Richard J. Pike, U.S. Geological Survey, Menlo Park, Calif., USA; E-mail: rpike@sierra.wr.usgs.gov

Terrain modeling, the study of ground-surface relief and pattern by numerical methods, has become integral to hydrology, tectonics, oceanography, climatology, and geohazard assessment. It is also important to such nongeophysical applications as land-use planning, civil engineering, and microwave communications. The field originated in 19th century work by Alexander von Humboldt and later German geographers. Modern terrain modeling is an amalgam of Earth and computer sciences, mathematics, and engineering. It is commonly known as (quantitative) terrain analysis, (geo)morphometry, or quantitative geomorphology. The computer processing of square-grid arrays of terrain heights, digital elevation models (DEMs), has revolutionized the discipline's two chief functions of topographic analysis and display. Geographic information system (GIS) technology further enables terrain-modeling results to be combined with nontopographic data. The field has recently been reviewed by Moore et al. [1991] and Pike [C1995].

The broad exposure and ease of communication afforded by the Internet are particularly important to terrain modelers, who are dispersed worldwide in many occupations. However, even search utilities on the World Wide Web (WWW) do not quickly deliver needed information for this evolving, cross-disciplinary field. To provide students and others new to terrain modeling with an immediate entry to the craft, 70 specialized Web addresses, or Uniform Resource Locators (URLs), are offered here. These URLs, which link to many more, emphasize the field's two essential ingredients-elevation data and computer software. All 70 URLs were active as of April 1998.

For an introduction to terrain modeling, see Web sites:

http://everest.hunter.cuny.edu/terrain/index.html, and then parts of Chapters 1 and 2 in http://www.geog.le.ac.uk/jwo/research/dem_char/thesis/. A brief online course, Digital Terrain Models, is available at http://www.geog.unsw.edu.au/~qiming/Teaching/GEOG9240/Lect-09/index.htm. The state-of-the-art may be gleaned from http://ncgia.ncgia.ucsb.edu/conf/SANTA_FE_CD-ROM/sessions.html;

Figure 1, from this symposium, illustrates a recent advance in basic surface representation. A current example of applied terrain modeling, which is available solely on the Internet, addresses landslide hazards in a large metropolitan area adversely affected by the 1997-1998 El Nino, http://wrgis.wr.usgs.gov/open-file/of97-745/montara.html.

This WWW sampling emphasizes topographic analysis, that is, surface parameterization and process modeling, rather than display via computer graphics. However, such techniques of terrain visualization as relief shading and color time-lapse animation are becoming intrinsic to surface-form analysis per se (http://ncgia.ncgia.ucsb.edu/conf/SANTA_FE_CD-ROM/sf_papers/mccullagh_michael/mjmpaper.html). Many examples of terrain display are posted on the Internet.

Data

Much raw data for terrain modeling--DEMs, digital bathymetry, and digitized contours (hypsography)--can be downloaded or ordered via the Internet. Cost varies greatly; some data are free. Global-scale measurements, at low spatial resolution (wide grid spacing), commonly are distributed as one large file; finer-scale data must be pieced together from many files. Availability of DEMs for a particular area, plus comments on quality and other information, may be checked at http://www.geo.ed.ac.uk/geoinfo/dem.send, Bruce Gittings' worldwide listing (updated frequently and feasible only on the Internet). Terrain data are subject to several types of error, vary widely in accuracy, and must not be applied blindly. Robert De Sawal reviews methods of DEM creation and various caveats at http://ncgia.ucsb.edu/conf/SANTA_FE_CD-ROM/sf_papers/desawal_robert/usgspost.html.

Most digital terrain data are sold by government agencies. Three United States sources are the Geological Survey's (USGS) EROS Data Center (EDC), (especially, DEM coverage of Hawaii and two thirds of the lower 48 states at a grid spacing of 30 m); and the National Imagery and Mapping Agency (NIMA, formerly Defense Mapping Agency) at http://www.nima.mil. The many overseas agencies include the United Kingdom's Ordnance Survey, at http://www.ordsvy.gov.uk, which sells DEMs (called digital terrain models (DTMs)) created from contour maps at 1 :50,000 and 1:10,000 scales (the latter at 10-m spacing). The Australian DEM, developed by Mike Hutchinson at 1/20 degree and 1/40 degree spacings for the continent and at 1/60 degree spacings for the individual states Data for Spain at 80-m spacing are at http://www.infocarto.es/dtmsp.htm.

Government DEM and bathymetry data are sold over the Internet by commercial repackagers. Costs can vary substantially. In the United States, Micropath Corporation has 34,000 of the USGS 30-m DEMs online at http://www.micropath.com and markets MapExplorer, a set of utilities for manipulating and reformatting them. Increasingly, private firms are creating DEMs to order from satellite images, air photos, and radar data.

Some digital terrain data are free over the Web. The 3 arc-second DEM for the United States (approximately 90-m spacing for conterminous states, 300-m spacing for Alaska) can be downloaded in one-degree blocks at the above USGS/EDC site. The Digital Chart of the World (DCW) was developed from 1:1,000,000-scale maps and other sources. NGDC's TerrainBase collection, also sold on CD-ROM, is free at the above NGDC Web address. It includes a global 5 arc-minute DEM (with bathymetry), the 30 arc-second DEM used for USGS' shaded-relief map of the conterminous United States (shown at http://geology.wr.usgs.gov/wgmt/shdrelmap.html), and several other public-domain topographic data sets.

Gridded bathymetric data include those synthesized from ship track soundings and Geosat and ERTS-1 gravity information for the recent Smith-Sandwell map of the Earth's seafloor topography. These "predicted" depths, spaced 1 to 12 km apart, are available free from the University of San Diego at http://topex.ucsd.edu/marine_topo/mar_topo.html. True bathymetric grids may be obtained from NGDC's TerrainBase archive. Other conventional seafloor data were released on a CD-ROM of the General Bathymetric Chart of the Oceans (GEBCO). Sold by the British Oceanographic Data Centre, the GEBCO Digital Atlas (GDA) of digitized depth contours and the accompanying PC/DOS software is described at http://www.nbi.ac.uk/bodc/gebco.html. Its coastline data have been found superior to those included with NGDC's older ETOPO5 "ridded depths (http://julius.ngdc.noaa.gov/mgg/global/etopo5.HTML).

Recent DEM releases commonly appear first on the Web. Two of the latest may be downloaded free. NGDC's new "ridded heights from the Global Land One-km Base Elevation (GLOBE) Project cover 60% of the Earth's land surface. Compiled from existing information, this hybrid DEM is expected to be completed in 1998 (http://julius.ngdc.noaa.gov/seg/globsys/globeup.html). Another hybrid, this DEM is thinned from Level 1 (15 arc-seconds) data. Completed coverage is expected in 1998, when a CD-ROM is scheduled for sale.

Software

Much free software for terrain modeling, commonly in DOS, Windows, and UNIX, resides on the Internet. Peter Guth's MicroDEM+ package, for Windows 95 and NT, is available at http://www.usna.edu/Users/oceano/pguth/website/microdem.htm. (Other analytical programs are archived at this site.) Several programs for terrain analysis and erosion modeling are included in Geographic Resources Analysis Support System (GRASS), the public-domain GIS originally developed by the U.S. Army but now maintained at http://www.baylor.edu/~grass/. Routines written to quantify the micro- and nano-scale roughness of manufactured surfaces, but equally applicable to continuous natural topography, are available at http://www.bell-labs.com/project/topo/.

Specialized packages for hydrologic analysis are free over the Internet. While Susan Jenson's original DEM-to-watershed transformation can be obtained from the EROS Data Center at ftp://edcftp.cr.usgs.gov/pub/software/topo/, recent variants of this procedure have greatly enhanced capabilities. Among the best of these is David Tarboton's algorithm to determine flow directions and contributing areas in DEMs at http://www.engineering.usu.edu/dtarb/. The Forest Science Laboratory in Corvallis, Oregon, is linked to much public-domain software for hydrologic analysis from DEMs. Software for terrain modeling is sold or licensed by Web advertisers. Among general-purpose GIS packages with morphometric capabilities are Clark University's IDRISI (http://www.idrisi.clarku.edu), the world's most widely used raster GIS, and GRASSLAND, a commercial upgrade of GRASS. GRID, the raster module of ESRI's ARC/INFO, also contains hydrologic modeling tools developed and augmented from Susan Jenson's algorithm. For examples of general GIS packages customized to study surface processes via terrain modeling, see http://www.ex.ac.uk/~yszhang/tool.htm

Among specialized terrain-modeling programs sold on the Web are Golden Software's SURFER 6 (http://www.golden.com/golden/) and John Fels' Oasis-TopoMetrix from Understanding Systems Inc. (http://www.undersys.com/TopoMetrix.html). Yvan Pannatier's VARIOWIN, a set of PC/DOS algorithms for geostatistical analysis, may be ordered with an explanatory book at http://www-sst.unil.ch/geostatistics.html. Software for the fractal analysis of surfaces accompanies two books on fractals, described briefly at http://www.amazon.com/exec/obidos/ISBN=0201626306/2832-5847111-251956 and http://www.amazon.com/exec/obidos/ISBN=0306447029/2832-5847111-251956. Wavelet Explorer (by Wolfram Research at http://www.wolfram.com/wpt) is a new tool to extend the Fourier and power-spectrum approaches to terrain representation (Figure 1 was not computed by this product).

Literature

Internet access to the diverse and scattered literature of terrain modeling is fair, but improving. Jo Wood's 260-item thesis bibliography is online at http://www.geog.le.ac.uk/jwo/research/dem_char/thesis/08biblio.htm. Many more references are found in some 20 terrain-related presentations at a key 1996 GIS conference, http://ncgia.ncgia.ucsb.edu/conf/SANTA_FE_CD-ROM/program.html. The author maintains a running bibliography, now at 4100 entries, that draws together terrain modeling's many activities. Most of the list already exists as USGS Open-file Reports Nos. 93-262, 95-046, and 96-726 (hardcopy upon request); preparations for placing the list online are under way.

Any use of trade, firm, or product names is for descriptive purposes only and does not imply endorsement by the U.S. government.

References

Moore, I. D., R. B. Grayson, and A. R. Ladson, Digital terrain modelling-a review of hydrological, geomorphological and biological applications, Hydrol. Proc. 5, 3-30, 1991.

Pike, R. J., Geomorphometry-progress, practice, and prospect, Z. Geomorph. Suppl. 101, 221-238, 1995.

Fig. 1. A new, Internet-introduced, model of topographic scale-dependence that yields an exactness not achieved previously. The 5-frequency distributions, here of an Australian sample, show proportion of small drainage areas decreasing with increasing topographic generalization. Scale values are breadths of a mathematically approximated "feature" derived iteratively from a positive-wavelet decomposition of a 20-m DEM by J. Gallant and M. Hutchinson at http://ncgia.ncgia.ucsb.edu/conf/SANTA_FE_CD-ROM/sf_papers/gallant_john/paper.html.

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