THE UNIVERSITY OF MICHIGAN
COLLEGE OF LITERATURE, SCIENCE, AND THE ARTS
Department of Geography
Technical Report
A DIGITAL TERRAIN LIBRARY
Waldo R. Tobler
Charles M. Davis, Principal Investigator
ORA Project 08055
under contract with:
U. S. ARMY RESEARCH OFFICE (DURHAM)
CONTRACT NO. DA-31-124-ARO-D-456
DURHAM, NORTH CAROLINA
administered through:
OFFICE OF RESEARCH ADMINISTRATION ANN ARBOR
March 1968
Reproduction in whole or in part is permitted for
any purpose of the United States Government

INTRODUCTION
Several years ago a number of investigators began exploring digital computer approaches to the analysis of topographical data. Unfortunately the
investigators involved often found it impractical to include their data in
the published reports. As a consequence each study began anew with compilations of information. This first came to our attention in attempting to
evaluate several computer programs which had been assembled for the manipulation of geographical information. At that time it seemed desirable to have
available several standard, modest-sized, sets of topographical information
on punched cards This need has not declined appreciably in the interim,
although it is now possible to obtain digitalized versions of the contours
pertaining to entire topographic sheets if the study objectives are of military interest, and if one is prepared to cope with the several reels of magnetic tape currently required to describe one topographic map. The need for
a digital terrain library of modest size for exploratory investigations has
remained. The current effort is an attempt in this direction and was undertaken as a more or less isolated sub-project of a larger study, In keeping
with these general objectives, the size of each described portion of terrain
is relatively small. The specific parcels were chosen to represent distinct
physiographic types by selection from the U.S. Geological Survey set of 100
topographic maps illustrating physiographic features in the United Statesc
No attempt at analysis of the resulting data are reported in this documentc
Requests for additional copies of the report or for copies of the data tape
should be addressed to the Cartography Laboratory, Department of Geography,
The University of Michigan, Ann Arbor, Michigan.
SELECTION OF AREAS
The choice of areas to be digitized is best described as a browsers
selection of interesting terrain from the 100 USGS physiographic features
quadrangles, with some attention to map scale A few sheets were chosen
for their relevance to other portions of the study, but this has not been an
overriding concern. Within each map sheet an attempt was made to isolate
relatively "pure" terrain types, with a balance between fineness of detail
and size of area. A strict requirement was that each area be rectangular.
After some experimentation a square area (10 in, on a side, digitized every
1/8th in.) was found to be the most practical compromise between ease of
computer storage and manipulation, fineness of detail, and amount of ground
covered.
1

DATA RECORDING
Elevations were recorded by overlaying each selected area with a transparent plastic sheet containing a square grid. Elevations were estimated at
each grid intersection and were recorded on large sheets of ruled paper for
subsequent keypunching. Contours were estimated to the nearest half contour
interval. This method has been described in detail by Drj Wood, and the
reader is referred to his report. The use of a uniform grid interval far the
data recording allows one to use a positional (matrix) notation which is
readily adaptable to computer manipulation and analyses. Discretization of
any continuous signal of course acts as a filter and introduces aliasing
effects at the Nyquist interval. The regular grid employed in this project
therefore acts as a two-dimensional filter but no effort has been made to
compensate for this effect. Data checking was provided by examination of
computer drawings produced from each deck of cards (Figure 1). As illustrated
by the figure, gross errors are immediately apparent and easily corrected"
This method of error detection was found to be relatively inexpensive, especially when one considers that in excess of 100,000 elevations are involved,
and that the graphic plotting program was available in house prior to initiation of the project, Minor errors are not detected by this tactic of course.
The several pages in the Appendix describe each individual topographic matrix
in greater detail, Further information can be obtained by consulting the individual topographical maps and the U.S Geological Survey descriptive folder
"A Set of One Hundred Topographic Maps Illustrating Specified Physiographic
Features" by W: B. Upton, Jr., 1955. Most of the selected areas are also
illustrated in the Atlas of Landforms. The original intention was to
digitize a larger number of topographic features than has been achieved. The
recording is, of course, very tedious. Nevertheless it is our hope that the
small library made available here will provide an incentive for further work
along these lines.
2

Figure 1. The figure illustrates the use of a computer drawing for
the rapid detection of errors in data recording.

ACKNOWLEDGMENT
We wish to thank the following individuals who have assisted on this
project: F. Asadi, A. Brazel, V. Herzog, S. Gale, M. Landman, F. Rens, and
S. Riesmann.
BIBLIOGRAPHY
W. C. Aumen, et al., "Digitizing Graphic Data at the Army Map Service."
Paper presented to the 1965 ASP-ACSM Convention, Washington, DC., 1965.
Autometric Corp., "Applicability of Certain Multifactor Computer Programs
to the Analysis, Classification, and Prediction of Landforms," ONR Task No.
387-030, Nonr 4145(00), Final Report, 1963.
B. W. Boehm, "Tabular Representations of Multivariate Functions-With
Applications to Topographic Modeling," RM-4636-PR, The RAND Corp., Santa
Monica, 1967.
J. L. Bogdanoff, et al., "Atlas of Off-Road Ground Roughness Power Spectral Densities and Report on Data Acquisition Technique," TR-9387 (LL 109),
U.S. Army Tank Automotive Center, Warren, Michigan, 1966 (AD 802503).
D. Carr and J. VanLopik, Terrain Quantification,Texas Instruments,
Inc., Dallas, 1962 (AD 297-492).
T. M. Griffiths, "A Comparative Study of Terrain Analysis Techniques,"
DA-31-124-ARO-D-79, Denver, 1964 (AD-450591).
G. Jenks and F. C. Caspall, "Vertical Exaggeration in Three-Dimensional
Mapping," TR-2, NR-389-146, Nonr 583(15), Lawrence, Kansas, 1967.
A. Rosenfeld and J. Pfaltz, "Sequential Operations in Digital Picture
Processing," Journal ACM, 14,4 (Oct. 1966), pp. 471-494.
J. Scovel, et al., Atlas of Landforms, J. Wiley, New York, 1965.
R. O. Stone and J. Dugundji, "A Study of Microrelief: Its Mapping,
Classification, and Quantification by Means of a Fourier Analysis," Waterways Experiment Station, Vicksburg, Miss., 1963 (AD 450828).
W. R. Tobler, "Of Maps and Matrices," Journal, Regional Science Assn.,
in press.
4

U. S. Army, "Conference on Numerical Topographic Data," 3-5 May 1966,
Corps of Engineers (AD-806740).
W. F. Wood and G. Lewandowski, "The Optimum Human Operator Method for
Digitizing a Map," paper submitted for presentation to the 1966 Annual Meeting of the Association of American Geographers.
B. Zakrzewska, "Trends and Methods in Land Form Geography," Annals,
Assoc. Am. Geographers, 57, 1 (March 1967), pp. 128-165.
5

APPENDIX
DESCRIPTION OF SPECIFIC TOPOGRAPHIC MATRICES
The data matrices have been written on one reel of magnetic tape as
simple (BCD) card images, one card per record, with a file mark at the end
of each matrix. Each matrix is preceded by a title card which also contains
the format and number of rows and columns in the matrix. Consequently, the
number of card images in each file is equal to the number of rows times the
number of cards per row plus one. Each card of each matrix row is numbered,
as are the individual rows, and the individual matrices, in columns 75
through 80 of the cards. The illustrations accompanying the matrix descriptions were produced as a part of the data checking procedure and have quite
arbitrary vertical exaggerations. Minor errors still evident in the illustrations have been corrected on the cards.
6

ALlMA. WISCONSIN
ALMA, Wisconsin
1/62,500 USGS Quadrangle, 20' contours
Map coordinates (X and Y), counterclockwise, of the area digitized,
in inches from the SW corner of the map:
(1.6, 9.4), (6.5, 9.4), (9.5, 17.4), (1.6, 17.4)
Digitized every 1/10 th inch on the map (520.8' on the ground) which yields a
matrix of 80 rows by 80 columns. The Fortran format for one row is:
( 4 ( 18 F 4 / ), 8 F 4 )
7

RYER.MRSS. CONTINENTAL GLACIATED TERRAIN - 2N 50 ROWS
AYER, Massachusetts
1/24,000 USGS Quadrangle, 10' contour interval
Map coordinates (X and Y), counterclockwise, of the area digitized,
in inches from the SW corner of the map:
(9.4 2.4), (, 2.4, (14., 4)4, 14 7.4), (9.4, 7.4)
Digitized every 1/20 th inch on the map (1001 on the ground) which yields a
matrix of 100 rows by 100 columns. The Fortran format for one row is:
( 4 ( 24 F 3 / )', 4 F 3 )
8

BRY.CAL.IF. VOLCANIC IOFOGRrPH 1r - isr so ROk
BRAY, California
1/62,500 USGS Quadrangle, 40' contour interval
Map coordinates (X and Y), counterclockwise, of the area digitized,
in inches from the SW corner of the map:
(7.4, 2.5), (12.4, 2.5), (12.4, 7.5), (7.4, 7.5)
Digitized every 1/20 th of an inch (260.4' on the ground) which yields a
matrix of 100 rows by 100 columns. The Fortran format for one row is:
( 5 ( 18 F 4 / ), 10 F 4 )
9

-'= —c- -1
CAIDEN.MO. FLOOD PLFIN
CAMDEN, Missouri
1/24,000 USGS Quadrangle, 10' contour interval
Map coordinates (X and Y), counterclockwise, of the area digitized,
in inches from the SW corner of the map:
(5.20, 2.35), (15.20, 2.35), (15.20, 12.35), (5.20, 12.35)
Digitized every 1/8 th inch on the map (250' on the ground) which yields a
matrix of 80 rows by 80 columns. The Fortran format for one row is:
( 3 ( 24 F3 / ), 8 F3 )
10

DELARmE.MICH.
DELAWARE, Michigan
1/24,000 USGS Quadrangle, 20' contour interval
Map coordinates (X and Y), counterclockwise, of the area digitized,
in inches from the SW corner of the map:
(1.2, 6.8), (9.2, 6.8), (9.2, 14.8), (1.2, 14.8)
Digitized every 1/10 th inch on the map (200' on the ground) which yields a
matrix of 80 rows by 80 columns. The Fortran format for one row is:
( 4 ( 18 F 4 / ), 8 F 4 )
11

ENERFWOO N.D. GLACIAL LAKE AGASSIZ
EMERADO, North Dakolta
1/62,500 USGS Quadrangle, 10' contour interval
Map coordinates (X and Y), counterclockwise, of the area digitized,
in inches from the SW corner of the map:
(1.85, 5.15), (11.85, 5.15), (11.85, 15.15), (1.85, 15.15)
Digitized every 1/8 th of an inch (651.04' on the ground) which yields a
matrix of 80 rows by 80 columns. The Fortran format for one row is:
( 4 ( 18 F 4 / ), 8 F 4 )
12

EMMET COUNTY MICH.
Emmet County, Michigan
CHEBOYGAN, Michigan 1/250,000 USGS Quadrangle, 50' contour interval
Map coordinates (X and Y), counterclockwise. of the area digitized,
in inches from the SW corner of the map:
(3.5, 8.5), (4.6, 8.7), (4.6, 10.5), ( 3.5, 10.4)
Digitized every 1/10 th inch on the map (2083.31 on the ground) which yields a
matrix of 95 rows by 56 columns. The Fortran format for one row is:
( 3 ( 18 F 4 / ), 2 F 4 )

FLAMING GORGE.UTRH -WYOM. CANYON. 2NE 50 ROWS
FLAMING GORGE, Utah-Wyoming
1/24,000 USGS Quadrangle, 40' contour interval
Map coordinates (X and Y), counterclockwise, of the area digitized,
in inches from the SW corner of the map:
(o.oo, 2.45), (5.oo, 2.45), (5.oo,7.45), (o.oo, 7o45)
Digitized every 1/20 th inch on the map (100' on the ground) which yields a
matrix of 100 rows by 100 columns. The Fortran format for one row is:
( 5 ( 18 F 4 / ), 10 F 4 )
14

HILLSBOO. KY.
HILLSBORO, Kentucky
1/24,000 USGS Quadrangle, 20' contour interval
Map coordinates (X and Y), counterclockwise, of the area digitized,
in inches from the SW corner of the map:
(2.7, 13.3), ( 10.7, 13.3), (10.7, 21.3), (2.7, 21.3)
Digitized every 1/10 th inch on the map (200' on the ground) which yields a
matrix of 80 rows byr 80 columnso The Fortran format for one row is:
( 3 ( 24 F 3 / ), 8 F 3 )
15

MROHIOTH CIVE.KY. KIIST TOPOGfAIHY. 2ND 50 ROWS
MAMMOTH CAVE, Kentucky
1/62,500 USGS Quadrangle, 20' contour interval
Map coordinates (X and Y), counterclockwise, of the area digitized,
in inches from the SW corner of the map:
(3.90, 1.35), (8.90, 1.35), (8.90, 6.35), (3.90, 6.35)
Digitized every 1/20 th inch on the map (260.4' on the ground) which yields a
matrix of 100 rows by 100 columns. The Fortran format for one row is:
( 4 ( 24 F 3 /), 4 F 3 )
16

HIAVERICK SPRING. WYM.
MAVERICK SPRINGS, Wyoming
1/24,000 USGS Quadrangle, 20' contour interval
Map coordinates (X and Y), counterclockwise, of the area digitized,
in inches from the SW corner of the map:
(2.10, 15o40), (7.50, 9.50), (13.35, 14.95), (7.90, 20.80)
Digitized every 1/10 th inch on the map (200' on the ground) which yields a
matrix of 80 rows by 80 columns. The Fortran format for one row is:
(4(18F4/), 8 F4)
17

MENNAN BUTTE. IDAHO. LAVA FLOW
MENAN BUTTES, Idaho
1/24,000 USGS Quadrangle, 10' contour interval
Map coordinates (X and Y), counterclockwise, of the area digitized,
in inches from the SW corner of the map:
(10.7, 13.7), (18o7, 13o7), ( 18o7, 22.7), (10.7, 22.7)
Digitized every 1/10 th inch on the map (200' on the ground) which yields a
matrix of 80 rows and 80 columns. The Fortran format for one row is:
( 4 ( 18 F 4 / ), 8 F 4 )
18

=_f/7
HOBILE.ALAR. MOILE COAST SHORELINE - IST 40 ROWS
MOBILE, Alabama
1/62,500 USGS Quadrangle, 10' contour interval
Map coordinates (X and Y), counterclockwise, of the area digitized,
in inches from the SW corner of the map:
(4.65, 2.20), (12.15, 2.20), (12.15, 9.70), (4.65, 9.70)
Digitized every 1/16 th inch on the map (325.5' on the ground) which yields a
matrix of 120 rows by 120 columns. The fortran format for one row is:
( 5 ( 24 F 3 ))
19

RLPINE GLACIRTION. MT.BONVILLE -1ST.50 ROWS
MOUNT BONNEVILLE, Wyoming
1/62,500 USGS Quadrangle, 50' contour interval
Map coordinates (X and Y), counterclockwise, of the area digitized,
in inches from the SW corner of the map:
(6.75, 8.65), (9.25, 8.65), (9.25, 11.15), (6.75, 11.15)
Digitized every 1/40 th inch on the map (130.2' on the ground) which yields a
martix of 100 rows by 100 columns. The Fortran format for one row is:
( 5 ( 18 F 4 / ), 10 F 4 )
20

/: X
Ogemaw County, Michigan
TRAVERSE CITY 1/25u,000 USGS Quadrangle, 50' contour interval
TAWAS CITY 1/250,000 USGS Quadrangle, 50' contour interval
Map coordinates (X and Y), counterclockwise, of the area digitized,
in inches from the SW corner of the maps.
Traverse city:(20.55,2o8),(25.15,2.8),(25.15,8.9),(20.55,8.9)
Tawas city:(o.o,2.8),(1.5,2.8),(1.5,8.8),(o.o,8.8)
Digitized every 1/10 th of an inch (2083.3' on the ground) which yields a
matrix of 60 rows and 61 columns. The fortran format for one row is:
(3 (18F 4 / ), 7 F 4 )
21

PEAKS OF OTTER, Virginia
1/62,500 USGS Quadrangle, 40' contour interval
Map coordinates (X and Y), counterclockwise, of the area digitized,
in inches from the SW corner of the map:
(2.1, 2.6), (2.0, 3.4), (7.5, 3.4), (7.5, 2.6)
Digitized every 1/10 th inch on the map (520.8' on the ground) which yields a
matrix of 80 rows by 80 columns. The Fortran format for one row ist
(4 ( 18 F 4 /),8 F 4)
22

"WOINME.NR3S.
PROVINCETOWN, Massachusetts
1/24,000 USGS Quadrangle, 10' contour interval
Map coordinates (X and Y), counterclockwise, of the area digitized,
in inches from the SW corner of the map:
(4o40, 3o55), (12.4, 3o55), (12.4, 11.55), (4.40, 11.55)
Digitized every 1/10 th inch on the map (200' on the ground) which yields a
matrix of 80 rows by 80 columns. The Fortran format for one row is:
(2 ( 36 F 2 /),8 F 2 )

UNIVERSITY OF MICHIGAN
3 9015 03526 7510