Rivers crossing growing folds

The interactions of fluvial systems with active deforming landscapes has provided fertile ground for exploration of the adjustments that rivers make when they are perturbed by deformation. Two ingredients are commonly combined in successful analyses of interactions between tectonic and geomorphic systems. First, the spatial and temporal characteristics of the deformation need to be defined. The magnitude and rate of displacements and the ways in which they vary across a landscape define a deformational framework. Typically, the relative vertical displacement of one area versus another is most important because such displacement defines how local base level, relief, and slope will change. Second, spatial variations in geomorphologic attributes should be characterized. In the case of rivers, these attributes likely include channel slope, width, and planform geometry, as well as discharge, grain size, and roughness. The combination of the geomorphic changes across a landscape with the pattern of tectonic displacement commonly permits us to deduce which geomorphic changes are induced by the tectonism and which occur independently of it.

How can the pattern and rate of folding be extracted from a landscape? If the fold is steadily growing by incremental displacement on a year-to-year basis, then repeated GPS surveys could delineate a deformation profile. Whereas such annual growth is uncommon for most folds, many folds seem to acquire much of their deformation during earthquakes. So, surveys of the coseismic displacement due to an earthquake could be used as a template for growth, if one assumes that future earthquakes are likely to produce a similar deformation pattern. Because earthquakes on any given fold typically occur once every few hundred years to many thousands of years, however, use of coseismic displacements is usually impractical. A more reliable method is to examine downstream changes in the height of one or more river terraces along the flanks of the river as it flows through the fold. Each terrace typically results from an interval of aggradation (usually driven by climate change) followed by incision. The gradient of the terrace is assumed to have been parallel to the modern gradient. Based on this assumption, downstream changes in the height of the terrace above the modern river can define the magnitude of differential uplift since the terrace was formed. If an age can be obtained on the terrace, then spatial variations in the rate of deformation can also be calculated. In the optimal situation, multiple terraces are preserved, and surveys reveal that the pattern of deformation defined by the youngest (and lowest) terrace is simply amplified through time. One of the most spectacular studies that used this methodology was conducted on a rapidly growing fold in the foothills of the Nepalese Himalaya (Figure 1) (Lavé and Avouac, 2000). There, three dated terraces yielded nearly identical patterns and rates of deformation across the fault-related fold. In fact, the crest of the fold was shown to be uplifting at more than 10 mm/yr, which is equivalent to 10 km in a million years!

How does a river sustain its course across a fold that is growing so rapidly? It helps if the rock within the fold is not too strong--as is the case in Nepal where the fold comprises relatively weakly lithified sedimentary rocks. Nonetheless, across the breadth of the anticline, relative rock uplift is very rapid. If erosion by the river channel did not keep pace with the rate of uplift, the river would either have to aggrade upstream to the height of the uplifted channel bottom in the core of the fold or the river's gradient would be reversed and the river would be deflected around the fold. But in the Nepalese fold, neither of these scenarios has occurred, and instead, two nearby rivers each flow completely across it. Therefore, we conclude that these rivers are eroding just fast enough to balance the rate of rock uplift. Because that rate varies along each river's course, an opportunity exists to explore how characteristics of the channel change across the fold as an apparent function of uplift or erosion rate.

Although the precise controls on river erosion are not agreed upon, the shear stress exerted by flowing water on the river's bed is likely to modulate erosion rates in some fashion. Such shear stress (force per unit area of the bed exerted parallel to the bed) is required not only for transporting the bedload, but also for scouring, plucking, or abrading the underlying bedrock surface. This stress (σ) is commonly quantified as σ = ρ g d sin α,where ρ is water density, g is gravitational acceleration, d is water depth, and α is channel slope or gradient. So, if a river needs to erode more quickly in order to counterbalance a faster uplift rate, what adjustments in channel geometry serve to increase the basal shear stress? The two most obvious are an increase in channel slope and/or a deepening of the flow. The latter is typically accomplished through channel narrowing, because in the absence of a change in slope, velocity and channel cross-sectional area remain about constant. Hence, narrowing of the channel causes deepening of the flow.

Detailed measurements of channel width and slope across the Nepalese fold show as much as 10-fold changes in channel width that correlate rather closely with changes in incision rates inferred from the uplifted terraces (Fig. 2). The Bakeya River, which is the smaller of the two rivers, also shows a steepening of the channel gradient across the zone of highest uplift rates, whereas the Bagmati River displays no significant steepening. When spatial variations in excess shear stress (the stress in excess of that needed to mobilize the bedload) are calculated, they also quite closely match the measured incision rates (Fig. 2).

Let's assume that both channel slope and width are key adjustable variables that serve to modulate river incision rates. As a river encounters a more rapid rate of rock uplift and begins to incise more quickly in order to sustain its course, do slope and width adjust synchronously or does one precede the other? The data from the Bagmati River suggests that changes in width may be sufficient to increase erosion rates several fold without concurrent channel steepening. Studies of much smaller folds in New Zealand bear this out. River width appears very responsive to subtle variations in rock uplift rates: as soon as those rates begin to increase, width begins to narrow (Fig. 3). If the uplift rate is fairly low, then narrowing may be the only adjustment needed. But if uplift is sufficiently rapid, then the channel also tends to steepen. This behavior appears to be exemplified along the Bakeya River where channel steepening occurs only across the zone of highest uplift/incision rates and begins several kilometers downstream of where channel width begins to narrow (Fig. 2).

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