A comparison of manual and automated slope maps

CATENA

Vol. 8,239-249

Braunschweig 1981

A COMPARISON OF MANUAL AND AUTOMATED SLOPE MAPS

G.Engelen & W. Huybrechts, Brussels

SUMMARY The authors propose an automated method of generating slope maps. Starting from a topographical map, a Digitized Terrain Model is build up and completed with a'morphological matrix'. By determining the representative slope for each grid cell an impression of the georaphical distribution of the different slope values is obtained. In two test areas in Dry Hesbaye • Belgium), where the results were compared with a detailed manually constructed slope map, the applicability and advantages of the method for general purposes are demontrated. 1. INTRODUCTION In geomorphological research, the investigation of slopes is frequently quite significant. It is often performed by means of slope maps. Several authors have described manual methods of constructing slope maps from published topographic maps. This article describes an automated method developed by the authors• Although it is possible for a detailed automated slope map to be compiled completely by means of modern technical methods and a thorough preparation of the topographic source map, the average investigator does not have at his disposal the necessary sophisticated digitizers, calculating and drawing equipment• In addition, a prolonged map preparation reduces the advantages of the automated method. These restrictions were given main considerations in this study which also considers the extent to which detailed hand-made slope maps can be approached.

2. METHOD 2.1. In the method to be followed four phases may be distinguished, of which the first two phases are manual and preparatory and the second two, computing (3) and compilation (4) of the slope values, are fully automatic. Feedbacks between the distinct steps may be necessary. In the initial phase, a source map has to be carefully selected for the study area at an appropriate scale, taking into account the morphology of the area on the one hand and the research objectives on the other.

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ENCIELEN & HU YBKECHI5

The second phase is the numerical arrangement of the altimetric data. In this respect a method was chosen whereby for each point ofan ordered grid, a height value is recorded. This results in a matrix which, depending on the fineness of the grid, gives a more or less true image of the relief on the source map (Digitized Terrain Model, YOELI 1975). The dimensions and the form of the grid cells - they can assume any rectangular form - are selected as a function of the relief, the equidistance and the scale of the topographic map, and the expected precision of the final result (YOELI 1975). Although a refinement of the grid enhances precision more time is required for reading. Consequently, a compromise must be sought (MARK 1975). The time-problem has been discussed by KORMANN (1969), who proposed a triangular network, the points of which are located on divides, drainage lines and breaks in slope. Grid points for map areas where readings of altitude can not be made, such as build-up areas, quarries, precipitous slopes etc., need to be marked so that they will be excluded from the computations. These areas will be left blank on the map (see phase four). In the third phase, the slope values are calculated by means of the tangent function: trij =

I Arctan

I with

ttij: Hij: Aij:

Hij

Aij

slope between points i and j difference in height between i and j horizontal distance between i and j

For any point not located on the border of the map, it will be possible for the slope between the eight surrounding points to be calculated (fig. la). Figure lb shows the condition per grid cell. After the elimination of double computations six possible slopes are left over i.e.: A1, A2, A3, B3, B4 and D1.

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COMPARISON: MANUAL AND AUTOMATED SLOPE MAPS

241

Using A1 and A3 unstead D1 and B3 respectively, a dislocation of the automated map over halfa cell to the right side below must be foreseen. As in the field and on the topographic map, the highest slope value will be retained as being representative of the cell. As only four slopes are measured instead of an unrestricted number, as in the case of a continuous approach, there will be many chances that measurements are not performed perpendicularly to the contours. The error in this respect is maximal when the perpendicular line is located midway between two computed slope values. It is the least for a square grid and will show a maximum deviation of 7.5% from the real value for a constant slope. From measurements for a number of random points on the test maps it appeared that also in other cases, the deviation remains small but may nevertheless be of importance when deviding into classes (see phase 4).

/

Fig. 2: Selectionof the representative slope in valleys and on watersheds. In cells such as those shown on fig. 2, slope 1 is retained although slope 4 is representative. When slope 1 and 4 belong to distinct classes this may lead to misinterpretation as the regular grid does not take any account of specific morphological units in the area. It was therefore decided to construct another matrix of morphological data jointly with the altitude matrix. For this purpose, the points located on watershed ridges or in alluvial plains need to be marked. As soon as in one cell two or more points have the same mark, the smallest slope between them will be retained as representative of this cell. If, however the alluvial plain or watershed ridge is particularly narrow as compared to the grid mesh, this appropriate method would lead to a distorted image in the other sense. The investigator must take this into account when compiling the second matrix. The same problem indeed occurs with the manual compilation of slope maps (STRAHLER 1956).

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ENGELEN & ttUYBRECttTS

As soon as the slope value per cell is known it is possible to proceed to the graphic presentation of the fourth phase. For this purpose the cells are grouped under a number of slope classes, the limits of which may be freely selected, and represented by a corresponding mark. In this study it was deemed sufficient to provide for a maximum ofeight classes. 2.2. The application of the method is possible with the aid of a FORTRAN IV EXTENDED program, SLOPE, developed for the VUB/ULB Computer Centre configuration (CDC6600 and Benson 411 plotter). The program allows large-scale data matrices to be processed whereby sheet upon sheet may be drafted.

3.

APPLICATION AND RESULTS

The method described above was tested in two areas located in Dry Hesbaye (E. Belgium). The first extends from the south of the village Herderen over an area of 9.8 square kilometers (sheet 34/6, scale 1/10 000).* The plateau is characterized by light depressions although it is also incised by ravines such as the Geer Valley and the lower courses of its small tributary streams. The altitude readings have been hindered considerably by the many abrupt slopes together with a broad railway (E-W) and a motor-road (NW-SE). The second test area lies to the south-east of Waremme (sheet 41/3-4, scale 1/25 000) and covers 26 square kilometers. It is in contrast a gently undulating plateau, only seldomly interrupted by steep slopes, although slightly indented by several valleys. In both areas a grid at intervals of.5 centimeters was constructed between every two points. In the case of Herderen this means reading altitudes at intevals of 50 metres from both east to west and north to south. In the case of Waremme, these intervals are 125 metres. By way of comparison, a detailed manual slope map was constructed according to the Moving Inteval Method (SCHOLZ 1972, WALSCHOT 1973 and DENNES & GRAINGER 1976).

3.1.

HERDEREN (fig. 3a and 3b)

An initial comparison of the automated and the manual map indicates that highly similar areas are found within corresponding slope classes. As however the isolines on an automated map are less smooth and dislocations of one grid cell are possible, the correspondence is not complete. The occurence of build up areas, roads etc., left blank on both maps (see phase two), does not affect the manual method so strongly. The automated map more than the manual map shows a spotted pattern. The reasons for this are many. Firstly, connections smaller than a grid cell are lost when altitudes are read. Secondly, the spots are formed by cells, the slope value of which approximates a class limit and are thus classified as belonging to higher or lower class with an exceptionally small margin. On the other hand it has been established that in drafting the manual map the investigator too often and erroneously tends towards greater entities which are rounded of and interconnected. The alluvial plain of the Geer is less broad on the automated map because an area with average slopes is encountered between the abrupt valley walls and the almost level bottom of * Edited by the National Geographical Institute, Brussels

COMPARISON: MANUAL AND AUTOMATED SLOPE MAPS

243

the valley. The systematic compilation of the height values in the present condition leads tO a more precise result. In this area it may be concluded that altitude readings at intervals of 50 metres have succeeded although to a restrictive extent at the level of the narrower and smaller areas.

3.2.

WAREMME (fig. 4a and 4b)

In the area near Waremme which is characterised by long and narrow valleys and watershed ridges the problem is raised of the design of elongated and narrow areas. Accordingly, additional information with respect to the morphology was gathered (see supra 2.1, phase 3). Moreover the dimensions of grid cells were fixed at 62.5 metres through linear interpolation. Although this does not give extra information, the graphic presentation becomes more precise. Taking into account a deviation of one grid cell, it may be concluded that there is agood resemblance of one map to the other, especially when larger areas are concerned. Despite the introduction of morphological data, the elongated narrow areas still remained heavily split up into seperate, small portions. The main reason is the inadequate resolution of the grid. It would have been better to have utilized a finer grid, for example 50 metres by 50 metres or a rectangular grid the long side of which should have been oriented from north to south. From this appears the importance of an initial phase in which the morphology must be studied thoroughly in order to arrive at an appropriate altitude reading.

4.

CONCLUSIONS

If we accept that the utility of a slope map mainly lies with the achievement of a general image of the slope distribution (KING 1966), then this automated method is highly satisfactory. The resemblance with the larger, more significant areas on the test maps proved that to a sufficient extent. The manual method, however, more than the automated method will give a more detailed picture. In the case of an altitude reading at intervals of 50 metres a good compromise is achieved between the precision of the result and the time required for the second phase. A significant advantage of the automated method is however its flexibility. In this way maps drafted on other scales or with other subdivisions into classes (which may be selected very precisely) may be obtained and without extra efforts. In addition, not only has a cartographic image been achieved but statistical processing becomes possible as the covered area per class may be defined (Ht)RMANN 1969). The DTM can also be used for other purposes such as a morphometric description of the study area. The suggested method is still in certain cases liable to improvement mainly with respect to the drafting of the DTM in the second phase. The operation with a semi-ordered grid or the complete digitalization of contour lines could have limited the inaccurancies in visual interpolation as from the source map. This however requires more specialised equipment. The National Geographical Institute of Belgium is making increasing use of computers for the publication of topographic maps. For Lower Belgium the presentation of the relief is already achieved automatically using a dense DTM. The extension of this work could considerably facilitate and accelerate the application of the proposed method (reduced second phase) and improve the precision.

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ENGELEN & HUYBRECHTS

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VRIJE UNIVERSITEIT BRUSSEL GEOGRAFISCH INSTITUUT PROGRAM TO CALCULATE AND TO PLOT SLOPE GRADIENTS ENGELEN GUY AND HUYBRECHTS WILLY, 1979 INPUT CARACTERISTICS TITLE OF JOB: HERDEREN NUMBER OF ROWS NUMBER OF COLUMNS INPUT MEDIUM = 8 OUTPUT FORM = 0

70 57 (8 = CARDS, 1 = DISK) ( 0 = SLOPE MAP AND SLOPE VALUES) (2 ~ HEIGHT VALUES AND SLOPE VALUES) (3 = HEIGHT VALUES) VARIABLE FORMAT TO READ INPUT MATRICES: (1 I(1X, AI,F5.7),3X) MAP CARACTERISTICS GRID DISTANCE IN X DIRECTION (IN METER ON THE GROUND) = 50.00 GRID DISTANCE IN Y DIRECTION (IN METER ON THE GROUND) = 50.00 VALUE GIVEN TO NONCLASSIFIED CELLS = 999.9 SCALE OF SLOPE MAP = 1 / 10000. INT ~ 1 (1 = NO INTERPOLATION, 2 ~ INTERPOLATION) SLOPES GROUPED IN 5 CLASSES: CLASS IN DEGREES 1 0. 0. 0. - 0.30. 0. 2 0.30. 0 . - 2. 0. 0. 3 2. 0. 0 . - 5. 0. 0. 4 5. 0. 0 . - 15. 0. 0. 5 15. 0. 0 . - 35. 0. 0.

IN RAD1ANS 0.00000000 - .00872665 .00872665 - .03490659 .03490659 - .08726646 .08726646 - .26179939 .26179939 - .61086524

STATISTICAL RESULTS (CLASSIFIED CELLS) NUMBEROFCELLS MEAN SLOPE STANDARD DEVIATION CLASS NUMBER ALL 1 2 3 4 5 Fig. 5:

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3438 3.23.30. 3.53.13.

SURFACE IN SQUARE METER 8595000. 1317500. 2377500. 3310000. 1337500. 252500.

.05920 .06784 PROPORTIONALLYTO: TOTAL CLASSIFIED CELLS 88.975 100.000 13.639 15.329 24.612 27.661 34.265 38.511 13.846 15.561 2.614 2.938

OutputofFortran IVprogram: SLOPE.

BIBLIOGRAPHY

DENNESS, B. & GRA1NGER, P. (1976): The preparation of slope maps by the moving interval method Area, 8, 213-218.

COMPARISON: MANUAL AND AUTOMATED SLOPE MAPS

249

HORMANN, K. (1969): Geomorphologische Kartenanalyse mit Hilfe elektronischer Rechenanlage. Zeitschrift f'tir Geomorphologie, 13, 75-98. KING, C.A~M. (1966): Techniques in geomorphology. Edward Arnold, London, 335 pp. MARK, D.M. (1975): Computer analysis of topography, a comparison of terrain storage methods. Geografiska Annaler, 57 A, 179-188. SCHOLZ, E. (1972): The construction ofmorphographic and morphometric maps. Manual of detailed geomorphological mapping ed. J. Demek, Academia, Praque, 50-56. STRAHLER, A.N. (1956): Quantitative slope analysis. Bulletin of the Geological Society of America, 67, 571-596. YOELI, P. (1975): Compilation of data for computer-assisted relief cartography. Display and analysis of spatial data ed. J.C. Davis and M.J. McCullagh, J. Wiley & Sons, London, 352-378. WALSCHOT, L. (1973): De hellingkaart. Natuurwetenschappelijk Tijdschrift, 55, 210-226.

Anschrift der Autoren: W. ttuybrechts & G. Engelen, Geografisch Instituut, Vrij Universiteit Brussel Pleinlaan 2, 1050 Brussel