Inferring erosional resistance of bedrock units in the east Tennessee mountains from digital elevation data

Geomorphology 55 (2003) 263 – 281 www.elsevier.com/locate/geomorph

Inferring erosional resistance of bedrock units in the east Tennessee mountains from digital elevation data Hugh H. Mills * Department of Earth Science, Tennessee Technological University, Cookeville, TN 38505, USA Received 26 November 2001; received in revised form 24 May 2002; accepted 10 March 2003

Abstract Measures of local relief, regional relief, and slope were calculated from digital elevation models (DEMs) for 50 bedrock units in the Ridge and Valley and Blue Ridge provinces of Tennessee. Each of these measures was normalized and the three were then averaged to produce the erosional resistance index (ERI). Bedrock units with higher ERI values include coarse clastics, intermediate clastics, and metaplutonics. Units with lower values include shales, limestones, limestones plus dolostones, and carbonates plus fine clastics. Dolostones tend to have intermediate values. The calculated ERI values were compared with subjective ratings by a geologist with decades of field experience in east Tennessee. Generally, the agreement between the two ratings was good, the most glaring exception being several shales with improbably high ERI values. These turned out to be thin units cropping out beneath very hard sandstones, allowing them to stand higher and steeper than would otherwise be possible. A systematic method for detecting such erroneously high ERI values is suggested. Inspection of a drainage map superimposed on the geology map shows that in a given area, streams tend to flow on rock units with the lowest ERI values. In addition, statistical analysis shows that bedrock units with the lowest ERI values are, on average, almost three times closer to the nearest stream and six times as likely to have streams flowing on them than are units with highest values. Further, the effect of ERI on stream location is strongest for streams with drainage areas between 1 and 30 km2. Thus, small streams appear to be subject to greater lithologic control than are larger streams. D 2003 Elsevier Science B.V. All rights reserved. Keywords: Tennessee; Appalachians; Rock resistance; Lithology; Relative relief; Lithologic control

1. Introduction The effect of geology on topography has attracted the interest of geologists and geographers since the earliest geologic maps were compiled. In the Appalachians, as early as 1856, Lesley (1856) described many relationships between bedrock and topography in the Ridge and Valley province. The Ridge and * Fax: +1-931-372-3363. E-mail address: [email protected] (H.H. Mills).

Valley is a particularly good location in which to study these relationships. Besides the regularity of landforms here, numerous rock units that vary greatly in erosional resistance crop out as narrow bands in close proximity, allowing the effects of differential erosion to be readily perceived. The rocks of the Blue Ridge province show more subtle differences in rock resistance and crop out in broader belts; but with by far the highest altitudes in the southern Appalachians, this province also invites research on erosional resistance.

0169-555X/03/$ - see front matter D 2003 Elsevier Science B.V. All rights reserved. doi:10.1016/S0169-555X(03)00144-2

264 H.H. Mills / Geomorphology 55 (2003) 263–281 Fig. 1. Index map and orthogonal plot of study area and adjacent areas in Tennessee and North Carolina. K = Knoxville, Tennessee; A = Asheville, North Carolina. Coordinates are Tennessee State Plane, in meters. Vertical exaggeration is approximately 14.

H.H. Mills / Geomorphology 55 (2003) 263–281

With the advent of high-resolution digital elevation data and digitized geologic maps, the relation of bedrock to topography can now be studied in a more systematic fashion than previously possible. Unfortunately, the grid approach appropriate for computer analysis does not lend itself to the analysis of the effect of structure on topography, as creating a dense grid of dip and strike values is very difficult. Therefore, the analyses herein will deal solely with the effect of lithology. Geographically, the study is confined to the Tennessee parts of the Ridge and Valley and Blue Ridge provinces (Fig. 1). Specifically, the thrust of the present study is an attempt to infer the erosional resistance of bedrock units from topographic evidence consisting of two indices of relief and an index of slope and to see how these indices correlate with stream location.

2. Previous work Efforts to link relative relief to lithology began in the 19th century. Hayes (1899), for example, published a diagram showing the relation of topographic relief to rock type in the Chattanooga district. Cooper (1944) published a histogram showing the ‘‘relative topographic potency’’ of bedrock units in the Burkes Garden 15’ quadrangle, SW Virginia. Neither of these efforts were based on actual quantitative data. Thompson (1941) tabulated summit elevations for various bedrock units in several quadrangles in western Virginia, clearly showing harder rocks to have higher summits. Apparently the first effort in the Appalachians to describe topography with gridded elevation data was by Flint (1963), who measured elevation points at 0.25- or 0.50-mile spacings to show differences in altitude distribution on various formations in the Fall Zone of Connecticut. A modern effort of this nature, utilizing digital data and computers, was by Clayton and Shamoon (1998), who made a study of the topography and geology of Great Britain in terms of the kilometer squares of the National Grid. They developed a system to classify the most common geologic units of Great Britain according to the extent to which they form high ground. They used a number of discriminating variables to arrange the units into rank order, eventually developing a sixfold classification of rock resistance. For each of the six classes, a

265

regression equation was calculated between the river distance from each grid square to tidewater and the mean elevation (highest – lowest points) of the square. They found that the pattern of mean altitude predicted from river distance values using regressions for each rock resistance class simulates very closely the overall pattern of British relief. Interestingly, they also reported that rank-order age is a stronger influence on relief than is lithology. Slope is another topographic attribute that reflects erosional resistance, with more resistant rocks generally maintaining steeper slopes (e.g., Selby, 1980). Apparently, the first effort in making slope measurements from gridded elevation data in the Appalachians was by Grender (1973) for an area near New Castle, SW Virginia. Using a grid with a resolution of 158 m, he was able to successfully distinguish the slope distribution of several rock units. Very low slopes ( < 0.05) were strongly associated with Devonian shales, whereas very high slopes were strongly associated with sandstones. The present research took advantage of standard digital elevation models (DEMs) for topographic analysis. A DEM is a regularly spaced and georeferenced grid of point elevations. These models have been utilized for geomorphic and other research for more than a decade (e.g., Moore et al., 1991), but apparently have not been used to study the effect of geology on topography. The best source of large-scale DEMs in the United States is the U.S. Geological Survey National Elevation Dataset (NED), which provides seamless coverage at a resolution of 1 arc sec (approximately 30 m). NED incorporates the highest quality and highest resolution data. Older DEMs have been filtered during the NED assembly process to minimize artifacts commonly found in these data, thereby greatly increasing the quality of the synthetic drainage networks derived from the elevation data (Anonymous, 1999).

3. Geologic setting The Ridge and Valley province of Tennessee consist of sedimentary rock ranging in age from Cambrian to Mississippian. The rocks are extensively folded and thrust-faulted. The province is lower than flanking provinces, with altitude ranging from about

266

H.H. Mills / Geomorphology 55 (2003) 263–281

200 to about 950 m. The Blue Ridge province (also known in Tennessee as the Unaka province, after the Unaka Mountains) consists of Precambrian rocks, ranging from low-grade metasedimentary rocks to gneiss and metaplutonic rocks. The southern Blue Ridge is the highest province in the Appalachians, with altitude in the Tennessee part ranging from about 250 to 2024 m. Fig. 2 is a simplified geologic map of the study area, with rock units divided into eight categories. In terms of these generalized categories, the Ridge and Valley consists mainly of limestone plus dolostone, carbonate with fine clastics, shale, and dolostone. There is little coarse or intermediate clastic rock. The Blue Ridge consists mainly of coarse and intermediate clastic rock (including low-grade metasedimentary rock) and metaplutonic rock.

4. Methods The first step was to construct three grids of topographic indices (regional relief, local relief, and slope) for the study area, and then overlay a geology map grid in order to determine the mean values of the indices for the various geologic units The topographic index grids were produced from an 800-quadrangle DEM from the U.S. Geological Survey National Elevation Dataset. The block included not only the study area but most of the area that drains into eastern Tennessee as well. The original DEM, obtained as an Arc Grid, was projected into the Tennessee State Plane projection in ARC/INFO and given a resolution of 60 m. (This decreased resolution was necessary to avoid excessive run times in processing the large grids. An exception was made for the slope map, which was calculated using a 30-m resolution and then transformed to a 60m grid by thinning.) The grid was exported to RiverTools, which was used to generate a flow-accumulation grid as well as a slope map. The grid was also exported to Idrisi, which was used for all the analysis. Surfer was used for generating orthogonal plots from grids and for interpolating the base-level surface from stream elevations, as explained below. For the bedrock geology, an unpublished digitized version of the Ridge and Valley and Blue Ridge parts of the 1:250,000-scale Geologic Map of Tennessee (Hardeman, 1966) was obtained. (This part of the map was

digitized by the U.S. Geological Survey for a hydrogeologic study of this area (Hollyday and Hileman, 1996).) The map was transformed into a grid with resolution of 60 m in ARC/INFO. Bedrock units with outcrop areas of at least 25 km2 were included in the study for a total of 50 units. The stratigraphic terminology of the 1966 map is used herein to avoid confusion, although some of it is dated. In Idrisi, DEM-derived grids were windowed to the same size as the geology map grid to allow overlays. When determining elevations or topographic indices from grids, larger reservoirs were masked to avoid counting data points from the water surface. The main indicator of erosional resistance for a given rock outcrop is the height of the outcrop. Most previous studies have simply used altitude as the measure of height. However, this approach does not take into account the position of the outcrop in the regional drainage system. Upstream outcrops tend to stand higher than downstream ones in a given drainage system, independently of differences in resistance. Clayton and Shamoon (1998) attempted to get around this problem by using statistics derived from the rate at which elevation increases with distance inland from the sea. As my study area does not border the sea, and in fact is connected to the sea via a very circuitous route, this approach did not seem appropriate. Instead, a measure of relief was devised that is based on the vertical distance of the land surface above base level, where the latter is the surface defined by the altitude of streams having drainage areas of 100 km2 or greater. To create this surface, elevation points along the streams were interpolated to produce a grid for the study area, using the Kriging option in Surfer. This grid was then smoothed by a 33  33-cell mean filter, then subtracted from the altitude grid to produce the ‘‘regional relief’’ grid (Fig. 3). Note that whereas the altitude grid (Fig. 3A) shows a rise in altitude to the NE, the regional relief grid (Fig. 3C) eliminates this trend. The mean regional relief was then calculated for each geologic unit. Although the regional relief measure is an improvement, a problem remains. Note that although mean regional relief values generally are much lower than mean altitudes (Table 1), the regional relief plot (Fig. 3C) is grossly similar to the altitude plot (Fig. 3A). Thus, despite correction for the effect of regional drainage, the Blue Ridge still stands well

H.H. Mills / Geomorphology 55 (2003) 263–281

267

Fig. 2. Map of rock types in study area. Low-grade metasedimentary rocks of Blue Ridge province have been included with sedimentary rocks. Coordinates are in Tennessee State Plane (m). Fig. 6. Map of bedrock units classified by erosional resistance index. Note that low-grade metasedimentary rocks have been classified together with sedimentary rocks. Coordinates are in Tennessee State Plane (m).

268

H.H. Mills / Geomorphology 55 (2003) 263–281

Fig. 3. Orthogonal plots of study area. Coordinates are Tennessee State Plane, in meters. (A) Plot of altitude. Vertical exaggeration is approximately 26. (B) Plot of base level derived from stream elevations. Vertical exaggeration is approximately 26. (C) Plot of regional relief (altitude minus base level). Vertical exaggeration is approximately 14.

H.H. Mills / Geomorphology 55 (2003) 263–281

269

Table 1 Mean altitude, regional relief, local relief, and slope of geologic units Geologic unit

Age

Mean altitude (m)

S.D.

Mean regional relief (m)

S.D.

Mean local relief (m)

S.D.

Mean slope (degrees)

S.D.

Athens Shale Bays Formation Beech Granite Cades Sandstone Chattanooga Shale Chepultepec Dolomite Chickamauga Group Clinch Sandstone Cochran Conglomerate Conasauga Group Copper Ridge Dolomite Cranberry Granite Erwin Formation Fort Payne Chert Grainger Formation Great Smoky Group Hampton Formation Hesse Sandstone Holston Formation Honaker Dolomite Juniata Formation Knox Group Lenoir Limestone Longview Dolomite and Chepultepec Dolomite undivided Longview Dolomite Martinsburg Shale Mascot Dolomite Maynardville Limestone Murray Shale Nebo Sandstone Newala Formation Newman Limestone Nichols Shale Nolichucky Shale Ocoee Supergroup Ottosee Shale Pennington Formation Pumpkin Valley Shale Rich Butt Sandstone Roan Gneiss Rockwood Formation and Clinch Formation undivided Rockwood Formation Rome Formation Sandsuck Formation Sequatchie Formation Sevier Shale Shady Dolomite

O O pC pC M O O S C C C pC C M M pC C C O C O O–C O O

291.8 418.2 1001.0 636.6 404.5 351.1 325.9 573.4 638.5 307.8 558.0 865.9 348.5 294.1 419.3 848.8 859.1 837.9 296.4 590.4 539.3 354.7 299.4 426.6

31.4 128.6 146.1 115.2 58.3 105.6 83.9 89.8 121.0 83.6 68.8 142.3 173.5 84.3 80.9 335.8 206.6 124.2 31.6 59.4 68.8 101.7 44.0 58.1

39.9 110.4 297.6 230.7 67.8 65.9 43.4 245.7 263.0 32.7 65.8 207.6 286.3 55.6 94.3 402.9 318.7 307.7 42.7 82.3 206.0 50.7 30.1 114.7

28.9 92.3 157.7 127.0 44.7 57.7 44.7 85.9 109.2 36.5 43.7 144.3 143.0 58.0 58.1 292.7 160.6 116.9 27.6 43.7 68.2 37.9 26.8 47.5

4.89 37.1 23.0 20.1 52.9 11.1 28.4 122.8 93.3 17.7 8.4 42.8 51.8 30.4 13.4 24.2 81.7 154.3 5.2 6.2 90.4 4.7 7.1 25.8

29.6 69.9 106.3 92.6 43.6 29.2 32.0 83.5 94.6 27.3 33.8 98.8 116.1 56.9 51.0 132.3 125.1 93.5 26.0 37.5 61.3 31.0 19.8 35.1

8.74 13.07 16.60 17.80 12.02 7.03 5.63 20.55 19.30 5.65 8.93 16.44 19.21 10.34 15.53 20.14 20.37 14.47 8.09 7.34 21.80 5.83 4.93 10.53

6.55 7.43 7.61 8.40 7.07 4.54 5.12 6.57 8.10 5.33 6.15 7.75 8.15 6.92 7.59 9.26 8.20 7.86 5.26 5.05 5.82 4.21 3.53 6.06

O O O C C C O M C C pC O M C pC pC S

348.9 417.0 349.5 490.3 319.0 342.3 363.3 369.4 640.0 593.3 640.4 283.5 426.9 602.7 757.6 1082.0 539.6

81.1 77.2 32.0 75.0 137.8 142.9 76.8 136.4 142.4 60.4 145.0 24.5 152.3 48.4 198.5 204.1 89.1

57.6 97.7 50.4 47.9 327.4 369.5 64.4 86.9 327.1 50.8 228.3 30.2 142.2 54.8 368.1 343.7 195.3

38.7 65.9 24.4 42.8 124.9 141.9 46.8 84.4 134.3 38.1 124.0 20.8 114.0 38.4 180.9 177.1 82.2

0.4 0.6 9.0 1.7 167.2 199.4 3.8 23.5 152.8 14.3 17.1 9.0 18.7 19.3 106.5 40.1 77.6

33.3 45.8 19.8 27.3 100.7 119.2 27.8 65.6 107.4 23.7 89.1 19.1 92.8 39.9 110.0 124.4 74.9

6.54 10.59 4.27 8.99 16.63 18.00 6.49 10.94 20.44 7.93 15.99 5.56 15.06 10.61 22.29 19.61 17.67

4.21 6.42 2.77 6.76 8.38 8.64 4.74 8.21 8.92 6.06 7.82 3.98 8.00 6.71 7.86 7.61 5.88

S C pC O O C

313.8 426.8 403.3 293.9 390.3 656.7

67.4 178.2 159.5 73.1 82.6 171.1

70.6 72.4 119.9 43.7 45.1 109.7

54.8 53.5 99.2 46.2 44.3 77.9

0.4 15.7 22.4 39.6 15.4 61.4

59.6 55.1 62.3 51.3 35.9 69.0

11.31 11.59 13.66 9.05 8.18 11.27

6.87 7.77 8.08 6.56 6.55 7.50

(continued on next page)

270

H.H. Mills / Geomorphology 55 (2003) 263–281

Table 1 (continued ) Geologic unit

Age

Snowbird Group Unicoi Formation Walden Creek Group

pC C pC

Mean altitude (m) 653.8 832.2 429.8

S.D.

Mean regional relief (m)

S.D.

Mean local relief (m)

S.D.

Mean slope (degrees)

S.D.

202.6 222.1 84.9

228.4 296.8 121.2

166.8 164.4 71.1

31.2 55.6 18.3

105.0 116.0 56.2

17.49 20.19 15.38

8.46 8.52 8.37

Abbreviations: pC = Precambrian, C = Cambrian, O = Ordovician, S = Silurian, M = Mississippian, S.D. = standard deviation. Note that Blue Ridge province bedrock units are Precambrian, except for units in the foothills, which are largely Cambrian. Ridge and Valley province units range from Cambrian to Mississippian.

above the Ridge and Valley. Does this mean that all the rocks in the Blue Ridge are more resistant than all those in the Ridge and Valley? Not necessarily. Perhaps a preponderance of rocks in the one province is harder than the preponderance of rocks in the other and that is sufficient to produce the observed difference in regional relief. Thus, nonresistant outcrops may appear resistant simply because of the influence of their neighbors. To address this difficulty, a second measure of relief was devised: ‘‘local relief,’’ which determines relief in a somewhat smaller area, thus allowing rock units to be compared with other units in the immediate vicinity. The desired area was that occupied by a typical mountain and adjacent valleys, commonly contained within a 7.5-min quadrangle. An area of 8  8 km (about 40% of the area of a quadrangle) seemed appropriate. To accomplish this, a generalized surface of the study area was first created by applying an 8  8-km (133  133 cells) unweighted mean filter to the altitude grid (Fig. 4A). This surface, when subtracted from the altitude grid, provides a measure of relief within an 8  8-km square (Fig. 4B). The result of this subtraction for a given cell is the vertical distance above or below the generalized surface. The mean local relief is then calculated for each geologic unit, as was done for the regional relief. Note that the generalized surface made with the 8km-wide mean filter (Fig. 4A) is much more irregular than the stream base-level surface (Fig. 3B), and unlike the regional relief plot, the local relief plot (Fig. 4B) shows little resemblance to the altitude plot (Fig. 3A). Note that whereas the foothills of the Blue Ridge (e.g., Chilhowee Mountain in Fig. 1) are much lower than the high peaks in altitude, they are much closer in amplitude on the local relief plot because they are steep and narrow and thus have high local relief.

The bedrock units with the highest mean local relief values occur in the Blue Ridge foothills and Ridge and Valley province, whereas the values on the high peaks of the Blue Ridge are relatively low. Such low values probably stem in part from the likelihood that many bedrock units in this province are similar in erosional resistance, so differential erosion does not produce high local relief. A related factor is that many outcrops of rocks in this province are quite broad, so that in the relatively small area imposed by an 8-km window, the generalized surface used for measuring relief is computed mainly on the same unit rather than on multiple units with varying resistance. In contrast, although it is true that rocks on the whole are softer in the Ridge and Valley, it is also true that there is much more variability in rock resistance than in the Blue Ridge. A hard rock unit surrounded by soft ones develops much more local relief in this province than would a comparable unit in the Blue Ridge. For resistant units, the regional relief measure thus tends to produce higher values in the Blue Ridge than in the Ridge and Valley, whereas the reverse is true for the local relief measure. It therefore seemed appropriate to use both measures to evaluate erosional resistance. A third measure of rock resistance is slope. This was determined by calculating a standard queen’scase (eight-way adjacency) slope map. The steepest slopes (Fig. 4C) occur in the Blue Ridge, the foothills of the Blue Ridge, and on some ridges in the NW part of the Ridge and Valley. Compare the plot of slope (Fig. 4C) with that of altitude (Fig. 3A). Note that the foothills on this surface are much more prominent than they are in the actual topography, because although low in altitude relative to the Blue Ridge, their slopes are somewhat steeper. Note also that in the Blue Ridge, the slope surface has few peaks, because the slope angles are fairly uniform here.

H.H. Mills / Geomorphology 55 (2003) 263–281

271

Fig. 4. Orthogonal plots of study area. Coordinates are Tennessee State Plane, in meters. (A) Plot of generalized surface (altitude smoothed with 8-km-wide mean filter). Vertical exaggeration is approximately 14. (B) Plot of local relief (altitude minus generalized surface). Vertical exaggeration is approximately 43. (C) Plot of slope (degrees) derived from altitude grid with 30-m resolution.

272

H.H. Mills / Geomorphology 55 (2003) 263–281

Table 2 Topographic indices and other data for bedrock units ERI rank

Geologic unit

Lithology

ERI

Regional relief index

Local relief index

Slope index

Hatcher’s rating

Area (km2)

Thickness (m)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Nebo Sandstone Rich Butt Sandstone Nichols Shale Murray Shale Hampton Formation Great Smoky Group Clinch Sandstone Hesse Sandstone Cochran Conglomerate Unicoi Formation Juniata Formation Erwin Formation Roan Gneiss Beech Granite Rockwood Fm and Clinch Sandstone undivided Cades Sandstone Snowbird Group Ocoee Supergroup Cranberry Granite Pennington Formation Bays Formation Walden Creek Group Grainger Formation Sandsuck Formation Longview Dolomite and Chepultepec Dolomite undivided Martinsburg Shale Rockwood Formation Rome Formation Newman Limestone Copper Ridge Dolomite Shady Dolomite Pumpkin Valley Shale Chattanooga Shale Maynardville Limestone Chepultepec Dolomite Fort Payne Chert Honaker Dolomite Holston Formation Athens Shale Nolichucky Shale Newala Formation Longview Dolomite Sevier Shale Sequatchie Formation Knox Group Ottosee Shale

CC CC-MS FC FC IC IC-MS CC CC CC IC FC CC MP MP IC

89.0 85.0 83.8 78.7 73.9 73.6 72.9 71.2 68.4 68.2 67.6 65.0 59.1 57.5 57.3

91.0 90.7 79.7 79.7 77.4 100.0 57.8 74.4 62.5 71.5 47.2 68.7 84.1 71.8 44.3

100.0 64.4 82.1 87.7 54.9 32.8 70.7 82.7 59.3 44.9 58.2 43.4 8.2 32.3 53.3

76.1 100.0 89.7 68.6 89.3 88.1 90.3 56.6 83.4 88.3 97.3 82.9 85.1 68.4 74.4

75.0 70.0 25.0 25.0 45.0 85.0 70.0 67.5 67.5 75.0 25.0 60.0 60.0 60.0 55.0

39.3 25.4 44.6 26.7 304.1 1238.0 108.1 60.3 96.2 469.6 35.0 444.0 67.1 259.4 62.1

76.2 457.2 213.4 152.4 381.0 5943.3 182.9 182.9 365.7 1066.7 91.4 381.0 – – 213.4

IC-MS IC-MS CC-MS MP FC IC IC-MS FC IC-MS LD

53.4 46.0 45.1 40.7 40.2 36.0 34.2 32.7 30.4 30.3

53.8 53.2 53.2 47.6 30.1 21.5 24.4 17.2 24.1 22.7

31.3 11.6 17.0 7.1 30.7 37.8 16.5 18.4 14.9 33.4

75.1 73.4 65.0 67.5 59.9 48.8 61.7 62.5 52.1 34.7

85.0 60.0 62.5 50.0 25.0 40.0 40.0 40.0 30.0 22.5

101.4 522.7 175.8 182.8 173.6 233.1 1176.0 95.9 266.4 517.1

457.2 5029.0 15,239.0 – 167.6 304.8 2438.3 365.7 609.6 335.3

CF IC CF CF DL LD SH SH LS DL CH DL CF SH FC LD LD SH CF LD SH

25.6 24.4 23.2 22.3 20.7 20.1 19.3 18.8 18.0 17.6 17.5 17.4 16.7 16.4 14.6 14.5 14.5 14.5 12.8 12.0 9.09

18.1 10.9 11.3 15.2 9.6 21.3 6.6 10.1 4.8 9.6 6.8 14.0 3.4 2.6 5.6 9.2 7.4 4.0 3.7 5.5 0.0

23.8 23.4 17.5 14.5 26.7 00.0 16.1 3.3 22.9 27.8 11.9 21.2 25.5 21.7 18.1 22.1 23.4 17.6 8.4 21.7 20.1

35.0 39.1 40.6 37.0 25.8 38.9 35.2 43.0 26.2 15.3 33.7 17.0 21.2 24.8 20.3 12.3 12.6 21.7 26.5 8.7 7.2

20.0 40.0 40.0 10.0 35.0 10.0 20.0 15.0 15.0 15.0 35.0 12.0 17.5 10.0 25.0 15.0 30.0 15.0 27.5 20.0 12.5

164.8 128.0 1086.0 190.1 2068.0 355.6 47.7 112.6 317.1 228.4 112.1 372.5 297.4 334.6 78.9 627.4 109.9 2456.0 68.0 5376.0 483.0

304.8 137.2 609.6 213.4 304.8 304.8 106.7 152.4 83.8 243.8 91.4 457.2 121.9 457.2 152.4 251.5 91.4 1371.5 91.4 838.2 304.8

16 17 18 19 20 21 22 23 24 25

26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46

H.H. Mills / Geomorphology 55 (2003) 263–281

273

Table 2 (continued) ERI rank

Geologic unit

Lithology

47 48 49 50

Mascot Dolomite Conasauga Group Lenoir Limestone Chickamauga Group

LD CF CF CF

ERI

Regional relief index

Local relief index

Slope index

5.4 0.7 0.0 3.6

20.1 16.8 20.8 12.7

0.0 7.7 3.7 7.6

8.51 8.37 8.16 7.92

Hatcher’s rating

Area (km2)

Thickness (m)

35.0 15.0 10.0 30.0

28.0 2624.0 206.4 1127.0

175.3 609.6 80.0 2011.6

Abbreviations: ERI = erosional resistance index, CC = coarse clastics (sandstone and conglomerate), CF = carbonate and fine clastics, CH = chert, DL = dolostone, FC = fine clastics (shale, siltstone, some thin-bedded sandstone), IC = intermediate clastics (sandstone with shale and siltstone), LD = limestone and dolostone, LS = limestone, MP = metaplutonic rocks, -MS = low-grade metasedimentary rocks, SH = shale.

To allow the three measures discussed above to be combined, the values of each were normalized to a value range of 0 –100; these products will be referred to as the regional relief index, the local relief index, and the slope index. The indices were weighted equally and averaged to yield the erosional resistance index (ERI). The mean values of all indices for all 50 geologic units are listed in Table 2. The final step in the analysis was to determine the effect of rock resistance on stream location. To accomplish this, a flow-accumulation grid was first calculated. (In a flow-accumulation grid, the value in each cell is the number of cells that drain to that cell. This in effect provides a stream map of the area.) This grid was much larger than the actual east Tennessee study area in order to allow an accurate determination of upstream areas for streams that head outside of the study area and then flow into it. Two measures of the effect of ERI on stream location were determined. First, a distance map was constructed, giving the distance of each grid cell to the nearest stream. In this manner, the mean distance to the nearest stream was calculated for each bedrock unit on the geology map. Second, the relative abundance of streams on each rock unit was determined by creating a boolean stream map and then using the Idrisi EXTRACT command to determine the total number of stream cells associated with each rock unit. The idea is that rock units with low ERI values should tend to be closer to streams and to have more streams overlying them than should units with high ERI values.

5. Erosional resistance index and lithology The correlation table for the topographic indices (Table 3) shows that the R2 between altitude and

regional relief is a fairly high 0.544, whereas that between altitude and local relief is virtually zero (0.043), in agreement with the visual impressions given by the orthogonal plots. Another interesting finding is that whereas the correlation between slope and altitude is only 0.435, that between slope and regional relief is a very high 0.800. On the other hand, the correlation between slope and local relief is only 0.260. Fig. 5 illustrates variations and relationships of erosional resistance indices in the two provinces. Altitude has been normalized to a 0 –100 range analogous to the indices. In Fig. 5A, Great Smoky Group and Roan Gneiss are in the Blue Ridge province. Typically, resistant units in this province show high mean altitudes and high regional relief indices but relatively low local relief indices. Slope indices are high. Thus, two out of three indices are high, resulting in relatively high ERI values. The Cochran Conglomerate and Hesse Sandstone are resistant units from the foothills. Note that values of regional relief and local relief indices are similar, unlike those of the two Blue Ridge units. Fig. 5B shows units from the Ridge and Valley province. The

Table 3 R2 values between topographic indices for 47 bedrock units

Altitude Regional relief Local relief Slope

Altitude

Regional relief index

Local relief index

Slope index

1.000 0.544

0.544 1.000

0.043 0.398

0.435 0.800

0.043 0.435

0.398 0.800

1.000 0.260

0.260 1.000

274

H.H. Mills / Geomorphology 55 (2003) 263–281

Fig. 5. Comparison of dimensionless indices (values 0 – 100) of mean altitude, regional relief, local relief, and slope for nine bedrock units. (A) Blue Ridge and foothills. (B) Ridge and Valley.

Chickamauga Group and Ottosee Shale are two of the weakest units of the province. They show very low values of all indices. Copper Ridge Dolomite and Rome Formation are slightly stronger, commonly forming low ridges. Their indices are moderately higher than those of the weaker two units. The Clinch is a strong quartz sandstone and shows a higher local than regional relief index. Its regional relief is still relatively high, however, and with the aid of a high slope index, the unit has a high ERI value. Table 2 shows the 50 geologic units ranked in order by ERI value. Also shown are the rock types so that it is possible to see the association of ERI to lithology. Units showing the highest ERI values generally are coarse clastics (CC), intermediate clastics

(IC), and metaplutonic rocks (MP). Units showing the lowest values generally are limestone (LS), limestone plus dolostone (LD), carbonate plus fine clastics (CF), and shale (SH). Dolostone (DL) values generally are higher than those of the low group, but much lower than those of the high group. Fig. 6 shows geologic units mapped by ERI values; it may be compared to the geologic map (Fig. 2). In Table 2, note that among the units with the highest ERI values are two shales and the Juniata Formation, which is mainly shale. Their high ERI values appear as suspect and will be discussed further below. One check on these findings is to compare them with our subjective knowledge of the association between lithology and topography. Of course, the

H.H. Mills / Geomorphology 55 (2003) 263–281

275

hope is that the ERI will be more dependable than the subjective knowledge, but nevertheless, a wide disparity between the two would raise suspicions about the ERI. In order to carry out this test, the subjective ratings of bedrock resistance would best be made by someone very well acquainted with rock units of the Ridge and Valley and Blue Ridge province. Therefore, Prof. Robert D. Hatcher Jr. of the University of Tennessee-Knoxville, an authority on southern Appalachian geology with decades of field experience in east Tennessee, was requested to rate the erosional resistance of the units in Tables 1 and 2. Hatcher said he based his ratings on his knowledge of the composition of each unit, together with ‘‘. . .the kinds of slopes or valleys or ridges that specific rock units produce on a local (say part of a [7.5-min] quadrangle) scale’’ (Hatcher, personal communication, 2001). Fig. 7 shows Hatcher’s ratings (expressed as 0– 100) plotted against ERI values. There is fairly good agreement between the two. Of the disparities, the lesser problem concerns units that have ERI values

Fig. 8. Plot of erosional resistance index values vs. distance to nearest hard (ERI>50) bedrock outcrop for units with ERI values at least 50% higher than Hatcher’s ratings.

Fig. 7. Plot of subjective ratings of erosional resistance by Robert D. Hatcher Jr. vs. computed erosional resistance index values.

that seem too low based on Hatcher’s ratings. The reasons for low ERI values for Great Smoky Group and Cades Sandstone, both Blue Ridge units, have been discussed previously. The greater problem, however, is that of units which, based on their lithology, would seem to be nonresistant but which have very high ERI values. The most glaring examples are the Juniata Formation, the Murray Shale, and the Nichols Shale. How might such high values for shales be explained? All three are relatively thin units immediately overlain by resistant sandstones. The Juniata underlies the Clinch Sandstone (ERI = 72.9), the Murray underlies the Hesse Sandstone (ERI = 71.2), and the Nichols underlies the Nebo Sandstone (ERI = 89.0). The relief and slope of these shale units are thus determined by the overlying sandstones. Although the cause of the high ERI values for these units was found by map inspection, such erroneous values can be detected in a more systematic way. For each unit with an ERI more than 50% greater

276

H.H. Mills / Geomorphology 55 (2003) 263–281

than Hatcher’s rating, the mean distance to the nearest hard rock unit was calculated, where ‘‘hard’’ was defined by an ERI of at least 50. (The value of 50 was selected from an inspection of Table 2, which shows that the cutoff between what we normally consider soft rock and what we consider hard falls in the 40 –60 interval, and so a median value of 50 was used.) Fig. 8 confirms the map observations—the three suspect shales are shown to lie very close to hard bedrock, on average, little more than 100 m. (Note that for two closely associated units, the question might be raised of which unit controls the ERI of the other. For example, the Murray Shale [ERI = 78.7] occurs very close to the Hesse Sandstone [ERI = 71.2]—might the Murray control the ERI of the Hesse, instead of vice-versa? Above, we simply assumed that the sandstone controlled the shale. However, in a less obvious case, this question could usually be re-

solved simply by looking at the mean altitudes of the two units—the higher unit being the controlling one.). The Hampton Formation and the Shady Dolomite show a more distant association with resistant units, while the Pennington Formation, the Newman Limestone, and the Athens Shale lie so far from the nearest hard rock that their apparently excessive ERI values (relative to Hatcher’s ratings) cannot be attributed to this cause. On the basis of these findings, the Juniata Formation, Murray Shale, and Nichols Shale were eliminated from further consideration, as their ERI values are clearly misleading. Note that the correlation of Hatcher’s ratings with the ERI is R2 = 0.764 after omission of the three above shale units. Looking at the R2 values between his ratings and regional relief (0.762), local relief (0.345), slope (0.696), and altitude (0.360) is also of interest.

Fig. 9. Stream network superposed on enlarged portion of Ridge and Valley geological map, showing affinity of streams for units with lowest ERI values. Coordinates are in Tennessee State Plane (m).

H.H. Mills / Geomorphology 55 (2003) 263–281

Despite his statement that he considered topography over part of a quadrangle, the correlation between his ratings and local relief is much lower than for regional relief. His ratings also show a fairly high correlation with slope, although this correlation may simply be due to the high correlation (0.800) that exists between regional relief and slope (Table 3).

6. Other factors that may affect ERI values Several other factors that might affect the ERI were investigated. (i) Thickness of bedrock units: The idea is that thicker units would be better able to demonstrate their erosional resistance. That is, thick resistant units would tend to resist erosion more than thin ones and so would tend to show higher relief and steeper slopes. Thick nonresistant units, in contrast, would erode more rapidly than thin ones (which might be influenced by nearby resistant rocks), resulting in lower relief and slope. This hypothesis was tested by, first, correlating the ERIs of all the harder rocks (ERI>50) with their thicknesses (obtained from descriptions on the state geologic map), the expectation being that a significant positive correlation would result. Second, the ERIs of all the weaker rocks (ERI < 20) were correlated, the expectation being that a significant negative correlation would result. However, the correlation (R2) for the harder rocks was only 0.003 and that for the weaker was 0.002. (ii) Age of bedrock units: Clayton and Shamoon (1998) showed a fairly good correlation between rank order of geologic periods and relative relief in Great Britain. An R2 value of only 0.104 between this age measure and ERI was found. However, unlike Clayton and Shamoon, no Cenozoic or Mesozoic rocks are present in this study area, so the range in ages may have been too small to see a higher correlation. (iii) Area of outcrop: The idea was that, for a given unit, really larger outcrops, compared to smaller outcrops, are more likely to stand higher and have steeper slopes if the unit is resistant and to stand lower and have lower slopes if the unit is nonresistant. This hypothesis was tested as follows. For each bedrock unit having at least 20 separate outcrops, the mean altitude, slope index, and local relief index for each

277

outcrop were determined. Each of these variables was then correlated with area. The idea was to see whether resistant units would produce significant positive correlations and nonresistant units, significant negative correlations. This procedure was carried out for 27 bedrock units. The highest positive correlation found was an R2 of 0.318 for the local relief index of the Cochran Conglomerate, and the highest negative correlation was an R2 of 0.115 for the altitude of the Knox Group. Most correlations, however, were much lower, with the average positive correlation (R2) for all variables being 0.020 and the average negative correlation (R2) being 0.017. Thus, the above three variables apparently have a small-to-negligible influence on the ERI and related topographic indices.

7. Effect of ERI on stream location Streams should have more of an affinity for bedrock units with low ERI values than for those with high ERI units, as the former should tend to underlie

Fig. 10. Plot of mean distance to nearest stream vs. erosional resistance index values.

278

H.H. Mills / Geomorphology 55 (2003) 263–281

to the nearest stream (defined in this case as having a drainage area of at least 3 km2, for reasons made clear below) was first determined. In Fig. 10, the mean distance to the nearest stream has been calculated for each geologic unit and plotted against the ERI for that unit. A fairly high correlation between distance and ERI results (R2 = 0.685). As Fig. 10 shows, the mean distance to the nearest stream is nearly three times as great for units with the highest ERI values as it is for units with the lowest values. A follow-up question that might be asked about this relationship concerns the size of the streams involved. Do all streams show a relation like this or only streams of a certain size? In Fig. 11, this question is explored by plotting the R2 values between the ERI and the mean distance to streams with the specified drainage area against the drainage area. Note that the highest correlations are found for a stream size between 1 and 30 km2 (the very highest is for 3 km2, hence the use of this value in Fig. 10). Beyond 30 km2, the R2 value drops off dramatically, declining to 0.1 for 100 km2. Fig. 11. Plot of correlation (R2) between ERI and mean distance to stream of specified drainage basin as a function of drainage basin area.

valleys and the latter should tend to underlie ridges. In Fig. 9, streams draining at least 1 km2 are superimposed on an enlarged section of the Ridge and Valley geologic map. The ERI values are shown for selected bedrock units. Note that strike-following streams consistently flow on the units with the lowest ERI values: the Chickamauga (7.9) and the Conasauga (8.4). For units with higher, but still relatively low, ERI values, such as the Rome (23.2) and Copper Ridge Dolomite (20.7), streams arise on or cut across the outcrops but do not follow their strike. For units with high ERI values, such as the Clinch (72.9), not a single stream occurs on the outcrops. Inspection of other Ridge and Valley areas on the state geologic map shows similar results. However, demonstrating the relationship between ERI and stream location systematically for the whole study area is desirable. Observations such as those provided by Fig. 9 suggest that, on average, bedrock units with low ERI values should be closer to, and more likely to be overlain by, streams. To test the first hypothesis, for each grid cell of each geologic unit, the linear distance

Fig. 12. Plot of proportion of grid cells with flow-accumulation value of 1 km2 or greater on a given geologic unit vs. the ERI of that unit.

H.H. Mills / Geomorphology 55 (2003) 263–281

An alternative approach to the relationship of drainage to bedrock erosional resistance is to see if streams are more likely to overlie units with low ERI values than they are units with high ERI values. This relationship was tested by determining, for each geologic unit, the proportion of cells that are overlain by grid cells with flow-accumulation values of 1 km2 or greater. This proportion was then plotted against the ERI for each geologic unit. Fig. 12 shows the expected relationship, although the correlation is lower than that obtained for the stream distance case. Note that the proportion of geology grid cells overlain by stream grid cells is more than six times greater for units with low ERI values than for units with high ERI values. In a manner analogous to that done for stream distance, the effect of stream size on this relationship can be determined. In Fig. 13, the R2 value between ERI and the proportion of cells of the specified flowaccumulation area overlying each geological unit is plotted against the flow-accumulation area. The

Fig. 13. Plot of correlation (R2) between ERI of a geologic unit and proportion of cells with specified flow-accumulation area on that unit, as a function of flow-accumulation area.

279

results show high values for most of the smaller stream sizes, with a maximum again in the 1 –30 km2 range. A steep drop-off in correlation occurs beyond 30 km2. The decline is not as precipitous as seen for stream distance, but the results still show low correlations for the largest streams. Thus, whereas relatively small streams show a strong relationship to bedrock resistance, large ones appear to be relatively independent of this factor.

8. Discussion The correlations between topographic indices (Table 3) show wide differences that suggest the two relief indices are distinct. As might be expected, the R2 value between regional relief and altitude is fairly high (0.544). Less expected, however, is a very strong 0.800 between regional relief and slope. Part of this may be explained by the tendency of the high mountains to have steeper slopes, yet it is not simply an effect of altitude, as the R2 between slope and altitude is only 0.435. The local relief index is very different from the regional relief index, showing an R 2 with altitude of only 0.043, and a relatively low R2 of 0.260 with slope. Because slope has such a high R2 with regional relief (0.800), the two relief variables alone can account for most of the variance. The two relief indices used in this study may be criticized in that they are arbitrary: 100 km2 or greater for the streams used to interpolate the baselevel surface for the regional relief index, and 8 km for the width of the moving window used to create the generalized surface for the local relief index. However, although the details would change according to the specific numbers, the same general results would probably be obtained as long as one index was based on large areas and the other based on small areas. Also, two different methods were used to generate the indices, but very likely, either method could be used to generate both indices. One problem with analysis of lithologic effects based on small-scale geologic maps such as the Geologic Map of Tennessee (Hardeman, 1966) is that, of necessity, many mapping units are quite broad. Commonly, several disparate lithologic units are combined to make larger map units. For exam-

280

H.H. Mills / Geomorphology 55 (2003) 263–281

ple, the Chickamauga Group includes (of the units considered herein) the Lenoir Limestone, the Holston Formation, and the Ottosee Shale. Obviously, greater accuracy would be achieved by measuring relief and slope of the individual units comprising the Chickamauga Group than of the Chickamauga as a whole, but the area of the study area mapped simply as Chickamauga Group far exceeds the area mapped as individual units of the Chickamauga. This generalization obviously decreases the relationship of map units to rock type and therefore to topography. To minimize this problem ideally, analyses such as the current one would be done using 1:24,000-scale geoquads. However, in areas where only a small fraction of quadrangles have been mapped, as in east Tennessee, this option is not yet available. The possible effect of neotectonics has been ignored in this paper. The assumption has been made that because of the thick crust in the Appalachians and the relatively small size of the study area, the only likely vertical movement would be a relatively uniform uplift due to isostatic adjustment to denudation. Such uplift should have no differential effect on relief and slope of bedrock units within the study area. If other Cenozoic tectonic activity has taken place in the study area, then interpretation of rock resistance may be in error. If, for example, the Blue Ridge rises above the Ridge and Valley partly because of differential uplift, then the resistance of rocks in that province has been overestimated. Hack (1980) has observed, however, that much of the topography in the Appalachian Highlands can be explained by differential erosion alone. Although not attempted in this paper, ultimately the goal of studies such as this should be to compare the topographic indicators of erosional resistance to physical parameters of the rocks. Applying Selby’s (1980) Rock Mass Strength Classification would be difficult in this environment because this method requires that outcrops must be on slopes that are natural and not actively undercut. In the Appalachian setting, natural outcrops of all but the hardest rocks are rare. An alternative method might be one in which measurements are made on fresh unweathered rock, mainly from artificial cuts and cores. Goudie (1990), following Bell (1983), suggested some additional parameters that might be useful to measure in this

context. Another problem is that such schemes commonly deal with susceptibility to slope failure. However, if the concern is with long-term landform evolution, solubility becomes an important factor. Limestones in the Appalachians, for example, may have high mechanical strength yet end up forming the valley floor. Several authors have related topography in the Appalachians to measurable characteristics of the bedrock. Significantly, in each case, the measured parameter reflected the susceptibility of bedrock to chemical weathering. Rahn (1971), for example, measured weathering rates on tombstones in New England and showed that the rates so determined can predict the average altitude of rock types within that region. Flint (1963) noted that the metamorphic rocks underlying the highest areas in the Connecticut Fall Zone were characterized by greater quartz content than metamorphic rocks underlying the lowest areas. Costa and Cleaves (1984) reported similar findings for the Piedmont region of Maryland. Therefore, it is likely that the appropriate rock parameters to measure in the Appalachians will differ from those used in alpine or dry regions. The finding that the mean ERI value of a geologic unit helps predict the affinity of streams for that unit, with units having low mean values being on average both closer to the nearest stream and more likely to be overlain by a stream than are units having high mean values, is not surprising. Likewise, the finding that this effect becomes weaker for larger streams is compatible with the accepted knowledge that the courses of master streams are less controlled by bedrock outcrop distribution than are their smaller tributaries, in part because their courses are thought to be determined as much by inheritance as by rock control (e.g., Feldman et al., 1968). However, the finding that the effect of rock type on stream location begins to decline at a drainage basin area of 30 km2 is perhaps surprising, as master streams generally have drainage areas much larger than this.

9. Conclusions The ERI (composed of indices of regional relief, local relief, and slope) is suggested as an index to characterize the erosional resistance of bedrock units

H.H. Mills / Geomorphology 55 (2003) 263–281

on a geologic map. The ranking of 47 geologic units in the study area by this index produces reasonable results based on their likely resistances inferred from lithology. Coarse clastic, intermediate clastic, and metaplutonic rocks have the highest ERI values, with limestone, limestone plus dolostone, and limestone plus fine clastics having the lowest. Dolomite generally has a value higher than the second group, although much less than the first group. Unit thickness, area of individual outcrops, and age of bedrock seem to have little effect on ERI. Mean ERI values accurately predict stream location in the Ridge and Valley, with along-strike streams generally located on units with lowest mean values. Statistically, geologic units with the lowest ERI values tend to be three times closer to the nearest stream and six times more likely to have a stream flowing on them. The correlation between ERI value and mean distance of the unit to the nearest stream and between ERI and the proportion of the unit outcrop occupied by streams are highest for streams with drainage areas between 1 and 30 km2, suggesting that the courses of larger streams are less affected by bedrock character than are the courses of smaller streams. The concept that the courses of large master streams are less affected by geology than are their tributaries is not new. What the analyses here do is to pin down the size of stream that is most affected by bedrock resistance. Future research would probably best be carried out on 7.5-min geoquads, where map units are less generalized and finer-resolution DEMs can be employed. For example, measures of hillslope convexity and concavity based on 10-m resolution DEMs may well be capable of differentiating bedrock units.

Acknowledgements Funds for NED data and some software were provided by a Tennessee Technological University Faculty Research grant. Thanks to Prof. Robert D. Hatcher Jr. for his rating of east Tennessee geologic units, to Scott Lucas for his assistance in an early version of this project, and to Dr. Peter Li for his helpful advice.

281

References Anonymous, 1999. National elevation dataset fact sheet. U.S. Geological Survey (1 – 4 pp.). Bell, F.G., 1983. Fundamentals of Engineering Geology. Butterworth, London. 648 pp. Clayton, K., Shamoon, N., 1998. A new approach to the relief of Great Britain: II. A classification of rocks based on relative resistance to denudation. Geomorphology 25, 155 – 171. Cooper, B.N., 1944. Geology and mineral resources of the Burkes Garden Quadrangle, Virginia. Virginia Geological Survey Bulletin, vol. 60. Virginia Geological Survey, Charlottesville, VA, 299 pp. Costa, J.E., Cleaves, E.T., 1984. The piedmont landscape of Maryland: a new look at an old problem. Earth Surface Processes and Landforms 9, 59 – 74. Feldman, S., Harris, S.A., Fairbridge, R.W., 1968. Drainage patterns. In: Fairbridge, R.W. (Ed.), Encyclopedia of Geomorphology. Dowden, Hutchinson & Ross, Stroudsburg, PA, pp. 284 – 291. Flint, R.F., 1963. Altitude, lithology, and the Fall Zone in Connecticut. Journal of Geology 17, 683 – 697. Goudie, A., 1990. The Landforms of England and Wales. Blackwell, Oxford, UK. Grender, G.C., 1973. Slope distribution and relationship to bedrock in Appalachian ridges near Roanoke, Virginia. American Journal of Science 273A, 391 – 395. Hack, J.T., 1980. Rock control and tectonism—their importance in shaping the Appalachian Highlands. U.S. Geological Survey 1126B, B1 – B17. Hardeman, W.D., 1966. Geologic Map of Tennessee. Tennessee Division of Geology Map, Nashville, TN, 4 sheets, scale 1:250,000. Hayes, C.W., 1899. Physiography of the Chattanooga District in Tennessee, Georgia, and Alabama. U.S. Geological Survey Annual Report, Pt. 2, Washington, DC, pp. 1 – 58. Hollyday, E.F., Hileman, G.E., 1996. Hydrogeologic terranes and potential yield of water to wells in the Ridge and Valley province in the eastern and southeastern United States. U.S. Geological Survey Professional Paper, vol. 1422-C. U.S. Geological Survey, U.S. Government Printing Office, Washington, DC, pp. C1 – C30. Lesley, J.P., 1856. Manual of Coal and its Topography. J.B. Lippincott, Philadelphia. 216 pp. Moore, I.D., Grayson, R.B., Ladson, A.R., 1991. Digital terrain modelling: a review of hydrological, geomorphological, and biological applications. Hydrological Processes 5, 3 – 30. Rahn, P.H., 1971. The weathering of tombstones and its relationship to the topography of New England. Journal of Geological Education 19, 112 – 118. Selby, M.J., 1980. A rock mass strength classification for geomorphic purposes with tests from Antarctica and New Zealand. Zeitschrift fu¨r Geomorphologie N.F. 24, 31 – 51. Thompson, H.D., 1941. Topographic of the analysis of the Monterey, Staunton, and Harrisonburg Quadrangles. Journal of Geology 49, 521 – 549.