Simulation modeling and statistical classification of escarpment planforms

Nearly horizontal sedimentary sequences are typically eroded into escarpments capped by resistant rock layers. These escarpments record in planform the spatial variation in erosional processes. Simulation models have been constructed of scarp development by three processes, scarp backwasting, fluvial erosion, and groundwater sapping, acting singly or in combination. Scarp backwasting produces planforms characterized by broad, shallow reentrants and sharply pointed headlands. Fluvial erosion creates dendritic, sharply terminated canyons which gradually widen downstream because of superimposed backwasting. Groundwater sapping produces weakly branched canyons of nearly constant width with generally rounded headwalls. A number of morphometric variables are measured on natural and simulated scarps as well as lava flows, glacially eroded mountain fronts, and eroded tabular igneous intrusions. A discriminant analysis is able to classify 478 of these planforms into 9 categories with 87% accuracy. I . I n t r o d u c t i o n Many landforms exhibit distinct boundaries between dissimilar terrain and can be well characterized by planimetric outlines. Examples include the outlines of escarpments and deep valleys, the shorelines of islands or lakes, the edges of basalt flows, drumlins, fluvial islands, some dune types, meteoric impact basins, tectonic basins and collapse depressions (sinkholes, periglacial alases, etc.). In some cases, such as remotely sensed images of planets and satellites, little information other than planform morphology is available to infer formative processes. The planimetric outline records the spatial variation in the processes creating the landform. The present paper addresses the information content of such outlines: Can the processes responsible for a planimetric shape be inferred from statistical characteristics of the 0169-555X/95/$09.50 © 1995 Elsevier Science B.V. All rights reserved SSDIO 169-555X(95)00004-6 outline? Most attention will be devoted to a particular class of landform boundary escarpments created by lateral retreat of scarps in layered rocks, that is, Schumm and Chorley's compound scarps (Schumm and Chorley, 1966) consisting of one resistant layer sandwiched between easily eroded rocks that are either nearly horizontal or uniformly dipping. Three major processes of scarp backwasting are identified: uniform backwasting, fluvial incision, and groundwater sapping. A simulation model of scarp retreat is introduced that incorporates the spatial pattern of these processes, acting alone or in combination. The simulated scarps are statistically compared with natural scarps using a multivariate suite of variables measuring planform shape. In addition to compound scarps, outlines of a few other landform types are included to test the discriminating power of the variables, including contours from areas of uniform relief, meandering 188 A.D. Howard/ Geomorphologv 12 f 199.5) 187-214 stream planforms, edges of lava flows, and mountain fronts strongly modified by glacial erosion. This approach to characterize scarp morphology is similar to that used earlier by Howard and Hemberger ( 1991 ) for stream meanders define a wide range of measurement techniques and associated variables and through statistical analysis determine which are useful in summarizing the morphological variation between classes of scarps formed by different processes. The variables most useful for distinguishing between scarp classes characterize the spatial series of direction changes (curvature) as well as the size distribution and shape of headlands and reentrants. The planimetric outline will be shown to carry significant information content about the processes creating it, such that the morphometric variables can distinguish between scarps formed by different process rate laws with reasonable accuracy. rockfall, slumping, and undermining of the caprock, weathering of the caprock debris and erosion of subcaprock units will be termed scarp backwasting. These backwasting processes are assumed not to depend upon the landform morphology or processes acting behind the brink of the scarp on the top or backslopes of the escarpment. Deep reentrant canyons are created by rapid erosion along a linear zone, generally byflul,ial erosion or groundwater sapping. Both of these processes depend upon water flow collected from the top or backslopes of the scarp. Structure often plays an indirect role by channeling surface or subsurface water along fractures. The role of areal variations in intensity of these three classes of processes in creating scarp planforms is illustrated by simulation modeling followed by multivariate comparison of the resulting scarp planforms with natural scarps. 2. I. Scarp backwasting 2. Modeling of scarp planform evolution The planforms of natural canyons and escarpments in layered rocks are quite varied, exhibiting characteristic shapes such as reentrants, projections, and inset canyons. Some scarps have rounded projections, or headlands, whereas others are sharply pointed; some are deeply incised by deep, narrow canyons while others have shallow, broadly rounded reentrants. The scarp form is determined by the spatial distribution of erosion and by lithologic and structural influences such as rock thickness and dip (Howard and Selby, 1994). The rate of scarp retreat may vary from place to place because of variations in rock resistance. Such variability tends to occur either at relatively small scales (e.g., variations in density of caprock fracturing; Nicholas and Dixon, 1986) or at a very large scale because of lateral variations in caprock thickness or lithology. At the intermediate scales discussed in this research, the main factor controlling scarp form is areal variations in process rates. Erosion of the scarp face by Natural scarps commonly exhibit sharply pointed, or cuspate projections (headlands, spurs) and broadly concave reentrants (embayments). The role of essentially uniform rates of scarp retreat in creating pointed headlands and broad embayments was first discussed by Dutton ( 1882, pp. 258-259) and Davis (1901, pp. 178-180), who noted the nearly uniform spacing between successively lower scarps on the walls of the Grand Canyon. Attack of an escarpment by areally uniform backwasting gradually makes embayments more shallow and the planform of the scarp face close to linear. Similar observations were made by Howard 11970) and Schipull (1980). Lange (1959) systematically studied the consequences of uniform erosional attack, which he called "uniform decrescence", on twoand three-dimensional surfaces, and demonstrated that uniform erosion acting on any arbitrary, rough surface produces rounded reentrants and cuspate spurs. He also showed that scarp retreat in the Grand Canyon is uniform to a first approximation, with some tendency towards more rapid erosion of embayments. FurtherFig. 1. Scarp formed by backwasting, with hypothetical erosion and reconstruction of the mesa. (A) Hypothetical erosion of the mesa (outer heavy line) by uniform backwasting eventually produces the stippled remnant with shallow, curving reentrants and sharp headlands. (B) An attempt to reproduce the original scarp by uniform addition of material is unsuccessful because these processes are not reversible. Only the possible minimum dimensions of the original escarpment can be inferred from an eroded remnant. South Caineville Mesa, Utah (Hanksville, UT and Loa, UT l: 100,000 quandrangles; natural scarps are generally identified by the I : 100,000 or ! :250,000 scale map on which they occur, although mapping utilized larger scale maps). A.D. Howard/Geomorphology 12 (1995) 187-214 189