FREDERICK J. DOYLEU.S. Geological Survey
Reston, VA 22092
Digital Terrain Models:An Overview*The definition, origin, acquisition, preprocessing, storageand management, applications, and future directions ofDTM data are discussed.
Frederick ]. Doyle
DEFINITION
ADIGITAL TERRAIN MODEL (DTM) is an ordered array of numbers that represents
the spatial distribution of terrain characteristics. In the most usual case, the spatial distribution is represented by an XY horizontalcoordinate system and the terrain characteristic which is recorded is the terrain elevation, Z. An alternate approach is to defineposition by latitude, cf>, and longitude, A, andthe terrain elevation by h. Recent literaturehas referred to these distributions as DigitalElevation Models (OEM) to distinguish themfrom other models which describe differentcharacteristics of the terrain. The data can beorganized as a matrix array of coordinate trip-
* Presented at the ASP DTM Symposium, May9-11, 1978, St. Louis, MO.
lets or as equations of surface defined bypolynomials or Fourier series. It is impOltantto note that characteristics other than elevation may also be included in the DTM. Thesecharacteristics may include such items asland value, ownership, soil type, depth tobedrock, land use, etc.
ORIGIN
The term Digital Terrain Model apparently had its origin in work performed byProf. Charles L. Miller at Massachusetts Institute of Technology about 1955-60 (Miller,1957; Miller and Laflamme, 1958a, 1958b).Prof. Miller and his colleagues were conducting research for the Massachusetts Department of Public Works and the U.S.Bureau of Public Roads. The objective wasto expedite highway design by digital computation based upon photogrammetricallyacquired terrain data.
Within each stereomodel, an X Y horizontal coordinate system was established withthe X-axis in the general direction of theproposed highway alignment. This coordinate system was tied to the State PlaneCoordinate System by suitable controlpoints. Profiles in the Y direction were takenat regular intervals, and the Z elevationalong these profiles was recorded either atregular intervals ofY or at significant breaksin terrain slope, or both. Data acquisitionwas by means of a jury rig attached to Kelshplotters. Initially coordinates were recordedby manual punch, but later paper tape recording was introduced. Conceptually, atleast, other terrain attributes, such as soiltype and land value, could be recorded inaddition to the elevation at each point. Inactuality this concept was never implemented, and only elevation was recorded.
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Vol. 44, No. 12, December 1978, pp. 1481-1485.
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Several computer programs were preparedto utilize the data.
• The operator would input a trial highwayalignment and the computer output wouldbe the center line profile.
• The operator would input a trial grade line,and the program would output the resulting grade line geometry with verticalcurves and annotations of cut and fill.
• The operator would input typical highwaycross sections in both cut and fill, and theprogram would output station cross sectionareas, together with earthwork computations, such as haul distances and mass diagrams.
• The most advanced program automaticallydetermined the optimum profile designbased upon limiting grades and curves, sitedistances, and earthwork computations.
The computer employed was the IBM 650,which had a maximum storage of 2,000words.
Although fairly simple according to today's standards, the MIT approach embodied all of the major elements of a DTMsystem:
• Data acquisition,• Data preprocessing,• Data storage and management, and• Data applications.
DIGITAL DATA ACQUISITION
DTM data may be acquired from existingmaps, from photogrammetric stereomodels,from ground surveys, or from other systemssuch as altimeters carried in aircraft andspacecraft.
The usual method of acquiring DTM datafrom existing maps is by manually followingcontour lines on one of the several digitizingtables which are available commercially.Though advertising brochures usually showa pretty girl happily at work, manual following of contour lines is actually a very tediousand boring operation with a high probabilityof errors, and either duplicating or omittinginformation.
To alleviate this situation, automatic linefollowing instruments have been devised.The usual procedure is to work with the original contour plate from an existing map. Theplate must be prepared by removing allnumbers from the contours and filling in thegaps in the lines. This plate is then scannedby the instrument which latches on to a lineat the edge of the sheet and follows it to itsconclusion. Data density may be 10 to 20points per millimetre of line. Operator assistance may be needed for closed contourswithin the sheet. The machine may have dif-
ficulty with lines of different weights, suchas index contours. There is also difficulty inautomatically assigning elevations to eachdigitized line. However, rapid progress isbeing made in this field, and new and morepowerful instruments may be expected inthe near future.
A second approach to automatic data acquisition from existing maps is to use a scanning device. The contour sheet is placed ona drum which either rotates under a fixedlight source or has the light source rotatingwith respect to the drum. Each time a line iscrossed, the X and Y position is recorded.These devices are excellent for acquiringand playing back digital data for purelygraphical recording. However, if the objective is to file contour lines as continuousstrings of digital data, an extensive amount ofcomputer processing is required to vectorizethe data and assign elevations to the digitized contours.
Still another approach to automatic acquisition of line data is to scan the map sheetwith a linear array. On a single scan, this willrecord all the line data within a band severalcentimetres wide. The next scan will coverthe adjacent band until the entire map sheethas been covered. This approach also requires a fair amount of computer processingto connect together the individual segmentsof lines and assign the proper elevations.
The second major source of digital data isfrom photogrammetric stereomodels. Digitizing systems based upon linear or rotaryencoders can be had for most photogrammetric plotting instruments. The most recentgeneration of photogrammetric instrumentshave these encoding devices built in, andrecord the data on paper or magnetic tape.Dsually stereomodel coordinates are recorded, but for some applications it is moreadvantageous to record the photographicimage coordinates. Elevation data can beformatted either as contour lines, profileswith elevations recorded at regular intervalsor at breaks in terrain slope, or as geomorphic points along drainage lines, hillcrests,etc.
Some photogrammetric instruments areequipped with automatic image correlators,and produce a high density of elevationpoints along scan profiles. The samplingstrategy may be to record elevations at constant increments, t.Y, along the profile, atconstant increments, t1Z, in elevation, or atconstant increments, lit, in time. One notable instrument (Gestalt Photomapper) performs correlation on small image patchesand outputs an array of digital elevation data
DIGITAL TERRAIN MODELS: AN OVERVIEW 1483
at 180 !-tm spacing on the original photographs.
Direct sources of digital elevation data areradar and laser altimeters carried in aircraftand spacecraft. Seasat-l, for example, presently in Earth orbit carries a laser altimeterwhicl; has the potential of providingworldwide coverage within the lifetime ofthe satellite. * To date, photogrammetristshave not been particularly concerned withprocessing these types of data, but it will certainly become a requirement in the fuhue.
DrGITAL DATA PREPROCESSING
DTM data, however acquired, is rarely infonn for immediate application, and extensive computer preprocessing may be required to arrange the data in the appropriatefonnat.
The first requirement is usually data editing. This may be done either by producing agraphic product on a digitally controlledplotting table, or by displaying the data on adigitally controlled cathode ray tube (CRT).The operator can then determine overlapping, erroneous, or missing data and eithersend the copy back for redigitizing or makethe corrections directly on the CRT. Most acquisition schemes acquire far more data thanare actually required in the final files. Therefore, techniques of data compression mustbe employed to reduce the amount of data toa manageable quantity.
Another requirement of the preprocessingsystem is format conversion. It is usuallynecessary to provide programs to convertdata interchangeably between contours, profiles, and regular grids of recorded elevation.For data acquired by raster scanning devices, it is usually necessary to transform tolinear data by vectorization.
Coordinate transformations are anotherimportant part of data preprocessing. Dataacquired in a stereomodel coordinate system, for example, may have to be convertedto a State Plane Coordinate System; or dataacquired in the State Plane Coordinate System may have to be transformed to UniversalTransverse Mercator coordinates or intolatitude and longitude before storage.
Some applications of DTM require that thesurface be expressed as a mathematical function. The parameters of such a function maybe found by any of the mathematicaltechniques of surface fitting.
Still another purpose of preprocessing isinterpolation. Even after coordinate trans-
* Seasat-l ceased operation in October 1978.
formation, elevation data may not be in theproper location for the final file. For example, elevation data may have been acquiredas profiles whereas the final file should be aregular grid of elevation data in the finalcoordinate system. Interpolation techniquesmay be as simple as bilinear interpolation oras complicated as multiparameter surface fitting by polynomials or series.
DATA STORAGE AND MANAGEMENT
One of the characteristics of digital cartographic systems is that they produce enormous amounts of data. In order to be useful,these data must be organized and carry sufficient collateral information so that they canbe identified, stored, and retrieved in an efficient manner.
For most modern systems, the basic storage medium is magnetic tape. Header information on each tape will identify the maparea, type of information, and the format inwhich it is recorded. For some applicationsit is necessary to transfer the informationfrom tape to disk files.
In order to manage the data files, theymust be cross-indexed by content and coverage.
There is an increasing awareness that DTMdata have much more value than simply producing products within an organization. Ifthis were the sole purpose, relatively simpleforn1ats compatible with the output plottingdevices would be adequate. But if the DTMinformation acquired by one organization isto be used for any of a number of applications in other organizations, it will usuallyby necessary to adjust the storage fonnat. Bythe time it becomes aware of the benefits ofinterchangeability, an organization will usually have such a large block of data that itbecomes very difficult and expensive tochange. The most that can be hoped for is tospecify what the information contents of afile must be. Then, either the supplying organization or the using organization can prepare relatively simple software to transfonnone file format into another.
ApPLICATIONS OF DTM DATA
The mathematical operations involved inthe application of DTM data can be summarized as follows:
• Given XY, find Z.• Given an array of XYZ coordinates, fit a
mathematical surface which will define Zas a function ofXY.
• Given an array of XYZ coordinate sets atfixed intervals, interpolate to find the valueof Z at any other value of XY.
1484 PHOTOGRAMMETRIC ENGINEERING & REMOTE SENSING, 1978
• Determine the intersection of straight orcurved lines with a mathematically definedsurface.
• Detennine the intersection of horizontal,vertical, or inclined planes with themathematically defined surface.
• Determine the volume between definedsurfaces.
Some of the direct applications of DTM areas follows:
• Determination of contour lines. This canbe done either by interpolation or by intersection of a horizontal plane with amathematically defined surface. A numberof programs are currently available for producing contours. A principal problem withdigital contouring is obtaining adequatecartographic expression, particularly fordetails like highway and railroad cuts andfills, overpasses, stream re-entrants, etc.
• Generation of profiles. Profiles may be required for controlling orthophoto printinginstruments, for transportation planning,for assuring adequate clearance of powerlines, etc. Profiles can be obtained by intersecting the DTM with vertical planes.
• Determining intervisibility of points. Thisprocedure has application to the determination of coverage patterns from groundradar or other tracking systems, to theplacement of microwave transmission towers and similar problems.
• Generation of perspective views. Aperspective center and direction of viewcan be defined mathematically in the samecoordinate system as the DTM. The perspective view is then generated by the intersection of lines from the DTM points to theperspective center with a plane perpendicular to the viewing direction. Techniques are available for eliminatingareas in the DTM which would not be visible from the selected viewpoint. The U.S.Forest Service applies this technique to determine the effect of forest operations onthe view from scenic highways. It was alsoemployed by NASA to generate simulatedviews of the lunar surface for the Apollocrews, both during their descent trajectoryand their travels in the Lunar RovingVehicle.
• Earthwork calculations. As indicated earlier, this was one of the first applications of DTM data. A number of highwaydepartments now use this as a routine procedure. It is also employed for monitoringstock piles, volume calculations in reservoirs, etc.
• Navigation control systems. A typicalexample is the minimum safe altitudewarning system (MSAW). This program establishes the position and elevation of allobstructions within a specified distance ofprincipal airports.
• Terrain simulation. Programs have been
developed to produce shaded relief byspecifying the direction of illumination andthe reflection of the terrain. The programthen assigns density levels at every pointdepending on the aspect ofthe terrain withrespect to the direction of illumination.The program output can then control ascanner-printer to make the final rendition.A similar program is used to produce simulated radar scenes. The flight path of theaircraft and the scan pattern of the radar aredescribed mathematically. Again, densitylevels are assigned to each point dependent upon the aspect of the terrain with respect to the radar illumination. Stillanother application is to produce stereopairs from Landsat data. Here the DTM elevation data are used to compute parallaxeswhich would have been generated on animage made from a different exposure station. The original Landsat pixels are thendisplaced according to these parallaxes toproduce the simulated stereo pair.
• Terrain models. DTM data has been used tocontrol milling machines which carve athree-dimensional plaster model for laterproduction of plastic relief maps.
Regardless of the application, an important part of DTM computations is to producethe final output data in a suitable form forcontrolling the output device, whether it bea plotting table, an image scanner-printer, ora milling machine.
DTM FUTURE DIRECTIONS
Some of the prospects for future applications of DTM data are as follows:
NATIONAL AND WORLD DATA BANKS
The Defense Mapping Agency has digitized the contour data on the 1:250,000scale maps of the entire United States. Thesedata have been turned over to the U.S.Geological Survey for storage, maintenance,and dissemination to users. Despite knowninadequacies in the data, there is a constantdemand to meet a wide variety of applications.
The U.S. Geological Survey has undertaken the long-range objective of producing adigital cartographic data base which willcontain essentially all of the informationnow shown on the existing 1:24,OOO-scaletopographic quadrangle maps. This includesnot only the elevation data but also all of theplanimetric data. The Survey has paid particular attention to fonnatting the data in away which will make it accessible to thewidest variety of users.
Other national mapping organizations,notably in Canada, Great Britain, and Aus-
DIGITAL TERRAIN MODELS, AN OVERVIEW 1485
tralia, are also producing digital cartographic data bases. The International Societyfor Photogrammetry, the International Cartographic Association, and the InternationalFederation of Surveyors all have committeesworking on the problem of standardization ofdata fomlats with the hope of being able toexchange data on an intemational basis.
However, before becoming too enthusiastic about a worldwide data base, it is instructive to consider the magnitude of this task.The land area of the Earth is approximately1014 m 2
• If the data base were to contain onepoint per square metre, there would then be1014 points. It requires approximately 16 bitsto document each elevation point so that thetotal data base would be 1.6 x 10 1
' bits. Astandard magnetic tape can store 109 bitswhich would mean a total of 1.6 x 106 tapesfor storage. The largest mass storage deviceon the technological horizon will contain 2.8x 1012 bits, so that a total of 570 of thesedevices would be requ ired. Furthermore,simply to transfer the data base from the fileto the computer would require three years ofcentral processing time. This is only a digitalelevation model (OEM) and the task would beenlarged many times if planimetric data andother terrain characteristics were included.
INTERACTION WITH OTHER DIGITAL DATA
Many other kinds of data are now beingaccumulated in digital files by a variety oforganizations. A representative project combining several fomls of digital data is theForest Service project Firescope. The objective of this project is to make the optimumdeployment of teams for fighting forest firesin the southern part ofthe State of California.The basic digital data files contain topography, access routes, hydrology, vegetationcover, land value, and building type andvalue. The variable input data files includeweather patterns, particularly wind directionand velocity and predicted rain fall, personnel availability, current equipment location, and location and intensity of fire. Whenall of this information is massaged by thecentral computer, the output gives the optimum deployment of the firefighting forcesto bring the fire under control in theminimum amount of time and with minimum loss of property values.
Other types ofterrain characteristics-landuse for example-are more efficiently storedby digitizing the boundaries of polygonsrather than on a point-by-point basis. Thetachniques of combining these two types offiles are largely unexplored.
COMBI 'ATION OF DTM WITH DIGITAL IMAGERY
Landsat and other space systems are currently producing imagery in digital form.Mention has already been made of the use ofDTM data to produce stereo views from Landsat. With an adequate DTM model, the reverse procedure could be applied to removeall relief displacements hom Landsat-typedata, with the expectation of producing cartographically accurate image maps veryrapidly. Furthermore, the demon stratedapplicability of multispectral digital imageryfor land classification can be appreciablyenhanced by consideration of other terrainfeatures, such as slope, aspect with respectto illumination, hydrology, etc., which canbe formatted in digital files.
COMPUTER-CONTROLLED CARTOGRAPHY
A number of organizations, both government and commercial, are rapidly developing techniques for computer controlled cartography which will employ DTM data. Onecan reasonably expect that most of the timeconsuming laborious manual operations willsoon be superseded by a completely automated system. Intervention of humanoperators will be limited to those functionsrequiring interpretation and judgement.Hopefully this will result in major economies in the cost and time required toproduce maps. A major expected benefit isthe ability to keep map data current on anearly real-time basis.
CONCLUSION
The rapid development in the ability tohandle terrain data in a completely digitalform holds forth the promise of reducing thedrudgery of cartographic operations, of providing a wide variety of data interactions,and of reducing time and cost so that managers and decision makers will know how tomake the maximum utility of the resources ofthe world.
REFERENCES
Miller, C. L. 1957. The Spatial Model Concept ofPhotogrammetry. Photogrammetric Engineering, Vol. XXIII, o. 1, p. 31, March1957.
Miller, C. L., and R. A. Laflamme. 1958a The Digital Terrain Model-Theory and Application. Photogrammetric Engineering, Vol.XXIV, No.3, p. 433, June 1958.
____1958b. Digital Terrain Model SystemManual, Massachusetts Department of PublicWorks and U.S. Bureau of Public Roads, MassHPS 1 (13), August 1958.