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Geological Society of America Bulletin

doi: 10.1130/0016-7606(1997)109<0043:GWSPWD>2.3.CO;2 1997;109;43-62Geological Society of America Bulletin

Sturchio and Zeinhom El AlfyWei Luo, Raymond E. Arvidson, Mohamed Sultan, Richard Becker, Mary Katherine Crombie, Neil Ground-water sapping processes, Western Desert, Egypt

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ABSTRACT

Depressions of the Western Desert of Egypt(specifically, Kharga, Farafra, and Kurkur re-gions) are mainly occupied by shales that areimpermeable, but easily erodible by rainfalland runoff, whereas the surrounding plateausare composed of limestones that are perme-able and more resistant to fluvial erosion un-der semiarid to arid conditions. Scallop-shaped escarpment edges and stubby-lookingchannels that cut into the plateau units aresuggestive of slumping of limestones byground-water sapping at the limestone-shaleinterfaces, removal of slump blocks by weath-ering and fluvial erosion, and consequentscarp retreat. Spring-derived tufa depositsfound near the limestone escarpments provideadditional evidence for possible ground-watersapping during previous wet periods. A com-puter simulation model was developed toquantify the ground-water sapping processes,using a cellular automata algorithm with cou-pled surface runoff and ground-water flow fora permeable, resistant layer over an imperme-able, friable unit. Erosion, deposition, slump-ing, and generation of spring-derived tufaswere parametrically modeled. Simulations us-ing geologically reasonable parameters dem-onstrate that relatively rapid erosion of theshales by surface runoff, ground-water sap-ping, and slumping of the limestones, and de-tailed control by hydraulic conductivity inho-mogeneities associated with structures explainthe depressions, escarpments, and associated

landforms and deposits. Using episodic wetpulses, keyed by δ18O deep-sea core record,the model produced tufa ages that are statisti-cally consistent with the observed U/Th tufaages. This result supports the hypothesis thatnortheastern African wet periods occurredduring interglacial maxima. The δ18O-forcedmodel also replicates the decrease in fluvialand sapping activity over the past millionyears, as northeastern Africa became hyper-arid. The model thus provides a promisingpredictive tool for studying long-term land-form evolution that involves surface and sub-surface processes and climatic change.

INTRODUCTION

Among the most prominent geomorphic fea-tures of the current hyperarid Western Desert ofEgypt are a series of depressions surroundingplateaus and escarpments. The escarpments ex-tend for hundreds of kilometers (Fig. 1). The de-pressions are largely floored by shales, whereasthe surrounding plateaus are composed mainly oflimestones (Hermina, 1990). Previous models forthe origin of these landforms include wind ero-sion (Ball, 1927), fluvial erosion (Said, 1983;McCauley et al., 1982), and ground-water sap-ping (e.g., Maxwell, 1982; Higgins, 1990). Windalone cannot erode the resistant limestone cap-rock. Fluvial erosion alone cannot explain somepeculiar geomorphic features, such as scallopedescarpments and large depressions. For the de-pressions and escarpments of the Western Desert,we believe that fluvial erosion and ground-watersapping working together offer the best explana-tion (e.g., Maxwell, 1982; Issar, 1982; Higgins,1990). Furthermore, these processes were muchmore important in the past as compared with to-

day. For example, McCauley et al. (1982, 1986)were able to identify the presence of a relict,buried drainage network in the eastern Sahara byusing Shuttle Imaging Radar (SIR) images.

Ground-water sapping is the process thatcauses entrainment of soil or rock when ground-water flows through and emerges from a porousmedium at a free slope surface. This leads toshear strength loss of the basal support and Cou-lomb failure of the overlying rock (Dunne, 1990;Uchupi and Oldale, 1994; Schumm et al., 1995).Characteristic requirements for ground-watersapping include a permeable aquifer, a recharge-able ground-water system, a free face at whichsubsurface water can emerge, and a means oftransporting material released from the scarpface (Laity, 1988). Structural control throughhigh hydraulic conductivity faults is also typical(Laity, 1988). Sapping processes produce chan-nels that migrate headward into escarpments,with steep sides, flat floors, and theater-likeheads that lack well-developed tributaries (Laityand Malin, 1985; Kochel and Piper, 1986;Uchupi and Oldale, 1994).

The objective of this paper is to gather and in-tegrate evidence to explore quantitatively the hy-pothesis that escarpments and depressions of theWestern Desert were caused by fluvial and sap-ping processes. The procedure followed is tofirst establish a qualitative conceptual model forthe processes involved, using published work,remote sensing, and field observations to pro-vide constraints. The next step is to quantify theprimary processes with a numerical computermodel that integrates the evidence into an over-all landform evolution system that includes cou-pled fluvial and sapping processes. The model-ing approach provides insights into the processesthat are no longer operating in the study area.

43

Ground-water sapping processes, Western Desert, Egypt

Wei Luo*Raymond E. ArvidsonMohamed Sultan McDonnell Center for the Space Sciences, Department of Earth and Planetary Sciences,

Richard Becker Washington University, St. Louis, Missouri 63130

Mary Katherine Crombie}

Neil Sturchio Argonne National Laboratory, Argonne, Illinois 60439

Zeinhom El Alfy Egyptian Geological Survey and Mining Authority, Cairo, Egypt

GSA Bulletin; January 1997; v. 109; no. 1; p. 43–62; 21 figures; 2 tables.

*Present address: Department of Geography,Northern Illinois University, DeKalb, Illinois 60115.E-mail address: [email protected].

Data Repository item 9636 contains additional material related to this article.



The approach is summarized in a flow diagramshown in Figure 2. The paper focuses on theKharga and Farafra regions, because these twoareas were visited by us in 1994 and 1995. Anadditional site, the Kurkur Oasis, was also vis-ited by us in 1995 and results were reported inCrombie et al. (1995, 1997). The Kurkur Oasissetting is similar to the ones found at the Khargaand Farafra areas. Thus, a detailed discussion ofthe Kurkur region will not be developed in thispaper.

OBSERVATIONS

Geology and Morphology

Kharga Region. Observations. The Khargadepression is ≈200 km north to south and ≈70 kmeast to west (Fig. 1). It is bounded by steep es-carpments and plateaus on all but the southernside. The elevation of the depression is about50 m above sea level; the plateau is about 400 mabove sea level (Defense Mapping Agency Topo-graphic Center, 1972). The strata are almost hor-izontal, with 1° to 2° dips to the west-southwestand to the east-northeast; the depression is ori-ented along a north-south–trending anticline(Said, 1962). Figure 3 is a simplified geologicmap for part of the Kharga study area, called El

Rufuf Pass, which we examined in 1994. Fig-ure 4 shows representative cross sections. El Ru-fuf Pass is the site of a major fault system strikingnortheast-southwest. Spring- and wadi-relatedtufa deposits crop out along and close to the es-carpments, providing direct evidence for emer-gent ground-water in the past (Caton-Thompsonand Gardner, 1932; Stringfield et al., 1974).

The Kharga depression is floored by theMaghrabi, Quseir, and Dakhla formations. Theoldest unit exposed is the Maghrabi Formation(Cretaceous), which consists of coastal mud-plain deposits and channel sandstones, deltaicand marginal marine sandstones and mudstones,and paleosol deposits. The thickness of this for-mation is ≈60 m (Hermina; 1990; Handley et al.,1987). The Quseir Formation consists of shale,claystones, siltstones, and flaggy sandstoneswith a thickness up to ≈70–90 m (Hermina,1990). The Dakhla Formation is primarily com-posed of shale in the study area, with minor in-tercalations of calcareous, sandy and silty de-posits. To the east of these outcrops is a smallplateau underlain by the Tarawan Formation, aunit composed of white neritic chalk and chalkylimestone of Paleocene age, having a thicknessof as much as ≈45 m (Hermina; 1990, Handleyet al., 1987). Farther to the east is the major es-carpment. The Esna Formation is exposed at the

base of the escarpment and consists of primarilymarl and green shales, enclosing minor carbon-ate intercalations. The thickness reaches ≈160 mand decreases toward the south (Hermina, 1990;Handley et al., 1987). Overlying the Esna For-mation and forming the large plateau is a se-quence of predominantly carbonate rocks calledthe Thebes Group. In the study area, the ThebesGroup is represented by the El Rufuf Formation,which consists of well-bedded lagoonal to plat-form limestones of early Eocene age, with amaximum thickness of 145 m (Hermina; 1990,Handley et al., 1987). The El Rufuf Formationforms the caprock of the plateau surrounding theKharga depression in the region shown in Fig-ure 3.

Figure 5 is a regional view from Landsat The-matic Mapper (TM) band 5 (1.55–1.75 µm inwavelength) showing the topographic contrast ofdepressions and escarpments. Extensive aeolianstreaks, which are most obvious in the middleportion of Figure 5, indicate the current hyper-arid conditions (average annual rainfall <1 mm,Wendorf and Schild, 1980). Numerous escarp-ments are evident, including stubby channel sys-tems that cut into the Tarawan Formation andscalloped forms that cut into the El Rufuf For-mation. Figure 6 shows the study area with TM

LUO ET AL.

44 Geological Society of America Bulletin, January 1997

Figure 1. Location map of Western Desert, Egypt, showing major depressions (dark stippleareas), plateaus, and aeolian sand deposits. Escarpments bordering the depressions extend forhundreds of kilometers. Box a denotes the study area shown in Figures 3 and 6. Boxes A and Bdenote footprints of Thematic Mapper data and Système Probatoire d’Observation de la Terre(SPOT) data shown in Figures 5 and 11, respectively. Study areas visited in the field include theKharga, Farafra, and Kurkur regions (adapted from Hermina, 1990).

Figure 2. Flow diagram of the modeling ap-proach of this study. The parameter valuesare selected based on independent measure-ments documented in the literature if possi-ble. The model was used to estimate the fewparameters that have no independent con-straint by comparing model outputs with theobservations. The result is a predictive modelthat can provide insights into processes thatare no longer operating.



GROUND-WATER SAPPING PROCESSES, WESTERN DESERT, EGYPT

Geological Society of America Bulletin, January 1997 45

bands 1 (0.45–0.52 µm in wavelength), 4(0.76–0.90 µm), and 7 (2.08–2.35 µm) to pro-vide hue and saturation and Système Probatoired’Observation de la Terre (SPOT) multispectralband 3 (0.79–0.89 µm) to provide intensity. Thisprocessing takes advantage of the higher spectralresolution of TM and the higher spatial resolu-tion (20 m) of SPOT. Scalloped edges are evi-dent (Fig. 6, B3, C to D and 4, E5) and individualslump blocks can be identified with a meanwidth of ≈170 m. Pediments covered with a thinlayer of alluvium composed of limestone andshale are on the Esna Formation (shale) betweenthe carbonate units (e.g., Fig. 6, E to F and 4 to5). A number of alluvial fans can also be identi-fied on the shale units (e.g., Fig. 6, F4-5, I to Jand 7). The mixture of limestone and local shalesediments on the fans is consistent with the color

patterns (spectral signatures) of the satellite dataand is also confirmed by observations in thefield.

Comparisons of the color image and geologi-cal map illustrate the close correlations betweenlandforms and bedrock geology. Channels su-perimposed on the Tarawan Formation (Fig. 6,E3-4, G to I and 4 to 6) are wide and have steepwalls and flat floors. Channels cut into the ElRufuf Formation on the escarpment and adjacentplateau show similar characteristics (Fig. 6, F toG and 6 to 8). Figure 7 is a map showing thedrainage pattern of the study area superimposedwith geologic boundaries. This map qualitativelyshows that the drainage density is higher in theshale unit (Tpe) than in limestone and chalkunits (Tetr and Tpt). The tributaries enter thehigher order channels at higher angles in the car-

bonate units and their lengths are relativelyshort, forming asymmetric patterns. However,the tributaries in the shale units enter the higherorder channels at lower angles and their lengthsare relatively long, forming parallel patterns.

The data also suggest a high degree of struc-tural control of sapping landforms. As noted, themajor fault systems in the study area are exten-sional and trend predominantly north-south withdeviations to north-northwest and north-northeastand subordinately east-west (Handley et al., 1987;Hermina, 1990). The channels in the TarawanFormation generally follow these trends. The in-cipient channels at the high escarpment associatedwith El Rufuf Pass even more strictly follow thenorth-south and east-west directions. Figure 8 is arose diagram of the channel trends in the carbon-ate units measured from Landsat and SPOT data

Figure 3. Simplified geologic map of region covered by box a in Figure 1. K = Cretaceous, T = Tertiary and Q = Quaternary. Units are de-scribed in text. Cross sections are shown in Figure 4. Units Kum and Kuq floor the Kharga depression, Tpt is located on a plateau 40–50 m abovethe depression, and Tetr crops out on the main plateau above the depression. Wadi deposits (Qw) map some of the stubby channels. Adapted af-ter Handley et al. (1987).

30°45′

25°40′

SandDunes

SandSheet

WadiDeposits

Travertine(Tufa)

El RufufFormation

EsnaFormation

TarawanFormation

DakhlaFormation

QuseirFormation

MaghrabiFormation



LUO ET AL.


Figure 4. Schematic cross sections alonglines AA′ and BB′ in Figure 2. Note the steepescarpment slopes for the limestone (Tetr) andchalky limestone (Tpt) units and the fact thatboth are underlain by shales (Kud, Tpe). Thetufa deposits on limestone bedrock are springderived. Topographic information from JointOperations Graphic, 1:250,000, El-Khargasheet, Defense Mapping Agency TopographicCenter (1972).

Figure 5. Part of a Landsat Thematic Mapper (TM) scene (band 5) showing a regional view of the northern portion of the Kharga depression. Aeo-lian streaks extend north-south, indicating dominant wind directions and the current hyperarid conditions. The black patches in the lower half of thescene are clouds and shadows. The box outlines the study area shown in Figures 3 and 6. Note the stubby-looking channels (in Tarawan Formation) andscallop-shaped plateau edges (in El Rufuf Formation) in the boxed area. TM scene product id = TM LS411760428935305. Pixel resolution is 30 m.





30°45′

25°40′

Figure 6. Image of El Rufuf Pass study area constructed by using Thematic Mapper (TM) bands 1, 4, and 7 to provide hue and saturation andSPOT multispectral band 3 to provide intensity, geometrically corrected to compare with geologic map in Figure 2. Sand dunes and wind streaksare visible from coordinates 1–3 and A–J. Areas shown as green (G1-2, J2-3) correspond to vegetation in the Kharga Oasis. Stubby channels areseen in the Tarawan Formation (C3, E3-4, G to I and 4 to 6) and are roughly oriented in north-south, northeast-southwest, east-west directions.Fluvial pediment and alluvial fan systems exist on the Esna Formation to the east of Tarawan Formation (e.g., E to F and 4 to 5, I to J and 7 to8). The high escarpment is located from A-2 to J-8 and delineates the boundary between the Esna and El Rufuf formations. The escarpment ex-tends into the plateau along a major fault at El Rufuf Pass area (F to G and 7 to 8). Note the scalloped nature of the high escarpment (B3, C toD and 3 to 4). The lack of drainage on the El Rufuf Formation is consistent with high intrinsic permeability associated with karstification. SPOTscene id = (11132981988111908311101X).



LUO ET AL.


(Fig. 6), showing that the dominant trends are innorth-south, north-east-southwest, and east-westdirections. On a regional scale, the locations andthe shapes of the depressions also show correla-tion with structures (Abritton et al., 1990). For ex-ample, a north-south–oriented fault passesthrough the middle of the Kharga depression, andthe eastern boundary of the Kharga depression(the big scarp) coincides with a fault (Said, 1962,1990; Gindy, 1991).

Interpretations. Table 1 is a comparison ofcharacteristics of sapping-dominated and runoff-dominated channels summarized from Hawaiiand the Colorado Plateau, two areas whereground-water sapping has been proposed (e.g.,Laity and Malin, 1985; Kochel and Piper, 1986;Baker, 1990; Schumm et al., 1995). The chan-nels cut into the El Rufuf Formation (limestone)show all the characteristic planform featurescaused by ground-water sapping. Moreover, tufadeposits (Fig. 3), in places interbedded with al-luvial deposits (Caton-Thompson and Gardner,1932), provide additional evidence for emergentsprings associated with previous epochs of en-hanced ground-water. The interbedding of tufaand alluvial deposits indicates that the tufa for-mation was episodic. Channels cut into the shaleunits show almost all the features of runoff-dom-

inated channels (Fig. 6 and 7, Table 1). The shiftfrom sapping features on the limestone andchalk units to alluvial features on the shale unitsis interpreted to be due to a shift in bedrock in-trinsic permeability (i.e., from high permeability

in carbonates with secondary porosity and highinfiltration to low permeability in shales withhigh runoff). This interpretation is supported bythe observation that carbonate rocks exhibit evi-dence for karstification and thus generation of

Figure 7. Drainage patterns of the El RufufPass area superimposed with geologic bound-aries. See Figure 3 caption for formationnames. Thin lines show the geologic bound-aries and the thick lines show the drainagesystems. The drainage density in the shaleunit (Tpe) is high compared with those in thecarbonates units (Tetr and Tpt). The tribu-taries enter the main streams at high angles inthe carbonate units, whereas those in the shaleform a parallel pattern. The drainage systemis constructed from the satellite data (Fig. 6)using a Geographic Information System soft-ware (MGE by Intergraph Corporation).

Figure 8. Rose diagramof the trends of channels inthe Tarawan Formationand El-Rufuf Formation,measured from SPOT andThematic Mapper data (i.e.,Fig. 6). The major trendsare in the north-south,northeast-southwest, andeast-west, generally consis-tent with structural trendsof this area documented inthe literature (e.g., Her-mina, 1990; Said, 1962).



secondary porosity and permeability in previouswet epochs (Stringfield et al., 1974; El Aref etal., 1987; Said, 1990).

The morphology of the channels in the Tara-

wan Formation shows features of both runoff-dominated channels (gradual head termination,widening valley downstream, less strong struc-tural control compared with those in the El Ru-

fuf formation) and sapping-dominated channels(e.g., dendritic pattern, high relief, low drainagedensity, steep wall, and flat floor). These featuresindicate that they have been inherited from flu-vial channels that existed when the Esna shalecovered the Tarawan Formation. These featuresare interpreted to have been modified and wi-dened by ground-water sapping processes as flu-vial erosion tapped into the ground-water table(e.g., see Baker, 1988).

The structural control of the orientations ofchannels in the carbonates units is interpreted tobe due to the increased hydraulic conductivitiesalong the fractures associated with the El RufufPass fault system. Sapping landforms developedpreferentially along the high hydraulic conduc-tivity zones because of more ground-water dis-charge along those zones. Figure 9 is a schematicblock diagram showing the major geologic andgeomorphic features of El Rufuf Pass. Correla-



TABLE 1. COMPARISON OF GEOMORPHIC CHARACTERISTICS OF SAPPING ANDFLUVIAL CHANNELS IN THE COLORADO PLATEAU AND HAWAII

Parameter Runoff-dominated Sapping-dominated

Basin shape Very elongate Lightbulb shapedHead termination Tapered, gradual Theater, abruptChannel trend Uniform VariablePattern Parallel DendriticJunction angle Low (40°–50°) Higher (55°–65°)Downstream tributaries Frequent RareRelief Low HighDrainage density High LowDrainage symmetry Symmetrical AsymmetricalCross-section shape V-shape U-shape, steep wall, flat floorValley width Widening downstream Relatively constantTributary length Relatively long Short stubby tributaryStructural control Less strong StrongBasin area/canyon area Very high Low

Note: Table compiled from Kochel and Pipe (1986) and Schumm et al. (1995).

Figure 9. Block diagram of El Rufuf Pass area showing major geomorphic features. A major scalloped escarpment formed in the limestoneplateau by differential erosion and ground-water sapping. The slumping blocks developed within the scallops and were disintegrated by weath-ering and transported downhill by surface runoff. Emerging ground water from the permeable limestone and chalky limestone units formedstubby-looking channels by headward erosion, sapping, and slumping in these units. On the impermeable shale units at the base of the escarp-ment, surface runoff formed pediments and alluvial fan systems. The lowest shale units formed the depression covered with aeolian sands.



LUO ET AL.


tions in location and shape between faults and de-pressions on a regional scale indicate that the de-pressions may have been initiated along zones ofstructural weakness through a combination ofprocesses (Abritton et al., 1990), including flu-vial erosion and ground-water sapping.

Farafra Region. Observations. Figure 10 is asimplified geologic map of the El Quss Abu SaidPlateau study region (area B in Fig. 1). Figure 11is a SPOT panchromatic image covering part ofthe Farafra study area. The plateau is about225 m above the depression floor (Said, 1962).The Khoman Formation, which occupies theeastern part of the depression in Figure 10, con-sists of white massive neritic chalk and chalkylimestone, interfingering with the Dakhla For-mation (Hermina, 1990; Klitzsch et al., 1987).The caprock of the oval-shaped plateau consistsof the Farafra Formation, which is a member ofthe Thebes Group and is composed of alveolinidlagoonal limestone (Klitzsch et al., 1987). A se-quence of cross-bedded sandstones in a partiallykaolinized matrix, known as the Minqar El TalhFormation (Klitzsch et al., 1987), crops out inthe southwestern part of the plateau. In thenorthwestern part of the area shown in Figure10, the top of the scarp and the plateau surfaceare composed of Naqb Formation (ThebesGroup), which consists of pinkish, dense andnummulitic platform limestones with local flintbands. As in the Kharga study area, the plateauconsists of carbonates, and sandstone deposits inthe south. The depression is floored by shale-bearing units and chalks. Other units in this areainclude playa deposits, sand sheets, and sanddunes.

A closer look at the adjacent escarpment re-veals a series of arcuate-shaped scallops (Fig. 12,F4, G3), with individual slump blocks inside thescallops. Similar features have also been ob-served in the Kharga, Kurkur, and Dakhla areas(e.g., Brookes, 1993; Crombie et al., 1995, 1997),where slump blocks slide and rotate downslope,forming a series of steps with tops facing back to-ward the plateau. The mean widths of theseslumping blocks are estimated to be about150–180 m, on the basis of field observations andmeasurements from Landsat and SPOT data. Vir-tually no drainage systems can be identified onthe plateau. However, drainage and pedimentscan be seen adjacent to the base of the escarp-ment within each scallop. Some alluvial fans de-velop farther downstream close to the depression(e.g., Fig. 12, I to J and 4 to 5). The southwesternpart of the escarpment (Fig. 13) shows more ir-regular and elongated scallops. In addition, iso-lated inselbergs are seen in the depression about1–2 km away from the escarpment. By compar-ing the geologic map and SPOT data, it is clearthat well-developed scallops formed in lime-

stones (Fig. 12), whereas more irregularly shapedand elongated scallops developed in sandstones(Fig. 13).

Interpretation. Arcuate-shaped scallops aretypically formed by rock failure and downslopeslumping (e.g., Selby, 1993, p. 258–260). Thescallops formed this way usually have the shapeof an amphitheater, an arcuate shape not only inplan view, but also in profile view. Studying sim-ilar features in the Dahkla area, Brookes (1993)attribute the formation of the scallops to ground-water saturation and deconsolidation of theunderlying shale, which leads to slides of theoverlying limestones, forming arcuate-shapedscallops. Issar (1982) also concluded that basalground-water seepage is usually a major trigger-ing factor for the slides that form the scallops (orerosion cirques) observed in the Sinai andNegev. In the Farafra area, the source water forthe drainage systems emanating from these scal-lops must have been ground-water from the car-bonates on the plateau. This interpretation isconsistent with the lack of upslope catchmentsand feeder channels on the plateau, implyingrapid infiltration of surface water into the sub-surface of the limestone plateau. The differencesin morphology at the escarpment edges betweenlimestone and sandstone caprocks indicate con-trol by bedrock type. The more resistant sand-stone may be less susceptible to sapping mobi-lization than limestone. The observations alsosuggest that surface runoff has been minimizedon the plateau due to infiltration into the subsur-face. Ground-water seeped out at the scarp face,causing weakening of the shales and mass wast-ing of overlying material, followed by retreat ofthe escarpment and formation of the arcuate-shaped scallops at the plateau edge. The emer-gent ground-water, coupled with local rainfalland runoff, formed the fan systems consisting ofa mixture of sandstone and local shales. Similarpatterns are evident in the Kharga and the Kur-kur areas.

Tufa Ages

To understand the timing of the ground-watersapping processes better, a number of tufa sam-ples were collected from Kharga, Farafra, andKurkur areas and dated using uranium-seriesdisequilibrium methods (Sultan et al., 1996;Crombie et al., 1995, 1997). Crombie et al.(1995, 1997) examined the samples petrograph-ically and point counted for micrite, sparite, andpore space. Samples with less than ≈75% micritecontained obvious recrystallization and sec-ondary recrystallization features. Samples withgreater than 75% micrite were homogeneouswith no obvious secondary alteration. The agesof samples with greater than 75% micrite are

therefore more reliable than those with lower mi-crite contents. These data cluster around 100 and200 ka, correlating with the major interglacialmarine oxygen isotope stages (Crombie et al.,1995, 1997). These data, along with those of Sz-abo et al. (1995), suggest that tufa-forming plu-vial episodes coincide with major intergalcialperiods.

CONCEPTUAL MODEL

On the basis of the observations describedabove and the climatic history of the area in theliterature, a qualitative conceptual model for thelandform development can be constructed(Fig. 2). Egypt is thought to have had a muchwetter climate throughout most of the TertiaryPeriod (Said, 1990) and to have become pro-gressively colder and drier since the Pliocene Pe-riod (3.2 Ma, Said, 1990) to late Pleistocene Pe-riod (1.8 Ma, Van Zinderen Bakker and Mercer,1986). The change is thought to be due to thechanges in atmospheric circulation patterns innortheastern Africa (Prell and Kutzbach, 1987).Under humid climatic conditions, karst dissolu-tion and fluvial erosion would have been thedominant geomorphic processes, forming thekarst features such as caves, karren, rainpits, andsinkholes commonly found in the limestonecountry of the mid-latitude Egypt (Stringfield etal., 1974; El Aref et al., 1987; Haynes, 1982).The karstic cavities with terra rosa soil fillings inthe plateau limestones (Haynes, 1982) are likelyto have formed during these humid periods. Asthe system changed from humid to arid, fluvialerosion (rather than karstification) would havebegun to dominate, including differential erosionto produce the escarpments between shale-floored depressions and limestone plateaus (Mc-Cauley et al., 1982; Albritton et al., 1990). Theinitiation of depressions is likely to have hap-pened at the structurally weak zones such asfault lines.

The characteristic requirements for ground-wa-ter sapping are met by a permeable limestoneaquifer with increased permeability formed dur-ing karstification processes, a ground-water sys-tem recharged by local rainfall and regionalground-water flow, a free surface formed by dif-ferential erosion, structural and lithologic inho-mogeneity, and fluvial processes to transport ma-terial released from the scarp face. As the climatebecame more arid, ground-water seeping from theinitial escarpment, the associated saturation anddeconsolidation of the shale units, subsequentbreakup and slumping of the overlying limestoneunits, and removal of broken materials by surfacerunoff would have become the major processesresponsible for the enhancement and retreat of es-carpments. As the climate transformed to the cur-



rent hyperarid conditions, escarpment retreatwould have slowed and aeolian processes wouldhave become dominant, forming the sand dunesand wind streaks found in the region.

NUMERICAL MODEL FORESCARPMENT GENERATION ANDEVOLUTION

With a conceptual model for development ofdepressions, escarpments, and associated fea-tures, the next step was to provide a predictive,quantitative model that simulates the processesand features (Fig. 2). The model should not beviewed as a detailed simulation of every aspect ofthe processes and resultant landforms and depos-its. For example, the model does not include kars-tification. We assume that karstification and asso-ciated permeability and porosity developed inearlier periods (most of the Tertiary), when north-eastern Africa was more humid (e.g., Said, 1990;Van Zinderen Bakker and Mercer, 1986). Tec-tonic activity is also ignored because the WesternDesert was tectonically quiescent during the timeperiod of interest (Gindy, 1991). The model con-centrates on simulating first-order processes as-sociated with fluvial erosion and ground-watersapping under semiarid to arid climatic condi-tions since the beginning of the Pleistocene. Thepurposes of the simulations are to gain insightsinto the interactions and coupling between hy-drology and geomorphology systems and theireffects on landform evolution, to test the impor-tance of structural control, and to show the extentto which resultant landforms and deposits main-tain evidence of past climatic changes.

In the model, fluvial processes are based onthe cellular automata technique (Chase, 1992).This technique merges the detailed small-scalegeomorphic processes into a few parameters anda set of simple rules that are iteratively applied toindividual cells of a topographic grid. This ap-proach is similar to studying heat transport ormechanics in physics by dealing with large-scalelaws rather than worrying about the motions ofindividual particles (Chase, 1992). The stochas-tic element is introduced in the model by ran-domly dropping rainfall events (termed “precipi-tons”) onto the topographic grid. The precipitonactivities are then determined by the rules andthe parameters of the cell where that precipitonresides and its neighbors.

The ground-water sapping part of the modelfollows the work of Howard (1988), with an ex-tension to transient flow conditions. The model isbased on the assumption that ground-water sap-ping occurs where a critical specific discharge rate(volume flux per unit area) is exceeded (Howard,1988, 1994). This is a reasonable assumption be-cause the seepage force, which is a body force act-

ing on some representative volume of the porousmedium by fluid drag (or shear) to reduce its in-ternal resistance to rupture (e.g., Dunne, 1990), isproportional to the specific discharge of ground-water flowing through the volume (e.g., Bear,1972, p. 184–186; Iverson and Major, 1986). Theseepage force is responsible for the entrainment ofsoil or rock and causes subsequent upslope fail-ure. Howard (1988) used this assumption in hismodel and produced landforms consistent withthose from physical sandbox experiment. Thesecond assumption is that the ground-water flowcan be approximated by an unconfined aquiferwith the Dupuit assumption (ignoring the verticalcomponent of flow, Howard, 1988). Consideringthe gentle dip of the limestone formations in theWestern Desert of Egypt and the lack of tectonicactivity in this area, this assumption is justified.The water table is calculated using an implicit fi-nite difference iteration method (Wang and An-derson, 1982) at each time step after the topogra-phy and recharge change. The amount of erosionwhen sapping is initiated is proportional to thedischarge rate over the critical value and to theerodibility of the material. The discharge rate iscalculated using Darcy’s law. Erosion and deposi-tion by ground-water sapping are incorporatedinto the cellular automata scheme. The slumpingassociated with ground-water sapping can bemodeled by cell-based diffusion if the cell size isset to the characteristic width of the slumpingblock. The slumping (cell-based diffusion) is de-termined by local surface slope.

The details of the modeling and the programcodes were documented in Luo (1995). Figure14 is a schematic flow diagram of the computersimulation. The simulation starts with an initialtopographic grid and ground-water table. If astorm occurs over a grid site, precipitation, dif-fusion, infiltration, fluvial erosion, and deposi-tion modules are executed. Sapping routines areexecuted if the conditions for ground-water sap-ping erosion are satisfied, i.e., the discharge rateexceeds some critical value (Howard, 1988). Thediffusion routine, which simulates mass wastingand soil creep (Chase, 1992), is also executedwhen sapping occurs. The diffusion mimics sap-ping failure because we selected the cell widthsbased on field observations of slump blocks. Tosimulate the contribution from regional ground-water flow, a regional recharge term is uniformlyapplied from the top to the model, because theregional flow does not change much spatiallyover the study area (Brinkmann et al., 1987). Theground-water table is then recalculated. The sim-ulation advances into the next time step and theabove procedures are repeated until the end ofthe simulation. Rainfall, storm frequency, andregional recharge can be varied over time, simu-lating climatic change.

Rainfall events (called precipitons) are mod-eled with a Poisson magnitude distribution forprecipitation and the surface flow velocity usedin erosion is calculated using the Chezy equation.The cellular automata algorithm of fluvial proc-esses works as follows (1) A storm of some para-meterized Poisson magnitude distribution (tomatch mean annual rainfall) is dropped randomlyonto a cell of the topographic grid with watermoving to the lowest of the eight neighboringcells. (2) As water moves downhill, it infiltratesinto the subsurface, based on an empiricalmethod of the U.S. Soil Conservation Service(Bras, 1990). (3)At the same time, erosion occursif the parameterized carrying capacity of thestorm is not exceeded. Erosion is proportional tothe surface flow velocity (calculated by theChezy equation) and to the erodibility of the ma-terial (bedrock and sediment have differenterodibility). (4) If the carrying capacity is ex-ceeded, deposition occurs. (5) The diffusion rou-tine is executed when each precipiton first dropsonto the topographic grid. Linear Fickean diffu-sion is assumed and is carried out by downhilltransport between the target cell and its four near-est neighbors. The material diffuses onto theneighbor cell if that neighbor cell is lower thanthe target cell. The direction of diffusion is oppo-site if the neighbor cell is higher than the targetcell. The amount of diffusion is proportional tolocal slope and is inversely proportional to thesquare of the cell size (Chase, 1992).

The interactions between surface and subsur-face processes are conducted as follows. Surfacewater infiltrates and feeds ground-water asrecharge, the amount that infiltrates being sub-tracted from the surface flow. Ground-water thatintersects the land surface flows downhill as sur-face overland flow using surface erosion and dep-osition routines. This event is called a sappaton(in contrast to precipiton, a rainfall event). Thewater table is then lowered by applying negativerecharge for the part becoming overland flow.

The generation of spring-derived tufa depositscan be described by the following reaction:

CO2 is released into the atmosphere (CO2[g]) asthe water emerges from the ground, driving thereaction toward the left. In other words, theground-water undersaturated with respect toCaCO3 becomes oversaturated as CO2 is re-leased. This process is modeled in a parametricway by having a tufa deposition rate propor-tional to the spring discharge rate. Once de-posited, the tufas are subject to fluvial and sap-ping erosion. The model keeps track of the

CO g

H O CaCO CO aq Ca 2HCO

2

2 3 22

3

( )

( ) .–

c

+ + ⇔ ++





times when tufas are first deposited or com-pletely eroded away (because keeping track ofall the deposition and erosion events is imprac-tical). This information is used herein to calcu-late the oldest age of the tufas preserved in eachcell. The calculated model tufa ages are thencompared with actual U/Th ages of tufa samplesacquired in Kharga, Farafra, and Kurkur by usas part of our ongoing research (e.g., Sultan etal., 1996; Crombie et al., 1995, 1997) to explorethe extent to which landforms and depositscarry evidence of past climatic changes.

The model has two rock layers, i.e., a resistantbut permeable top layer simulating limestones (orsandstones) and an erodible but impermeablebottom layer simulating shales (Fig. 15). The toplayer will be referred to as limestone and the bot-tom layer as shale. For simplicity, both layers areassumed to be horizontal (Fig. 15). Because thedeep Nubian aquifer (beneath the shales) is notincluded in this two-layer model, possible contri-butions to recharge by upward leakage from theNubian aquifer are only implicitly included in theregional recharge term, which is applied uni-formly from the top to the model. Explicit treat-ment of upward leakage from the Nubian aquiferwould require a multilayer model, which wouldconsiderably increase the complexity of themodel and is beyond the scope of this paper. Thepresent two-layer treatment suffices to simulatethe first-order features, because the emergentground-water would have the same sapping ef-fects on geomorphology, regardless of its source.

The boundary conditions for the ground-waterflow within the permeable limestone layer are noflow through the boundaries parallel to the longsides, no flow through the boundary with the high-est elevation, and constant head at the side that co-incides with the outcrop of the limestone-shaleboundary (Fig. 15). The no-flow boundary condi-tion at the boundary with highest elevation simu-lates the ground-water divide. Because the localhydraulic gradient is from the plateau toward thedepression, the no-flow boundary conditions at theboundaries parallel to the long sides are reason-able. The constant head is taken as the height of thebottom of the limestone layer, because that is thelowest head under the assumption that the under-lying shale is impermeable. This set of boundaryconditions also mimics a physical sandbox modelwith one side open (Howard, 1988).

MODEL PARAMETER ESTIMATION

The next step in model development was to se-lect appropriate values for each parameter so thatthe model produced realistic results (Fig. 2). Theparameters involve paleogeomorphology, paleo-climate, paleohydrology, lithology, and structure.Wherever possible, we selected parameter values

based on independent measurements (direct orindirect) documented in the literature. For the pa-rameters that lacked independent measurements,model results were used to determine the mostprobable values, based on comparisons of modellandforms, generated using different values, withactual observations. The parameters, their values,and categories are listed in Table 2 and aregrouped by the ways that their values were deter-mined, i.e., whether the values were indepen-dently known, or solved using the model.

Independently Known Parameters

The critical discharge rate represents the sus-ceptibility of the bedrock to ground-water sap-ping failure. Many landslide and slope-failurestudies measure the critical conditions for failurein terms of rainfall duration and intensity (e.g.,Caine, 1980; Larsen and Simon, 1993). How-ever, the timing, duration, and speed of slidemovement do not always correlate directly withthe timing and amount of rainfall (Iverson andMajor, 1987). Iverson and Major (1987) con-ducted detailed measurements of ground-waterconditions in the Minor Creek landslides, north-western California, and found that the ground-water hydraulic gradient is the factor most re-sponsible for failure. On the basis of theirdetailed head measurements, they found that themean hydraulic gradient that triggers seasonalmotion at Minor Creek landslide correspondswell with typical wet-season hydraulic gradient,which was estimated as 0.6–0.7 (Iverson andMajor, 1987). Their hydraulic conductivitiesbased on slug tests were approximately log-nor-mally distributed and the representative value(geometric mean) is 5 × 10–8 m/s, which willgive a critical discharge rate estimate of about≈0.002 m/day, according to Darcy’s law. Due tothe lack of other measurements and the difficultyof dealing with a paleohydrology system, thisvalue was used in our model.

The model simulates slumping by cell-baseddiffusion. Thus, the cell size selected must re-flect the characteristic size of the slumpingblocks observed in the field. On the basis of fieldobservations in Kharga, Farafra, and Kurkur ar-eas, and measurements on Landsat and SPOTdata, a size of 170 m was selected.

The only direct hydraulic conductivity mea-surements in the study area are for the deep Nu-bian sandstone aquifer (e.g., Hesse et al., 1987).Hydraulic conductivities for limestones are vari-able, ranging from 0.00008 m/day for crystallinerocks to 0.5 m/day for rocks with secondary per-meability through fracturing or dissolution (Do-menico and Schwartz, 1990). On the basis of thefact that there are secondary porosities fromkarstification under earlier humid conditions in

the study area, the hydraulic conductivities forlimestones in the model were assumed to be0.1 m/day. The storage coefficient, which repre-sents the volume of water released from storageper unit area of aquifer per unit decline in head,was taken to be 0.2, within the range of uncon-fined sandstone and limestone aquifers (Domen-ico and Schwartz, 1990).

Linear zones of high hydraulic conductivityand erodibility were introduced at ≈5° from thegrid directions (assuming north-south, east-west) to simulate the control of fractures on ero-sional features (Fig. 15). This orientation of frac-tures was selected because the major faultdirections in the study area were primarily along,but slightly off, the north-south, east-west direc-tions (Fig. 6 and 8). The fractures can be turnedon or off for comparison.

To model the climatic change of the area, acomposite deep-sea core δ18O record (Prell andKutzbach, 1987; Clemens et al., 1991; Imbrie etal., 1993) was used to scale the mean rainfall his-tory. The following reasons justify the use of theδ18O record as the first-order estimate of climateconditions of the study area. The deep-sea coreδ18O record is known to be controlled by globalice volume and sea-surface temperature (e.g.,Dawson, 1992). High values correspond to gla-cial epochs, whereas low values correspond tointerglacial epochs. This record is directly re-lated to Northern Hemisphere summer insola-tion and is a proxy for overall climatic condi-tions in northeastern Africa (Imbrie and Imbrie,1980; Prell and Kutzbach, 1987; Clemens et al.,1991). High solar insolation is thought to inten-sify summer monsoonal activity, moving the Sa-hel wetting front into northeastern Africa (Nich-olson and Folhn, 1980; Rossignol-Strick, 1985;Haynes, 1987; Prell and Kutzbach, 1987). U/Thand radiocarbon dating of lacustrine deposits ofsouthern Egypt and northern Sudan by Szabo etal. (1995) correlate well with the major inter-glacial marine oxygen isotope stages. Faunal as-semblages of the same general area also point tonorthward displacement of the monsoon beltduring interglacial times (Kowalski et al., 1989).Furthermore, the δ18O record matches the lake-level data of Street-Perrott and Harrison (1984).The advantage of using the δ18O record overlake-level data is that the δ18O record extendsover millions of years, whereas the lake dataonly go back to 140 ka.

The present mean annual rainfall was takenand the values for the past were scaled using asmoothed version of the deep-sea core δ18Orecord (Fig. 16). A smoothed version of the δ18Orecord was used to scale rainfall because theU/Th dating of tufa samples suggests that tufasonly form during major pluvial times (Szabo etal., 1995; Crombie et al., 1995, 1997). The indi-

LUO ET AL.




vidual peaks are not as important as the generaltrend. The smoothed version also shows the gen-eral drying trend more clearly (Fig. 16). Further-more, with this scaling, the average rainfall twomillion years ago is similar to the present valueat the southern Sahel wetting front (Thompson,1965), consistent with the supposedly northwardmovement of this wetting front in the past. Theregional recharge and storm interval (inverse offrequency) were also varied according to therainfall history. The regional recharge was set tobe proportional to the rainfall function. The in-terval between storms was scaled according tothe rainfall function so that there are more rain-fall events (short intervals) during wet periodsand fewer events during dry periods.

Model-Derived Parameters

The erodibility is a dimensionless parameter.The relative values of erodibility reflect the dif-

ferences in lithology and the absolute values setthe time scale of the model and the denudationrates. The shale erodibility listed in Table 2 wasselected by running the model and comparingthe resultant denudation rates with continentaldenudation rates (2–50 mm/k.y.) independentlyestimated from the mechanical and chemicalload of catchment rivers (e.g., Gilchrist andSummerfield, 1992; Berner and Berner, 1987;Thomas, 1994; Pavich, 1985). The erodibility ofthe limestones was assigned to be two orders ofmagnitude lower than that of the shales(Table 2), because this difference was needed toproduce escarpment relief consistent with obser-vations. Tufa and limestone are both observed inthe field to be more resistant than shales, so theywere assigned the same erodibilities. Materialeroded from the bedrock was regarded as uncon-solidated sediment and had an erodibility twotimes higher than that of shales. This value was

selected on the basis of comparison of actual andmodeled depositional patterns. Higher values re-sulted in little sediment deposition and alluvialfan accumulation.

The sapping erosion scaling factor is the pro-portionality constant for calculating the amountof sapping erosion (Howard, 1988). The valuelisted in Table 2 was determined by comparisonof model runs with observations. The criteriawere that the overall resultant model morphologyshould look similar to the observations (i.e., withan escarpment and scallops in the limestone andalluvial fans and pediments in the shale) andthere should be no unrealistic singular points(deep holes or high spikes) in the resultant modeltopography. The product of the scaling factor andthe discharge needed to be small enough so as notto make deep holes in the limestones. Model runswith different values (10 at the low end and100 at the high end) for the sapping scaling fac-



Figure 10. Simplified geologic map of Quss Abu Said Plateau, Farafra. K = Cretaceous, T = Tertiary, Q = Quaternary. Units are described intext. Details of areas A and B are shown in Figures 12 and 13, respectively. Adapted after Klitzsch et al. (1987).

Sand Dunes

Sand sheet, Serir

Playa deposits

Minqar el-Talh Formation

Thebes GroupNaqb Formation

Esna Formation

Tarawan Formation

Dakhla Formation

Khoman Formation

Thebes GroupFarafra Formation



tor did not result in significantly different land-forms. However, the retreat rates of the escarp-ment were different. An erosion scaling factorvalue of 50 generated escarpment retreat ratessimilar to a rough estimate based on tufas on theoutliers several hundred meters in front of the es-carpment (see model results). Thus, the value of50 is a reasonable estimate for this parameter.

The scaling factor (proportional constant) fortufa generation listed in Table 2 was set so thatthe deposition of tufa was distributed close to theescarpment and did not generate topographicspikes. Tests with the tufa generation scaling fac-tor showed that models with a higher value (e.g.,0.1) would generate excessive tufa buildups infront of the escarpment, which would impede theescarpment generation and retreat. With the valuelisted in Table 2, the model produced tufa thick-nesses within the range of observation (2–10 m,

Crombie, 1996). Thus, this value seems reason-able.

The initial topography was represented by a100 × 200 grid with elevation at each point cov-ering an area of about 17 km by 34 km (Fig. 15).The grid size was chosen as a compromise be-tween the computation time and edge effects. Alarger grid size takes more time to run and asmaller size will have edge effects. The modelwith a smaller grid size of 50 × 100 took lesscomputer time and produced scalloped escarp-ments with sizes and shapes similar to those pro-duced by the model with a grid size of 100 ×200. The grid size did not seem to affect theplanform morphology. However, in the 50 × 100model, headward and sideways erosion quicklyreached the edges of the modeling domain andresulted in unrealistic excessive downward ero-sion. With a grid size of 100 × 200, the model

usually takes about 2.5 days to finish 2 m.y. ofsimulation on a Silicon Graphics Challenge sys-tem, without causing any edge effects. Grid sizeslarger than 100 × 200 also produced similarplanform morphology with no edge effects, butthey take weeks. Thus, a size of 100 × 200 is rea-sonable for the simulations.

The initial topography two million years ago isunknown. A simple peneplain was selected as aconvenient initial topography for the modeling.The slope of the peneplain is set to be very gentle(1%) because the plateau surface has very gentleregional tilt toward the depressions (≈1%, De-fense mapping Agency Topographic Center,1972) and the area is thought to have been tec-tonically quiescent (Gindy, 1991). Model runswith an initial topographic slope greater than10% resulted in smooth topography and largerspacings between channels, because the amount

LUO ET AL.


ofthedif-fu-sionispro-por-

Figure 11. SPOT panchromatic image covering the Farafra studyarea. The oval-shaped body in the western portion of the image is ElQuss Abu Said Plateau. The plateau is composed of mostly limestoneof Farafra Formation. The areas with dark albedo in the southwesterncorner of the plateau are sandstones of Mingqar El-Talh Formation.White arrows delineate the eastern escarpment, along which a seriesof pediments and alluvial fans can be identified. Details of areas A andB are shown in Figures 12 and 13, respectively. To the east of the es-carpment is the Farafra depression. The black patches in the north-eastern part of the scene are playa deposits. SPOT scene id =(11062961993070909083401P)

Figure 12. Enlargement of box A in Figure 11. The escarpment ex-tends from coordinates J-1 to B-7. To the west of this line is the lime-stone plateau and to the east is the depression underlain by DakhlaFormation (shales) and Khoman Formation (chalks). No drainage sys-tem is evident on the plateau, but there are channels emanating fromthe base of the escarpment and draining into the depression. The scal-lop-shaped features along the edge of the escarpment are located at co-ordinates F to G and 3 to 4. Also note the linear ridges trending north-west-southeast between adjacent scallops (H to G and 3 to 4, E6-7).



tional to slope. An initial topography with an ex-isting escarpment was also attempted. The resultwas not significantly different from that with agently tilted peneplain because for a tilted pene-plain, differential erosion between limestone andshale quickly developed an escarpment. In otherwords, a dynamic equilibrium is established afterthe model started. Thus, the initial topographydoes not seem to affect the final landform and asimple gently tilted peneplain is a reasonablestarting condition.

Hydraulic conductivities in fractures shouldbe higher than the surroundings. However, there

are no data that we are aware of in the study areaabout how high conductivities would be. In themodel, the hydraulic conductivities were in-creased by a factor of two over that of the lime-stone, because model runs with higher valuescaused the water table to drop rapidly, and fewtufas were formed and none preserved.

Discussion

To summarize, most of the key model para-meters were estimated based on some indepen-dent measurements (Table 2). The rest, most of

which are dimensionless parameters, were deter-mined based on the model by comparing themodel results with the observed landform, sedi-ment distribution, and thickness (Table 2). Onemay argue that the second method of determin-ing the parameters is self-serving and that themodeling is circular reasoning. To address thisconcern, we conducted numerous model runs inwhich we varied these parameters one at a timeto determine their control on model results. Testsindicate that initial topography does not affectthe final landform as dynamic equilibrium isachieved. Furthermore, we have used a grid sizethat did not result in any edge effects. In addi-tion, the tufa generation scaling factor producedtufa thicknesses within the range of observationsand the sapping scaling factor generated scarpretreat rates consistent with rough estimatesfrom observations. Thus, these model-deter-mined parameters are reasonable. The estima-tion of erodibilities was model derived, but wasalso based on independently measured continen-tal denudation rates. The model results based onthese values should be predictive and the modelshould at least provide some insights into thelong-term evolution of surface and subsurfaceprocesses under a changing climate.



Figure 13. Enlargement of box B in Figure 11. The escarpment extends from B1 to G9. Tothe north of the escarpment is the plateau, composed of sandstone of the Minqar El-Talh For-mation. To the south is the depression underlain by the Esna (shales) and Tarawan formations(chalks). The scallops along the escarpment (E to F and 3 to 4, E to G and 7) are more elongatedand more irregular compared to those shown in Figure 10. The ridges between the scallops arealso wider and isolated inselbergs are left in the depression (G to H and 3 to 4, H6).

Figure 14. Flow diagram of the computersimulation illustrating erosion, deposition,and ground-water sapping processes andtheir interactions. See text for details.



MODEL RESULTS

With a reasonable set of parameter values de-termined, in this section we discuss the modelresults and the insights the predictive model canprovide (Fig. 2). Two cases, with and withoutsimulated fracture zones, are presented. For thecase with no fractures (Fig. 20a), an initial es-carpment formed at the outcrop of the boundarybetween the limestone and shale due to differen-tial erosion. This initial scarp face is essential forground-water sapping processes to be initiatedbecause it provided a free surface for ground-water to seep out easily. The initial escarpmentwas then enhanced and retreated by ground-wa-ter sapping and slumping processes. Thus, it isdifferential erosion that initiated ground-watersapping and slumping processes, and caused thelandform evolution. In addition, scallops and lin-ear ridges between adjacent scallops formed inthe limestones. Pediments and alluvial fansformed on the shale units. Tufas were depositedwhere the ground-water intercepted the surfaces(Fig. 20a). They were also removed by fluvialerosion processes. The ground-water tabledropped with time as the climate became dry.Some older tufas were preserved on the plateaubetween scallops (Fig. 20a). The model kepttrack of the amount of erosion, and thus verticalerosion and horizontal retreat as a function oftime and their rates (slope) can be inferred

(Fig. 17). The vertical erosion rate and scarp re-treat rate declined with time. The scarp retreatdecreased from several kilometers in the firstmillion years to several hundred meters duringthe most recent million years. The tufas on scarpoutliers northwest of Kharga are thought to bemid-Pleistocene, and they are only a few hun-dred meters in front of the scarp, implying thatheadward erosion accounts for several hundredmeters per million years (Maxwell, 1995, per-sonal commun.). The model-predicted values areconsistent with this interpretation.

The models also provided insight into the de-tails of ground-water sapping processes. The flu-vial erosion not only created a scarp face at thesurface boundary between shale and limestone,but also generated local depressions in the lime-stone along the scarp face. Because precipitonsare not uniformly but randomly dropped onto thetopographic surface, some points along the ini-tial scarp face will be eroded before others, evenif they have the same erodibility. This createssmall local depressions. The ground-water table,which was very close to the surface at the initialscarp face, became depressed at those local de-pressions, because the water table followedtopography (Fig. 18a). The depressed watertable led to concentration of ground-water flowlines toward the local depressions and an in-crease in discharge due to higher water-tablegradients (Fig. 18a). Sapping events (sappatons)

were initiated at those places where ground-wa-ter flow exceeded the critical discharge value forground-water sapping. Sapping erosion, i.e., as-sociated slumping and removal of materials outof the sapping site by fluvial transport, furtherdepressed the topography and ground-watertable, causing even more erosion. This positivefeedback mechanism continued to favor erosionat those initial local depressions and the initialscarp face, which eventually formed scallopsand a retreating escarpment (Fig. 20a). Thus, flu-vial process and ground-water sapping workingtogether generated the landform and deposits.Without fluvial processes, there would be nocontinued scarp retreat.

Examination of the model landforms at shorttime intervals shows that the sappatons initiallycreated the lightbulb-shaped scallops that weresubsequently expanded upslope and laterally.Similar phenomena have been observed in mod-ern humid environments in Madagascar and havebeen attributed to basal sapping by diffuseground-water flow (Wells and Andriamihaja,1993). As time progressed, the scallops contin-ued to expand headward and sideways, leavinglinear ridges between adjacent scallops. An addi-tional reason that these linear ridges are pre-served in areas between scallops is because theground-water flow is diverted away from theridges (Figs. 20a and 18a). The linear ridges ob-served in the Farafra area (Figs. 12 and 13) are

LUO ET AL.


Figure 15. Initial topography and stratigraphy. The slope of the topography surface is 1% (thus Dupuit assumption is valid). The pink is lime-stone and the bluish-green is shale. Bright lines are high hydraulic conductivity and erodibility zones to simulate fractures (in the shale layer,the bright zones only represent high erodibility). The two layers are assumed to be horizontal. Ground-water flow only operates in the limestonelayer.

Initial Topography(100 × 200 Grid)

(20× Vertical Exaggeration)

Fractures

Limestone

Shale

34 km17 km



most likely formed by the same processes. Theisolated inselbergs in the depressions are rem-nants of ridges. As noted by Dunne (1990) andHoward (1988), there was strong competition forground-water among sapping features. Onlythree mature scallops developed out of the nineinitial small scallops at the escarpment (Fig. 20a).

Model runs show that the model is very sensi-tive to critical discharge and that it controls themorphology of the scallops: the higher the criti-cal discharge, the more elongated the scallop

(Fig. 21). This is because the high critical dis-charge can only be satisfied at the scallop head,where the water table is the steepest. The posi-tive feedback mechanism causes more headwardretreat than lateral retreat. The higher critical dis-charge rate physically represents sapping condi-tions for rocks more resistant to failure (e.g.,sandstones), because higher ground-water dis-charges are needed to mobilize them. The mod-eling results are consistent with the observationsand interpretations in Egypt. Bedrock type con-

trols morphology. The sandstone caprock of thesouthwestern El Quss Abu Said Plateau (Fig. 13)is more resistant to sapping, whereas the lime-stone caprock of the eastern part of the plateau(Fig. 12) is more susceptible to sapping. Thescarp form of the Gilf Kebir Plateau (southwestof the study area), which is capped by ferrug-inized sandstone, is much more “channelized”than the limestone-capped plateau (Maxwell,1982; Higgins, 1990), similar to the southern es-carpment in the Farafra region.

For the model with fractures (Fig. 20b), ero-sion was concentrated preferentially along frac-ture zones due to higher ground-water dischargerates and therefore more sapping erosion. Thisprocess disrupted the natural development ofscallops and formed channel systems in the lime-stone that followed structural trends (Fig. 20b), asobserved in El Rufuf Pass area (Fig. 6). Tufa de-posits were preferentially deposited along thefractures, because sapping erosion tapped intothe ground-water table along high conductivityzones and generated springs. This situation isconsistent with observations in Kharga andKurkur. Less tufa was generated in the modelwith fractures as compared with the model withno fractures because higher discharge loweredthe water table so that there were fewer springs togenerate tufa deposits. The older tufas were pre-served in the channels on the plateau as the cli-mate became dry, and there was not enough ero-sion power to remove them. The vertical erosionrate and scarp retreat rate also decreased withtime (Fig. 17b). The present values are about7 times lower than those 1–2 m.y. ago. The ero-sions with fractures are generally lower thanthose with no fractures, because erosions wereconcentrated in the fracture zones. Figure 18bshows that ground-water flow is concentrated to-ward the scallop depressions and fracture zones.

The U/Th ages for samples with greater than75% micrite (reliable ages, Sultan et al., 1996;Crombie et al., 1995, 1997) are shown in his-togram form in Figure 19a in 20 k.y. increments.Also shown in Figure 19 are histograms of modelages for the oldest tufas preserved over the pastmillion years. The histograms of the δ18O-forcedchanging climate models (Fig. 19, b and c) areconsistent with the U/Th tufa age histogram(Fig. 19a). The younger peaks in the no-fracturecase (Fig. 19b) are mainly from tufas forming inthe scallops as the scallops tapped into theground-water table and generated springs. Thesepeaks also mimic the input rainfall function, i.e.,δ18O record (Figs. 19b and 16). Thus, the modelnot only simulates the first-order geomorphicfeatures and deposits, but also generates similartufa ages. In addition, the model results show thata majority of the tufas generated during older wetepisodes were eroded away, but there may be tu-



Figure 16. Average annual rainfall function (bottom) as defined from the composite deep-seacore δ18O record (top, Imbrie et al., 1993). Also shown in top panel is the smoothed version of theδ18O record, which is used to scale the changing climate rainfall function. The smoothed versionwas obtained by taking a three-point average of the original data consecutively for 200 times.

TABLE 2. PARAMETERS AND VALUES USED IN MODELING

Parameter Value Category

Independently knownCritical discharge rate for sapping 0.002 m/day HydrologyCell size (dimension of each cell) 170 m Initial conditionHydraulic conductivity 0.1 m/day HydrologyStorage coefficient 0.2 (dimensionless) HydrologyFracture direction 5° Initial conditionRainfall as a function of time Scaled by δ18O record Climate

Model derivedShale erodibility 0.04 (dimensionless) LithologyLimestone erodibility 0.0004 (dimensionless) LithologyTufa erodibility 0.0004 (dimensionless) LithologySediment erodibility 0.08 (dimensionless) LithologySapping erosion scale factor 50.0 (dimensionless) HydrologyTufa generation scale factor 0.001 (dimensionless) HydrologyGrid size (number of cells) 100 × 200 Initial conditionSlope of initial topography 1% (dimensionless) Initial conditionHydraulic conductivity in fractures 0.2 m/day Hydrology

Note: The erodibilities were listed under model-derived group, but they were determinedby comparing model results with independently measured denudation rates.



fas older than the U/Th detection limit (≈300 ka)that survived the erosion. Dating techniques thatgo beyond the U/Th limit will reveal more infor-mation about the paleoclimatic changes that areprobably locked in these sediments.

CONCLUSIONS

Remote sensing and field observations dem-onstrate that differential erosion between friable

shales and resistant limestones, ground-watersapping, associated slumping, and escarpmentretreat are responsible for the generation andmodification of the escarpments in the WesternDesert of Egypt. This paper provides a predictivemodel that replicates the first-order morphologyof escarpments by simulating coupled surfacefluvial processes and ground-water sapping withgeologically reasonable parameters. Observa-tions and simulations also indicate that the scarp

retreat rate is controlled by climatic conditionsand has decreased as the climate changed fromwet to hyperarid.

Simulations also provide insights into the de-tails of ground-water sapping processes. Scal-loped escarpment edges are the result of concen-tration of ground-water flow lines toward localdepressions and mass wasting of the overlyingrocks as the underlying shales are weakened byground-water saturation. The competition forground-water, the positive feedback mechanism,and structural controls contribute to the finalmorphology of the scallops. Ground-water sap-ping is dominant on the more permeable lime-stone units, forming characteristic sapping chan-nels and scallops at the plateau edge, whereassurface runoff dominates on the impermeableshale units and forms the pediment and alluvial-fan systems. The model also predicts ages ofpreserved spring-derived tufa deposits. Simula-tions and U/Th ages of tufa samples indicate thatthe tufa-forming recharge events are episodic,consistent with the deep-sea core δ18O paleocli-matic record and wetter periods that correlatewith interglacial times. Furthermore, the δ18O-forced model replicates the changes toward aridconditions in northeastern Africa, with currentfluvial and sapping rates that are much lowercurrently than 1 to 2 m.y. ago.

ACKNOWLEDGMENTS

This work was supported by National Aero-nautics and Space Administration Geology Pro-gram grant 1358 to Washington University. Wethank Stephen G. Wells, Ted A. Maxwell, and ananonymous reader for reviews. We also thankRoger J. Phillips, who kindly provided the Sili-con Graphics system for running the simulations.

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Figure 18. Ground-water flowlines and contours at 0.8 m.y. in time. The grid is resampled tohalf resolution for clarity (otherwise arrows clutter together) and only the active ground-wa-ter cells of the grid are shown. The numbers along x and y axes identify the columns and rowsof the resampled grid. (Each dimension is 17 km.) The outcrop of the original contact bound-ary between limestone and shale is along the x axis of the figure. The areas filled with arrowsare limestone and the white areas are exposed shales. (a) With no fractures. Ground-waterflowlines converge toward the scallop depressions and diverge away from the ridges betweenscallops. (b) With fractures. Flowlines not only converge toward scalloped depressions, but alsoconcentrate toward the fracture zones.

a

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MANUSCRIPT RECEIVED BY THE SOCIETY AUGUST 4, 1995REVISED MANUSCRIPT RECEIVED APRIL 29, 1996MANUSCRIPT ACCEPTED JUNE 29, 1996

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Figure 19. U/Th ages of tufas from the Farafra (1 sample) and Kurkur (7 samples) areas areshown in histogram (a). Model tufa age histograms for δ18O-forced changing climate (b and c)are aligned vertically for comparison. The δ18O-forced models (b and c) produced tufa agesconsistent with U/Th ages. Note that the scales of the y axes are different. U/Th data from Sul-tan et al. (1996) and Crombie et al. (1995, 1997).





With Fractures, Changing Climate

(1.6 m.y.) (0.8 m.y.) (Present)

Limestone Shale Sediments Tufaa

b

No Fractures, Changing Climate

(1.6 m.y.) (0.8 m.y.) (Present)

Limestone Shale Sediments Tufa

Figure 20. Resultant topography of modeling shown at 1.6, 0.8, and 0 m.y. in time. The viewing angle is from top and light source is from thesoutheast, similar to the sun angle when satellite images were taken. Pink is limestone, blue-green is shale, yellow is sediment, and red is spring-derived tufa. (a) Without fractures. The escarpment formed at the outcrop of the contact between limestone and shale. Scallop-shaped local de-pressions started at the escarpment and expanded headward and sideways. Pediment covered with sediments formed in the shale close to theescarpment and coalescing alluvial fans or bajada plains formed in the distal portion of shales. Linear ridges formed as adjacent scallops ex-panded. Each scallop formed its own drainage system emanating from the base of the escarpment. Tufas deposited on the plateau at earlier timewere nearly eroded away; some were preserved on the plateau between scallops. Younger tufas were preserved in the scallops. (b) With frac-tures. Erosion preferentially occurred along the fractures and formed channels along structural trends. The scallop-shaped local depressionsseen in the no-structure cases were disrupted. Tufa deposits are mostly found along fractures and at the intersection of the fractures.



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Low Critical Discharge

(1.6 m.y.) (0.8 m.y.) (Present)

Limestone Shale Sedimentsa

High Critical Discharge

(1.6 m.y.) (0.8 m.y.) (Present)

Limestone Shale Sedimentsb

Figure 21. Sensitivity test of critical discharge. Viewing angle and color coding are the same as those in Figure 17. Tufa deposits are not shownto emphasize the morphology. (a) Critical discharge (0.001 m/day) lower than the independently determined value (0.002 m/day): scallops arewider and more open as compared with a higher value (b). (b) Critical discharge rate (0.004 m/day) higher than the independently determinedvalue: scallops are narrower and more elongated. The ridges between adjacent scallops are also wider. Higher critical discharge represents arock more resistant to sapping failure (e.g., sandstone). Simulation result is consistent with observation in Farafra.



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