Low internal relief, aridity, and internal drainage characterize the Puna-Altiplano Plateau and the Tibetan Plateau and the Tarim basin. Structurally, these areas are reverse fault bounded terrains with intervening wedge-top basins that store thick accumulations of sediment for millions of years. Orographic barriers along the margins of these basins are oriented normal to moisture bearing winds, resulting in regional aridity. The combination of this aridity, rapid shortening and uplift rates, and resistant exposed lithologies coincides with the location of these internally drained basins. We hypothesize that these large, internally drained areas persist indefinitely when uplift overwhelms the fluvial systems and defeats the channel network. To test this hypothesis, we developed models of channel defeat to examine the threshold conditions required to fragment the channel network. The results of these models suggest that low-erodibility rocks, moderate to high uplift rates, and low precipitation favor defeat of orogen-traversing channels. Most coupled tectonic-landscape development models prevent the development of internal drainage and so may overestimate the voracity of erosion in regimes that favor internal drainage, profoundly influencing predicted orogenic growth patterns.
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 Long-lasting, internally drained basins often constitute a first-order geomorphic feature of contractional tectonic settings. In some cases, these have apparently existed for millions of years and store large sediment volumes [e.g., Einsele and Hinderer, 1997; Métivier et al., 1998; Horton et al., 2002]. The Puna-Altiplano of the central Andes and the Tibetan Plateau constitute the largest intraorogenic plateaus on Earth and host a complex amalgamation of internally drained basins and intervening ranges where the transition from formerly open to closed drainage can be studied [e.g., Isacks, 1988; Alonso et al., 1991; Alonso, 1992; Horton and DeCelles, 1997; Tapponnier and Molnar, 1979; Tapponnier et al., 2001]. Similarly, the Tarim basin of China comprises several late Cenozoic contractile basins that have coalesced to form a single immense internally drained basin [e.g., Li et al., 1996]. Structurally, these regions are thrust or reverse fault bounded terrains with intervening basins; the latter are often wedge-top basins. Another unifying characteristic of these structural provinces is that orographic barriers along their basin margins are oriented normal to moisture bearing winds, resulting in pronounced regional aridity (Figure 1).
 Following the original hypothesis of Gilbert , we propose that formation of internal drainage in contractional regions results from the outpacing of incision by tectonic uplift, leading to fragmentation and defeat of their fluvial systems, and subsequent coalescence of the resulting internally drained basins. Whether rivers remain connected to a constant base level in the foreland or are defeated in favor of internal drainage depends on interactions among stream power, upstream deposition, sediment flux, bedrock resistance, uplift rate, and range width [e.g., Burbank et al., 1996; Whipple and Tucker, 1999]. Successive marginal uplifts can lead to or enhance aridification, thereby aiding the formation or persistence of closed basins. The resulting internally drained wedge-top basins can fill beyond the structurally controlled topographic basin margins, permitting the storage of significant quantities of sediment. Some landscape development models [e.g., Willett, 1999] suggest that such basins are transient features that are eventually reintegrated into the fluvial system, forcing the drainage network to remain connected to an approximately constant, regional base level. However, the existence and persistence of large basins over millions of years suggests that the fluvial systems of the orogen have been disconnected from a steady base level over similar timescales as the development of the orogen. These long-lasting internally drained basins in arid environments show that the orogen is far from a flux or topographic steady state [e.g., Willett and Brandon, 2002]; thus, they offer an opportunity to test surface process models that should reflect the evolution of orogenic features.
 In the first part of this paper, we review the morphology, climate, and geologic and tectonic history of the Tibetan Plateau, the Tarim basin, and the Puna-Altiplano Plateau. In particular, we highlight the timing of basin aridification and uplift at the basin margins, exposure of different rock types, and the onset of internal drainage. We emphasize that it is unlikely that fluvial systems have been integrated with a regional, constant base level for millions of years. As might be expected, high uplift rates and exposure of resistant lithologies coincide with arid environments within the interior of these regions. Second, we use formulations of fluvial incision [Howard and Kerby, 1983; Whipple et al., 1999; Whipple and Tucker, 1999; Paola et al., 1992] to estimate the threshold conditions of uplift, climate, and rock erodibility that lead to defeat of the fluvial channels and establishment of internal drainage. From these models, we find that sustained moderate to high uplift rates, moderate to low rock erodibilities, and dry climates eventually lead to the establishment of internal drainage. Finally, we extrapolate the theoretical and field-based modeling results 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 to remove mass from uplifting, internally drained basins stores gravitational potential energy in the crust, favoring migration of deformation to lower-elevation areas. This suggests that inefficient mass transfer by fluvial erosion may influence the lateral growth of orogens.
2. Geology, Morphology, and Climate of the Tibetan Plateau, Tarim Basin, and Puna-Altiplano Plateau
2.1. Northeastern Tibetan Plateau Margin
 The transpressive tectonic regime in northeast Tibet has resulted in crustal-scale thrusts propagating to the northeast [Tapponnier et al., 1990]; the northern portion of this system uplifted the reverse and thrust-fault bounded blocks of the ∼700 km long Qilian Shan (Figures 2a and 2b). Northeast propagation of deformation and uplift are kinematically linked to left-lateral strike-slip displacements along the Altyn Tagh fault [Tapponnier et al., 1990, 2001]. Internally drained rhomboidal basins younging to the northeast have formed behind these rising tectonic barriers. In some cases, these basins were filled to elevations of the previously formed Tibetan Plateau [Meyer et al., 1998]. On the basis of extrapolated Pliocene-Quaternary accumulation rates and isostatic compensation, Métivier et al.  estimated that the surface of the largest basin on the plateau edge (Qaidam basin), could rise 2200 m to the level of the Tibetan Plateau in about 9 million years. To test this hypothesis, we compared these accumulation rates to exhumation rates at the margins through a conservative mass balance, which assumes that horizontal shortening is uniformly distributed along the transect but rock uplift relative to the basin surface is restricted to outcropping basement ranges underlain by faults. The conservative nature of this balance is emphasized by disregarding the possible contribution of sediment sourced from south of the crest of the Kunlun Shan. We found a general agreement between the solid mass volume being exhumed in basin-bounding ranges and being deposited in the basins [Métivier et al., 1998]. Therefore, if the present tectonic and erosional regime persists, the Qaidam basin could plausibly become indistinguishable from the adjacent high plateau.
 The Qaidam basin is bounded by the Altyn Tagh, Qilian Shan, and Kunlun Shan ranges on its north, northeast, and southern margins, respectively. The latter range separates the Tibetan Plateau from the Qaidam basin. The ranges are primarily composed of granitoids and Precambrian-Triassic (meta)sediments [e.g., Li et al., 1991]. Cenozoic relief likely initiated in the Kunlun Shan, along the southern and western margin of the basin (Figure 2a). Potassium feldspar 40Ar/39Ar data indicate that significant exhumation began at circa 30 Ma [Mock et al., 1999] and apatite fission track data suggest that rapid exhumation continued into the early Miocene [Lewis, 1990; Jolivet et al., 2001]. We interpret the scarcity of young apatite fission track ages to indicate slowing of exhumation rates since that time; therefore, the southern margin of the Qaidam basin likely formed in and has persisted without significant erosion since the early Miocene.
 Transpression along the Altyn Tagh Fault system has created a linear topographic barrier that hydrologically isolated the Qaidam basin from the Tarim basin (Figure 1a). The fault apparently formed in part along a reactivated Paleozoic suture [Sobel and Arnaud, 1999]. Significant cooling along thrust and strike-slip faults is documented by Oligocene to early Miocene apatite fission track ages [Sobel et al., 2001; Jolivet et al., 2001; Delville et al., 2001] and potassium feldspar 40Ar/39Ar data [Cowgill et al., 2001]. Diverging Oligocene and Miocene paleocurrent directions on either side of the Altyn Tagh range demonstrate that it has been a positive topographic feature since this time [Hanson, 1999]. Sedimentary basin piercing points bounding the eastern and central portions of the fault suggest a late Oligocene-early Miocene initiation of slip [Yue et al., 2001].
 The location and trend of the ranges comprising the Qilian Shan is likely controlled by reactivated Paleozoic structures [e.g., Meyer et al., 1998]. Shortening and uplift along these laterally extensive structures provides few or no outlets for the fluvial networks draining the area. Extrapolation of studies along the northern margin of the range implies that the Qilian Shan has been largely constructed since the late Miocene [Meyer et al., 1998]. However, apatite fission track data show that the southern and northern range fronts experienced early Miocene exhumation [Jolivet et al., 2001; George et al., 2001]. In addition, deposition of northwardly derived coarse conglomerates in the southern range is magnetostratigraphically dated as circa 21 Ma, and likely records initiation of thrusting in the South Qilian Shan [Gilder et al., 2001]. These data indicate that the range was being uplifted during the early Miocene, likely creating a topographic barrier at that time.
 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 the Oligocene in local, structurally controlled basins; biomarker analysis demonstrates that these lakes were hypersaline and anoxic [Song and Wang, 1993; Hanson et al., 2001]. Expansion of lacustrine facies and increasing sedimentation rates during the Pliocene reflect internal drainage and storage of sediment within the basin [Métivier et al., 1998], and perhaps more efficient erosion due to greater climatic variability [e.g., Peizhen et al., 2001]. Compared to Oligocene strata, Pliocene deposits are more widespread, thicker, and include abundant evaporites [Song and Wang, 1993; Métivier et al., 1998], suggesting increased aridity in an internally drained basin. Thus the basin was separated from the foreland by the Pliocene, and perhaps even as early as the Miocene.
 Aridity in Tibet and the Qaidam basin results from the orographic barriers formed by the Tian Shan, Qilian Shan, and the Himalaya, to the north, northeast, and south, respectively, amplified by the effects of the subtropical high-pressure belt (Figures 1a and 1c). Well-dated loess sequences to the east of the Qaidam basin constrain the onset of aridity to be 22 Ma; this is inferred to result from elevated topography in central Asia [Guo et al., 2002]. A striking example of an orographic barrier is the Himalaya: precipitation on the south side of the range exceeds 2000 mm/yr, while the Qaidam basin receives ∼100 mm/yr (Figure 1a). While large precipitation gradients are observed over the high mountain chain, southeast derived moisture penetrates into the southeastern section of the Tibetan Plateau, where the ranges trend parallel to the moisture transport direction. Interestingly, these high-precipitation regions of the orogen are not internally drained.
 Finally, local relief is concentrated within narrow zones along the edges of the Qaidam, Tarim, and Hexi Corridor basins (Figure 1a); the interior of the plateau has little relief and approximately corresponds to internally drained areas of the landscape [Fielding et al., 1994]. The zone of high relief is much broader along the southeastern margin, similar to the diffuse precipitation gradient in the area. Prior to basin closure along the dry northern plateau margin, rivers from the previously formed highland of northeastern Tibet likely drained through Qaidam into either the Hexi corridor, to the northeast and/or the Tarim basin, to the north.
 Although the data provide scant direct information on paleotopography, the synchronicity of the onset of basin margin exhumation, and significant deposition and aridification within the Qaidam basin suggests that it has been surrounded by high topography for much of the Neogene. The construction of topographic barriers along all margins of the basin and the resulting aridity apparently isolated the basin from the regional base level between the Miocene and the Pliocene [Meyer et al., 1998].
2.2. Tarim Basin
 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 Kunlun Shan mountains (Figures 1c and 3a). Northward indentation of the Pamir along thrusts and strike-slip faults during Oligo-Miocene time separated the Tarim basin from basins farther west [Burtman and Molnar, 1993; Burtman, 2000].
 Deposition of coarse conglomerates in the northern Tarim basin commenced at 21–24 Ma, providing a lower bound on the onset of basin-vergent thrusting in the area near Kuqa (Figure 3a) [Yin et al., 1998]. Sediment from the Tian Shan accumulated in the Tarim and Junggar basins during the Miocene, indicating significant topographic development [Métivier and Gaudemer, 1997]. Deformation in the range has continued through the present and also affects basin margins [e.g., Yin et al., 1998; Burchfiel et al., 1999; Tapponnier and Molnar, 1979]. Along the northwestern margin of the basin, Pleistocene synsedimentary deformation is documented by paleomagnetic data [Chen et al., 2002], indicating that this region now lies in a wedge-top position. Geodetic surveys suggest that the present shortening rate across the range in this region is ∼20 mm/yr [Abdrakhmatov et al., 1996].
 Marine deposition in the Tarim basin was superseded by transitional, and ultimately terrestrial sedimentation by Oligo-Miocene time. This is indicated by up to 6 km of Oligo-Miocene marginal marine or hypersaline lacustrine deposits that 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 and north Tarim during the Miocene [Ma and Wen, 1991]; these discrete depocenters eventually coalesced in the center of Tarim, where strata gently onlap older units [Li et al., 1996] (Figure 3d). Thus internal drainage must have been established during the Miocene.
 The Tian Shan and Pamir shelter the Tarim basin from northwardly and westwardly derived precipitation sources, respectively [Aizen et al., 1995]. Aridity is further enhanced by the Tibetan Plateau, to the south (Figure 1c) [World Meteorological Organization (WMO), 1981], and the effects of the subtropical high-pressure belt. Within the basin itself, mean annual precipitation rarely exceeds 100 mm/yr; along the basin margins, it is commonly between 400 and 800 mm/yr (Figure 1c).
 Along the southwestern edge of the basin, high local relief within the Karakorum range generally coincides with higher mean annual precipitation in the area [Fielding et al., 1994]. The large rivers that flow into the basin dry out toward the center. At present, the spill point of Tarim lies at an elevation of 1139 m within the rugged topography of the Tian Shan, well above the basin's lowest point of ∼760 m. Additional spill points at 1329 and 1390 m lie to the north of the Qilian Shan, in low-relief areas.
2.3. Puna-Altiplano Plateau and Its Margins
 The Cenozoic arid Puna-Altiplano Plateau is composed of internally drained basins, often with thick evaporite deposits, lying between the present volcanic arc of the Western Cordillera and the rugged topography of the Eastern Cordillera (Figures 1b and 4a) [Jordan and Alonso, 1987; Alonso et al., 1991; Vandervoort et al., 1995]. The Altiplano consists of a single large basin in contrast to the numerous smaller basins of the Puna; all of these basins currently lie in an arid environment that resulted from the Oligocene-Miocene uplift of the east bounding Eastern Cordillera [Kley et al., 1997; Coutand, 1999; Horton et al., 2001].
 The Altiplano basin is bounded on the west and east by the presently active volcanic arc (Western Cordillera), and a 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 that this region drained to the west prior to the Eocene [Horton et al., 2001]. In the Eocene, the Western Cordillera was created by thrusting that formed an elevated basin margin (see discussion and references of Horton et al. ); subsequently, the modern volcanic arc was constructed [Allmendinger et al., 1997]. Sedimentary petrography and paleocurrent data show the Eastern Cordillera thrust belt became a sediment source during the Oligocene and Miocene, suggesting that the Altiplano basin has likely been a closed piggyback basin since circa 25 Ma [McQuarrie and DeCelles, 2001; Horton et al., 2002]. Apatite fission track data corroborates strong exhumation and relief development during the Oligocene [Tawackoli et al., 1996; Ege et al., 2002]. Late Oligocene-early Miocene conglomeratic strata in the western portion of the Eastern Cordillera and similar early to middle Miocene strata in the Altiplano basin includes 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 Oro regional erosion surface within the Eastern Cordillera shows that this region is now tectonically inactive; since the late Miocene, deformation has instead propagated eastward into the thin-skinned Subandean fold and thrust belt [Gubbels et al., 1993].
 Meandering river facies associated with vertebrate and plant fossils typical of a humid environment show that highlands to the west drained eastward into an unbroken basin during the Paleogene [Alonso, 1992]. Stratigraphic and apatite fission track data suggest that the Eastern Cordillera and its transition to the northwesternmost extensions of the Sierras Pampeanas basement blocks began to be exhumed in Oligocene time [Andriessen and Reutter, 1994; Coutand et al., 2001]. Sediment from proximal uplifts was deposited in basins within the Puna. For instance, much of the 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 of the Neogene succession imaged by seismic reflection data from the Tres Cruces basin (Figure 4a) [Coutand et al., 2001], suggest that deformation had propagated into the basin by this time. Flat-lying upper Miocene and Pliocene strata unconformably overlie these basins [Gangui, 1998; Coutand et al., 2001]. In the Antofalla basin, in the southern Puna, a lower Miocene shift from an eastward draining foreland setting to westward transport of conglomerates marks the creation of an intramontane basin, laterally bounded by volcanic edifices [Kraemer et al., 1999]. Paleocurrent and compositional data in 10.7 Ma basal conglomerates of the Campo Arenal basin, east of the present southern Puna border, documents high topography by that time [Strecker et al., 1989]. Farther east, asynchronous deformation and uplift after about 7 and 5 Ma in the Quilmes and Aconquija ranges, respectively, established additional precipitation barriers that increased aridification to the west [Kleinert and Strecker, 2001].
 In the Puna, the appearance of evaporites dated by interbedded ashes suggests that by 15 Ma and as early as 24 Ma, the Eastern Cordillera formed a significant barrier to easterly moisture-bearing winds [Vandervoort et al., 1995; Alonso et al., 1991]. The details of this aridification vary spatially. For instance, in the Arizaro basin, evaporites first occur at circa 24 Ma (Figure 4c) [Vandervoort et al., 1995]. In the Atacama Desert (Figure 4a), the cessation of supergene alteration and copper-sulfide enrichment between 14.7 ± 0.6 and 8.7 ± 0.4 Ma has been used to infer the maximum age of the onset of aridification [Alpers and Brimhall, 1988]. In the Antofalla basin, lacustrine strata and evaporites document hydrologic isolation and aridity by about 8 Ma (Figure 4a) [Kraemer et al., 1999].
 Although moisture-bearing winds impinge on the east facing margin of the Puna, the high topography of the Eastern Cordillera and the northwestern extension of the Sierras Pampeanas borders the full length of the Puna Plateau, shielding the high plateau from significant amounts of eastwardly derived precipitation (Figure 1b) [WMO, 1975; Masek et al., 1994; Hilley and Strecker, 2001]. As in the Tarim basin, the boundary of the low-relief, internally drained region approximately coincides with the 400 mm/yr isohyet. In contrast to the Qaidam and Tarim basins, local relief within the interior of the plateau results from both volcanism and thrust- and reverse-fault-block uplifts (compare volcano locations in Figure 4a to areas of high local relief in Figure 1c) [Isacks, 1988]. The linear belt of high topography that extends for hundreds of kilometers along its length likely prevents maintenance of the bedrock fluvial system, isolating the high plateau from the foreland base level.
3. Fluvial Bedrock Incision and Defeat
 Observations presented above from the Qaidam, Tarim, and Puna-Altiplano basins suggest that internal drainage may persist within the interior of an orogen for long or indefinite periods of time. The conditions that lead to the long-term persistence of internal drainage appear to be high uplift rates, exposure of resistant rocks, and aridity. This internal drainage prevents mass transfer from orogen interiors to foreland areas. In this section, we use a theoretical approach to understand the basic controls that might lead to the long-term isolation and filling of the basins discussed.
 Internal drainage results when an integrated fluvial system is defeated by an uplifted barrier. This defeat may occur when the uplift rate of a foreland range exceeds the aggradation rate of the channel traversing the uplifting zone [e.g., Humphrey and Konrad, 2000] (Figure 5). If aggradation is rapid enough to keep pace with the rising topographic barrier, the headwaters of the fluvial system remain connected to the stable foreland base level and the slopes of the channels within the uplift zone steepen, thereby accelerating erosional processes. However, when aggradation cannot keep pace with the rising barrier, stretches of the channel within the uplift zone rise faster than their upstream counterparts, cutting off the headwaters of the channel and reducing the total discharge in its downstream portions. As rock uplift within the foreland range continues, both fluvial relief between the stable base level and the headwaters of the rivers, and average channel slopes increase. These increased slopes accelerate erosional processes, leading to transport of greater amounts of material from the uplifting orogen toward both the stable foreland base level and the filling basin in the hanging wall. Thus a deceleration of the surface uplift within the uplifting foreland range will occur over time, accompanied by filling of the basin behind it. If the rock uplift persists indefinitely, the material shed from the range into the basin may eventually overtop the range and reintegrate the drainage system.
 At least two processes may conspire to prevent the fluvial network from remaining connected indefinitely or reintegrating as the internally drained basin is filled. First, in the case that aggradation is sufficient to maintain a connection from the headwaters to the foreland base level, channel slopes within the uplifting zone may exceed those observed for fluvial processes (this process hereafter referred to as “basin isolation”). In this case, the elevated slopes within the channels at the beginning of the uplifting zone may over steepen beyond their observed limits, requiring other transport processes (e.g., debris flow scour [Sklar and Dietrich, 1998]) to erode the channel to maintain continuity of the fluvial system. Second, in the event that the bedrock channels are initially defeated, the rising foreland uplift may generate an enormous amount of fluvial relief before the rock uplift rate is balanced by erosion. The topographic load of this high-relief area and that of the filling basin behind it may favor the migration of deformation into foreland areas [e.g., Willett and Beaumont, 1994; Royden, 1996] (this process is hereinafter referred to as “crustal strength”). In both scenarios, persistent disruption of the fluvial system leads to the maintenance of internal drainage in the interior of the orogen.
 To explore the circumstances that give rise to initial and persistent disruption of the channel network, we consider the rate-limiting process of the fluvial system in the foreland uplift to be the rate at which the river can incise bedrock [e.g., Whipple et al., 1999; Whipple and Tucker, 1999; Kirby and Whipple, 2001]. First, we examine the conditions under which the fluvial system traversing a bedrock uplift may not aggrade rapidly enough to maintain a continuous channel network. In this case, the fluvial system will be defeated, leading to temporary disruption of the channel network. Next, we use the bedrock power law incision model [e.g., Whipple et al., 1999] to evaluate the conditions that may lead to the persistence of internal drainage within the interior of an orogen by either basin isolation or crustal strength mechanisms proposed above.
3.1.1. Initial Defeat of a Channel Traversing Foreland Bedrock Uplift
 First, we examine the temporal development of a fluvial channel that transects a bedrock uplift to determine the conditions necessary for the initial isolation of the channel headwaters from their downstream portions. In our idealization, we consider a basin with a width Wb that is truncated downstream by a bedrock uplift of width, Wu (Figure 5). The bedrock uplift is laterally continuous in our model and so we do not consider outlets for a river deflected behind the rising topographic barrier as others have [Humphrey and Konrad, 2000]. Under these conditions, the initial formation of internal drainage takes place when the slope of the channel directly behind the foreland uplift slopes back toward the headwaters of the channel.
 Our modeled channel geometry has two sections: a lower reach that traverses the bedrock foreland uplift and an upper reach that aggrades in response to uplift of the downstream portion of the channel (Figure 5). For simplicity, we assume that the channel initially slopes toward the foreland with a constant slope, So (Figure 5). Because the upper reach aggrades as sediment is deposited behind the foreland uplift, fluvial processes within this portion of the channel are limited by the rate at which the fluvial system can transport sediment downstream. Under these conditions, the sediment flux carried by the channel is the product of the local channel slope (dz/dx) and discharge, roughly encapsulated in the product of a transport coefficient (Dc) and the contributing area (A) [e.g., Paola et al., 1992]:
In addition, because the channel must aggrade the entire area behind the rising topographic barrier, the transport of sediment within this portion of the channel is one-dimensional, and thus the upstream contributing area scales directly with position along the profile, x. Thus
Neglecting any changes in sediment density during deposition, the rate of change in elevation of the aggrading portion of the channel is
where Ub is the uplift rate within this section of the basin. By combining equations (2) and (3), we find that the rate of change of the channel bed through time is a nonlinear diffusion equation [e.g., Paola et al., 1992]:
Analytical solutions to equation (4) are difficult to obtain; therefore, following Humphrey and Konrad , we assume 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 effective constant, D, that represents this average value and scales with the total basin width, Wb (D = DcWb [Humphrey and Konrad, 2000]). Under these assumptions, we rewrite equation (4) as
Finally, letting Ub = 0 within the basin, we find that
for the portion of the channel that aggrades behind the foreland uplift.
 Next, we find a specific solution for equation (6) by assuming that the basin behind the foreland uplift has an initial slope of So and the farthest downstream portion of this reach of the river (at x = Wb) is displaced at the rate of uplift of the foreland bedrock uplift, U. Implicit within this formulation is that the rate of sediment delivery to the basin headwaters is sufficient to support the initial slope for selected values of Dc and Wb [Humphrey and Konrad, 2000]. With these conditions, the channel slope at the transition between the basin and the foreland uplift may be written as a function of time [Humphrey and Konrad, 2000; Carslaw and Jaeger, 1959]:
where St is the slope of the aggrading channel at the basin-bedrock uplift transition. This channel is defeated when it slopes back toward the basin at the point of the foreland uplift (St ≤ 0). By letting St = 0, we can determine the time at which uplift of the foreland will back tilt the aggrading channel, leading to the formation of internal drainage:
Equation (8) indicates that aggrading channels subjected to indefinite uplift at the basin-bedrock uplift transition will eventually be back tilted and defeated. However, if the surface uplift of the downstream channel segment ceases before this time, the drainage system will remain integrated indefinitely.
 While the channel segment upstream of the uplift zone aggrades in response to the rising barrier, the downstream segment erodes the bedrock uplift. We idealize the rate of change of the channel elevation in this downstream portion, (dz/dt) to be a power function of the upslope source area and the local slope at each point in the channel [Howard and Kerby, 1983; Howard et al., 1994]:
where K is a dimensional coefficient of erosion that includes the effects of rock erodibility, effective precipitation, and downstream changes in the channel's hydraulic geometry; A is the source area (proxy for discharge in the fluvial system [Howard and Kerby, 1983; Howard et al., 1994; Stock and Montgomery, 1999]); S is the bedrock channel gradient; and m and n are constants that may be related to the processes of bedrock incision at the bed of the channel [Whipple et al., 2000a, 2000b]. To express A in terms of the downstream profile position, x, we employ Hack's law [Hack, 1957], in which the source area is a power function of the downstream profile length:
where ka and h are constants that depend on catchment geometry. By combining equations (9) and (10), we express the rate of change of the channel elevation in terms of the downstream profile distance, x:
Equation (11) is a kinematic wave equation with a wave speed of [Whipple and Tucker, 1999]. In this formulation of bedrock erosion, uplift of an initially sloping profile will migrate toward the headwaters of the channel at this velocity. This uplift signal is communicated upstream as a migrating “knick slope” [Whipple and Tucker, 1999; Humphery and Konrad, 2000]. Once this knick slope reaches 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 knick slope to migrate through the uplift zone with equation (8), we can infer the conditions under which the channel will remain continuous through the basin and uplift zone.
 First, noting that dx = v(x) dt, v(x) equals the kinematic wave speed of the migrating knick slope, S is equal to the initial channel slope, So, we rearrange to solve for dt and integrate:
where xs and xf are the downstream and upstream locations of the uplift zone in our model (Wb + Ws and Wb, respectively; Figure 5). In the limiting case that the surface uplift of the downstream bedrock portion of the channel reaches the aggrading portion of the channel at exactly the moment that the slope at the basin's edge is zero, internal drainage is prevented. By substituting Wb + Ws for xs and Wb 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 transport constant (Dc), we find the conditions that define the threshold between internal and external drainage. After combining and rearranging, we obtain
Equation (13) states that for a given basin and uplift zone geometry (Wb and Wu), basin geometric properties (ka and h), bedrock power law exponents (m and n), and initial channel slope (So), basins that are uplifted and eroded under conditions of greater and less than those indicated by equation (13) will lead to internal and external drainage, respectively.
3.1.2. Persistence of Internal Drainage by Basin Isolation
 While drainages may initially be defeated by uplift of the foreland, eventually, material shed from the back side of the topographic divide may fill the basin behind the range and reintegrate the fluvial system. To evaluate if the basins behind the foreland uplift will remain internally drained indefinitely by our “basin isolation” process, we first consider the case where the bedrock channel gradient becomes larger than that observed within bedrock channels. Sklar and Dietrich  argue that the transition between debris flow transport and bedrock fluvial incision occurs at a slope of ∼0.2 (∼11°), although recent studies by Whipple and Meade  argue that this transition may lie at much steeper slopes. However, these latter studies may be hampered by the quality and spatial resolution of the base topographic data sets, preventing differentiation of these processes within the areas studied [Stock et al., 2002]. In the absence of additional studies using high-resolution topographic data clarifying the slope-area relations that govern debris flow transport, we have used the estimates of Sklar and Dietrich . Portions of the channel where slopes exceed this threshold value are dominated by debris flows. While it is conceivable that debris flows may maintain an integrated fluvial network for short distances, typically, they dominate transport only near the upstream ends of the channel [e.g., Montgemery and Foufoula-Georgiou, 1993]. Therefore, in situations where large portions of the bedrock fluvial channel within the uplift zone require slopes steeper than 0.2, we expect the fluvial bedrock system to be overwhelmed by debris flows and defeated indefinitely. We identify this condition in the context of equation (11) by examining the case when rock uplift is exactly balanced by erosion. In this case, the channel geometry remains invariant over time, as it has reached its steady state profile [Whipple et al., 1999; Whipple, 2001]. First, we let the channel gradient in equation (11) equal that of the onset of debris flows (this threshold referred to as Sc) and then rearrange to solve for the basin area that is required to maintain slopes at this value at the upstream portion of the bedrock uplift:
where Ac is the basin area required to maintain channel slopes at the upstream end of the uplift zone that are equal to Sc. In this formulation, Ac represents the threshold basin area that is required to maintain fluvial bedrock incision and a continuous connection between the foreland and the headwaters of the orogen.
3.1.3. Persistence of Internal Drainage by Crustal Strength
 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 support these high elevations. In this case, the resulting large gravitational stresses favor the migration of deformation to lower areas [Willett and Beaumont, 1994; Royden, 1996]. Thus uplift may cease where elevations are high, forcing deformation, uplift, and fluvial incision toward the margins of the orogen. In addition, propagation of deformation into the foreland may reduce precipitation along the margins of high topography, further favoring aridity, reduced stream power, and internal drainage in these areas.
 In our model of this crustal strength effect, we simplify the coupled interactions of erosion and deformation [e.g., Willett, 1999] by postulating that uplift will be unsustainable if the relief within the foreland uplift zone becomes larger than that observed on Earth. That is, if relief within the uplift zone exceeds a critical value, we assume that uplift within the bedrock portion of the channel will cease, deformation will migrate toward the foreland, and the process of defeat and filling will repeat downstream. In this case, internally drained basins behind the rising topographic uplift will never fill to the limit of the steady state topographic channel profile and the fluvial system will not reintegrate.
 To determine the uplift rate and rock erodibility conditions necessary to produce a specific fluvial relief, we examine the steady state fluvial bedrock profiles within the uplift zone. Under these conditions, steady state fluvial relief within the bedrock uplift may be written as [Whipple et al., 1999]:
where L is the width of the uplifting zone (L = Wu). Importantly, equation (15) indicates that wider uplift zones will produce greater amounts of fluvial relief than those that are narrow. To define a threshold beyond which the crustal strength mechanism will force deformation to migrate to lower relief areas, we assign a value for the maximum possible fluvial relief in the uplifting zone and rearrange equation (15) to solve for the uplift zone width that is required to produce this relief:
For given values of U, K, m, n, ka, and h, foreland uplift zones wider and narrower than Wu(max) will produce fluvial relief greater and less than Rc at steady state. In our formulation, this would lead to the persistence of uplift within the foreland uplift zone and migration of uplift toward areas of low topography, respectively.
 To separate the effects of crustal thickening from the basin isolation effect, we do not place a constraint on the maximum bedrock channel gradient. Many numerical simulations suggest that the maximum relief is related to crustal thickness [Willett and Beaumont, 1994; Royden, 1996]; we consider a maximum value of Rc = 10 km. This value is over a kilometer more than the largest total relief observed on Earth, and so represents a conservative maximum value for Rf.
3.2. Model Results
3.2.1. Initial Defeat of a Channel Traversing Foreland Bedrock Uplift
 We evaluated the threshold conditions that lead to the initial defeat of a channel traversing a foreland uplift (Figure 5) using equation (13). Inspection of equation (13) reveals that there are many factors that may control the initial defeat of these channels, including the initial channel slope (So), the basin geometric properties of the bedrock portion of the channel (ka and h), the width of the filling basin (Wb) and foreland 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 channel length (Wb + Wu) to 200 km. We show the effects of changing So, Wu, and the power law exponents on the threshold conditions of that lead to initial defeat of the channel network in Figure 6. In Figures 6a–6c, different combinations of the power law exponents are shown, the x axis shows the initial channel slope, and three different values of Wu are shown as different labeled thresholds. 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 value that permits the drainage system to remain integrated, and so values of above the threshold lines result in initial fragmentation of the fluvial network and internal drainage. To determine a range of that is applicable to natural systems when m = 0.4 and n = 1, we assume a 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 and Konrad, 2000; Whipple and Tucker, 2002]. Under these conditions, ranges from 0.1 mm to 316.2 mm. Finally, if an order of magnitude decrease in precipitation effects K and Dc equally, will increase by an order of magnitude; however, if this precipitation decrease effects only K, will increase by ∼3.2 times its original value.
 We first consider the case where m = 0.4, n = 1 (Figure 6b). As So decreases and Wb increases, smaller values of are required to maintain an integrated drainage system. Values of range 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/yr will lead to internal drainage and an integrated fluvial system, respectively. An order of magnitude decrease in effective 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 K increases to 1 × 10−4 m1–2m/yr, the uplift rate threshold becomes 3.3 × 10−3 m/yr when all other parameters are held constant.
 As the power law exponents decrease and increase (Figures 6a and 6b, respectively), so does the range in ranges from 1 × 10−2 mm to 2 mm. When m = 1 and n = 2, the range of So, Wb, and Wu investigated leads to values between 4 × 10−2 mm and 1 × 104 mm. As Wu increases, the threshold value of decreases. In a qualitative sense, moderate to high uplift rates, low values of K resulting from low-erodibility rocks or reduced effective precipitation, and wide foreland uplift zones favor defeat of the fluvial system, leading to the formation of internal drainage behind the uplifting zone.
3.2.2. Persistence of Internal Drainage by Basin Isolation
 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 100 mm/yr as solid and dotted lines for each rock type, respectively. Figures 7a–7c show different combinations of the m and n power law exponents in the bedrock incision law. For reference, we label the size of the Amazon basin (6.1 × 106 km2) with an “A” on the right side of Figures 7a and 7b.
 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 by channel gradient oversteepening and basin isolation is influenced by the power law exponent values. However, K may vary with these exponents and so we emphasize the results where m, n, and K have been calibrated independently at several 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, metamorphic/granitoid rocks (K ≅ 1 × 10−7 m1–2m/yr) undergoing high uplift rates (U = 0.01 m/yr) may require large source areas (Ac ≅ 1 × 104 km2) for the channel to persist when uplift rates are high. A reduction of the effective precipitation by an order of magnitude results in large changes in the critical source area Ac. Resistant granitoid rocks subject to high uplift rates and low effective precipitation may require source areas larger than the entire Amazon basin (Ac > 6 × 106 km2) to maintain gradients less than the debris flows threshold. Moderately resistant rocks (K = 5 × 10−6 m1–2m/yr; roughly equivalent to basalt/metamorphic rocks) undergoing high rock uplift rates (0.01 m/yr) with 1000 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 flow threshold.
Table 1. Rock Type and Corresponding Values of K for Approximately 1000 mm/yr of Effective Precipitation
 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 required to maintain the bedrock fluvial system under the most extreme circumstances. For all values of m and n explored, low rock erodibilities, high uplift rates, and dry climates are apparently required to defeat bedrock channels by this mechanism.
3.2.3. Persistence of Internal Drainage by Crustal Strength
 We investigate the effects of the crustal strength mechanism of bedrock defeat in Figure 8. In Figure 8 we plot the uplift zone width required to produce Rc = 10 km for different uplift rates, precipitation rates, rock type erodibilities, and values of m and n. Uplift zones larger than the maximum uplift zone width (Wu(max) in equations (16a) and (16b)) produce maximum fluvial relief greater than Rc; therefore, in our formulation, these conditions build sufficient gravitational potential energy to force deformation and uplift elsewhere and prohibit the development of steady state topography. The three different rock types are plotted in 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 of the fluvial bedrock incision model power law exponents m and n. For reference, we show 10 km and 100 km wide uplift zones with dashed lines.
 When m = 0.4, n = 1, and K = 1 × 10−7 m1–2m/yr (roughly equivalent to granitoid rocks), fluvial relief in excess of 10 km is produced at steady state for the uplift rates investigated. Conversely, when K = 1 × 10−4 m1–2m/yr (mudstones/volcaniclastic rocks), <10 km of fluvial relief is 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 at moderate to high (>0.003 m/yr) uplift rates and reasonable (10–100 km) uplift zone widths. K values between these two extreme end-member rock types lead to thresholds that fall within the range of uplift rates investigated. For example, when K = 5 × 10−6 m1–2m/yr (roughly equivalent to bedrock fluvial erosion of basalt flows in a humid environment), 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 lower effective precipitation may cause these moderate erodibility rock types to accrue large amounts of fluvial relief, potentially defeating the bedrock channel due to the crustal strength mechanism proposed.
 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 when uplift rates are low (0.0001 m/yr) and resistant rocks are exposed. An order of magnitude decrease in K requires Wu(max) = 1 × 10−18 km. K values of 5 × 10−6 m1–2m/yr also produce topography in excess of Rc for uplift rates greater than ∼0.0005 m/yr, and an order of magnitude decrease in K results in relief greater than Rc for all uplift rates investigated. Finally, low K values (1 × 10−4 m1–2m/yr, associated with mudstones/volcaniclastic rocks) fail to build relief in excess of 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 when Wu = 10 km.
 Finally, large m and n values result in steady state fluvial relief less than Rc for most U and K values when Wu ≤ 10 km. However, when K = 1 × 10−7 m1–2m/yr and there is an order of magnitude decrease in effective precipitation, narrow (Wu = 10 km) uplift zone widths are required to produce fluvial relief less than Rc. Therefore, even when m and n are large, high uplift rates, low rock erodibilities, and low effective precipitation may produce fluvial relief that 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 may produce fluvial relief in excess of 10 km. These conditions may lead to sustained defeat of the areas of the bedrock fluvial system above this critical relief and the establishment of internal drainage in such areas.
4.1. Comparison of Model Results With Other Landscape Development Models
 Our models provide a means of estimating the conditions required to create and maintain internal drainage and comparing these conditions with those observed within the internally drained Tarim, Qaidam, and Puna-Altiplano basins. It is important to acknowledge that the fluvial bedrock incision models employed suffer from several important shortcomings. First, incision of fluvial systems into bedrock in many situations may not be as simple as that implied by the power law relations expressed in the bedrock power law incision model. For example, sediment delivered to channels via hillslope processes may be important agents in abrading the channel bed [e.g., Sklar and Dietrich, 1998, 2001]. Consequently, the decoupling between hillslope and fluvial response implied by the bedrock power law incision model may neglect this potentially important factor.
 Second, even within the context of the bedrock power law incision model, important uncertainties exist in the model parameters of equation (11). For example, K includes the units of m [Whipple and Tucker, 1999], and so its value likely scales with the power law exponents. However, the relationship between the exponents and K is unknown [e.g., Sklar and Dietrich, 1998]. K incorporates the effects of allometric changes in channel geometry with discharge, sediment flux entering the channel, the relation between effective discharge and drainage basin area, and the resistance of bedrock to fluvial erosion. Most of these factors likely change with m, but to date, no comprehensive study has been conducted that defines this scaling relationship. Contrary to the work of others [e.g., Sklar and Dietrich, 1998; Whipple and Tucker, 1999], we do not scale K by 1/n in our models to maintain a constant topographic form for changing n, as it is not apparent that the unknown scaling law of K and m supports this approach. Instead, we fixed K to values determined by Stock and Montgomery  for n = 1 and m = 0.4, and emphasize our results in the context of these calibrated values. If increasing power law exponent values reduce the value of K, our models overestimate and underestimate the voracity of erosion when the exponents are high and low, respectively. As new scaling laws relating K to the exponents emerge, the range of K in our model results, when n = 2/3, m = 1/3 and n = 5/2, m = 5/4, may be readjusted. While these scaling problems lead us to view our conclusions based on these uncalibrated power law exponent values as preliminary and subject to change upon further work, all studies that strive to understand orogen-scale relief using the power law bedrock incision model suffer from this deficiency. Also, the value of K may not directly correspond to rock type, but also may be strongly influenced by the degree of fracturing and structural damage the eroding rocks have sustained [Whipple et al., 2000b]. K values applicable at the orogen scale likely incorporate the lithologic and structural heterogeneity encountered within the range-traversing fluvial systems.
 Third, we simulate the effect of an order of magnitude precipitation in our model by reducing K an equivalent amount. It is important to point out that K depends on the effective discharge during an event of unspecified magnitude and frequency [Sklar and Dietrich, 1998]. Therefore, while we simplify the effect of changing precipitation as a linear change in K, it is possible that this relation is not as simple as our analysis implies. For example, reduced precipitation may lead to less frequent, but larger magnitude rainfall events whose net effect may increase transport efficiency [Molnar, 2001]. In addition, changes in effective discharge that result from decreases in precipitation may cause the relations between channel width and basin area to change, potentially exacerbating or buffering the change in K that results from the decreased rainfall. While these uncertainties are important to acknowledge, the underlying relations between effective discharge and K are unknown, so we opted not to consider complicated relationships between these two factors in our models.
 Fourth, our models of maintenance of bedrock channel defeat by the crustal strength mechanism do not explicitly couple the geomorphic and kinematic evolution of an orogen as in other modeling studies [e.g., Willett, 1999; Willett and Brandon, 2002]. However, our analysis provides two important advantages to these more complex coupled tectonic-geomorphic numerical models: (1) our formulations explicitly allow the defeat of the fluvial bedrock channels, whereas previous numerical models assume that the resulting closed basins will be recaptured, thus maintaining the fluvial network; and (2) a range of geomorphic processes represented by different combinations of and may be explored in our models. In coupled orogen-scale tectonic-geomorphic models, in contrast, these values are typically chosen to be m = n = 1 [e.g., Willett, 1999]. Our results and those of others [Whipple and Tucker, 1999] show that the response of the bedrock fluvial system is highly dependent on these values. Neglecting these factors may cause the coupled geodynamic erosion models to artificially preserve an integrated fluvial system across the orogen. While a drainage divide may move across the orogen in these models, loss of source area on one side of the drainage divide is compensated by a corresponding increase in area on the opposite side. Importantly, the establishment of internal drainage decreases the source area of fluvial bedrock systems on both sides of the orogen. Thus coupled models may overestimate the voracity of erosion in real landscapes, fundamentally changing the relationship between convergence, erosion, and topographic construction.
 Finally, our geomorphic model assumes that the process of bedrock incision controls relief at the scale of an orogen. We do not explicitly consider the potentially important effects of sediment flux on incision rates in our model [e.g., Sklar and Dietrich, 1998, 2001; Whipple and Tucker, 2002], which may decelerate incision rates by sediment abrasion when there is not enough sediment to abrade the channel bed or too large a sediment flux that reduces incision rates due to bed armoring. Both sediment flux controls on incision rates (leading to mixed bedrock-alluvial channels) and other important erosional processes, such as glacial erosion, may exert important controls on the relief of the orogen. Indeed, the upper headwaters of some of the closed basins discussed above (Tian Shan, Qilian Shan, Puna-Altiplano Plateau) are currently or have been glaciated during the Pleistocene [e.g., Peltzer et al., 1988; Haselton et al., 2002]. In these circumstances, total orogen relief may be limited by this process, rather than fluvial bedrock incision [e.g., Whipple et al., 1999]. Finally, regardless of the efficiency of glacial erosion, fluvial bedrock incision must still be sufficient to maintain bedrock channels in lower elevation areas to prevent internal drainage from developing. Many of the arid, low-erodibility models show that even the lower sections of the drainage network may be susceptible to defeat by the basin isolation process when m and n are small (Figure 7). Thus fluvial bedrock incision models likely provide a conservative bound on the conditions necessary to create internal drainage.
Figure 8 indicates that there is always an uplift zone width that is sufficiently small to produce steady state relief below the critical value. Uplift zones in our study areas are likely tens to hundreds of kilometers wide. While our model allows any uplift zone width, it is difficult to imagine that small uplift zones (<1 km) are of regional significance in actively uplifting orogens. Indeed, some of the stable uplift zone widths are unrealistically small (10−38 km). Therefore, while our choice of reasonable uplift zone widths between 10 and 100 km is somewhat subjective, they are likely fair values relative to the total range of uplift zone widths produced by our calculations. Also, it is important to note that the smallest uplift zone widths produced in the model lead to bedrock channel slopes greatly in excess of the debris flow threshold slope angle. We intentionally allowed these steep slopes to occur to dissociate the effects of our basin isolation and crustal strength fluvial bedrock channel defeat processes. In reality, these steep slopes would lead to bedrock channel defeat by the basin isolation process long before the critical bedrock fluvial relief was attained.
4.2. Formation and Persistence of Internally Drained Basins
 The Qaidam and Puna–Altiplano basins formed as wedge–top basins while the larger Tarim basin comprises coalesced wedge–top and foreland basin systems (in the sense of DeCelles and Giles ) bounded by actively growing anticlines and faults, similar to the scenario depicted in Figure 9. Such basins can be dammed by structural features with far greater relief than a flexurally controlled forebulge [DeCelles and Giles, 1996]. As the channels within the uplifts at the basin margins are defeated by a combination of aridity, exposure of resistant rocks, and high uplift rates, a positive feedback likely develops in which the loss of discharge from the catchment area of the basin allows rapid construction of fluvial relief. The overfilled basins located behind these rapidly rising barriers may often contain thicker sediment packages than might be predicted in flexural foreland basins [Flemings and Jordan, 1989]. This accumulation of mass and subsequent advance of the deformation front may transform a wedge–top basin into a tectonically inactive piggyback basin. Such a scenario may be recorded by flat–lying sediments unconformably overlying strata related to fault growth, such as in the late Tertiary reverse–fault bounded basins of the northern Puna [e.g., Gangui, 1998; Coutand et al., 2001] and the Qaidam basin [Song and Wang, 1993]. These examples show that wedge–top basins can be long–lasting and may store large quantities of sediment if the newly formed barrier is not breached [e.g., Inman and Jenkins, 1999; Collier et al., 2000; Métivier et al., 1998]. Eventually, basins may fill above the internal spill point, causing a series of internally drained basins to coalesce. In Tibet, these overfilled basins are topographically indistinguishable from the earlier formed plateau [e.g., Métivier et al., 1998].
 The essential process leading to the creation and maintenance of internal drainage in these areas is the defeat of fluvial outlets around the margins of the basin. Our models of initial channel defeat indicate that aggradation will not be sufficient to maintain a fluvial connection with the foreland base level when uplift rates are low to moderate, rock erodibilities are moderate to small, and if there is low effective precipitation. In fact, even when rock erodibilities are high (1 × 10−4), uplift zones are narrow (10 km), and the initial channel slope is relatively steep (10−2), only uplift rates of ∼3 mm/yr within the foreland uplift can be tolerated before aggradation is outpaced by surface uplift. Although we fixed the total fluvial length to 200 km, the qualitative relations reported are robust for shorter fluvial systems. In addition, reduction in effective precipitation may lead to decreased delivery of sediment to the upstream end of the channel from the hillslopes. While our model formulation does not directly treat the effect of reduced sediment input at the channel's upstream end, but instead includes this in So, we might expect a reduction in effective precipitation to lead to decreases in the equilibrium initial slope. In these cases, lower precipitation may favor bedrock defeat by reduced initial slopes in addition to a reduction in K and possibly Dc. Therefore, in dry climates, we expect all but the largest fluvial systems to be initially defeated. In cases where the rock types exposed are especially difficult to erode, we expect all drainages, regardless of their size, to be defeated, resulting in internal drainage and infilling of the basin behind the foreland uplift. To prevent internal drainage conditions by our basin isolation mechanism under high uplift rates and arid climates, extremely large basin areas are required. Finally, for typical uplift zone widths, an enormous amount of fluvial relief (>10 km) is created when uplift rates are moderate to high, rock types are resistant to bedrock erosion, and climates are arid. By our crustal strength mechanism, these sets of rates favor the migration of deformation to areas of low elevation.
 All of these model observations agree well with the conditions observed within and around the internally drained basins reviewed. For example, in northeast Tibet, high uplift and shortening rates [Meyer et al., 1998], low precipitation (<400 mm/yr; Figure 1a) and an orographic barrier broad enough to resist breaching have allowed closed basins to grow during the late Cenozoic. Likewise, the Tarim basin and Puna-Altiplano Plateau are bounded by ranges dominated by pre-Mesozoic sediments, metamorphic, and crystalline lithologies, with high relief and low mean annual precipitation. These basins developed in areas of significant crustal shortening behind orographic barriers, where limited precipitation prevents fluvial incision from keeping pace with tectonic uplift. Such an orographic rain shadow may be caused by significant growth of a frontal range that shields the older, still rising ranges from precipitation and protects them from fluvial incision. Alternatively, a reverse-fault-bounded barrier range might grow far in front of the main thrust belt where its location is controlled by preexisting crustal heterogeneities (e.g., the northern portion of the Argentine Eastern Cordillera 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 these internally drained basins are oriented at high angles to prevailing moisture-bearing winds. In contrast to these examples, the structural setting of southeastern Tibet includes predominantly north-northeast trending ranges parallel to the dominant moisture-bearing winds; here, the plateau has a diffuse topographic boundary [Fielding et al., 1994] (Figure 1a) and heavy monsoon rains from the southeast readily penetrate far into this portion of the plateau and apparently prevent the formation of closed basins. This wetter portion of the high plateau constitutes greater local relief than the more arid, internally drained sectors (Figure 1a). Similarly, the late Cenozoic Sierras Pampeanas basement uplifts (27–33°S) in the foreland of the Argentine Andes [e.g., Jordan and Allmendinger, 1986] and the Cretaceous to Eocene Laramide uplift province of North America [e.g., Gries and Dyer, 1985] may represent such settings. Over long periods of time; however, these basins may eventually fill and be subsequently reintegrated with the foreland base level as the spill point of the basin is exceeded. In contrast, the high Tibetan Plateau and Puna-Altiplano Plateau have nearly completely filled, yet fail to be reintegrated with the regional base level, implying that transient basin filling effects cannot explain their persistence. Importantly, failure of these basins to reintegrate with the external fluvial system strengthens the idea that other mechanisms (i.e., basin isolation and crustal strength) control the persistence of these features.
Meyer et al.  posit that such basins are closed primarily because of rapid faulting. In contrast to the high plateau and Tarim basin, landscapes in humid climates such as in the Himalaya support major rivers that traverse resistant bedrock lithologies and remain integrated despite high uplift rates. This suggests that high uplift rates and low rock erodibilities are insufficient to defeat bedrock channels where there is abundant precipitation. For instance, shortening and uplift rates in the Himalaya are similar to those in northeastern Tibet [Bilham et al., 1997; Meyer et al., 1998]. Rock types in both areas are also similar. In contrast, the Himalaya receives 10 to 20 times more precipitation than the Qaidam basin [WMO, 1981]. The abrupt decrease in precipitation across the crest of the Himalaya lies well south of the transition from internal to foreland-integrated drainage (Figure 1a). In this case, arid areas in close proximity to large orographic gradients may represent transitional parts of the landscape in which efficient headward erosion allows external drainage to extend into the low-precipitation highlands south of the internally drained Tibetan Plateau. Indeed, this transition between external and internal drainage at or near large orographic gradients is observed along the margins of several of the study areas. For example, the sole fluvial outlet from Northeast Tibet is the Huang He, which drains an area roughly 25% the size of the internally drained portion of the plateau (Figure 1a) [Fielding et al., 1994]. This river was temporarily dammed in the Gong He basin, resulting in 1200 m of Quaternary deposits [Métivier et al., 1998] (Figures 1a and 2a). Subsequently, the river has broken through this natural dam and downcut through at least 600 m of its own fill, as well as incising a steep bedrock gorge downstream. Similarly, along the eastern margin of the Argentine Puna, deposits within the intramontane Quebrada del Toro, Humahuaca, and Valles Calchaquíes basins (Figures 1b and 4a) record intermittent basin closure and reintegration with the foreland fluvial system [Strecker et al., 2000, 2002]. Since the Pliocene, these basins have experienced multiple cycles of closure and filling, followed by downcutting and sediment evacuation. It is likely that these basins represent transitional areas of the landscape in which large rainfall gradients result in effective headward erosion, drainage capture, and ultimately basin exhumation [Strecker et al., 2002]. In these cases, the transiently closed basins may be close to the tectonic and climatic conditions necessary to maintain internal drainage. The filling and reexhumation of marginal basins may reflect oscillations in climate or uplift rates that are superposed on the long-term rise of the topography and the resulting reduction in precipitation along the leeward slopes of the landscape [Strecker et al., 2000].
 Our models suggest that the conditions under which bedrock channels are defeated may vary with the value of in the bedrock power law incision model [Whipple and Tucker, 1999; Whipple et al., 2000a; Kirby and Whipple, 2001] if K is independent of the power law exponents. Processes such as hydraulic lifting of channel blocks in highly fractured environments may result in low values of n (2/3) [Whipple et al., 2000a], leading to the defeat of bedrock channels if rocks resistant to erosion and aridity exist. When cavitation and abrasion(n = 7/2 and n = 5/2, respectively [Whipple et al., 2000a]) are the dominant erosional processes, bedrock channels may be difficult to defeat relative to other types of bed erosion. The processes acting at the channel bed may vary depending on the rock types being eroded or the amount of structural damage the rocks have sustained [Whipple et al., 2000b]. In active orogens, sustained crustal shortening and exhumation are likely to expose deeper structural levels and hence more resistant lithologies with time. Thus the presence of certain rock types and the effects of a complex structural history may also exert a strong control on the sensitivity of a bedrock channel to defeat. Finally, high marginal topography may shield the headwaters of the bedrock fluvial system from large amounts of precipitation, encouraging channel defeat.
4.3. Tectonic, Climatic, and Landscape Responses to Internal Drainage
 The persistence of internal drainage may affect relationships between landscape relief, uplift, and precipitation. Whipple et al.  postulated that all else being equal, decreasing precipitation results in greater fluvial relief, as steeper slopes are required to evacuate uplifted material from the bedrock fluvial system. In addition, they argued that relief in mountain belts is controlled by the fluvial bedrock incision process. This is likely the case in many active mountain belts where the bedrock fluvial systems are controlled by some regional base level (e.g., sea level for Taiwan and the Olympic Mountains in North America). However, where internal drainage and bedrock channel defeat disconnect this fluvial system from a regional base level, the relationship between landscape relief and precipitation is less clear. Channels connected to closed basins must eventually aggrade as the basin fills and base level continually rises. For example, along the Puna Plateau, high and low landscape relief apparently is associated with high precipitation on the windward flanks of the plateau and the dry central interior of the plateau, respectively. Within the bedrock fluvial system there is an increase in the landscape relief with decreasing precipitation; however, a regional landscape view that includes the internally drained Puna Plateau and other intramontane sectors indicates that low precipitation clearly coincides with low relief [Hilley and Strecker, 2001]. The negative relationship between fluvial relief and precipitation is predicted by the bedrock incision model [Whipple et al., 1999]; however, the positive correlation on the plateau apparently arises because the internally drained basins continually aggrade and reduce relief as orographic effects at the plateau margins maintain reduced precipitation. Therefore, while the predicted negative correlations may hold within the bedrock channels, when large portions of an orogen are internally drained, this relationship may be convoluted and may not necessarily reflect that predicted by models of fluvial bedrock incision.
 The model results of others [e.g., Willett and Beaumont, 1994; Royden, 1996] suggest that the formation of internal drainage and the resultant storage of large volumes of sediment in wedge-top basins may exert an important control on the kinematics of deformation in an orogen. The accumulation of kilometers of sediment in a high-elevation basin such as the Altiplano or Qaidam increases gravitational potential energy and may force the locus of deformation to shift toward the margins of the orogen [Willett and Beaumont, 1994; Royden, 1996; Willett, 1999]. Even if the fluvial systems were to eventually reintegrate, the time required to aggrade behind the uplifting ranges and incise through the low-erodibility rocks may be longer than the duration of contraction within the orogen. Thus these mass storage areas may constitute persistent features of an orogen. This may cause the erosional system to be overwhelmed by tectonic deformation (e.g., the Puna-Altiplano [Montgomery et al., 2001]), and the internally drained sectors of the orogen to continually expand outward as deformation moves away from the areas of significant crustal thickening. Decreased erosional efficiency due to an overall reduction of erosion and greater continentality has been invoked to explain the Miocene widening of the European Alps [Schlunegger and Willett, 1999; Schlunegger and Simpson, 2002] and along-strike differences in the thin-skinned eastern Bolivian Andes [Horton, 1999]. In these two examples, orogen structure results from a coupled response of the erosional, tectonic, and topographic properties of the mountain belt.
 In contrast, the areas examined in this paper have crossed the threshold of fluvial channel defeat. In these cases, internal drainage prevents the erosional export of mass from the orogen, decoupling erosional and tectonic processes. This decoupling may complicate the relations explored in recent geodynamic models linking tectonic and erosional processes, and topography. In these models [e.g., Willett, 1999], erosional mass removal accelerates as channel slopes become steeper and drainage area increases until a steady state is reached where material uplifted by crustal shortening is exactly balanced by removal through surface processes [Willett and Brandon, 2002]. These studies provide valuable insights into orogenic processes in the humid regions commonly selected for comparison with model results [e.g., Taiwan, the New Zealand South Alps, and the Olympic Mountains; Willett and Brandon, 2002]. In contrast, where internally drained basins persist, widening of an orogen does not necessarily increase the erosive capacity at its margins as drainage area is continually reduced by bedrock channel defeat. In this case, mass storage in the arid interior of the orogen prevents a steady state condition from developing. Therefore, under conditions where the fluvial channel defeat threshold is surpassed, the creation and persistence of internally drained basins may profoundly influence the structure of these orogens.
 1. The northeastern margin of the Tibetan Plateau (Qaidam basin), the Tarim basin, and Puna-Altiplano Plateau have remained internally drained since the Pliocene or Miocene. It is likely that the high Tibetan Plateau has been internally drained for a longer period. The margins of each of these internally drained basins are characterized by actively uplifting ranges, low-erodibility rock types, and low mean annual precipitation. Fission track ages along the Qilian Shan, Altyn Tagh, and Tian Shan mountains suggest that topography along the margins of the Tarim and Qaidam basins rose in the Miocene and have undergone only slow to moderate exhumation since that time. Similar conditions may 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 the Plio-Pleistocene as bedrock channel outlets are defeated and reintegrated with regional base level.
 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 all required to defeat channels traversing orogens. The susceptibility of a bedrock channel to defeat is highly sensitive to the power law exponents in the bedrock incision equation, and hence the processes acting at the channel bed. Large and small values of n inhibit and favor defeat of bedrock channels, respectively.
 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 the orogen, reduction of erosional capacity within channels eroding the margins inevitably results from the establishment of internal drainage. Coupled tectonic-landscape development models that prevent the development of internal drainage may overestimate the voracity of erosion in regimes that favor internal drainage.
 4. Establishment of internal drainage likely stores mass within the interior of an orogen. Where this mass storage is large, deformation may be driven to exterior areas as a result of increased gravitational potential. The inability of the fluvial system to evacuate material from orogen interiors may thus prevent development of an erosional steady state in which uplifted material is fully removed from the orogen by erosion.
 Eric Fielding kindly provided digitized WMO precipitation data for the Andes. We are grateful to the Deutsche Forschungsgemeinschaft for funding SFB 267, “Deformation Processes in the Andes”. G.E.H. thanks the Alexander von Humboldt Foundation and the IQN Potsdam for support of his postdoctoral research at the Universität Potsdam. Brian Horton and Isabelle Coutand graciously provided versions of the components of Figures 4b–4d. Kirk Haselton contributed to an earlier version of this manuscript; this was improved by constructive comments by Teresa Jordan, Jeff Masek, and an anonymous reviewer. The present manuscript benefited from thorough reviews by Kelin Whipple, Frank Pazzaglia, and Gregory Hancock.