Groundwater recharge in the Kalahari, with reference topaleo-hydrologic conditions

J.J. de Vriesa,* , E.T. Selaolob, H.E. Beekmanc,d

aFaculty of Earth Sciences, Vrije Universiteit, De Boelelaan 1085, 1081 HV Amsterdam, The NetherlandsbDepartment of Geological Survey, Private bag 14, Lobatse, Botswana

cCenter for Development Cooperation Services, Vrije Universiteit, De Boelelaan 1115, 1081 HV Amsterdam, The NetherlandsdUniversity of Botswana, Gaborone, Botswana

Received 25 January 2000; revised 4 August 2000; accepted 25 August 2000

Abstract

The Kalahari is situated in the semi-arid center of southern Africa and can be characterized as a savannah with a sandysubsurface, deep groundwater tables and annual rainfall ranging from 250 mm in the southwest to 550 mm in the northeast. Ahigh infiltration rate and high retention storage during the wet season and subsequent high transpiration by the dense vegetationduring the dry season, make that very little water passes the root zone and contributes to aquifer recharge. A lively debate hascontinued for almost a century on the question whether the Kalahari aquifers are being replenished at all under present climaticconditions. The present paper reports on results of an extensive recharge research project at the eastern fringe of the Kalahari,which is the most favorable part for groundwater replenishment. Additional observations were made in the central Kalahari.Environmental tracer studies and groundwater flow modeling indicate that present-day recharge is in the order of 5 mm yr21 atthe eastern fringe of the Kalahari where annual rainfall exceeds 400 mm. Figures in the order of 1 mm were obtained from thecentral Kalahari with lower precipitation. A dry valley system refers to more humid paleo-climatic conditions with a highergroundwater recharge. A tentative reconstruction of the groundwater depletion history suggests a time lapse of severalthousands of years since the end of the last wet period.q 2000 Elsevier Science B.V. All rights reserved.

Keywords: Groundwater recharge; Tracer studies; Dry valleys; Kalahari desert; Paleo-hydrology

1. Introduction

The semi-arid Botswana Kalahari is situated on thesouthern African plateau, which is characterized by aflat, slightly undulating topography and an elevationof around 1000 m above sea level. The Kalahari formsa tectonic as well as a morphological basin, filled withtens of meters of unconsolidated sandy deposits ofTertiary and Quaternary age. It is underlain mainly

by Paleozoic to Mesozoic sedimentary rocks andbasalt of the Karoo Supergroup. Rainfall is restrictedto the summer period from September to April and onaverage ranges from 250 mm yr21 in the southwest to550 mm yr21 in the northeast (Fig. 1). Perennial waterat the surface is restricted to the far north where theOkavango and Chobe Rivers bring water from catch-ments in Angola and Zambia.

Groundwater is mainly found in Karoo rocks withwater tables ranging from 20 m below surface at thefringe of the Kalahari to more than 100 m in thecentral part. The main regional groundwater flow is

Journal of Hydrology 238 (2000) 110–123www.elsevier.com/locate/jhydrol

0022-1694/00/$ - see front matterq 2000 Elsevier Science B.V. All rights reserved.PII: S0022-1694(00)00325-5

* Corresponding author. Fax:131-20-646-2457.E-mail address:vrij@geo.vu.nl (J.J. de Vries).

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Fig. 1. Botswana: physiographic features and locations referred to in text; hydraulic head contours inferred after Hydrogeological Reconnais-sance Map of Botswana, scale 1:500,000.

from the water divide in the southwest at a landsurface elevation of 1250 m, to the lowest depression,the Makgadikgadi Pan, 600 km to the northeast at anelevation of 925 m. The groundwater table slopesfrom 1125 m at the divide to near surface at theMakagadikgadi Pan (Fig. 1). The regional hydraulicgradient is thus 0.03% whereas the surface slope isslightly higher with 0.05%. A small groundwatercomponent flows southward to the depression of theMolopo dry valley. No springs or other groundwateroutcrops occur in the area under present climaticconditions. The Kalahari thus forms more or less aclosed basin with an internal groundwater drainagesystem.

The large Okwa-Mmone dry valley system followsthe main groundwater system to the northeast. Thispoorly integrated system, with low tributary bifurca-tion ratios, consists of broad shallow depressions withmore deeply incised headwater branches (Figs. 1 and3). Other depressions are formed by hundreds of panswhich probably reflects poor drainage conditionsduring wet paleo-climatic periods with high ground-water tables. Extensive calcrete and silcrete duricrustprecipitates are found along the depressions, producedby subsurface leaching of the felspathic matrix andremoval and precipitation of calcite. Virtually nopaleo-climatic information is available for theKalahari because of a lack of datable organicremnants. Proxy data of cave and pan deposits in thenorthern part of South Africa, just south of Botswana,gave evidence for a pluvial period during the last partof the Pleistocene, from 30,000–11,000 yr BP,followed by another wet episode during the earlyHolocene, from about 8000–4500 yr BP. From4500 BP onwards more variable conditions withsecond order fluctuations prevailed (see Thomas andShaw, 1991 and references therein). The latePleistocene pluvial period is also known from thepaleo-lake Makgadikgadi and the Okavango Delta inthe northern Kalahari. The paleo-hydrologic condi-tions in this area however, were dominated by theOkavango and Zambezi river systems, coming fromthe northern wet tropical area.

The average annual rainfall of about 400 mmsupports rather dense vegetation, classifying most ofthe Kalahari as a bush and tree savannah with alter-nating grass steppe. Real desert conditions in thesense of poorly vegetated and unstable moving

sands only prevail in the extreme southwest whererainfall is below 250 mm. Groundwater has beenencountered almost everywhere in Karoo and olderPrecambrian rocks beneath the Kalahari Beds, butthe Kalahari sand itself does not at present form exten-sive aquifers. Perched water bodies are found locallyin the Kalahari Beds in areas with large pans, relatedto episodic flooding and rapid infiltration throughfractured duricrust deposits. For a detailed accountof the Kalahari environment, one is referred toThomas and Shaw (1991).

A lively debate has continued for almost a centuryas to whether groundwater recharge by infiltratingrainwater through Kalahari sands is taking placeunder the present climate (De Vries and Von Hoyer,1988). Early studies (Boocock and Van Straten, 1961,1962) contested the occurrence of recharge because ofthe high moisture retention storage in the sandysubsoil during the rainfall season and subsequenthigh evapotranspiration by the dense savannahvegetation during the dry season. Similar conclusionswere drawn by Foster et al. (1982) from a few tracerprofiles in the unsaturated zone at the eastern fringe ofthe Kalahari.

De Vries (1984) considered regional flow throughthe Kalahari from southwest to northeast, on the basisof hydraulic gradient and transmissivity andconcluded a flux of less than 1 mm yr21, which forsteady-state conditions would mean an overallrecharge of the same order. He argued however, thatthe present gradient could also be a residual from aprevious wet period, which would mean an even lowerrecharge. Starting from a wet period with the ground-water table close to the surface, it would, according tohis calculations, take more than 10,000 yr of depletionby discharge to reach the present groundwater table.The present hydraulic head could thus equally beexplained as a residual of a previous wet pluvialperiod.

To the contrary, several environmental tracerstudies since the early 1970s demonstrated evidenceof widespread and active replenishment by the occur-rence of high14C and tritium contents in groundwaterfar below the root zone (Jennings, 1974; Mazor et al.,1974, 1977). Subsequent exploitation and explorationstudy at the fringe of the Kalahari also revealedevidence for recharge. The question then arose, ifrecharge is substantial, what then happens to this

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water, taking into consideration the low regionalgroundwater discharge flow and the fact that thegroundwater table is everywhere below the rootzone so that evapotranspiration from the saturatedzone is apparently not possible. Some researchershowever, have speculated in (oral) discussions aboutthe possibility of the loss of water from greater depthsby vapor transport.

To solve this groundwater recharge question, anextensive research project has been carried out bythe present authors since 1992, via the BotswanaDepartment of Geological Survey in cooperationwith the Vrije Universiteit Amsterdam and theUniversity of Botswana. The main aim of thisproject was to assess the recharge in the Kalahariand to investigate the reason for the discrepancybetween recharge and discharge flux evidences.This Groundwater Recharge and EvaluationStudy (GRES II project) focused on the fringeof the Kalahari where the most favorable condi-tions for replenishment were expected fromevidence of earlier exploration. Additional obser-vations were carried out in the central and dryerpart of the Kalahari (Fig. 1).

An extensive account on the results of thisGRES II project (as well as a former GRES Iproject that focused on the Precambrian hardrockarea in the east) is reported by the present authorsand their collaborators in Beekman et al. (1996,1997) and Selaolo (1998). The present papersummarizes and evaluates part of the results ofGRES II, viz., groundwater recharge assessmentby application of environmental tracers andgroundwater modeling. It furthermore presents atentative evaluation of paleo-hydrologic conditionsto distinguish a possible influence of residual flowcomponents. Finally a discussion is added onmoisture and vapor transport from depths belowthe root zone, because such processes couldcause an imbalance between the total amount ofpercolation to the groundwater table and the totalregional discharge flux through the saturated zone.The overall result of the present study is thatsubstantial recharge occurs at the eastern fringeof the Kalahari, whereas very little groundwaterreplenishment prevails in the central en westernpart of the area, covering 80% of the BotswanaKalahari.

2. Results of the groundwater rechargeinvestigations

2.1. The Letlhakeng–Botlhapatlou (L–B area, Figs. 1and 3)

The study area covers 65× 75 km2 and is situatedat the eastern fringe of the Kalahari, close to theboundary of Precambrian and Karoo outcrops. Itforms the headwater catchment of the Mmone dryvalley system, which is characterized by several tribu-taries with a width up to several kilometers and amaximum depth of tens of meters. This paleo-streamsystem forms a marked topography in this otherwiseflat area. The Kalahari sand cover reaches a thicknessof 10–40 m, with extensive horizons of calcrete andsilcrete precipitates along (former) drainage lines andshallow pan depressions. The topographic slope is in anorthwesterly direction with a gradient of about 0.2%.These huge valleys with small catchments and gorgetype valley heads are most likely initiated by subsur-face leaching of the felspathic matrix along fractures,producing pseudo-karstic features, followed bygroundwater sapping erosion during wetter periodswith higher groundwater tables (Shaw and de Vries,1988). The relatively deep incision is caused bygradual uplift along the Zimbabwe–Kalahari Axisduring the Tertiary. The present groundwater tablein the L–B area is at a depth of about 50 m andmore or less reflects the topography. Fig. 3 showsthe dry valley system and the piezometric headcontours.

The main aquifer is formed by the MmabulaSandstone which subcrops the Kalahari sand in thesoutheast. Toward the northwest the Mmabula aquiferdips underneath less pervious mudstone and basaltfrom the Dibete Formation and the Stormberg LavaGroup. The unconfined part forms the main rechargearea, as indicated by the groundwater head culmina-tion in the southeast, and by an increasing14C and4Hegroundwater age in a northwesterly direction; fromhundreds of years in the unconfined area to morethan 10,000 of years at the western fringe of thestudy area (Beekman et al., 1997; Selaolo, 1998).

The recharge process was studied by sampling soilmoisture in vertical profiles for the environmentaltracers, chloride, tritium,18O and deuterium. (A fullaccount on the applied methods and the results are

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Fig. 2. Examples of vertical soil moisture and chloride profiles for the Letlhakeng-Botlhapatlou area (for locations see Fig. 3), for two level areas (a,c), a pan (b) and a dry valley (d); average chloride content at Dikgonnyane is 65 ppm. (Redrawn from Beekman et al., 1997; Selaolo, 1998.)

given by Selaolo, 1998.) A compilation of results isgiven in Fig. 2, showing representative chlorideprofiles for two flat areas, a pan and a dry valley. Achloride mass balance for steady state conditions inthe soil moisture zone means that the total input of

chloride by wet and dry atmospheric depositionshould equal chloride output by transport throughthe unsaturated zone, assuming that the Kalaharibeds itself do not produce any chloride. For diffuseinfiltration the following equation applies (see, e.g.

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Fig. 3. Chloride and hydraulic head distribution in the Letlhakeng–Botlhapatlou area; for location see Fig. 1. (Compiled from Nijsten andBeekman, 1997; Beekman et al., 1997.)

Lerner et al., 1990):

TD � Vsm × Clsm �1�where TD is the total chloride deposition at thesurface (mg m22 yr21), Vsm the downward soilmoisture flux through the unsaturated zone(mm yr21 or l m22 yr21) and Clsm is the chlorideconcentration of soil moisture (mgl21). From a chlor-ide deposition observation network, with long-termregional monitoring and intensive local observationsduring the GRES II period, a TD value between 400and 600 mg m22 yr21 was determined, with500 mg m22 yr21 applied henceforth as the mostprobable average for the study area (Beekman et al.,1996). Clsm varies for level areas from 50 to500 mgl 21, so that diffuse transport through the unsa-turated zone ranges between 1 and 10 mm yr21, withan areal average of about 3 mm yr21 (Fig. 2a and c).Higher values are found in depressions (pans and dryvalleys) where water accumulates at the surfaceduring high rainfall events (Fig. 2b and d). The chlor-ide content often decreases and stabilizes below theroot zone, indicating that part of the infiltrationbypasses this zone of strong evapotranspiration viapreferential flow paths, formed by cracks, rootchannels and funneling through unstable wettingfronts. Therefore the chloride balance calculationswere based on the chloride concentrations below theroot zone where diffuse percolation prevails.

Average chloride content in the saturated zone inthe recharge area is about 75 ppm (Fig. 3). ApplyingEq. (1) for the saturated zone, withV and Cl repre-senting the groundwater flux and groundwaterchloride content, leads to a total areal discharge(including diffuse and concentrated components) inthe order of 7 mm yr21. For long-term steady stateconditions, discharge equals recharge. This thusmeans that total recharge is about twice the averagediffuse percolation through the unsaturated zone. Apreferential and concentrated flow component thatmoves directly to the water table is therefore likely.This rapid concentrated percolation most probablyoriginates from surface water accumulation in pansand dry valleys and fast percolation through fracturedcalcrete surfaces. The Legape Pan, for example, showeda chloride concentration of 10 ppm (Fig. 2b), suggestinga locally enhanced annual recharge of 50 mm. The 42 mdeep borehole in the Dikgonnyane dry valley exhibits an

intermediate position with an average chlorideconcentration of 65 ppm; this means an annualrecharge of 8 mm (Fig. 2d). A tritium content of 4–5 TU in the samples from depths of 39, 40 and 42 m inthis borehole, supports the concept of a rapid prefer-ential flow component, so that the total rechargethrough this valley is more than 8 mm yr21 (Selaolo,1998). The total chloride content of this profile is225 g m22; with an annual chloride deposition of500 mg m22, this would indicate an accumulationperiod of 450 yr in case of a piston like flow. Thetritium content however, indicates younger water,which can only be explained by a fast percolationcomponent.

Hydraulic head contours (Fig. 3) indicate a hydraulicgradient of 0.2%, which combined with an averagetransmissivity of 500 m2 day21 (Nijsten and Beekman,1997) accounts for a groundwater flux in the order of1 m2 day21. Averaging this flow rate over the rechargearea, which shows a maximum length of about 50 kmperpendicular to the head contours, gives an overallminimum recharge of 7 mm yr21. A more sophisticatedand distributed finite element groundwater flow modelproduced an average figure of 6 mm yr21 (Nijsten andBeekman, 1997). These results are thus comparablewith those from the chloride mass balance approach.Calculation of residence time bycombined geochemicaland13C, 14C and3He/4He — isotope modelinghowever,produced a much higher maximum age of groundwaterin downstream direction than the groundwater flowmodel: up to 10,000 yr at a distance of 50 km from theintake area, resulting in average long-term annualrecharge figures of between 1 and 3 mm (Beekman etal., 1997). These high ages might be caused by an inap-propriate assessment of the interaction between waterand the mineral phase and/or the presence of stagnatingwater pockets. Taking into account the rather consistentresults of the chloride balance and the groundwater flowcalculation, an average recharge estimate of 6 mm yr21

is applied henceforth as the most likely value for thetime being.

According to the finite element model (Nijsten andBeekman, 1997), part of the groundwater from thestudy area discharges downstream in wide and deeplyincised fossil dry valley depressions, where thegroundwater table comes, according to boreholeobservations, within a depth of 15–30 m below thefloor. A concentration of deeply rootingAcacia tree

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species, known for possible root depths of more than50 m (Ringrose et al., 1997; Selaolo, 1998), indicatesthat abstraction by root uptake probably occurs. Thishypothesis is supported by the preservation of greenleaves, as a testimony of continuous transpiration, onseveral of the larger trees at the end of the dry seasonwhen almost all trees and shrubs in the surroundingarea have a grey–brown appearance. An increase insalt concentration and precipitates of calcrete giveadditional evidence of a local loss of groundwaterby evapotranspiration, which according to the ground-water model is in the order of 20–30 mm yr21 in these

depressions. It is very likely that these areas ofdischarge did form real groundwater outcrops(springs) during wet climatic periods with highergroundwater tables. The valleys evidently form asurface expression of deeply weathered fractureswith concentrated groundwater flow and seepage(Shaw and De Vries, 1988).

2.2. The Central Kalahari (CK-area, Figs. 1 and 4)

The observed general increase in chloride concen-tration in a downstream direction (Fig. 3) indicates a

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Fig. 4. Central Kalahari deep profile;18O and deuterium are expressed in mil deviation (d) from the V-MSOW standard; for location see Fig. 1.(Redrawn from Beekman et al., 1997; Selaolo, 1998.)

general decrease in recharge due to a decrease in rain-fall in a westerly direction as well as the occurrence ofmudstone and basalt confining layers overlying thesandstone aquifer. The latter will result in perchedwater horizons, facilitating evapotranspiration bydeeply rooting trees. Further to the northwest, in theCentral Kalahari at 120 km from the L–B-study area(Fig. 1), a 28 m deep profile was core-sampled formoisture, chloride, oxygen-18, deuterium and tritium(Fig. 4). The groundwater table at this site is at 70 m,and groundwater samples were taken from two bore-holes with a depth of 150 m. The upper 23 m consistsof Kalahari sand and calcrete with macropores, under-lain by 24 m of partly weathered Stormberg basalt,followed by fine-grained massive Ntane Sandstonewith traces of dissolution features.

The chloride peak between 6 and 9 m is in loamysediments and probably reflects an accumulation ofsalt in the small pores, whereas the decrease in chlor-ide below this zone indicates preferential percolationthrough the larger pores. A chloride mass balancecalculation for this lower zone with more or lessconstant chloride content of 900 ppm, gives an

average annual flux of 0.6 mm. Below 20 m the chlor-ide content further reduces, probably due to preferen-tial percolation through larger cracks. The tritiumpeaks of more than 3 TU at this depth also suggestsa rapid flow component. The downward decrease of18O and deuterium isotopes in the upper 15 m isexplained by evaporation enrichment near the surfaceand subsequent dilution by downward percolation oflighter rainwater (Allison et al., 1984).

Groundwater samples from the saturated zone gavea chloride content of 360 ppm, suggesting an overall(diffuse and concentrated) recharge of 1.2 mm yr21.The chloride content in the saturated zone, however,might have been affected by groundwater from theupstream area with a lower Cl-concentration, so thatthe average overall recharge is probably below1.2 mm.

3. Stable isotopes and tritium

The groundwater recharge figures presented in thispaper are based mainly on the chloride balancemethod and groundwater flow modeling. Another

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Fig. 5. Relation betweend 2H and d 18O for rainwater (59 samples), soil moisture (108 samples) and groundwater (59 samples) from theLetlhakeng-Botlhapatlou area (symbols represent data clusters); rainwater in monthly weighted values at Malwelwe (period 1993–1995);LBMWL � L–B area Meteoric Water Line. (Redrawn from Selaolo, 1998; original data in Beekman and Selaolo, 1997.)

aspect of the GRES project was the use of environ-mental isotopes for dating and tracing. Apart from theearlier mentioned dating and hydrochemical processstudies in the saturated zone, seven18O, deuteriumand tritium profiles were established in the unsatu-rated zone; see for example CK-3B in Fig. 4. All18O and deuterim profiles show the same trend asCK-3B, with an evaporation enrichment near thesurface, decreasing to lower values at greater depths.(A full account of the other profiles is given inSelaolo, 1998.)

Stable isotope figures for rainfall, soil moistureand groundwater for the L–B area are summarizedin Fig. 5. The average monthly weighted rainvalues showd 18O figures between 0 and25‰and d 2H figures between 0 and235‰ (59samples from the period 1993–1995). The mostdepleted values originate from months with thehighest rainfall amounts; individual high-intensitystorms hardly exceeded these highest monthlydepletion values. Soil moisture samples showd 18O values ranging from 0 to210‰, and d 2Hvalues between220 and265‰. It is remarkablethat the highest depletion values of soil moistureexceed the maximum values of individual high-intensity storm events during the period 1993–1995. An explanation could be the occurrence ofmore depleted rainstorms in the past.

Groundwater in the saturated zone shows a remark-able uniform stable isotope content:d18O�25:22‰ ^ 0:21 and d2H � 232:8‰ ^ 2:0: Thismeans that the isotopic character of groundwaterclosely reflects the average isotopic condition of soilmoisture. This also suggests that the 1993–1995sampling period is not representative for a long periodisotopic situation.

Recharge estimations for the Kalahari using thesemi-empirical heavy-isotope dilution methodproposed for Australia by Allison et al. (1984), gavefigures of the same order of magnitude as thoseobtained from the chloride mass balance calculation(Selaolo, 1998). Less successful were recharge deter-minations with tritium decay modeling. In accordancewith findings of others in areas with low recharge, thecalculated recharge figures were much too high(Beekman et al., 1996). This failure is attributed tothe relatively high influence of vapor transport on thedistribution of tritium (Cook and Walker, 1995).

4. Water and vapor transport from below the rootzone

From the foregoing it is evident that almost all rain-water disappears from the root zone in the uppermeters by evapotranspiration. Less than 1% of therainfall on average percolates to greater depths, andwill either reach the saturated zone or can locally beextracted by deep rootingAcacias. Recent analysis ofstable isotope profiles suggests that ascending capil-lary transport in bare soils under desert conditions, isdetectible from water table depths up to 20 m. Theflux from such depths is in the order of 1 mm yr21

(Coudrain-Ribstein et al., 1998). For Kalahari condi-tions, this could form an additional mechanism for theloss of groundwater from local high (perched) watertables in the vicinity of pans and dry valleys.

In earlier discussions on Kalahari groundwaterrecharge (see Section 1), researchers have speculatedabout the possibility of a substantial upward transportof water from below the root zone by vapor transport,due to a temperature gradient. This then could possi-bly explain the discrepancy between the indicationsfor substantial recharge or percolation through theunsaturated zone below the root zone and the lowregional groundwater discharge flux. To test thishypothesis, seasonal temperature measurements to adepth of 7 m were carried out during the GRESproject (Fig. 6). The maximum temperature differencebelow the root zone, between 3 m and 7 m, is 48C,with respective average temperatures of 26.5 and23.58C during the summer, and 21 and 248C during

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Fig. 6. Seasonal temperature fluctuations to a depth of 7 m for theperiod 1995–1996; location near LBA-7 (see Fig. 3).

the winter period. This indicates that the averagedifference in saturated vapor pressure in summer isabout 3:8 × 1026g cm23 and during winter 2:3 ×1026 g cm23 (see, e.g. Hanks and Ashcroft, 1980).The downward vapor transport component duringthe summer and the upward flow component duringthe winter thus seem to be in the same order of magni-tude. Steady-state vapor movement is given by:

J � 2D dr=ds �2�whereJ is the vapor flux (g cm22 s21), D the diffusioncoefficient (cm2 s21), r the vapor density (g cm23)and s is distance in cm;D is in the order of0.2 cm2 s21 (Hanks and Ashcroft, 1980). Accordingto Eq. (2) upward flux during the winter period(150 days) is in the order of 0.2 mm, whereas down-ward flux during the summer (150 days) is about0.3 mm. Net transport in the vapor phase is thereforeprobably low and seems not to play an important rolein soil moisture loss from below the root zone. More-over, if it did, it would have increased the chlorideconcentration and would thus have been taken intoaccount in the net recharge calculation from thechloride balance. The same applies for the previousmentioned loss of water from greater depths by capil-lary suction.

Transport in the liquid as well as the vapor phasethus cannot explain a possible discrepancy between asubstantial recharge, as determined for the L–B area,and the low regional groundwater discharge flux ofless than 1 mm yr21 as calculated by de Vries(1984) for the central and eastern Kalahari. It isevident that the low recharge rate that was determinedduring the present study for the central Kalahari (CKarea), exemplifies the condition of most of theKalahari, and thus explains the low regional ground-water flux.

5. Drying out of the valley system

The lapse of time since the dry valley system in thisarea lost its groundwater drainage function, is esti-mated to evaluate a possible residual nature of thehydraulic gradient in the L–B area. At the beginningof the depletion, the groundwater table must havebeen above the valley floor. This means a hydraulichead at the divide which was about 50 m higher than

at present, or an elevation of 1200 m above m.s.l. (Fig.3). It is plausible that during this wet period thehydraulic head further to the west, at say 100 kmfrom the L–B study area towards the center of theKalahari, was not much higher than at present,because the present head at that distance is about950 m (Selaolo, 1987) which is close to the drainagebase of the Makgadikgadi Pan (Fig. 1). To estimatethe time needed to produce a decay of the ground-water table at the divide from 1200 to 1150 m dueto a decrease in recharge from the wet period to thepresent-day annual recharge of 6 mm at this fringingarea, the following linear-reservoir depletionapproach can be applied.

For continuity:

Sdh� �N 2 q� dt �3�whereSis the specific yield;h the average head abovethe discharge base (L);N the recharge (LT21); q thedischarge (LT21).

Schematizing the groundwater discharge as hori-zontal flow to a parallel drainage system (Dupuitassumptions) lead to a parabolic groundwater table,thus:

h� 2=3�hm� �4�wherehm is hydraulic head at the divide. The specificdrainage resistanceR (T) is:

R� hm=q; thus dhm � Rdq �5�The parameterR is a function of the length of theconsidered flow path and the transmissivity. Substitut-ing Eqs. (4) and (5) in Eq. (3) gives:

2=3�SR� dq� �N 2 q� dt �6�or:

dq� j�N 2 q�dt �7�where

j � 1:5�S:R�21 �8�j is the reaction factor or reservoir outflow recessionconstant (T21).

Integrating Eq. (6) with boundary conditionsq�q0 : t � 0 andq� qt : t � t with N� constant, gives:

qt � q0e2jt 1 �1 2 e2jt �N �9�

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And (recall Eq. (5)):

ht � h0e2jt 1 �1 2 e2jt �N:R �10�

whereht is present head above the drainage base at thedivide: 11502 950� 200 m; h0 is height at thedivide above drainage base at the beginning ofdepletion�t � 0� : 12002 950� 250 m:

Since the discharge calculated from the ground-water model accords reasonably with rechargedetermined by the chloride mass balance (seeSection 2), it is concluded that the present condi-tions are close to steady-state. Substitution of thepresent recharge,N � 6 mm=yr; and the presenthydraulic head,ht � 200 m; in Eq. (5) givesR�33;000 yr: Assuming a specific yield of 0.15 forthe median coarse Kalahari sand and substitutionof this value with R in Eq. (8), gives j �3 × 1024 yr21

: Substituting these values in Eq.(10) gives a decay in groundwater head of 50%every 2500 yr. This means that a lowering of thegroundwater table with 50 m required a period ofat least thousands of years in the case of a rechargeof 6 mm/yr during the depletion period. The calcu-lated time lapse is reduced if the recharge during thedepletion period would have been lower than atpresent, and is less than 1000 yr for zero-recharge.However, such a low recharge figure for thedepletion phase is not likely because in that casethe present groundwater-chloride concentrationwould have been higher.

The reconstruction is in accordance with thepaleo-climatic information from other sourceswhich suggests the end of a major wet period atabout 4500 BP (see Section 1). In other words:this analysis makes plausible that the presenthydraulic gradient is in steady state if indeed thelast major wet period ended some thousands ofyears ago. A similar approach by De Vries (1984)for the western and central Kalahari resulted in arequired time lapse of more than 10,000 yr underconditions of zero-recharge, to reach the presentgroundwater level. This suggests that only theeastern fringe experienced wet conditions with ahigh groundwater table during the Holocene. TheKalahari proper seems to have had its last majorwet-phase during the Pleistocene pluvial period,when also the Makgadikgadi Pan was full of water.

6. Summary and conclusions

In conclusion, the groundwater recharge studiesresulted in an average figure in the order of5 mm yr21 for the fringe of the Kalahari, decreasingto 1 mm or less for the central part. Since no clearchanges in morphological conditions occur, it is likelythat the decrease in a recharge reflects the rainfallpattern, which decreases from about 450 mm at theedge of the Kalahari to less than 350 mm in the center.It is remarkable that also in South Africa underdifferent geological and morphological conditions,groundwater recharge seems to become very low ornegligible below an average annual rainfall thresholdof 400 mm (Bredenkamp et al., 1995).

Part of the relatively high recharge in the fringearea will be depleted into dry valley depressionsthrough transpiration by deep rootingAcacias fromdepths of tens of meters. In addition, water lossesfrom greater depths (up to 20 m) by capillary transportmay occur from perched water tables in areas ofenhanced recharge, such as depressions and fracturedduricrust surfaces, in the fringe as well as in thecentral parts of the Kalahari. An average regionalgroundwater discharge flow of less than 1 mm yr21

for the whole of the Kalahari, as suggested by theregional hydraulic gradient of Fig. 1 and earlierargued by De Vries (1984), seems therefore quitelikely, and in accordance with the results of thepresent tracer studies in the central Kalahari. Thismeans that the present regional hydraulic gradient ismore or less in steady state and that the depth of thegroundwater table is the result of a head decay over aperiod of more than 10,000 yr. This suggests that thelate-Pleistocene pluvial was the last major wet periodthat affected the whole of the Kalahari (first orderclimatic effect).

The fossil dry valley system at the Kalahari fringerefers to more humid paleo-climatic conditions withhigher recharge and higher groundwater tables in thisarea during the Holocene. A tentative reconstructionof the water table decline suggests a time lapse ofseveral thousands of years since the end of thesewet conditions (second order climatic effect).Restoration of the previous high groundwater tableup to at least the depth of the dry valley floor,would require a rise in the groundwater head ofabout 25%, which will result in an increase in

J.J. de Vries et al. / Journal of Hydrology 238 (2000) 110–123 121

saturated thickness of the aquifer by about 50 m. Withan average hydraulic conductivity of about10 m day21 for Kalahari sand, this means a doublingof the total transmissivity. To establish and maintainthis groundwater table would thus require an increasein annual recharge to about 10–15 mm at the fringe ofthe Kalahari for a period of thousands of years.Recharge figures of 10–15 mm in sandy areas arefound in eastern Botswana in areas with a rainfall ofaround 500 mm (Gieske, 1992; Beekman et al., 1996).To restore the wet conditions would therefore prob-ably require an annual rainfall increase in the Kalahariin the order of 100 mm.

Acknowledgements

The authors wish to thank the former Botswanaand Netherlands MSc-students G.B. Dekker, T.Jongewaard, N. Lenderink, G.J. Nijsten, O.T.O.Obakeng and R. van Elswijk for their contributionsto this study. They thank Dr C. Leduc (Grenoble) andan anonymous reviewer, whose comments substan-tially improved of the manuscript. The GRES projectswere funded by the Botswana Ministry of MineralResources and Water Affairs and the NetherlandsDirectorate General for International Cooperation.Isotope analyses were carried out by the Center forIsotope Research (CIO) in Groningen and the VrijeUniversiteit, Amsterdam.

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