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DR. KAM W. WONG University of-Illinois at Urbana-C hampaign Urbana, IL 61801 DR. T. H. THORNBUR Las Vegas, NV 89109 M. A. KHOURY University of Illinois at Urbana-Champaign Urbana, IL 61801

Automatic Identification from Data

Small differences in soil types can be distinguished by the use of quantitative factors which are computed from digital terrain data.

INTRODUCTION pends primarily on the ability of the in­ HE CHARACTERISTICS of a soil and by terpreter, and (3) they are relatively time­ T extension its engineering properties are consuming. With the advance of electronic chiefly a function of the , to­ computers and the corresponding develop­ pography, vegetation, climate, and time. ments in automatic topographic mapping Thus, having a thorough understanding of and remote sensing, the automation of soil and the natural forces ofero­ classification has become an interesting as sion and such as wind, ice, and as promising possibility. water, a soil scientist experienced in air This paper describes a systems approach photo interpretation techniques can identify for the automatic identification of by soil characteristics from the land forms, ero- the combined application of remote sensing

ABSTRACT: A reliable method ofautomatic soil identification can be developed by the combined application ofremote sensing and digital terrain data. Research results have demonstrated that small differ­ ences in soil types can be distinguished by the use of quantitative terrain factors which are computed from digital terrain data. Con­ tinuing research effort is dil-ected towards the improvement of the terrain factors, the development ofstatistical prediction techniques, and testing the effectiveness ofthese factors in the identification of soils.

sion patterns, vegetative cover, , and and digital terrain data. The major problem the tonal distribution in the air photos. The in the development of such a system is the accuracy of the interpretation will depend successful development of a set of quantita­ chiefly on the technical skill of the interpre­ tive factors which can adequately describe ter and his unique and instinctive ability to the geometric characteristics of the topog­ detect, correlate, and deduce from the many raphy. A research program directed towards minute hints present in air photos. the development of such 11 set of factors for Conventional photo interpretation the purpose ofsoil identification is presently techniques have three major shortcomings: in progress at the University of Illinois. Pre­ (1) they require highly trained personnel, liminary results are very encouraging and (2) the accuracy of de- will also be reported in this paper. 73 PHOTOGRAMMETRIC ENGINEERING AND REMOTE SENSING, Vol. 43, No.1, January 1977, pp. 73-80. 74 PHOTOGRAMMETRIC E GINEERING & REMOTE SENSING 1977

M ULTISPECTRAL ANALYSIS ic and reliable soil identification technique cannot be based entirely on multispectral Several investigators have reported in the analysis. The accuracy of soil identification literature attempts to identify soil types di­ using either spectral analysis or rectly from their multispectral signatures. Anuta et al. (1971) reported an attempt to radiation techniques has been degraded classify two types of fine , four loamy greatly by the data noise caused by vegeta­ tive cover, atmospheric condition, instability soils, and one clayey soil in the area of El Centro in the Imperial Valley, California. Al­ of the sensors, and sun angles. Even differ­ ences in tillage practices on agricultural though many bare soil fields were correctly identified, the computer classification was fields alter greatly the spectral of the surface soil and confound identification found to be incorrect for areas covered by by spectral analysis (Kristof and Zachary, vegetation. Cihlar and Protz (1972) achieved 1971). Another reason for the failure of an identification accuracy of39.7 percent for spectral analysis techniques is that the sur­ ideal training sets and reported that the ac­ face , which is a major soil form­ curacy decreased gradually if these sets were modified to suit practical require­ ing factor, is not used as a characteristic fac­ ments. Kristof and Zachary (1974) reported tor for soils identification. similarly limited accuracy in an attempt to classify soils in Indiana. In a slightly differ­ A SYSTEMS ApPROACH ent approach, Piech and Walker (1974) used Figure 1 illustrates the basic concept of the -to- reflectance ratio to identify using the systems approach for the automatic the effects of moisture and texture on the identification of soils. The approach makes tone of the soil. Although the tonal differ­ use ofmodern remote sensing and automatic ence between a dark and a light color soil mapping techniques to identify all the soil can be attributed to either moisture or tex­ forming factors (such as vegetation, ground tural difference from the ratio test, the rela­ temperature, moisture, drainage, topog­ tionship between the ratio values and the raphy) as well as ground signatures of soil degree of moisture and textural change can­ types (such as land use, texture, and spectral not be presently quantified. characteristics). These data can then be The principle ofthe multispectral analysis supplemented by environmental informa­ approach differs significantly from that ofthe tion such as climate and geological history of traditional method of photo interpretation. the area to predict the soil types. While a photo interpreter attempts to iden­ Digital models of the relief of the terrain tify from the air photos the factors which can now be obtained as direct output from cause the formation of a particular type of photogrammetric mapping instruments such soil, the multispectral approach attempts to as the Automated Analytical Stereoplotter identify directly the surface characteristics (AS-H), the Universal Automatic Map Com­ of a particular type of soil. pilation Equipment (UNAMACE), and It is generally recognized that an automat- stereoplotters. The first two types of instru-

Data Source Data Vegetation

Landuse

Remote Sens i n9 Mo; sture

Color Correlation

Ground temperature Classification ==:;;> SOILS Ora inage Identification

Automatic Cartography Digital terra; n

C1 imate

I nfonna ti on Time Data Bank Geological History

FIG. 1. A systems approach for soil identification. AUTOMATIC SOIL IDENTIFICATION FROM REMOTE SENSING DATA 75 ments are being used for routine automatic direction changes) to successfully delineate map compilation in the military agencies; 25 distinct regions in Central Europe be­ and the conventional stereoplotters, because tween 48° and 52° OIth latitude and 16° East of their lower cost, are widely used in civi­ longitude. These regions agreed quite well lian applications. In addition, automatic re­ with a qualitatively formed physiographic mote sensing techniques based on the prin­ map of the area. James (1961) used a rough­ ciple of spectral analysis and slicing ness index to distinguish various Wisconsin have been developed for the automatic clas­ substages in Indiana. sification of vegetation and identification of Salisbury (1962), using a random grid drainage ways, bodies of water, and snow sampling technique, found high correlation coverage. Thus, instrumentation and coefficients between the landslopes of techniques are presently available for pro­ selected points and the type ofglaciated ter­ ducing the digital data necessary for the au­ in which the points were located. tomatic classification of soils by this ap­ Several of the more recent efforts in the proach. field have been conducted, or sponsored, by The development of such automatic soil the U. S. Army Waterways Experiment Sta­ classification technique will involve (1) the tion, with primary emphasis on evaluating development of a set of quantitative factors the terrain for vehicular ground mobility which either individually or in combination (Dornbusch, 1967; Garrett and Shamburger, can be used to describe the geometry of the 1967; Wright and Burns, 1968). surface topography; (2) the development of The work by Vadnais (1965) and Philips suitable computation techniques to compute (1970) at the University of Illinois were the these terrain factors from digital terrain data; first attempts directed toward the applica­ (3) the determination of the quantitative ter­ tion of quantitative terrain factors to soil rain factors for different soil types, and classification. Vadnais conducte,d his study (4) the development of statistical methods with test areas located within the Wisconsin for the identification and classification of glacial deposits in Wisconsin, Illinois, and soils based on their quantitative terrain fac­ Indiana. A total of 221 test cells of I-mile tors and on data collected from remote sens­ radius each were used. The soil associations ing. found in these test areas included sandy Recent research at the University of Il­ till, loam till under prairie vegetation, linois has shown that quantitative terrain fac­ loam till under forest vegetation, loam till tors can be computed from digital terrain with 42 to 60 inch cover under prairie data to describe the terrain and that direct vegetation, silty loam till under prairie correlation exists between these terrain fac­ vegetation, silty clay loam till under forest tors and soil types. vegetation, and medium and moderately fine-textured outwash under prairie vegeta­ QUANTITATIVE TERRAIN FACTORS tion. Sixteen terrain factors were used for The use of quantitative terrain factors and classification purposes, including average analytical techniques for terrain description slope, local relief, roughness index, is presently an active area of research (J un­ elevation-relief ratio, , con­ kins and Jancaitis, 1974; Speight, 1974; stant of channel maintenance, ruggedness Eyton, 1974; Collins, 1973; Mather, 1972; number, mean valley depth, mean number and Evans, 1972). of slope changes per mile of traverse, and The earliest quantitative factors used to texture. The terrain factors for each test cell describe the land surface were average were computed by statistically sampling slope, slope, and relief measurements. Vari­ from existing 1:24,000, scale U. S. Geologi­ ous means of computing representative av­ cal Survey topographic maps. It was found erage slopes were devised by S. Finsterwal­ that, for 18 of the 21 possible combinations der (1890), Rich (1916), and Wentworth ofsoil association areas, an average ofsix ter­ (1930). Using Wentworth's method to com­ rain factors were significantly different pute average slope for 70 maps, Peltier when the mean values of each of the soil (1954) found that average slope was related association areas were compared. to average local relief and the average tex­ Instead of topographic maps, Philips ture of the topography-that is, the number (1970) used air photos and a Zeiss of gullies, ravines, and small valleys per Stereotope to measure the terrain factors linear mile of transit. within the test areas. He attempted to dif­ Wood and Snell (1960) used six factors ferentiate nine soil types using ten terrain (average slope, , relief, average factors. The soil groups included loamy elevation, elevation-relief ratio, and slope till, sandy loam till, loam and loam 76 PHOTOGRAMMETRIC E lGINEERING & REMOTE SE ISING 1977 till, silty clay loam till, silty clay till, clay till, the development of an automatic soils iden­ sandy and sands, medium and moder­ tification system. ately fine textured outwash, and thin loess over . The terrain factors included CURRENT RESEARCH five surface factors (mean slope, local relief, A current research project, which is spon­ number of slope direction changes per mile sored by the U. S. Army Research Office and of traverse, roughness index, and elevation­ conducted in the Department of Civil En­ relief ratio) and five surface drainage factors gineering at the University of Illinois at (drainage density, ruggedness number, tex­ Urbana-Champaign, is aimed towards the ture on random traverse, texture on circum­ development of methods and procedures for ference, and mean valley depth). It was using quantitative terrain factors and digital found that, at the 95 percent confidence terrain data for soils identification. The level, any two soil association areas can be quantitative terrain factors which were used differentiated by at least one of the ten ter­ by Philips have been modified for use with rain factors. At the 99 percent confidence digital terrain data. The effectiveness of level, only the combination of loam till with these factors in discriminating between dif­ 42 to 60 inch loess cover and medium to ferent soil types is being tested using sample moderately fine textured outwash cannot be areas for which detailed soil maps, topo­ differentiated by at least one of the ten ter­ graphic maps, and aerial photos are available. rain factors. Philips also made a comparison The digital terrain data for a sample area on the relative efficiency of air photos and consists of both elevation and drainage data, topographic maps as a data base. Basing his and are generated from 1:24,000-or comparison on five soil associations in­ l:62,500-scale U. S. Geological Survey top­ cluded in both his and Vadnais' study, he ographic maps and aerial photographs. A found that at the 95 percent confidence sample area measures 10 cm by 10 cm on a level, the air photo data could differentiate l:24,000-scale topographic map, and the all ten possible combinations of soil types, elevation data is generated from the topo­ but the topographic map data failed to dif­ graphic map in a grid pattern at a grid interval ferentiate one combination. Philips con­ of 5 mm on the map. Thus, the topographic cluded that the photogrammetric method relief of a sample area is represented by 400 provided better measurements on the factors data points. Drainage data are generated associated with fluvial features. using both the topographic map and stereo­ Although Vadnais and Philips had dem­ scopic pairs of air photos. The air photos are onstrated the capability of terrain factors used to delineate small streams or drainage for soil classification, they had not fully ways which are not shown on the map. Each exploited the potential of the method be­ drainage way is digitized as a series ofpo'ints cause of the use of air photos and topo­ for which the x and y rectangular coordinates graphic maps as data base. Since manual are recorded. methods were used in measuring data points ine different soil associations are pres­ for the terrain factors, only a small number of ently included in the study. These associa­ data points could be measured for each test tions are all found in Illinois and are clas­ cell. This resulted in relatively large uncer­ sified according to the types of parent mate­ tainties in the computed values for the ter­ rials, , degree ofdevelopment (A, B, rain factors. However, their procedures can and C horizons), and the natural drainage be easily automated for computation using capability of the soils. Table 1 summarizes digital terrain models. By performing the the basic characteristics ofthese soil associa­ sampling and computation in a high-speed tions. Soil associations A, I,], and K have electronic computer, a large number of data very similar properties. They are all dark points can be computed within each test cell colored soils developed from loess deposits to produce highly accurate values for the ter­ overlying tills or drifts from the Wisconsinan rain factors. Higher accuracy will also be glacial period. Their slight differences are made possible by the higher positional ac­ due to thickness of surface loess deposit and curacies on relief, drainage, and vegetation to small variations in texture. Association L afforded by the advanced photogrammetric has basically the same soil materials as as­ compilation equipment which produces the sociation A except that the soils in L are digital terrain model. The use of a computer medium dark to light colored because they will also open the additional opportunity of have developed under forest vegetation. The using remote sensing data and supplemental soils in association G are dark-colored soils information to support the quantitative ter­ developed from thin medium-texture mate­ rain factors, and this will eventually lead to rial on gravel, and the soils of association X AUTOMATIC SOIL IDENTIFICATION FROM REMOTE SENSI G DATA 77

TABLE l. SOIL ASSOCIATIONS INCLUDED IN CURRENT EXPERIMENT

Soil Parent Surface Classification Typical Association Materials Vegetation Color AASHO Unified Substrata A Loess 4-5 ft Prairie Dark A-6 CL Silt loam loess thick G Medium textured Prairie Dark A-2-4 GP Gravel and material 2 to 3% ft thick on gravel Loess < 3-ft Prairie Dark A-6 CL Loam till thick on loam till ] Medium texture Prairie Dark A-6 CL Silty clay loam material < 4 ft. till thick on silty clay loam till K Medium texture Prairie Dark A-7-6 CL Silty clay till material < 4 ft or drift thick on silty clay drift L Loess > 4-5 ft. Forest or Medium A-4 ML Silt loam loess thick mixed prairie dark to A-6 CL and forest light Q Loess < 4-ft Forest Light A-6 CL Loam till, clay thick on till Illinoian drift R Loess < 7-ft Forest Light A-4 CL Sandstone thick over bedrock A-6 ML residuum X Sand, fine sand, Varied Light or A-2-4 SM Sand loamy sand, or dark loamy fine sand

are sandy and variable in sub-soil develop­ • bifurcation angle (degrees) ment. The parent materials of the soils in • texture (number of bifurcations/mile) associations G and X are also from the Wis­ • ruggedness number = local relief x drain­ consinan period. The soils in association R age density are developed from thin loess deposits on • mean valley depth (ft) bedrock residuum, and the soils in associa­ Tables 2 and 3 list the mean values of the tion Q are developed from thin loess de­ terrain factors for surface geometry and posits on Illinoian drift. drainage features respectively. These aver­ The sample areas are carefully selected so age values were computed from ten sample that all the soils in a sample area belong to areas for each of the nine soil associations. the same association. Digital data were gen­ Univariate analysis of variance was per­ erated from ten sample areas of each of the formed to test the statistical significance of above nine soil associations. the difference in the value of each terrain The following terrain factors were com­ factor for each combination of two soil as­ puted for each sample area: sociations. The test of significance was per­ formed using Fisher's test at the 5 percent Factors on Surface Geometry • average slope (percent) significance level. Figure 2 shows for each • mean slope change (number of slope combination of soil associations the terrain changes/mile of traverse) factors which were found to be significantly • roughness index = surface area/plane area different. of orthogonal projection Results from the univariate analysis ofvar­ • sample relief (maximum elevation ­ iance showed that quantitative terrain fac­ minimum elevation) tors could distinguish between areas having • sample variance (6 x standard deviation of rather small differences in soil characteris­ the elevations in the sample) tics. The findings may be summarized as • elevation-relief ratio = mean elevation ­ minimum elevation/sample relief follows: Factors on Drainage Features • Both soil associations A and L have the • drainage density (miles/sq. mile) same parent material, which is silt loess in 78 PHOTOGRAMMETRIC ENGINEERING & REMOTE SENSING 1977

TABLE 2. MEAN VALUES OF TERRAIN FACTORS FOR SURFACE GEOMETRY

Average Mean slope Sample Sample Elevation- Soil slope change (slope Roughness relief variance Relief Association (%) changes/mile) index (ft) (ft) Ratio

A 0.74 3.28 1.00009 46 54 0.63 G 0.62 2.12 1.00011 47 55 0.49 I 0.78 3.15 1.00007 59 76 0.48 ] 0.75 3.21 1.00008 54 69 0.50 K 0.58 2.40 1.00002 57 72 0.48 L 3.61 4.70 1.00326 147 190 0.64 Q 1.94 2.94 1.00074 105 140 0.50 R 4.49 3.91 1.00447 233 287 0.60 X 0.59 2.96 1.00006 42 45 0.40

excess of 4-ft thick, the only difference on Wisconsinan age silty clay or clay drift, being that A is a dark colored soil de­ whereas the soils in I and] have developed veloped under prairie vegetation, and L is a on Wisconsinan age loam till (1) or silty clay medium to light colored soil developed loam till (j). This small difference was dis­ under forest or mixed prairie and forest. tinguished by the measure ofthe number of This difference was distinguished by 8 of slope changes per mile. the 11 terrain factors. In general, areas of • The small difference in silt and clay con­ association L had larger average slope, tents of associations I and] could not be more frequent slope change, and higher differentiated by any of the terrain factors. drainage density. Previous statistical studies of the physical • Soil associations I, ], and K are soils de­ properties of these two glacial tills have in­ veloped from thin loess deposits (less than dicated that they are essentially similar in 3-ft thick) over fine-grained glacial drift. their engineering properties. They differ from association A in that soils of association A have developed from leoss • The soils in association Q differ from those deposits greater than 4-ft thick. This differ­ of all other associations in that they have ence was distinguished by the texture of developed from 1% to 4 feet of loess on the sample areas (Le., number of stream Illinoian drift, which is considerably older bifurcations per mile). than Wisconsinan drift or tills. Association • Association X differs from all other associa­ Q was clearly distinguished from other as­ tions, in that its soils have developed from sociations. Most noticeably the sample water and/or wind deposited sands. This areas in this association had much higher soil association was easily distinguished drainage density. from the others by the lower drainage den­ • Association R also differs significantly from sity in the sample areas although the dif­ all other associations. The sample areas in ferences in relation to association G, under­ this association had the largest average lain by gravel, was not statistically signifi­ slope, the highest sample relief, and high­ cant. est mean valley depth. The soils in associa­ • Association K differs from associations I tion R are developed from thin loess on and] in that the soils in K have developed bedrock (sandstone) or bedrock residuum.

TABLE 3. MEAN VALUES OF TERRAIN FACTORS FOR DRAINAGE FEATURES

Drainage Mean Density Bifurcation Texture Valley Soil (miles/ Angle (Bifurcations/ Ruggedness Depth Association sq. miles) (Degrees) mile) Number (ft)

A 2.52 76 1.61 0.024 12 G 0.74 79 0.31 0.007 15 I 2.05 77 0.93 0.025 14 ] 2.10 86 0.84 0.026 12 K 1.94 77 0.80 0.021 13 L 3.75 76 1.81 0.106 41 Q 5.06 70 1.96 0.102 34 R 3.74 79 1.53 0.160 61 X 0.55 77 0.15 0.005 10 AUTOMATIC SOIL IDENTIFICATION FROM REMOTE SENSING DATA 79

soil G I J KL Q R X ~ssociation

7 1 7 1 7 1 7 7 9 9 9 2 2 2 9 3 3 10 9 A 4 10 4 11 10 4 11 5 5 11 5 6 6 6 6 6 6

1 1 7 1 2 7 2 7 7 2 7 2 2 7 2 G 3 3 9 9 4 9 4 9 4 9 5 10 5 10 5 10 6 11 11 6 11 6

1 1 1 2 2 7 7 2 7 7 3 3 4 9 4 9 4 9 9 I 5 10 5 10 5 10. 6 11 11 6 11

1 1 7 1 7 7 2 2 7 8 2 3 9 3 9 9 J 4 9 4 10 4 10 5 10 5 11 5 11 6 11 6 6

1 1 7 1 7 7 2 7 2 2 2 The terrain factors in each 3 9 3 9 9 K box are those ·factors which show 4 9 4 10 4 10 significant di fferences between 5 10 5 11 5 11 the two soi 1 associations. 6 11 6 NlII1er1cal code for the terrain factors are : 1 7 1 1 7 1. average slope 7. drai nage density 2 2 2 2. mean 51 ope change 8. bifurcation angle 3 3 3 9 L 3. roughne55 index 9. texture 4 4 10 4 10 4. sample relief 10. roughness nwnber 5 5 11 5 11 5. sample variance 11. mean vall ey depth 6 6 6. elevation-rel ief ratio 1 7 1 7 2 3 9 Q 4 4 10 5 10 5 11 6 11 6

1 7 2 3 9 4 10 R 5 11 6 FIG. 2. Significant differences between soil associations at the 5 percent level.

CONCLUSIONS so that the automatic classification technique Research results have clearly dem­ can be applied throughout the world and can onstrated that small differences in soil be used to differentiate soil groups that are types and soil characteristics can be distin­ of importance to engineering, agriculture, guished by the use of quantitative terrain and land use planning. factors which are computed from digital ter­ rain data. Continuing research efforts are di­ ACKNOWLEDGMENT rected towards the improvement of the ter­ Current research effort on this project is rain factors, the development of statistical supported by the U. S. Army Research Of­ prediction techniques, and testing the effec­ fice. The contributions made by Mr. Finn tiveness of these factors in the prediction Bronner, Chief of Terrestrial Sciences Re­ and identification of soils. Because of the search of the Army Research Office, on the promising results that have been achieved, it technical development and conduct of this is reasonable to expect that a reliable program of research are gratefully acknowl­ method of automatic soil identification can edged. be based on the combined application of quantitative terrain factors and remote sens­ REFERENCES ing data. It is hoped that ultimately a system An uta, P. E., et al., "Crop, Soil, and Geological of quantitative can be developed Mapping from Digitized Multispectral Satel- 80 PHOTOGRAMMETRIC ENGINEERING & REMOTE SENSING 1977

lite Photography," Proceedings of the Kristof, S. J., and A. L. Zachary, "Mapping Soil Seventh Symposium on Remote Sensing of Types from Multispectral Scanner Data," Environment, Ann Arbor, Michigan, May Proceedings of the Seventh Symposium on 17-21, 1971, pp. 1983-2016. Remote Sensing of Environment, Ann Arbor, Cihlar, J., and R. Protz, "Color-Film for Michigan, May 12-21, 1971, pp. 2095-2108. Soils P. I.," Photogrammetric Engineering, Mather, P. M., "Aerial Classification in Geomor­ Vol. XXXVIII, No. 11, November 1972, pp. phology," in Spatial Analysis in Geomor­ 1091-1098. phology, Harper and Rowe, ew York, 1972, Collins, S. H., "Terrain Parameters Directly from pp. 305-322. a Digital Terrain Model," Proceedings of the Philips, M. L., Quantitative Differentiation of Fall Convention 1973, American Congress on Soil Association Areas Using Aerial Photo­ and Mapping, October 2-5, 1973, graphs, Ph.D. Thesis; Department of Civil pp. 403-418. Engineering, University of Illinois at Dornbusch, W. K., Jr., Mobility Environmental Urbana-Champaign, Urbana, Illinois, 1970. Research Study of a Qualitative Method for Piech, K. R., and J. E. Walker, "Interpretation of Describing Terrain for Ground Mobility: Soils," Photogrammetric Engineering, Vol. Surface Geometry, Technical Report No. XL, No.1, January 1974, pp. 87-94. 3-726, U. S. Army Waterways Ex­ Rich, J. L., "A Graphical Method of Determining periment Station, Corps of , 1967. the Average Inclination of A Land Surface Evans, I. S., "General Geomorphometry, Deriva­ from a Contour Map," Illinois Academy of tives of Altitude and Descriptive Statistics," Science, Transactions, V. 9, 1916, pp. 195­ in Spatial Analysis in Geomorphology, 199. Harper and Rowe, New York, 1972, pp. 17-90. Salisbury, N. E., "Relief: Slope Relationship in Eyton, J. R., An Analytical Surfacing Methodol­ Glacial Terrain," paper presented at Miami ogy for Application to the Geometric Mea­ Beach Meeting ofthe American Association of surement and Analysis of , Ph.D. Geographers, April 24, 1962. dissertation, Dept. of Geography, University Speight, J. G., "A Parametric Approach to Land­ of Illinois at Urbana-Champaign, 1974, 227 form Regions," in Progress in Geomorphol­ pp. ogy, Papers in Honor of David L. Linton, Finsterwalder, S., "Uber Mittleren Bos­ Alden Press, Oxford, England, 1974, pp. 213­ chungewinkel und Das Wahre Areal Einer 230. Topographischen Flache," Stisber, K. Ak. der Vadnais, R. R., Jr., Quantitative Terrain Factors Wiss., Math.-Phys., Kl., v. 20, 1890, p. 35-82. As Related to Soil Parent Materials and Their Garrett, E. E., and J. H. Shamburger, Mobility Engineering Classification, ­ Environmental ReSearch Study of A Quan­ ing Studies, Soil Mechanics Series No. 10, titative Method for Describing Terrain for University of Illinois at Urbana-Champaign, Ground Mobility, Technical Report o. Urbana, Illinois, June 1965. 3-726, Hydrologic Geometry; U. S. Army En­ Wentworth, Chester K., "A Simplified Method of gineer Waterways Experiment Station, Corps Determining the Average Slope of Land Sur­ of Engineers, 1967. faces," American Journal of Science, V. 220, James, W. P., The Classification of Wisconsin 1930, p. 184. Ground Moraine by Airphoto Interpretation, Wood, W. F., and J. B. Snell, A Quantitative Sys­ Joint Highway Research Project File 1-4-18, tem for Classifying Landforms, Quartermas­ Project C-36-32R, Purdue University, 1961. ter Research and Engineering Command, Junkins, J. L., and J. R. Jancaitis, "Piecewise Con­ U. S. Army Technical Report EP-124, 1960. tinuous Surfaces: A Flexible Basis for Digital Wright, R. C., and J. R. Burns, Mobility Environ­ Mapping," Proceedings of the ASP, Fall Con­ ment Research Study of a Quantitative vention, September 10-13, 1974, pp. 1-18. Method for Describing Terrain for Ground Kristof, S. J., and A. L. Zachary, "Mapping Soil Mobility, Vol. 2, Technical Report No. 3-726, Features from Multispectral Scanner Data," Surface Composition, U. S. Army Engineer Photogrammetric Engineering, Vol. XL, No. Waterways Experiment Station, Corps of En­ 12, December 1974, pp. 1427-1434. gineers, 1968.

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