Andes, and (c) Tarim basin. Contourinterval is 100 mm/yr; for Asia, contours interval increases to every 1000 mm/yr above 1200 mm/yr so that spatialvariations can be discerned for both arid and humid regions. Isopleths for 400, 800, 1200, 2000, and 3000 mm/yr are solidlines; others are dashed. Arrows indicate general direction of moisture transport. Areas of internal drainage are outlined inwhite. Dotted white line delineates upper Huang He drainage basin that was formerly dammed in the Gong He basin (whitesquare). Heavy black elevation contours roughly delineate the Tibetan Plateau and the Tian Shan (4000 m) and the Puna(3800 m). Local relief was calculated by moving a 7 km wide circular search window over the DEM. At each point, themaximum range of elevation values within the window was determined and plotted at the center of the circle. Majorstructures are parallel to topographic crests. Abbreviations in Figure 1a are QS, Qilian Shan; KS, Kunlun Shan; AT, AltynTagh; the Altyn Tagh Fault bounds the southern side of this range. Abbreviation in Figure 1b are A, Aconquija; AD,Atacama Desert; CA, Campo Arenal; H, Humahuaca; QT, Quebrada del Toro; SA, Salar de Antofalla; SQ, Sierra Quilmes;VC, Valles Calchaquıes basin.

SOBEL ET AL.: FORMATION OF INTERNALLY DRAINED BASINS ETG 6 - 3

Qilian Shan [Gilder et al., 2001]. These data indicate thatthe range was being uplifted during the early Miocene,likely creating a topographic barrier at that time.[9] The Qaidam basin contains as much as 3 and 8 km of

Oligocene and Neogene nonmarine strata, respectively(Figures 2c and 2d) [Huang et al., 1996]. Large anticlines

with recent growth strata (Figure 2b) [Song and Wang,1993] document that the basin lies in a wedge-top setting.Thick lacustrine mudstones were deposited during theOligocene in local, structurally controlled basins; biomarkeranalysis demonstrates that these lakes were hypersaline andanoxic [Song and Wang, 1993; Hanson et al., 2001].


Expansion of lacustrine facies and increasing sedimentationrates during the Pliocene reflect internal drainage andstorage of sediment within the basin [Metivier et al.,1998], and perhaps more efficient erosion due to greaterclimatic variability [e.g., Peizhen et al., 2001]. Compared toOligocene strata, Pliocene deposits are more widespread,thicker, and include abundant evaporites [Song and Wang,1993; Metivier et al., 1998], suggesting increased aridity inan internally drained basin. Thus the basin was separatedfrom the foreland by the Pliocene, and perhaps even as earlyas the Miocene.[10] Aridity in Tibet and the Qaidam basin results from

the orographic barriers formed by the Tian Shan, QilianShan, and the Himalaya, to the north, northeast, andsouth, respectively, amplified by the effects of the sub-tropical high-pressure belt (Figures 1a and 1c). Well-datedloess sequences to the east of the Qaidam basin constrainthe onset of aridity to be 22 Ma; this is inferred to resultfrom elevated topography in central Asia [Guo et al.,2002]. A striking example of an orographic barrier is theHimalaya: precipitation on the south side of the rangeexceeds 2000 mm/yr, while the Qaidam basin receives�100 mm/yr (Figure 1a). While large precipitation gra-dients are observed over the high mountain chain, south-east derived moisture penetrates into the southeasternsection of the Tibetan Plateau, where the ranges trendparallel to the moisture transport direction. Interestingly,these high-precipitation regions of the orogen are notinternally drained.[11] Finally, local relief is concentrated within narrow

zones along the edges of the Qaidam, Tarim, and HexiCorridor basins (Figure 1a); the interior of the plateau haslittle relief and approximately corresponds to internallydrained areas of the landscape [Fielding et al., 1994]. Thezone of high relief is much broader along the southeasternmargin, similar to the diffuse precipitation gradient in thearea. Prior to basin closure along the dry northern plateaumargin, rivers from the previously formed highland ofnortheastern Tibet likely drained through Qaidam into eitherthe Hexi corridor, to the northeast and/or the Tarim basin, tothe north.[12] Although the data provide scant direct information

on paleotopography, the synchronicity of the onset of basinmargin exhumation, and significant deposition and aridifi-cation within the Qaidam basin suggests that it has beensurrounded by high topography for much of the Neogene.The construction of topographic barriers along all marginsof the basin and the resulting aridity apparently isolated the

basin from the regional base level between the Miocene andthe Pliocene [Meyer et al., 1998].

2.2. Tarim Basin

[13] North of the Tibetan Plateau lies the 560,000 km2

Tarim basin (Figure 3a). It is surrounded by the Tian Shan,Altyn Tagh-East Kunlun Shan, and Pamir-West KunlunShan mountains (Figures 1c and 3a). Northward indentationof the Pamir along thrusts and strike-slip faults duringOligo-Miocene time separated the Tarim basin from basinsfarther west [Burtman and Molnar, 1993; Burtman, 2000].[14] The Tian Shan comprises approximately east-west

striking reverse-fault bounded basement blocks upliftedalong Paleozoic structures that separate intramontane basins[e.g., Burtman, 1980; Yin et al., 1998] (Figure 3a). Apatitefission track data show that these ranges have been exhumedby thrusting since circa 25 Ma. [Hendrix et al., 1994; Sobeland Dumitru, 1997; Sobel et al., 2000; Dumitru et al., 2001;Bullen et al., 2001]. Although the ranges have high relief(Figure 1c), the abundance of pre-Cenozoic apatite fissiontrack ages indicates the total amount of exhumation islimited (Figure 3a), in agreement with a preserved wide-spread erosion surface cut into basement rocks in the westernTian Shan [Sadybakasov, 1990].[15] Deposition of coarse conglomerates in the northern

Tarim basin commenced at 21–24 Ma, providing a lowerbound on the onset of basin-vergent thrusting in the areanear Kuqa (Figure 3a) [Yin et al., 1998]. Sediment from theTian Shan accumulated in the Tarim and Junggar basinsduring the Miocene, indicating significant topographicdevelopment [Metivier and Gaudemer, 1997]. Deformationin the range has continued through the present and alsoaffects basin margins [e.g., Yin et al., 1998; Burchfiel etal., 1999; Tapponnier and Molnar, 1979]. Along thenorthwestern margin of the basin, Pleistocene synsedimen-tary deformation is documented by paleomagnetic data[Chen et al., 2002], indicating that this region now liesin a wedge-top position. Geodetic surveys suggest that thepresent shortening rate across the range in this region is�20 mm/yr [Abdrakhmatov et al., 1996].[16] Marine deposition in the Tarim basin was superseded

by transitional, and ultimately terrestrial sedimentation byOligo-Miocene time. This is indicated by up to 6 km ofOligo-Miocene marginal marine or hypersaline lacustrine depositsthat unconformably overlie marine strata (Figures 3b and 3c)[Hao et al., 1982; Zhou et al., 1984; Zhou and Chen, 1990].Subsequently, deep foreland basins formed in southwest andnorth Tarim during the Miocene [Ma and Wen, 1991]; these

Figure 2. (opposite) Synthesis of data from the northeastern margin of the Tibetan Plateau. (a) Shaded relief map, basedon GTOPO30 data. Numbers show representative thermochronologic and paleomagnetic stratigraphic data (Ma). Cenozoicages and older ages record significant exhumation and <5 km of Cenozoic exhumation, respectively. Annotations after theage indicate source. For apatite fission track data, s, Sobel et al. [2001]; j, Jolivet et al. [2001]; g, George et al. [2001];d, Delville et al. [2001]. For potassium feldspar 40Ar/39Ar data, m, Mock et al. [1999]. For magnetic stratigraphy dating ofconglomerate sedimentation, sg, Gilder et al. [2001]. Faults are modified from Dumitru et al. [2001]; Meyer et al. [1998],and Jolivet et al. [2001]. Bold line shows the location of cross section. ATF, Altyn Tagh Fault. (b) Cross section through theQaidam basin between the east Kunlun Shan and the Qilian Shan, modified from Meyer et al. [1998] (with permission fromBlackwell). Gr, growing anticlines; A, active faults. Structures and topography have no and 4 times vertical exaggeration,respectively. (c) Neogene and (d) Oligocene isopach maps based on seismic and borehole data, modified from Huang et al.[1996] (with permission from Geological Publishing House). Isolated Oligocene depocenters up to 3 km thick are overlainby up to 8 km of Neogene strata.


discrete depocenters eventually coalesced in the center ofTarim, where strata gently onlap older units [Li et al., 1996](Figure 3d). Thus internal drainage must have been estab-lished during the Miocene.[17] The Tian Shan and Pamir shelter the Tarim basin

from northwardly and westwardly derived precipitationsources, respectively [Aizen et al., 1995]. Aridity is furtherenhanced by the Tibetan Plateau, to the south (Figure 1c)[World Meteorological Organization (WMO), 1981], and

the effects of the subtropical high-pressure belt. Withinthe basin itself, mean annual precipitation rarely exceeds100 mm/yr; along the basin margins, it is commonlybetween 400 and 800 mm/yr (Figure 1c).[18] Along the southwestern edge of the basin, high local

relief within the Karakorum range generally coincides withhigher mean annual precipitation in the area [Fielding et al.,1994]. The large rivers that flow into the basin dry outtoward the center. At present, the spill point of Tarim lies at


an elevation of 1139 m within the rugged topography of theTian Shan, well above the basin’s lowest point of �760 m.Additional spill points at 1329 and 1390 m lie to the northof the Qilian Shan, in low-relief areas.

2.3. Puna-Altiplano Plateau and Its Margins

[19] The Cenozoic arid Puna-Altiplano Plateau is com-posed of internally drained basins, often with thick evapo-rite deposits, lying between the present volcanic arc of theWestern Cordillera and the rugged topography of theEastern Cordillera (Figures 1b and 4a) [Jordan and Alonso,1987; Alonso et al., 1991; Vandervoort et al., 1995]. TheAltiplano consists of a single large basin in contrast to thenumerous smaller basins of the Puna; all of these basinscurrently lie in an arid environment that resulted from theOligocene-Miocene uplift of the east bounding EasternCordillera [Kley et al., 1997; Coutand, 1999; Horton etal., 2001].[20] The Altiplano basin is bounded on the west and east

by the presently active volcanic arc (Western Cordillera), anda wide fold and thrust belt composed primarily of well-cemented Ordovician strata (Eastern Cordillera), respectively(Figure 4a) [e.g., Allmendinger et al., 1997; Kley et al.,1997]. The basin contains up to 12 km of Tertiary sediment[e.g., Allmendinger et al., 1997, and references therein].Paleocurrent and provenance measurements indicate thatthis region drained to the west prior to the Eocene [Hortonet al., 2001]. In the Eocene, the Western Cordillera wascreated by thrusting that formed an elevated basin margin(see discussion and references of Horton et al. [2002]);subsequently, the modern volcanic arc was constructed[Allmendinger et al., 1997]. Sedimentary petrography andpaleocurrent data show the Eastern Cordillera thrust beltbecame a sediment source during the Oligocene and Mio-cene, suggesting that the Altiplano basin has likely been aclosed piggyback basin since circa 25 Ma [McQuarrie andDeCelles, 2001; Horton et al., 2002]. Apatite fission trackdata corroborates strong exhumation and relief developmentduring the Oligocene [Tawackoli et al., 1996; Ege et al.,2002]. Late Oligocene-early Miocene conglomeratic stratain the western portion of the Eastern Cordillera and similarearly to middle Miocene strata in the Altiplano basinincludes growth structures deposited in a wedge-top setting[Horton and DeCelles, 1997; McQuarrie and DeCelles,2001]. The undeformed circa 10.7 Ma San Juan del Ororegional erosion surface within the Eastern Cordillera showsthat this region is now tectonically inactive; since the late

Miocene, deformation has instead propagated eastward intothe thin-skinned Subandean fold and thrust belt [Gubbels etal., 1993].[21] Farther south, the Puna is characterized by a series of

high-angle basement uplifts separating discrete depocenters,some of which have subsequently coalesced (Figure 4a)[Schwab, 1985; Jordan and Alonso, 1987; Kraemer et al.,1999; Coutand et al., 2001]. The eastern margin of the Punais composed of the Eastern Cordillera and the transitionto the northwestern Sierras Pampeanas basement uplifts[Mon, 1979; Allmendinger et al., 1983; Allmendinger andGubbels, 1996]. Oblique volcanic belts [Alonso et al., 1984;Jordan and Alonso, 1987; Vandervoort et al., 1995;Kraemer et al., 1999] and faults [Segerstrom and Turner,1972; Alonso, 1992; Riller and Oncken, 2000] transectingthe plateau have been invoked to explain lateral basinclosure. Depending on the poorly constrained growth pat-tern of these basins behind the Eastern Cordillera, theregion of high, smoothed relief may have migrated towardthe barrier or the entire region may have slowly risen[Allmendinger and Gubbels, 1996].[22] Meandering river facies associated with vertebrate

and plant fossils typical of a humid environment show thathighlands to the west drained eastward into an unbrokenbasin during the Paleogene [Alonso, 1992]. Stratigraphicand apatite fission track data suggest that the EasternCordillera and its transition to the northwesternmost exten-sions of the Sierras Pampeanas basement blocks began to beexhumed in Oligocene time [Andriessen and Reutter, 1994;Coutand et al., 2001]. Sediment from proximal uplifts wasdeposited in basins within the Puna. For instance, much ofthe deposition in the Arizaro basin, of the northern Puna,occurred during the Oligocene-middle Miocene in a reverse-fault-bounded basin (Figures 4c and 4d) [Donato, 1987;Coutand et al., 2001]. Growth structures in the upper part ofthe Neogene succession imaged by seismic reflection datafrom the Tres Cruces basin (Figure 4a) [Coutand et al.,2001], suggest that deformation had propagated into thebasin by this time. Flat-lying upper Miocene and Pliocenestrata unconformably overlie these basins [Gangui, 1998;Coutand et al., 2001]. In the Antofalla basin, in the southernPuna, a lower Miocene shift from an eastward drainingforeland setting to westward transport of conglomeratesmarks the creation of an intramontane basin, laterallybounded by volcanic edifices [Kraemer et al., 1999].Paleocurrent and compositional data in 10.7 Ma basalconglomerates of the Campo Arenal basin, east of the

Figure 3. (opposite) Synthesis of data from the Tarim basin and surrounding ranges. (a) Shaded relief map, based onGTOPO30 data. Numbers show representative thermochronologic and paleomagnetic stratigraphic data (Ma). Cenozoicages and older ages record significant exhumation and <5 km of Cenozoic exhumation, respectively. Data from the CentralTian Shan are from Dumitru et al. [2001]; data from the Western Kunlun Shan and southwestern Tian Shan are from Sobeland Dumitru [1997], and, in addition, a study from the Western Tian Shan is from Bullen et al. [2001]. For these studies,each age represents a group of samples. Data from the Western Tian Shan are from Sobel et al. [2000] and E. R. Sobel(unpublished data, 1998–2002). Annotations after the age indicate citation: s, Sobel et al. [2001]; j, Jolivet et al. [2001];b, Bullen et al. [2001]. For magnetic stratigraphy dating of conglomerate sedimentation, with arrow showing direction ofpaleoflow direction, y, Yin et al. [1998]. Faults are modified from Dumitru et al. [2001], Yin et al. [1998], and Jolivet et al.[2001]. (b) Neogene and (c) Paleogene isopach maps based on seismic and borehole data, modified from Ma and Wen[1991]. A–A0 marks location of cross section in Figure 3d. (d) Cross section through the Tarim basin between the WestKunlun Shan and the Tian Shan, modified from Li et al. [1996]. (AAPG copyright 1996, reprinted by permission of theAAPG whose permission is required for further use.)


present southern Puna border, documents high topographyby that time [Strecker et al., 1989]. Farther east, asynchro-nous deformation and uplift after about 7 and 5 Ma in theQuilmes and Aconquija ranges, respectively, establishedadditional precipitation barriers that increased aridificationto the west [Kleinert and Strecker, 2001].[23] In the Puna, the appearance of evaporites dated by

interbedded ashes suggests that by 15 Ma and as early as24 Ma, the Eastern Cordillera formed a significant barrier toeasterly moisture-bearing winds [Vandervoort et al., 1995;Alonso et al., 1991]. The details of this aridification varyspatially. For instance, in the Arizaro basin, evaporites firstoccur at circa 24 Ma (Figure 4c) [Vandervoort et al., 1995].In the Atacama Desert (Figure 4a), the cessation of super-gene alteration and copper-sulfide enrichment between14.7 ± 0.6 and 8.7 ± 0.4 Ma has been used to infer themaximum age of the onset of aridification [Alpers andBrimhall, 1988]. In the Antofalla basin, lacustrine strataand evaporites document hydrologic isolation and aridity byabout 8 Ma (Figure 4a) [Kraemer et al., 1999].[24] Although moisture-bearing winds impinge on the

east facing margin of the Puna, the high topography ofthe Eastern Cordillera and the northwestern extension of theSierras Pampeanas borders the full length of the PunaPlateau, shielding the high plateau from significant amountsof eastwardly derived precipitation (Figure 1b) [WMO,1975; Masek et al., 1994; Hilley and Strecker, 2001]. Asin the Tarim basin, the boundary of the low-relief, internallydrained region approximately coincides with the 400 mm/yrisohyet. In contrast to the Qaidam and Tarim basins, localrelief within the interior of the plateau results from bothvolcanism and thrust- and reverse-fault-block uplifts (com-pare volcano locations in Figure 4a to areas of high localrelief in Figure 1c) [Isacks, 1988]. The linear belt of hightopography that extends for hundreds of kilometers along itslength likely prevents maintenance of the bedrock fluvialsystem, isolating the high plateau from the foreland baselevel.

3. Fluvial Bedrock Incision and Defeat

[25] Observations presented above from the Qaidam,Tarim, and Puna-Altiplano basins suggest that internaldrainage may persist within the interior of an orogen forlong or indefinite periods of time. The conditions that leadto the long-term persistence of internal drainage appear tobe high uplift rates, exposure of resistant rocks, and aridity.This internal drainage prevents mass transfer from orogeninteriors to foreland areas. In this section, we use a theo-retical approach to understand the basic controls that mightlead to the long-term isolation and filling of the basinsdiscussed.[26] Internal drainage results when an integrated fluvial

system is defeated by an uplifted barrier. This defeat mayoccur when the uplift rate of a foreland range exceeds theaggradation rate of the channel traversing the uplifting zone[e.g., Humphrey and Konrad, 2000] (Figure 5). If aggrada-tion is rapid enough to keep pace with the rising topographicbarrier, the headwaters of the fluvial system remainconnected to the stable foreland base level and the slopesof the channels within the uplift zone steepen, thereby accel-erating erosional processes. However, when aggradation

Figure 4. (a) Shaded relief map of the central Andes,based on GTOPO30 data. Locations of Figures 4b and 1bare shown by northern and southern dashed boxes,respectively. Heavy lines crossing the Puna show thelocation of cross section in Figure 4d. Abbreviations areAB, Arizaro Basin; AD, Atacama Desert; TC, Tres Crucesbasin; A, Aconquija; CA, Campo Arenal; H, Humahuaca;QT, Quebrada del Toro; SA, Salar de Antofalla; SQ, SierraQuilmes; VC, Valles Calchaquıes basin. Dots denote activevolcanoes of the Western Cordillera. Faults are modifiedfrom Coutand et al. [2001], McQuarrie and DeCelles[2001], Reutter et al. [1994], and Urreiztiata et al. [1996].(b) Schematic diagram showing the evolution of theAltiplano basin [Horton et al., 2002] (with permission fromSEPM, Society for Sedimentary Geology). Westwardpaleoflow directions in the mid-Paleocene reversed in theEocene-Oligocene due to the construction of the WesternCordillera. Subsequently, converging paleoflow directionsrecord contraction within the Eastern Cordillera that led tobasin closure. (c) Stratigraphic column for the Arizarobasin, from Coutand et al. [2001], modified from Donato[1987]. (d) Composite cross section through the northernPuna Plateau, modified from Coutand et al. [2001].


Figure 4. (continued)


cannot keep pace with the rising barrier, stretches of thechannel within the uplift zone rise faster than their upstreamcounterparts, cutting off the headwaters of the channel andreducing the total discharge in its downstream portions. Asrock uplift within the foreland range continues, both fluvialrelief between the stable base level and the headwaters of therivers, and average channel slopes increase. These increasedslopes accelerate erosional processes, leading to transport ofgreater amounts of material from the uplifting orogen towardboth the stable foreland base level and the filling basin in thehanging wall. Thus a deceleration of the surface uplift withinthe uplifting foreland range will occur over time, accompa-nied by filling of the basin behind it. If the rock uplift persistsindefinitely, the material shed from the range into the basinmay eventually overtop the range and reintegrate the drain-age system.[27] At least two processes may conspire to prevent the

fluvial network from remaining connected indefinitely orreintegrating as the internally drained basin is filled. First, inthe case that aggradation is sufficient to maintain a connec-

tion from the headwaters to the foreland base level, channelslopes within the uplifting zone may exceed those observedfor fluvial processes (this process hereafter referred to as‘‘basin isolation’’). In this case, the elevated slopes withinthe channels at the beginning of the uplifting zone may oversteepen beyond their observed limits, requiring other trans-port processes (e.g., debris flow scour [Sklar and Dietrich,1998]) to erode the channel to maintain continuity of thefluvial system. Second, in the event that the bedrockchannels are initially defeated, the rising foreland upliftmay generate an enormous amount of fluvial relief beforethe rock uplift rate is balanced by erosion. The topographicload of this high-relief area and that of the filling basinbehind it may favor the migration of deformation intoforeland areas [e.g., Willett and Beaumont, 1994; Royden,1996] (this process is hereinafter referred to as ‘‘crustalstrength’’). In both scenarios, persistent disruption of thefluvial system leads to the maintenance of internal drainagein the interior of the orogen.[28] To explore the circumstances that give rise to initial

and persistent disruption of the channel network, weconsider the rate-limiting process of the fluvial system inthe foreland uplift to be the rate at which the river canincise bedrock [e.g., Whipple et al., 1999; Whipple andTucker, 1999; Kirby and Whipple, 2001]. First, we exam-ine the conditions under which the fluvial system travers-ing a bedrock uplift may not aggrade rapidly enough tomaintain a continuous channel network. In this case, thefluvial system will be defeated, leading to temporarydisruption of the channel network. Next, we use thebedrock power law incision model [e.g., Whipple et al.,1999] to evaluate the conditions that may lead to thepersistence of internal drainage within the interior of an

Figure 5. (opposite) Schematic model depiction. Weconsider the temporal response of a channel to uplift ofareas in the foreland. Changes in topography are driven byrock uplift with no horizontal component of displacementfor simplicity. While the model faults are strictly vertical inthis formulation, they serve to approximate the upliftconditions when the vertical component of displacementalong a dipping fault is considered. The basin behind theuplift aggrades in response to the surface uplift, while anupstream migrating knick slope communicates the upliftrate change through the channel. If this migrating knickslope reaches the basin before aggradation is outpaced bythe surface uplift of the foreland uplift zone, the channel isinitially defeated, leading to internal drainage behind therising barrier. We consider the indefinite persistence ofthe continuity of the fluvial network by (1) calculating thesource areas required (Ac) to maintain slopes less than thedebris flow threshold (S = 0.2) within the upstream portionsof the uplift zone (left, bottom) and comparing these to therange of observed basin areas, and (2) calculating theamount of fluvial relief created within the foreland uplift atsteady state (right, bottom) and comparing this value to themaximum total relief observed on Earth. Where the modelvalues exceed the largest observed values, we speculate thatthe fluvial system is outpaced by uplift, leading topermanent defeat of the fluvial system and the persistenceof internal drainage.


orogen by either basin isolation or crustal strength mech-anisms proposed above.

3.1. Model

3.1.1. Initial Defeat of a Channel TraversingForeland Bedrock Uplift[29] First, we examine the temporal development of a

fluvial channel that transects a bedrock uplift to determinethe conditions necessary for the initial isolation of thechannel headwaters from their downstream portions. Inour idealization, we consider a basin with a width Wb thatis truncated downstream by a bedrock uplift of width, Wu

(Figure 5). The bedrock uplift is laterally continuous in ourmodel and so we do not consider outlets for a river deflectedbehind the rising topographic barrier as others have[Humphrey and Konrad, 2000]. Under these conditions,the initial formation of internal drainage takes place whenthe slope of the channel directly behind the foreland upliftslopes back toward the headwaters of the channel.[30] Our modeled channel geometry has two sections: a

lower reach that traverses the bedrock foreland uplift and anupper reach that aggrades in response to uplift of thedownstream portion of the channel (Figure 5). For simplic-ity, we assume that the channel initially slopes toward theforeland with a constant slope, So (Figure 5). Because theupper reach aggrades as sediment is deposited behindthe foreland uplift, fluvial processes within this portion ofthe channel are limited by the rate at which the fluvial systemcan transport sediment downstream. Under these conditions,the sediment flux carried by the channel is the product of thelocal channel slope (dz/dx) and discharge, roughly encapsu-lated in the product of a transport coefficient (Dc) and thecontributing area (A) [e.g., Paola et al., 1992]:

Q ¼ �DcAdz

dx: ð1Þ

In addition, because the channel must aggrade the entirearea behind the rising topographic barrier, the transport ofsediment within this portion of the channel is one-dimensional, and thus the upstream contributing area scalesdirectly with position along the profile, x. Thus

Q ¼ �Dcxdz

dx: ð2Þ

Neglecting any changes in sediment density duringdeposition, the rate of change in elevation of the aggradingportion of the channel is

dz

dt¼ Ub �

dQ

dx; ð3Þ

where Ub is the uplift rate within this section of the basin.By combining equations (2) and (3), we find that the rate ofchange of the channel bed through time is a nonlineardiffusion equation [e.g., Paola et al., 1992]:

dz

dt¼ Ub �

d

dxDcx

dz

dx

� �: ð4Þ

Analytical solutions to equation (4) are difficult to obtain;therefore, following Humphrey and Konrad [2000], weassume that an average value of Dc along the profile

approximates the effects of the scaling of Q with discharge.In making this assumption, we define a new effectiveconstant, D, that represents this average value and scaleswith the total basin width, Wb (D = DcWb [Humphrey andKonrad, 2000]). Under these assumptions, we rewriteequation (4) as

dz

dt¼ Ub þ D

d2z

dx2: ð5Þ

Finally, letting Ub = 0 within the basin, we find that

dz

dt¼ D

d2z

dx2¼ DcWb

d2z

dx2ð6Þ

for the portion of the channel that aggrades behind theforeland uplift.[31] Next, we find a specific solution for equation (6) by

assuming that the basin behind the foreland uplift has aninitial slope of So and the farthest downstream portion ofthis reach of the river (at x = Wb) is displaced at the rate ofuplift of the foreland bedrock uplift, U. Implicit within thisformulation is that the rate of sediment delivery to the basinheadwaters is sufficient to support the initial slope forselected values of Dc and Wb [Humphrey and Konrad,2000]. With these conditions, the channel slope at thetransition between the basin and the foreland uplift maybe written as a function of time [Humphrey and Konrad,2000; Carslaw and Jaeger, 1959]:

St ¼ So � 2U

ffiffiffiffiffiffiffiffiffiffiffiffit

DcWb

r; ð7Þ

where St is the slope of the aggrading channel at the basin-bedrock uplift transition. This channel is defeated when itslopes back toward the basin at the point of the forelanduplift (St � 0). By letting St = 0, we can determine the timeat which uplift of the foreland will back tilt the aggradingchannel, leading to the formation of internal drainage:

t ¼ 1

4S2oU

�2 �DcWbð Þ: ð8Þ

Equation (8) indicates that aggrading channels subjected toindefinite uplift at the basin-bedrock uplift transition willeventually be back tilted and defeated. However, if thesurface uplift of the downstream channel segment ceasesbefore this time, the drainage system will remain integratedindefinitely.[32] While the channel segment upstream of the uplift

zone aggrades in response to the rising barrier, the down-stream segment erodes the bedrock uplift. We idealize therate of change of the channel elevation in this downstreamportion, (dz/dt) to be a power function of the upslope sourcearea and the local slope at each point in the channel[Howard and Kerby, 1983; Howard et al., 1994]:

dz

dt¼ Uðx; tÞ � KAmSn; ð9Þ

where K is a dimensional coefficient of erosion that includesthe effects of rock erodibility, effective precipitation, and


downstream changes in the channel’s hydraulic geometry; Ais the source area (proxy for discharge in the fluvial system[Howard and Kerby, 1983; Howard et al., 1994; Stock andMontgomery, 1999]); S is the bedrock channel gradient; andm and n are constants that may be related to the processes ofbedrock incision at the bed of the channel [Whipple et al.,2000a, 2000b]. To express A in terms of the downstreamprofile position, x, we employ Hack’s law [Hack, 1957], inwhich the source area is a power function of thedownstream profile length:

A ¼ kaxh; ð10Þ

where ka and h are constants that depend on catchmentgeometry. By combining equations (9) and (10), we expressthe rate of change of the channel elevation in terms of thedownstream profile distance, x:

dz

dt¼ Uðx; tÞ � Kkma x

hmSn: ð11Þ

Equation (11) is a kinematic wave equation with a wavespeed of Kka

mxhmSn�1 [Whipple and Tucker, 1999]. In thisformulation of bedrock erosion, uplift of an initially slopingprofile will migrate toward the headwaters of the channel atthis velocity. This uplift signal is communicated upstream asa migrating ‘‘knick slope’’ [Whipple and Tucker, 1999;Humphery and Konrad, 2000]. Once this knick slopereaches the downstream end of the aggrading basin (at x =Wb), surface uplift within the bedrock channel ceases.Therefore, by combining the time it takes for this knickslope to migrate through the uplift zone with equation (8),we can infer the conditions under which the channel willremain continuous through the basin and uplift zone.[33] First, noting that dx = v(x) dt, v(x) equals the

kinematic wave speed of the migrating knick slope, S isequal to the initial channel slope, So, we rearrange to solvefor dt and integrate:

t ¼Z

1

vðxÞ dx ¼Z

�K�1k�ma S1�nx�hm

¼ �K�1k�ma S1�nð1� hmÞ�1ðxð1�hmÞ

s � xð1�hmÞf Þ; ð12Þ

where xs and xf are the downstream and upstream locationsof the uplift zone in our model (Wb + Ws and Wb,respectively; Figure 5). In the limiting case that the surfaceuplift of the downstream bedrock portion of the channelreaches the aggrading portion of the channel at exactly themoment that the slope at the basin’s edge is zero, internaldrainage is prevented. By substituting Wb + Ws for xs andWb for xf in equation (12), setting equations (8) and (12)equal to each other, and rearranging to solve for the uplift(U), bedrock erodibility constant (K), and fluvial transportconstant (Dc), we find the conditions that define thethreshold between internal and external drainage. Aftercombining and rearranging, we obtain

UffiffiffiffiffiffiffiffiffiKDc

p ¼ 1

2S nþ1=2o ðpWbÞ1=2kma ð1� hmÞ1=2

ðWb þWuÞ1�hm �W 1�hmb

h i�1=2: ð13Þ

Equation (13) states that for a given basin and uplift zonegeometry (Wb andWu), basin geometric properties (ka and h),bedrock power law exponents (m and n), and initial channelslope (So), basins that are uplifted and eroded underconditions of U=

ffiffiffiffiffiffiffiffiffiKDc

pgreater and less than those indicated

by equation (13) will lead to internal and external drainage,respectively.3.1.2. Persistence of Internal Drainageby Basin Isolation[34] While drainages may initially be defeated by uplift

of the foreland, eventually, material shed from the back sideof the topographic divide may fill the basin behind therange and reintegrate the fluvial system. To evaluate if thebasins behind the foreland uplift will remain internallydrained indefinitely by our ‘‘basin isolation’’ process, wefirst consider the case where the bedrock channel gradientbecomes larger than that observed within bedrock channels.Sklar and Dietrich [1998] argue that the transition betweendebris flow transport and bedrock fluvial incision occurs ata slope of �0.2 (�11�), although recent studies by Whippleand Meade [2002] argue that this transition may lie at muchsteeper slopes. However, these latter studies may be ham-pered by the quality and spatial resolution of the basetopographic data sets, preventing differentiation of theseprocesses within the areas studied [Stock et al., 2002]. Inthe absence of additional studies using high-resolutiontopographic data clarifying the slope-area relations thatgovern debris flow transport, we have used the estimatesof Sklar and Dietrich [1998]. Portions of the channel whereslopes exceed this threshold value are dominated by debrisflows. While it is conceivable that debris flows maymaintain an integrated fluvial network for short distances,typically, they dominate transport only near the upstreamends of the channel [e.g., Montgemery and Foufoula-Georgiou, 1993]. Therefore, in situations where largeportions of the bedrock fluvial channel within the upliftzone require slopes steeper than 0.2, we expect the fluvialbedrock system to be overwhelmed by debris flows anddefeated indefinitely. We identify this condition in thecontext of equation (11) by examining the case when rockuplift is exactly balanced by erosion. In this case, thechannel geometry remains invariant over time, as it hasreached its steady state profile [Whipple et al., 1999;Whipple, 2001]. First, we let the channel gradient inequation (11) equal that of the onset of debris flows (thisthreshold referred to as Sc) and then rearrange to solve forthe basin area that is required to maintain slopes at thisvalue at the upstream portion of the bedrock uplift:

Ac ¼U

K

� 1=m

S�n=mc ; ð14Þ

where Ac is the basin area required to maintain channelslopes at the upstream end of the uplift zone that are equalto Sc. In this formulation, Ac represents the threshold basinarea that is required to maintain fluvial bedrock incision anda continuous connection between the foreland and theheadwaters of the orogen.3.1.3. Persistence of Internal Drainageby Crustal Strength[35] Another situation that may lead to the isolation of the

bedrock fluvial system from the foreland is the construction


of topography that exceeds the ability of the crust to supportthese high elevations. In this case, the resulting largegravitational stresses favor the migration of deformationto lower areas [Willett and Beaumont, 1994; Royden, 1996].Thus uplift may cease where elevations are high, forcingdeformation, uplift, and fluvial incision toward the marginsof the orogen. In addition, propagation of deformation intothe foreland may reduce precipitation along the margins ofhigh topography, further favoring aridity, reduced streampower, and internal drainage in these areas.[36] In our model of this crustal strength effect, we

simplify the coupled interactions of erosion and deforma-tion [e.g., Willett, 1999] by postulating that uplift will beunsustainable if the relief within the foreland uplift zonebecomes larger than that observed on Earth. That is, if reliefwithin the uplift zone exceeds a critical value, we assumethat uplift within the bedrock portion of the channel willcease, deformation will migrate toward the foreland, and theprocess of defeat and filling will repeat downstream. In thiscase, internally drained basins behind the rising topographicuplift will never fill to the limit of the steady state topo-graphic channel profile and the fluvial system will notreintegrate.[37] To determine the uplift rate and rock erodibility

conditions necessary to produce a specific fluvial relief,we examine the steady state fluvial bedrock profiles withinthe uplift zone. Under these conditions, steady state fluvialrelief within the bedrock uplift may be written as [Whippleet al., 1999]:

Rf ¼U

K

� 1=n

k�m=na 1� hm

n

� �1

L1�hmn

hm

n6¼ 1 ð15aÞ

Rf ¼U

K

� 1=n

k�m=na ln Lð Þ hm

n¼ 1 ð15bÞ

where L is the width of the uplifting zone (L = Wu).Importantly, equation (15) indicates that wider uplift zoneswill produce greater amounts of fluvial relief than those thatare narrow. To define a threshold beyond which the crustalstrength mechanism will force deformation to migrate tolower relief areas, we assign a value for the maximumpossible fluvial relief in the uplifting zone and rearrangeequation (15) to solve for the uplift zone width that isrequired to produce this relief:

WuðmaxÞ ¼ Rc

U

K

� �1=n

km=na 1� hm

n

� " #1�hm=nhm

n6¼ 1 ð16aÞ

WuðmaxÞ ¼ exp Rc

U

K

� �1=n

km=na

" #1�hm=nhm

n¼ 1 ð16bÞ

For given values of U, K, m, n, ka, and h, foreland upliftzones wider and narrower than Wu(max) will produce fluvialrelief greater and less than Rc at steady state. In ourformulation, this would lead to the persistence of uplift

within the foreland uplift zone and migration of uplifttoward areas of low topography, respectively.[38] To separate the effects of crustal thickening from the

basin isolation effect, we do not place a constraint on themaximum bedrock channel gradient. Many numericalsimulations suggest that the maximum relief is related tocrustal thickness [Willett and Beaumont, 1994; Royden,1996]; we consider a maximum value of Rc = 10 km. Thisvalue is over a kilometer more than the largest total reliefobserved on Earth, and so represents a conservative max-imum value for Rf.

3.2. Model Results

3.2.1. Initial Defeat of a Channel TraversingForeland Bedrock Uplift[39] We evaluated the threshold conditions that lead to the

initial defeat of a channel traversing a forelanduplift (Figure5)using equation (13). Inspection of equation (13) reveals thatthere are many factors that may control the initial defeat ofthese channels, including the initial channel slope (So), thebasin geometric properties of the bedrock portion of thechannel (ka and h), the width of the filling basin (Wb) andforeland uplift (Wu), and the power law exponents (m and n).In our calculations, we fix ka = 6.69 and h = 1.67 [Hack,1959; Whipple and Tucker, 1999], and the total channellength (Wb + Wu) to 200 km. We show the effects ofchanging So, Wu, and the power law exponents on thethreshold conditions of U=


pthat lead to initial defeat

of the channel network in Figure 6. In Figures 6a–6c,different combinations of the power law exponents areshown, the x axis shows the initial channel slope, and threedifferent values of Wu are shown as different labeled thresh-olds. Because the total channel length remains constant,increases in Wu result in commensurate decreases in Wb.The y axis of each panel shows the maximum U=


p

value that permits the drainage system to remain integrated,and so values of U=


pabove the threshold lines result

in initial fragmentation of the fluvial network and internaldrainage. To determine a range of U=


pthat is appli-

cable to natural systems when m = 0.4 and n = 1, we assumea range in U and K to be 0.0001 to 0.01 m/yr, and 1 � 10�4

to 1 � 10�7 m1–2m/yr [Stock and Montgomery, 1999],respectively, and fix Dc to be 0.01 m/yr [Humphery andKonrad, 2000; Whipple and Tucker, 2002]. Under theseconditions, U=


pranges from 0.1 mm to 316.2 mm.

Finally, if an order of magnitude decrease in precipitationeffects K and Dc equally, U=


pwill increase by an order

of magnitude; however, if this precipitation decrease effectsonly K, U=


pwill increase by �3.2 times its original

value.[40] We first consider the case where m = 0.4, n = 1

(Figure 6b). As So decreases and Wb increases, smallervalues of U=


pare required to maintain an integrated

drainage system. Values of U=ffiffiffiffiffiffiffiffiffiKDc

prange between 1 �

10�2 mm and 1 � 102 mm for the parameters investigated.As an example, a channel where So = 1 � 10�2, Wu =50 km,Wb = 150 km, K = 5 � 10�6 m1–2m/yr, and Dc = 1 �10�2 m/yr, uplift rates greater and less than 7.4 � 10�4 m/yrwill lead to internal drainage and an integrated fluvialsystem, respectively. An order of magnitude decrease ineffective precipitation may lower this threshold to 7.4 �10�5 m/yr and 2.3 � 10�4 m/yr if K and Dc, and K are


reduced by an order of magnitude, respectively. As Kincreases to 1 � 10�4 m1–2m/yr, the uplift rate thresholdbecomes 3.3 � 10�3 m/yr when all other parameters areheld constant.[41] As the power law exponents decrease and increase

(Figures 6a and 6b, respectively), so does the range inU=


pvalues for the values of So investigated, respec-

tively. When m = 0.4 and n = 1, U=ffiffiffiffiffiffiffiffiffiKDc

pranges from 1 �

10�2 mm to 2 mm. When m = 1 and n = 2, the range of So,Wb, and Wu investigated leads to U=


pvalues between

4 � 10�2 mm and 1 � 104 mm. As Wu increases, thethreshold value of U=


pdecreases. In a qualitative

sense, moderate to high uplift rates, low values of Kresulting from low-erodibility rocks or reduced effectiveprecipitation, and wide foreland uplift zones favor defeat ofthe fluvial system, leading to the formation of internaldrainage behind the uplifting zone.3.2.2. Persistence of Internal Drainage byBasin Isolation[42] In Figure 7 we plot the critical drainage area (Ac in

equation (14)) as a function of uplift rate. In Figures 7a–7c,lines denoting for different rock types are labeled.We plot the

results for effective precipitation rates of 1000 and 100mm/yras solid and dotted lines for each rock type, respectively.Figures 7a–7c show different combinations of the m and npower law exponents in the bedrock incision law. Forreference, we label the size of the Amazon basin (6.1 �106 km2) with an ‘‘A’’ on the right side of Figures 7a and 7b.[43] Importantly, if the value of the bedrock erodibility

coefficient, K, does not vary with the power law exponents,the ability to defeat portions of the bedrock fluvial system bychannel gradient oversteepening and basin isolation is influ-enced by the power law exponent values. However, K mayvary with these exponents and so we emphasize the resultswhere m, n, and K have been calibrated independently atseveral study sites in different rock types (m = 0.4, n = 1,range in K values shown in Table 1 [Stock and Montgomery,1999]). For these calibrated m, n, and K values, metamor-phic/granitoid rocks (K ffi 1 � 10�7 m1–2m/yr) undergoinghigh uplift rates (U = 0.01 m/yr) may require large sourceareas (Ac ffi 1 � 104 km2) for the channel to persist whenuplift rates are high. A reduction of the effective precipita-tion by an order of magnitude results in large changes inthe critical source area Ac. Resistant granitoid rocks subject

Figure 6. Diagrams showing the maximum values of U=ffiffiffiffiffiffiffiffiffiKDc

ppermissible to maintain continuity of

the fluvial system. For uplift zone widths (Wu), basin widths (Wb), basin geometries (ka and h), and initialslopes (So) explored in these models, values of U=


plarger than those shown result in the outpacing

of aggradation by surface uplift within the foreland and the initiation of internal drainage. Figures 6a, 6b,and 6c show the effect of different power law exponents on this threshold.

Figure 7. Diagrams showing the ability of uplift to defeat bedrock fluvial systems by the basin isolationprocess. The critical drainage area (Ac) required to maintain channel gradients less than the threshold ofmass wasting in the landscape is plotted versus uplift rate. Rock types are labeled on each line; 1000 mm/yrand 100 mm/yr of effective precipitation are denoted by solid and dotted lines, respectively. Differentvalues used for and in the power law bedrock incision model are shown in Figures 7a, 7b, and 7c.


to high uplift rates and low effective precipitation mayrequire source areas larger than the entire Amazon basin(Ac > 6 � 106 km2) to maintain gradients less than thedebris flows threshold. Moderately resistant rocks (K = 5 �10�6 m1–2m/yr; roughly equivalent to basalt/metamorphicrocks) undergoing high rock uplift rates (0.01 m/yr) with1000 and 100 mm/yr of effective precipitation require small(1 km2) and moderate (100 km2) source areas, respectively,to maintain channel gradients less than the debris flowthreshold.[44] When m = 1 and n = 2, the fluvial bedrock system

is less sensitive to uplift rate and climate. In these cases,smaller source areas (Ac � 1 � 105 km2) are requiredto maintain the bedrock fluvial system under the mostextreme circumstances. For all values of m and n explored,low rock erodibilities, high uplift rates, and dry climatesare apparently required to defeat bedrock channels by thismechanism.3.2.3. Persistence of Internal Drainageby Crustal Strength[45] We investigate the effects of the crustal strength

mechanism of bedrock defeat in Figure 8. In Figure 8 weplot the uplift zone width required to produce Rc = 10 kmfor different uplift rates, precipitation rates, rock typeerodibilities, and values of m and n. Uplift zones largerthan the maximum uplift zone width (Wu(max) in equations(16a) and (16b)) produce maximum fluvial relief greaterthan Rc; therefore, in our formulation, these conditions buildsufficient gravitational potential energy to force deformationand uplift elsewhere and prohibit the development of steadystate topography. The three different rock types are plottedin each panel; the effects of 1000 mm/yr and 100 mm/yr of

effective precipitation are denoted by solid and dotted lines,respectively. Figures 8a–8c show different combinations ofthe fluvial bedrock incision model power law exponents mand n. For reference, we show 10 km and 100 km wideuplift zones with dashed lines.[46] When m = 0.4, n = 1, and K = 1 � 10�7 m1–2m/yr

(roughly equivalent to granitoid rocks), fluvial relief inexcess of 10 km is produced at steady state for the upliftrates investigated. Conversely, when K = 1� 10�4 m1–2m/yr(mudstones/volcaniclastic rocks), <10 km of fluvial reliefis built for even the highest uplift rates (0.01 m/yr)investigated. Reduced effective precipitation (100 mm/yr)for these rocks produces 10 km of fluvial relief atmoderate to high (>0.003 m/yr) uplift rates and reasonable(10–100 km) uplift zone widths. K values between thesetwo extreme end-member rock types lead to thresholds thatfall within the range of uplift rates investigated. For exam-ple, when K = 5 � 10�6 m1–2m/yr (roughly equivalentto bedrock fluvial erosion of basalt flows in a humidenvironment), fluvial relief exceeds 10 km when uplift rates>0.002 mm/yr are sustained indefinitely. Importantly,decreases in K within this range of rock types due to lowereffective precipitation may cause these moderate erodibilityrock types to accrue large amounts of fluvial relief, poten-tially defeating the bedrock channel due to the crustalstrength mechanism proposed.[47] When m and n are small, and K remains constant with

changing m and n,Wu(max) is extremely sensitive to U and K.In particular, uplift zones must be extremely small (10�2 km)to maintain steady state fluvial relief of less than 10 km whenuplift rates are low (0.0001 m/yr) and resistant rocks areexposed. An order of magnitude decrease in K requires

Table 1. Rock Type and Corresponding Values of K for Approximately 1000 mm/yr of Effective Precipitation

Class K, m1 – 2m/yr Reference

Mudstones and volcaniclastics 1 � 10�4 Stock and Montgomery [1999],Whipple et al. [2001], andKirby and Whipple [2001]

Basalt flows and metamorphics(slate and gneissic granitoids)

1 � 10�6 Stock and Montgomery [1999]

Granitoid rocks and metamorphics(granitoids, sandstones, and limestones)

1 � 10�7 Stock and Montgomery [1999]

a b c

Figure 8. Diagrams showing ability of uplift to defeat bedrock fluvial systems by the crustal strengthprocess. The maximum uplift zone width (LcWu(max)) required to create fluvial relief equal to 10 km isplotted versus uplift rate. Rock types are labeled on each line; 1000 mm/yr and 100 mm/yr of effectiveprecipitation are denoted by solid and dotted lines, respectively. Different values used for m and n in thepower law bedrock incision model are shown in Figures 8a, 8b, and 8c.


Wu(max) = 1� 10�18 km. K values of 5� 10�6 m1–2m/yr alsoproduce topography in excess of Rc for uplift rates greaterthan �0.0005 m/yr, and an order of magnitude decrease in Kresults in relief greater than Rc for all uplift rates investigated.Finally, low K values (1 � 10�4 m1–2m/yr, associated withmudstones/volcaniclastic rocks) fail to build relief in excessof Rc for all uplift rates investigated when Wu = 10 km.When K decreases an order of magnitude, uplift rates >0.0009 m/yr produce fluvial relief greater than Rc whenWu = 10 km.[48] Finally, large m and n values result in steady state

fluvial relief less than Rc for most U and K values whenWu � 10 km. However, when K = 1 � 10�7 m1–2m/yr andthere is an order of magnitude decrease in effective precip-itation, narrow (Wu = 10 km) uplift zone widths are requiredto produce fluvial relief less than Rc. Therefore, even whenm and n are large, high uplift rates, low rock erodibilities,and low effective precipitation may produce fluvial reliefthat exceeds the critical value imposed by crustal strength.In general, a relatively wide range of realistic geologic rates,uplift zone widths, and bedrock incision processes mayproduce fluvial relief in excess of 10 km. These conditionsmay lead to sustained defeat of the areas of the bedrockfluvial system above this critical relief and the establishmentof internal drainage in such areas.

4. Discussion

4.1. Comparison of Model ResultsWith Other Landscape Development Models

[49] Our models provide a means of estimating theconditions required to create and maintain internal drainageand comparing these conditions with those observed withinthe internally drained Tarim, Qaidam, and Puna-Altiplanobasins. It is important to acknowledge that the fluvialbedrock incision models employed suffer from severalimportant shortcomings. First, incision of fluvial systemsinto bedrock in many situations may not be as simple as thatimplied by the power law relations expressed in the bedrockpower law incision model. For example, sediment deliveredto channels via hillslope processes may be important agentsin abrading the channel bed [e.g., Sklar and Dietrich, 1998,2001]. Consequently, the decoupling between hillslope andfluvial response implied by the bedrock power law incisionmodel may neglect this potentially important factor.[50] Second, even within the context of the bedrock

power law incision model, important uncertainties exist inthe model parameters of equation (11). For example, Kincludes the units of m [Whipple and Tucker, 1999], and soits value likely scales with the power law exponents.However, the relationship between the exponents and K isunknown [e.g., Sklar and Dietrich, 1998]. K incorporatesthe effects of allometric changes in channel geometry withdischarge, sediment flux entering the channel, the relationbetween effective discharge and drainage basin area, and theresistance of bedrock to fluvial erosion. Most of thesefactors likely change with m, but to date, no comprehensivestudy has been conducted that defines this scaling relation-ship. Contrary to the work of others [e.g., Sklar andDietrich, 1998; Whipple and Tucker, 1999], we do not scaleK by 1/n in our models to maintain a constant topographicform for changing n, as it is not apparent that the unknown

scaling law of K and m supports this approach. Instead, wefixed K to values determined by Stock and Montgomery[1999] for n = 1 and m = 0.4, and emphasize our results inthe context of these calibrated values. If increasing powerlaw exponent values reduce the value of K, our modelsoverestimate and underestimate the voracity of erosionwhen the exponents are high and low, respectively. Asnew scaling laws relating K to the exponents emerge, therange of K in our model results, when n = 2/3, m = 1/3 andn = 5/2, m = 5/4, may be readjusted. While these scalingproblems lead us to view our conclusions based on theseuncalibrated power law exponent values as preliminary andsubject to change upon further work, all studies that strive tounderstand orogen-scale relief using the power law bedrockincision model suffer from this deficiency. Also, the valueof K may not directly correspond to rock type, but also maybe strongly influenced by the degree of fracturing andstructural damage the eroding rocks have sustained[Whipple et al., 2000b]. K values applicable at the orogenscale likely incorporate the lithologic and structural heteroge-neity encounteredwithin the range-traversing fluvial systems.[51] Third, we simulate the effect of an order of magni-

tude precipitation in our model by reducing K an equivalentamount. It is important to point out that K depends on theeffective discharge during an event of unspecified magni-tude and frequency [Sklar and Dietrich, 1998]. Therefore,while we simplify the effect of changing precipitation as alinear change in K, it is possible that this relation is not assimple as our analysis implies. For example, reducedprecipitation may lead to less frequent, but larger magnituderainfall events whose net effect may increase transportefficiency [Molnar, 2001]. In addition, changes in effectivedischarge that result from decreases in precipitation maycause the relations between channel width and basin area tochange, potentially exacerbating or buffering the change inK that results from the decreased rainfall. While theseuncertainties are important to acknowledge, the underlyingrelations between effective discharge and K are unknown,so we opted not to consider complicated relationshipsbetween these two factors in our models.[52] Fourth, our models of maintenance of bedrock chan-

nel defeat by the crustal strength mechanism do not explic-itly couple the geomorphic and kinematic evolution of anorogen as in other modeling studies [e.g., Willett, 1999;Willett and Brandon, 2002]. However, our analysis providestwo important advantages to these more complex coupledtectonic-geomorphic numerical models: (1) our formula-tions explicitly allow the defeat of the fluvial bedrockchannels, whereas previous numerical models assume thatthe resulting closed basins will be recaptured, thus main-taining the fluvial network; and (2) a range of geomorphicprocesses represented by different combinations of and maybe explored in our models. In coupled orogen-scale tectonic-geomorphic models, in contrast, these values are typicallychosen to be m = n = 1 [e.g., Willett, 1999]. Our results andthose of others [Whipple and Tucker, 1999] show that theresponse of the bedrock fluvial system is highly dependenton these values. Neglecting these factors may cause thecoupled geodynamic erosion models to artificially preservean integrated fluvial system across the orogen. While adrainage divide may move across the orogen in thesemodels, loss of source area on one side of the drainage


divide is compensated by a corresponding increase in areaon the opposite side. Importantly, the establishment ofinternal drainage decreases the source area of fluvial bedrocksystems on both sides of the orogen. Thus coupled modelsmay overestimate the voracity of erosion in real landscapes,fundamentally changing the relationship between conver-gence, erosion, and topographic construction.[53] Finally, our geomorphic model assumes that the

process of bedrock incision controls relief at the scale ofan orogen. We do not explicitly consider the potentiallyimportant effects of sediment flux on incision rates in ourmodel [e.g., Sklar and Dietrich, 1998, 2001; Whipple andTucker, 2002], which may decelerate incision rates bysediment abrasion when there is not enough sediment toabrade the channel bed or too large a sediment flux thatreduces incision rates due to bed armoring. Both sedimentflux controls on incision rates (leading to mixed bedrock-alluvial channels) and other important erosional processes,such as glacial erosion, may exert important controls on therelief of the orogen. Indeed, the upper headwaters of someof the closed basins discussed above (Tian Shan, QilianShan, Puna-Altiplano Plateau) are currently or have beenglaciated during the Pleistocene [e.g., Peltzer et al., 1988;Haselton et al., 2002]. In these circumstances, total orogenrelief may be limited by this process, rather than fluvialbedrock incision [e.g., Whipple et al., 1999]. Finally,regardless of the efficiency of glacial erosion, fluvialbedrock incision must still be sufficient to maintain bedrockchannels in lower elevation areas to prevent internal drain-age from developing. Many of the arid, low-erodibilitymodels show that even the lower sections of the drainagenetwork may be susceptible to defeat by the basin isolationprocess when m and n are small (Figure 7). Thus fluvialbedrock incision models likely provide a conservativebound on the conditions necessary to create internal drain-age.[54] Figure 8 indicates that there is always an uplift zone

width that is sufficiently small to produce steady state reliefbelow the critical value. Uplift zones in our study areas arelikely tens to hundreds of kilometers wide. While our modelallows any uplift zone width, it is difficult to imagine thatsmall uplift zones (<1 km) are of regional significance inactively uplifting orogens. Indeed, some of the stable upliftzone widths are unrealistically small (10�38 km). Therefore,while our choice of reasonable uplift zone widths between10 and 100 km is somewhat subjective, they are likely fairvalues relative to the total range of uplift zone widthsproduced by our calculations. Also, it is important to notethat the smallest uplift zone widths produced in the modellead to bedrock channel slopes greatly in excess of thedebris flow threshold slope angle. We intentionally allowedthese steep slopes to occur to dissociate the effects of ourbasin isolation and crustal strength fluvial bedrock channeldefeat processes. In reality, these steep slopes would lead tobedrock channel defeat by the basin isolation process longbefore the critical bedrock fluvial relief was attained.

4.2. Formation and Persistence of InternallyDrained Basins

[55] The Qaidam and Puna–Altiplano basins formed aswedge–top basins while the larger Tarim basin comprisescoalesced wedge–top and foreland basin systems (in the

sense of DeCelles and Giles [1996]) bounded by activelygrowing anticlines and faults, similar to the scenariodepicted in Figure 9. Such basins can be dammed bystructural features with far greater relief than a flexurallycontrolled forebulge [DeCelles and Giles, 1996]. As thechannels within the uplifts at the basin margins are defeatedby a combination of aridity, exposure of resistant rocks, andhigh uplift rates, a positive feedback likely develops inwhich the loss of discharge from the catchment area of thebasin allows rapid construction of fluvial relief. The over-filled basins located behind these rapidly rising barriers mayoften contain thicker sediment packages than might bepredicted in flexural foreland basins [Flemings and Jordan,1989]. This accumulation of mass and subsequent advanceof the deformation front may transform a wedge–top basininto a tectonically inactive piggyback basin. Such a scenariomay be recorded by flat–lying sediments unconformablyoverlying strata related to fault growth, such as in the lateTertiary reverse–fault bounded basins of the northern Puna[e.g., Gangui, 1998; Coutand et al., 2001] and the Qaidambasin [Song and Wang, 1993]. These examples show thatwedge–top basins can be long–lasting and may store largequantities of sediment if the newly formed barrier is notbreached [e.g., Inman and Jenkins, 1999; Collier et al.,2000; Metivier et al., 1998]. Eventually, basins may fillabove the internal spill point, causing a series of internallydrained basins to coalesce. In Tibet, these overfilled basinsare topographically indistinguishable from the earlierformed plateau [e.g., Metivier et al., 1998].[56] The essential process leading to the creation and

maintenance of internal drainage in these areas is the defeatof fluvial outlets around the margins of the basin. Ourmodels of initial channel defeat indicate that aggradationwill not be sufficient to maintain a fluvial connection withthe foreland base level when uplift rates are low to moder-ate, rock erodibilities are moderate to small, and if there islow effective precipitation. In fact, even when rock erodi-bilities are high (1 � 10�4), uplift zones are narrow (10 km),and the initial channel slope is relatively steep (10�2), onlyuplift rates of �3 mm/yr within the foreland uplift can betolerated before aggradation is outpaced by surface uplift.Although we fixed the total fluvial length to 200 km, thequalitative relations reported are robust for shorter fluvialsystems. In addition, reduction in effective precipitationmay lead to decreased delivery of sediment to the upstreamend of the channel from the hillslopes. While our modelformulation does not directly treat the effect of reducedsediment input at the channel’s upstream end, but insteadincludes this in So, we might expect a reduction in effectiveprecipitation to lead to decreases in the equilibrium initialslope. In these cases, lower precipitation may favor bedrockdefeat by reduced initial slopes in addition to a reduction inK and possibly Dc. Therefore, in dry climates, we expect allbut the largest fluvial systems to be initially defeated. Incases where the rock types exposed are especially difficultto erode, we expect all drainages, regardless of their size, tobe defeated, resulting in internal drainage and infilling ofthe basin behind the foreland uplift. To prevent internaldrainage conditions by our basin isolation mechanism underhigh uplift rates and arid climates, extremely large basinareas are required. Finally, for typical uplift zone widths, anenormous amount of fluvial relief (>10 km) is created when


uplift rates are moderate to high, rock types are resistant tobedrock erosion, and climates are arid. By our crustalstrength mechanism, these sets of rates favor the migrationof deformation to areas of low elevation.[57] All of these model observations agree well with the

conditions observed within and around the internallydrained basins reviewed. For example, in northeast Tibet,high uplift and shortening rates [Meyer et al., 1998], lowprecipitation (<400 mm/yr; Figure 1a) and an orographicbarrier broad enough to resist breaching have allowedclosed basins to grow during the late Cenozoic. Likewise,the Tarim basin and Puna-Altiplano Plateau are boundedby ranges dominated by pre-Mesozoic sediments, meta-morphic, and crystalline lithologies, with high relief and

low mean annual precipitation. These basins developed inareas of significant crustal shortening behind orographicbarriers, where limited precipitation prevents fluvial inci-sion from keeping pace with tectonic uplift. Such anorographic rain shadow may be caused by significantgrowth of a frontal range that shields the older, still risingranges from precipitation and protects them from fluvialincision. Alternatively, a reverse-fault-bounded barrier rangemight grow far in front of the main thrust belt where itslocation is controlled by preexisting crustal heterogeneities(e.g., the northern portion of the Argentine Eastern Cordil-lera and the Sierras Pampeanas [Allmendinger et al., 1983]or the Cenozoic Tian Shan and Qilian Shan [Burtman, 1980;Meyer et al., 1998]). In addition, the windward boundaries of

Figure 9. Schematic model of the creation of internally drained wedge-top basins. (top) Stage 1,existing plateau with ongoing crustal shortening. Frontal range is not high enough to create significantrain shadow. Basin B is filled with meandering fluvial and lacustrine strata. (middle) Stage 2, topographicload of high topography may cause deformation to propagate into the foreland. Frontal ranges attainsufficient elevation to create an orographic barrier, reducing precipitation in basin B. Water starved riversin basin B are defeated as incision is overwhelmed by rock uplift. Basins A and B become internallydrained; depocenters include playa deposits, while basin margins are dominated by coarse alluvial fansextending into braided fluvial deposits. (bottom) Stage 3 Internally drained basin fills beyond thetectonically controlled basin margin. Basins A and B coalesce. Lateral basin closure (not shown) canoccur due to transpression or volcanism.


these internally drained basins are oriented at high angles toprevailing moisture-bearing winds. In contrast to theseexamples, the structural setting of southeastern Tibetincludes predominantly north-northeast trending ranges par-allel to the dominant moisture-bearing winds; here, theplateau has a diffuse topographic boundary [Fielding etal., 1994] (Figure 1a) and heavy monsoon rains from thesoutheast readily penetrate far into this portion of the plateauand apparently prevent the formation of closed basins. Thiswetter portion of the high plateau constitutes greater localrelief than themore arid, internally drained sectors (Figure1a).Similarly, the late Cenozoic Sierras Pampeanas basementuplifts (27–33�S) in the foreland of the Argentine Andes[e.g., Jordan and Allmendinger, 1986] and the Cretaceousto Eocene Laramide uplift province of North America [e.g.,Gries and Dyer, 1985] may represent such settings. Overlong periods of time; however, these basins may eventuallyfill and be subsequently reintegrated with the foreland baselevel as the spill point of the basin is exceeded. In contrast,the high Tibetan Plateau and Puna-Altiplano Plateau havenearly completely filled, yet fail to be reintegrated with theregional base level, implying that transient basin fillingeffects cannot explain their persistence. Importantly, failureof these basins to reintegrate with the external fluvial systemstrengthens the idea that other mechanisms (i.e., basinisolation and crustal strength) control the persistence ofthese features.[58] Meyer et al. [1998] posit that such basins are closed

primarily because of rapid faulting. In contrast to the highplateau and Tarim basin, landscapes in humid climates suchas in the Himalaya support major rivers that traverseresistant bedrock lithologies and remain integrated despitehigh uplift rates. This suggests that high uplift rates and lowrock erodibilities are insufficient to defeat bedrock channelswhere there is abundant precipitation. For instance, short-ening and uplift rates in the Himalaya are similar to those innortheastern Tibet [Bilham et al., 1997; Meyer et al., 1998].Rock types in both areas are also similar. In contrast, theHimalaya receives 10 to 20 times more precipitation thanthe Qaidam basin [WMO, 1981]. The abrupt decrease inprecipitation across the crest of the Himalaya lies well southof the transition from internal to foreland-integrated drain-age (Figure 1a). In this case, arid areas in close proximity tolarge orographic gradients may represent transitional partsof the landscape in which efficient headward erosion allowsexternal drainage to extend into the low-precipitation high-lands south of the internally drained Tibetan Plateau.Indeed, this transition between external and internal drain-age at or near large orographic gradients is observed alongthe margins of several of the study areas. For example, thesole fluvial outlet from Northeast Tibet is the Huang He,which drains an area roughly 25% the size of the internallydrained portion of the plateau (Figure 1a) [Fielding et al.,1994]. This river was temporarily dammed in the Gong Hebasin, resulting in 1200 m of Quaternary deposits [Metivieret al., 1998] (Figures 1a and 2a). Subsequently, the river hasbroken through this natural dam and downcut through atleast 600 m of its own fill, as well as incising a steepbedrock gorge downstream. Similarly, along the easternmargin of the Argentine Puna, deposits within the intra-montane Quebrada del Toro, Humahuaca, and Valles Cal-chaquıes basins (Figures 1b and 4a) record intermittent

basin closure and reintegration with the foreland fluvialsystem [Strecker et al., 2000, 2002]. Since the Pliocene,these basins have experienced multiple cycles of closureand filling, followed by downcutting and sediment evacu-ation. It is likely that these basins represent transitionalareas of the landscape in which large rainfall gradients resultin effective headward erosion, drainage capture, and ulti-mately basin exhumation [Strecker et al., 2002]. In thesecases, the transiently closed basins may be close to thetectonic and climatic conditions necessary to maintaininternal drainage. The filling and reexhumation of marginalbasins may reflect oscillations in climate or uplift rates thatare superposed on the long-term rise of the topography andthe resulting reduction in precipitation along the leewardslopes of the landscape [Strecker et al., 2000].[59] Our models suggest that the conditions under which

bedrock channels are defeated may vary with the value of inthe bedrock power law incision model [Whipple and Tucker,1999; Whipple et al., 2000a; Kirby and Whipple, 2001] if Kis independent of the power law exponents. Processes suchas hydraulic lifting of channel blocks in highly fracturedenvironments may result in low values of n (2/3) [Whippleet al., 2000a], leading to the defeat of bedrock channels ifrocks resistant to erosion and aridity exist. When cavitationand abrasion(n = 7/2 and n = 5/2, respectively [Whipple etal., 2000a]) are the dominant erosional processes, bedrockchannels may be difficult to defeat relative to other types ofbed erosion. The processes acting at the channel bed mayvary depending on the rock types being eroded or theamount of structural damage the rocks have sustained[Whipple et al., 2000b]. In active orogens, sustained crustalshortening and exhumation are likely to expose deeperstructural levels and hence more resistant lithologies withtime. Thus the presence of certain rock types and the effectsof a complex structural history may also exert a strongcontrol on the sensitivity of a bedrock channel to defeat.Finally, high marginal topography may shield the head-waters of the bedrock fluvial system from large amounts ofprecipitation, encouraging channel defeat.

4.3. Tectonic, Climatic, and Landscape Responsesto Internal Drainage

[60] The persistence of internal drainage may affect rela-tionships between landscape relief, uplift, and precipitation.Whipple et al. [1999] postulated that all else being equal,decreasing precipitation results in greater fluvial relief, assteeper slopes are required to evacuate uplifted material fromthe bedrock fluvial system. In addition, they argued thatrelief in mountain belts is controlled by the fluvial bedrockincision process. This is likely the case in many activemountain belts where the bedrock fluvial systems are con-trolled by some regional base level (e.g., sea level for Taiwanand the Olympic Mountains in North America). However,where internal drainage and bedrock channel defeat discon-nect this fluvial system from a regional base level, therelationship between landscape relief and precipitation isless clear. Channels connected to closed basins must even-tually aggrade as the basin fills and base level continuallyrises. For example, along the Puna Plateau, high and lowlandscape relief apparently is associated with high precipi-tation on the windward flanks of the plateau and the drycentral interior of the plateau, respectively. Within the


bedrock fluvial system there is an increase in the landscaperelief with decreasing precipitation; however, a regionallandscape view that includes the internally drained PunaPlateau and other intramontane sectors indicates that lowprecipitation clearly coincides with low relief [Hilley andStrecker, 2001]. The negative relationship between fluvialrelief and precipitation is predicted by the bedrock incisionmodel [Whipple et al., 1999]; however, the positive correla-tion on the plateau apparently arises because the internallydrained basins continually aggrade and reduce relief asorographic effects at the plateau margins maintain reducedprecipitation. Therefore, while the predicted negative corre-lations may hold within the bedrock channels, when largeportions of an orogen are internally drained, this relationshipmay be convoluted and may not necessarily reflect thatpredicted by models of fluvial bedrock incision.[61] The model results of others [e.g., Willett and

Beaumont, 1994; Royden, 1996] suggest that the formationof internal drainage and the resultant storage of largevolumes of sediment in wedge-top basins may exert animportant control on the kinematics of deformation in anorogen. The accumulation of kilometers of sediment in ahigh-elevation basin such as the Altiplano or Qaidamincreases gravitational potential energy and may force thelocus of deformation to shift toward the margins of theorogen [Willett and Beaumont, 1994; Royden, 1996; Willett,1999]. Even if the fluvial systems were to eventuallyreintegrate, the time required to aggrade behind the upliftingranges and incise through the low-erodibility rocks may belonger than the duration of contraction within the orogen.Thus these mass storage areas may constitute persistentfeatures of an orogen. This may cause the erosional systemto be overwhelmed by tectonic deformation (e.g., the Puna-Altiplano [Montgomery et al., 2001]), and the internallydrained sectors of the orogen to continually expand outwardas deformation moves away from the areas of significantcrustal thickening. Decreased erosional efficiency due to anoverall reduction of erosion and greater continentality hasbeen invoked to explain the Miocene widening of theEuropean Alps [Schlunegger and Willett, 1999; Schluneggerand Simpson, 2002] and along-strike differences in the thin-skinned eastern Bolivian Andes [Horton, 1999]. In these twoexamples, orogen structure results from a coupled responseof the erosional, tectonic, and topographic properties of themountain belt.[62] In contrast, the areas examined in this paper have

crossed the threshold of fluvial channel defeat. In thesecases, internal drainage prevents the erosional export ofmass from the orogen, decoupling erosional and tectonicprocesses. This decoupling may complicate the relationsexplored in recent geodynamic models linking tectonic anderosional processes, and topography. In these models [e.g.,Willett, 1999], erosional mass removal accelerates as chan-nel slopes become steeper and drainage area increases untila steady state is reached where material uplifted by crustalshortening is exactly balanced by removal through surfaceprocesses [Willett and Brandon, 2002]. These studies pro-vide valuable insights into orogenic processes in the humidregions commonly selected for comparison with modelresults [e.g., Taiwan, the New Zealand South Alps, andthe Olympic Mountains; Willett and Brandon, 2002]. Incontrast, where internally drained basins persist, widening

of an orogen does not necessarily increase the erosivecapacity at its margins as drainage area is continuallyreduced by bedrock channel defeat. In this case, massstorage in the arid interior of the orogen prevents a steadystate condition from developing. Therefore, under condi-tions where the fluvial channel defeat threshold is sur-passed, the creation and persistence of internally drainedbasins may profoundly influence the structure of theseorogens.

5. Conclusions

[63] 1. The northeastern margin of the Tibetan Plateau(Qaidam basin), the Tarim basin, and Puna-Altiplano Pla-teau have remained internally drained since the Pliocene orMiocene. It is likely that the high Tibetan Plateau has beeninternally drained for a longer period. The margins of eachof these internally drained basins are characterized byactively uplifting ranges, low-erodibility rock types, andlow mean annual precipitation. Fission track ages along theQilian Shan, Altyn Tagh, and Tian Shan mountains suggestthat topography along the margins of the Tarim and Qaidambasins rose in the Miocene and have undergone only slow tomoderate exhumation since that time. Similar conditionsmay apply to the eastern border of the Andean Puna Plateau.Windward of the internal drainage divide of the Puna,basins record cyclic filling and reexhumation during thePlio-Pleistocene as bedrock channel outlets are defeated andreintegrated with regional base level.[64] 2. Models of the defeat of bedrock channels confirm

field observations suggesting that low-erodibility rocks,moderate to high uplift rates, and low precipitation are allrequired to defeat channels traversing orogens. The suscep-tibility of a bedrock channel to defeat is highly sensitive tothe power law exponents in the bedrock incision equation,and hence the processes acting at the channel bed. Largeand small values of n inhibit and favor defeat of bedrockchannels, respectively.[65] 3. At the scale of an orogen, internal drainage

apparently removes erosional capacity from the system.While mass may be redistributed within the interior of theorogen, reduction of erosional capacity within channelseroding the margins inevitably results from the establish-ment of internal drainage. Coupled tectonic-landscapedevelopment models that prevent the development ofinternal drainage may overestimate the voracity of erosionin regimes that favor internal drainage.[66] 4. Establishment of internal drainage likely stores

mass within the interior of an orogen. Where this massstorage is large, deformation may be driven to exterior areasas a result of increased gravitational potential. The inabilityof the fluvial system to evacuate material from orogeninteriors may thus prevent development of an erosionalsteady state in which uplifted material is fully removedfrom the orogen by erosion.

[67] Acknowledgments. Eric Fielding kindly provided digitizedWMO precipitation data for the Andes. We are grateful to the DeutscheForschungsgemeinschaft for funding SFB 267, ‘‘Deformation Processes inthe Andes’’. G.E.H. thanks the Alexander von Humboldt Foundation andthe IQN Potsdam for support of his postdoctoral research at the UniversitatPotsdam. Brian Horton and Isabelle Coutand graciously provided versionsof the components of Figures 4b–4d. Kirk Haselton contributed to an


earlier version of this manuscript; this was improved by constructivecomments by Teresa Jordan, Jeff Masek, and an anonymous reviewer.The present manuscript benefited from thorough reviews by Kelin Whipple,Frank Pazzaglia, and Gregory Hancock.

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