Skip to Main Content
Book Chapter

Tectonics from topography: Procedures, promise, and pitfalls

By
Cameron Wobus
Cameron Wobus
Department of Earth, Atmospheric and Planetary Sciences, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
Search for other works by this author on:
Kelin X. Whipple
Kelin X. Whipple
Department of Earth, Atmospheric and Planetary Sciences, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
Search for other works by this author on:
Eric Kirby
Eric Kirby
Department of Geosciences, The Pennsylvania State University, University Park, Pennsylvania 16802, USA
Search for other works by this author on:
Noah Snyder
Noah Snyder
Department of Geology and Geophysics, Boston College, Chestnut Hill, Massachusetts 02467, USA
Search for other works by this author on:
Joel Johnson
Joel Johnson
Department of Earth, Atmospheric and Planetary Sciences, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
Search for other works by this author on:
Katerina Spyropolou
Katerina Spyropolou
Department of Earth, Atmospheric and Planetary Sciences, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
Search for other works by this author on:
Benjamin Crosby
Benjamin Crosby
Department of Earth, Atmospheric and Planetary Sciences, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
Search for other works by this author on:
Daniel Sheehan
Daniel Sheehan
Information Systems, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
Search for other works by this author on:
Published:
January 01, 2006
Present address: Cooperative Institute for Research in Environmental Sciences (CIRES), University of Colorado, Boulder, Colorado 80309, USA; cameron. wobus@colorado.edu

Empirical observations from fluvial systems across the globe reveal a consistent power-law scaling between channel slope and contributing drainage area. Theoretical arguments for both detachment- and transport-limited erosion regimes suggest that rock uplift rate should exert first-order control on this scaling. Here we describe in detail a method for exploiting this relationship, in which topographic indices of longitudinal profile shape and character are derived from digital topographic data. The stream profile data can then be used to delineate breaks in scaling that may be associated with tectonic boundaries. The description of the method is followed by three case studies from varied tectonic settings. The case studies illustrate the power of stream profile analysis in delineating spatial patterns of, and in some cases, temporal changes in, rock uplift rate. Owing to an incomplete understanding of river response to rock uplift, the method remains primarily a qualitative tool for neotectonic investigations; we conclude with a discussion of research needs that must be met before we can extract quantitative information about tectonics directly from topography.

1. INTRODUCTION

Across the globe, with few notable exceptions, the steepest landscapes are associated with regions of rapid rock uplift. Given this empirical observation, one might expect that meaningful tectonic information could be extracted from some parameterization of landscape morphology, such as mean topographic gradient. Hillslopes, however, reach threshold slopes wherever erosion rates approach the surface soil production rate (Burbank et al., 1996; Heimsath et al., 1997; Montgomery and Brandon, 2002), limiting their utility as a “fingerprint” of tectonic forcing to relatively low uplift rate environments. Only the fluvial network consistently maintains its connection to tectonic forcing, and therefore contains potentially useful information about variations in rock uplift rates across the landscape. A number of studies have laid the groundwork for extracting this information by exploring the theoretical response of channels to variations in rock uplift rate, and by analyzing fluvial profiles in field settings where the tectonics have been independently determined (e.g., Whipple and Tucker, 1999, 2002; Snyder et al., 2000; Kirby and Whipple, 2001; Lague and Davy, 2003). Against this theoretical and empirical backdrop, however, there remains some uncertainty as to what can and cannot be learned from an analysis of river profiles, and there still exists no standard method for extracting tectonic information from these data.

In this contribution we attempt to bridge this gap, and discuss the state of the art in our ability to extract tectonic information directly from river profiles. The discussion focuses on the use of digital elevation models (DEMs), which are inexpensive, easily obtained, and can be used to extract much of this information quickly and easily prior to embarking on field campaigns. We discuss the methods employed in delineating tectonic information from DEMs, including data sources, data handling, and interpretation. Case studies from diverse settings are then used to illustrate the utility of DEM analyses in extracting tectonic information from the landscape. We conclude with a discussion of research needs that must be met before we can have a reliable quantitative tool for neotectonics. Throughout the paper, we purposefully restrict our focus to empirical data analysis, discussing theory only as a rudimentary backdrop and in the context of unresolved issues that limit our ability to extract quantitative tectonic information from stream profiles.

2. BACKGROUND

In a variety of natural settings, topographic data from fluvial channels exhibit a scaling in which local channel slope can be expressed as a power-law function of contributing drainage area (e.g., Hack, 1973; Flint, 1974; Howard and Kerby, 1983):

 

formula

where S represents local channel slope, A is the upstream drainage area, and ks and [thetas] are referred to as the steepness and concavity indices, respectively. Equation 1 holds only for drainage areas above a critical threshold, A cr, variably interpreted as the transition from divergent to convergent topography or from debris-flow to fluvial processes (Tarboton et al., 1989; Montgomery and Foufoula-Georgiou, 1993). While many stream profiles will exhibit a single slope-area scaling for their entire length downstream of A cr, segments of an individual profile are often characterized by different values of k s, [thetas], or both. These aberrations may appear to be exceptions to the empirical result in equation 1; however, it is actually these variations we wish to exploit to extract tectonic information from the landscape. Much of the remainder of this paper outlines the methodologies employed to extract this information.

As has often been reported, simple models for both detachment- and transport-limited river systems predict power-law relations between channel gradient and drainage area in the form of equation 1 (e.g., Howard, 1994; Willgoose et al., 1991; Whipple and Tucker, 1999). In these models the concavity index, [thetas], is independent of rock uplift rate, U, assuming U is spatially uniform (Whipple and Tucker, 1999). These models further predict direct power-law relations between the steepness index, k s, and rock uplift rate (e.g., Howard, 1994; Willgoose et al., 1991). However, although there is strong empirical support for a positive correlation between k s and U, many factors not incorporated into these simple models can be expected to influence the quantitative relation between k s and U. Known complexities include: (1) nonlinearities in the incision process (e.g., Whipple et al., 2000; Whipple and Tucker, 1999), including the presence of thresholds (e.g., Tucker and Bras, 2000; Snyder et al., 2003b; Tucker, 2004), and possible changes in dominant incision processes with increasing incision rate (Whipple et al., 2000); (2) adjustments in channel width or sinuosity, herein referred to as channel morphology (e.g., Harbor, 1998; Lavé and Avouac, 2000, 2001; Snyder et al., 2000, 2003a); (3) adjustments in the extent of alluvial cover, bed material grain size, bed morphology, and hydraulic roughness, herein referred to as bed state (e.g., Sklar and Dietrich, 1998, 2001; Hancock and Anderson, 2002; Whipple and Tucker, 2002; Sklar, 2003); (4) changes in the frequency of erosive debris flows (Stock and Dietrich, 2003); and (5) orographic enhancement of precipitation (e.g., Roe et al., 2002, 2003; Snyder et al., 2000, 2003a). Due to the possible influence of each of these complexities, the functional relationship between k s and U can be expected to vary depending on the geologic setting. While many of these complexities will be important over large length scales, over which rock uplift rates are likely to be nonuniform, we must nonetheless consider these varied feedbacks and nonlinearities if we hope to quantitatively map steepness to rock uplift rates. Additional climatic factors and substrate rock properties also strongly influence ks , and are difficult to deconvolve from uplift rate signals. Thus at present we do not know how to quantitatively map channel steepness to incision rate (or rock uplift rate at steady state) except, to some extent, through local calibration of incision model parameters, as discussed in the Siwalik Hills example.

Most models predict that profile concavity will be independent of rock uplift rate (if spatially uniform); however, any river response that differs at small and large drainage areas could theoretically induce a change in concavity. For instance, at greater drainage area, one might expect the channel to have more freedom to adjust channel width and sinuosity. Similarly at smaller drainage area, one might expect more variability in the fraction of exposed bedrock, hydraulic roughness, and the relative influence of debris flows. Despite these theoretical considerations, available data suggest little change in the concavity index, [thetas], of adjusted river profiles as a function of rock uplift rate (e.g., Tucker and Whipple, 2002). Because k s is a function of U, however (see below, and Snyder et al., 2000; Kirby and Whipple, 2001; Kirby et al., 2003), a downstream change in rock uplift rate may be manifested as a change in profile concavity (e.g., Kirby and Whipple, 2001). Thus, changes in profile concavity can also be exploited in evaluating regional tectonics from topography.

While the qualitative relationships among steepness, concavity, and rock uplift rates can be readily predicted for “adjusted” longitudinal profiles, we note that temporal changes in the climatic and/or tectonic state can complicate these relationships. For example, fluvial systems in a transient state may contain knickpoints caught sweeping through the system in response to base-level fall. If such discontinuities in channel profiles and slope-area scaling are always assumed to reflect spatial variations in rock uplift rate, these profiles may be subject to misinterpretation. However, plan view maps illustrating the spatial distribution of these knickpoints, along with an examination of long profiles and slope-area data, will typically allow these situations to be readily identified, as discussed in section 3.3. Furthermore, such transient profiles, if properly identified, can provide extremely useful information for neotectonic analysis, as described in the San Gabriel Mountains example.

Because the steepness and concavity indices each reflect spatial variations in rock uplift rate, stream profile parameters derived from regressions on natural slope-area data allow us to extract information about regional tectonics. We proceed by discussing the methodologies for extracting these data and delineating breaks in slope-area scaling. We then discuss applications of these methods to deriving tectonic information from longitudinal profile form. We stress that our approach is empirical, and is therefore not tied to any particular river incision model.

3. METHODS

3.1 Data Handling

Digital topographic data suitable for long profile analysis are widely available for sites within the United States, and can be obtained for download directly from the U.S. Geological Survey (USGS) or its affiliated data repositories (http://seamless.usgs.gov/ or http://www.gisdatadepot.com/dem/). For field areas outside of the United States, DEMs can be obtained from local sources or from the National Aeronautics and Space Administration's (NASA) Shuttle Radar Topography Mission (SRTM) (http://www.jpl.nasa.gov/srtm/). DEMs can also be created from stereo pairs of spaceborne satellite imagery (e.g., Advanced Spaceborne Thermal Emission and Reflection Radiometer [ASTER] http://asterweb.jpl.nasa.gov/, or Satellite Probatoire d'Observation de la Terre [SPOT] http://www.spot.com), or from digitized aerial photographs, where available. Note that any DEMs created from remotely sensed data may contain data holes or anomalies due to extreme relief or cloud cover. Depending on the data source, DEMs may also require a projection from geographic coordinates to a format with rectangular, equidimensional pixels throughout the region of interest (c.f. Finlayson and Montgomery, 2003).

Once digital data have been obtained, a variety of methods is appropriate for extracting the requisite stream profile parameters. In practice, any suite of computer scripts that can follow a path of pixels downstream while recording elevation, cumulative streamwise distance, and contributing drainage area data is sufficient for collecting long profile data from a DEM. The methods developed by Snyder et al. (2000) and Kirby et al. (2003) utilize a group of built-in functions in ARC/INFO to create flow accumulation arrays and delineate drainage basins, a suite of MAT-LAB scripts to extract and analyze stream profile data from these basins, and an Arcview interface for color-coding stream profiles by their steepness and concavity indices in a geographic information system (GIS). While pits and data holes in a DEM usually need to be filled to create flow direction and flow accumulation arrays for basin delineation, profile data should be extracted from the raw DEM matrix to ensure that no data are lost or created at this early stage in the processing.

Once the elevation, distance, and drainage area data are compiled, the next step is to calculate local channel slopes to be used in slope-area plots. If using built-in ARC/INFO functions, slope values should not be extracted from a slope grid computed from a 3 × 3 moving window across the entire DEM: high slopes on channel walls will cause significant upward bias in channel slopes in this case, particularly at large drainage area in narrow bedrock canyons. There are also several problems with using raw pixel-to-pixel slopes from the channel itself (rise/run): (1) many DEMs are created by interpolation of digitized topographic contour maps, grossly oversampling the available data at large drainage area and low channel gradient and leading to bias toward the data at large drainage area in regressions of log S on log A; (2) the algorithms used to convert topographic maps to a raster format often give rise to interpolation errors, which characteristically produce artificial stair-steps associated with each contour crossing of the stream line and tremendous artificial scatter in pixel-to-pixel slope data (Figs. 1 and 2); (3) these stair-steps and the integer format of many DEMs produce multiple flats with zero slope, which cannot be handled in a log-log plot of slope and area (see Fig. 1A); and (4) DEMs with low resolution will often short-circuit meander bends in a river profile, resulting in an overestimate of local channel slope, typically in floodplains at large drainage area.

Figure 1. Example of contour extraction method for high-quality U.S. Geological Survey (USGS) 10 m digital elevation model (DEM). (A) Prior to contour extraction, DEM is characterized by abundant artificial data between contour crossings, resulting in a stepped pattern on the profile. Subsampling data at equal vertical intervals (gray dots) produces a smoother, more realistic profile consistent with the source data (see text for discussion). (B) Contour extraction method faithfully reproduces stream profile crossings of contour lines on original USGS topographic map (gray dots). Dashed line—stream line extracted from DEM (compare to dash-dot stream line on the map).

Figure 1. Example of contour extraction method for high-quality U.S. Geological Survey (USGS) 10 m digital elevation model (DEM). (A) Prior to contour extraction, DEM is characterized by abundant artificial data between contour crossings, resulting in a stepped pattern on the profile. Subsampling data at equal vertical intervals (gray dots) produces a smoother, more realistic profile consistent with the source data (see text for discussion). (B) Contour extraction method faithfully reproduces stream profile crossings of contour lines on original USGS topographic map (gray dots). Dashed line—stream line extracted from DEM (compare to dash-dot stream line on the map).

Figure 2. Effects of smoothing on longitudinal profile data, from San Gabriel Mountains in southern California. (A) Profile data extracted from U.S. Geological Survey (USGS) 10 m digital elevation model (DEM), showing raw profile (light-gray crosses) and data extracted at equal vertical intervals of 12.192 m (40 ft) (black crosses). (B) Profile data extracted from Shuttle Radar Topography Mission (SRTM) 90 m DEM, showing raw profile data (light-gray crosses) and data extracted at 12.192 m intervals (black crosses). Note the considerable reduction in scatter in both cases. (C) Superposition of smoothed data from SRTM 90 m DEM (720 m smoothing window, light-gray crosses), log-bin averaged data for SRTM 90 m DEM (light-gray squares), smoothed data from USGS 10 m DEM (180 m smoothing window, black crosses), and log-bin averaged data for USGS 10 m DEM (black squares). Note general correspondence among all data sets despite variations in resolution. (D) Plot of ksn , normalized to average value of each group, versus smoothing window. (E) Plot of [thetas], normalized to average value of each group, versus smoothing window. Note that steepness and concavity indices for any data set are consistent within ∼10%, regardless of the choice of smoothing window size or style.

Figure 2. Effects of smoothing on longitudinal profile data, from San Gabriel Mountains in southern California. (A) Profile data extracted from U.S. Geological Survey (USGS) 10 m digital elevation model (DEM), showing raw profile (light-gray crosses) and data extracted at equal vertical intervals of 12.192 m (40 ft) (black crosses). (B) Profile data extracted from Shuttle Radar Topography Mission (SRTM) 90 m DEM, showing raw profile data (light-gray crosses) and data extracted at 12.192 m intervals (black crosses). Note the considerable reduction in scatter in both cases. (C) Superposition of smoothed data from SRTM 90 m DEM (720 m smoothing window, light-gray crosses), log-bin averaged data for SRTM 90 m DEM (light-gray squares), smoothed data from USGS 10 m DEM (180 m smoothing window, black crosses), and log-bin averaged data for USGS 10 m DEM (black squares). Note general correspondence among all data sets despite variations in resolution. (D) Plot of ksn , normalized to average value of each group, versus smoothing window. (E) Plot of [thetas], normalized to average value of each group, versus smoothing window. Note that steepness and concavity indices for any data set are consistent within ∼10%, regardless of the choice of smoothing window size or style.

In order to circumvent many of the problems with raw pixel-to-pixel slopes, raw elevation data can be resampled at equal vertical intervals (▵z), using the contour interval from the original data source as ▵z (if known). This step has several benefits: (1) it remains true to the original contour data from which many DEMs are derived; (2) it yields a data set much more evenly distributed in log S–log A space, reducing bias in regression analysis; and (3) it results in considerable smoothing of raw DEM profiles (see Figs. 2A and 2B). As the last two benefits apply even to DEM data not derived from contour maps, we favor the implementation of this resampling in all cases. For high-quality data sources such as the USGS 10-m-pixel DEMs, contour-interval subsampling can be shown to recover faithfully the original contour crossings (Fig. 1B). Profiles extracted from lower-resolution data sources, however, will often exhibit considerable scatter on slope-area plots even after this subsampling (e.g., Fig. 2B); in these cases, additional smoothing can significantly aid interpretation.

As noted by many researchers, slope-area data often exhibit a pronounced break in scaling at A cr ≤ 106 m2, which in unglaciated environments may represent the transition from debrisflow–dominated colluvial channels to stream-flow–dominated fluvial channels (e.g., Montgomery and Foufoula-Georgiou, 1993) (see Figs. 3A and 3B). This scaling break may be less pronounced in some settings, as a gradual transition from debrisflow–dominated to stream-flow–dominated conditions is reasonably expected (Stock and Dietrich, 2003). Figure 2C between a drainage area of 104 and 106 m2 may be an example of this behavior. Regardless of the details at low drainage area, plots of slope-area data at this stage in the processing may reveal a smooth, linear trend below this scaling break, or multiple segments with easily identifiable values of k s and [thetas], as illustrated in Figures 3A and 3B. More often, however, slope-area data will exhibit considerable scatter, which may be obscuring natural breaks in scaling along the profile. Further smoothing of the slope data greatly aids identification of scaling breaks without influencing their position, and with predictable effects on the values of k s and [thetas] (see below). Smoothing methods include using a moving-window average to smooth elevation data prior to calculating channel slopes over a specified vertical interval; regressing on elevation data over a fixed number of elevation points to derive local slope estimates; or averaging the logarithm of raw slopes over log-bins in the drainage area (termed log-bin averaging).

Figure 3. Schematic long profile and map view plots comparing transient and steady-state systems. (A) Transient long profile showing short oversteepened reach separating old and new equilibrium states. (B) Profile crossing from one uplift regime to another, showing channel reaches with constant ks values separated by a high or low concavity transition zone in between. In this and all subsequent plots, long profile data (elevation versus distance) will be shown as solid lines with linear axes labeled on top and at right; slope-area data (log S vs. log A) will be shown as crosses with logarithmic axes labeled at bottom and at left. A cr marks transition to fluvial scaling (see text); slope of log S vs. log A scaling is the concavity index [thetas]; y-intercept is the steepness index ks . (C) Transient wave of incision propagates through system at a nearly constant vertical rate; knickpoints (white dots) should therefore closely follow lines of constant elevation (dashed line) in plan view. (D) In contrast, knickpoints separating zones of high and low uplift rates (white dots) follow the trend of the accommodating shear zone in map view (dashed line). In many cases, the map pattern of knickpoints may be a better diagnostic of a transient state than long profile form.

Figure 3. Schematic long profile and map view plots comparing transient and steady-state systems. (A) Transient long profile showing short oversteepened reach separating old and new equilibrium states. (B) Profile crossing from one uplift regime to another, showing channel reaches with constant ks values separated by a high or low concavity transition zone in between. In this and all subsequent plots, long profile data (elevation versus distance) will be shown as solid lines with linear axes labeled on top and at right; slope-area data (log S vs. log A) will be shown as crosses with logarithmic axes labeled at bottom and at left. A cr marks transition to fluvial scaling (see text); slope of log S vs. log A scaling is the concavity index [thetas]; y-intercept is the steepness index ks . (C) Transient wave of incision propagates through system at a nearly constant vertical rate; knickpoints (white dots) should therefore closely follow lines of constant elevation (dashed line) in plan view. (D) In contrast, knickpoints separating zones of high and low uplift rates (white dots) follow the trend of the accommodating shear zone in map view (dashed line). In many cases, the map pattern of knickpoints may be a better diagnostic of a transient state than long profile form.

While the position of scaling breaks tends to be insensitive to the choice of smoothing window style and size, steepness indices can be expected to decrease subtly but systematically as the smoothing window grows, and spikes in the data are reduced in magnitude (Fig. 2D). The effects of smoothing on concavity values will also be predictable, but will depend on the relative position of outliers in a particular profile: if the data contain spikes high in the profile, we expect the concavities to decrease with increased smoothing as the regression pivots counterclockwise (flattens); the opposite will be true for data containing spikes near the toe of the channel. Despite these systematic and predictable biases, note that steepness and concavity values will typically fall within ∼10% of one another for a wide range of smoothing windows (Figs. 2C–2E). The data in Figure 2 also demonstrate that with appropriate smoothing, data from different sources with greatly varying resolution and quality in fact yield comparable results at long wavelength.

Each smoothing method has its strengths and weaknesses. Log-bin averaging has the advantage that the smoothing window both grows in size with distance downstream and does not produce any averaging of disparate slope values across tributary junctions with a large change in drainage area—the two primary weaknesses of the moving-window averaging approach. However, log-bin averaging alone is susceptible to outliers in particularly rough or low-resolution DEM profiles. Smoothing elevation data with a moving window that grows in size proportional to drainage area may be preferable in some cases.

We stress that investigators must be circumspect about the appropriate scale of observation for DEM analysis. For example, while our algorithms can be shown to recover contour crossings from 10 m DEMs and therefore reproduce the information provided by the original contour map, there may be considerable information missed between these contour crossings. Montgomery et al. (1998) noted up to a fourfold difference in reach-scale channel slopes measured in the field versus those derived from contour maps; Massong and Montgomery (2000) found that slopes derived from field surveys and high-resolution DEMs can be different by up to 100%. In general, we expect the tectonic signals we are interested in to manifest themselves at a scale significantly greater than the contour interval of a topographic map; indeed, Finlayson and colleagues have had success extracting useful information from 30 arc second (∼1 km) GTOPO30 data (Finlayson et al., 2002; Finlayson and Montgomery, 2003). However, without extremely high resolution digital topographic data (e.g., laser altimetry), it is clearly inappropriate to extend DEM analysis to geomorphic questions addressed below the reach scale.

3.2 Model Fits

Following data smoothing, we can begin to examine the slope-area data and make decisions about the number of distinct channel segments and the appropriate regression limits for each segment. Many channels can be adequately modeled below A cr with only a single segment, using unique values of k s and [thetas] (e.g., Fig. 2C). Others may contain multiple segments, reflecting spatial or temporal variations in rock uplift rate, climatic factors, or the mass strength of rock exposed along the profile (e.g., Fig. 3B). In either case, linear regressions on slope-area data are typically conducted in two ways for each segment to allow intercomparison among different profiles in the basin.

In the first of the two regressions, segments of slope-area data with distinct steepness and/or concavity indices are identified, and are fit with k s and [thetas] as free parameters, using equation 1 as the regression model. In the second regression, individual segments of slope-area data are fit using a “reference” concavity, [thetas]ref, to determine normalized steepness indices, k sn. A reference concavity is required for interpretation of steepness values, because k s and [thetas] as determined by regression analysis are, of course, strongly correlated (see equation 1). In practice, [thetas]ref is usually taken as the regional mean of observed [thetas] values in undisturbed channel segments (i.e., those exhibiting no known knickpoints, uplift rate gradients, or changes in rock strength along stream), and can be estimated from a plot superimposing all of the data from a catchment. Reference concavities typically fall in the range of 0.35–0.65 (Snyder et al., 2000; Kirby and Whipple, 2001; Brocklehurst and Whipple, 2002; Kirby et al., 2003; Wobus et al., 2003).

If raw data from a previously completed analysis are not readily available, one can approximately determine the normalized steepness index, ksn, for a reference concavity,[thetas]ref, as follows:  

formula
and  
formula
where ks and [thetas] are determined by regression, Amin and Amax bound the segment of the profile analyzed, and Acent is the midpoint value for the segment analyzed. In practice, equation 2 is found to match ksn calculated by regression analysis to within ∼10%. Where the difference between [thetas] and [thetas]ref is large, however, (>0.2), the ksn value is meaningful only over a short range of drainage area near Acent.

The normalized steepness index is analogous to the Sr index proposed by Sklar and Dietrich (1998). Where a regional concavity index is apparent, normalized steepness indices can be shown to correspond closely to Sr indices (see Kirby et al., 2003, Fig. 5B therein). The advantage of the normalized steepness index k sn is that the reference area (A cent here) need not be the same for all channels, or channel segments, analyzed. However, where no typical regional concavity index is apparent, the Sr index may be preferable. Other measures of channel gradient have also been used in tectonic analyses, including the Hack gradient index (e.g., Hack, 1973). Where basin shapes are similar throughout a region, comparison of Hack gradient indices among different channels may be appropriate. However, if we assume that incision rate is related to fluvial discharge, normalized steepness indices may be a more appropriate metric, since contributing drainage area (and thus basin shape) is explicitly incorporated into the analysis as a proxy for fluvial discharge.

3.3 Tectonic Analysis

In the context of extracting tectonic information from longitudinal profiles, the data obtained for steepness and concavity will often yield similar information: a downstream transition between disparate steepness values will typically be bridged by a zone of very high or low concavity (see Fig. 3 and following). This transition zone may be a result of spatially or temporally varying rock uplift rates, temporally varying climatic conditions, or spatially varying rock mass strength. Even abrupt spatial changes in either rock uplift rate or rock properties (across a fault, for instance) may be manifested as a gradual transition in channel gradient (i.e., a high concavity zone) due to gradual downstream changes in sediment size, transport of resistant boulders downstream, or other blurring agents that may diffuse knickpoints in space and time (see Whipple and Tucker, 2002). Moreover, some data-smoothing algorithms have the disadvantage of blurring abrupt changes in channel gradient or elevation (knickpoints). In practice, normalized steepness data are often more useful than concavity data for evaluating regional tectonics, especially for short channel segments, given the sensitivity of [thetas] to scatter in slope data, both real and artificial. However, concavity data are often useful for gross delineation of zones where uplift rates may be systematically changing along a profile (e.g., Kirby and Whipple, 2001; Kirby et al., 2003).

It should be emphasized here that slope-area data are plotted in log-log space, and it is important to be mindful of the compression of data at large drainage area. In particular, when selecting the downstream regression limit for channel segments, small changes in log drainage area are typically associated with large changes in distance along the profile. Large errors may therefore be inherent in any estimates of the distribution of rock uplift rates based on the width of high concavity zones. In addition, one needs to be wary of possible downstream changes in river characteristics not necessarily associated with the underlying tectonics, such as a transition to increasingly alluviated, or even depositional, conditions that may be associated with a rapid decrease in slope and therefore locally high concavity. In other cases, concavity may actually decrease where channels transition to increasingly transport-limited, but incisional, conditions with distance downstream (e.g., Whipple and Tucker, 2002; Sklar, 2003). In other words, some apparent downstream changes in channel steepness or concavity indices may simply be associated with an increase in drainage area. Comparing slope-area data on smaller tributaries that enter orthogonal to the mainstem throughout the zone of interest has proven an effective tool in this regard (see Kirby et al., 2003, Section 6.2 therein; Wobus et al., 2003), as will be illustrated in the Nepal case study here.

Once slope-area data have been extracted and smoothed from each tributary in a basin, it is often useful to superimpose all of the profile data from a catchment on a single plot (e.g., Figs. 4D and 5D). This tool aids in determination of the upper and lower bounds on steepness values in the catchment, segregation of populations with distinct steepness values, and determination of an appropriate reference concavity, as discussed above. With these composite plots, the analysis can be extended from individual tributaries to the regional scale.

Figure 4. Long profile and slope-area data from a 10-m-resolution digital elevation model (DEM) of the King Range in northern California. Top three plots show pairs of tributaries from high uplift zone (black) and low uplift zone (gray). In all plots, solid lines are fits to data with [thetas]ref = 0.57; dashed lines are fits to data with concavity as a free parameter. Squares are slope-area data using log-bin averaging method; crosses are data using 200 m smoothing window to calculate channel slopes (see text). Arrows above long profiles show regression limits for slope-area fits. (A) Gitchell Creek and Hardy Creek. (B) Shipman Creek and Howard Creek. (C) Big Creek and Juan Creek. (D) Composite slope-area data from all six rivers. Note that in all cases the channels from the high uplift zone are consistently steeper than those in the low uplift zone. Dramatic drop in channel gradient in lowermost segments of the channels reflects a transition to increasingly alluviated conditions, reflecting a decrease in effective rock uplift rate due to Holocene rise in sea level (Snyder et al., 2002), alluviation at channel mouth, or both.

Figure 4. Long profile and slope-area data from a 10-m-resolution digital elevation model (DEM) of the King Range in northern California. Top three plots show pairs of tributaries from high uplift zone (black) and low uplift zone (gray). In all plots, solid lines are fits to data with [thetas]ref = 0.57; dashed lines are fits to data with concavity as a free parameter. Squares are slope-area data using log-bin averaging method; crosses are data using 200 m smoothing window to calculate channel slopes (see text). Arrows above long profiles show regression limits for slope-area fits. (A) Gitchell Creek and Hardy Creek. (B) Shipman Creek and Howard Creek. (C) Big Creek and Juan Creek. (D) Composite slope-area data from all six rivers. Note that in all cases the channels from the high uplift zone are consistently steeper than those in the low uplift zone. Dramatic drop in channel gradient in lowermost segments of the channels reflects a transition to increasingly alluviated conditions, reflecting a decrease in effective rock uplift rate due to Holocene rise in sea level (Snyder et al., 2002), alluviation at channel mouth, or both.

The plan view distribution of normalized steepness indices for all the tributaries in a catchment can be an extremely useful tool for delineating tectonic boundaries (e.g., Kirby et al., 2003; Wobus et al., 2003). In tectonic settings containing a discrete break in rock uplift rates, we expect channels with high steepness indices to characterize the high uplift zone, while those with lower steepness indices should characterize the low uplift zone (e.g., Snyder et al., 2000). Channels crossing spatial gradients in rock uplift rate may exhibit readily identifiable knickpoints on a longitudinal profile (z versus x) and slope-area plots. In plan view, the boundary between zones of high and low steepness will also help us to evaluate whether we are seeing a temporally stable break in rock uplift rates (i.e., a fault or shear zone) or a transient condition; the rate of knickpoint migration, and therefore the position of knickpoints in a catchment through time, can be predicted (e.g., Whipple and Tucker, 1999; Niemann et al., 2001) and indicates a spatial distribution of knickpoints very different from that expected in regions of spatially varying uplift rates (Figs. 3C and 3D). In particular, if erodibility is spatially uniform, we expect the vertical rate of knickpoint migration to be constant, suggesting that knickpoints recording a transient condition (due to base-level fall, for example) should lie near a constant elevation (e.g., Niemann et al., 2001). This condition is demonstrated in the San Gabriel Mountains example discussed below.

If regional geologic maps or field observations are available, a superposition of important lithologic contacts is also useful to determine whether regional trends in channel steepness values might be correlative with lithologic boundaries, rather than with a tectonic signal (e.g., Hack, 1957; Kirby et al., 2003, Fig. 9 therein). In such efforts it is critical to recall that lithology is not synonymous with rock properties: a competent, well-cemented sandstone can be stronger than a fractured and weathered granite, and the strength of a single unit may vary markedly along strike. However, if depositional or intrusive lithologic boundaries can be demonstrated to correspond to changes in channel gradient, we can often rule out breaks in rock uplift rate as the cause of the channel steepening.

4. CASE STUDIES

Utilizing the methodologies outlined above, we now discuss a series of case studies in which river profile data have been used to extract tectonic information from the landscape. In the first two case studies, both from California, channel steepness values correlate with known variations in rock uplift and exhumation rates as determined from marine terraces, thermochronologic data, and cosmogenic data; however, there is insufficient data available at present to calibrate and uniquely test river incision models. In the third case study, steepness and concavity values derived from stream profiles correlate with the distribution of rock uplift rates above a fault-bend fold in the Siwalik Hills of south-central Nepal, and allow a local calibration of the stream power river incision model. Comparison of two independent calibration methods and application of the calibrated model to predict incision rates across the rest of the landscape allows a semiquantitative verification of the model in this field site. Finally, in the central Nepal Himalaya, breaks in steepness values across the landscape help us to delineate a recently active and previously unrecognized shear zone, the tectonic significance of which is corroborated by 40Ar/39Ar thermochronology and structural observations in the field.

4.1 California: King Range and San Gabriel Mountains

In the King Range and San Gabriel Mountains of northern and southern California, respectively, strong spatial gradients in rock uplift and exhumation rates provide excellent opportunities to test the stream profile method in a controlled environment. In the King Range, rock uplift rates near the Mendocino triple junction are quantified from flights of uplifted marine terraces, using radiocarbon dating and correlations with a eustatic sea-level curve (Merritts and Bull, 1989; Merritts, 1996). Based on the record from marine terraces, the field area can be divided into high and low uplift zones, with rock uplift rates varying over approximately an order of magnitude between the two zones (3–4 mm/yr and 0.5 mm/yr, respectively). In the San Gabriel Mountains, a restraining bend on the San Andreas fault creates strong east-west gradients in long-term exhumation rates, as determined from (U-Th)/He and apatite fission-track (AFT) thermochronology. Based on the thermochronologic data, the eastern and western San Gabriel Mountains can be divided into blocks with distinct exhumation histories, with AFT ages ranging from 4 to 64 Ma and rock uplift rates from 0.5 mm/yr in the western block to 2–3 mm/yr in the eastern block (e.g., Blythe et al., 2000; Spotila et al., 2002).

4.1.1 King Range

Using a 30 m USGS DEM of the King Range, Snyder et al. (2000) extracted 21 mainstem river profiles and calculated model parameters for equation 1 from slope-area data. Most of the tributaries in the study area were found to have relatively smooth, concave profiles for much of their length, suggesting a condition in which the rivers have equilibrated with local rock uplift rates. Our data handling methods have been refined and improved over the years since our initial efforts in stream profile analysis (Snyder et al., 2000). That analysis also predates the extensive field work in the region reported in Snyder et al. (2003a). In addition, since that time higher-resolution and higher-quality 10-m-pixel USGS DEMs have become available for the entire King Range study area. We take the opportunity here to revisit the King Range stream profile analysis using better data, refined methods, and field observations. This reanalysis is at once a cautionary tale regarding the uncertainty in best-fit profile concavity indices, and an encouraging example of the robustness of measured channel steepness indices for a reference concavity (k sn), especially within a study area. The two principal conclusions of Snyder et al. (2000) are upheld in this reanalysis: (1) channel steepness increases by a factor of ∼1.8 between the low and high uplift rate zones, and (2) there is no statistically significant difference in the concavity index between channels in the low and high uplift rate zones (Fig. 4).

Here we reanalyze only a subset of the 21 drainages studied by Snyder et al. (2000): the largest of the drainages in the high uplift zone (Gitchell, Shipman, Bigflat, and Big Creeks), and the most comparable low uplift zone channels (Hardy, Juan, Howard, and Dehaven Creeks) using 10 m USGS DEMs. We select regression bounds on a case by case basis, rather than simply adhering to the common set of regression limits (0.1 km2–5 km2) used by Snyder et al. (2000). The upstream regression limit is still typically near 0.1 km2, as defined by a kink in the slope-area data, but varies somewhat from drainage to drainage (Fig. 4). The downstream regression limit is set by the sudden reduction in channel gradient associated with the transition to alluviated conditions (typically at ∼107 m2; Fig. 4). This transition was mapped in the field (Snyder et al., 2003a) and was likely driven by rapid Holocene sea-level rise (Snyder et al., 2002). Between these regression limits, we find uncorrelated residuals to the model fits.

This revised analysis finds no statistically significant difference in concavity index between the channels sampled in the low and high uplift rate zones, and a regional best-fit mean value of 0.57 ± 0.1 (2σ), considerably higher than, and yet within error of the estimate reported by Snyder et al. (2000), 0.43 ± 0.22 (2σ). Reanalysis of the 30 m DEMs with our original data handling methods (contour extraction but no smoothing) on this subset of drainages confirms that the difference in best-fit concavity results mostly from the change in regression limits, rather than a difference in data quality or data handling methods. Using a reference concavity of 0.45 (for convenience of comparison to data from the other case studies presented here), we find mean k sn values of 66 and 117 m0.9 in the low and high uplift rate zones, respectively, yielding a ratio of k sn(high)/k sn(low) of 1.8. Further, the ratio of high uplift zone to low uplift zone average k sn values varies by less than 5% when using all permutations of smoothing, no smoothing, 30 m data, 10 m data, new regression limits, and old regression limits. Thus while the concavity index may be sensitive to the choice of regression limits, steepness indices appear to be robust across a broad range of data quality and user-chosen regression limits. In all cases, we find no statistically significant difference in the concavity index of channels in the high and low uplift rate zones.

The positive relationship between steepness index and rock uplift rate is expected, and is consistent with Merritts and Vincent's (1989) data. However, despite the reanalysis with higher-quality data, a number of conditions limit our ability to quantitatively relate steepness indices to uplift rates in this field setting. First, steepness values in the high uplift zone show considerable variability. Although this may reflect the spatial variations seen in Holocene uplift rates of marine platforms (Merritts, 1996), it does suggest that other variables may influence channel steepness despite the lithologic homogeneity among these drainages. Second, although the uplift rates vary over approximately an order of magnitude, the most reliable estimates of rock uplift rates in the field area are confined to the low and high ends of this range (∼0.5 mm/yr and ∼3–4 mm/yr). We therefore have only two reliable points to define the functional relationship between steepness index and uplift rate, which does not strongly constrain the range of models that can be fit to the data (e.g., Snyder et al., 2000, 2003a, 2003b).

4.1.2 San Gabriel Mountains

In the San Gabriel Mountains, stream profile data for over 100 streams were extracted from a 10 m USGS DEM of the region, and a composite plot was created from the slope-area data. Most of the tributaries analyzed in the San Gabriel Mountains exhibit smoothly concave profiles, with uniform slope-area scaling below a threshold drainage area of 106 m2 or less (Fig. 5). Among these profiles, concavity indices again show no systematic relationship to rock uplift rates, and a reference concavity of 0.45 was chosen based on the composite slope-area data. Normalized steepness indices in the San Gabriel Mountains range from ∼65 to 175 m0.9; the highest ksn values (∼150–175) are coincident with the youngest cooling ages and highest long-term erosion rates, while the lowest k sn values (∼65–80) are coincident with the oldest cooling ages and lowest long-term erosion rates (Fig. 5).

Figure 5. Long profile and slope-area data from a 10-m-resolution digital elevation model (DEM) from the San Gabriel Mountains east of Los Angeles, California. Top three plots show pairs of tributaries from high uplift zone (black) and low uplift zone (gray). In all plots, solid lines are fits to data with [thetas]ref = 0.45; dashed lines are fits to data with concavity as a free parameter. Squares are slope-area data using log-bin averaging method; crosses are data using 400 m smoothing window to calculate channel slopes (see text). Arrows above/below long profiles show regression limits from slope-area data. Rivers shown are: (A) Minegulch and Beartrap; (B) Iron Fork and Little Tujunga; (C) Coldwater and Pacoima. (D) Composite slope-area data from all six rivers. Steps in profiles and spikes in slope-area data are dams and reservoirs in the lower reaches of the drainage basins.

Figure 5. Long profile and slope-area data from a 10-m-resolution digital elevation model (DEM) from the San Gabriel Mountains east of Los Angeles, California. Top three plots show pairs of tributaries from high uplift zone (black) and low uplift zone (gray). In all plots, solid lines are fits to data with [thetas]ref = 0.45; dashed lines are fits to data with concavity as a free parameter. Squares are slope-area data using log-bin averaging method; crosses are data using 400 m smoothing window to calculate channel slopes (see text). Arrows above/below long profiles show regression limits from slope-area data. Rivers shown are: (A) Minegulch and Beartrap; (B) Iron Fork and Little Tujunga; (C) Coldwater and Pacoima. (D) Composite slope-area data from all six rivers. Steps in profiles and spikes in slope-area data are dams and reservoirs in the lower reaches of the drainage basins.

In addition to the adjusted fluvial profiles from which the relationship between steepness and rock uplift rate can be evaluated, a number of rivers in the western San Gabriel Mountains contain abrupt knickpoints that separate upstream and downstream channel segments with distinct steepness indices. The best examples of this are in the Big Tujunga drainage basin, within the slowly uplifting western San Gabriel Mountains (e.g., Blythe et al., 2000; Spotila et al., 2002). In this basin, knickpoints in multiple rivers are found at different points in the basin but nearly constant elevation, suggesting a transient condition as the channels adjust to changing boundary conditions (Fig. 6). Regressions on slope-area data above this knickpoint find k sn values indistinguishable from the regional lower bound (e.g., Fig. 5D), while k sn values below the knickpoint are slightly higher (Fig. 6A). In some of the tributaries, the boundary between these zones is characterized by a significantly oversteepened reach, possibly reflecting a disequilibrium state related to changes in sediment flux during landscape adjustment (e.g., Sklar and Dietrich, 1998; Gasparini, 2003; Gasparini et al., 2005). A preliminary interpretation is that these profiles record a transient response to a recent increase in rock uplift rate—probably during the Quaternary, given the plausible range of rock uplift rates and the height of the knickpoints. A total offset of ∼300 m during this period can be inferred from the height of knickpoints and the downstream projection of the less-steep upper-channel segments (Fig. 6A), and may be important both for interpreting young fission-track cooling ages along the lower Big Tujunga (e.g., Blythe et al., 2000), and for understanding the long-term evolution of active fault systems in the Los Angeles region.

Figure 6. (A) Long profiles of four tributaries to the Big Tujunga River and slope-area data from Trail Canyon, showing apparent transient in long profiles and map pattern. Note that transient is easily seen in z vs. x plots for Mill, Fox, and Clear Creek, but slope-area plot greatly aids interpretation for Trail Canyon. Dashed line extending from Mill Creek shows projection of upper profile to mountain front. (B) Map pattern of knickpoints (white dots) in Big Tujunga basin. Close correspondence of knicks to 1000 m contour (black line) and irregular pattern in map view again suggests a transient feature (see Fig. 3).

Figure 6. (A) Long profiles of four tributaries to the Big Tujunga River and slope-area data from Trail Canyon, showing apparent transient in long profiles and map pattern. Note that transient is easily seen in z vs. x plots for Mill, Fox, and Clear Creek, but slope-area plot greatly aids interpretation for Trail Canyon. Dashed line extending from Mill Creek shows projection of upper profile to mountain front. (B) Map pattern of knickpoints (white dots) in Big Tujunga basin. Close correspondence of knicks to 1000 m contour (black line) and irregular pattern in map view again suggests a transient feature (see Fig. 3).

In neither the King Range nor the San Gabriel Mountains are we able to quantify the relationship between k sn and U. In the King Range, we do not have enough data to differentiate among various threshold and nonlinear models of k s versus U and the potential effects of changing bed state on erosional efficiency (e.g., Snyder et al., 2003a); in the San Gabriel Mountains, modern rock uplift rates are not as well constrained and an analysis of (approximately) steady-state channel segments would suffer from similar limitations. Despite these complexities, however, the qualitative results from both field areas are both robust and important: the highest steepness values consistently correspond to the regions with the highest rock uplift and exhumation rates, while the lowest steepness values correspond to the lowest rock uplift and exhumation rates. In both field areas, lithologic differences between the high and low uplift regions are minimal, suggesting that channel steepness is tracking rock uplift rate. If we were to approach either of these field areas without any a priori knowledge of the tectonic setting, a map of steepness indices across the range would provide a great deal of information about the underlying tectonics. A plan view map of knickpoints in longitudinal profiles can also provide constraints on the location and magnitude of recent deformation in the region: in the San Gabriel Mountains, this analysis reveals an apparently recent (ca. 1 Ma?) change in rock uplift rates in the Big Tujunga basin. Importantly, with high-resolution DEMs throughout the United States publicly available, these analyses could be conducted in a matter of hours.

4.2 Siwalik Hills, Nepal

The case study from the Siwalik Hills in central Nepal is similar to the previous examples, in that steepness indices can be compared from zones of different rock uplift rates in a region of spatially uniform lithology. However, the Siwalik Hills provide the additional opportunity to examine the topographic signature of rock uplift rate gradients along individual channel profiles, particularly as these gradients affect channel concavities (e.g., Kirby and Whipple, 2001). The Siwalik Hills record modern deformation above a fault-bend fold in the Himalayan foreland, along the Main Frontal Thrust system. Deformation rates inferred from the distribution of Holocene terraces vary from ∼4 mm/yr north of the range, to ∼17 mm/yr at the range crest, and back to near zero just south of the Main Frontal Thrust. Multiple flights of terraces suggest relatively constant incision rate with time, and data from transverse drainages suggest steady-state profiles in these catchments (Lavé and Avouac, 2000). The fault-bend fold is dissected by drainages oriented both parallel and perpendicular to the strike of the range, and all of the rivers traverse relatively uniform sandstones and siltstones of the Lower and Middle Siwalik Hills (Lavé and Avouac, 2000).

Kirby and Whipple (2001) analyzed 22 channels in the Siwalik Hills, using a 90 m DEM of the region in an effort to assess to what degree strong spatial gradients in rock uplift rate influenced channel concavity and steepness. They argued that systematic changes in concavity indices could be exploited to place bounds on the relationship between channel gradient and incision rate. Here we update those results with analysis of a higher-resolution (30 m) DEM generated from ASTER stereo scenes. Channels parallel to the range crest, and therefore undergoing relatively uniform rock uplift rate, again yield concavity indices ranging from 0.45 to 0.55. Moreover, these strike-parallel drainages exhibit a predictable and quantifiable pattern of k sn values: channels in high uplift settings have the highest steepness indices, while those in low uplift zones have the lowest steepnesses. A plot of steepness coefficients versus uplift rate for these strike-parallel drainages reveals a linear relationship with an intercept statistically indistinguishable from zero (Fig. 7A). This relationship is consistent with a simple detachment-limited stream power model with n = 1, where  

formula
and K is an erodibility coefficient (e.g., Howard, 1994). Normalized steepness indices, k sn, for [thetas]ref = 0.52 range from ∼85 in low uplift regions (∼7 mm/yr) to ∼200 in high uplift regions (∼14 mm/yr).

Figure 7. (A) Plot of normalized steepness index (ksn ) versus uplift rate (U) for seven strike-parallel channels from the Siwalik Hills in southern Nepal. Data suggest a linear correlation between ksn and U with a zero intercept, consistent with a stream power scaling with n = 1. Uplift rates were estimated by Hurtrez et al. (1999) from a fault-bend-fold kinematic model and bedding dips. (B) Example of slope-area data from the Siwalik Hills in southern Nepal. Gray crosses show data from a representative strike-parallel stream in the low uplift rate regime (U = 7 mm/yr). Black crosses show data from a representative strike-parallel stream in the high-uplift-rate regime (U = 13 mm/yr). Open dots show data from a strike-perpendicular stream crossing the entire anticline, from low rock uplift rate (U = 4 mm/yr) to high rock uplift rate (U = 13 mm/yr) and back. Negative concavity segment in strike-perpendicular stream can be explained by spatially varying rock uplift rate along the profile (e.g., Kirby and Whipple, 2001). (C) Channel profiles shown in part B. Thick gray lines show approximate extent of slope-area fits used in part B. Negative concavity in transitional profile manifests as a rollover just above junction with the high uplift channel.

Figure 7. (A) Plot of normalized steepness index (ksn ) versus uplift rate (U) for seven strike-parallel channels from the Siwalik Hills in southern Nepal. Data suggest a linear correlation between ksn and U with a zero intercept, consistent with a stream power scaling with n = 1. Uplift rates were estimated by Hurtrez et al. (1999) from a fault-bend-fold kinematic model and bedding dips. (B) Example of slope-area data from the Siwalik Hills in southern Nepal. Gray crosses show data from a representative strike-parallel stream in the low uplift rate regime (U = 7 mm/yr). Black crosses show data from a representative strike-parallel stream in the high-uplift-rate regime (U = 13 mm/yr). Open dots show data from a strike-perpendicular stream crossing the entire anticline, from low rock uplift rate (U = 4 mm/yr) to high rock uplift rate (U = 13 mm/yr) and back. Negative concavity segment in strike-perpendicular stream can be explained by spatially varying rock uplift rate along the profile (e.g., Kirby and Whipple, 2001). (C) Channel profiles shown in part B. Thick gray lines show approximate extent of slope-area fits used in part B. Negative concavity in transitional profile manifests as a rollover just above junction with the high uplift channel.

Although most of the channels contained within uniform uplift regimes have moderate concavities near 0.5, channel segments crossing spatially varying rock uplift rates have anomalously high or low concavities, depending on the direction of flow relative to the gradient in uplift rate. Channels entering the Siwalik anticline from the north have rapidly increasing slopes (negative concavities), as uplift rates increase downstream. Of note is the observation that changes in gradient on these channels span the entire range of increase in gradients on strike-parallel channels (Fig. 7B), suggesting that both the strike-parallel and strike-perpendicular systems exhibit the same manner and degree of response to increasing rock uplift rates. This observation, coupled with the lack of abrupt knickpoints within these channels and the consistency between two independent estimates of the erosion coefficient K (see below), lends support to the hypothesis that these channels have reached a steady-state balance between channel incision and rock uplift.

Using the known range in uplift rates and observed channel geometries across these channel segments, Kirby and Whipple (2001) note that the concavity index provides an independent means of determining n and K. These authors argued that the change in gradient along two tributaries (Dhansar and Chadi Khola) was consistent with n ranging between 0.6 and 1. Reanalysis of the ASTER DEM gives estimated values for n of 0.72 and 0.88, close to the value of n = 1 derived in Figure 7A from strike-parallel drainages. The erosion coefficient (K) determined from the k s versus U relation (Fig. 7A) is 7.41 × 10−5 m−.04yr−1, while K derived independently from the strike-perpendicular channels ranges from 5.25 × 10−5 to 5.76 × 10−5 m−.04yr−1. Note that k sn and K are dimensional coefficients, the dimensions of which depend on the ratio of m/n and the value of m, respectively: the estimates reported here assume that m/n = [thetas]ref, and use [thetas]ref = 0.52, and n = 1 (i.e., m = 0.52). The consistency between estimates derived using both strike-parallel and strike-perpendicular channels suggests that we may be well on our way to deriving quantitative estimates of uplift rates directly from topography in regions with relatively simple tectonics and uniform lithology. For example, a map of the distribution of predicted channel incision rates from calibrated model parameters displays good correspondence with an independent estimate of rock uplift rate in this landscape that has been argued to be in steady state (Hurtrez et al., 1999; Lavé and Avouac, 2000) (Fig. 8).

Figure 8. Comparison of incision rate estimates derived from (A) stream profile method, assuming a stream-power incision rule with n = 1, and (B) structural study of Hurtrez et al. (1999) and Lavé and Avouac (2000). Note general correspondence of location and magnitude of high incision rate zones from the two methods, suggesting that quantitative estimates of incision rates may be attainable in regions with relatively simple patterns of lithology and uplift. Figure B is adapted from Hurtrez et al. (1999).

Figure 8. Comparison of incision rate estimates derived from (A) stream profile method, assuming a stream-power incision rule with n = 1, and (B) structural study of Hurtrez et al. (1999) and Lavé and Avouac (2000). Note general correspondence of location and magnitude of high incision rate zones from the two methods, suggesting that quantitative estimates of incision rates may be attainable in regions with relatively simple patterns of lithology and uplift. Figure B is adapted from Hurtrez et al. (1999).

If this type of analysis can be extended to other field settings, it represents a promising avenue for neotectonic research—if calibration sites can be identified with known uplift rates and similar channel morphologies to a field site of interest, it may be possible to obtain quantitative estimates of uplift rates and their spatial variability at the catchment scale prior to ever setting foot in the field. In the absence of a calibration site, the spatial patterns of uplift rates can still be estimated from the patterns of steepness and concavity identified from stream profiles. The accuracy of our quantitative estimates may decrease with decreasing knowledge of the field site; in particular, downstream changes in channel width (W) that differ from the typical scaling of W A 0.4 (e.g., Whipple, 2004, and references therein) will not be captured on slope-area plots, and may substantially modify the relationships between uplift rates and steepness indices in ways that must be explored through future work. At a minimum, however, the method provides a quick and easy way to evaluate patterns of rock uplift with a high degree of spatial resolution.

4.3 Central Nepal Himalaya

The preceding case studies illustrate a consistent relationship between steepness and uplift rate in regions where rock uplift rates have been independently determined. The next logical step is to utilize stream profiles for tectonic analysis in regions where modern rock uplift rates are less well understood. The case study discussed here is from central Nepal, where stream profiles are used along with thermochronologic and structural analysis to evaluate two competing models for the tectonic architecture of the Himalaya.

The High Himalayan peaks in central Nepal are bounded to the south by a sharp topographic break, which can be delineated on a map of hillslope gradients as a WNW-ESE−trending line separating the High Himalaya to the north from the Lesser Himalaya to the south (Wobus et al., 2003; Fig. 1). This physiographic transi tion—herein referred to as PT2 for consistency with Wobus et al. (2003) and Hodges et al. (2001)—may be consistent with one of two end-member models for Himalayan tectonics (Fig. 9). In the first model, the topographic transition is sustained entirely by rock uplift gradients due to material transport over a ramp in the Himalayan Sole Thrust. This model predicts similar thermal and deformational histories for rocks on opposite sides of PT2, and broadly distributed gradients in rock uplift rates from south to north (e.g., Cattin and Avouac, 2000; Lavé and Avouac, 2001). In the second model, surface-breaking thrusts—perhaps including young strands of the Main Central Thrust system (MCT)—remain active at the foot of the High Himalaya. This model predicts disparate thermal and structural histories on either side of PT2, and more abrupt changes in rock uplift and exhumation rates across discrete structures (e.g., Hodges et al., 2004; Wobus et al., 2003).

Figure 9. Schematic showing two competing models for Himalayan tectonic architecture and predicted patterns of rock uplift rates for each model. (A) Ramp model predicts uplift gradient spread over 20–30 km, with Main Central Thrust (MCT) carried passively over ramp in Himalayan Sole Thrust (HST). Uplift gradient should be broadly distributed (B), and thermal history for rocks on opposite sides of PT2 should be similar. Surface breaking thrust model (C) predicts more abrupt break in rock uplift rates centered at PT2 (D) and distinct thermal histories for rocks on opposite sides of the inferred surface breaking shear zone. MFT—Main Frontal Thrust; MBT—Main Boundary Thrust; MT—Mahabarat Thrust; STF—South Tibetan fault system; HST—Himalayan Sole Thrust; KTM—Kathmandu; PT2—physiographic transition; GHS—Greater Himalayan sequence. (Adapted from Wobus et al., 2003)

Figure 9. Schematic showing two competing models for Himalayan tectonic architecture and predicted patterns of rock uplift rates for each model. (A) Ramp model predicts uplift gradient spread over 20–30 km, with Main Central Thrust (MCT) carried passively over ramp in Himalayan Sole Thrust (HST). Uplift gradient should be broadly distributed (B), and thermal history for rocks on opposite sides of PT2 should be similar. Surface breaking thrust model (C) predicts more abrupt break in rock uplift rates centered at PT2 (D) and distinct thermal histories for rocks on opposite sides of the inferred surface breaking shear zone. MFT—Main Frontal Thrust; MBT—Main Boundary Thrust; MT—Mahabarat Thrust; STF—South Tibetan fault system; HST—Himalayan Sole Thrust; KTM—Kathmandu; PT2—physiographic transition; GHS—Greater Himalayan sequence. (Adapted from Wobus et al., 2003)

As a first step in evaluating which of these models is most relevant to central Nepal, stream profiles were extracted from a 90 m DEM of the region (see Fielding et al., 1994, for description of the data set). Composite plots of slope-area data from all tributaries define regional upper and lower limits of steepness values of 650 and 95 m0.9, respectively. In each case, the upper limit is defined by northern tributaries and trunk stream segments, and the lower limit is defined by southern tributaries and trunk stream segments (Fig. 10). This trend is consistent with a decrease from north to south in rock uplift rate, rock strength, or both. Because rock mass quality is typically very similar across these transitions, and because both of the tectonic models considered for the Himalaya include a decrease in rock uplift rates from north to south, we assume that a change in rock uplift rate is the major driving force for the change in ksn . Furthermore, monsoon precipitation appears to be focused just upstream of this major break in steepness indices (Hodges et al., 2004), suggesting that our estimate of the southward decrease in ksn for central Nepal may be conservative as a proxy for rock uplift rate. We focus here on the nature and spatial extent of this steepness transition, to evaluate which of the competing tectonic models is most appropriate for this portion of the Himalaya.

Figure 10. Slope-area plots and trunk stream longitudinal profiles from (A) Trisuli River catchment, (B) Burhi Gandaki catchment, and (C) Marsyandi catchment, all in central Nepal. Smoothing method and contour interval for all cases are 10 km moving average and 30 m, respectively. In each plot, gray crosses show data from representative southern (low uplift zone) tributaries; black crosses show data from representative northern (high uplift zone) tributaries; and open circles show data from trunk streams carving through the range. Dashed lines show approximate regional upper and lower bounds on steepness indices of 650 and 95 m0.9, respectively ([thetas]ref = 0.45). Gray shading on slope area and long profile data shows extent of high concavity zone in trunk streams, representing a maximum estimate of the width of rock uplift gradients (see text). Open stars show position of abrupt physiographic transition (PT2) in central Nepal, as identifi ed from slope maps and satellite photography (see text and Fig. 9). Note that Marsyandi long profile begins on a valley sidewall due to a data gap at the western edge of the catchment.

Figure 10. Slope-area plots and trunk stream longitudinal profiles from (A) Trisuli River catchment, (B) Burhi Gandaki catchment, and (C) Marsyandi catchment, all in central Nepal. Smoothing method and contour interval for all cases are 10 km moving average and 30 m, respectively. In each plot, gray crosses show data from representative southern (low uplift zone) tributaries; black crosses show data from representative northern (high uplift zone) tributaries; and open circles show data from trunk streams carving through the range. Dashed lines show approximate regional upper and lower bounds on steepness indices of 650 and 95 m0.9, respectively ([thetas]ref = 0.45). Gray shading on slope area and long profile data shows extent of high concavity zone in trunk streams, representing a maximum estimate of the width of rock uplift gradients (see text). Open stars show position of abrupt physiographic transition (PT2) in central Nepal, as identifi ed from slope maps and satellite photography (see text and Fig. 9). Note that Marsyandi long profile begins on a valley sidewall due to a data gap at the western edge of the catchment.

The analysis is similar to that used in the Siwalik Hills (e.g., Kirby and Whipple, 2001), in that tributaries both parallel and perpendicular to the inferred uplift rate gradient are utilized. For the trunk streams perpendicular to the uplift gradient, the width of the high concavity channel segments (the downstream transition from high to low steepness values) provides one estimate of the distance over which rock uplift rates are decreasing downstream (Fig. 10). Note that this should be a maximum estimate of the distance over which uplift rates are changing: downstream adjustments in sediment load across the tectonic boundary may diffuse any uplift rate signal (e.g., Whipple and Tucker, 2002), as will the smoothing algorithm applied in analysis of the data. The smaller tributary channels subparallel to the structural grain typically exhibit smooth profiles without abrupt knickpoints, normal concavities in the range of 0.4–0.6, and uniform steepness values down to the trunk stream junction. Furthermore, either of the tectonic models for central Nepal predicts nearly constant uplift rate within these narrow, east-west trending basins. We therefore infer that these channels record equilibrium profile forms, and use the spatial distribution of high and low steepness tributaries as a second means of estimating the distance over which uplift rates are changing in the system.

Slope-area data from the Burhi Gandaki trunk stream allow us to delineate a high concavity zone along ∼40 km of stream-wise distance, which spans the range in steepness values on a composite plot of slope-area data (Fig. 10B). As discussed above, this represents a maximum estimate of the width of the assumed uplift gradient. Tributary profiles allow us to place more precise constraints on the width of the transition zone: steepness values in strike-parallel streams decrease from ∼400 to ∼100 over ∼20 km in map view (Fig. 11). 40Ar/39Ar thermochronologic data from detrital muscovites in the Burhi Gandaki and Trisuli catchments suggest a profound change in time-averaged exhumation rates (or total depth of late Cenozoic exhumation) over an even narrower zone (8–10 km), suggesting that stream profile analysis is capturing a profound tectonic boundary in this setting. Similar results from the Trisuli River suggest that this boundary may continue along strike (Fig. 11; Wobus et al., 2003).

Figure 11. Digital elevation map (DEM) of central Nepal, showing transition zone between high and low uplift rates as determined from stream profile analyses. Diamonds along Trisuli and Burhi Gandaki Rivers show locations of detrital 40Ar/39Ar thermochronologic analysis: gray diamonds represent Miocene and younger apparent ages; white diamonds represent Paleozoic and older apparent ages. Note general correspondence of break in cooling history with change in stream profiles, suggesting a long-lived structure accommodating differential exhumation in this region. Dashed white lines in Marsyandi basin show location of intense Quaternary deformation, possibly responsible for accommodating the inferred gradient in rock uplift rates (e.g., Hodges et al., 2004).

Figure 11. Digital elevation map (DEM) of central Nepal, showing transition zone between high and low uplift rates as determined from stream profile analyses. Diamonds along Trisuli and Burhi Gandaki Rivers show locations of detrital 40Ar/39Ar thermochronologic analysis: gray diamonds represent Miocene and younger apparent ages; white diamonds represent Paleozoic and older apparent ages. Note general correspondence of break in cooling history with change in stream profiles, suggesting a long-lived structure accommodating differential exhumation in this region. Dashed white lines in Marsyandi basin show location of intense Quaternary deformation, possibly responsible for accommodating the inferred gradient in rock uplift rates (e.g., Hodges et al., 2004).

Similar methodologies can be used to delineate the width of the transition zone throughout central Nepal, and additional structural and thermochronologic data can be used to corroborate the stream profile analyses in many cases (Fig. 11). In the Marsyandi trunk stream, a high concavity zone across the topographic break spans a streamwise distance of ∼40 km, suggesting a decrease in rock uplift rates over this distance. Tributaries along this segment of the basin allow us to narrow this estimate to between 15 and 20 km (Fig. 11). Detailed structural mapping along the Marsyandi trunk and its tributaries indicates a penetrative brittle shear zone crosscutting all previous fabrics along the upper part of this same river reach. Consistent top-to-the-south kinematics on these north-dipping shear zones suggest that these structures may be accommodating differential motion in this zone, consistent with a model including recently active surface-breaking thrusts in this region (e.g., Hodges et al., 2004).

In the absence of a detailed stream profile analysis to guide structural and thermochronologic studies, sparse data coverage and model uncertainties render geophysical and geodetic data equivocal in discriminating between a surface breaking shear zone and a subsurface ramp in central Nepal. Stream profiles provide an additional piece of data that favors a narrowly distributed rock uplift gradient throughout the study area, and informs our sampling strategy for thermochronologic analyses. Although we are unable to provide an exact estimate of the distance over which rock uplift rates are increasing, stream profiles are a crucial tool in this setting for evaluating a range of tectonic models and identifying sites for future field and laboratory work.

5. DISCUSSION

The correlation between steepness and uplift rate in established tectonic settings, and the ability to delineate temporal and spatial breaks in rock uplift rate in more poorly constrained settings, demonstrate the power of stream profile analysis. However, a number of shortcomings must yet be overcome if stream profile analysis is to become a mainstream tool for neotectonic investigations. In particular, if we wish to derive quantitative estimates of rock uplift rates directly from topography, a great deal of work remains to be done (e.g., Whipple, 2004).

Foremost among our research needs is a continued, systematic dissection of the varied influences on river incision into rock. For example, how does the relative importance of meso-scale processes, such as plucking and abrasion, change with channel slope and incision rate, and how do the rates of these processes differ from simple shear-stress–dependent incision at the bed (e.g., Whipple et al., 2000)? How do changes in bed roughness, sediment flux, and bed cover influence erosion rates (e.g., Sklar and Dietrich, 1998, 2001; Hancock and Anderson, 2002; Sklar, 2003)? What controls changes in bedrock channel width, and how do changes in width influence erosion rates (e.g., Hancock and Anderson, 2002; Montgomery and Gran, 2001; Snyder et al., 2003a; Lague and Davy, 2003)? How do we incorporate critical thresholds for river incision and a stochastic distribution of storms into our erosion models (e.g., Tucker and Bras, 2000; Snyder et al., 2003b; Tucker, 2004)? We have only begun to ask these questions, and more comprehensive field, experimental, and numerical studies must be undertaken before we can hope to have a reliable quantitative tool for neotectonics (e.g.,Whipple, 2004).

Although we cannot yet deconvolve the relative contributions of lithology, adjustments in channel morphology and bed state, climatic variables, and uplift rate on channel steepness, we must continue to incorporate as much of this information as we can into our analysis. Where available, lithologic and climatic information can already be used to qualitatively ascertain the importance of rock uplift rate variations on long profile form. For example, in some settings large breaks in channel steepness across lithologic boundaries may be entirely contained within a single uplift regime; ignoring the effects of lithology would lead to dramatic misconceptions of tectonic signals. In other field areas, a decrease in rock uplift rate may be co-located with an increase in rock strength across major structures, such that the two effects moderate one another in the context of profile steepness. Ultimately, utilizing stream profile analysis to inform detailed structural, thermochronologic, and cosmogenic analyses will continue to be the best approach for neotectonic investigations (e.g., Kirby et al., 2003; Wobus et al., 2003; Hodges et al., 2004). Stream profile analyses cannot be conducted in a vacuum; informing our investigations with as much additional data as possible must remain a priority in any topographic analysis.

Numerical experiments incorporating an orographic forcing of precipitation predict systematic, if minor, changes in profile concavity due to an uneven distribution of precipitation at the range scale (e.g., Roe et al., 2002, 2003). Because precipitation effects are manifested in models of fluvial erosion only through their contribution to river discharge, we typically do not expect fluvial profiles to change abruptly due to spatial gradients in climate. However, the effects of temporal changes in climate may be more pronounced, particularly in settings where river systems take over previously glaciated valleys, or where glacial-interglacial cycling high in a basin creates profound changes in sediment flux within the fluvial part of the system (e.g., Brocklehurst and Whipple, 2002; Hancock and Anderson, 2002). Spatial and temporal changes in climate must both be more fully incorporated into our models if we hope to one day derive quantitative estimates of uplift rates from topography.

The stream profile method measures only changes in channel slope. However, a river's response to changes in uplift rate may include adjustments in a variety of other factors related to dominant incision processes, channel morphology, and bed state (e.g., Whipple and Tucker, 1999, 2002; Sklar and Dietrich, 1998, 2001; Sklar, 2003). Where channels cross boundaries between rocks with considerable differences in rock strength without any change in steepness index, adjustments in channel morphology or bed state may be fully compensating for the change in rock properties (see Montgomery and Gran, 2001; Sklar, 2003). Alternatively, transport-limited, rather than detachment-limited, conditions may be indicated (e.g., Whipple and Tucker, 2002). As discussed in section 2, our ability to quantify many of these feedbacks and internal adjustments is limited. As our understanding of the mechanisms of fluvial response to differential rock uplift improves, these additional degrees of freedom should be incorporated into both modeling and empirical studies of the interrelations among climate, erosion, tectonics, and topography. Until then, we must recognize that adjustments in channel slope are only part of a more complicated equation.

In order to make the connection between topography and tectonics, an assumption is often made that a steady-state balance between uplift and erosion prevails. In many landscapes, this condition will not be met, leading to transient forms such as propagating knickpoints, knickzones, and other disequilibrium channel forms (e.g., Whipple and Tucker, 1999; Stock et al., 2004; Anderson et al., 2005). The severe limitations of the steady-state assumption are well known. However, it is incorrect to presume that model parameters can be constrained only through analysis of steady-state forms. Where data quality is high, deviations from steady-state are often readily discernible through analysis of stream profiles and plan view maps (e.g., Figs. 3 and 6). Recognition of such transient forms is important for at least two reasons. First, they can be useful indicators of tectonic history, such as a sudden base-level fall or a change in differential rock uplift rate at the outlet of a drainage network, as illustrated for the San Gabriel Mountains (Fig. 6). Second, under the right circumstances, profiles with such forms can provide information about two steady-state conditions, when the channel is incising at different, often knowable, rates, above and below the knickpoint, such that an upper steady-state profile is “replaced” by a lower steady-state profile as the knickpoint advances (e.g., Whipple and Tucker, 1999; Niemann et al., 2001). Where sediment flux and channel bed state play important roles, transient response may be complex. For example, these disequilibrium channels may be characterized by transient oversteepened reaches downstream of knickpoints (Gasparini, 2003; Gasparini et al., 2005), which may be mistaken for equilibrium high concavity segments if data quality and resolution are low. It is potential complexities in the transient response of rivers such as this that afford the best opportunity to quantitatively test competing river incision models.

Finally, many DEMs, particularly those with low spatial resolution, contain “bad” data points along a channel due to topographic variability at a smaller spatial scale than the cell size, short-circuiting of sinuous channels in extraction of long profile data, or errors in the algorithm converting an original data source to a raster format. As a result, we often must make a decision as to whether unusual data represent noise or real geological complexity. One potential source of the latter is the influence of large landslides, which may temporarily block fluvial systems causing alternating flats and steps in long profiles. Often the distinction between data noise and geologic complexity is easily made; however, at present there are no quantitative criteria to evaluate whether or not anomalies in stream profiles are real without complementary field investigation. As data quality improves across the globe, part of this difficulty will gradually be overcome. Until then, determining the difference between bad data and geological complexity will typically require field observations to resolve satisfactorily.

6. CONCLUSIONS

Empirical observations and simple models of fluvial erosion suggest a positive correlation between channel gradient and rock uplift rate, which we exploit in the method of stream profile analysis outlined here. Despite our incomplete understanding of the varied processes contributing to fluvial erosion, the stream profile method is an invaluable qualitative tool for neotectonic investigations. In northern and southern California, we show that channel steepness is directly related to rock uplift rate. In the Siwalik Hills, Nepal, changes in steepness and concavity each correlate in a predictable way with rock uplift rate variations, and we can begin constructing a quantitative means of translating topography into tectonics through local calibration of a simple river incision model. Finally, in central Nepal, stream profile analysis provides a crucial discriminator between two models of Himalayan tectonics, and has led to identification of a previously unrecognized shear zone. Our next steps should be focused on refining this promising qualitative tool by incorporating recent advances in process geomorphology into models of stream profile evolution and form. While further numerical studies will be useful in this regard, we are ultimately limited by our lack of empirical data to characterize fluvial response. As such, we should focus on field and laboratory work geared toward understanding variations in fluvial erosion processes and rates with changes in incision rate, bed morphology and bed state, and climate. Only when we can confidently describe all of these feedbacks can we hope to have a reliable quantitative tool for neotectonic analysis.

This work was funded by National Science Foundation (NSF) Tectonics grant EAR-008758 to K.X Whipple and K.V. Hodges that supported the work of C. Wobus, and additional NSF grants to K.X. Whipple that supported the work of B. Crosby (NSF GLD EAR-0208312) and J. Johnson (NSF GLD EAR-0345622). We thank Jerome Lavé for providing access to data and figures for the Siwalik Hills case study, and Bob Anderson and David Montgomery for thoughtful reviews of the original manuscript. Finally, we thank all of the organizers and participants of the Penrose Conference for a fantastic meeting.

Blythe
,
A.E.
,
Burbank, D.W., Farley, K.A., and Fielding, E.J.,
2000
, Structural and topographic evolution of the central Transverse Ranges, California, from apatite fission-track, (U-Th)/He and digital elevation model analyses:
Basin Research
 , v.
12
p.
97
-114 doi: 10.1046/j.1365-2117.2000.00116.x.
Brocklehurst
,
S.H.
,
and Whipple, K.X.,
2002
, Glacial erosion and relief production in the Eastern Sierra Nevada, California:
Geomorphology
 , v.
42
p.
1
-24 doi: 10.1016/S0169-555X(01)00069-1.
Burbank
,
D.W.
,
Leland, J., Fielding, E., Anderson, R.S., Brozovic, N., Reid, M.R., and Duncan, C.,
1996
, Bedrock incision, rock uplift and threshold hillslopes in the northwestern Himalayas:
Nature
 , v.
379
, no. 6565 p.
505
-510 doi: 10.1038/379505a0.
Cattin
,
R.
,
and Avouac, J.P.,
2000
, Modeling mountain building and the seismic cycle in the Himalaya of Nepal:
Journal of Geophysical Research
 , v.
105
p.
13389
-13407 doi: 10.1029/2000JB900032.
Fielding
,
E.
,
Isacks, B., Barazangi, M., and Duncan, C.,
1994
, How flat is Tibet?:
Geology
 , v.
22
p.
163
-167 doi: 10.1130/0091-7613(1994)022<0163: HFIT>2.3.CO;2.
Finlayson
,
D.P.
,
and Montgomery, D.R.,
2003
, Modeling large-scale fluvial erosion in geographic information systems:
Geomorphology
 , v.
53
p.
147
-164 doi: 10.1016/S0169-555X(02)00351-3.
Finlayson
,
D.P.
,
Montgomery, D.R., and Hallet, B.,
2002
, Spatial coincidence of rapid inferred erosion with young metamorphic massifs in the Himalayas:
Geology
 , v.
30
, no. 3 p.
219
-222 doi: 10.1130/0091-7613(2002)030<0219:SCORIE>2.0.CO;2.
Flint
,
J.J.
,
1974
, Stream gradient as a function of order, magnitude, and discharge:
Water Resources Research
 , v.
10
, no. 5 p.
969
-973.
Gasparini
,
N.
,
2003
, Equilibrium and transient morphologies of river networks: Discriminating among fluvial erosion models [Ph.D. thesis]: Cambridge, Massachusetts, Massachusetts Institute of Technology.
105
p.
Hack
,
J.T.
,
1957
, Studies of longitudinal stream profiles in Virginia and Maryland: U.S. Geological Survey Professional Paper 294-B.
97
p.
Hack
,
J.T.
,
1973
, Stream profile analysis and stream-gradient index:
U.S. Geological Survey Journal of Research
 , v.
1
, no. 4 p.
421
-429.
Hancock
,
G.S.
,
and Anderson, R.S.,
2002
, Numerical modeling of fluvial strath-terrace formation in response to oscillating climate:
Geological Society of America Bulletin
 , v.
114
, no. 9 p.
1131
-1142 doi: 10.1130/0016-7606(2002)114<1131:NMOFST>2.0.CO;2.
Harbor
,
D.J.
,
1998
, Dynamic equilibrium between an active uplift and the Sevier River, Utah:
Journal of Geology
 , v.
106
p.
181
-198.
Heimsath
,
A.M.
,
Dietrich, W.E., Nishiizumi, K., and Finkel, R.C.,
1997
, The soil production function and landscape equilibrium:
Nature
 , v.
388
p.
358
-361 doi: 10.1038/41056.
Hodges
,
K.
,
Hurtado, J.M., and Whipple, K.,
2001
, Southward extrusion of Tibetan crust and its effect on Himalayan tectonics:
Tectonics
 , v.
20
p.
799
-809.
Hodges
,
K.
,
Wobus, C., Ruhl, K., Schildgen, T., and Whipple, K.,
2004
, Quaternary deformation, river steepening and heavy precipitation at the front of the Higher Himalayan ranges:
Earth and Planetary Science Letters
 , v.
220
, no. 3–4 p.
379
-389 doi: 10.1016/S0012-821X(04)00063-9.
Howard
,
A.D.
,
1994
, A detachment-limited model of drainage basin evolution:
Water Resources Research
 , v.
30
, no. 7 p.
2261
-2285 doi: 10.1029/94WR00757.
Howard
,
A.D.
,
and Kerby, G.,
1983
, Channel changes in badlands:
Geological Society of America Bulletin
 , v.
94
p.
739
-752 doi: 10.1130/0016-7606(1983)94<739:CCIB>2.0.CO;2.
Hurtrez
,
J.E.
,
Lucazeau, F., Lavé, J., and Avouac, J.P.,
1999
, Investigation of the relationships between basin morphology, tectonic uplift, and denudation from the study of an active fold belt in the Siwalik Hills, central Nepal:
Journal of Geophysical Research
 , v.
104
, no. B6 p.
12779
-12796 doi: 10.1029/1998JB900098.
Kirby
,
E.
,
and Whipple, K.X.,
2001
, Quantifying differential rock-uplift rates via stream profile analysis:
Geology
 , v.
29
, no. 5 p.
415
-418 doi: 10.1130/0091-7613(2001)029<0415:QDRURV>2.0.CO;2.
Kirby
,
E.
,
Whipple, K., Tang, W., and Chen, Z.,
2003
, Distribution of active rock uplift along the eastern margin of the Tibetan Plateau: Inferences from bedrock channel longitudinal profiles:
Journal of Geophysical Research
 , v.
108
, no. B4 doi: 10.1029/2001JB000861.
Lague
,
D.
,
and Davy, P.,
2003
, Constraints on the long-term colluvial erosion law by analyzing slope-area relationships at various tectonic uplift rates in the Siwalik Hills (Nepal):
Journal of Geophysical Research
 , v.
108
, no. B2 doi: 10.1029/2002JB001893.
Lavé
,
J.
,
and Avouac, J.P.,
2000
, Active folding of fluvial terraces across the Siwalik Hills, Himalayas of central Nepal:
Journal of Geophysical Research
 , v.
105
, no. B3 p.
5735
-5770 doi: 10.1029/1999JB900292.
Lavé
,
J.
,
and Avouac, J.P.,
2001
, Fluvial incision and tectonic uplift across the Himalayas of central Nepal:
Journal of Geophysical Research
 , v.
106
, no. B11 p.
26561
-26591 doi: 10.1029/2001JB000359.
Massong
,
T.M.
,
and Montgomery, D.R.,
2000
, Influence of sediment supply, lithology, and wood debris on the distribution of bedrock and alluvial channels:
Geological Society of America Bulletin
 , v.
112
p.
591
-599 doi: 10.1130/0016-7606(2000)112<591:IOSSLA>2.3.CO;2.
Merritts
,
D.J.
,
1996
, The Mendocino triple junction: Active faults, episodic coastal emergence, and rapid uplift:
Journal of Geophysical Research
 , v.
101
p.
6051
-6070 doi: 10.1029/95JB01816.
Merritts
,
D.J.
,
and Bull, W.B.,
1989
, Interpreting Quaternary uplift rates at the Mendocino triple junction, northern California, from uplifted marine terraces:
Geology
 , v.
17
p.
1020
-1024 doi: 10.1130/0091-7613(1989)017<1020:IQURAT>2.3.CO;2.
Merritts
,
D.
,
and Vincent, K.R.,
1989
, Geomorphic response of coastal streams to low, intermediate, and high rates of uplift, Mendocino junction region, northern California:
Geological Society of America Bulletin
 , v.
101
p.
1373
-1388 doi: 10.1130/0016-7606(1989)101<1373: GROCST>2.3.CO;2.
Montgomery
,
D.R.
,
and Brandon, M.T.,
2002
, Topographic controls on erosion rates in tectonically active mountain ranges:
Earth and Planetary Science Letters
 , v.
201
p.
481
-489 doi: 10.1016/S0012-821X(02)00725-2.
Montgomery
,
D.R.
,
and Gran, K.B.,
2001
, Downstream variations in the width of bedrock channels:
Water Resources Research
 , v.
37
, no. 6 p.
1841
-1846 doi: 10.1029/2000WR900393.
Montgomery
,
D.R.
,
and Foufoula-Georgiou, E.,
1993
, Channel network representation using digital elevation models:
Water Resources Research
 , v.
29
p.
3925
-3934 doi: 10.1029/93WR02463.
Montgomery
,
D.R.
,
Dietrich, W.E., and Sullivan, K.,
1998
, The role of GIS in watershed analysis: in Lane, S.N., Richards, K.S., and Chandler, J.H., eds., Landform monitoring, modelling and analysis: Chichester, England, John Wiley and Sons, p.
241
-261.
Niemann
,
J.D.
,
Gasparini, N.M., Tucker, G.E., and Bras, R.L.,
2001
, A quantitative evaluation of Playfair's law and its use in testing long-term stream erosion models:
Earth Surface Processes and Landforms
 , v.
26
, no. 12 p.
1317
-1332 doi: 10.1002/esp.272.
Roe
,
G.H.
,
Montgomery, D.R., and Hallet, B.,
2002
, Effects of orographic precipitation variations on the concavity of steady-state river profiles:
Geology
 , v.
30
, no. 2 p.
143
-146 doi: 10.1130/0091-7613(2002)030<0143: EOOPVO>2.0.CO;2.
Roe
,
G.H.
,
Montgomery, D.R., and Hallet, B.,
2003
, Orographic precipitation and the relief of mountain ranges:
Journal of Geophysical Research
 , v.
108
, no. B6.
2315
doi: 10.1029/2001JB001521.
Sklar
,
L.
,
2003
, The influence of grain size, sediment supply, and rock strength on rates of river incision into bedrock [Ph.D. thesis]: Berkeley, University of California.
343
p.
Sklar
,
L.
,
and Dietrich, W.E.,
1998
, River longitudinal profiles and bedrock incision models: Stream power and the influence of sediment supply: in Tinkler, K.J., and Wohl, E.E., eds., Rivers over rock: Fluvial processes in bedrock channels: Washington, D.C., American Geophysical Union, p.
237
-260.
Sklar
,
L.S.
,
and Dietrich, W.E.,
2001
, Sediment and rock strength controls on river incision into bedrock:
Geology
 , v.
29
, no. 12 p.
1087
-1090 doi: 10.1130/0091-7613(2001)029<1087:SARSCO>2.0.CO;2.
Snyder
,
N.
,
Whipple, K., Tucker, G., and Merritts, D.,
2000
, Landscape response to tectonic forcing: DEM analysis of stream profiles in the Mendocino triple junction region, northern California:
Geological Society of America Bulletin
 , v.
112
, no. 8 p.
1250
-1263 doi: 10.1130/0016-7606(2000)112<1250:LRTTFD>2.3.CO;2.
Snyder
,
N.P.
,
Whipple, K.X., Tucker, G.E., and Merritts, D.M.,
2002
, Interactions between onshore bedrock-channel incision and nearshore wave-base erosion forced by eustasy and tectonics:
Basin Research
 , v.
14
p.
105
-127 doi: 10.1046/j.1365-2117.2002.00169.x.
Snyder
,
N.P.
,
Whipple, K.X., Tucker, G.E., and Merrits, D.J.,
2003a
, Channel response to tectonic forcing: Field analysis of stream morphology and hydrology in the Mendocino triple junction region, northern California:
Geomorphology
 , v.
53
p.
97
-127 doi: 10.1016/S0169-555X(02)00349-5.
Snyder
,
N.P.
,
Whipple, K.X., Tucker, G.E., and Merrits, D.J.,
2003b
, Importance of a stochastic distribution of floods and erosion thresholds in the bedrock river incision problem:
Journal of Geophysical Research
 , v.
39
doi: 10.1029/2001WR001057.
Spotila
,
J.A.
,
House, M.A., Blythe, A., Niemi, N.A., and Bank, G.C.,
2002
, Controls on the erosion and geomorphic evolution of the San Bernardino and San Gabriel Mountains, southern California: in Barth, A.P., ed., Contributions to crustal evolution of the southwestern United States: Geological Society of America Special Paper 365, p.
205
-230.
Stock
,
G.M.
,
Anderson, R.S., and Finkel, R.C.,
2004
, Pace of landscape evolution in the Sierra Nevada, California, revealed by cosmogenic dating of cave sediments:
Geology
 , v.
32
, no. 3 p.
193
-196 doi: 10.1130/ G20197.1.
Stock
,
J.D.
,
and Dietrich, W.E.,
2003
, Valley incision by debris flows: Evidence of a topographic signature:
Water Resources Research
 , v.
39
, no. 4 doi: 10.1029/2001WR001057.
Tarboton
,
D.G.
,
Bras, R.L., and Rodriguez-Iturbe, I.,
1989
, Scaling and elevation in river networks:
Water Resources Research
 , v.
25
p.
2037
-2051.
Tucker
,
G.E.
,
2004
, Drainage basin sensitivity to tectonic and climatic forcing: Implications of a stochastic model for the role of entrainment and erosion thresholds:
Earth Surface Processes and Landforms
 , v.
29
p.
185
-205 doi: 10.1002/esp.1020.
Tucker
,
G.E.
,
and Bras, R.L.,
2000
, A stochastic approach to modeling the role of rainfall variability in drainage basin evolution:
Water Resources Research
 , v.
36
p.
1953
-1964 doi: 10.1029/2000WR900065.
Tucker
,
G.E.
,
and Whipple, K.X.,
2002
, Topographic outcomes predicted by stream erosion models: Sensitivity analysis and intermodel comparison:
Journal of Geophysical Research
 , v.
107
, no. B9 doi: 10.1029/2001JB000162.
Whipple
,
K.
,
2004
, Bedrock rivers and the geomorphology of active orogens:
Annual Reviews of Earth and Planetary Science
 , v.
32
p.
151
-185 doi: 10.1146/annurev.earth.32.101802.120356.
Whipple
,
K.X.
,
and Tucker, G.E.,
1999
, Dynamics of the stream-power river incision model: Implications for height limits of mountain ranges, landscape response timescales, and research needs:
Journal of Geophysical Research
 , v.
104
p.
17661
-17674 doi: 10.1029/1999JB900120.
Whipple
,
K.X.
,
and Tucker, G.E.,
2002
, Implications of sediment-flux-dependent river incision models for landscape evolution:
Journal of Geophysical Research
 , v.
107
, no. B2 doi: 10.1029/2000JB000044.
Whipple
,
K.X.
,
Hancock, G.S., and Anderson, R.S.,
2000
, River incision into bedrock: Mechanics and relative efficacy of plucking, abrasion, and cavitation:
Geological Society of America Bulletin
 , v.
112
, no. 3 p.
490
-503 doi: 10.1130/0016-7606(2000)112<490:RIIBMA>2.3.CO;2.
Willgoose
,
G.
,
Bras, R.L., and Rodriguez-Iturbe, I.,
1991
, A coupled channel network growth and hillslope evolution model: I. Theory:
Water Resources Research
 , v.
27
, no. 7 p.
1671
-1684 doi: 10.1029/91WR00935.
Wobus
,
C.W.
,
Hodges, K.V., and Whipple, K.X.,
2003
, Has focused denudation sustained active thrusting at the Himalayan topographic front?:
Geology
 , v.
31
p.
861
-864 doi: 10.1130/G19730.1.

Figures & Tables

Figure 1. Example of contour extraction method for high-quality U.S. Geological Survey (USGS) 10 m digital elevation model (DEM). (A) Prior to contour extraction, DEM is characterized by abundant artificial data between contour crossings, resulting in a stepped pattern on the profile. Subsampling data at equal vertical intervals (gray dots) produces a smoother, more realistic profile consistent with the source data (see text for discussion). (B) Contour extraction method faithfully reproduces stream profile crossings of contour lines on original USGS topographic map (gray dots). Dashed line—stream line extracted from DEM (compare to dash-dot stream line on the map).

Figure 1. Example of contour extraction method for high-quality U.S. Geological Survey (USGS) 10 m digital elevation model (DEM). (A) Prior to contour extraction, DEM is characterized by abundant artificial data between contour crossings, resulting in a stepped pattern on the profile. Subsampling data at equal vertical intervals (gray dots) produces a smoother, more realistic profile consistent with the source data (see text for discussion). (B) Contour extraction method faithfully reproduces stream profile crossings of contour lines on original USGS topographic map (gray dots). Dashed line—stream line extracted from DEM (compare to dash-dot stream line on the map).

Figure 2. Effects of smoothing on longitudinal profile data, from San Gabriel Mountains in southern California. (A) Profile data extracted from U.S. Geological Survey (USGS) 10 m digital elevation model (DEM), showing raw profile (light-gray crosses) and data extracted at equal vertical intervals of 12.192 m (40 ft) (black crosses). (B) Profile data extracted from Shuttle Radar Topography Mission (SRTM) 90 m DEM, showing raw profile data (light-gray crosses) and data extracted at 12.192 m intervals (black crosses). Note the considerable reduction in scatter in both cases. (C) Superposition of smoothed data from SRTM 90 m DEM (720 m smoothing window, light-gray crosses), log-bin averaged data for SRTM 90 m DEM (light-gray squares), smoothed data from USGS 10 m DEM (180 m smoothing window, black crosses), and log-bin averaged data for USGS 10 m DEM (black squares). Note general correspondence among all data sets despite variations in resolution. (D) Plot of ksn , normalized to average value of each group, versus smoothing window. (E) Plot of [thetas], normalized to average value of each group, versus smoothing window. Note that steepness and concavity indices for any data set are consistent within ∼10%, regardless of the choice of smoothing window size or style.

Figure 2. Effects of smoothing on longitudinal profile data, from San Gabriel Mountains in southern California. (A) Profile data extracted from U.S. Geological Survey (USGS) 10 m digital elevation model (DEM), showing raw profile (light-gray crosses) and data extracted at equal vertical intervals of 12.192 m (40 ft) (black crosses). (B) Profile data extracted from Shuttle Radar Topography Mission (SRTM) 90 m DEM, showing raw profile data (light-gray crosses) and data extracted at 12.192 m intervals (black crosses). Note the considerable reduction in scatter in both cases. (C) Superposition of smoothed data from SRTM 90 m DEM (720 m smoothing window, light-gray crosses), log-bin averaged data for SRTM 90 m DEM (light-gray squares), smoothed data from USGS 10 m DEM (180 m smoothing window, black crosses), and log-bin averaged data for USGS 10 m DEM (black squares). Note general correspondence among all data sets despite variations in resolution. (D) Plot of ksn , normalized to average value of each group, versus smoothing window. (E) Plot of [thetas], normalized to average value of each group, versus smoothing window. Note that steepness and concavity indices for any data set are consistent within ∼10%, regardless of the choice of smoothing window size or style.

Figure 3. Schematic long profile and map view plots comparing transient and steady-state systems. (A) Transient long profile showing short oversteepened reach separating old and new equilibrium states. (B) Profile crossing from one uplift regime to another, showing channel reaches with constant ks values separated by a high or low concavity transition zone in between. In this and all subsequent plots, long profile data (elevation versus distance) will be shown as solid lines with linear axes labeled on top and at right; slope-area data (log S vs. log A) will be shown as crosses with logarithmic axes labeled at bottom and at left. A cr marks transition to fluvial scaling (see text); slope of log S vs. log A scaling is the concavity index [thetas]; y-intercept is the steepness index ks . (C) Transient wave of incision propagates through system at a nearly constant vertical rate; knickpoints (white dots) should therefore closely follow lines of constant elevation (dashed line) in plan view. (D) In contrast, knickpoints separating zones of high and low uplift rates (white dots) follow the trend of the accommodating shear zone in map view (dashed line). In many cases, the map pattern of knickpoints may be a better diagnostic of a transient state than long profile form.

Figure 3. Schematic long profile and map view plots comparing transient and steady-state systems. (A) Transient long profile showing short oversteepened reach separating old and new equilibrium states. (B) Profile crossing from one uplift regime to another, showing channel reaches with constant ks values separated by a high or low concavity transition zone in between. In this and all subsequent plots, long profile data (elevation versus distance) will be shown as solid lines with linear axes labeled on top and at right; slope-area data (log S vs. log A) will be shown as crosses with logarithmic axes labeled at bottom and at left. A cr marks transition to fluvial scaling (see text); slope of log S vs. log A scaling is the concavity index [thetas]; y-intercept is the steepness index ks . (C) Transient wave of incision propagates through system at a nearly constant vertical rate; knickpoints (white dots) should therefore closely follow lines of constant elevation (dashed line) in plan view. (D) In contrast, knickpoints separating zones of high and low uplift rates (white dots) follow the trend of the accommodating shear zone in map view (dashed line). In many cases, the map pattern of knickpoints may be a better diagnostic of a transient state than long profile form.

Figure 4. Long profile and slope-area data from a 10-m-resolution digital elevation model (DEM) of the King Range in northern California. Top three plots show pairs of tributaries from high uplift zone (black) and low uplift zone (gray). In all plots, solid lines are fits to data with [thetas]ref = 0.57; dashed lines are fits to data with concavity as a free parameter. Squares are slope-area data using log-bin averaging method; crosses are data using 200 m smoothing window to calculate channel slopes (see text). Arrows above long profiles show regression limits for slope-area fits. (A) Gitchell Creek and Hardy Creek. (B) Shipman Creek and Howard Creek. (C) Big Creek and Juan Creek. (D) Composite slope-area data from all six rivers. Note that in all cases the channels from the high uplift zone are consistently steeper than those in the low uplift zone. Dramatic drop in channel gradient in lowermost segments of the channels reflects a transition to increasingly alluviated conditions, reflecting a decrease in effective rock uplift rate due to Holocene rise in sea level (Snyder et al., 2002), alluviation at channel mouth, or both.

Figure 4. Long profile and slope-area data from a 10-m-resolution digital elevation model (DEM) of the King Range in northern California. Top three plots show pairs of tributaries from high uplift zone (black) and low uplift zone (gray). In all plots, solid lines are fits to data with [thetas]ref = 0.57; dashed lines are fits to data with concavity as a free parameter. Squares are slope-area data using log-bin averaging method; crosses are data using 200 m smoothing window to calculate channel slopes (see text). Arrows above long profiles show regression limits for slope-area fits. (A) Gitchell Creek and Hardy Creek. (B) Shipman Creek and Howard Creek. (C) Big Creek and Juan Creek. (D) Composite slope-area data from all six rivers. Note that in all cases the channels from the high uplift zone are consistently steeper than those in the low uplift zone. Dramatic drop in channel gradient in lowermost segments of the channels reflects a transition to increasingly alluviated conditions, reflecting a decrease in effective rock uplift rate due to Holocene rise in sea level (Snyder et al., 2002), alluviation at channel mouth, or both.

Figure 5. Long profile and slope-area data from a 10-m-resolution digital elevation model (DEM) from the San Gabriel Mountains east of Los Angeles, California. Top three plots show pairs of tributaries from high uplift zone (black) and low uplift zone (gray). In all plots, solid lines are fits to data with [thetas]ref = 0.45; dashed lines are fits to data with concavity as a free parameter. Squares are slope-area data using log-bin averaging method; crosses are data using 400 m smoothing window to calculate channel slopes (see text). Arrows above/below long profiles show regression limits from slope-area data. Rivers shown are: (A) Minegulch and Beartrap; (B) Iron Fork and Little Tujunga; (C) Coldwater and Pacoima. (D) Composite slope-area data from all six rivers. Steps in profiles and spikes in slope-area data are dams and reservoirs in the lower reaches of the drainage basins.

Figure 5. Long profile and slope-area data from a 10-m-resolution digital elevation model (DEM) from the San Gabriel Mountains east of Los Angeles, California. Top three plots show pairs of tributaries from high uplift zone (black) and low uplift zone (gray). In all plots, solid lines are fits to data with [thetas]ref = 0.45; dashed lines are fits to data with concavity as a free parameter. Squares are slope-area data using log-bin averaging method; crosses are data using 400 m smoothing window to calculate channel slopes (see text). Arrows above/below long profiles show regression limits from slope-area data. Rivers shown are: (A) Minegulch and Beartrap; (B) Iron Fork and Little Tujunga; (C) Coldwater and Pacoima. (D) Composite slope-area data from all six rivers. Steps in profiles and spikes in slope-area data are dams and reservoirs in the lower reaches of the drainage basins.

Figure 6. (A) Long profiles of four tributaries to the Big Tujunga River and slope-area data from Trail Canyon, showing apparent transient in long profiles and map pattern. Note that transient is easily seen in z vs. x plots for Mill, Fox, and Clear Creek, but slope-area plot greatly aids interpretation for Trail Canyon. Dashed line extending from Mill Creek shows projection of upper profile to mountain front. (B) Map pattern of knickpoints (white dots) in Big Tujunga basin. Close correspondence of knicks to 1000 m contour (black line) and irregular pattern in map view again suggests a transient feature (see Fig. 3).

Figure 6. (A) Long profiles of four tributaries to the Big Tujunga River and slope-area data from Trail Canyon, showing apparent transient in long profiles and map pattern. Note that transient is easily seen in z vs. x plots for Mill, Fox, and Clear Creek, but slope-area plot greatly aids interpretation for Trail Canyon. Dashed line extending from Mill Creek shows projection of upper profile to mountain front. (B) Map pattern of knickpoints (white dots) in Big Tujunga basin. Close correspondence of knicks to 1000 m contour (black line) and irregular pattern in map view again suggests a transient feature (see Fig. 3).

Figure 7. (A) Plot of normalized steepness index (ksn ) versus uplift rate (U) for seven strike-parallel channels from the Siwalik Hills in southern Nepal. Data suggest a linear correlation between ksn and U with a zero intercept, consistent with a stream power scaling with n = 1. Uplift rates were estimated by Hurtrez et al. (1999) from a fault-bend-fold kinematic model and bedding dips. (B) Example of slope-area data from the Siwalik Hills in southern Nepal. Gray crosses show data from a representative strike-parallel stream in the low uplift rate regime (U = 7 mm/yr). Black crosses show data from a representative strike-parallel stream in the high-uplift-rate regime (U = 13 mm/yr). Open dots show data from a strike-perpendicular stream crossing the entire anticline, from low rock uplift rate (U = 4 mm/yr) to high rock uplift rate (U = 13 mm/yr) and back. Negative concavity segment in strike-perpendicular stream can be explained by spatially varying rock uplift rate along the profile (e.g., Kirby and Whipple, 2001). (C) Channel profiles shown in part B. Thick gray lines show approximate extent of slope-area fits used in part B. Negative concavity in transitional profile manifests as a rollover just above junction with the high uplift channel.

Figure 7. (A) Plot of normalized steepness index (ksn ) versus uplift rate (U) for seven strike-parallel channels from the Siwalik Hills in southern Nepal. Data suggest a linear correlation between ksn and U with a zero intercept, consistent with a stream power scaling with n = 1. Uplift rates were estimated by Hurtrez et al. (1999) from a fault-bend-fold kinematic model and bedding dips. (B) Example of slope-area data from the Siwalik Hills in southern Nepal. Gray crosses show data from a representative strike-parallel stream in the low uplift rate regime (U = 7 mm/yr). Black crosses show data from a representative strike-parallel stream in the high-uplift-rate regime (U = 13 mm/yr). Open dots show data from a strike-perpendicular stream crossing the entire anticline, from low rock uplift rate (U = 4 mm/yr) to high rock uplift rate (U = 13 mm/yr) and back. Negative concavity segment in strike-perpendicular stream can be explained by spatially varying rock uplift rate along the profile (e.g., Kirby and Whipple, 2001). (C) Channel profiles shown in part B. Thick gray lines show approximate extent of slope-area fits used in part B. Negative concavity in transitional profile manifests as a rollover just above junction with the high uplift channel.

Figure 8. Comparison of incision rate estimates derived from (A) stream profile method, assuming a stream-power incision rule with n = 1, and (B) structural study of Hurtrez et al. (1999) and Lavé and Avouac (2000). Note general correspondence of location and magnitude of high incision rate zones from the two methods, suggesting that quantitative estimates of incision rates may be attainable in regions with relatively simple patterns of lithology and uplift. Figure B is adapted from Hurtrez et al. (1999).

Figure 8. Comparison of incision rate estimates derived from (A) stream profile method, assuming a stream-power incision rule with n = 1, and (B) structural study of Hurtrez et al. (1999) and Lavé and Avouac (2000). Note general correspondence of location and magnitude of high incision rate zones from the two methods, suggesting that quantitative estimates of incision rates may be attainable in regions with relatively simple patterns of lithology and uplift. Figure B is adapted from Hurtrez et al. (1999).

Figure 9. Schematic showing two competing models for Himalayan tectonic architecture and predicted patterns of rock uplift rates for each model. (A) Ramp model predicts uplift gradient spread over 20–30 km, with Main Central Thrust (MCT) carried passively over ramp in Himalayan Sole Thrust (HST). Uplift gradient should be broadly distributed (B), and thermal history for rocks on opposite sides of PT2 should be similar. Surface breaking thrust model (C) predicts more abrupt break in rock uplift rates centered at PT2 (D) and distinct thermal histories for rocks on opposite sides of the inferred surface breaking shear zone. MFT—Main Frontal Thrust; MBT—Main Boundary Thrust; MT—Mahabarat Thrust; STF—South Tibetan fault system; HST—Himalayan Sole Thrust; KTM—Kathmandu; PT2—physiographic transition; GHS—Greater Himalayan sequence. (Adapted from Wobus et al., 2003)

Figure 9. Schematic showing two competing models for Himalayan tectonic architecture and predicted patterns of rock uplift rates for each model. (A) Ramp model predicts uplift gradient spread over 20–30 km, with Main Central Thrust (MCT) carried passively over ramp in Himalayan Sole Thrust (HST). Uplift gradient should be broadly distributed (B), and thermal history for rocks on opposite sides of PT2 should be similar. Surface breaking thrust model (C) predicts more abrupt break in rock uplift rates centered at PT2 (D) and distinct thermal histories for rocks on opposite sides of the inferred surface breaking shear zone. MFT—Main Frontal Thrust; MBT—Main Boundary Thrust; MT—Mahabarat Thrust; STF—South Tibetan fault system; HST—Himalayan Sole Thrust; KTM—Kathmandu; PT2—physiographic transition; GHS—Greater Himalayan sequence. (Adapted from Wobus et al., 2003)

Figure 10. Slope-area plots and trunk stream longitudinal profiles from (A) Trisuli River catchment, (B) Burhi Gandaki catchment, and (C) Marsyandi catchment, all in central Nepal. Smoothing method and contour interval for all cases are 10 km moving average and 30 m, respectively. In each plot, gray crosses show data from representative southern (low uplift zone) tributaries; black crosses show data from representative northern (high uplift zone) tributaries; and open circles show data from trunk streams carving through the range. Dashed lines show approximate regional upper and lower bounds on steepness indices of 650 and 95 m0.9, respectively ([thetas]ref = 0.45). Gray shading on slope area and long profile data shows extent of high concavity zone in trunk streams, representing a maximum estimate of the width of rock uplift gradients (see text). Open stars show position of abrupt physiographic transition (PT2) in central Nepal, as identifi ed from slope maps and satellite photography (see text and Fig. 9). Note that Marsyandi long profile begins on a valley sidewall due to a data gap at the western edge of the catchment.

Figure 10. Slope-area plots and trunk stream longitudinal profiles from (A) Trisuli River catchment, (B) Burhi Gandaki catchment, and (C) Marsyandi catchment, all in central Nepal. Smoothing method and contour interval for all cases are 10 km moving average and 30 m, respectively. In each plot, gray crosses show data from representative southern (low uplift zone) tributaries; black crosses show data from representative northern (high uplift zone) tributaries; and open circles show data from trunk streams carving through the range. Dashed lines show approximate regional upper and lower bounds on steepness indices of 650 and 95 m0.9, respectively ([thetas]ref = 0.45). Gray shading on slope area and long profile data shows extent of high concavity zone in trunk streams, representing a maximum estimate of the width of rock uplift gradients (see text). Open stars show position of abrupt physiographic transition (PT2) in central Nepal, as identifi ed from slope maps and satellite photography (see text and Fig. 9). Note that Marsyandi long profile begins on a valley sidewall due to a data gap at the western edge of the catchment.

Figure 11. Digital elevation map (DEM) of central Nepal, showing transition zone between high and low uplift rates as determined from stream profile analyses. Diamonds along Trisuli and Burhi Gandaki Rivers show locations of detrital 40Ar/39Ar thermochronologic analysis: gray diamonds represent Miocene and younger apparent ages; white diamonds represent Paleozoic and older apparent ages. Note general correspondence of break in cooling history with change in stream profiles, suggesting a long-lived structure accommodating differential exhumation in this region. Dashed white lines in Marsyandi basin show location of intense Quaternary deformation, possibly responsible for accommodating the inferred gradient in rock uplift rates (e.g., Hodges et al., 2004).

Figure 11. Digital elevation map (DEM) of central Nepal, showing transition zone between high and low uplift rates as determined from stream profile analyses. Diamonds along Trisuli and Burhi Gandaki Rivers show locations of detrital 40Ar/39Ar thermochronologic analysis: gray diamonds represent Miocene and younger apparent ages; white diamonds represent Paleozoic and older apparent ages. Note general correspondence of break in cooling history with change in stream profiles, suggesting a long-lived structure accommodating differential exhumation in this region. Dashed white lines in Marsyandi basin show location of intense Quaternary deformation, possibly responsible for accommodating the inferred gradient in rock uplift rates (e.g., Hodges et al., 2004).

Contents

GSA Special Papers

Tectonics, Climate, and Landscape Evolution

Sean D. Willett
Sean D. Willett
Search for other works by this author on:
Niels Hovius
Niels Hovius
Search for other works by this author on:
Mark T. Brandon
Mark T. Brandon
Search for other works by this author on:
Donald M. Fisher
Donald M. Fisher
Search for other works by this author on:
Geological Society of America
Volume
398
ISBN print:
9780813723983
Publication date:
January 01, 2006

References

Blythe
,
A.E.
,
Burbank, D.W., Farley, K.A., and Fielding, E.J.,
2000
, Structural and topographic evolution of the central Transverse Ranges, California, from apatite fission-track, (U-Th)/He and digital elevation model analyses:
Basin Research
 , v.
12
p.
97
-114 doi: 10.1046/j.1365-2117.2000.00116.x.
Brocklehurst
,
S.H.
,
and Whipple, K.X.,
2002
, Glacial erosion and relief production in the Eastern Sierra Nevada, California:
Geomorphology
 , v.
42
p.
1
-24 doi: 10.1016/S0169-555X(01)00069-1.
Burbank
,
D.W.
,
Leland, J., Fielding, E., Anderson, R.S., Brozovic, N., Reid, M.R., and Duncan, C.,
1996
, Bedrock incision, rock uplift and threshold hillslopes in the northwestern Himalayas:
Nature
 , v.
379
, no. 6565 p.
505
-510 doi: 10.1038/379505a0.
Cattin
,
R.
,
and Avouac, J.P.,
2000
, Modeling mountain building and the seismic cycle in the Himalaya of Nepal:
Journal of Geophysical Research
 , v.
105
p.
13389
-13407 doi: 10.1029/2000JB900032.
Fielding
,
E.
,
Isacks, B., Barazangi, M., and Duncan, C.,
1994
, How flat is Tibet?:
Geology
 , v.
22
p.
163
-167 doi: 10.1130/0091-7613(1994)022<0163: HFIT>2.3.CO;2.
Finlayson
,
D.P.
,
and Montgomery, D.R.,
2003
, Modeling large-scale fluvial erosion in geographic information systems:
Geomorphology
 , v.
53
p.
147
-164 doi: 10.1016/S0169-555X(02)00351-3.
Finlayson
,
D.P.
,
Montgomery, D.R., and Hallet, B.,
2002
, Spatial coincidence of rapid inferred erosion with young metamorphic massifs in the Himalayas:
Geology
 , v.
30
, no. 3 p.
219
-222 doi: 10.1130/0091-7613(2002)030<0219:SCORIE>2.0.CO;2.
Flint
,
J.J.
,
1974
, Stream gradient as a function of order, magnitude, and discharge:
Water Resources Research
 , v.
10
, no. 5 p.
969
-973.
Gasparini
,
N.
,
2003
, Equilibrium and transient morphologies of river networks: Discriminating among fluvial erosion models [Ph.D. thesis]: Cambridge, Massachusetts, Massachusetts Institute of Technology.
105
p.
Hack
,
J.T.
,
1957
, Studies of longitudinal stream profiles in Virginia and Maryland: U.S. Geological Survey Professional Paper 294-B.
97
p.
Hack
,
J.T.
,
1973
, Stream profile analysis and stream-gradient index:
U.S. Geological Survey Journal of Research
 , v.
1
, no. 4 p.
421
-429.
Hancock
,
G.S.
,
and Anderson, R.S.,
2002
, Numerical modeling of fluvial strath-terrace formation in response to oscillating climate:
Geological Society of America Bulletin
 , v.
114
, no. 9 p.
1131
-1142 doi: 10.1130/0016-7606(2002)114<1131:NMOFST>2.0.CO;2.
Harbor
,
D.J.
,
1998
, Dynamic equilibrium between an active uplift and the Sevier River, Utah:
Journal of Geology
 , v.
106
p.
181
-198.
Heimsath
,
A.M.
,
Dietrich, W.E., Nishiizumi, K., and Finkel, R.C.,
1997
, The soil production function and landscape equilibrium:
Nature
 , v.
388
p.
358
-361 doi: 10.1038/41056.
Hodges
,
K.
,
Hurtado, J.M., and Whipple, K.,
2001
, Southward extrusion of Tibetan crust and its effect on Himalayan tectonics:
Tectonics
 , v.
20
p.
799
-809.
Hodges
,
K.
,
Wobus, C., Ruhl, K., Schildgen, T., and Whipple, K.,
2004
, Quaternary deformation, river steepening and heavy precipitation at the front of the Higher Himalayan ranges:
Earth and Planetary Science Letters
 , v.
220
, no. 3–4 p.
379
-389 doi: 10.1016/S0012-821X(04)00063-9.
Howard
,
A.D.
,
1994
, A detachment-limited model of drainage basin evolution:
Water Resources Research
 , v.
30
, no. 7 p.
2261
-2285 doi: 10.1029/94WR00757.
Howard
,
A.D.
,
and Kerby, G.,
1983
, Channel changes in badlands:
Geological Society of America Bulletin
 , v.
94
p.
739
-752 doi: 10.1130/0016-7606(1983)94<739:CCIB>2.0.CO;2.
Hurtrez
,
J.E.
,
Lucazeau, F., Lavé, J., and Avouac, J.P.,
1999
, Investigation of the relationships between basin morphology, tectonic uplift, and denudation from the study of an active fold belt in the Siwalik Hills, central Nepal:
Journal of Geophysical Research
 , v.
104
, no. B6 p.
12779
-12796 doi: 10.1029/1998JB900098.
Kirby
,
E.
,
and Whipple, K.X.,
2001
, Quantifying differential rock-uplift rates via stream profile analysis:
Geology
 , v.
29
, no. 5 p.
415
-418 doi: 10.1130/0091-7613(2001)029<0415:QDRURV>2.0.CO;2.
Kirby
,
E.
,
Whipple, K., Tang, W., and Chen, Z.,
2003
, Distribution of active rock uplift along the eastern margin of the Tibetan Plateau: Inferences from bedrock channel longitudinal profiles:
Journal of Geophysical Research
 , v.
108
, no. B4 doi: 10.1029/2001JB000861.
Lague
,
D.
,
and Davy, P.,
2003
, Constraints on the long-term colluvial erosion law by analyzing slope-area relationships at various tectonic uplift rates in the Siwalik Hills (Nepal):
Journal of Geophysical Research
 , v.
108
, no. B2 doi: 10.1029/2002JB001893.
Lavé
,
J.
,
and Avouac, J.P.,
2000
, Active folding of fluvial terraces across the Siwalik Hills, Himalayas of central Nepal:
Journal of Geophysical Research
 , v.
105
, no. B3 p.
5735
-5770 doi: 10.1029/1999JB900292.
Lavé
,
J.
,
and Avouac, J.P.,
2001
, Fluvial incision and tectonic uplift across the Himalayas of central Nepal:
Journal of Geophysical Research
 , v.
106
, no. B11 p.
26561
-26591 doi: 10.1029/2001JB000359.
Massong
,
T.M.
,
and Montgomery, D.R.,
2000
, Influence of sediment supply, lithology, and wood debris on the distribution of bedrock and alluvial channels:
Geological Society of America Bulletin
 , v.
112
p.
591
-599 doi: 10.1130/0016-7606(2000)112<591:IOSSLA>2.3.CO;2.
Merritts
,
D.J.
,
1996
, The Mendocino triple junction: Active faults, episodic coastal emergence, and rapid uplift:
Journal of Geophysical Research
 , v.
101
p.
6051
-6070 doi: 10.1029/95JB01816.
Merritts
,
D.J.
,
and Bull, W.B.,
1989
, Interpreting Quaternary uplift rates at the Mendocino triple junction, northern California, from uplifted marine terraces:
Geology
 , v.
17
p.
1020
-1024 doi: 10.1130/0091-7613(1989)017<1020:IQURAT>2.3.CO;2.
Merritts
,
D.
,
and Vincent, K.R.,
1989
, Geomorphic response of coastal streams to low, intermediate, and high rates of uplift, Mendocino junction region, northern California:
Geological Society of America Bulletin
 , v.
101
p.
1373
-1388 doi: 10.1130/0016-7606(1989)101<1373: GROCST>2.3.CO;2.
Montgomery
,
D.R.
,
and Brandon, M.T.,
2002
, Topographic controls on erosion rates in tectonically active mountain ranges:
Earth and Planetary Science Letters
 , v.
201
p.
481
-489 doi: 10.1016/S0012-821X(02)00725-2.
Montgomery
,
D.R.
,
and Gran, K.B.,
2001
, Downstream variations in the width of bedrock channels:
Water Resources Research
 , v.
37
, no. 6 p.
1841
-1846 doi: 10.1029/2000WR900393.
Montgomery
,
D.R.
,
and Foufoula-Georgiou, E.,
1993
, Channel network representation using digital elevation models:
Water Resources Research
 , v.
29
p.
3925
-3934 doi: 10.1029/93WR02463.
Montgomery
,
D.R.
,
Dietrich, W.E., and Sullivan, K.,
1998
, The role of GIS in watershed analysis: in Lane, S.N., Richards, K.S., and Chandler, J.H., eds., Landform monitoring, modelling and analysis: Chichester, England, John Wiley and Sons, p.
241
-261.
Niemann
,
J.D.
,
Gasparini, N.M., Tucker, G.E., and Bras, R.L.,
2001
, A quantitative evaluation of Playfair's law and its use in testing long-term stream erosion models:
Earth Surface Processes and Landforms
 , v.
26
, no. 12 p.
1317
-1332 doi: 10.1002/esp.272.
Roe
,
G.H.
,
Montgomery, D.R., and Hallet, B.,
2002
, Effects of orographic precipitation variations on the concavity of steady-state river profiles:
Geology
 , v.
30
, no. 2 p.
143
-146 doi: 10.1130/0091-7613(2002)030<0143: EOOPVO>2.0.CO;2.
Roe
,
G.H.
,
Montgomery, D.R., and Hallet, B.,
2003
, Orographic precipitation and the relief of mountain ranges:
Journal of Geophysical Research
 , v.
108
, no. B6.
2315
doi: 10.1029/2001JB001521.
Sklar
,
L.
,
2003
, The influence of grain size, sediment supply, and rock strength on rates of river incision into bedrock [Ph.D. thesis]: Berkeley, University of California.
343
p.
Sklar
,
L.
,
and Dietrich, W.E.,
1998
, River longitudinal profiles and bedrock incision models: Stream power and the influence of sediment supply: in Tinkler, K.J., and Wohl, E.E., eds., Rivers over rock: Fluvial processes in bedrock channels: Washington, D.C., American Geophysical Union, p.
237
-260.
Sklar
,
L.S.
,
and Dietrich, W.E.,
2001
, Sediment and rock strength controls on river incision into bedrock:
Geology
 , v.
29
, no. 12 p.
1087
-1090 doi: 10.1130/0091-7613(2001)029<1087:SARSCO>2.0.CO;2.
Snyder
,
N.
,
Whipple, K., Tucker, G., and Merritts, D.,
2000
, Landscape response to tectonic forcing: DEM analysis of stream profiles in the Mendocino triple junction region, northern California:
Geological Society of America Bulletin
 , v.
112
, no. 8 p.
1250
-1263 doi: 10.1130/0016-7606(2000)112<1250:LRTTFD>2.3.CO;2.
Snyder
,
N.P.
,
Whipple, K.X., Tucker, G.E., and Merritts, D.M.,
2002
, Interactions between onshore bedrock-channel incision and nearshore wave-base erosion forced by eustasy and tectonics:
Basin Research
 , v.
14
p.
105
-127 doi: 10.1046/j.1365-2117.2002.00169.x.
Snyder
,
N.P.
,
Whipple, K.X., Tucker, G.E., and Merrits, D.J.,
2003a
, Channel response to tectonic forcing: Field analysis of stream morphology and hydrology in the Mendocino triple junction region, northern California:
Geomorphology
 , v.
53
p.
97
-127 doi: 10.1016/S0169-555X(02)00349-5.
Snyder
,
N.P.
,
Whipple, K.X., Tucker, G.E., and Merrits, D.J.,
2003b
, Importance of a stochastic distribution of floods and erosion thresholds in the bedrock river incision problem:
Journal of Geophysical Research
 , v.
39
doi: 10.1029/2001WR001057.
Spotila
,
J.A.
,
House, M.A., Blythe, A., Niemi, N.A., and Bank, G.C.,
2002
, Controls on the erosion and geomorphic evolution of the San Bernardino and San Gabriel Mountains, southern California: in Barth, A.P., ed., Contributions to crustal evolution of the southwestern United States: Geological Society of America Special Paper 365, p.
205
-230.
Stock
,
G.M.
,
Anderson, R.S., and Finkel, R.C.,
2004
, Pace of landscape evolution in the Sierra Nevada, California, revealed by cosmogenic dating of cave sediments:
Geology
 , v.
32
, no. 3 p.
193
-196 doi: 10.1130/ G20197.1.
Stock
,
J.D.
,
and Dietrich, W.E.,
2003
, Valley incision by debris flows: Evidence of a topographic signature:
Water Resources Research
 , v.
39
, no. 4 doi: 10.1029/2001WR001057.
Tarboton
,
D.G.
,
Bras, R.L., and Rodriguez-Iturbe, I.,
1989
, Scaling and elevation in river networks:
Water Resources Research
 , v.
25
p.
2037
-2051.
Tucker
,
G.E.
,
2004
, Drainage basin sensitivity to tectonic and climatic forcing: Implications of a stochastic model for the role of entrainment and erosion thresholds:
Earth Surface Processes and Landforms
 , v.
29
p.
185
-205 doi: 10.1002/esp.1020.
Tucker
,
G.E.
,
and Bras, R.L.,
2000
, A stochastic approach to modeling the role of rainfall variability in drainage basin evolution:
Water Resources Research
 , v.
36
p.
1953
-1964 doi: 10.1029/2000WR900065.
Tucker
,
G.E.
,
and Whipple, K.X.,
2002
, Topographic outcomes predicted by stream erosion models: Sensitivity analysis and intermodel comparison:
Journal of Geophysical Research
 , v.
107
, no. B9 doi: 10.1029/2001JB000162.
Whipple
,
K.
,
2004
, Bedrock rivers and the geomorphology of active orogens:
Annual Reviews of Earth and Planetary Science
 , v.
32
p.
151
-185 doi: 10.1146/annurev.earth.32.101802.120356.
Whipple
,
K.X.
,
and Tucker, G.E.,
1999
, Dynamics of the stream-power river incision model: Implications for height limits of mountain ranges, landscape response timescales, and research needs:
Journal of Geophysical Research
 , v.
104
p.
17661
-17674 doi: 10.1029/1999JB900120.
Whipple
,
K.X.
,
and Tucker, G.E.,
2002
, Implications of sediment-flux-dependent river incision models for landscape evolution:
Journal of Geophysical Research
 , v.
107
, no. B2 doi: 10.1029/2000JB000044.
Whipple
,
K.X.
,
Hancock, G.S., and Anderson, R.S.,
2000
, River incision into bedrock: Mechanics and relative efficacy of plucking, abrasion, and cavitation:
Geological Society of America Bulletin
 , v.
112
, no. 3 p.
490
-503 doi: 10.1130/0016-7606(2000)112<490:RIIBMA>2.3.CO;2.
Willgoose
,
G.
,
Bras, R.L., and Rodriguez-Iturbe, I.,
1991
, A coupled channel network growth and hillslope evolution model: I. Theory:
Water Resources Research
 , v.
27
, no. 7 p.
1671
-1684 doi: 10.1029/91WR00935.
Wobus
,
C.W.
,
Hodges, K.V., and Whipple, K.X.,
2003
, Has focused denudation sustained active thrusting at the Himalayan topographic front?:
Geology
 , v.
31
p.
861
-864 doi: 10.1130/G19730.1.

Related

A comprehensive resource of eBooks for researchers in the Earth Sciences

This Feature Is Available To Subscribers Only

Sign In or Create an Account

This PDF is available to Subscribers Only

View Article Abstract & Purchase Options

For full access to this pdf, sign in to an existing account, or purchase an annual subscription.

Subscribe Now