science 

USGS

fora changing world

A Bibliography of Geomorphometry, 

the Quantitative Representation of 

Topography Supplement 3.0

By RICHARD J. PIKE

Provides over 900 additions and corrections to the 1993 

Bibliography of Geomorphometry and its 1995 

and 1996 Supplements, with an update 

of recent advances

OPEN-FILE REPORT 99-140

1999

This report is preliminary and has not been reviewed for conformity with U.S. Geological Survey 

editorial standards or with the North American Stratigraphic Code. Any use of trade, firm, or product 

names is for descriptive purposes only and does not imply endorsement by the U.S. Government

U.S. DEPARTMENT OF THE INTERIOR 

U.S. GEOLOGICAL SURVEY

aMENLO PARK, California
A Bibliography of Geomorphometry, the Quantitative Representation of

Topography Supplement 3.0

by 

Richard J. Pike

Abstract This report adds over 900 references on the numerical characterization of 

topography (geomorphometry, or terrain modeling) to a 1993 review of the literature 

and its 1995 and 1996 supplements. A number of corrections are included. The report 

samples recent advances in several morphometric topics, featuring six in greater 

depth landslide hazards, barchan dunes, sea-ice surfaces, abyssal-hill topography, 

wavelet analysis, and industrial-surface metrology. Many historical citations have 

been added. The cumulative archive now approaches 4400 references.

T

he practice of terrain quantification 

continues to grow through its many 

applications to geomorphology, hydrology, 

geohazards mapping, tectonics, and sea-floor and 

planetary exploration. Geomorphometry (or 

simply morphometry) is an amalgam of Earth 

science, mathematics, engineering, and computer 

science. It is known variously as terrain analysis 

or quantitative geomorphology, although the 

newer term terrain modeling increasingly seems 

to be preferred. Dating back at least to Humboldt 

(1843a/ b) and Ritter (1852), the discipline has 

been revolutionized by the computer 

manipulation of square-grid arrays of terrain 

heights, or digital elevation models (DEM's), 

that quantify and portray ground-surface form 

over large areas (Florinsky, 1998a, b). 

Morphometric procedures are now implemented 

routinely by geographic information systems 

(GIS) and other computer software.

This is the third update of a bibliography and 

introductory essay on geomorphometry (Pike, 

1993,1995,1996). The purpose of these reports is 

to draw together the diverse, scattered literature 

on surface characterization and make it 

accessible to the research community typically 

at two-year intervals. The need for a running 

archive of citations remains clear from the 

accelerating use of DEM's, at all resolutions, in 

many areas of science and technology including 

manufacturing (Thomas, 1999). Here I add more 

than 900 items to the 3400-odd entries contained

in the earlier three reports 1 . Some 20 references 

(p. 56-57) correct the most serious errors found in 

the three listings. The new entries in this report 

include both publications postdating the second 

supplement (current through mid-1996) and many 

older works overlooked previously. Coverage is 

representative, but not exhaustive, through late 

1998.

The appended listing is alphabetized and 

largely unannotated, following the format of its 

two predecessors, although recently I have begun 

to append brief notes to most citations. The 60- 

topic organization of geomorphometry developed 

initially (Pike, 1993, Table 2) still accommodates 

the latest entries. The same qualifications and 

caveats on accuracy and completeness stated 

earlier apply equally to this third supplement. 

The combined reference file now is nearing 4400 

entries (a 1-Mb digital file). Preparations for 

distributing the cumulative bibliography in 

digital form and over the Internet continue but 

remain incomplete. Similarly, no plans for 

sorting the listing topically or chronologically 

have been finalized (the file is not encoded in 

specialized bibliographic software). Earlier 

references to morphometry on the Internet (Pike, 

1996) have been updated and 70 World Wide 

Web addresses published (Pike, 1998).

* The few text citations not in the main bibliography (p. 

10-56) are on either p. 9 or in 'Corrections' (p. 56-57).

RJ.Pike / USGS OF 99-140
Noted here briefly are advances in established 

areas of morphometric research since the last 

supplement. Progress in industrial-surface 

metrology has been sufficient to warrant a 

substantial update. A selection of early (pre1900) morphometric work is also included, and 

two important new books are described. In 

continuing the practice of previous reports, to 

feature several active if not necessarily new 

areas in which morphometric analysis plays a 

central role, here I briefly review work on 

landslide hazards, barchan dunes, sea-ice 

surfaces, sea-floor abyssal hills, and wavelet 

analysis. The literature in most of these areas is 

vast, and none of my summaries is intended to 

accomplish more than introduce each topic and 

then guide the reader into its morphometric 

aspects.

Landslide hazards

Slope failure exacts a costly "environmental tax" 

on society, and the resulting expenses are 

mounting worldwide as many urban centers 

expand from early-settled flatlands into 

surrounding hills. Widespread winter damage 

from landslides across coastal California during 

the 1997-98 El Nino exemplifies the need to 

reduce this economic penalty by better 

understanding the hazard and its spatial 

distribution (El Nino Response Group, 1998; 

http://elnino.usgs.gov/landslides-sfbay/). 

Because landslide activity correlates closely 

with ground-surface slope and other attributes of 

terrain form that can be measured from DEM's 

(Brabb and others, 1989), slope-failure is 

perhaps the natural hazard most amenable to 

study by quantitative techniques (Soeters and 

van Westen, 1996). Much of the morphometric 

literature on landslides is referenced in the first 

report in this series (Pike, 1993).

Two overall approaches, not sharply 

distinguished in many publications, employ 

quantitative topographic data to analyze 

processes of slope failure the landslide-specific 

and the regional. By the first, and older, 

approach landslides are treated individually, as 

discrete landforms. Measurements, usually from 

field surveys or contour maps, are taken of such 

variables as landslide length, breadth, volume, 

planimetric shape, compass orientation, and

height of head scarp. These quantities are 

compared with each other and with bedrock and 

soil properties, local hydrology, and other 

physical characteristics to isolate causative 

factors and model the physics of the process 

(Bhandari and Kotuwegoda, 1996; Hylland and 

Lowe, 1997).

Increasing availability of large square-grid 

DEM's and GIS technology has led to the use of 

the second, regional, approach whereby slope 

angle, curvature, relative relief, and other 

measures that relate to landsliding are computed 

continuously over broad areas (Carrara and 

others, 1995; Mark and Ellen, 1995). Digital 

maps of geology, materials properties, and 

landslide inventories are then compared and 

combined with those maps of terrain geometry to 

obtain a set of variables that can be used to 

delineate potentially hazardous areas (Brunori 

and others, 1996; Fernandez and others, 1996; 

Ellen and others, 1997).

In carrying out such regional modeling it is 

critical to distinguish among different processes 

of slope failure. The topographic and geologic 

conditions triggering debris flows, for example, 

differ markedly from those giving rise to slumps, 

slides, and earthflows. Recent work on debris 

flows that incorporates DEM-based 

morphometry is described in Boelhouwers and 

others (1998), Dietrich and others (1995), 

Campbell and others (1998), Walsh and Butler 

(1997), and in a book edited by C.-L. Chen 

(Campbell and Bernknopf, 1997; Wieczorek and 

others, 1997). Proceedings volumes edited by K. 

Senneset (Chandra, 1996) and by Chacon and 

others (Fernandez and others, 1996) address 

morphometric analysis of slope failure other 

than debris flow.

Barchan dune morphometry

Barchans are migrating sand dunes that pose a 

hazard to dwellings, highways, railroads, and 

other infrastructure of desert settlements 

(Beadnell, 1910; Al-Janabi and others, 1988; 

Khalaf and Al-Ajmi, 1993). These crescentic 

dunes are unique among landforms in that size, 

shape, degree of complexity, and location all can 

change markedly over the life of the feature 

(Bagnold, 1941, p. 208-221; Norris, 1966).

R.J.Pike / USGS OF 99-140
Modeling the development and migration rate of 

barchans is facilitated by the crisp definition 

and consequent ease of measurement of isolated 

dunes (Howard and others, 1978). In the search 

for clues to barchan-forming processes, dune 

length, cusp-to-cusp width, slip-face height and 

overall height, differences in cusp length, and 

dune volume all have been measured and 

compared. Some of these dimensions correlate 

with dune spacing, rate of movement, wind 

direction, and sand supply (Lancaster, 1989a,b; 

Shehata and others, 1992; Haff and Presti, 1995). 

Such relations are vital in predicting the speed 

and trajectory of migrating barchans.

The morphometry of barchans currently is 

unsystematic in several respects, which impedes 

the understanding of process and evolution of 

form. For example, available measurements do 

not cover the observed size-range; in plan 

dimensions, barchans vary from soup-plate size 

(Norris, 1956) to several hundreds of meters 

across (Bagnold, 1941; Embabi and Ashour, 1993). 

Although a 1:10 height:width relation 

commonly is assumed for barchans from published 

measurements (Hesp and Hastings, 1998), data 

from other areas (Embabi and Ashour, 1993) do 

not support this generalization, even across the 

size-range for which measurements exist. Graphs 

in a recent compilation of some published 

dimensions (Hesp and Hastings, 1998) suggest 

that barchan height may be a non-linear function 

of size, but no attempt has been made to test for 

size-dependency of form. Also, barchans in the 

Middle East (Embabi and Ashour, 1993) and the 

Sahara (Sarnthein and Walger, 1975) may be 

larger than those measured in Peru (Hastenrath, 

1967,1987) and the western United States (Long 

and Sharp, 1964). Nor has it been determined 

whether the size-frequency distribution of 

barchans is normal or otherwise.

To address these problems, fresh measurements 

are needed to adequately represent the entire 

size-range, particularly the smaller barchans 

which move so fast and are so ephemeral that 

they tend not to be measured (Norris, 1956). 

Much work remains before barchan systematics 

are sufficiently well established to support 

robust form-process modeling throughout the 

observed size-continuum (Mulligan, 1995).

Morphometry of sea-ice surfaces

A hazard to winter navigation and a danger to 

such offshore structures as oil pipelines, sea ice is 

an ephemeral, seasonal and continually changing 

landscape of the high latitudes. Sea ice may be 

either undeformed, as initially frozen, or 

deformed by a number of processes. A field of 

deformed sea ice is level overall, but its 

mesoscale morphology (only a few meters of 

relief) can be very rough because of varying forms 

of ridged ice (Weeks and Kovacs, 1970). Pressure 

ridges are irregular slabs of ice imbricated by 

wind and other agents. Although complex objects 

that vary greatly in size and shape, these ridges 

appear to be limited in vertical extent 

(Parmerter and Coon, 1972). Ridge morphology 

above and below the sea surface can be 

represented statistically from measurements of 

salient features. Kankaanpaa (1997) gives a 

good recent sampling of the voluminous 

literature. Earlier morphometric work on sea ice 

includes Hibbler and Mock (1974), Wadhams 

(1981), Williams and others (1975), Rothrock and 

Thorndike (1980), and Wadhams and Davy 

(1986).

The surface relief of pressure ridges is measured 

by standard field methods of ice surveying 

drilling, sectioning, and photography 

(Kankaanpaa, 1997), as well as by sonar 

(McLaren, 1988), laser profiling (Lewis and 

others, 1993), and other techniques of remote 

sensing. Detailed measurement of ridge 

morphometry accelerated during the Cold War, 

when high-latitude terrains were anticipated as 

potential battlefields. The underside 

topography of floating ice was systematically 

profiled to assist submarine operations 

(Williams and others, 1975; McLaren, 1988).

The sail is that portion of a pressure ridge above 

the surrounding ice surface; the (much larger) 

portion projecting below the water surface is the 

keel. The size, shape, spacing, and areal density 

of sails and keels have been investigated by 

various techniques (Wadhams and Davy, 1986; 

Kankaanpaa, 1997). Size-frequency distributions 

of such sail and keel parameters as height, 

depth, width, cross-sectional area, and slope 

angle have been determined for different ice 

packs and compared with each other and with 

theoretical models (Lowry and Wadhams, 1979).

R.J.Pike/USGSOF99-140
Pack-ice surfaces have also been modeled 

statistically by the variance (power) spectrum 

and other techniques of random-field analysis 

(Lewis and others, 1993). Among generalizations 

reached thus far: new (first-year) ridges differ 

significantly from older (multiple-year) ridges 

and sail height is related to keel depth (Timco 

and Burden, 1997; Kankaanpaa, 1997); ridge size, 

but not shape, differs from sea to sea (McLaren, 

1988; Kankaanpaa, 1997) and with ridge age 

(Timco and Burden, 1997); and keel profiles 

appear to have a fractal distribution (Melling 

and others, 1993).

Abyssal hills on Earth's sea floor

Abyssal hills are small, elongate features 

created at mid-ocean-ridge spreading centers by 

faults that offset fresh basaltic sea floor (Pratson 

and Haxby, 1997; Smith, 1998). These hills are 

the most common morphologic feature on the 

ocean floor, arguably rivaling subaerial drainage 

basins in frequency, but they remain among the 

least understood of Earth's landforms. Because 

abyssal-hill morphology reflects processes and 

rates of ridge-crest spreading (Ma and Cochran, 

1997), abyssal-hill topography constitutes a 

major piece of the overall plate-tectonics puzzle. 

A number of generalizations were established 

earlier: both simple and complex morphologies 

are observed, hills in the Atlantic ocean basin 

are larger than those in the Pacific, and both 

volcanic and tectonic processes evidently are 

involved in their origin (Menard, 1967).

As deep-sea imaging has improved in resolution 

and areal coverage, morphometry has played an 

expanding role in probing the nature of abyssal 

hills. Because individual hills are still too 

small to be measured accurately by available 

imaging systems (Vogt and Tucholke, 1986; Smith 

and Sandwell, 1997), the hills are analyzed as 

continuous swaths of textured topography (Goff 

and Jordan, 1988; Shaw and Lin, 1993; Goff and 

others, 1997). Among the generalized measures 

by which this texture is captured are relief, 

azimuth, slope, slope curvature, ridge-parallel 

spacing, ridge-normal spacing, and the 

proportion of coarse- to fine-scale roughness (Goff 

and Jordan, 1988; Shaw and Lin, 1993). Recently, 

Small (1994) and Ma and Cochran (1997) have 

statistically distinguished abyssal-hill

roughness from the basic shape of the ridge axis, 

and processes other than faulting and volcanism 

have been found to modify the hills (Goff and 

Tucholke, 1997). In attributing abyssal hills to 

stretching of the oceanic lithosphere, Buck and 

Poliakov (1998) further suggest that the process 

exhibits self-organized criticality.

Abyssal-hill topography is most recently 

discussed by Goff (1998), who contrasts analytic 

approaches to these surface forms as either 

continuous or discrete. Emphasizing the chaotic 

appearance of continuous abyssal-hill terrain, 

"observationalist" workers treat the problem 

more stochastically, via second-order statistics 

of hill dimensions and spacing (Goff and Jordan, 

1988; Goff and others, 1997). The "physical 

modelers", in contrast, emphasize the regular 

spacing of discrete deep-sea faults and their 

offsets in the hilly terrain and thus address the 

issue more deterministically (Shaw and Lin, 

1993; Malinverno and Cowie, 1993). The detailed 

modeling of Buck and Poliakov (1998) is 

important because it begins to reconcile the two 

approaches (although much remains to be done).

Goff (1998) closes his methodological discussion 

with comments on the fractal concept. In a caveat 

that extends beyond abyssal hills to other 

aspects of terrain modeling (for example, 

Gallant, 1997, and Evans, 1998), he cites the "gulf 

between merely describing the statistical 

behavior of a natural phenomenon ... and 

understanding the physical principles which 

lead to such behavior..." By implication, selforganized criticality is the latest such "scientific 

bandwagon" (see also Agterberg, 1998, 

Bhattacharya, 1997, and Traut, 1998), as 

investigators try "... to understand how this 'new1 

... way of thinking about nature might bear on 

their particular specialty."

Wavelet analysis of landforms

Scale-dependence of the ground surface, 

particularly since the advent of fractal measures 

(Mandelbrot, 1975), has become a key research 

area in much of morphometry (Moore, Lewis, and 

Gallant, 1993; Bloschl and Sivapalan, 1995; 

Bishop and others, 1998). The problem is 

addressed by analyzing relief (Z) and 

planimetric (X,Y) attributes of topography over

R.J.Pike / USGS OF 99-140
several spatial scales, either for areally discrete 

landforms or over continuous-surface landscapes. 

In pursuing the latter approach, Gallant & 

Hutchinson (1996) and Gallant (1997) found the 

fractal concept wanting and as a consequence 

Gallant has introduced wavelets to landform 

morphometry. This analytical method 

decomposes a topographic surface into a set of 

oscillatory functions at different frequencies in a 

similar manner to the Fourier transform in 

spectral analysis. The wavelet transform 

employs localized functions (wavelets) rather 

than infinitely repeating sine and cosine 

functions. Among its advantages over the 

elevation-variance spectrum are an improved 

representation of azimuthally non-homogeneous 

terrain and the provision of spatially variable 

descriptions. To accomplish this, the process 

superposes multiple mathematical "features" at 

various scales.

The modeled feature chosen by Gallant to 

develop the method on representative 

Australian OEM's has an elliptical plan and a 

smooth polynomial profile, the simplest 

geometric form with sufficient flexibility to 

represent most topographic surfaces. Gallant's 

(1997) examination of scale and spatial structure 

of relief in continuous topography has identified 

at least three descriptive parameters terrain 

"complexity," "positivity," and "orientation" 

attributes which almost certainly relate to 

descriptors computed by other approaches to 

terrain quantification. Work is needed to 

investigate possible correlations. The results of 

Gallant's pioneering work are difficult to judge 

now, because relatively few other wavelet 

studies have been carried out on natural 

topography (Foufoula-Georgiou and Kumar, 1994; 

Weissel and Stark, 1997; Kumar and FoufoulaGeorgiou, 1997; and three others listed in Pike, 

1995,1996).

Metrology update

Industrial surface-metrology (hereafter 

metrology2) is the quantification of micro- and 

nano-scale surfaces in manufacturing (Pike, 1996).

^ The discipline commonly is known within industry 

albeit somewhat confusingly to Earth scientists as 

surface topography. A specialized journal of that same 

title existed briefly from 1988 to 1990.

The explosive expansion of metrology, driven 

most recently by research in high-technology 

industries and far outstripping the growth of its 

parallel discipline of topographic 

quantification, is paced by three important new 

books. Thomas (1999) revises a standard 1982 

text weighted toward mechanical engineering, 

and Bhushan (1997) has updated developments 

in the metrology of magnetic tape and computer 

disk drives. The proceedings of a 1996 conference 

on metrology and the properties of engineering 

surfaces ("the best we've ever had", T.R. 

Thomas, 1998, pers. comm.) were published in 

1997 (Rosen and Crafoord, eds., 1997). All three 

volumes contain industry analogs of Earthsurface terrain quantification, including fractal 

modeling, self-organization, power-spectral and 

wavelet representation, and functional linkages 

between form and process. Two slightly older 

books, the standard handbook on metrology 

(Whitehouse, 1994) and a manual of methods for 

3-D characterization of surfaces (Stout and 

others, 1993), are no less significant.

Recent shorter works on the topography of 

industrial surfaces include Bhushan and Koinkar 

(1995), Mainsah and others (1996), He and Zhu 

(1997), and Othmani and Kaminsky (1998). 

Hahner and Spencer's 1998 review of the related 

field of tribology the study of friction, 

lubrication, and wear is helpful background. A 

paper by Medeiros-Ribeiro and others (1998) is of 

particular interest. They have revealed and 

quantified a nanoscopic transition, from smaller 

pyramids to larger domes, in the morphology of 

germanium crystals grown on a silicon substrate 

by physical vapor deposition. The sizedependent change, which conceptually resembles 

the transition from central peaks to inner rings in 

large planetary impact craters (Pike, 1982), is 

marked by pyramids that"... nucleate and grow 

to a maximum volume that is smaller than the 

volume for which the domes are more stable than 

the pyramids plus (a critical volume of added) 

germanium ..." This transition, which seems to 

mark a shift from one equilibrium form to another 

with increasing input of energy or material, may 

have other geomorphologic parallels that help 

to explain size-dependent differences observed in 

some landforms.

Many publications on industrial-surface 

metrology are referenced in a new, 

chronologically ordered, bibliography that

R.J.Pike / USGS OF 99-140
improves access to research on surface 

quantification not found in the usual 

geomorphology-related sources (Pike and 

Thomas, 1998). A brief essay prefacing the 4800 

literature citations introduces metrology to Earth 

scientists, describes similarities and differences 

between the two realms (Scott, 1994,1997), and 

raises issues that must be addressed in any 

attempt to unify the practice of surface 

quantification. A sampling of Internet Web-site 

addresses and full abstracts of papers on 

metrology rounds out the main listing.

Other recent morphometry

More conventional areas of morphometry continue 

to thrive as well. Several of these are described 

above. A most important new development is the 

rapid increase in publication exclusively by CDROM and by posting on the Internet (Pike, 1998). 

Recent major contributions include Joseph Wood's 

thesis on digital terrain modeling 

(http://www.geog.le.ac.uk/jwo/research/dem_c 

har/thesis/); two software packages for the 

hydrogeomorphic analysis of DEM's Scott 

Peckham's RiverTools

(http://cires.colorado.edu/people/peckham.scot 

t/RT.html) and David Tarboton's TARDEM 

(http://www.engineering.usu.edU/cee/faculty/d 

tarb/dem.htm); proceedings of the 1996 Santa Fe, 

NM, GIS Conference and Workshop 

(http://ncgia.ncgia.ucsb.edu/conf/SANTA_FE_ 

CD-ROM/sessions.html); and the latest release 

of Peter Guth's MicroDEM+ terrain-modeling 

software

(http://www.usna.edu/Users/oceano/pguth/web 

site / microdem.htm).

Briefly, other new developments include:

 the morphometry of continental ice surfaces 

(Bahr, 1997; Etzelmiiller and Sollid, 1997); 

Davis and others, 1998; Scambos and 

Fahnestock, 1998; Tabacco and others, 1998;

 calculation of the DEM-to-watershed

transformation (Tarboton, 1997; Rieger, 1998), 

with special attention to problems posed by 

low-relief topography (Garbrecht and Martz, 

1997a; Martz and Garbrecht, 1998) and the 

inclusion of lakes (Fern and others, 1998; 

Mackay and Band, 1998);

 new DEM databases (Clayton and Shamoon, 

1998a, b ; Smith, 1998; Welch and others, 

1998);

 geomorphologic modeling other than that 

reported in the 1998 book edited by Lane and 

others (Ahnert, 1996; Tarboton, 1996; Ahnert 

and Williams, 1997; Beven and Kirkby, 1997; 

Costa-Cabral and Burgess, 1997; Willgoose 

and Hancock, 1998);

 characterization of glacial U-valleys (Duncan 

and others, 1998; Pattyn and Van Huele, 1998) 

and cirques (Hassinen, 1998; Sauchyn and 

others, 1998);

 DEM-based tectonic geomorphology (Seber and 

others, 1997; Demoulin, 1998);

 geometric and geomorphic signatures (Sulebak 

and others, 1997; Brown and others, 1998; 

Giles, 1998; Giles and Franklin, 1998);

 characterization of fractured rock surfaces 

(Glover, 1998a, b);

 morphometric applications to soil development 

and agriculture (Thompson and others, 1997; 

DeBruin and Stein, 1998; Florinsky and 

Arlashina, 1998; Souchere and others, 1998);

 the geometry of seamounts (Smith and others, 

1995; Rappaport and others, 1997; von Huene 

and others, 1997; Wessel, 1997);

 planetary surface features (Craddock and 

Maxwell, 1997; Yingst and Head, 1997; Oberst 

and others, 1997; Kreslavsky and Basilevsky, 

1998; Smith, Zuber and others, 1997,1998; 

Williams and Zuber, 1998);

 pre- and post-eruption morphometry of volcanic 

edifices (Mizukoshi and others, 1995; Jones 

and Newhall, 1996; Mizukoshi and 

Murakami, 1997); and

 large-area visualization of topography by 

computer graphics, exemplified by, 

respectively, Australia, Alaska, and Earth's 

seafloor (Milligan and others, 1997; Riehle 

and others, 1997; Smith and Sandwell, 1997).

New books

Book-length publications that showcase 

advances in morphometry continue to appear. 

Among the most important recent additions 

outside of industrial surface-metrology are those 

by Rodriguez-Iturbe and Rinaldo (1997), Lane and 

others, eds. (1998), and Marcus and others (1996). 

The last volume, on biological objects, is a major 

development in non-topographic morphometry.

R.J.Pike / USGS OF 99-140
However, because it focuses on the representation 

of closed two- and three-dimensional forms only 

(sedimentary particles, mineral grains, fossils, 

tree leaves), notably through the "landmark 

analysis" pioneered by Bookstein (1995), its 

application to surfaces per se is limited.

Appearance of the monograph by RodriguezIturbe and Rinaldo (1997) is a major event. 

Linking two modern concepts, fractal geometry 

and the theory of self-organized criticality, it 

addresses the fundamental nature of river basins 

and their structure and evolution. The book 

contains much more than just these two concepts, 

and treats the complexities of both spatial 

(planform) and temporal structures and patterns. 

Building on voluminous published work with 

colleagues, Rodriguez-Iturbe and Rinaldo 

synthesize a conceptual and mathematical 

framework within which the great variety of 

river networks spanning some five orders of 

magnitude, 100 m to 10,000 km and the 

underlying order can be studied. This tour-deforce in applied science includes enough 

background material to be largely self-contained. 

It contributes to physics as well as to theoretical 

hydrology and other geomorphically-oriented 

aspects of Earth science. For reviews see 

Agterberg (1998), Levy (1998), Tsonis (1998), and 

Turcotte (1998).

The proceedings of the 1995 Cambridge 

Fitzwilliam Symposium of the British 

Geomorphological Research Group (Lane and 

others, eds., 1998), reprises an important meeting 

(and 1972 proceedings volume edited by R.J. 

Chorley) held in England a quarter of a century 

earlier. Edited to a high standard, the 19 

diverse chapters in the 1998 book offer a good 

sampling of contemporary morphometry 

particularly in the UK. Included are McCullagh 

on Quality, use and visualization in terrain 

modelling, Evans on What do terrain statistics 

really mean?, Wise on The effect of GIS 

interpolation errors on the use of digital 

elevation models in geomorphology, Wilson and 

Gallant on Terrain-based approaches to 

environmental resource evaluation, Montgomery 

and others on The role of GIS in watershed 

analysis, Lamb and others on A generalized 

topographic-soils hydrologic index, and Lane on 

The use of digital terrain modelling in the 

understanding of dynamic river channel systems.

Early morphometry

Here I begin to remedy a shortcoming of previous 

reports in this series, neglect of old work in 

morphometry much of it in languages other 

than English. These (annotated) citations both 

constitute the early history of the field and 

provide context for later work (Dainville, 1958, 

1970). Addition of much of the older material 

began with my finding discrepancies in published 

literature citations of Alexander von Humboldt. 

(His prolific career spanned 70 years of active 

publication in various languages.) This discovery 

led to inspection of one of the several von 

Humboldt bibliographies (Lowenberg, 1960; 

itself not free of contradictory entries), with 

ensuing correction of errors in Pike (1993,1996) 

and the addition here of six more papers by von 

Humboldt. Exposure to this pioneering 

morphometry prompted inclusion of other work, 

for example that of Carl Ritter (1852) regarded 

by many, with von Humboldt, as the founder of 

the craft. However, any attempt to identify an 

"ultimate" origin for geomorphometry would be 

fruitless. The earliest systematic measurement of 

topography undoubtedly predating Roman 

hydrology, Greek geodesy, and Egyptian civil 

engineering is "lost in antiquity."

Some 60 pre-1900 references, the oldest of which 

is to the isobath map by Buach (1756), are added 

here. Most of the early writing describes efforts 

to accurately measure terrain height (Humboldt, 

1817) and produce good contour maps (Du Carla, 

1782), the primary source material for 

morphometry per se until advent of the DEM. 

Securing good elevations with spirit level and 

aneroid barometer was cutting-edge work in its 

day (Alien and Woods, 1817; Cuvier and 

Brongniart, 1835, p. 597-607; Pick, 1855), and the 

need to measure so elementary a quantity as 

surface height has not diminished only the 

instrumentation has changed. The role of 

barometer and level has passed to such satelliteborne technologies as GPS and digital 

radargrammetry. The accurate determination of 

surface elevation poses a special challenge to 

planetary scientists (Smith and others, 1998; 

Williams and Zuber, 1998) and geophysicists 

working with seafloor terrain (Smith, 1998).

A number of the references added here are 

neither old enough to be of great historic interest

R.J.Pike / USGS OF 99-140
nor sufficiently recent to bear directly upon 

contemporary work. They are valuable, 

however, in establishing a continuous historical 

record of geomorphometry as the field developed 

in several countries, from Humboldt and Ritter to 

Horton, fractals, and DEM's (Beer and Madler, 

1837; Schmidt, 1856; Hofer, 1879; Peucker, 1892; 

Romer, 1911; Horton, 1914; Blanchard, 1919; 

Jones, 1924, 1951; Matui, 1930; Burckhardt, 1934; 

Hollingworth, 1931, 1938; Cressy, 1938). This 

report also adds a dozen papers by Polish 

geographers, active contributors to morphometry 

in the 1920s and 1930's (Joerg, 1933), to better 

represent Eastern European work (Pawlowski, 

1929; Zaborski, 1931; Strada, 1932). Several 

additions to later Soviet-era morphometry have 

been identified as well (Zakharov, 1940; 

Sharapov, 1967; Leder, 1973; Devdariani, 1976; 

Piriev, 1986; Lastochkin, 1987; Yakimenko, 1990).

New entries

As before, I encourage additions and corrections to 

this archive from its users. I am especially 

interested in morphometric work that is unlikely 

to be available in the United States, for 

example, non-English-language publications from 

central and eastern Europe. My files on French 

work also are inadequate. I will be happy to 

exchange copies of reports in this series for those 

papers. To ensure accuracy and reduce ambiguity, 

please send reprints or photocopies of 

contributions rather than just the citations, if 

possible. However, I can add new entries from 

only the following information:

1. photocopy of title page, or

 title of the work, and

 the name(s) of author(s); surname

plus two initials (or, if one 

given name, then spelled out)

2. year of publication

3. complete citation of serial or other form of 

publication (book, conference proceedings, and 

so forth), including volume number, issue 

number, and inclusive pages. For meetings give 

location and dates; for books the name of city 

and publisher

4. for non-English-language publications, an 

English translation of the title.

Address correspondence to:

Richard J. Pike

M/S975

U.S. Geological Survey

345 Middlefield Road

MenloPark,CA 94025 U.S.A.

FAX [415] 329-4936

e-mail: <rpike@sierra.wr.usgs.gov>

Acknowledgments: Comments by USGS 

colleague Russ Evarts improved the report.

References

Lowenberg, Julius, 1960, Alexander von Humboldt 

Bibliographische Ubersicht seiner Werke, 

Schrif ten und zerstreuten Abhandlungen 

(unabridged reprint of that part of Bruhns, 

Karl, ed., 1872, A. v. H., a Scientific 

Biography): Stuttgart, F.A. Brockhaus Komm.- 

Gesch. GMBH Abt. Antiquarium, 68 p.

Pike, R.J., 1993, A bibliography of 

geomorphometry, with a topical key to the 

literature and an introduction to the numerical 

characterization of topographic form: U.S. 

Geological Survey Open-file Report 93-262A, 

132 p. Open-file Report 93-262B, one 31/2 inch 

1.44 MB diskette. Formatted in Microsoft 

Word, version 5.0, for Macintosh. Open-file 

Report 93-262C, one 31/2 inch 1.44 MB 

diskette. Formatted in WordPerfect, version 

5.0 for IBM-PC or compatible.

 1995, A bibliography of geomorphometry, 

the quantitative representation of 

topography Supplement 1.0: U.S. Geological 

Survey, Open-file Report 95-046, 30 p. [paper 

copy only; 124 kb if in digital format]

 1996, A bibliography of geomorphometry, 

the quantitative representation of 

topography Supplement 2.0: U.S. Geological 

Survey, Open-file Report 96-726, 52 p. [paper 

copy only; 228 kb if in digital format]

R.J.Pike / USGS OF 99-140
BIBLIOGRAPHY OF GEOMORPHOMETRY

ADDITIONS

Abdel, S.M., 1982, Study of factors affecting accuracy 

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Abdel-Rahman, M.A., Embabi, M.S., EI-Etr, H.A., and 

Mostafa, A.A., 1980-1981, Some geomorphological 

aspects of Siwa Depression, the Western Desert, 

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1993]

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Walker, J.C., 1994, Evolution of ground line-of-sight 

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A., and Weeks, W.F., 1974, Thickness and 

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Jiancheng, Dozier, Jeff, and Fielding, Eric, 1998, 

Classification of surface types using SIR-C/X-SAR, 

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Geomorphology, v. 21, nos. 3-4, p. 207-216.

R.J.Pike / USGS OF 99-140

1 0
Alien, William, and Woods, Samuel, 1817, Barometrical 

measurements: Transactions of the Geological 

Society of London, v. 4, part II, article 29, p. 434-437. 

[paper read Nov. 19, 1812; instr. & calc. after Henry 

Englefield (Nicholson's Jour., v. 14); Mt. Snowdon: 

3596' (3560' by modern meas.); others]

Allison, R.J., and Davies, K.C., 1996, Ploughing blocks 

as evidence of down-slope sediment transport in the 

English Lake District: Zeitschrift fur Geomorphologie, 

Supplementband 106, p. 199-219.

Allison, R.J., and Higgitt, 1998, Slope form and 

associations with ground boulder cover in arid 

environments, northeast Jordan: Catena, v. 33, no. 1, 

p. 47-74. [slope-profile analysis via length/height 

integral (ER, elev skew?)]

Allmaras, R.R., Burwell, R.E., Larson, W.E., Holt, R.F., 

and Nelson, W.W., 1966, Total porosity and random 

roughness of the interrow zone as influenced by 

tillage: U.S. Department of Agriculture, Conservation 

Research Report 7, 21 p.

Amlien, Jostein, 1997, Cartographic generalization of 

topographic maps examples from Svalbard: Norsk 

geogr. Tidsskr. (Norwegian J. of Geography), v. 51, 

no. 1, p. 71-80.

Andrle, Robert, 1997, Misuse of R^ values from linear 

regression in fractal analysis: Physical Geography, v. 

18, no. 6, p. 559-567. [do residual analysis or other 

tests for linearity]

Aniya, Masamu, and Welch, Roy, 1981, Morphometric 

analyses of Antarctic cirques from photogrammetric 

measurements: Geografiska Annaler, v. 63 A, no. 1- 

2, p. 41-53.

Arai, Tadashi, 1997, Characteristics of basin 

morphology of lakes in Japan: Japan Journal of 

Limnology, v. 58, p. 231-240. [area-depth curves 

compared]

Armbrust, D.V., Chepil, W.S., and Siddoway, F.H., 

1964, Effects of ridges on erosion of soil by wind: Soil 

Science Society of America, Proceedings, v. 28, no. 

4, p. 557-560.

Arrouays, Dominique, Daroussin, Joel, Kicin, J.L, and 

Hassika, Paulin, 1998, Improving topsoil carbon 

storage predictions using a digital elevation model in 

temperate forest soils of France: Soil Science, v. 163, 

no. 2, p. 103-108. [carbon decreases with 

increasing slope; curvature not signif.]; 100 m DEM

Aumen, W.C., 1970, A new map form numbers, in 

Frenzel, Konrad, ed., International Yearbook of 

Cartography: London, George Philip and Son, v. 10, 

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maps]

Avnir, David, Biham, Ofer, Lidar, Daniel, and Malcai, 

Ofer, 1998, Is the geometry of nature fractal?: 

Science, v, 279, no. 5347, p. 39-40. [see two 

comments (by B.B. Mandelbrot & Peter Pfeifer) & 

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1616]

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classification for digital terrain models: International 

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issued?]

B

Bagnold, R.A., 1941, The barchan dune, /nThe Physics 

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Journal of Glaciology, v. 43, no. 145, p. 557-562.

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Kargel, J.S., and Lewis, J.S., 1992, Channels and 

valleys on Venus Preliminary analysis of Magellan 

data: Journal of Geophysical Research, v. 97, no. E8, 

p. 13,421-13,444. [morphometry of meanders & 

islands from SAR images]

Bakker, J.P., and Le Heux, J.W.N., 1946, Projectivegeometric treatment of O. Lehmann's theory of the 

transformation of steep mountainslopes: Koninklijke 

Nederlandsche Akademie van Wettenschappen, 

Proceedings, v. 49, p. 533-547.

Bakker, J.P., and Le Heux, J.W.N., 1952, A remarkable 

new geomorphological law, I and II: Koninklijke 

Nederlandsche Akademie van Wettenschappen, 

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quantitative investigations of slopes, in Congress of 

the International Geographical Union, Rio de Janeiro, 

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Versants: Amsterdam, p. 33-41.

Balchin, W.G.V., 1937, The erosion surfaces of North 

Cornwall: Geographical Journal, v. 90. no. 1, p. 52-63. 

[altimetric freq.]

Balchin, W.G.V., 1952, The evidence for late Tertiary 

eustatic changes of sea level in western Europe, in 

General Assembly 8th and International Congress 

17th, Washington, D.C., August 8-15, International 

Geographical Union: Proceedings, p. 296-300. 

[altimetric freq.]

R.J.Pike / USGS OF 99-140

1 1
Baldwin, Jonathan, Fisher, Peter, Wood, Joseph, and 

Langford, Mitchel, 1996, Modelling environmental 

cognition of the view with GIS: International 

Conference on Integrating GIS and Environmental 

Modeling, 3rd, January 21-25, Santa Fe NM, National 

Center for Geographic Information and Analysis, 

Proceedings, NCGIA CD-ROM and 

<http://severn.geog.le.ac.uk/wo/research/dem_char/ 

santafe/index.htmlx

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Geometric boundary conditions for modelling the 

velocity field of the Antarctic ice sheet: Annals of 

Glaciology, v. 23, p. 364-373.

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from digital elevation data (presentation only): 

International Symposium on Remote Sensing of 

Environment 18th, Paris, October 1-5. [early work]

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natural channels: U.S. Geological Survey, Watersupply Paper 1849, 213 p. [Manning n (0.024- 

0.079), x-sect., & color pix for 50]

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atmospheric interactions: Journal of Geophysical 

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to the 3/4 power]

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Joaqum, 1996, Delimitacion de unidades homogeneas 

del relieve a partir de un modelo digital de elevaciones 

(in Spanish; Delimitation of homogeneous relief units 

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643.

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jerarquica a la cartograf fa del espesor del suelo en 

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Landform Monitoring, Modelling and Analysis: New 

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"fractals" in soil science demixing apples and 

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migration rates]

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v. 25, no. 12, p. 1063-1066. [they say "no"]

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program maps geoscience data sets interactively: 

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79. no. 42, p. 505 & 508. ['iGMT', a graphical 

interface for GMT]

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German): Berlin, Simon Schropp, paging unknown. 

["Madlei^s Rule"; 148 crater-diameter measurements 

& 830 heights; important detailed map published in 

1834]

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och tektoniska studier av de nord-vastskanska 

urbergsasarna, sarskilt Kullaberg (in Swedish): Royal 

University of Lund, Meddelanden fran Lunds 

Universitets Geografiska Institution, Avhandlingar 

24, 255 p. + one vol. of maps.

Behrens, S.E., 1953b, Morphometrische, 

morphogenetische und tektonische Studien der 

nordwest-schonischen Urgebirgsrucken, mit 

besonderer Berucksichtigung von Kullaberg (in 

German;... studies of the Great NW ... Mts., with 

special ref. to Kullaberg): Royal University of Lund,

R.J.Pike / USGS OF 99-140

1 2
Sweden, Lund Studies in Geography, Ser. A, No. 5, 

34 p. + maps.

Beketsky, S.P., 1998, Thickness distribution of 

consolidation hummock layer offshore Sakhalin, in 

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D.C., Optical Society of America, paging unknown, 

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floods in a humid region of diverse terrain: U.S. 

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basins in Sweden Measurements and graphical 

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1996, GEODATA 9 SECOND DEM: Canberra, 

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8, August, p. 42-47. [emph. forestry; 3-D software 

pkgs.]

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Hydrological Processes, v. 11, no. 9, p. 1069-1085.

Beven, Keith, and Kirkby, M.J., eds., 1997, Special 

Issue TOPMODEL: Hydrological Processes, v. 11, 

no. 9, p. 1069-1356.

Beven, Keith, Lamb, R., Quinn, P., Romanowicz, and 

Freer, J., 1995, TOPMODEL, Ch. 18 in Singh, V.P., 

ed., Computer Models of Watershed Hydrology: 

Highlands Ranch, CO, Water Resources Publications, 

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Consideration of landslide geometry and runout in a 

landslide inventory, in Senneset, Kaare, ed., 

Landslides, International Symposium, 7th, 

Trondheim, June 17-21, Proceedings: Rotterdam, 

Balkema, v. 3, p. 1859-1864.

Bhattacharya, Shobo, 1997, Review of "How Nature 

Works: The Science of Self-Organized Criticality" by 

Per Bak: Physics Today, v. 50, no. 12, p. 71-72. 

[critiques Bak as too advocative of SOC]

Bhushan, Bharat, 1997, Tribology and Mechanics of 

Magnetic Storage Devices (2nd ed.): Piscataway, NJ, 

IEEE, 1152 p. [nano-scale; incl. surface roughness, 

etc.]

Bhushan, Bharat, and Koinkar, V.N., 1995, Macro and 

microtribological studies of CrO2 video tapes: Wear, 

v. 180, nos. 1-2, p. 9-16. [use AFM and FFM, friction 

force micr.]

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Morfometricheskaya otsenka ovragov po dannym 

naturnykh izmereniy (in Russian with English 

summary; morphometric evaluation of gullies 

according to field measurement data): 

Geomorphologiya (Moscow), 1990, no. 4, p. 36-38.

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Siebenburgens (in German): Sitzungsberichte der 

mathematisch-naturwissenschaften Classe der 

kaiserlichen Akademie der Wissenschaften (Vienna), 

Abt. 1, v. 6, no. 5, p. 602-655. [orometry of some 

central European mountains]

Bindschadler, D.L., Schubert, Gerald, and Kaula, W.M., 

1992, Coldspots and hotspots Global tectonics and 

mantle dynamics of Venus: Journal of Geophysical 

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maps, profiles, & shaded relief from SAR images]

Bingner, R.L., Garbrecht, Jurgen, Arnold, J.G., and 

Srinivasan, 1997, Effect of watershed subdivision on 

simulation runoff and fine sediment yield: 

Transactions of the American Society of Agricultural 

Engineers, v. 40, no. 5, p. 1329-1335.

Bischetti, G.B., Gandolfi, C., and Whelan, M.J., 1998, 

The definition of stream channel head location using 

digital elevation data, in Kovar, K., Tappeiner, U., 

Peters, N.E., and Craig, R.G., eds., Conference on 

HeadWater '98, Meran/Merano, Italy, April 20-23, 

Proceedings: IAHS Publication no. 248, p. 545-552.

Bishop, G.C., and Chellis, S.E., 1990, A fractal 

description of ice keel small-scale surface 

roughness, in Ackley, S.F., and Weeks, W.F., eds., 

Sea Ice Properties and Processes: U.S. Army CRREL 

(Cold Regions Research and Engineering Laboratory) 

Monograph 90-1, p. 141 -145. [keel- & non-keel-like 

features not distinguishable (both 1.2<D<1.7)]

Bishop, M.P., Shroder, J.F. Jr., Hickman, B.L., and 

Copland, Luke, 1998, Scale-dependent analysis of 

satellite imagery for characterization of glacier 

surfaces in the Karakoram Himalaya: 

Geomorphology, v. 21, nos. 3-4, p. 217-232. 

[semivariogram & fractal analysis of 6 diff. terrains on 

SPOT images]

R.J.Pike / USGS OF 99-140

1 3
Blanchard, R., 1919, Altitudes moyennes des regions 

naturelles des Alpes Francaises: Trav. de L'lnst. de 

Geogr. Alpine de L'Univ. de Grenoble, p. 245-308.

Blaszczynski, J.S., 1993, HTAS hydrologic terrain 

analysis software user's manual: U.S. Bureau of Land 

Management, BLM Publication No. BLM/SC/ST94/007+7000, paging unknown.

Blaszczynski, J.S., 1997, Landform characterization 

with geographic information systems: 

Photogrammetric Engineering and Remote Sensing, 

v. 63, no. 2, p. 183-191.

Bleakly, D.R., and Thomas, R.P., 1992, Comparison of 

four procedures for estimating basin and sub-basin 

slopes based on a geographic informsation system, in 

1992 ASPRS-ACSM annual convention, Albuquerque, 

New Mexico, ACSM Technical Papers, v. 2, p. 19-28.

Blondel, Philippe, and Parson, L.M., 1997, Quantitative 

characterization of geological processes using 

sidescan sonar imagery (abs.): Fall Meeting 

Supplement to Eos, Transactions of the American 

Geophysical Union, v. 78, no. 46, p. F350.

Bloschl, Gunter, and Sivapalan, Murugesu, 1995, Scale 

issues in hydrological modelling A review, in Kalma, 

J.D., and Sivapalan, Murugesu, eds., Scale Issues in 

Hydrological Modelling: New York, John Wiley, p. 9- 

48. [inventory & prospect]

Boelhouwers, J, Duiker, J.M.C., and van Duffelen, E.A., 

1998, Spatial, morphological and sedimentological 

aspects of recent debris flows in Du Toit's Kloof, 

Western Cape: South African Journal of Geology, v. 

101, no. 1, p. 73-89. [morphometry, but paramaters 

too variable to be helpful]

Bogdanoff, J.L., (and others), 1966, Atlas of off-road 

ground roughness P.S.D.'s and report on data 

acquisition technique: Warren, Michigan, Land 

Locomotion Laboratory, U.S. Army Tank-Automotive 

Center, ATAC Rept. No. 9387 (LL 109), paging 

unknown.

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R.J.Pike/USGSOF99-140

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fractal]

[slope, hypso., incision, sinuosity

Rice-Snow, Scott, 1997, Terrain description as a 

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Ridley, H.M., Atkinson, P.M., Aplin, Paul, Muller-J.-P., 

and Dowman, lan, 1997, Evaluating the potential of 

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Rieger, Wolfgang, 1998, A phenomenon-based 

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Riehle, J.R., Fleming, M.D., Molnia, B.F., Dover, J.H., 

Kelley, J.S., Miller, M.L, Nokelberg, W.J., Plafker, 

George, and Till, A.B., 1997, Digital shaded-relief 

image of Alaska: U.S. Geological Survey 

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Rigon, Riccardo, Rodriguez-lturbe, Ignacio, and 

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Riley, S., 1993, The automated extraction of drainage 

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Rinaldi, Massimo, and Johnson, P.A., 1997, 

Characterization of stream meanders for stream 

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Rinaldo, Andrea, Rodriguez-lturbe, Ignacio, and Rigon, 

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optimal channel networks]

Ritter, Carl, 1852, Bemerkungen uber 

Veranscnaulichungsmittel raumlicher Verhaltnisse bei

R.J.Pike / USGS OF 99-140

43
graphischen Darstellungen durch Form und Zahl (On 

illustrative methods for spatial properties using 

diagrams of form and number; in German; includes 

1826 calc. of circularity index of the continents; read 

Jan. 17, 1828), in Einleitung zur allgemeinen 

vergleichenden Geographie, und Abhandlungen zur 

Begrundung einer mehr wissenschaftlichen 

Behandlung der Erdkunde: Berlin, Sammlung d. Abh. 

Ritters, p. 129-150 (alt. ref.: p. 103ff) [among v. 

earliest morphometry; re-release of "Einleitung," & 

"Allgemeine Vorbemerkungen iiber die festen Formen 

der Erdrinde" (Erdkunde, 1817) & 5 lectures at Akad. 

d. Wissenschaften, Berlin, 1826, 1828, 1833, 1836, 

1850, published before in Abhandlung d. kgl. Akad.... 

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R.J.Pike / USGS OF 99-140

46
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[liked it very much; distinguishes SOC vs.

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Willis, I.C., Arnold, N.C., Sharp, M.J., Bonvin, J.-M., 

and Hubbard, B.P., 1998, Mass balance and flow 

variations of Haul Glacier d'Arolla, Switzerland, 

calculated usinbg digital terrain modelling techniques, 

Chapter 15 in Lane, S.N., Richards, K.S., and 

Chandler, J.H., eds., Landform Monitoring, Modelling 

and Analysis: New York, Chichester UK, John Wiley, 

p. 343-361.

Wilson, J.P, and Gallant, J.C., 1998, Terrain-based 

approaches to environmental resource evaluation, 

Chapter 10/n Lane, S.N., Richards, K.S., and 

Chandler, J.H., eds., Landform Monitoring, Modelling 

and Analysis: New York, Chichester UK, John Wiley, 

p. 219-240.

Wilson, J.P., Spangrud, D.J., Nielsen, G.A., Jacobsen, 

J.S., and Tyler, D.A., 1998, Global positioning system 

sampling intensity and pattern effects on computed 

topographic attributes: Journal of the Soil Science 

Society of America, v. 62, no. 5, p. 1410-1417. 

[truck-mounted GPS; small elev. diffs. have big 

effects on topo. params.]

Wilson, T.H., and Dominic, Jovita, 1998, Fractal 

interrelationships between topography and structure: 

Earth Surface Processes and Landforms, v. 23, no. 

6, p. 509-525. [24 profiles @ 15-m res.]

Wingham, D.J., Ridout, A.J., Scharroo, Remko, Arthern, 

R.J., and Shum, C.K., 1998, Antarctic elevation 

change from 1992 to 1996: Science, v. 282, no. 5388, 

p. 456-458. [low dimin. (1cm/yr) fr ERS radar 

altimetry; clever color elev-change map]

Wise, S.M., 1998, The effect of GIS interpolation errors 

on the use of digital elevation models in 

geomorphology, Chapter 7 in Lane, S.N., Richards, 

K.S., and Chandler, J.H., eds., Landform Monitoring, 

Modelling and Analysis: New York, Chichester UK, 

John Wiley, p. 139-164.

Wojcik, Antoni, 1997, Landslides in the Koszarawa 

drainage basin Structural and geomorphological 

control (Western Carpathians, Beskid Zywiecki Mts.) 

(in Polish with English summary and figure and table

captions): Biuletyn Panstwowego Instytutu 

Geologicznego (Warsaw), no. 376, p. 5-42. [n= 475; 

slope angle; concave, flat, convex slopes; azimuth 

freq.]

Woldenberg, M.J., 1968, Hierarchical systems cities, 

rivers, alpine glaciers, bovine livers, and trees: 

Cambridge, MA, Harvard University, Harvard Papers 

in Theoretical Geography, No. 19, paging unknown.

Woo, A., Poulin, P., and Fournier, A., 1990, A survey of 

shadow algorithms: IEEE Computer Graphics and 

Applications, v. 10, no. 6, p. 13-32.

Wood, J.D., 1996, Scale-based characterisation of 

digital elevation models, Chapter 14 in Parker, D., ed., 

Innovations in GIS 3: London, Taylor & Francis, 

paging unknown.

Woods, E.B., 1974, Spatial variation of hillslope profiles 

in the Cumberland Plateau, Kentucky: The 

Professional Geographer, v. 26, no. 4, p. 416-420.

Woods, Ross, Sivapalan, Murugesu, and Duncan, 

Maurice, 1995, Investigating the representative 

elementary area concept An approach based on 

field data, in Kalma, J.D., and Sivapalan, Murugesu, 

eds., Scale Issues in Hydrological Modelling: New 

York, John Wiley, p. 49-70. [the REA concept]

Wright, Dawn, Wood, Ray, and Sylvander, Brendan, 

1998, ArcGMT a suite of tools for conversion 

between ARC/INFO and Generic Mapping Tools 

(GMT): Computers and Geosciences, v. 24, no. 8, p. 

737.744. [useful!; UNIX shell scripts & AML files w/ 

menu interface for Arc/INFO]

Xia, Z.-G., and Clarke, K.C., 1997, Approaches to 

scaling of geo-spatial data, Chapter 15 in Quattrochi, 

D.A., and Goodchild, M.F., eds., Scale in Remote 

Sensing and GIS: New York, Lewis Publ. (CRC), p. 

309-360. [mostly fractals of random-field topog., 

<'95; good review & biblio.]

Xiekang, Wang, and Duo, Fang, 1998, A new index of 

quantitative study on (sic) the drainage geomorphic 

system (in Chinese with English abstract): Mountain 

Research (Chengdu), v. 16, no. 1, p. 8-12. [intro to 

fractals]

Yakimenko, E.L., 1990, Morfometriya rel'yefa i 

geologiya (Morphometry of relief and geology; in 

Russian): Trudy Instituta Geologii i Geofiziki 

(Novosibirsk), no. 736, 200 p. [313 references]

Yang, Chenghai, Peterson, C.L., Shropshire, G.J., and 

Otawa, Toru, 1998, Spatial variability of field

R.J.Pike/USGSOF99-140

54
topography and wheat yield in the Palouse region of 

the Pacific Northwest: Transactions of the American 

Society of Agricultural Engineers: v. 41, no. 1, p. 17- 

27. [slope & aspect affect yield]

Yasso, W.E., 1965, Plan geometry of headland bay 

beaches: Journal of Geology, v. 73, no. 5, p. 702- 

714. [logarithmic spiral fit to Half Moon Bay, CA]

Yeh, Harry, 1998, Tsunami researchers outline steps for 

better data: Eos, Transactions American Geophysical 

Union, v. 79, no. 40, p. 480 & 481. [need better 

bathymetry, smaller grid spacing as ocean depth 

decreases]

Yesyunin, R.Y., 1975, Description of bottom relief by 

means of the spatial correlation function: 

Oceanology, v. 15, p. 719-721.

Yingst, R.A., and Head, J.W. Ill, 1997, Volumes of lunar 

lava ponds in South Pole-Aitken and Orientale 

basins Implications for eruption conditions, 

transport mechanisms, and magma source regions: 

Journal of Geophysical Research, v. 102, no. E5, p. 

10,909-10,931.

Yoeli, Pinhas, 1959, Relief shading: Surveying and 

Mapping, v. 19, no. 2, p. 229-232. [pre-computer 

revolution]

Young, W.H., and Isbell, D.M., 1978, Production 

mapping with orthophoto digital terrain models, in New 

Technology for Mapping, International Symposium, 

Ottawa, October 2-6, Commission IV, International 

Society of Photogrammetry: Proceedings, p. 328- 

353. [also 1978, Photogrammetric Engineering, v. 

44, no. 12, p. 1521-1536]

Zaborski, Bogdan, 1931, Analiza morfometryczna 

rzezby terenu nizowego (Morphometric analysis of 

the relief of a lowland territory; in Polish with English 

summary p. 36-39): Wiadomosci Sluzby 

Geografocznej, Wart. Wojskowego Inst. Geogr. 

Warszawie, v. 12, p. 1-39. [important: illustr. 

methods incl. azimuth freq.; rel. relief not enough, 

esp. in gentle areas; 40-item biblio.; ref. elsewhere: 

"Travaux de I'lnst. Geogr. de I'Univ. de Cracovie, no. 12"]

Zaborski, Bogdan, 1959, The role of the 'development of 

surface' in the description of relief (abs.): Annals of 

the Association of American Geographers, v. 49, no. 

2, p. 221. [mentions this in his 1931 paper]

Zakharov, S.A., 1940, Importance of slope aspect and 

gradient for soil and vegetation distribution in the 

Great ("High"?) Caucasus (in Russian): USSR Journal 

of Botany, v. 4, no. 5, p. 378-405. [see Zingg, 1940]

Zamorano O., J.J., 1990, Analysis ingenierogeomorfologico de la Cuenca de Mexico (in Spanish): 

State Univ. Moscow, Lomonosov, USSR, unpublished 

doctoral dissertation, 234 p.

Zavoianu, Ion, 1968, Morphometrical features of the net 

in the Doftana basin (in Roumanian): Stud. Cercet. 

Geol. Geofiz., Geogr., Ser. Geogr., v. 15, no. 2, p. 

195-204.

Zavoianu, Ion, 1975, A morphometric model for the 

surface area of hydrographic basins (in Romanian): 

Rev. Roum. Geol. Geophys., Geogr., Ser. Geogr., v. 

19, no. 2, p. 199-210.

Zhan, F.B., and Buttenfield, B.A., 1996, Multi-scale 

representation of a digital line: Cartography and 

Geographic Information Systems, v. 23, no. 4, p. 206- 

228.

Zhao, Kelin, 1996, Fuzzy identification and manipulation 

of source channels in channel networks derived from 

digital models: University of Saskatchewan, 

unpublished M.Sc. thesis, paging unknown, 

[complex; reproduced blue-line networks on maps]

Zingg, A.W., and Woodruff, N.P., 1951, Collaboration of 

a portable tunnel for simple determination of 

roughness and drag on field surfaces: Agronomy 

Journal, v. 43, p. 191 -194. [cited by Saleh, 1997]

Zlatopolsky, A.A, 1997, Description of texture 

orientation in remote sensing data using computer 

program LESSA: Computers and Geosciences, v. 23, 

no. 1, p. 45-62.

Zobeck, T.M., and Onstad, C.A., 1987, Tillage and 

rainfall effects on random roughness A review: Soil 

Tillage Research, v. 9, no. 1, p. 1-20.

Zwally, H.J., Bindschadler, R.A., Brenner, A.C., Martin, 

T.V., and Thomas, R.H., 1983, Surface elevation 

contours of Greenland and Antarctic ice sheets: 

Journal of Geophysical Research, v. 88, no. C3, p. 

1589-1596. [SEASAT-1]

R.J.Pike / USGS OF 99-140

55
CORRECTIONS

Baulig, Henri, 1926, Sur une methode altimetrique 

d'analyse morphologique appliquee a la Bretagne 

Peninsulaire (in French): Bulletin de I'Association de 

Geographies Francais, v. 10, no. 1, p. 7-9. [altimetric 

freq. from contour map data]

Clarke, K.C., 1995, Terrain Analysis, p. 249-276 

(Chapter 13) in Analytical and Computer Cartography, 

2nd ed.: Englewood Cliffs, NJ, Prentice-Hall, 334 p. 

[with diskette; 1st ed. (1990): p. 204-237]

Devdariani, A.S., 1976, Mathematical analysis in 

geomorphology (in Russian): Moscow, Izd. Nedra, 

155 p. [47 figs., 88 refs.]

Humboldt, Alexander von, 1816, Sur ('elevation des 

montagnes de I'lnde (in French): Annales de Chimie et 

de Physique, v. 3, p. 297-317. [also cited as "1816, 

Memoire sur les montagnes de I'lnde" (same serial & 

vol.), p. 303"; "1820, (same title & serial), v.14"; and 

"1816, (same title), Annales de Chimie, (same vol. & 

pg.)"] [among his earlier height determinations; said 

to have observed in 1807 that heights of only 62 

mountains had been measured and he had accounted 

for half]

Humboldt, Alexander von, 1825, De quelques 

phenomenes physiques et geologiques qu'offrent les 

Cordilleres des Andes de Quito, et al partie 

occidentale de Himalaya (in French): Annales des 

Sciences Naturelles, v. 4, p. 225. [also cited in 

German as Kamm- und Gipfelhohe der wichtigsten 

Gebirge (Crest and summit heights of the most 

important mountains), same ref.]

Humboldt, Alexander von, 1828, Hohenbestimmungen in 

der peruanischen Andeskette (Elevation 

determinations in the Peruvian Andes chain; in 

German): Poggendorff's Annalen der Physik und 

Chemie, v. 13, no. 3, art. XV, p. 514-522. [also cited 

in German as Hohenverhaltnisse zwischen den 

Kammen und Gipfeln der Gebirge (Height ratios 

between mountain crests and summits), same ref.]

Humboldt, Alexander von, 1842, Versuch die mittlere 

Hohe der Continente zu bestimmen (Attempt to 

determine average elevations of the continents; in 

German): Abhandlungen der beriiner Akademie der 

Wissenchaften (paper read July 18), Monatsberichte, 

p. 233-244. [also published: 1842, Poggendorff's 

Annalen der Physik und Chemie, v. 57, no. 3, art. VIII, 

p. 407-419; 1843, Edinb. New Phil. Jour., v. 34, p. 

326-337; 1843, Napoli, Rendiconto, v. 2, p. 315-321] 

[average height, the morphometric innovation for 

which he is best known]

Jackson, Julian, 1843, Hints on the subject of 

geographical arrangement and nomenclature: Journal 

of the Royal Geographical Society, v. 4, p. 72-88. 

[earliest known topological ordering of streams in 

plan]

Kiuchi, S., 1935, Hypsographic curves of Japanese 

volcanoes (in Japanese): Geographical Review of 

Japan (Tokyo), v. 11, p. 688-702.

Milne, John, 1878, On the form of volcanoes: Geological 

Magazine, v. 15, no. 8, article I, p. 337-345. 

[accurate concave profiles, traced from photos, said 

to resembles logarithmic curve. "... the first attempt 

to assign a definite geometrical form to a natural 

surface." (Becker, 1885)]

Palmer, Bruce, 1984, Symbolic feature analysis and 

expert systems, in International Symposium on 

Spatial Data Handling, August 20-24, University of 

Zurich-lrchel, Switzerland: Proceedings, v. 2, p. 465- 

478.

Row, LW. Ill, Hastings, D.A., and Dunbar, P.K., 1995, 

TerrainBase worldwide digital terrain data, 

Documentation Manual: Boulder CO, National 

Geophysical Data Center, for CD-ROM Release 1.0, 

179 p.

Schroter, J.H., 1791, Selenotopographische Fragmente 

zur genauern Kenntniss der Mondflache, ihren 

erlittenen Veranderungen und Atmosphare (in 

German), vol. 1: Lilienthal, self-published; Helmstadt, 

Carl Gottfr. Fleckeisen, 676 p., plates 1-43. 

["Schroter's Rule", equivalence of crater bowl & rimcrest volumes, from measured crater dimensions]

Schroter, J.H., 1802, Selenotopographische Fragmente 

zur genauern Kenntniss der Mondflache, ihren 

erlittenen Veranderungen und Atmosphare (in 

German), vol. 2: Gottingen, Vandenhoech & 

Ruprechschen (printer: J.C. Baier), 565 p., plates 44- 

75. ["Schroter's Rule", equivalence of crater bowl & 

rim-crest volumes, from measured crater dimensions]

Slaymaker, H.O., ed., 1968, Morphometric analysis of 

maps: British Geomorphological Research Group, 

Occasional Paper No. 4, 67 p. [1966 symposium; 7 

separate papers; mimeo]

Turcotte, D.L., 1997, Fractals and chaos in geology and 

geophysics (2nd ed.): Cambridge University Press, 

UK, 398 p. [1sted. 1992, 221 p.]

Turner, A.K., D'Agnese, F.A., and Faunt, C.C., 1996, 

Digital Elevation Model (DEM) file of topographic 

elevations for the Death Valley Region of southern 

Nevada and southeastern California processed from 

U.S. Geological Survey 1-Degree (3-arc-second) 

Digital Elevation Model data files: U.S. Geological 

Survey, Open-file Report 95-287, 9 p.

R.J.Pike / USGS OF 99-140

56
Turner, M.G., O'Neill, R.V., Gardner, R.H., and Milne, 

B.T., 1989, Effects of changing spatial scale on the 

analysis of landscape pattern: Landscape Ecology, 

v. 3, nos. 3-4, p. 153-162. [use indices Diversity, 

Dominance, & Contagion to assess Grain & Extent]

Xia, Zong-Guo, 1993, The Uses and Limitations of 

Fractal Geometry in Terrain Modeling: New York, City 

University of New York, Department of Geography, 

unpublished Ph.D. dissertation, 252 p.

Young, R.N., 1954, The philosophy of landform 

classification, Part I in A Geographic Classification of 

the Landforms of Puerto Rico: Madison, Wl, 

University of Wisconsin, Department of Geography, 

unpublished Ph.D. dissertation, p. 1-ca. 60. [stateof-art review & discuss, of morphometry; climate 

taxonomy analog; much old German material; v. likely 

the source of W.F. Wood's direction]

R.J.Pike / USGS OF 99-140

57