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Holocenedynamicsofthesalt-freshgroundwaterinterfaceunderasandisland,Inhaca,Mozambique

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DOI:10.1016/j.quaint.2011.11.020

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Quaternary International xxx (2011) 1e9

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Holocene dynamics of the saltefresh groundwater interface under a sand island,Inhaca, Mozambique

Lars Været a,*, Anton Leijnse b, Fortunato Cuamba c, Sylvi Haldorsen a

aDepartment of Plant and Environmental Sciences, Norwegian University of Life Sciences, P.O. Box 5003, N 1432 Aas, NorwaybDepartment of Environmental Sciences; Soil Physics, Ecohydrology and Groundwater Management Group, Droevendaalsesteeg 4, P.O. Box 47, 6700 AA,Wageningen, The NetherlandscDepartment of Geology, University of Eduardo Mondlane, Mozambique

a r t i c l e i n f o

Article history:Available online xxx

* Corresponding author. Markveien 23V, N-1406 SkE-mail addresses: lars.varet@gmail.com (L. Væ

(A. Leijnse), sylvi.haldorsen@umb.no (S. Haldorsen).

1040-6182/$ e see front matter � 2011 Elsevier Ltd adoi:10.1016/j.quaint.2011.11.020

Please cite this article in press as: Været, LMozambique, Quaternary International (201

a b s t r a c t

The configuration of coastal groundwater systems in southeast Africa was strongly controlled by theHolocene sea-level changes, with an Early Holocene transgression w15 m (10,000e5000 cal BP), and twoassumed high-stand events in the Middle and Late Holocene with levels higher than the present. Thefluctuation of the saltefresh groundwater interface under Inhaca Island in Mozambique during theHolocene has been studied using an adapted version of the numerical code SUTRA (Saturated-UnsaturatedTransport). In this study, small-scale variations such as tidal effects have not been considered. A number oftransient simulations were run with constant boundary conditions until the steady state condition wasreached in order to study the sensitivity of response time, saltefresh interface position, and thickness of thetransition zone to different parameters such as hydraulic conductivity, porosity, recharge, and dispersivity.A 50% increase in horizontal hydraulic conductivity yields a rise in the location of the interface of >15 m,while an increase in recharge from 8% to 20% of mean annual precipitation (MAP) causes a downward shiftin the interface position of >40 m. A full transient simulation of the Holocene dynamics of the saltefreshgroundwater interface showed a response time of several hundred years, with a duration sensitive toporosity, hydraulic conductivity and recharge and a position determined by the recharge rate and thehydraulic conductivity. Dispersivity controls the thickness of the transition zone in this non-tidal model.Physical processes, such as changes in recharge and/or the sea level, may cause rapid shifts in the interfaceposition and affect the thickness of the transition zone.

� 2011 Elsevier Ltd and INQUA. All rights reserved.

1. Introduction

Climatefluctuations have forced sea-levelfluctuations throughoutgeologic time, with a magnitude of ca 130 m during the Late Pleis-tocene and Holocene (Fleming et al., 1998; Lambeck and Chappell,2001; Lambeck et al., 2002; Peltier, 2002). In addition, isostatic ortectonic depression and rise of continental plates have resulted invariable sea-level fluctuations worldwide. Ghyben (1888) andHerzberg (1901) were the first to describe how density differencesbetween salt and freshwater determine the shape andposition of thesaltefresh groundwater interface. Major shifts of the saltefreshgroundwater interface, and of the thickness of the fresh groundwaterlens, have therefore taken place along the world’s coastlines. TheGhybeneHerzberg relation assumes a sharp interface and a stagnant

i, Norway.ret), toonleijnse@gmail.com

nd INQUA. All rights reserved.

., et al., Holocene dynamics o1), doi:10.1016/j.quaint.2011.1

salt-water zone, which is not strictly true. Their theories only holdapproximately if the freshgroundwater lens is in equilibriumwith thepresent sea level and climate.

Several studies have focused on factors influencing the behav-iour of the saltefresh transition zone in coastal aquifers, includingchanges in the thickness and the position of the transition zonefollowing from changes in base level (i.e. sea-level variations) (e.g.Meisler et al., 1984; Underwood et al., 1992; Essink, 1996; Kiro et al.,2008; Yechieli et al., 2010). Many of the studies also focus on thetime involved for a new equilibrium to be established between thenew base level (i.e. sea-level) and the interface position and/ortransition zone thickness. Lambrakis and Kallergis (2001) andLambrakis (2006) studied freshening times of coastal groundwaterin Greece after it had first gone through salinization due to over-pumping.

Meisler et al. (1984) studied the effects of large-scale eustaticsea-level fluctuations on the seawaterefreshwater interface alonga cross section (240 km long) in thenorthernAtlantic Coastal Plain. Afinite-difference computer model was developed to simulate

f the saltefresh groundwater interface under a sand island, Inhaca,1.020

mailto:lars.varet@gmail.commailto:toonleijnse@gmail.commailto:sylvi.haldorsen@umb.nowww.sciencedirect.com/science/journal/10406182http://www.elsevier.com/locate/quainthttp://dx.doi.org/10.1016/j.quaint.2011.11.020http://dx.doi.org/10.1016/j.quaint.2011.11.020http://dx.doi.org/10.1016/j.quaint.2011.11.020https://www.researchgate.net/publication/248807924_Groundwater_Lens_Dynamics_of_Atoll_Islands?el=1_x_8&enrichId=rgreq-adb31d41f40f045889df76186baf0e2b-XXX&enrichSource=Y292ZXJQYWdlOzI1NDg1NjU4OTtBUzoxNDI2ODkwMzUxMDAxNjJAMTQxMTAzMTEyNTkxNA==https://www.researchgate.net/publication/236538812_Time_response_of_the_water_table_and_saltwater_transition_zone_to_a_base_level_drop?el=1_x_8&enrichId=rgreq-adb31d41f40f045889df76186baf0e2b-XXX&enrichSource=Y292ZXJQYWdlOzI1NDg1NjU4OTtBUzoxNDI2ODkwMzUxMDAxNjJAMTQxMTAzMTEyNTkxNA==https://www.researchgate.net/publication/236538812_Time_response_of_the_water_table_and_saltwater_transition_zone_to_a_base_level_drop?el=1_x_8&enrichId=rgreq-adb31d41f40f045889df76186baf0e2b-XXX&enrichSource=Y292ZXJQYWdlOzI1NDg1NjU4OTtBUzoxNDI2ODkwMzUxMDAxNjJAMTQxMTAzMTEyNTkxNA==https://www.researchgate.net/publication/236537149_Response_of_the_Mediterranean_and_Dead_Sea_coastal_aquifers_to_sea_level_variations?el=1_x_8&enrichId=rgreq-adb31d41f40f045889df76186baf0e2b-XXX&enrichSource=Y292ZXJQYWdlOzI1NDg1NjU4OTtBUzoxNDI2ODkwMzUxMDAxNjJAMTQxMTAzMTEyNTkxNA==https://www.researchgate.net/publication/228602274_On_Eustatic_Sea_Level_History_Last_Glacial_Maximum_to_Holocene?el=1_x_8&enrichId=rgreq-adb31d41f40f045889df76186baf0e2b-XXX&enrichSource=Y292ZXJQYWdlOzI1NDg1NjU4OTtBUzoxNDI2ODkwMzUxMDAxNjJAMTQxMTAzMTEyNTkxNA==https://www.researchgate.net/publication/222516791_Multicomponent_heterovalent_chromatography_in_aquifers_Modelling_salinization_and_freshening_phenomena_in_field_conditions?el=1_x_8&enrichId=rgreq-adb31d41f40f045889df76186baf0e2b-XXX&enrichSource=Y292ZXJQYWdlOzI1NDg1NjU4OTtBUzoxNDI2ODkwMzUxMDAxNjJAMTQxMTAzMTEyNTkxNA==https://www.researchgate.net/publication/222516791_Multicomponent_heterovalent_chromatography_in_aquifers_Modelling_salinization_and_freshening_phenomena_in_field_conditions?el=1_x_8&enrichId=rgreq-adb31d41f40f045889df76186baf0e2b-XXX&enrichSource=Y292ZXJQYWdlOzI1NDg1NjU4OTtBUzoxNDI2ODkwMzUxMDAxNjJAMTQxMTAzMTEyNTkxNA==https://www.researchgate.net/publication/222455721_Refining_the_eustatic_sea-level_curve_since_the_Last_Glacial_Maximum_using_far-_and_intermediate-field_sites?el=1_x_8&enrichId=rgreq-adb31d41f40f045889df76186baf0e2b-XXX&enrichSource=Y292ZXJQYWdlOzI1NDg1NjU4OTtBUzoxNDI2ODkwMzUxMDAxNjJAMTQxMTAzMTEyNTkxNA==https://www.researchgate.net/publication/222301363_Reaction_of_subsurface_coastal_aquifers_to_climate_and_land_use_changes_in_Greece_Modelling_of_groundwater_refreshening_patterns_under_natural_recharge_conditions?el=1_x_8&enrichId=rgreq-adb31d41f40f045889df76186baf0e2b-XXX&enrichSource=Y292ZXJQYWdlOzI1NDg1NjU4OTtBUzoxNDI2ODkwMzUxMDAxNjJAMTQxMTAzMTEyNTkxNA==https://www.researchgate.net/publication/27346204_Impact_of_Sea_Level_Rise_on_Groundwater_Flow_Regimes_A_Sensitivity_Analysis_for_the_Netherlands?el=1_x_8&enrichId=rgreq-adb31d41f40f045889df76186baf0e2b-XXX&enrichSource=Y292ZXJQYWdlOzI1NDg1NjU4OTtBUzoxNDI2ODkwMzUxMDAxNjJAMTQxMTAzMTEyNTkxNA==https://www.researchgate.net/publication/12010364_Sea_Level_Change_Through_the_Last_Glacial_Cycle?el=1_x_8&enrichId=rgreq-adb31d41f40f045889df76186baf0e2b-XXX&enrichSource=Y292ZXJQYWdlOzI1NDg1NjU4OTtBUzoxNDI2ODkwMzUxMDAxNjJAMTQxMTAzMTEyNTkxNA==https://www.researchgate.net/publication/12010364_Sea_Level_Change_Through_the_Last_Glacial_Cycle?el=1_x_8&enrichId=rgreq-adb31d41f40f045889df76186baf0e2b-XXX&enrichSource=Y292ZXJQYWdlOzI1NDg1NjU4OTtBUzoxNDI2ODkwMzUxMDAxNjJAMTQxMTAzMTEyNTkxNA==https://www.researchgate.net/publication/11162400_Links_between_climate_and_sea_level_for_the_past_three_million_years?el=1_x_8&enrichId=rgreq-adb31d41f40f045889df76186baf0e2b-XXX&enrichSource=Y292ZXJQYWdlOzI1NDg1NjU4OTtBUzoxNDI2ODkwMzUxMDAxNjJAMTQxMTAzMTEyNTkxNA==https://www.researchgate.net/profile/L_Vaeret?el=1_x_100&enrichId=rgreq-adb31d41f40f045889df76186baf0e2b-XXX&enrichSource=Y292ZXJQYWdlOzI1NDg1NjU4OTtBUzoxNDI2ODkwMzUxMDAxNjJAMTQxMTAzMTEyNTkxNA==https://www.researchgate.net/profile/Anton_Leijnse?el=1_x_100&enrichId=rgreq-adb31d41f40f045889df76186baf0e2b-XXX&enrichSource=Y292ZXJQYWdlOzI1NDg1NjU4OTtBUzoxNDI2ODkwMzUxMDAxNjJAMTQxMTAzMTEyNTkxNA==https://www.researchgate.net/profile/Sylvi_Haldorsen2?el=1_x_100&enrichId=rgreq-adb31d41f40f045889df76186baf0e2b-XXX&enrichSource=Y292ZXJQYWdlOzI1NDg1NjU4OTtBUzoxNDI2ODkwMzUxMDAxNjJAMTQxMTAzMTEyNTkxNA==

L. Været et al. / Quaternary International xxx (2011) 1e92

density-driven groundwater flow within the freshwater system forseveral static sea-level positions. A broad transition zone of300e600 mwas attributed to sea-level fluctuations over millions ofyears. The study concluded that the saltefresh interface is not inequilibrium with present sea levels. This is in agreement with theconclusion by Essink (1996) who also found that a time lag betweencause and effect can be expected to be a few centuries for smallhydrogeologic systems (

L. Været et al. / Quaternary International xxx (2011) 1e9 3

Evergreen forest covers the tall dune ridges down to the sea. Theundulating plain in the central part of the island has grassland andopen evergreen bush land. The lower part of the wetlands isovergrown with freshwater-demanding reeds, while the drierbordering parts are cultivated. Mangroves fringe parts of thecoastline (Fig. 1) (Kalk, 1995).

The change of landscape morphology in Inhaca during theHolocene is not taken into consideration in this study. In general,the main landscape elements are believed to be of pre-Holoceneage (Sénvano et al., 1997).

2.2. Hydrogeology

Drilling of 8 wells in Inhaca showed aeolian sand from thesurface to 30 m below the ground (Muianga, 1992), all assumed tobe of Quaternary age (Sénvano et al., 1997). Little is known aboutthe deeper and older geology, although observations at PontaTorres (Fig. 1) suggested that the sand dunes overlie a base ofcalcareous sandstone (Hobday, 1977) most probably of Neogeneage, as in other places in the Maputo District (Direcção Nacional deGeologia de Moçambique, 1995).

The groundwater level is below the ground surface in most ofthe wetlands, except during heavy rainfall and cyclonic events. Thewetland sediments consist of 0.3e2 m thick peat, which commonlyoverlies aeolian or estuarine sand (Cuamba et al., 2007).

Palaeoclimate data from southern Africa displays a relationshipbetween warm climate and wet conditions, while cooling is asso-ciated with drought (Partridge, 1997; Tyson, 1999; Tyson andPartridge, 2000; Holmgren et al., 2003). This applies to the scaleof a glacial cycle, a millennium, as well as a few centuries. Duringthe Last Glacial Maximum (LGM) (18e16,000 cal BP) the subcon-tinent was cooler and drier than today (Partridge, 1997; Partridge

Fig. 2. Reconstruction of the Maputo Bay based on bathymetric map (Ministério de Defesa Nlevels. Diagonal lines: present land surface. Light grey: dry land in Maputo Bay. Dark grey:

Please cite this article in press as: Været, L., et al., Holocene dynamics oMozambique, Quaternary International (2011), doi:10.1016/j.quaint.2011.1

et al., 1999), but the temperature rose by 6e7 C� towards theHolocene Altithermal (7500e5100 cal BP), with an increase inannual rainfall up to 5e10 % above present (Partridge, 1997;Partridge et al., 1999; Scott and Lee-Thorp, 2004). The effect oftemporary changes in vegetation has not been addressed specifi-cally in this study.

2.3. Sea-level fluctuations and freshwater lens

The Holocene development of Maputo Bay (Fig. 2) has beenreconstructed from the bathymetric data and the Holocenesea-level curve for southeast Africa (Ramsay, 1995). During therapid sea-level rise in the Early Holocene the level reached �10 maround 10,000 cal BP (Ramsay and Cooper, 2002). For profile AeA0

in Fig. 1 a sea-level rise from �10 m at 10,000 cal BP to the presentlevel at around 7400 cal BP (Fig. 2) would have reduced the totalrecharge of Inhaca by >30% due to a gradual reduction in areaabove sea level. Most of this reduction took place on the westernside of the island, where the surface gradient is gentler than in theeast.

Ramsay (1995) found amid-Holocene (5000 cal BP) marine highstand of w3.5 m. The low-lying wetland areas in central Inhacahave an elevation of only 1e2 m a.s.l., and were probably floodedduring the transgression towards this sea-level maximum. This issupported by the occurrence of up to 6 m thick sediments withmarine and estuarine diatoms and bivalves under peat in thepresent freshwater swamp of Lake Tivanine (Fig. 1) (Cuamba et al.,2007), and by the development of a Holocene palaeotidal flat in thecentral area of Inhaca (Sénvano et al., 1997). A high stand of around3 mwould not only have reduced the recharge area, but would alsohave caused a dramatic shift in the position of discharge bound-aries. In addition to this, a marine flooding of central Inhaca would

acional, 1985) and the Holocene sea-level curve (Ramsay, 1995) for three different sea-sea.

f the saltefresh groundwater interface under a sand island, Inhaca,1.020

https://www.researchgate.net/publication/285974052_The_late_Holocene_evolution_of_the_tropical_Island_of_Inhaca_Mozambique?el=1_x_8&enrichId=rgreq-adb31d41f40f045889df76186baf0e2b-XXX&enrichSource=Y292ZXJQYWdlOzI1NDg1NjU4OTtBUzoxNDI2ODkwMzUxMDAxNjJAMTQxMTAzMTEyNTkxNA==https://www.researchgate.net/publication/285974052_The_late_Holocene_evolution_of_the_tropical_Island_of_Inhaca_Mozambique?el=1_x_8&enrichId=rgreq-adb31d41f40f045889df76186baf0e2b-XXX&enrichSource=Y292ZXJQYWdlOzI1NDg1NjU4OTtBUzoxNDI2ODkwMzUxMDAxNjJAMTQxMTAzMTEyNTkxNA==https://www.researchgate.net/publication/285974052_The_late_Holocene_evolution_of_the_tropical_Island_of_Inhaca_Mozambique?el=1_x_8&enrichId=rgreq-adb31d41f40f045889df76186baf0e2b-XXX&enrichSource=Y292ZXJQYWdlOzI1NDg1NjU4OTtBUzoxNDI2ODkwMzUxMDAxNjJAMTQxMTAzMTEyNTkxNA==https://www.researchgate.net/publication/285973988_Late_Quaternary_sedimentary_history_of_Inhaca_Island_Mozambique?el=1_x_8&enrichId=rgreq-adb31d41f40f045889df76186baf0e2b-XXX&enrichSource=Y292ZXJQYWdlOzI1NDg1NjU4OTtBUzoxNDI2ODkwMzUxMDAxNjJAMTQxMTAzMTEyNTkxNA==https://www.researchgate.net/publication/283858250_Atmospheric_circulation_changes_and_palaeoclimates_of_southern_Africa?el=1_x_8&enrichId=rgreq-adb31d41f40f045889df76186baf0e2b-XXX&enrichSource=Y292ZXJQYWdlOzI1NDg1NjU4OTtBUzoxNDI2ODkwMzUxMDAxNjJAMTQxMTAzMTEyNTkxNA==https://www.researchgate.net/publication/274201172_A_Natural_History_of_Inhaca_Island_Mozambique?el=1_x_8&enrichId=rgreq-adb31d41f40f045889df76186baf0e2b-XXX&enrichSource=Y292ZXJQYWdlOzI1NDg1NjU4OTtBUzoxNDI2ODkwMzUxMDAxNjJAMTQxMTAzMTEyNTkxNA==https://www.researchgate.net/publication/249823281_Cainozoic_environmental_change_in_southern_Africa_with_special_emphasis_on_the_last_200_000_years?el=1_x_8&enrichId=rgreq-adb31d41f40f045889df76186baf0e2b-XXX&enrichSource=Y292ZXJQYWdlOzI1NDg1NjU4OTtBUzoxNDI2ODkwMzUxMDAxNjJAMTQxMTAzMTEyNTkxNA==https://www.researchgate.net/publication/249823281_Cainozoic_environmental_change_in_southern_Africa_with_special_emphasis_on_the_last_200_000_years?el=1_x_8&enrichId=rgreq-adb31d41f40f045889df76186baf0e2b-XXX&enrichSource=Y292ZXJQYWdlOzI1NDg1NjU4OTtBUzoxNDI2ODkwMzUxMDAxNjJAMTQxMTAzMTEyNTkxNA==https://www.researchgate.net/publication/249823281_Cainozoic_environmental_change_in_southern_Africa_with_special_emphasis_on_the_last_200_000_years?el=1_x_8&enrichId=rgreq-adb31d41f40f045889df76186baf0e2b-XXX&enrichSource=Y292ZXJQYWdlOzI1NDg1NjU4OTtBUzoxNDI2ODkwMzUxMDAxNjJAMTQxMTAzMTEyNTkxNA==https://www.researchgate.net/publication/248478368_Synthetic_reconstructions_of_southern_African_environments_during_the_Last_Glacial_Maximum_21-18_kyr_and_the_Holocene_Altithermal_8-6_kyr?el=1_x_8&enrichId=rgreq-adb31d41f40f045889df76186baf0e2b-XXX&enrichSource=Y292ZXJQYWdlOzI1NDg1NjU4OTtBUzoxNDI2ODkwMzUxMDAxNjJAMTQxMTAzMTEyNTkxNA==https://www.researchgate.net/publication/248478368_Synthetic_reconstructions_of_southern_African_environments_during_the_Last_Glacial_Maximum_21-18_kyr_and_the_Holocene_Altithermal_8-6_kyr?el=1_x_8&enrichId=rgreq-adb31d41f40f045889df76186baf0e2b-XXX&enrichSource=Y292ZXJQYWdlOzI1NDg1NjU4OTtBUzoxNDI2ODkwMzUxMDAxNjJAMTQxMTAzMTEyNTkxNA==https://www.researchgate.net/publication/248478368_Synthetic_reconstructions_of_southern_African_environments_during_the_Last_Glacial_Maximum_21-18_kyr_and_the_Holocene_Altithermal_8-6_kyr?el=1_x_8&enrichId=rgreq-adb31d41f40f045889df76186baf0e2b-XXX&enrichSource=Y292ZXJQYWdlOzI1NDg1NjU4OTtBUzoxNDI2ODkwMzUxMDAxNjJAMTQxMTAzMTEyNTkxNA==https://www.researchgate.net/publication/229100767_Late_Quaternary_Sea-Level_Change_in_South_Africa?el=1_x_8&enrichId=rgreq-adb31d41f40f045889df76186baf0e2b-XXX&enrichSource=Y292ZXJQYWdlOzI1NDg1NjU4OTtBUzoxNDI2ODkwMzUxMDAxNjJAMTQxMTAzMTEyNTkxNA==https://www.researchgate.net/publication/222319388_9000_Years_of_sea-level_change_along_the_southern_African_coastline?el=1_x_8&enrichId=rgreq-adb31d41f40f045889df76186baf0e2b-XXX&enrichSource=Y292ZXJQYWdlOzI1NDg1NjU4OTtBUzoxNDI2ODkwMzUxMDAxNjJAMTQxMTAzMTEyNTkxNA==https://www.researchgate.net/publication/222319388_9000_Years_of_sea-level_change_along_the_southern_African_coastline?el=1_x_8&enrichId=rgreq-adb31d41f40f045889df76186baf0e2b-XXX&enrichSource=Y292ZXJQYWdlOzI1NDg1NjU4OTtBUzoxNDI2ODkwMzUxMDAxNjJAMTQxMTAzMTEyNTkxNA==https://www.researchgate.net/publication/200033068_Persistent_Millennial-Scale_Climatic_Variability_Over_the_Past_25_thousand_Years_in_Southern_Africa?el=1_x_8&enrichId=rgreq-adb31d41f40f045889df76186baf0e2b-XXX&enrichSource=Y292ZXJQYWdlOzI1NDg1NjU4OTtBUzoxNDI2ODkwMzUxMDAxNjJAMTQxMTAzMTEyNTkxNA==

L. Været et al. / Quaternary International xxx (2011) 1e94

have reduced the volume of the fresh groundwater lens consider-ably. The opposite effect of the 5e10 % higher than present rainfall,simulated by Partridge (1997) for the same period, is believed to benegligible in this setting. For this reason, and due to the low reso-lution of palaeorainfall data, Holocene variation in rainfall has beenignored in this study. Ramsey (1995) indicated a second marinehigh stand in the Late Holocene of about 1.5 m around 1500 cal BP(see Fig. 2), which ended w800 cal BP. Afterwards, relatively stablesea-level conditions have prevailed. The last high stand is includedin the groundwater simulations although it is not as well docu-mented as the one in the Middle Holocene.

3. Materials and methods

Numerical simulations were performed for a simplifiedtwo-dimensional cross section using an adapted version of thefinite element code SUTRA (Voss and Provost, 2003). The modelincluded

i) time-dependent boundary conditions and sources and sinksthrough independent input files and

ii) calculation of spatial statistical moments of the concentrationfield to characterize the transition zone over time

The input files to SUTRA, apart from the moment input file andtime dependency input files, were generated using the graphicaluser interface (GUI) SutraGUI (Winston and Voss, 2004) that isdesigned to run with the ArgusONE� package, and which provides2D Graphical Information Systems (GIS) and meshing support.

A time-dependent sea-level boundary condition was used. Fornodes with vertical coordinates lower than sea level, a prescribedpressure is assumed, with the pressure being determined by thereference pressure at sea level, and a hydrostatic pressure distri-bution below sea level. For nodes above sea level, a freshwaterinflux is assumed.

Spatial statistical moments of the vertical derivative of theconcentration (C) field were calculated along vertical linesdistributed along the length of the cross section (Fig. 3).

The moments are defined as (Govindaraju and Das, 2007):

Fig. 3. Model domain represented by a deformable grid of quadrilaterals. Spatial statist

Please cite this article in press as: Været, L., et al., Holocene dynamics oMozambique, Quaternary International (2011), doi:10.1016/j.quaint.2011.

0th moment:

M0 ¼Z

y

vCvy

dy (1)

1st moment:

M1y ¼Z

y

vCvy

ydy (2)

Considering the derivative of the salt concentration with depthto be a probability density function (PDF), the scaled first momentthat follows from (1) and (2) is then given by:

y ¼ M1yM0

(3)

This first scaled moment, or centre of mass is the mean of thePDF. If the salt concentration with depth would be symmetric, thisis the depth where the derivative of the salt concentration is at itsmaximum, and the salt concentration itself is at 50% of the seawaterconcentration. For the dispersive system, although no saltefreshinterface exists, the first scaled moment is used as an approxima-tion of the vertical position of the interface between salt and freshwater. It has been shown (Eeman et al., 2011) that this is a goodapproximation, even for salt concentration distributions that arenot completely symmetric.

The 2nd central moment of the PDF is defined by:

M2yy ¼Z

y

vCvy

ðy� yÞ2dy (4)

and the variance follows from:

s2yy ¼M2yyM0

(5)

Twice the standard deviation, syy, is used as a measure of thethickness of the transition zone between salt and fresh water. If the

ical moments of the concentration field were calculated along the lines a, b and c.

f the saltefresh groundwater interface under a sand island, Inhaca,11.020

https://www.researchgate.net/publication/252755411_Moment_Analysis_for_Subsurface_Hydrologic_Applications?el=1_x_8&enrichId=rgreq-adb31d41f40f045889df76186baf0e2b-XXX&enrichSource=Y292ZXJQYWdlOzI1NDg1NjU4OTtBUzoxNDI2ODkwMzUxMDAxNjJAMTQxMTAzMTEyNTkxNA==https://www.researchgate.net/publication/249823281_Cainozoic_environmental_change_in_southern_Africa_with_special_emphasis_on_the_last_200_000_years?el=1_x_8&enrichId=rgreq-adb31d41f40f045889df76186baf0e2b-XXX&enrichSource=Y292ZXJQYWdlOzI1NDg1NjU4OTtBUzoxNDI2ODkwMzUxMDAxNjJAMTQxMTAzMTEyNTkxNA==https://www.researchgate.net/publication/229224197_Analysis_of_the_thickness_of_a_fresh_water_lens_and_of_the_transition_zone_between_this_lens_and_upwelling_saline_water?el=1_x_8&enrichId=rgreq-adb31d41f40f045889df76186baf0e2b-XXX&enrichSource=Y292ZXJQYWdlOzI1NDg1NjU4OTtBUzoxNDI2ODkwMzUxMDAxNjJAMTQxMTAzMTEyNTkxNA==

Table 1The range of parameter value input that have been used in the different simulations.

Value Units

Porosity, n 0.30e0.42 eHorizontal K, Khor 12e18 m/dayVertical K, Kver 2.5e3.5/10.5 m/dayRecharge 0.002e0.005 (8e20% of MAP) m/dayLongitudinal dispersivity, aL 15e30 mTransverse dispersivity, aT 1.5e3 m

Table 2Combination of parameter values that generated the best fit to the analytical solu-tion for interface position (Fig. 4).

Parameter Value Units

Porosity 0.42 eKhor/Kver 18/3.5 m/dayRecharge 0.002 (8% of MAP) m/dayaL/aT 15/1.5 m

L. Været et al. / Quaternary International xxx (2011) 1e9 5

salt concentration distribution were to be completely symmetric,twice the standard deviation would give the distance between the16 and 84 percentile.

A single aquifer set-up was used according to the conceptualmodel described earlier. A grid of deformed quadrilaterals was usedto represent a vertical cross section of the Inhaca Island (Fig. 3) fromthe Maputo Bay to the Indian Ocean along the line AeA0 shown inFig.1. The total distance isw8700mwhile the distance from the top(þ3.5 m a.s.l.) to the bottom of the domain was set to w300 m. Anaverage size of 25 � 5 m was used for elements below the presentsea level. Denser vertical element spacing was applied above thepresent sea level in order to be able to redefine nodes from speci-fied pressure to source of fluid and vice versa, reflecting the sameorder of magnitude as experienced for sea-level variations duringthe Middle to Late Holocene.

The estimates of average recharge, permeability and porosity(Table 1) are based on literature data (Bredenkamp et al., 1993;Meyer and Godfrey, 1995; Schwartz and Zhang, 2003; Hiscock,2005), instrumental records (precipitation data), and field data(grain-size distribution). Grain-size analyses of sediments from thesaturated zone showwell-sorted fine tomedium sand, and porosityvalues of 30e42% have been applied in themodel. This is within therange presented by Schwartz and Zhang (2003) for similar sedi-ments. Hydraulic conductivity (K) has been estimated using theempirical Hazen’s formula (Hazen, 1911) which relates grain sizeproperty d10 to K for sediments samples having a uniformitycoefficient d60/d10 < 5. For the grain size samples in this study thismethod indicates K-values of typically w3e20 m/day. Thehydraulic conductivities of the calcareous sandstones that areassumed to underlie the island (Hobday, 1977) are in other areasfound to be in the same range as the K-values of the unconsolidatedsediments on Inhaca (Fish, 1988; Fish and Stewart, 1991). Therefore,it is appropriate to assume the entire model domain ashomogeneous.

At 10,000 cal BP the transition zone did not instantaneouslyreach equilibrium after the preceding rapid sea-level rise. To usethe steady state as an initial condition for the transient model, a fewhundred years was simulated to reach equilibrium with sea-level10,000 cal BP. After this adjustment, the simulated rate of changewas kept constant for w2000 years until present sea level wasreached w7400 cal BP, after which the rate of sea-level rise againchanged.

Longitudinal (aL) and transverse (aT) dispersivity were appliedto account for intrinsic inhomogeneities. It is well known thatdispersivities are scale dependant (Dagan, 1989; Gelhar et al., 1992;Hiscock, 2005). Based on the lower limit for dispersivity, the cellPeclet number

Fig. 4. The best simulated fit to analytical solution for the vertical position of the saltefresh interface. The analytical solution is based on average piezometric heads measured in2003e2005, and the GhybeneHerzberg relation (Ghyben (1888) and Herzberg (1901)), and was obtained for the set of parameters listed in Table 2.

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Center of mass: K = 12/2.5 2x(sq.rt. of var.): K = 12/2.5Center of mass: K = 12/10.5 2x(sq.rt. of var.): K = 12/10.5

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Center of mass: 0.5 mm/day 2x(sq.rt. of var.): 0.5 mm/dayCenter of mass: 0.2 mm/day 2x(sq.rt. of var.): 0.2 mm/day

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Center of mass: por = 0.3 2x(sq.rt. of var.): por = 0.3Center of mass: por = 0.42 2x(sq.rt. of var.): por = 0.42

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Center of mass: Disp.L/T = 30/3 m 2x(sq.rt. of var.): Disp.L/T = 30/3 mCenter of mass: Disp.L/T = 15/1.5 m 2x(sq.rt. of var.): Disp.L/T = 15/1.5 m

f

a b

Fig. 5. Plot of spatial statistical moments of the concentration field along lines a, b and c in Fig. 3 along which spatial statistical moments have been calculated, illustrating theeffects of a) distance to the specified head boundary, b) variable vertical hydraulic conductivity, c) variable horizontal hydraulic conductivity, d) variable recharge rate, e) variableporosity, f) variable dispersivity. For Fig. 5bef the results are only shown for line c in Fig. 3.

L. Været et al. / Quaternary International xxx (2011) 1e96

Please cite this article in press as: Været, L., et al., Holocene dynamics of the saltefresh groundwater interface under a sand island, Inhaca,Mozambique, Quaternary International (2011), doi:10.1016/j.quaint.2011.11.020

Table 3Changes in parameter value input to the model and the effects on simulated interface position, lens thickness, and response time. Only one parameter has been changed at thetime compared to Table 2 if nothing else is stated.

Parameter Value change Change in interfaceposition (m)

Change in lensthickness (m)

Time to reach SSfor interface position

Recharge 0.0002 / 0.0005 (m/day) �w40 �w1.5 fasterKhor/Kver 18/3.5 / 12/2.5 (m/day) �w16 þw3 slowerKhor/Kver 12/2.5 / 12/10.5 (m/day) none �w1.5 no differencePorosity 0.42 / 0.30 none �w2.5 fasteraL/aT 15/1.5 / 30/3 (m) none þw16 no difference

L. Været et al. / Quaternary International xxx (2011) 1e9 7

Later in the simulation, the flow is almost parallel to the interface,in which case the smaller transversal dispersion takes over, causingless mixing. For this reason there is an increase in the thickness ofthe transition zone, followed by a decrease (Fig. 5 aef). This is inline with the findings of Eeman et al. (2011). Another contributingfactor to the spatial distribution of the interface is that the verticalline, along which spatial statistics are calculated, is perpendicularto the interface in the centre of the domain, while this is not thecase close to the seepage boundaries. Also, converging streamlinesclose to the seepage boundaries influence the thickness of thetransition zone close to these boundaries (Eeman et al., 2011).

If the sea-level curve established by Ramsay (1995) is correctInhaca was split into several smaller islands in parts of the Middleand Late Holocene, each developing separate freshwater lenses(Fig. 6). Along the cross-section AeA0 (see Fig. 1) four smaller“islands” are indicated, ranging in width from 600 to 1800 m, asopposed to the present single island. The transient calculationsseen in Fig. 7 are done in the centre of the domain (C in Fig. 3) whichrepresents the transition from one big island (w7000 m across) toseveral smaller islands, and vice versa, as sea-level rises above ordrops below the set flooding threshold of the central low-lyingareas. The timing of the shift in node condition (pressure vs.source of fluid) is driven by the changing sea level according to thesea-level curve constructed by Ramsay (1995) (Fig. 2).

5. Discussion

The response times (hundreds of years) in the saltefreshgroundwater system of Inhaca are affected by horizontal perme-ability, recharge rate, and porosity. A higher permeability allows fora greater flux of water, and thereby shorter response times (Fig. 5c).Similarly, but on a considerably shorter time scale (hours),Underwood et al. (1992) showed response time to tidal variationsto be shorter for higher permeability values in their study of small(250me1000m inwidth) atoll islands. A faster pore flow is neededto account for a higher recharge rate; hence response time becomesshorter (Fig. 5d). The opposite effect is seen for an increased

Fig. 6. The development of multiple groundwater lenses along

Please cite this article in press as: Været, L., et al., Holocene dynamics oMozambique, Quaternary International (2011), doi:10.1016/j.quaint.2011.1

porosity due to the ability to store greater volumes of water(Fig. 5e).

In their study of the lens dynamics of atoll islands Underwoodet al. (1992) concluded that the position of the salt/fresh interfaceis not very sensitive to tidal movement. Therefore, the use ofa non-tidal model is considered adequate to study response times,and variations in the interface position during the Holocene.Underwood et al. (1992) also regarded tidal movement to bedecisive for the mixing process in the transition zone, and usedresponses to tidal variations in the transition zone for calibration.However, the island they studied was considerably smaller thanInhaca and in this case the tidal effect plays a smaller role. Thelength of the time steps used in this study is much longer (1month)than tidal movement. A similar calibration therefore would havebecome meaningless, and transient calibration would in generalhave been difficult due to lack of control data.

The development of a freshwater lens is considerably faster inthe early phase of the process than in the late phase (Fig. 5 aef),i.e. the freshening process goes more slowly as the position of thetransition zone moves towards equilibrium with the given sealevel. The main factors that are decisive for the vertical positioningof the saltefresh interface are horizontal permeability (Fig. 5c)and total recharge. The latter is a function of the recharge rate(Fig. 5d) and recharge area (here: island size) (Fig. 7). Also, asdemonstrated by Yechieli et al. (2010), a low-angle coastaltopography, which particularly is the case for the Maputo Bay onthe western side of Inhaca (see Fig. 2), will have a greater inlandshift of the interface position due to sea-level change compared toa steep coastal topography. Underwood et al. (1992) found that theability to form a lens of fresh water under atoll islands dependedon the relationship between island widths and recharge rate.Generally, for the smaller islands a greater recharge rate wasneeded to form a lens of potable water. For Inhaca the split intofour smaller islands would have meant a great reduction in thevolume of fresh water.

The simulation in Fig. 7 shows repeating freshening and salini-zation processes during the Holocene in response to varying sealevel, indicating response times of a few centuries. Similar response

line AeA0 (Fig. 1) during Holocene sea-level high stands.

f the saltefresh groundwater interface under a sand island, Inhaca,1.020

https://www.researchgate.net/publication/248807924_Groundwater_Lens_Dynamics_of_Atoll_Islands?el=1_x_8&enrichId=rgreq-adb31d41f40f045889df76186baf0e2b-XXX&enrichSource=Y292ZXJQYWdlOzI1NDg1NjU4OTtBUzoxNDI2ODkwMzUxMDAxNjJAMTQxMTAzMTEyNTkxNA==https://www.researchgate.net/publication/248807924_Groundwater_Lens_Dynamics_of_Atoll_Islands?el=1_x_8&enrichId=rgreq-adb31d41f40f045889df76186baf0e2b-XXX&enrichSource=Y292ZXJQYWdlOzI1NDg1NjU4OTtBUzoxNDI2ODkwMzUxMDAxNjJAMTQxMTAzMTEyNTkxNA==https://www.researchgate.net/publication/248807924_Groundwater_Lens_Dynamics_of_Atoll_Islands?el=1_x_8&enrichId=rgreq-adb31d41f40f045889df76186baf0e2b-XXX&enrichSource=Y292ZXJQYWdlOzI1NDg1NjU4OTtBUzoxNDI2ODkwMzUxMDAxNjJAMTQxMTAzMTEyNTkxNA==https://www.researchgate.net/publication/248807924_Groundwater_Lens_Dynamics_of_Atoll_Islands?el=1_x_8&enrichId=rgreq-adb31d41f40f045889df76186baf0e2b-XXX&enrichSource=Y292ZXJQYWdlOzI1NDg1NjU4OTtBUzoxNDI2ODkwMzUxMDAxNjJAMTQxMTAzMTEyNTkxNA==https://www.researchgate.net/publication/248807924_Groundwater_Lens_Dynamics_of_Atoll_Islands?el=1_x_8&enrichId=rgreq-adb31d41f40f045889df76186baf0e2b-XXX&enrichSource=Y292ZXJQYWdlOzI1NDg1NjU4OTtBUzoxNDI2ODkwMzUxMDAxNjJAMTQxMTAzMTEyNTkxNA==https://www.researchgate.net/publication/236537149_Response_of_the_Mediterranean_and_Dead_Sea_coastal_aquifers_to_sea_level_variations?el=1_x_8&enrichId=rgreq-adb31d41f40f045889df76186baf0e2b-XXX&enrichSource=Y292ZXJQYWdlOzI1NDg1NjU4OTtBUzoxNDI2ODkwMzUxMDAxNjJAMTQxMTAzMTEyNTkxNA==https://www.researchgate.net/publication/229224197_Analysis_of_the_thickness_of_a_fresh_water_lens_and_of_the_transition_zone_between_this_lens_and_upwelling_saline_water?el=1_x_8&enrichId=rgreq-adb31d41f40f045889df76186baf0e2b-XXX&enrichSource=Y292ZXJQYWdlOzI1NDg1NjU4OTtBUzoxNDI2ODkwMzUxMDAxNjJAMTQxMTAzMTEyNTkxNA==https://www.researchgate.net/publication/229224197_Analysis_of_the_thickness_of_a_fresh_water_lens_and_of_the_transition_zone_between_this_lens_and_upwelling_saline_water?el=1_x_8&enrichId=rgreq-adb31d41f40f045889df76186baf0e2b-XXX&enrichSource=Y292ZXJQYWdlOzI1NDg1NjU4OTtBUzoxNDI2ODkwMzUxMDAxNjJAMTQxMTAzMTEyNTkxNA==

-180-160-140-120-100-80-60-40-20020406080

0

1000

2000

3000

4000

5000

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7000

8000

9000

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Cal yr BP

m a.s.l.

Center of mass 2x(sq.rt. of var.)

Fig. 7. Plot of spatial statistical moments of the concentration field along line c in Fig. 3illustrating the Holocene dynamics of the saltefresh groundwater interface underInhaca Island. In this case it illustrates the effect of changing the configuration froma big island to a considerably smaller island.

L. Været et al. / Quaternary International xxx (2011) 1e98

times were found by Lambrakis and Kallergis (2001) and Lambrakis(2006) in their studies of freshening times of saline coastal aquifersin Greece.

Steady state simulations indicate that for an initial recharge of0.2 mm/day (8% of MAP) a �10% change in recharge rate will causea vertical shift in the interface position of �4 m. The steady statesimulationwas done for present sea level, hence one island. As bothsea-level rise and wetter than present conditions are associatedwith warmer climate during the Holocene it is likely that a þ10%recharge rate will occur at a time when the recharge area of Inhacawas considerably smaller than today. Hence, the effect of anincreased recharge rate of 10% would have been negligible for theposition of the interface compared to the impact of reducedrecharge area. The same applies to the period of sea-level rise priorto 7000 cal BP. The most recent drier than present period was theLittle Ice Age (700e200 cal BP). Decreased recharge in this periodwould have lifted the interface, but the effect is likely to have beensmall compared to earlier Holocene fluctuations. Thus the Holoceneswitches from terrestrial to marine back to terrestrial conditions,are believed to have effected the interface positionmuchmore thandid the variations in rainfall.

In their study of the effects of large scale sea-levelfluctuations onthe seawaterefreshwater interface in the northern Atlantic CoastalPlain Meisler et al. (1984) concluded that the saltefresh interface isnot in equilibriumwith present sea level. This is in agreement withthe conclusion by Essink (1996) that a time lag between cause andeffect explains why the present groundwater flow regime along theDutch coast is not yet in equilibrium. Essink (1996) further foundthat small hydrogeologic systems (60 m depth ofpotable water. Many of the present drinking water wells close tothe wetlands will be at risk of seawater intrusion and undrinkablein less than two centuries. Of more immediate concern, however, isthe potential development of large scale tourist industry witha high demand for water resulting in over-consumption followedby salt-water intrusion. As seen from the studies by Lambrakis andKallergis (2001) and Lambrakis (2006) freshening time may beconsiderable.

6. Conclusions

The adapted version of SUTRA has proven useful for studyingthe effects of dynamic changes in the saltefresh groundwaterinterface in response to sea-level fluctuations, i.e. the boundarycondition is related to the time-dependent sea level. The calcula-tion of spatial statistical moments of the concentration fieldprovides the opportunity to characterize the transition zone overtime, and to illustrate and compare the results.

The response time is sensitive to porosity, hydraulic conduc-tivity and recharge. Reduced porosity, increased hydraulicconductivity, and increased recharge rate all reduce the responsetime, while dispersivity has no effect. Interface position is deter-mined by the recharge rate and the hydraulic conductivity, whilethe thickness of the transition zone in this non-tidal model iscontrolled by the dispersivity values applied.

The transient model reflects the concept of a changing boundaryconfiguration as a response to fluctuating Holocene sea level, i.e.moving from a one-island concept, as seen today, to a multi-islandconcept during sea-level high stands. The thickness of the transi-tion zone is affected by the vertical movement, and is reducedduring periods of stability. In the multi-island setting the totalrecharge area is dramatically reduced, and so is the volume of freshwater. The effects on future water supply could therefore becomeseverewhere existing coastal aquifers run the risk of fragmentationdue to sea-level rise.

The geomorphologic and hydrogeologic setting seen at InhacaIsland is not believed to be unique, and so the knowledge of thissetting, along with responses to changes in the past, need to betaken into consideration when establishing future managementplans for coastal aquifers.

Acknowledgements

We want to thank the following institutions and persons:Financial funding was provided by the Norwegian Council forHigher Education’s Programme for Development Research andEducation, and by the Norwegian University of Life Sciences. Thefollowing persons have assisted during the different stages of fieldwork: M. Achimo, J. Mugabe and E. Massuanganhe at the EduardoMondlane University, and B. Lirhus, H. Risdal and C. Oddenes, MScstudents at the Norwegian University of Life Sciences. Thanks to the

f the saltefresh groundwater interface under a sand island, Inhaca,11.020

L. Været et al. / Quaternary International xxx (2011) 1e9 9

Soil Physics, Ecohydrology and Groundwater Management Group atthe Wageningen University for their kind hospitality and valuableinput to the modelling work.

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f the saltefresh groundwater interface under a sand island, Inhaca,1.020

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Holocene dynamics of the salt–fresh groundwater interface under a sand island, Inhaca, Mozambique1 Introduction2 Regional setting2.1 Area description and present climate2.2 Hydrogeology2.3 Sea-level fluctuations and freshwater lens

3 Materials and methods4 Results5 Discussion6 ConclusionsAcknowledgementsReferences