mapping north african landforms using continental scale...

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Remote Sensing of Environm

Mapping North African landforms using continental scale unmixing

of MODIS imagery

John-Andrew C. Ballantine a,*, Gregory S. Okin b, Dylan E. Prentiss a, Dar A. Roberts a

aDepartment of Geography, University of California Santa Barbara, EH3611, Santa Barbara, CA 93106, USAbDepartment of Environmental Sciences, University of Virginia, Charlottesville, VA 22904-4123, USA

Received 14 December 2004; received in revised form 25 April 2005; accepted 29 April 2005

Abstract

We describe the production of a landform map of North Africa utilizing moderate resolution satellite imagery and a methodology that

is applicable for sub-continental to global scale landform mapping. A mosaic of Moderate Resolution Imaging Spectroradiometer

(MODIS) apparent surface reflectance imagery was compiled for Africa north of 10- N. Landform image endmembers were chosen to

characterize ten different types of vegetated and unvegetated desert surfaces: alluvial complexes, dunes, dry and ephemeral lakes, open

water, basaltic volcanoes and flows, mountains, regs, stripped, low-angle bedrock surfaces, sand sheets, and Sahelian vegetation. Multiple

Endmember Spectral Mixture Analysis (MESMA) was applied to the MODIS mosaic to estimate landform and vegetation endmember

fractions. The major landform in each MODIS pixel was identified based on the majority endmember fraction in two- or three-endmember

models. Accuracy assessment was conducted using two data sources: the historic Landform Map of North Africa [Raisz, E. (1952).

Landform Map of North Africa. Environmental Protection Branch, Office of the Quartermaster General.] and Landsat Thematic Mapper

(TM) data. Comparison with the Raisz landform map gave an overall classification accuracy of 54% with significant confusion between

alluvial surfaces and regs, and between sandy and clayey surfaces and dunes. A second validation using 20 Landsat images in a stratified

sampling scheme gave a classification accuracy of 70%, with confusion between dunes and sand sheets. Both accuracy assessment

schemes indicated difficulty in vegetation classification at the margin of the Sahel. A comparison with minimum distance and maximum

likelihood supervised classifications found that the MESMA approach produced significantly higher classification accuracies. This digital

landform map is of sufficiently high quality to form the basis for geomorphic studies, including parameterization of the surface in global

and regional dust models.

D 2005 Elsevier Inc. All rights reserved.

Keywords: Sahel; Sahara; Landform; Desert; Dust source; MESMA; Landform endmembers; Wind erosion

1. Introduction

The Sahara Desert is the largest in the world and

arguably the most diverse in terms of the range of landforms

found within it. Tucker and Nicholson (1999) found the

mean size of the Sahara Desert, between 1980 and 1997,

was 9,149,000 km2. The size of this region makes the

traditional mapping methods of aerial photography and field

surveying of limited use. Moderate resolution multispectral

0034-4257/$ - see front matter D 2005 Elsevier Inc. All rights reserved.

doi:10.1016/j.rse.2005.04.023

* Corresponding author. Tel.: +1 207 299 3703.

E-mail address: [email protected] (J.-A.C. Ballantine).

data allows continental- to global-scale mapping of the

Earth’s surface while retaining sufficient resolution for

geomorphic and ecological studies.

In this paper we describe the production of a landform

map of North Africa (Fig. 1) using data from the moderate

resolution imaging spectroradiometer (MODIS) reflectance

products and a modified spectral mixture analysis (SMA)

approach. The principal purpose of creating a landform map

is to provide a basis for geomorphic studies and providing

greater insight into the landforms in a zone that is often

referred to as ‘‘barren’’ in land cover studies.

SMA models each pixel in an image as a mixture

between a landform endmember (spectrum), vegetation

ent 97 (2005) 470 – 483

10oW

30oN

20oN

30oN

20oN

0oE 10oE 20oE 30oE 40oE

10oW 0oE 10oE 20oE 30oE 40oE

Lake

Study Area

Country

River

0 337.5 675 1,350 2,025 2,700Kilometers

Legend

Morocco

WesternSahara

Mauritania

Senegal

Mali

Algeria

Niger

Libya

Chad Sudan

Egypt

Tunisia

Niger River

Lake Chad

Lake Nasser

Nile River

N

Fig. 1. A map of the study area covering North Africa from 20- W to 40- E and 10- N to 40- N. Political boundaries and major water bodies are included as

references for locations described in the paper.

J.-A.C. Ballantine et al. / Remote Sensing of Environment 97 (2005) 470–483 471

endmember (if it is present and detectable) and shade, an

endmember included to account for shadows and variable

illumination. Multiple Endmember Spectral Mixture Anal-

ysis (MESMA) (Roberts et al., 1998), used here, allows the

optimal spectral endmember to vary between pixels

enabling simultaneous mapping of landform and fractional

vegetation cover.

Landforms are the surface expression of the interaction

between geomorphic processes (erosion, transport, and

deposition) and the underlying lithologies. Landform maps

provide a tool for identifying locations where different

geomorphic processes dominate. As an example, more of

the world’s atmospheric aerosol load comes from dust

eroded from Saharan sources than from any other region

(Prospero et al., 2002). The Sahara includes many signifi-

cant dust sources, including the two largest source areas in

the world (Goudie & Middleton, 2001; Prospero et al.,

2002). Atmospheric modelers seek to understand dust

transport and the role of dust in the radiation budget of

the atmosphere, but the large-scale surface conditions

associated with the mobilization of dust are still uncertain

(e.g. Gillette, 1999; Luo et al., 2003; Mahowald et al., 2002;

Marticorena et al., 1999).

In addition to their importance for geomorphic and

atmospheric studies, landform maps are also good predictors

of soil types, runoff/recharge potential, and vegetation

cover. Because of the relative ease of modeling the distinct

spectral character of vegetation and the importance of

vegetation communities in global models, most global-scale

mapping has focused on the vegetation component of land

cover (Friedl et al., 2002; Hansen et al., 2000; Myneni et al.,

2002). Tucker and Nicholson (1999) examined changes in

land cover in the Sahel and Sahara from 1980 to 1997 and

found that changes in the desert margin follow climatic

trends. Defries et al. (2000) used SMA with temporal

endmembers to map woody vegetation cover at the global

scale.

Land cover mapping, from forest stand to global scale,

has seen considerable research but is biocentric, classifying

areas of sparse vegetation as ‘‘barren’’ or ‘‘bare ground’’.

The mapping of landforms has received less attention. The

geomorphology of Africa, in particular, has not been

approached, in spite of the clarity and diversity of landforms

in Africa’s vast desert regions. Where Saharan nations have

had the means to perform mapping studies, they have

focused on geology (mostly for mineral, oil, and water

exploration), soils (for agriculture), and vegetation cover;

each of these map types gives hints about landforms (e.g.

aeolian deposits, aridisols, or bare ground). Some interna-

tional agencies have created global maps of soil and

vegetation properties, but the data are at a coarse scale

and are often suspect in remote regions.

Tsvetsinskaya et al. (2002), produced a map of surface

albedo for North Africa and the Arabian Peninsula from

MODIS, and compared these values with soil and lithology,

but did not go so far as attempting to describe landforms. A

landform map of the Sahara Desert was created by Erwin

Raisz (1952) from aerial photos, existing maps, and ground

surveys. This hand-drawn product remains the most detailed

landform map of the Sahara in existence. The Raisz

landform map of North Africa is available for purchase

through www.raiszmaps.com or on loan at many academic

http://www.raiszmaps.com

J.-A.C. Ballantine et al. / Remote Sensing of Environment 97 (2005) 470–483472

map libraries. In spite of its many qualities, the Raisz map is

an analog product of indeterminate resolution (minimum

mapping unit on the order of kilometers), and therefore

better for use as a reference than as a basis for the analysis

of landform properties. The map we produced improves on

the Raisz map in that it is reproducible, digital, and based on

a single data source. The approach used here also enables

simultaneous analysis of fractional vegetation coverage, and

thus supplements existing vegetation monitoring method-

ologies and more traditional land cover classifications.

2. Methods

2.1. Desert landforms

The Soil Science Society of America (www.soils.org)

defines a landform as ‘‘any physical, recognizable form or

feature on the earth’s surface, having a characteristic shape,

and produced by natural causes’’. One of the challenges of

creating a landform map from satellite imagery was trans-

lating from this form-based definition of landforms to a

spectral definition wherein all of the sub-pixel scale elements

of a given landform created a signature in spectral space that

could define that landform. For the purposes of this work, a

landform was considered to be a landscape element that was

spatially and spectrally distinct using 500-m resolution and

seven wavelength bands of MODIS reflectance imagery. In

cases where landforms might be spectrally confused (e.g.

dune fields and sand sheets), we attempted to distinguish

them spectrally, but also noted that many landforms with

similar spectra are also functionally similar. Ultimately,

classes where there is confusion may need to be combined or

further defined using other data sources.

Clements et al. (1957) described 10 major landforms for

the deserts of the world, including alluvial fans, sand seas,

playas, river plains, dry watercourses, mountains, recent

volcanic deposits, low-angle bedrock surfaces, desert flats,

and badlands. A similar set appears in the landform map of

Raisz (1952). Drawing on the landform classes of Raisz

and refining them to the set of landforms that may be

identified spectrally at the scale of MODIS, we identified

nine classes of landforms. These were alluvial fan systems,

dune fields, dry lakebeds, open water bodies, basaltic

volcanoes and flows, sedimentary mountain ranges, regs,

stripped bedrock surfaces, and sandsheets. Vegetated

surfaces were added as a class for areas where vegetative

cover was significant enough to obscure the underlying

landform.

The alluvial fan class includes both complexes of

alluvial fans that flank mountains and some incised plateaus.

The fan complexes are composed of unsorted sediments and

are frequently incised by ephemeral or paleo-channels.

Some alluvial systems may also have vegetation cover

because of runoff and recharge from adjacent mountains or

proximity to desert margins. The fan complexes of the

southern flank of the Atlas Mountains in Tunisia, Algeria,

and Morocco (e.g. 33.5- N, 2.5- E) are good examples of

this landform.

Ergs and dunefields are regions where sand piles into

systems of dunes or sandy plains. In the great ergs of the

central Sahara, sand dunes hundreds of meters high are

common. In relatively sediment-starved situations linear

dunes and barchan dunes with bedrock, gravel flats (regs),

or packed clayey surfaces between dunes predominate (e.g.

Thomas, 1997). In general, ergs appear bright in the MODIS

imagery. A classic dunefield example is the Erg Occidental

of Algeria (31- N, 2.5- E).Ephemeral and paleo-lakes are characterized by fine

sediments laid down by floods in recent times and/or during

previous pluvial episodes. Lake sediments have the charac-

teristic brightness of fine sediments, especially in the short-

wave infrared (SWIR) wavelengths (Okin & Painter, 2004).

The lakebed associated with paleo-lake mega-Chad in the

Bodele Basin of Chad (17- N, 18- E) is a good example of

this landform.

Open water occurs in the Sahara, associated with the

Niger and Nile Rivers, Lake Chad, Lake Nasser, and coastal

zones. Open water bodies are the darkest features in the

Sahara. As an example, Lake Nasser is located in southern

Egypt at 23.2- N, 32.8- E.Basaltic volcanoes and flows are spectrally almost as

dark as open water. Basaltic features can be found as

extensive formations in various parts of the central Sahara

such as the Black Haruj flows of Libya (27.5- N, 17.5- E).Mountain ranges in the Sahara are characterized by

uplifted sedimentary and metamorphic rocks (e.g. the

Ahaggar Mountains of Algeria, 23.2- N, 6- E). Sedimentary

and metamorphic mountain ranges appear dark in the

MODIS imagery, but not as dark as basaltic features.

Because of orographic rainfall, some vegetation can be

found in mountainous areas, even in the core of the desert.

As a result, there is a component of vegetation spectra in the

mountain landform class.

Regs or serirs may either represent deflationary land-

scapes, where aeolian activity has removed fine particles

leaving lag gravels, or accretionary landscapes, where

gravels protect underlying fine sediments from wind erosion

(e.g. McFadden et al., 1987). Whether deflationary or

accretionary, these surfaces appear darker than surfaces of

sandy or finer texture, due to the darker coloring of larger

clasts, coarser particles casting shadows, and possibly due to

the development of varnish on these particles. The Serir of

Kalansho in Libya (27.5- N, 21.5- E) typifies this landform.

Stripped bedrock includes low-angle bedrock surfaces

where erosive processes have removed the majority of the

surface regolith. These landforms may be cut by drainages or

marked by hummocky features and sinkholes in limestone

landscapes, with some sand collecting in hollows (Taylor &

Howard, 1999). Stripped bedrock surfaces are more common

in the western part of the Sahara Desert in countries such as

Mauritania and Western Sahara (23- N,13.5- W).

http://www.soils.org


Sandsheets are sedimentary plains covered in fine

sediments from loose sand to packed silt or clay. In systems

of large linear dunes, this may include the troughs between

dunes. This class is widespread with an example in Sudan at

17- N, 25- E.Vegetation is the dominant land cover in some mountain-

ous areas and in the Sahel (e.g. 17.5- N, 12.5- E). A variety

of vegetation exists in North Africa from sparse shrubs in

the arid core of the Sahara to the more densely vegetated

surfaces of the northern Sahara (e.g. Atlas plateaus, subaltic

alluvial complexes, and the Fezzan region of Libya). In the

central Sahara, more vigorous vegetation may be found in

mountainous areas (where orographic effects are strong

enough to generate rainfall), near phreatic oases, and along

the riparian zones of rivers. Vegetation has a characteristic

spectral signature and vegetation cover can be separated

from the land surface using the MESMA technique.

Although vegetation was treated as static in this study,

vegetation is a dynamic quantity, and varies in its cover

extent depending on the time of year and the amount of

rainfall during the year in question (e.g. Weiss et al., 2004).

2.2. Data collection

A mosaic of MODIS 500-meter resolution, land-surface

reflectance product (MOD09GHK) covering North Africa

from 10- N to 40- N and 20- W to 40- E was created (Fig.

2). Cloud-free imagery was chosen from the period between

November 1 and December 26, 2000. For one MODIS tile

covering Tunisia and Algeria, two images from this period

were combined to avoid clouds. These dates represent the

dry season on the southern edge of the Sahara and come

before most winter rains in the North.

2.3. MESMA

The digital landform map was created using MESMA

(Roberts et al., 1998), applied to theMODISmosaic for North

Fig. 2. A false color mosaic of MODIS MOD09GHK imagery for North Africa (R

The coverage of Landsat scenes used for validation is shown in translucent red. (Fo

referred to the web version of this article.)

Africa shown in Fig. 2. SMA typically assumes that the

reflectance of a given pixel (qVk) is composed of a linear

combination of a few ‘‘pure’’ endmember spectra (e.g. Smith et

al., 1990). Endmember spectra can be chosen from represen-

tative, homogeneous areas in the image (image endmembers)

or an existing library of reference spectra for materials

common to the image in question (reference endmembers).

qVk ¼XNi¼1

fi4qik þ ek ð1Þ

Where qik is the reflectance of endmember i in band k and fi is

the fraction of thatendmember. N is the number of endmem-

bers and ek; the residual error. Thefractions are constrained by:

XNi¼1

fi ¼ 1 ð2Þ

The fit of the endmember models can be assessed using the

root mean squarederror (RMSE) of ek:

RMSE ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiXMk¼1

ekð Þ2

M

vuuuutð3Þ

where M is the number of bands (7 for this MODIS product)

(Dennison & Roberts, 2003).

The MESMA approach differs from SMA in that the

spectrum for each pixel in the image is allowed to be

unmixed by a different set of endmembers from an overall

endmember library for the image (Roberts et al., 1998). In

our study, the MESMA technique allowed a greater

number of endmembers, representing a greater number

of surface materials, to be used. As a result, MODIS

images of widely varying surface covers were able to be

modeled based on the spectra of these surface covers. The

SMA and MESMA techniques have been described in

greater detail in Dennison and Roberts (2003) and Roberts

et al. (1998).

ed=2130 nm, Green=859 nm, Blue=555 nm). The projection is sinusoidal.

r interpretation of the references to colour in this figure legend, the reader is


2.4. Endmember selection

The spectral response of a landform is a composite of the

spectral response of the landform’s soils, exposed rock,

green vegetation, non-photosynthetic vegetation (NPV) and

shading due to topography and surface materials. Therefore,

a landform’s reflectance spectrum is a mixture of the spectra

of its materials. Each MODIS pixel may cover multiple

landforms and therefore have a reflectance spectrum that is a

mixture of landform spectra. We assumed that no more than

two landforms or vegetation spectra, in addition to shade,

described any given pixel.

Previous studies using the MESMA technique (e.g.

Dennison & Roberts, 2003; Roberts et al., 1998) were at a

scale fine enough to distinguish individual surface materials

and therefore were able to use laboratory and field reference

spectra of these materials. Thesseira et al. (2002) compared

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A1A2A3L1L2L3M1M2M3

BursageBig Leaf Sage Rabbit BrushImage Riparian

Fig. 3. Spectra of the endmembers being used in the MESMA. Spectra for the all

illustrating the similarity between dune (D), sandsheet (S), and reg (R) classes are

number representing the subclass. Vegetation (part c) and NPV (part d) endmember

MODIS wavelengths.

the SMA and MESMA approaches for studying semi-arid

landscapes in Namibia at moderate spatial and spectral

resolution and found that mixture methods produced poor

results when identifying vegetation community cover

fractions. Defries et al. (2000) used SMA on a number of

metrics derived from multi-temporal imagery for determin-

ing global land fields of woody vegetation cover. We also

had to move away from data that directly represents

individual surface materials in expanding the MESMA

methodology to sub-continental scale. We made use of

composite endmembers to capture all of the spectral mixing

within a given landform (a similar approach could be used

for vegetation cover at this scale). Endmembers were

extracted from image locations that were known to be

representative of a given landform. Landform endmembers

are shown in Fig. 3a,b. This approach was similar to the

image endmember concept (Smith et al., 1990) in that each

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Dry GrassPlant LitterRed Stems

uvial (A), Lake (L), and mountain (M) classes are shown in part a. Spectra

shown in part b. Each broad landform class is indicated with a letter and a

s are taken from lab spectra (except in the case of riparian) and resampled to


landform endmember was considered to represent a pure

landform drawn from the MODIS imagery. Landform

endmembers were chosen from desert areas where vegeta-

tion cover would be minimal so as to avoid components that

would vary in time.

Because vegetation cover changes on interseasonal and

interannual time scales, while landform type is typically

stable on the order of 100s to 1000s of years, separate

endmembers for vegetation were used. Three reference NPV

(plant litter, dry grass, and red stems), three reference

vegetation (big leaf sage, rabbit brush, and bursage), and

one image vegetation endmember representing riparian

vegetation were used for vegetated regions in the image.

The vegetation and NPV spectra are shown in Fig. 3c and d,

respectively. The reference endmembers come from the

library described in Roberts et al. (1993) which is largely

composed of North American vegetation. No significant

library of Saharan and sub-Saharan vegetation was available

for this study. Although the spectra were collected from

North American sites, these spectra are broadly representa-

tive of the range of semiarid to arid NPV and vegetation

spectra. The spectral library was convolved to MODIS

wavelengths using the MODIS filter functions. Reference

endmembers were used in the case of vegetation because

vegetation was rarely the dominant endmember in a pixel

for our study area. Leafy irrigated or riparian vegetation

dominated where vegetation was the major endmember in

the pixel. Desert vegetation tends to be more sparse and

woody or grassy. It was therefore difficult to locate a ‘‘pure’’

vegetation pixel that would also represent sparse desert

vegetation. For pixels modeled by one of the vegetation

endmembers, the vegetation fraction gave an indication of

percent vegetation cover within that pixel. Using several

vegetation endmembers allowed for a range of semiarid,

riparian, and non-photosynthetic vegetation types to be

accounted for, but for the purpose of the landform map, all

of the vegetation endmembers were lumped into one

vegetation class.

One-hundred and nine endmember sites were chosen

from the MODIS mosaic using the map of Raisz (1952) as a

guide for landform type. Spectra from each of these sites

were compiled to form a spectral library of landform

endmembers for North Africa. These sites fell into six

broad landform classes (alluvial, dunes, lakes, mountains,

regs, and sandsheets) based on the classes identified in the

Raisz map. The spectra from each broad class were

statistically divided into two to three subclasses using a k-

means unsupervised cluster analysis (Funk et al., 2001). As

an example, the broad mountain class had three statistically

separate subclasses, two of which were identified as

representing mountains, and the other identified as repre-

senting basaltic volcanoes and flows.

Tompkins et al. (1997) emphasized the importance of the

selection of good spectral endmembers for any SMA.

Because of the diversity of classes in this study, we chose

the endmember average RMS (EAR) method of Dennison

and Roberts (2003) as the principal method for selecting

landform endmembers. The EAR technique selects the

endmember that is most representative of a class of

endmembers to represent that class. EAR worked well for

the broadly defined classes of this study where finding

extreme endmembers might not have represented the full

diversity of each landform class.

In order to identify the landform spectrum that was most

distinct, the spectral library of 109 landform endmembers

was unmixed by two endmember models of shade and each

of the other endmembers in the library to calculate EAR

values as described by Dennison and Roberts (2003). The

model constraints described by Dennison and Roberts were

found to work well for these data. Endmember fractions

were constrained to less than 106% with best-fit models

greater than this value being set to 106% and the RMSE

calculated from this value.

The EAR method selected an endmember representative

for a subclass by finding the endmember with the lowest

RMSE when modeling other endmembers in its subclass:

EARAi;A ¼

Xnj¼1

RMSEAi;Aj

n� 1ð4Þ

where A was the subclass, Ai was the landform endmember

in question, n was the number of spectra in subclass A, and

Aj was the spectrum being modeled by Ai. Thus, the

endmember representing basaltic flows in the Ahaggar

Mountains of Algeria was used to model the other basalt

endmembers (basalt is subclass M1 in Fig. 3a). The average

of the RMSE values from each model was the EAR value

for the Ahaggar basaltic endmember. Because the Ahaggar

basaltic endmember’s EAR value was lower than that of the

Tibesti Mountains and the other basalt endmembers, the

Ahaggar basaltic endmember was picked as the representa-

tive endmember for subclass M1. The landform spectra thus

picked are shown in Fig. 3a.

3. Modeling with MESMA

The modeling of the image with MESMA followed the

methodology of Dennison and Roberts (2003). Two-

endmember models (an endmember and shade) were run

with the constraint that non-shade fractions had to be

between �6% and 106% of the pixel. Cases where

residuals exceeded 2.5% of reflectance for more than 7

contiguous bands or RMSE exceeded 2.5% of reflectance

were left unmodeled. Similar constraints were used for

three endmember models (two endmember spectra and

shade). All possible models were considered such that

there were 24 possible two-endmember models (17 land-

form subclasses and 7 vegetation endmembers) and 276

three-endmember models. For each pixel, the lowest

RMSE two-endmember model was chosen unless the

RMSE of the three-endmember improved upon that of

Fig. 4. The shade endmember fraction image derived from the MODIS mosaic in Fig. 2. The shading bar shows % shade from �6% to 100% with values of

�100 representing bright desert surfaces with effectively no shade. Bright areas near the coast indicate deep water that has not been masked out. Note that the

shade fraction is greater on the east-side of each MODIS tile, expressing the BRDF of vegetation.


the two endmember model by more than 0.8% of

reflectance (Roberts et al., 2003).

4. Results

MESMA produced fraction images of the dominant and

secondary (in three endmember cases) endmembers, along

with the fraction of shade present. Each pixel was coded

with the classes that describe it and the fraction of each

class.

4.1. Shade fraction

In Fig. 2, it is apparent that the east side of each MODIS

tile in the mosaic is darker than the west, particularly in

vegetated regions. This occurs because the bi-directional

reflectance distribution function (BRDF) of surface materi-

als is asymmetrical with more light being back-scattered

than forward-scattered in the case of vegetation. The

variation in brightness across the tile is a function of the

amount of shadowing imaged by the sensor. An advantage

Fig. 5. The vegetation endmember fraction derived from the MODIS mosaic in Fig

of the transects shown in Fig. 6 are indicated.

of using a spectral unmixing approach is that the shade

fraction contains most of this BRDF effect. As a result, the

landform and/or vegetation endmember(s) used to determine

the landform class did not exhibit any variation due to

BRDF effects. The expression of the anisotropic BRDF of

vegetation is apparent in the shade fraction image (Fig. 4).

4.2. Vegetation fraction

The modeled vegetation endmember fraction represents

the fractional ground cover of vegetation (Fig. 5). Fig. 5

expresses the vegetation cover increase from the Sahara

south into the Sahel. Vegetation along the northern margin

of the continent is also apparent. Scattered vegetation in the

core of the Sahara is usually associated with mountain

ranges where orographic rainfall and springs make signifi-

cant vegetation viable. If multi-temporal imagery had been

used, the vegetation fraction could tracked be to show

changes in vegetation cover and its response to rainfall

variation.

The red stems vegetation endmember dominated the

scene because it best modeled Sahel vegetation (Table 1). In

. 2. The shading bar shows percent vegetation cover. Approximate locations

Table 1

Areal coverage and proportion of vegetation fractions in the Fig. 5

Class # Name Area (km2) % Vegetation

18 Dry grass 92,886.75 4.89

19 Plant litter 28,845.25 1.52

20 Red stems 1,568,183.8 82.48

21 Bursage 180.75 0.01

22 Big leaf sage 1226 0.06

23 Rabbit brush 27,119 1.43

24 Image riparian 182,950 9.62

Class # is relative to all endmembers used in this study. Class name

corresponds to those used in Fig. 3b. The ‘‘% Vegetation’’ column describes

the percentage of all vegetated pixels covered by the class in question.


terms of areal coverage, the image riparian vegetation

endmember was the next most common endmember

because of its occurrence in a few dense areas including

the Niger Delta, Lake Chad, and along the Nile River and

into the Nile Delta. The elevated vegetation in southern

Libya (Fig. 5) classified as dry grass and was mixed with the

reg class.

Variation in vegetation cover across the Sahara is further

illustrated by the three transects shown in Fig. 6. All three

transects clearly show the steady rise in vegetation from

north to south in the Sahel (towards the right in the shaded

zone at the right of Fig. 6). At longitude 4.5- W, there is a

zone of higher vegetation cover along the northern margin

of the Sahel because of the vigorous vegetation of the Niger

Delta in southern Mali. North of that, there is very little

vegetation across the Sahara until one reaches the Atlas

Fig. 6. Transects of vegetation fraction oriented north–south across the vegetation

north edge of the image to the south, and show locations of high and low vegetat

shaded squares (16- E), and black triangles (30- E). The Sahel and Nile River and D

arrows.

Mountains in Morocco. The high vegetation fraction at

about 3000 km south in the 16- E transect indicates the

location of Lake Chad. This transect shows an elevated

vegetation fraction in the heart of the Sahara where it

crosses the western side of the Tibesti Mountain range. At

the northern end of the transect, there is a notable vegetated

zone extending from southern Libya to the coast, possibly

representing the Fezzan region which has historically been a

fertile pastoral zone (Bovill, 1968). This agrees with the

selection of dry grass as the endmember for this region.

Traversing the 30- E transect northward from the Sahel, one

finds little vegetation until reaching the Nile River and its

floodplain in the center of Fig. 6. The 30- E transect follows

the northward course of the Nile into the Nile Delta from

this point, showing elevated vegetation cover.

4.3. Classification

In many cases, a two endmember model was adequate to

describe the spectral response of the pixel, in which case the

pixel was labeled as the dominant class. In cases where

shade was the majority class, the pixel was labeled as

unclassified. These high-shade unclassified pixels occurred

in mountainous or basaltic regions, in heavily vegetated

regions of the Sahel, and over open water. Should any these

classes be important to a given user, the class could be

assigned manually.

Some very bright areas were also unclassified because

the brightness of the pixels exceeded 106% of the brightest

fraction image shown in Fig. 5. Samples are taken every 2500 m from the

ion cover. Points on each transect are symbolized by open circles (4.5- W),

elta are shaded and other zones of elevated vegetation fraction are noted by

Table 2

Distribution of landform classes in classified image

Class Cover fraction Color

Alluvial 0.14 Olive

Dunes 0.22 Yellow

Open water 0.01 Blue

Lakebed 0.01 Cyan

Basalt 0.01 Purple

Mountain 0.09 Brown

Reg 0.21 Red

Bedrock 0.03 Magenta

Sandsheet 0.15 Orange

Vegetation 0.13 Green


endmember (D1 in Fig. 3b). Some pixels were brighter

than the brightest endmember because the EAR endmem-

ber selection technique picked endmembers that were

representative of classes, as opposed to the most extreme

in the image. The most prominent case was in the Tenere

Desert of Niger where active dunes had a very high

albedo. This unclassified area was small and encompassed

by the dune class and therefore could easily be corrected

by hand.

In cases where the three endmember model was chosen,

the class with the greatest fraction was considered the

landform class but the relative fractional abundances were

retained. This was particularly useful in the case where

vegetation was the secondary class because a percentage

vegetation cover value could be determined (Elmore et al.,

2000).

4.4. Landform map

The results of the landform classification are shown in

Table 2 and Fig. 7. Dunes and regs were the dominant

landform classes (22% and 21% cover respectively). Dunes

are areas of high sediment availability, limited by transport

capacity, whereas regs are areas of potentially high sediment

storage that have low sediment availability due to the

armoring of the surface (Kocurek & Lancaster, 1999). The

Fig. 7. The landform map of North Africa produced through MESMA applie

(For interpretation of the references to colour in this figure legend, the reader is

sandsheet class is in an intermediate position on this

sediment availability continuum. Although lakebeds and

alluvial complexes are affected by wind erosion and

deposition, they are also heavily influenced by fluvial

activity. Other classes are less affected by the wind transport

system. All of the mosaic, except for very dark and very

bright regions, was classified.

All of the vegetation classes, including NPV, were

lumped into a single vegetation class for the map. The

dominant component of the vegetation class was red stems,

with approximately an order of magnitude more coverage

than any other vegetation type. The dominance of the

vegetation class by an NPV endmember was an indication

both of the dominance of woody vegetation in the Sahel,

and the fact that these images were taken during the

Sahelian dry season.

Some classes appeared in particular regions. The alluvial

class largely occurred in the north in Algeria and from the

coast to the Fezzan region of Libya. This may have been a

result of distinct lithologies in this region (e.g. limestone

bedrock), the more frequent occurrence of alluvial fans

along the flanks of the Atlas Mountains, or the possibility

that the alluvial endmember contained some fraction of

vegetation which was stronger in the north during Novem-

ber and December (the beginning of the Mediterranean wet

season). Both the alluvial and mountain classes appeared in

the transition zone between the Sahel and the Sahara. There

is no mountain range in this zone and this effect will be

discussed in the next section.

With the exception of the band of the mountain class in

the northern Sahel, most occurrences of the mountain and

basalt classes coincided with well known mountain ranges

and basaltic formations. Dry lakebeds were largely confined

to zones in the Bodele Depression of Chad, the coastal

sabkhas of Mauritania, and the ephemeral chotts of Tunisia

and northern Algeria.

Another notable regional tendency was that the stripped

bedrock surfaces occurred in the plateaus of the western

Sahara and along the coast of the Red Sea in the east. The

d to the MODIS mosaic in Fig. 2. Unclassified areas appear in black.

referred to the web version of this article.)

Table 3

Error matrix showing reference classes from the Raisz landform map on the

x-axis and modeled classes from the MODIS-derived landform map on the

y-axis

Model Raisz

A D L B M R T S User’s Sum

Alluvial 84 11 2 0 8 3 1 19 0.66 128

Dune 17 131 0 2 3 25 4 63 0.53 245

Lakebed 0 2 4 0 0 1 0 2 0.44 9

Basalt 0 0 0 6 0 0 0 0 1.00 6

Mountain 12 3 0 0 34 2 1 6 0.59 58

Reg 44 10 1 1 5 48 2 40 0.32 151

Bedrock 5 0 0 0 4 0 27 0 0.75 36

Sandsheet 19 24 0 0 6 15 0 100 0.61 164

Producer’s 0.46 0.72 0.57 0.67 0.57 0.51 0.77 0.43 0.54 797

User’s accuracies are in the right column and producer’s accuracies in the

bottom row, with overall accuracy in the lower right. The class columns are

labeled according to the first letter of the class as spelled out in the model

column with the exception of T which represents the Stripped Bedrock

class. User’s accuracy shows the error of commission and producer’s

accuracy shows the error of omission. The sum column shows the total

number of reference samples in the class. Kappa=0.53.


Raisz landform map confirmed that these areas are

composed of low-angle bedrock surfaces.

4.5. Validation

The lack of existing data sources covering landforms in

the Sahara posed a particular challenge for assessing the

accuracy of a map such as this one. Although coarse in scale

and interpretive by nature, the landform map of Raisz

(1952) was the best source of landform data for the whole of

the Sahara. Trusting that the combination of aerial photo

interpretation and ground surveys applied in the making of

Raisz’ map provided an accurate product, we used this as

our first validation dataset. Landsat images from the Global

Landcover Facility at the University of Maryland (http://

glcf.umiacs.umd.edu/index.shtml) were also used as a

source of validation. Finally, we compared the accuracy of

our landform map to the results of minimum distance and

maximum likelihood classifications of the MODIS mosaic.

4.6. Raisz map

Because the Raisz map was the basis for choosing the

landform classes in this study, the classes from each

dataset were comparable. Although 24 landform and

vegetation endmembers were identified and used in the

making of our landform map, it was found that several of

these landform endmembers were not distinguishable from

one another in the context of the Raisz landform map, in

spite of being statistically separable based on spectral

properties. The 7 vegetation and NPV classes were

collapsed into one vegetation class and the 17 landform

subclasses were condensed to 9 landform classes, making a

total of 10 classes for the purposes of mapping and accuracy

assessment.

To minimize the problems of circularity in using Raisz

for both endmember selection and validation, a regular grid

of locations at latitude–longitude crossings was chosen and

the landform at each crossing was identified independently

in both the Raisz map and the MODIS landform map

produced here. The regular grid sampled the landforms on

the map while retaining the convenience of being able to use

the tic marks provided on the Raisz map. The Raisz map

only described landforms (not vegetation) and only

extended as far south as 16- N so validation sites were

taken every degree from 17- N to the Mediterranean Sea and

from the Atlantic Ocean to the Red Sea. This grid amounted

to 797 validation sites. The error matrix of classes is shown

in Table 3.

Accuracy statistics were calculated as described in

Congalton (1991) and kappa for the Raisz error matrix

was 0.53. The overall accuracy was considered to be the

number of sites where the class was correctly modeled,

divided by the total number of sites and was 54% in this

case. Although lower than desirable, some of this poor fit

may have been due to using a secondary-source, analog map

product for validation. The sources of data and methodology

used in making the map are vaguely defined, but Raisz’

work is well regarded and it is the only landform map

available. It was hard to define the minimum size element of

such a map, but it was considerably larger than the pixels of

the MODIS imagery and therefore fine-scale features may

not have been captured in the reference data.

Open water was not a part of the validation dataset

because of the lack of large water bodies on the continent —

Lake Chad is south of 16 degrees and Lake Nasser had not

yet been flooded in 1952 when the Raisz map was made.

Vegetation was not a part of this validation dataset because

the Raisz map only described landforms with a few

annotations about shrubs or cultivation, and its southern

border was north of the Sahel.

In addition to the potential errors due to the reference

map, there were systematic errors of commission and

omission, as shown by the user’s and producer’s accuracies

(Congalton, 1991), respectively, that illuminated problems

with the creation of the map itself. Producer’s accuracies

ranged from 43% for the sandsheet class to 77% for stripped

bedrock surfaces. The numbers for the basalt and lakebed

classes are deceiving because of the few samples in these

classes. A stratified random sampling approach (Congalton,

1991) would help to clarify the accuracy in classification of

these endmembers and was pursued for the second

validation using Landsat imagery. The low producer’s

accuracy of the alluvial class highlights the confusion with

the reg class and, to a lesser degree, the dune and sandsheet

classes. Low producer’s accuracies also occurred for regs

which were modeled as dunes and sandsheets, and

sandsheets which were modeled as dunes.

The confusions between regs, sandsheets, and dunes are

indicative of the sediment availability continuum with regs

at the availability-limited end, sandsheets in an intermediate

http://glcf.umiacs.umd.edu/index.shtml


position, and dunes at the transport-limited end of the

continuum. Because some validation sites were at inter-

mediate positions along this continuum, the model had

difficulty picking a class. In some cases, even identifying

the class on the Landsat imagery was difficult. In mixed

cases in the arid core of the Sahara, the three-endmember

model picked two of these landforms and indicated the

relative proportion of each, allowing for a more exact

placement of the landform on the sediment supply

continuum.

User’s accuracies showed a pattern of confusion where

modeled regs were actually alluvial or sandsheet surfaces

almost as often as they correctly modeled regs. Modeled

dunes frequently represented sandsheets as well. The

lakebed class had poor accuracies that were partly a function

of the low number of model and reference samples for this

class. This allowed misclassifications or misinterpretations

of the validation dataset to have a greater effect on the

accuracy metrics for this class.

4.7. Landsat imagery

Twenty cloud-free Landsat images from within the

MODIS mosaic study area were randomly selected for

validation with the further constraint that they be from the

same time period as the MODIS imagery (November 1 to

December 26, 2000). The geographic coverage of these

scenes is shown in Fig. 2. The higher spatial resolution of

these images made it possible to identify distinguishing

features for validating surface landforms. For example,

specific duneforms identifiable in the Landsat imagery aided

the distinction between dunefields and sandsheets. The tell-

tale barchan dunes that move across many dry lakebeds

were also apparent in the Landsat imagery.

A stratified random sampling program was developed to

pick 30 sampling sites from each of the 10 classes of the

MODIS landform map in the areas covered by the Landsat

imagery. The Landsat imagery was independently examined

at each sample location and the landform for that location

Table 4

Error matrix of classes from Landsat imagery and modeled classes in the landfor

Model Landsat

A D L W B M

Alluvial 18 3 0 0 0 0

Dune 3 17 0 0 0 0

Lakebed 0 0 23 0 0 1

Water 0 0 0 21 0 0

Basalt 1 0 0 0 20 2

Mountain 4 2 0 0 2 18

Reg 1 1 0 0 0 2

Bedrock 1 1 0 0 1 1

Sandsheet 1 10 1 0 0 1

Vegetation 4 0 0 1 0 1

Producer’s 0.55 0.50 0.96 0.95 0.87 0

Landsat samples were chosen from a stratified random sampling scheme using 30 s

errors. The format of the table is the same as for Table 3. Kappa=0.69.

interpreted. For each class there were between one and nine

sample sites that occurred along a margin between classes,

in very mixed terrain, or off the scene edge due to

reprojection inaccuracies; these samples were discarded.

Table 4 shows the error matrix for all valid samples.

These results covered all classes and gave notably better

overall error numbers (error=0.70, kappa=0.69) than Table

3 (error=0.54, kappa=0.53), in part because of the high

accuracy associated with classes such as water which were

not covered in the Raisz map validation.

Of particular note were the very low producer’s and

user’s accuracies of the sandsheet class and the marginal

numbers of the dune class. A large part of both of these

errors resulted from spectral similarity between these two

classes and considerable confusion. By merging the

sandsheet and dune classes into one, we were able to

increase the overall accuracy from Table 4 to 75% and

Kappa increased to 0.75. Similarly, the user’s accuracy for

the combined class rose to 72% and the producer’s accuracy

to 69%. If combining the sandsheet and dune classes was

performed for the Raisz results, the overall accuracy rose

significantly to 65%, with Kappa rising to 0.63. The

combined Sandsheet/Dunes user’s accuracy rose to 78%

and producer’s accuracy to 77%. The greater increase in

accuracy in the case of the Raisz map was not surprising

given that samples from the sandsheet and dune classes

represented more than 50% of the samples acquired from

the map.

Confusion between the alluvial class and vegetation is

apparent along the Sahara–Sahel margin where the alluvial

class appears in an east–west band just north of a thicker

band of the mountain class. The mountain class is north of a

band of vegetation which marks the Sahel proper. This

zonation is indicative of the increasing sparseness of

vegetation from the Sahel into the Sahara (Tucker et al.,

1991).

There were two possible reasons for the confusion

between these classes. First, mountains and alluvial surfaces

often have higher vegetation cover than other desert

m map

R T S V User’s Sum

1 0 4 2 0.64 28

1 2 6 0 0.59 29

1 2 1 0 0.82 28

0 0 0 0 1.00 21

0 0 1 0 0.83 24

1 1 0 1 0.62 29

21 2 1 0 0.75 28

1 22 1 0 0.79 28

3 3 8 1 0.29 28

0 1 0 19 0.73 26

.69 0.72 0.67 0.36 0.83 0.70 269

amples per class with some images discarded due to bad registration or other


landforms. Many of the training sites for the alluvial class

came from hamadas where springs and watercourses, and

therefore vegetation, may occur, and plateaus where

seasonal grasslands may be found. Orographic rainfall

effects in mountains, even in the Sahara, allows for some

vegetation cover.

A second reason for confusion is spectral. The existence

of vegetation on alluvial and mountain surfaces effectively

makes this an impure endmember because the reflectance

spectrum of these sites is some combination of a plant or

NPV spectrum and a mineral soil spectrum. In addition,

both plant and mountain spectra are dark, with the

mountain spectra bearing some resemblance to NPV,

especially dry grass (Fig. 3a,c,d). As vegetation thins from

the Sahel into the Sahara, the mountain and alluvial classes

act as transitional classes from vegetation to unvegetated

landforms where a three-endmember class combination

with vegetation does not represent these areas as well. This

results in the east–west banding in Fig. 7 from the Sahel

to the Sahara with the mountain class just north of

vegetation, probably representing dry grasses. North of

the ‘‘mountain’’ band is a band of reg where three-

endmember models between vegetation and reg are

required with the reg class having a greater cover fraction.

As is typical of the Sahel, the red stems endmember is

most frequently paired with reg, but the rabbitbrush and

dry grass endmembers are also common. Finally, the

alluvial class represents the edge of the vegetated zone

south of the arid heart of the desert.

Although these confusions require further investigation

of the three-endmember cases and how the classes overlap,

the accuracy of the landform map produced by the MESMA

is good, considering the spatial resolution of the imagery.

4.8. Maximum likelihood classification

To test the efficacy of the MESMA methodology, we

compared our results to those of a standard supervised

Table 5

Error matrix of classes from Landsat imagery and modeled classes from the max

Model Landsat

A D L W B M

Alluvial 15 1 2 0 4 3

Dune 1 20 3 0 0 0

Lakebed 0 1 16 0 0 0

Water 0 0 0 17 0 0

Basalt 1 0 0 0 13 9

Mountain 0 2 0 1 5 12

Reg 4 6 0 0 0 0

Bedrock 3 1 3 2 1 1

Sandsheet 1 3 0 2 0 1

Vegetation 8 0 0 0 0 0

Producer’s 0.45 0.59 0.67 0.77 0.57 0

Landsat samples were chosen from a stratified random sampling scheme using 30 s

errors. The format of the table is the same as for Table 3. Kappa=0.55.

classification of the MODIS imagery in Fig. 2. We chose a

maximum likelihood classifier so as to be able to express the

statistical distribution of training spectra for each class.

The classifier was trained using the Landsat imagery,

which was deemed to be the highest quality dataset

available. Each of the 20 scenes used for the error analysis

shown in Table 4 was examined for areas that were

interpretable as being indisputably of a given class. These

areas were transferred to the MODIS imagery to create the

training polygons. Each class had from 4 to 18 training

polygons, with the more common classes having more

polygons. The mountain class was the only class with

greater than 10% aerial coverage in Fig. 7 that had fewer

than 10 training sites. The basalt and vegetation classes were

supplemented with training sites from outside of the Landsat

coverage that were still clearly from those classes in the

MODIS imagery (e.g. the Black Haruj basalt flows of Libya

and Sahelian vegetation).

The results of this classification were compared with the

same Landsat validation sites used to create the error matrix,

Table 4. Although the same training set was used for the

error analysis, we feel this was justified because the training

sites and error analysis sites were chosen independently. The

Landsat data represented the best available dataset for both

of these tasks. The error matrix comparing the maximum

likelihood classifier to the Landsat reference is shown in

Table 5.

The maximum likelihood classification’s error results

were significantly worse than those of the MESMA derived

landform map when compared with the Landsat reference

data (overall accuracy of 56% and kappa of 0.55 as

compared with 70% overall accuracy and a kappa of 0.69

for the MESMA derived map). In the case of the maximum

likelihood classification, the alluvial, mountain, reg, and

sandsheet classes were poorly classified with user’s and

producer’s accuracies below 50%.

It is probable that the maximum likelihood classifier did

not perform well in this case because of the broad spectral

imum likelihood classification

R E S V User’s Sum

5 4 2 2 0.39 38

0 0 4 0 0.71 28

0 1 3 0 0.76 21

0 0 0 0 1.00 17

0 0 0 0 0.57 23

3 7 0 0 0.40 30

13 1 4 1 0.45 29

3 17 1 0 0.53 32

5 3 8 1 0.33 24

0 0 0 19 0.70 27

.46 0.45 0.52 0.36 0.83 0.56 269

amples per class with some images discarded due to bad registration or other


definition of each landform class which produces a high

variance at each wavelength. At this resolution, many of the

landforms truly are mixtures which MESMA was able to

account for. The supervised classification, which tried to

force each pixel’s spectrum to fit a mean spectrum with a

large variance, had a more difficult time with these mixed

pixels. Furthermore, MESMA accounts for the variance that

is added to each class as a result of surface roughness and

shadowing because these are modeled by the shade

endmember. Variability in brightness around the mean can

be a problem for supervised classifiers.

We also performed a minimum distance to the mean

supervised classification using the endmember spectra shown

in Fig. 3a–d. The results of this classification were

considerably worse than both the MESMA-based, and the

maximum likelihood classifications (overall accuracy=47%,

Kappa=0.45).

Given the poor classification performance of the super-

vised classifications, there is a clear accuracy benefit in the

MESMA approach. Furthermore, the MESMA approach

provides additional information about the fractional cover-

age of landforms and vegetation that is not available in other

classification methods.

As a final assessment of the quality of the landform map

product, we compared our accuracy results with those of

Hansen et al. (2000). This was the closest study in

methodology and scale that we could find, but it is worth

noting that they used decision trees to estimate fractional

cover and were studying land cover at the global scale. Our

overall accuracy result of 70% is marginally better than their

overall accuracy of 65%, showing that this range of

accuracy is acceptable for a product at the sub-continental

scale.

5. Conclusions

Moderate resolution satellite imagery is an effective tool

for mapping desert landforms. This paper demonstrates the

use of MESMA at the subcontinental scale where previous

studies using SMA techniques have largely focused on

smaller regions. Endmembers representing pure landforms

were used to model the imagery with the addition of a set of

mostly reference vegetation spectra to provide a separate

vegetation endmember where applicable. A landform map

of Africa north of 10- was produced with 10 landform

classes based on majority endmember fractions.

The landform map improved on the existing Raisz (1952)

landform map by creating a digital product, at moderate

resolution, to which properties could be assigned for

analytical or modeling purposes. Furthermore, the use of

vegetation spectra allowed the creation of a map of

fractional vegetation cover for the Sahara.

The modeled landform map identified dunes and regs as

the dominant landform classes in North Africa at 22% and

21% coverage, respectively. Sandsheets comprised 15% of

the surface area, alluvial fans 14%, mountains 9%, and

etched bedrock 3%. Areas where vegetation was the

majority cover fraction were 13% of the study area, but

because the majority of the vegetation is in the Sahel, this

figure is dependent on the arbitrary southern cutoff of 10- Nlatitude. Minor classes with 1% or less areal coverage were

basalt, lakebeds, and open water.

The total accuracy of the landform classification was

54% when the image classification results were compared to

the Landform Map of North Africa of Raisz (1952), used in

the original image endmember determination. These results

showed some confusion between regs and alluvial surfaces

as well as between sandsheets and dunes. A stratified

random sampling approach using Landsat data for valida-

tion produced a higher accuracy of 70% and eliminated the

confusion between the alluvial and reg classes. However,

there was considerable spectral confusion between dunes

and sandsheets. Combining these classes increased overall

accuracy to 73% for the Raisz map and 75% for the Landsat

validation. The gradation of vegetation from the Sahel

northward into the Sahara also posed classification problems

with mountain and alluvial classes mimicking dark, semi-

vegetated surfaces.

When compared with a maximum likelihood supervised

classification, the MESMA approach improved the classi-

fication accuracy considerably from 56% to 70%. The

maximum likelihood classifier had particular difficulty

classifying the alluvial, mountain, reg, and sandsheet

classes.

In this paper, we established an accurate sub-continental

scale landform classification. These landforms could be

used as the basis for an erodibility map for continental-

scale wind erosion studies, or for other purposes where

geomorphic properties are significant. The creation of a

spectrally based map of the permanent background land-

forms of the Sahara also allows for the use of a partial

unmixing (Boardman et al., 1995) of vegetation to monitor

changing vegetation cover over time. In this way seasonal

and interannual variations in vegetation vigor could be

assessed where vegetation is present in the marginal lands

at the fringes of the Sahara. Furthermore, the MODIS

imagery is at a fine enough resolution that changes in land

use could be assessed with these methods, thereby

providing another tool for trying to understand the

influence of human activities and how the natural environ-

ment might respond to those activities based on the

underlying landforms. The methodology presented here is

also transportable to other arid and semi-arid parts of the

world where an understanding of landforms would be

desirable.

Acknowledgements

The authors gratefully acknowledge the financial support

of NASA through an Inter-disciplinary Science Grant


(NAG5-9671) and an Earth System Science 33 Graduate

Fellowship (NGT5-30332). We also thank Thomas Dunne,

Natalie Mahowald, and Oliver Chadwick for their helpful

comments.

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