Naomi Lubick

Lamont Doherty Earth Observatory, Department of Earth and Environmental Sciences, Columbia University, New York

Studies of knickpoints in the Finger Lakes Region of New York have yielded varying rates of erosion in different bedrock-bottomed streams. This variation allows consideration of the subtleties of knickpoint migration in the area as related to different rock types serving as bedrock channel bottom. Comparison of stream profiles, knickpoint migration rates, and stratigraphy indicate that slope conditions are the primary factor affecting knickpoint migration rates (and therefore erosion along bedrock-bottomed streams in the region). For streams in regions with steep initial slopes, lithology is most likely the secondary control on knickpoint migration; for streams with gentle initial slopes, the secondary control seems to be discharge.

1. Introduction

Bedrock channels are a relatively little-studied environment in fluvial geomorphology, as past theoretical and quantitative work has been applied mostly to alluvial and gravel channels (Tinkler & Wohl, 1998). Bedrock incision is not the same as erosion of alluvial sediments, though it often has been treated as such (Howard et al., 1994). Recent work on bedrock channels has focused on basinwide to small sectional studies of profile evolution, erosional processes, and modeling (Tinkler & Wohl, 1998; Wohl, 1998). However, only broad conclusions presently can be made about erosional processes (Wohl, 1998), and much work remains to be done. For example, bedrock channel incision is the underlying constraint on rates of erosion of most terranes (Stock & Montgomery, 1999). Erosion rate is influenced by rock type and structure, but erosion rates as well as the contributions of these factors are difficult to determine owing to the long time scale of erosion processes (Tinkler & Wohl, 1998; Howard et al., 1994; Weissel & Seidl, 1997).

The Finger Lakes region presents an ideal laboratory for examining the role of tectonics, lithology, and structure on bedrock stream erosion. The region is tectonically stable, although it continues to undergo isostatic rebound, after the Laurentide glaciation (Tushingham & Peltier, 1991; Peltier, 1986). Glaciation "reset" the topography of the region, providing a probable time of initiation of knickpoints in the region. This "clean slate" has provided an opportunity to determine long-term rates of knickpoint migration in a different tectonic and lithologic setting than previous studies, in order to address the larger question of how erosional processes work in bedrock fluvial systems, specifically how lithology, catchment size, and slope conditions affect knickpoint migration rates.

A knickpoint is defined as a relatively steeper portion of a stream channel between lower-gradient sections (Howard et al., 1994; Tinkler & Wohl, 1998). Knickpoints can be initiated by tectonic changes to a landscape, base-level changes to a stream, or varying resistance of rock type (Howard et al., 1994). Tectonic changes, with regard to landscape denudation and isostatic rebound in general, affect relief and drainage patterns over a wide area (Gilchrist & Summerfield, 1990; Howard et al., 1994). Lithology and structure have more localized effects, particularly with regard to knickpoint migration.

Erosion of a bedrock channel has no "universal law," though there are known variables, such as mechanical scour and plucking, weathering, rock type, channel hydraulics, water/climate, and sediment load (Howard et al., 1994). In some bedrock channels, lithology and structure seem to be the controlling factors in knickpoint erosion. In their knickpoint retreat studies in the southeastern Australia passive continental margin, Weissel & Seidl (1997) concluded that knickpoint migration is determined by mass-wasting and lithology, if fluvial transport capacity meets certain thresholds. Catchment drainage size does not matter, nor does the amount of water that passes through the catchment, if the stream power is sufficient (for example, in Australian New England streams, to clear alluvium and debris; Weissel & Seidl, 1997). Instead, the cracking and jointing of a stratigraphic layer (through weathering and other processes) and slope failure move knickpoints upstream. Miller (1991) also concluded that knickpoint development is limited by the strata (e.g. knickpoint "face and tread" are related to bed thickness in "homogeneous" lithologies). He also noted that resistant rock "overlies and protects" weaker rocks, although this original scenario of waterfall development is no longer considered adequate (Young, 1985). Also, varying portions of streams may have different erosion rates, depending on stream/catchment conditions (see discussion by Seidl & Dietrich, 1992, and others, with regard to stream power law; also see Appendix).

The lithology of the Finger Lakes Region is Devonian shales, sandstones, and limestones, deposited in a delta that prograded from east to west (Rogers et al., 1990; Younes & Engelder, 1999; see Figure 2). The Devonian beds dip gently to the south-southwest (Mullins & Hinchey, 1989), and a layer of Silurian salt underlies the region (Younes & Engelder, 1999). A gentle anticline trends across Cayuga Lake, visible above water level; Alleghanian-aged (Mid-Carboniferous) jointing across the region has been reported to be approximately perpendicular to this and other observed anticlines (042Ú fold axes), and further work has shown that the region underwent a clockwise stress rotation (Younes & Engelder, 1999). Younes & Engelder (1999) reported the following clockwise sequence of Alleghanian joint sets: (320Ú-330Ú) à [East Ithaca (006Ú-021Ú) and West Ithaca (342Ú)] à (352Ú) à (003Ú). Other post-Alleghanian joint sets present include 070Ú (cut by Middle Jurassic kimberlite dikes) and 000Ú (parallel to Mesozoic kimberlite dikes; Younes & Engelder, 1999).

The Finger Lakes are a parallel series of eleven long thin lakes that run north-south, carved into bedrock in the general flow direction of the Laurentide Ice Sheet, at its southeast margin (Figure 3). The Laurentide glacial maximum occurred approximately 18 ka, and the passing ice reset the regional topography (smoothing it out) as it scoured out the Finger Lakes (Clayton, 1972; Isachsen et al., 1991). Piston cores have shown that the last ice rapidly withdrew from the north end of Seneca Lake around 13.9 ka (Anderson et al., 1997). Retreat of the ice sheet led to glacial isostatic rebound of the region, but present-day rates of vertical motion around the Great Lakes region (~0-0.5 mm/year) indicate relative isostatic equilibrium (Peltier, 1986).

The lakes themselves have an overall "spoon-shaped longitudinal profile": the north ends of the lakes have broad shallow basins that become much more narrow and deeply incised to the south (Mullins et al., 1991). The gently dipping Onandaga limestone controlled the depth of erosion during the carving of the Cayuga and Seneca lake valleys, and once the unit was deep enough, the ice could carve more sharply into the overlying Hamilton and Geneseo Groups (see Figure 4; Mullins et al., 1991).

The Finger Lakes basins may have been scoured by multiple glacial events; however, Mullins & Hinchey (1989) hypothesized that the bedrock of the lake valleys was eroded all at once, by "strong ice-stream flow facilitated by large volumes of pressurized subglacial meltwater and sediment as the Laurentide ice sheet began to collapse after the last glacial maximum" (p. 624). Seismic profiles and cores show that the lakes are filled with up to 275 m of late Quaternary sediments, composed of unconsolidated sediments, lacustrine and alluvial deposits, clays, muds, and diapirs occurring in the mud deposits at the north end of some lakes, indicating rapid deposition (Mullins & Hinchey, 1989; Mullins et al., 1991). The bottom-most layers appear to correlate with the Valley Heads moraine, but they have not been dated (Mullins et al., 1991). The last 14,000 years have seen regional surface deposits of approximately 10-15 m (Dwyer et al., 1996).

The main knickpoints on the streams in the area tend to be waterfalls, though some of the streams have knickzones or a series of knickpoints (see Wohl, 1998, for a discussion of knickzones). A prime example of a well-studied waterfall/knickpoint in this region is to the west of this study's field area, Niagara Falls. Radiocarbon dating has shown that Niagara Falls, which is 46 m tall, migrated at rates of 50-700 mm/year from 10.5-5.5 ka. Rates of migration before and after that time period were similar to present-day rates, at 1,570 mm/year (Wohl, 1998). A general rate of migration, if the initial starting point is assumed to be 16 ka, is about 1,200 mm/year. Niagara Falls sits in slightly less resistant lithology (Wohl, 1998) and has higher rates of erosion than those found in the current study. However, these dating measurements further underscore that migration rates probably varied in the past, which this study is unable to consider at this time.

Stream profiles, knickpoint migration rates, and catchment basin information were extracted from digital elevation models (DEMs). Field observations provided further information on rock type and jointing structures, in addition to providing the opportunity to "groundtruth" the DEM data. Accessibility to streams and their waterfalls determined which would be subject to study, and a broad range of lithologies was chosen in order to allow comparison through the stratigraphy.

The DEMs used were created from aerial photographs and topographic quadrangles by the U.S. Geological Survey (USGS, 1998). Vertical resolution is 1 m and each pixel is 10 m by 10 m. Data sets consisting of height, distance, and slope values based on the DEMs were extracted using a suite of manipulation algorithms (Route, authored by Colin Stark, 1999). See the Appendix for complete illustrations of each stream, including Strahler networks showing branches of orders 2-3, joint measurements (discussed below), and stream profiles.

Route algorithms extracted stream elevation profiles for mainstream channels, catchment area measurements (in terms of pixels through which water would flow), and slope values calculated from pixel to pixel within the main stream profile. Initial algorithms correct the DEM, by infilling areas with missing data and using a randomized step-function to raise flat-lying areas, in order to determine probable flow directions from such regions. Outlets are determined in flat regions by finding lower heights in surrounding pixels. For stream profiles, the elevation of the surfaces of Cayuga, Seneca, and Keuka Lakes (i.e. the endpoints of streams) were given as mask levels, i.e. relative zero point. Minimum catchment sizes were set to 300 m², in order to isolate streams of desired magnitude. Catchment area is used here as a proxy for stream discharge, under the assumption that main channel discharge is a function of drainage area (Seidl & Dietrich, 1992). (For further information on stream extraction algorithms, see Freeman, 1991; Jensen, 1991.)

Eighteen stream profiles acquired with Route were fieldchecked, and rock type was determined as best possible. Joint measurements also were gathered at bedrock exposures in each streambed, above, below, and at knickpoints. Joints studied were chosen according to persistence, i.e. length of exposure in bedrock and clarity of face, as well as extent of stratigraphic height. Such criteria may have served to bias the joint sets measured; however, certain qualitative statements can be made from the observations. (See the Appendix for complete joint data and Rose diagrams for streams in similar lithologies.)

The results reported here are candidate parameters that potentially control knickpoint migration rates. Joint measurements, catchment areas, and stream longitudinal profiles are the main results of fieldwork and flow route extraction. Further observations were made with relation to lithology and regional topographic conditions in the field.

jointing Streams were observed to follow a set of persistent joints, switching flow orientation from one joint to another and back, creating gentle meanders, and sometimes creating tight U-turns. [See the planform view of streams in Figure 5 and in the Appendix.]

As noted above, jointing/structure has been created mostly by compressive forces across the region, which created several major joint sets (Younes & Engelder, 1999). These joint sets are close to vertical, and waterfall faces were noted in almost all cases to follow a dominant joint face (see Figure 6). However, the faces of minor knickpoints on a stream reach may be persistent joints that are almost perpendicular to the major knickpoint face. Other observed knickpoints follow multiple joint orientations or none at all. Anecdotal evidence from field observations points to slope failure as one mechanism of knickpoint retreat; great slabs of rock tend to peel off at joints and fractures (see Figure 7).

catchment area Overall, the streams studied in the Finger Lakes Region showed a positive relationship between total streamlength and catchment area (Figure 8), as expected. However, each stream yielded catchment areas at major knickpoints that did not correlate definitively (see Table 1 and Figure 9). For example, major knickpoints on Hector and Rock streams have not traveled as far as one might expect, in comparison to other streams' knickpoint distances, and Plum Point and Taughannock knickpoints are at the same distance upstream despite dramatically different catchment sizes. Also to be considered is whether the streams are lying in previously eroded stream valleys, which is most likely for Hector and Taughannock, which may affect the knickpoint migration pattern.

lithology According to stream profiles and estimates of position in the stratigraphic column, several groupings can be made of major knickpoints that occur in certain units (Figure 10). Knickpoints seem to occur in the upper Geneseo Group, the Tully limestone (Dt in Figure 5 and others), and the Lower Hamilton.

In general, the streams studied were eroding friable shales and siltstones, with occasional well-lithified units that sometimes contained knickpoints. Stream and gully side walls tended to be very friable shales (from gray to black, with only one observed instance of red shale at Eggleston's major knickpoint). The large knickpoints tended to be situated in more massive units, sometimes with observable bedding layers. Several streams had knickpoints that sat above units containing concretions (e.g. Powell, Atwater). Other streams had fossiliferous layers at their major knickpoints that can serve as marker beds (e.g. Paine, Little, Powell, Groves, possibly in the Skaneateles Shale of the Lower Hamilton).

regional slope controls The interfluves between the Finger Lakes progressively gain elevation to the south. At the southern end of the lake basins, streams have profiles that are relatively steeply sloped (Figure 11a, blue stream profiles; see 11b for stratigraphy imposed on stream profiles by regional group). Northern streams have shallower, gentler stream profiles and show a positive correlation between knickpoint migration upstream to catchment size (Figure 11a, orange and green data points have a relatively positive trend).

migration rates Based on the assumption that initiation of knickpoints occurred at ~16 ka, when most of the glacial ice had been removed from the area, present-day positions of knickpoints upstream are used to calculate general migration rates over that time period (Table 2). (Another possible initiation time is ~12-14 ka, when damming from remnant ice was removed and water levels in post-glacial lakes dropped; see Mullins & Hinchey, 1989.) Precise rates of erosion are not determinable currently; however, these estimated values are useful for comparison between streams. As shown in Table 2, each stream had a different long-term estimated rate of knickpoint migration of upstream. The rates reported here are high; for example, the bedrock-bottomed Indus River in the northwest Himalayas has "high rates" of erosion of 2-12 mm/year (Burbank et al., 1996).

factors governing knickpoint propogation With regard to the above observations-jointing, catchment area, lithology, topographic controls, and rates of erosion-regional slope seems to have had the greatest effect on how stream profiles have evolved and resulting knickpoint migration rates. The following section addresses the observations outlined above.

The expected controls on knickpoint migration along the bedrock streams of the Finger Lakes Region were hypothesized to be jointing and lithology, not catchment area. However, jointing seems to have had more of an impact on stream meander directions (see planform views) than on knickpoint migration rates. This study does not indicate that joints are controlling the rate of migration of a knickpoint. Lithology and catchment area, on the other hand, do seem to have an impact on migration rates (with slope as the defining parameter).

Streams with knickpoints in the Geneseo Group (Dg: limestone, shale) have catchment sizes that differ over an order of magnitude, yet their knickpoints have eroded upstream at the same long-term rates (Figure 9). The catchment areas of Hector, Inwood, and Rock streams range from ~2-31 km², but these streams share similar rates of migration of ~5-8 mm/year (Glenwood shares the same rate with the second major knickpoint on Inwood, at ~15 mm/year).

On the other hand, comparison can be made of Plum Point and Taughannock streams, which also erode through the Geneseo Group. Despite the fact that Taughannock's catchment area is four times greater than that of Plum Point, the major knickpoints on the mainstreams have traveled the same distance upstream. This distance places them at almost the same level in the regional stratigraphy. (See profiles for Taughannock and Plum Point, Figure 12; see also Figures 9 and 10, and figures in the Appendix). At first glance, these similarities indicate that discharge (as proxied by catchment size) has less effect on rates of knickpoint migration than does the lithology (see Figure 9).

Streams grouped in other lithologies (see Figure 9) show no such similarities in migration rates. They instead show a positive correlation between knickpoint migration distance upstream and catchment area; see, for example, the streams that have knickpoints in the Hamilton Group (Dhl and Dhu: shales, thin limestone, siltstone; Figure 9). However, Groves, Excelsior, and Big Hollow streams all have the same migration rates but differing lithology and catchment areas at their knickpoints. Drainage area differences among these streams are not so great as in other examples. In general, lithology (as related to distance of knickpoints upstream) did not seem to be the major component in determining migration rates.

Categorization of streams according to slope indicates that such conditions may be the primary control on rates of migration of knickpoints and evolution of stream profiles. Similar longitudinal stream profiles cluster according to regional slope type (Figure 11). The streams where slope is steepest overall, in the southern portions of Seneca and Cayuga lakes, have similar rates of knickpoint migration, with some exceptions (see Table 3), that seem to indicate that lithology plays a secondary role in these rates after slope. In the northern portions of the lakes, shallower stream profiles are the norm, and catchment area has a positive correlation with knickpoint migration rates (the larger the area, the farther upstream the major knickpoints have migrated).

quantitative models Luke (1972) wrote that erosion rate "depends in some way on the local steepness of the landscape" (p. 2460), with steepness meaning slope. His work modeled kinematic waves in two-dimensions to show landform evolution; change in height with respect to time depends on a nonlinear function of height related to change in position (x, y) with regard to time (t):

where h = h(x,y,t). At progressive values of t, multivalued solutions require what Luke (1972) called a "shock" in order to remove discontinuities along h, giving continuous solutions with "sharp-cornered" convexities. Such shocks, or waves, may travel at different speeds and overtake each other, and different materials with different erosion rates produce stratified slopes (Figure 13). He adds a height dependent variable, a , that allows description of horizontally bedded systems with evolving stream profiles:

"h/"t = -a F("h/"x), (2)

where "h/"x is slope (Figure 14). Here, a may be proxy for lithology resistance. Weissel & Seidl (1998) extended Luke's (1972) work by incorporating it into stream power law (see Appendix); however, they applied this model to uniform stratigraphy only.

Initial topographic conditions, instead of lithology and catchment size, may be the primary factors in knickpoint migration rates. The observations made on streams in the Finger Lakes Region indicate that on a large scale, slope influences the rates of knickpoint migration. Only after considering slope effects can catchment size and lithology be considered in the parameters that potentially control the migration of knickpoints (and possibly erosion) along bedrock-bottomed streams.

Initial results indicated that across the Finger Lakes Region, catchment size seems to correlate positively with knickpoint migration rates with some exceptions. However, further scrutiny shows that streams can be categorized by slope: gentle to steep, with a gradual shift to steeper profiles from north to south. Initial slope conditions, determined by glaciation that was directed by lithology, have a large effect on evolution of stream longitudinal profile. Thus, initial slope conditions may be the initial primary factor in knickpoint location, and lithology or catchment area is a secondary control. Lithology seems to be the secondary control in development of similar bedrock stream profiles with steep initial slope. Gentle slope profiles may give streams characteristics that allow drainage area to become the more dominant factor in knickpoint erosion, as indicated by streams at the northern ends of the Finger Lakes valleys.

The knickpoint migration rates presented here were used to determine relative rates of erosion, as represented by knickpoint migration upstream. These varying rates allowed comparison between streams for determination of possible primary and secondary controls. Results show that although this region is tectonically stable, the differences in slope conditions are enough to influence the rates of knickpoint migration along streams in different slope regimes. Lithology and catchment size also have effects on the complex systems of fluvial erosion in bedrock.

Further work would be useful in sorting out these complexities. As noted above, different portions of a stream may have different rates of erosion (Seidl & Dietrich, 1992). As applied to this dataset, for example, the knickpoints on the Powell and Groves streams could have had very different rates of migration, with the Groves knickpoint (Oak Tree Falls) travelling upstream relatively quickly and then stalling at its current position, and Powell's knickpoint heading around at the same fast speed but taking a longer route before stalling at the same point in the stratigraphy. In order to constrain such variations, future work should include geochemical dating for ages of exposure of bedrock in streams. Such dating would also determine whether some stream valleys were carved during earlier glacial events, or if the Finger Lakes and their feeder streams were created during the Laurentide glaciation.

Also useful would be application and further modeling of the stream power law with the values obtained for streams in the Finger Lakes Region, while incorporating Luke's (1972) concepts of landform evolution (see Appendix). Weissel & Seidl (1998) applied their stream power law model extending Luke's (1972) work to single-rock-type channels. Application of this model in streams with multiple lithologies along their longitudinal profiles, such as those in the Finger Lakes Region, may help to determine further the interactions of slope conditions and lithology with regard to erosion of bedrock-bottomed streams.

Many thanks to those who helped me in the field: Marisa Lianghammphai, for her assistance and patience; Don Oliver and Tony Ingraham at Taughannock Falls State Park; the Weissels; and Ray and Lorraine. Thanks to Mike Evans, Anu Gupta, Joan Ramage, Colin Stark, Marc Spiegelman, and Rose Anne Weissel, and to my committee members, Kim Kastens, Nick Christie-Blick, and Jeff Weissel.