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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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.