processes active on hillslopes summarized in several excellent books, including those by Brunsden (1971), Carson and Kirkby (1972), and Young (1972), as well as by the rediscovery and popularization by Schumm and Mosley (1973) of several classic but generally forgotten works. Enough is now known about these processes that analytical modeling of the degradation of hillslopes has become possible. Two of these models have been tested and found to be sufficiently accurate for some hillslopes to be dated (morphologic dating) by matching their observed profile with that predicted by the properly calibrated model.

The hillslopes that will be modeled here are assumed to be closed systems, isolated from the surrounding landscape. Although this assumption is not valid for all hillslopes, it is appropriate for some. Scarps bounded by horizontal or gently inclined bases and crests, such as fault scarps produced by normal faulting, of alluvial fans, abandoned fluvial cutbanks (terrace scarps), and abandoned wave-cut bluffs, on which debris derived from the scarp face accumulates at its base (i.e., debris is not removed by fluvial or wave undercutting) and where degradation is by soil creep or by the raveling of sand and gravel may be modeled as a closed system.

OBSERVED PATTERNS OF HILLSLOPE DEGRADATION

The degradation of most natural, vegetated hillslopes is extremely slow and difficult to observe directly, and the pattern of degradation observed on more rapidly eroding, man-made slopes, such as slag heaps and tailing piles, is not necessarily the same as on natural hillslopes. The degradation of natural hillslopes, however, may be observed indirectly by comparing the morphology of a series of different aged hillslopes assumed to have had the same initial morphology. This approach was probably first used by Savigear (1952), who studied differences in morphology among a series of coastal cliffs isolated from wave undercutting by the progressive lateral growth of a protective beach.

In similar studies, Welch (1970) documented the change in scarp morphology with time from observations of active and abandoned wave-cut bluffs along the north shore of Lake Erie, and Brunsden and Kesel (1973) presented differences between active and abandoned cut-banks along the Mississippi River. Nash (1980b) compared the morphology of wave-cut bluffs abandoned 10,500 yr before present (BP) and 4000 yr BP along the shore of Lake Michigan with that of nearby, actively forming wave-cut bluffs underlain by the same material (Figure 12.1). A pattern of degradation similar to that observed by Savigear (1952), Welch (1970), and

FIGURE 12.1 Profiles of modern, wave-cut bluffs similar to bluffs abandoned 4000 and 10,500 yr BP along the shores of Lake Michigan. All bluffs are underlain by a similar sandy morainal material.

Brunsden and Kesel (1973) is observed on the Lake Michigan bluffs—modern bluffs have a nearly horizontal crest and base separated from a straight, steeply inclined midsection by a sharp crestal convexity and basal concavity (Figure 12.2a). The midsection gradient of the 4000-yr-old bluff has decreased slightly from that of the modern bluff, and the crestal convexity and basal concavity of the profile have become more rounded. This pattern of degradation is more pronounced on the 10,500-yr-old bluffs. These hillslopes appear to have reclined with age, but did they also retreat?

Some fault scarps near the town of West Yellowstone in southwest Montana apparently did not retreat. In 1959 the Yellowstone earthquake occurred close to the town of West Yellowstone, Montana, forming numerous scarps in the overlying obsidian sand and gravel deposit. These scarps have a morphology similar to the



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