the influence of temporal hydrological randomness on seawater intrusion in coastal aquifers

Journal of Hydrology (2006) 330, 285–300

ava i lab le a t www.sc iencedi rec t . com

journal homepage: www.elsevier .com/ locate / jhydrol

The influence of temporal hydrological randomnesson seawater intrusion in coastal aquifers

Carmen Prieto a,*, Anastasia Kotronarou b, Georgia Destouni c

a Department of Land and Water Resources Engineering, Royal Institute of Technology, KTH,Brinellv. 32, SE-100 44 Stockholm, Swedenb Institute for Environmental Research and Sustainable Development, National Observatory of Athens,I. Metaxa and Vas. Pavlou, GR-152 36 P. Penteli, Athens, Greecec Department of Physical Geography and Quaternary Geology, Stockholm University, SE-106 91 Stockholm, Sweden

Received 8 November 2004; received in revised form 24 March 2006; accepted 27 March 2006

Summary We investigate general effects of temporal hydrological randomness on seawaterintrusion in coastal aquifers, using a 2D conceptualization and model parameterization of threecoastal aquifer zones on the Mediterranean Sea. These three aquifer cases represent quite dif-ferent examples of hydrogeological conditions and temporal hydrological and groundwatermanagement variability and statistics. A general result for all aquifer cases is that the effectsof temporal randomness on expected salinity in pumped groundwater are greater for spatiallyhomogeneous than for spatially heterogeneous aquifer representations. We quantify also pre-diction uncertainty around expected groundwater salinity, in terms of the salinity standarddeviation and coefficient of variation (CV) in the different aquifer cases. In general, the salinityCV appears to depend much more on the aquifer depth than on the input temporal fluctuationstatistics of each aquifer case. Aquifer depth may thus be a main indicator for resulting predic-tion uncertainty in salinity of pumped groundwater due to temporal hydrological randomness.

�c 2006 Elsevier B.V. All rights reserved.

KEYWORDSSeawater intrusion;Temporal randomness;Natural recharge;Heterogeneity;Monte-Carlo simulations;Expected salinity;Coefficient of variation

0d

Introduction

Contamination of groundwater by seawater intrusion is amajor concern in many coastal aquifers (Bear et al.,1999; IHP/OHP, 2002; Llamas and Custodio, 2003). Seawa-ter intrusion is a density-dependent flow and solute trans-

022-1694/$ - see front matter �c 2006 Elsevier B.V. All rights reservedoi:10.1016/j.jhydrol.2006.03.024

* Corresponding author. Tel.: +46 8 7908690; fax: +46 8 7908689.E-mail address: [email protected] (C. Prieto).

port problem, which has usually been investigated using adeterministic modelling approach. Density-dependent flowand transport processes, and thereby saltwater intrusionin coastal aquifers, however, have been shown to be sig-nificantly affected by the common and essentially randomspatial variability of hydraulic properties in geologic for-mations (Dagan and Zeitoun, 1998; Simmons et al.,2001; Diersch and Kolditz, 2002; Prasad and Simmons,2003).

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286 C. Prieto et al.

Furthermore, hydrological processes, such as naturalgroundwater recharge are also inherently random in timeand this randomness may also greatly affect subsurface flowand transport processes (Marshall et al., 2000; Foussereauet al., 2000, 2001). Potential effects of temporal random-ness, however, have commonly been neglected in seawaterintrusion studies, which often consider constant annualaverage values of groundwater recharge and other boundaryinflows (e.g., Ghassemi et al., 1996; Oki et al., 1998; Yakire-vich et al., 1998; Paniconi et al., 2001). There is therefore aneed to also investigate the effects of temporal hydrologicalrandomness on the seawater intrusion problem.

In this paper, we present a comparative analysis of sea-water intrusion in three different coastal aquifer zones lo-cated on the Mediterranean Sea. The main objective is toassess, to our best knowledge for the first time, the effectsof temporally random rainfall and boundary conditions onseawater intrusion into coastal aquifers. The three specificcase studies considered here for this purpose are the Coastalaquifer in Israel, the Tsairi basin aquifer on the island ofRhodes, in Greece, and the Akrotiri aquifer in Cyprus, whichhave also previously been studied and reported in the scien-tific literature (Koussis, 2001; Prieto, 2001; Prieto et al.,2001; Koussis et al., 2003; Mazi et al., 2004). From thesethree different aquifer cases, in terms of hydrogeologicaland socio-economically determined groundwater demanddetails and statistics of natural recharge, we specificallyaim at identifying possible general temporal randomnesseffects that may be useful for understanding and quantifyingthe problem of saltwater intrusion in coastal aquifers.

Modelling methodology

General

We simulate deterministically and stochastically groundwa-ter flow and transport dynamics in representative cross-sec-tions of the Coastal aquifer in Israel, the Tsairi basin aquiferon the island of Rhodes, in Greece, and the Akrotiri aquiferin Cyprus (Koussis, 2001; Prieto, 2001; Prieto et al., 2001;Koussis et al., 2003).

Fig. 1a–c shows the two-dimensional cross-sections thatconceptualize typical conditions for the three studied coast-al aquifer zones, illustrating for each case the simulationdomain, assigned boundary conditions, locations of consid-ered representative point sink (pumping, P) and source(artificial recharge, R), and (saturated) hydraulic conductiv-ity value (constant K for homogenous aquifer, or geometricmean KG for heterogeneous aquifer). The three differentconceptual cross-sections and considered pumping and re-charge rates and locations have basically been determinedand parameterized in previous studies (Koussis, 2001;Prieto, 2001; Prieto et al., 2001; Koussis et al., 2003). Atwo-dimensional representation of the Israel aquifer casewith only one point sink for pumping and one point sourcefor artificial recharge may be a reasonable representationof this case’s coastal conditions of relatively uniformly dis-tributed well locations and pumping rates (see Fig. A1Appendix, for case and well locations). For the Rhodesand Cyprus case studies (see Figs. A2 and A3, Appendix,for case and well locations), a flow-weighted-average

pumping rate and location were considered for defining asingle representative pumping well in each case.

In all three case studies, the chosen 2D conceptualiza-tions and parameterizations quantitatively reproduce regio-nal groundwater balances per unit coast-line length and arejustified by the main interest of this paper being to identifygeneral effects of temporal hydrological randomness onlarge-scale regional seawater intrusion problem in coastalaquifers, rather than to predict site-specific salinity distri-butions at given points in space and time. The SUTRA code(Voss, 1984) was used to solve the coupled density-depen-dent groundwater flow and transport equations in all threecross-sections.

Table 1 summarizes the different types of simulation sce-narios considered in each case study. The deterministichomogeneous aquifer scenario (A) does not consider anytype of uncertainty due to either spatial or temporalrandomness. This simulation scenario thus assumes homoge-neous hydraulic conductivity value, K, and deterministicallyknown temporal variability of natural recharge NR (specifiedin all aquifer cases) and upstream boundary inflow QINF

(specified only in the Cyprus aquifer case) (see also Fig. 1for illustrated flow definitions). In the temporally random,homogeneous aquifer scenario (B), the modelled aquifer isassumed to be homogenous and uncertainty stems from ran-dom temporal variability in natural recharge (NR) in the Is-rael and Rhodes case studies, and also from randomtemporal variability in the specified inland boundary inflow(QINF) in the Cyprus case study. In the temporally determin-istic, heterogeneous aquifer scenario (C), the modelledaquifer is assumed to be heterogeneous, with randomnessand uncertainty prevailing only from random spatial variabil-ity in hydraulic conductivity (K); the same hypothetical mag-nitude of random spatial variability is then assumed for allaquifer case studies. Finally, in the temporally random, het-erogeneous aquifer scenario (D), uncertainty stems fromboth spatial (K) and temporal (NR and QINF) randomness.

In all the various stochastic simulation scenarios (B–D),we use the Monte-Carlo approach with 100 different,equally probable realizations of the considered spatialand/or temporal random fields. This number of realizationsassures clearly stable results for the mean groundwatersalinity dynamics, whereas a larger number of realizationsmay be required for greater stability in all details of thestandard deviation dynamics. The number of 100 realiza-tions was a practically chosen trade off between consideredsufficient stability criteria for the overall level (rather thanpoint-wise time and space detail) comparisons of this studyand the necessary computational flexibility for making thesecomparisons between all different spatial–temporal vari-ability scenarios and input data possibilities in and betweenthe three investigated aquifer cases, which was limited bythe computational time involved in each realization.

Initial conditions, model parameters and all input dataexcept hydraulic conductivity, K, and temporally variableNR and QINF, are the same in the purely deterministic (A,Table 1) and all corresponding stochastic (B–D, Table 1)simulation scenarios for each case study. Initial conditionsfor all simulated scenarios are determined by preliminarysimulations, which are calibrated to represent the average(assumed deterministically known) state of the fresh–salt-water transition zone in year 1999, according to available

Temporal average of natural recharge,[NR]aver= 23 m2/month, C= 100 ppm (TDS)

3000 m

500 m

8.5 m

R(1150,-30.45)

QR(t)K= KG= 3.24 10-4 (m/s)

QP(t)

P(1300,-27.9)

Temporalaverage ofspecifiedinflow,

No-flow

Hydrostaticseawaterpressure 50 m

5 m

Initial water table

C= 35000 ppm (TDS)

[QINF]aver= 48 m2/month

c

3500 m500 m

20 m 5 m

100 m

Temporal average of natural recharge, [NR]aver= 209 m2/month, C= 100 ppm (TDS)

No-flow

No-flow

HydrostaticseawaterpressureC= 35000 ppm (TDS)

Initial water table

K= KG= 1.75 10-4 (m/s)QR(t)

R (1350,-60)

QP(t)

P (1500,-60)

a

Temporal average of natural recharge,[NR]aver= 28.5 m2/month, C= 500 ppm (TDS)

K2= 3.24 10-4 (m/s)

K1= K1G= 4.86 10-5 (m/s)

4000 m

500 m

20 m12 m

Hydrostaticseawaterpressure

QR(t) QP(t)

P (1500,-64)R (1350,-67.6)

No-flow

No-flow25 m

1 250 m

Initial water table

C= 35000 ppm (TDS)

150 m

b

Figure 1 Schematic 2D cross-sections used in the groundwater dynamics simulations for: (a) the Israel case study, (b) the Rhodescase study, and (c) the Cyprus case study; the geometric mean value, KG, of hydraulic conductivity, K, in simulation scenarios ofheterogeneous aquifer (C and D, Table 1) is the same as the constant K value used in simulation scenarios of homogeneous aquifer (Aand B, Table 1). The pumping and artificial recharge well positions, P(XP, ZP) and R(XR, ZR), respectively, are given in meters,quantifying horizontal distance from shoreline for the X coordinate and vertical distance from sea level for the Z coordinate. Thetemporal average values of natural recharge (in all aquifer cases) and specified inflow at the upstream inland boundary (in theCyprus aquifer case) are given in m2/month (=m3/month/m coastline), in order to quantify the boundary recharge and inflowentering the aquifer per unit aquifer width normal to mean flow direction in the simulated cross-sections.

Table 1 Types of simulation scenarios considered in each aquifer case

Simulated scenario Hydraulic conductivity, K Natural recharge rate, NR Inland boundary inflowrate, QINF

(A) Homogeneous aquifer,no temporal randomness

Constant Deterministic temporal variability Deterministic temporalvariability

(B) Homogeneous aquiferwith temporal randomness

Constant Random temporal variability Random temporalvariability

(C) Heterogeneous aquifer,no temporal randomness

Random spatial variability Deterministic temporal variability Deterministic temporalvariability

(D) Heterogeneous aquiferwith temporal randomness

Random spatial variability Random temporal variability Random temporalvariability

The influence of temporal hydrological randomness on seawater intrusion in coastal aquifers 287


site-specific information for each case study (Koussis,2001). This state is then perturbed by either starting orchanging of monthly variable pumping and artificial re-charge rates, QP and QR, respectively, to represent futuresite-specific groundwater management practices, accordingto pumping/injection rates and temporal development pro-posed by site-specific water demand projections and eco-nomic QP and QR optimization calculations in earlierstudies (Koussis, 2001; Koussis et al., 2003).

In addition to QP and QR, the effective (infiltration fromrainfall, minus evapotranspiration and surface runoff) nat-ural groundwater recharge NR (in all case studies) and theinland boundary inflow QINF (in the Cyprus case study) arealso monthly variable inputs in both the temporally deter-ministic (A and C, Table 1) and the temporally random (Band D, Table 1) scenarios. In all simulation scenarios (A–D), the total simulation period was 20 years, which was di-vided into 345 time steps of variable size. Initial time stepwas 1129 s and every five time steps, the time step size

Table 2 Physical and numerical parameter values used in the SU

Parameter

Length of simulated cross-section (m)Representative width of simulated cross-section (m)Formation (unsaturated and saturated zone) depthb (m)Mean unsaturated zone depthc (m)Number of elementsNumber of nodesSpatial discretizationHorizontal: Dx (m)Vertical 1: Dy1 (m)Vertical 2: Dy2 (m)

Geometric mean saturated hydraulic conductivity (m/s)Effective porosityLongitudinal dispersivity (m)Transverse dispersivity (m)Fluid compressibility (m s2/kg)Fluid viscosity (kg/m s)Aquifer matrix compressibility (m s2/kg)Parameter a in Van Genuchten equation (m s2/kg)Parameter n in Van Genuchten equationResidual degree of saturationMolecular diffusivity of solute in fluid (m2/s)Base solute concentration (ppm TDS)Freshwater density (kg/m3)Seawater density (kg/m3)Density change with concentration coefficient (kg2/kg TDS m3)a Of which 500 m is on the seaside; over this length, the sea depth go

8.5 m in Cyprus.b On the landside.c Varies in time and space.d For elements above sea level.e For elements within the uppermost soil layer of 25 m.f For elements within the uppermost soil layer of 5 m.g For elements below sea level.h For elements below the uppermost soil layer of 25 m.i For elements below the uppermost soil layer of 5 m.j The uppermost soil layer of 25 m and 1250 m length on the land si

conductivity of 3.24 · 10�4 m/s.

was increased by a factor of 1.4 up to a maximum stepof 1 month.

Table 2 lists all site-specific model parameters used in allsimulation scenarios (A–D, Table 1). The longitudinal andtransverse dispersivity values used in all simulations wererelatively small (Gelhar et al., 1992) in order to representonly intragrid dispersion, since possible field-scale disper-sion due to spatially variable K is explicitly taken into ac-count in the spatial stochastic simulation scenarios (B andD). The longitudinal dispersivity (aL) is 50% of the horizontalmesh size (Dx in Table 2) in all case studies, and the trans-verse dispersivity (aT) is 12.5% of the vertical mesh size (Dy1in Table 2) in the Israel and Rhodes case studies, and 25% ofDy1 in the Cyprus case study.

The selected dispersivity values, however, are still great-er than local dispersivity values measured in the laboratory,which are of the order of a decimeter or less (Nielsen et al.,1986; Gelhar, 1993; Destouni et al., 1994). The dispersivityvalues for the numerical simulations are based on the

TRA simulations for the three case studies

Israel Rhodes Cyprus

4000a 4500a 3500a

16000 2500 4000125 175 55�5 �23 �252200 4460 16402375 4666 1793

25 25 252.5d 2.5e 2.5f

10g 10h 5i

1.75 · 10�4 4.86 · 10�5j 3.24 · 10�4

0.36 0.36 0.212.5 12.5 12.51.25 1.25 1.250 0 010�3 10�3 10�3

0 0 05 · 10�5 5 · 10�5 5 · 10�5

2 2 20.3 0.3 0.310�9 10�9 10�9

100 500 100998 998 9981024 1024 1024750 750 750

es from 0 to 20 m in Israel, from 0 to 12 m in Rhodes, and from 0 to

de in the Rhodes case has a differing assumed constant hydraulic


necessary trade-off between approaching the small labora-tory values as much as possible, while securing a computa-tionally manageable spatial discretization with numericallystable and accurate solution. The numerical limits are givenby the mesh Peclet number, Pe � DL/aL < 4, for the longitu-dinal dispersivity and by aT P DT/10 for the transverse dis-persivity (Voss and Souza, 1987), where DL and DT are thespatial discretizations along the local flow direction andtransverse to it, respectively. The mesh Peclet number,Pe, needs to be smaller than 4 in order to avoid oscillationsin resulting salinity values, and transverse dispersivity (aT)needs to be greater than DT/10 in order to avoid non-real-istic numerical dispersion (Voss and Souza, 1987).

The CPU time on a 2.5 GHz Pentium 4 for each realiza-tion ranges from 5 to 10 min depending on the aquifer casestudy, which means that the maximum simulation time for aset of 100 realizations is about 16 h. This computationaltime may in future studies be significantly reduced bynew advances in adaptive numerical methods, such as adap-tive finite element (Diersch and Kolditz, 2002), finite differ-ence (Alves et al., 2002) and collocation methods (Vasilyevand Bowman, 2000; Gotovac et al., 2003). The adaptive ap-proach uses in cases of narrow transition zone and small dis-persivities a denser discretization only around the transitionzone in order to avoid classical numerical oscillations andartificial dispersion. The efficiency of this adaptive ap-proach is described by the compression ratio, CR, which isthe ratio between the number of non-adaptive points toadaptive points for the same accuracy. For instance byusing the adaptive collocation method of Vasilyev and Bow-man (2000), CR is nearly 50 for most problems, which meansthat for cases such as those of the present paper, the CPUtime for each realization may be reduced 50 times. In fu-ture studies it appears also promising to use parallel algo-rithms (Diersch and Kolditz, 2002) because the Monte-Carlo procedure can then be divided between a number ofprocessors.

Temporally deterministic base scenarios

For the comparative purposes of this paper, the temporallydeterministic simulation scenarios (A and C, with determin-istic NR and QINF flow rates) are hereafter considered as basescenarios for homogeneous and heterogeneous aquifers. Tothe results of these base scenarios, we compare the corre-sponding results of temporally random simulation scenarios(B and D, with random NR and QINF) for all case studies, inorder to identify possible general effects of temporalrandomness.

For consideration of random spatial heterogeneity, weused in all considered aquifer cases a similar, hypotheticalheterogeneity assumption, due to lack of real site-specificcharacterization of spatial heterogeneity and in order to fo-cus on the temporal randomness effects in each case siteand not risk confusing them with site-specific spatial ran-domness effects. Specifically, we generated with HYDRO_GEN (Bellin and Rubin, 1996) 100 spatially correlated ran-dom fields of K assuming a log-normal distribution of K(Y = lnK) and an anisotropic exponential correlation struc-ture. We have for consistency assumed the same rathersmall degree of spatial heterogeneity ðr2

Y ¼ 0:5Þ and thesame horizontal integral scale of Y (Ih[Y] = 100 m) in order

to have at least four nodes per integral scale in the horizon-tal direction in all three case studies. This number of gener-ation points of log conductivity per integral scale has beenfound to be the minimum required for accuracy and conver-gence of computations (Bellin et al., 1992; Rubin, 2003). Inorder to have at least four nodes per integral scale also inthe vertical direction, the anisotropy ratio between the ver-tical integral scale Iv[Y] and Ih[Y] was chosen to be equal to0.4 for the Israel and Rhodes case studies and 0.2 for the Cy-prus case study.

Moreover, the geometric mean of K, denoted KG (seeFig. 1 and Table 2), for heterogeneous aquifer scenarios(C and D, Table 1) was chosen equal to the constant K-valuein homogeneous aquifer scenarios (A and B, Table 1; thespatial domains in which randomly variable K is consideredin the different case studies are indicated by thick surround-ing lines in Figs. 1a–c), which is consistent with the factthat KG is the effective conductivity for 2-D, constant-den-sity steady flow in an isotropic, lognormal K field (Rubin,2003). By using K = KG and the same dispersivity values inboth the homogeneous (scenarios A and B) and the hetero-geneous (scenarios C and D) scenarios, the homogeneoussimulations have the same average flow and intra-grid dis-persion conditions as any field realization of the correspond-ing heterogeneous simulations and, direct comparisonbetween their results is justified.

Fig. 2 shows for all three aquifer cases their differing 20-year time series of assumed deterministically known, yettemporally variable total groundwater inflow, NR + QINF, inthe base simulation scenarios A and C, as generated andused by previous site-specific studies (Koussis, 2001; Koussiset al., 2003). Fig. 2 also shows the monthly variable pump-ing QP and artificial recharge QR rates used in all simulationscenarios (A–D) for each case study.

Temporally random scenarios

In the temporally random, homogeneous aquifer scenario(B), 100 different realizations of temporally random naturalrecharge rate, NR, are used as the specified upper boundarycondition (Fig. 1). All different realizations have the sameassumed homogeneous hydraulic conductivity, initial andother boundary conditions, and other input parameter val-ues (see Fig. 1 and Table 2). In the temporally random, het-erogeneous aquifer scenario (D), each one of 100 randomspatial K field realizations is coupled with one of 100 inde-pendently generated temporally random NR realizations. Inthe Cyprus case study, each spatial K-field realization is cou-pled with two K-independent, but mutually correlated tem-poral random variables, the natural recharge NR and theinflow through the inland boundary QINF.

For the Israel case study, the deterministic and randomtime series of annual NR values were generated in a previ-ous study (Koussis, 2001), based on statistics from a 62-year record of annual groundwater recharge value andassuming a normal distribution for groundwater recharge.Monthly values were then generated from the annual ones,by distributing the total recharge volume of each hydro-logic year evenly over the five winter months, Novemberto March.

In the Rhodes case study, the used deterministic and ran-dom time series of monthly NR has also been obtained in

0 5 10 15 20Time (yr)

0

100

200

300

400

500

600

700

800

Flo

wra

tes

(m3

mon

th-1

m-1) Israel case study QP QR

NR+QINF

a

0 5 10 15 20Time (yr)

0200400600800

100012001400160018002000

Flo

wra

tes

(m3

mon

th-1

m-1) Cyprus case study

QP

NR+QINF

QR

c

0 5 10 15 20Time (yr)

0

50

100

150

200

250

300

350

400

450

Flo

wra

tes

(m3

mon

th-1

m-1) Rhodes case study

NR+QINF

QPQR

b

Figure 2 Temporally deterministic total inflow sum NR + QINF of monthly variable natural recharge, NR, and inland boundaryinflow, QINF, used in the temporally deterministic base scenarios (A and C, Table 1), along with the deterministic monthly variablepumping, QP, and artificial recharge, QR, rates used in all simulation scenarios (A–D, Table 1) for: (a) the Israel case study, (b) theRhodes case study, and (c) the Cyprus case study. The total inflow NR + QINF, pumping, QP, and artificial recharge, QR, rates are givenin m2/month (=m3/month/m coastline) in order to quantify them all per unit aquifer width normal to mean flow direction in thesimulated cross-sections (Fig. 1).


previous studies (Koussis, 2001; Koussis et al., 2003), byapplying and calibrating the surface hydrologic model SWAT(soil and water assessment tool, Neitsch et al., 1999) onavailable hydrologic data for the Tsairi basin. A set of 100random rainfall time series was generated by the weathergenerator ClimGen (Nelson, 1996), based on a 10-year re-cord of daily precipitation and maximum and minimum airtemperature, and used as input to SWAT.

Also in the Cyprus case study, previous studies (Koussis,2001) generated the random monthly time series of NR

and QINF considered here, by use of the multivariate sea-sonal or monthly generation model of Matalas (1967),

assuming correlation between NR and QINF. This generatorused as seed the deterministic 20-year time series ofmonthly NR and QINF, obtained from the hydrological PRMSmodel (precipitation-runoff modelling system; Leavesleyet al., 1983; Leavesley and Stannard, 1995) [operated withinthe USGS’MMS (modular modelling system; Leavesley et al.,1996a,b; Leavesley et al., 2002)] that was calibrated for theconsidered study basin (Mazi et al., 2004).

Fig. 3 shows the main statistics of the temporally randominput field NR + QINF for the different aquifer cases. Specifi-cally, Fig. 3 illustrates the monthly variable expected value(Fig. 3a), standard deviation, SD, (Fig. 3b) and coefficient of

0 5 10 15 20Time (yr)

0

100

200

300

400

500

600

E[N

R+

QIN

F](

m3

mon

th-1

m-1)

a

RhodesIsrael Cyprus

0 5 10 15 20Time (yr)

0

50

100

150

200

250

300

SD

[NR+

QIN

F](

m3

mon

th-1

m-1)

b

c

RhodesIsrael Cyprus

0 5 10 15 20Time (yr)

0

2

4

6

8

10

CV

[NR+

QIN

F]

RhodesIsrael Cyprus

Figure 3 Monthly variable ensemble statistics of the temporally random total inflow sum NR + QINF, of random natural recharge,NR, and inland boundary inflow, QINF, used in the temporally random simulation scenarios (B and D, Table 1), on terms of:(a) expected value E[NR + QINF], (b) standard deviation SD[NR + QINF], and (c) coefficient of variation CV[NR + QINF].


variation, CV, (Fig. 3c) of NR + QINF, resulting from all 100realizations of NR and QINF for each case study. As shownin Fig. 3, the temporally random total inflow sum NR + QINF

is quite different from case to case. The Israel aquifer casehas the generally highest expected inflow NR + QINF (Fig. 3a),but the smallest CV of NR + QINF (Fig. 3c). On the contrary,Rhodes has the generally lowest expected (Fig. 3a) but thehighest CV (Fig. 3c) value of the inflow sum NR + QINF. Theabsolute standard deviation of NR + QINF, however, exhibitsits largest values for Cyprus and the smallest for Rhodes(Fig. 3b). On the average over the 20-year simulation peri-od, however, the Israel case has higher standard deviationthan Cyprus.

In all aquifer cases, the average values of NR and QINF

over the 20-year simulation period are equal in both the

temporally deterministic (A and C, Table 1) and the tempo-rally random (B and D, Table 1) simulation scenarios. Thisequality means that the cumulative freshwater volumesprovided by the expected NR and QINF over the 20-year sim-ulation period in the random scenarios B and D equal thoseprovided by the deterministic scenarios A and C.

Results

Temporally deterministic base scenarios

Figs. 4a–c show the temporal evolution of expected salinityin pumped groundwater resulting from the simulation of thetemporally deterministic base scenarios for homogenous (A

0 5 10 15 20Time (yr)

100

200

300

400

500

600

TD

S(p

pm)

atP

(150

0,-6

0)

0

0.2

0.4

0.6

0.8

1

CV

[CS]a

tP(1

500,

-60)

CD for homogeneous aquifer

CV[CS] forheterogeneousaquifer

aE[CS] for heterogeneous aquiferIsrael case study

0 5 10 15 20Time (yr)

6000

7000

8000

9000

10000

11000

12000

13000

14000

15000

TD

S(p

pm)

atP

(150

0,-6

4)

0

0.2

0.4

0.6

0.8

1

CV

[CS]a

tP(1

500,

-64)

CD forhomogeneousaquifer

E[CS] forheterogeneousaquifer

CV[CS] forheterogeneousaquifer

b

Rhodes case study

c

0 5 10 15 20Time (yr)

300

600

900

1200

TD

S(p

pm)

atP

(130

0,-2

7.9)

0

0.2

0.4

0.6

0.8

1

CV

[CS]a

tP(1

300,

-27.

9)CD for homogeneous aquifer

CV[CS] forheterogeneousaquifer E[CS] for

heterogeneousaquifer

Cyprus case study

Figure 4 Resulting expected salinity in pumped groundwater from the temporally deterministic base scenario A (Table 1) forhomogeneous aquifer (CD, dashed line) and C (Table 1) for heterogeneous aquifer (E[CS], solid line), as well as the resultingcoefficient of variation of salinity in pumped groundwater CV[CS] (dashed-dot-dot line) for the heterogeneous base scenario C (Table1) for: (a) the Israel case study, (b) the Rhodes case study, and (c) the Cyprus case study.


in Table 1, with salinity denoted CD) and heterogeneous (C inTable 1, with expected salinity denoted E[CS]) aquifer in eachcase study. In addition to CD and E[CS], each figure also showsthe coefficient of variation, CV[CS], of salinity in pumpedgroundwater obtained from the heterogeneous aquifer sce-nario (C).

In all three aquifer cases, the salinity results CD and E[CS]for the homogeneous and heterogeneous aquifer scenarios,respectively, follow the same general patterns of temporaldevelopment and dynamics. However, there are still somedifferences between the homogenous and heterogeneousaquifer results, and there are also random fluctuationsaround expected salinity E[CS] in the heterogeneous aquiferscenario, as quantified by CV[CS], due to the detailed differ-ences among the 100 equally probable aquifer realizations.

In general, the overall magnitude and temporal evolutionof salinity in pumped groundwater is for each case study

determined by the site-specific location and extent of theinitial transition zone, and the actual locations and intro-duced changes from initial conditions in pumping and re-charge flow rates, which all differ between the three casestudies. These case-specific conditions determine the dif-fering general trends of salinity development in the differ-ent cases, yielding: a general salinity increase from aninitial low salinity level until reaching a higher (than the ini-tial) salinity plateau in the Israel aquifer case; a generalsalinity decrease from an initial high salinity level untilreaching a lower (than initial) salinity plateau in the Rhodesaquifer case; and no general salinity change trend from, butonly temporal fluctuations around the low initial salinity le-vel of 100 ppm in the Cyprus case. The different aquifercases represent different overall salinity developments sim-ply due to their differing initial conditions and differinggroundwater management changes (in pumping and


artificial recharge rates, as determined by site-specificwater demand projections and economic viability) fromthese respective initial conditions.

In order to distinguish possible general effects of tempo-ral randomness on expected salinity development, regard-less of case-specific initial and trend differences in thisdevelopment, we illustrate in the following results of thetemporally random scenarios, E[CT] for homogeneous aqui-fer (scenario B, Table 1) and E[CST] for heterogeneous aqui-fer (scenario D, Table 1) relative to the correspondingtemporally deterministic results (scenarios A and C, Table1) in each case study. That is, we illustrate temporal ran-domness effects on expected salinity in terms of the ratiosE[CT]/CD and E[CST]/E[CS].

Regarding the resulting coefficient of variation, CV[CS],Fig. 4 shows that its overall magnitude and temporal evolu-tion is consistently determined by the differing salinity ini-tial conditions and expected development trends in thedifferent case studies. In the Israel and Rhodes cases, CV[CS]exhibits a general trend of increasing to a maximum valueuntil the expected salinity reaches its overall plateau valuein each of these cases, after which time also the CV[CS] sta-bilizes, or starts to decrease again. Also in the Cyprus casestudy, CV[CS] follows similar temporal fluctuation patternsas the corresponding site-specific expected concentration.Generally for all aquifer cases, the peaks in CV[CS] coincidewith the timing of the greatest differences between ex-pected and deterministic salinity values. In analogy with ex-pected salinity results, we normalize away the differingCV[CS] trends in the different case studies by illustratingsalinity fluctuations CV[CT] and CV[CST] in the temporallyrandom scenarios (B and D) relative to the correspondingfluctuations CV[CS] due to spatial heterogeneity only. Thatis, we illustrate temporal randomness effects on salinityCV in terms of the ratios CV[CT]/CV[CS] and CV[CST]/CV[CS],in order to identify possible general effects beyond case-specific salinity development trends.

Temporally random scenarios

Fig. 5 shows the effect of temporally random rainfall andupstream inflow on expected salinity in pumped groundwa-ter, in terms of the resulting ratios E[CT]/CD and E[CST]/E[CS] for the homogeneous and heterogeneous aquifer sce-narios, respectively. In all three case studies, the effectof temporal randomness on expected salinity is negligibleinitially, due to the considered same, deterministic initialconditions for all simulation scenarios, until the movementof the initial salinity transition zone due to site-specificgroundwater management (pumping and artificial recharge)changes starts to affect pumped groundwater. After thatinitial period, deviations of E[CT] from CD and of E[CST] fromE[CS] start to occur due to the temporally random inflowconditions. The ratios E[CT]/CD and E[CST]/E[CS], for homo-geneous and heterogeneous aquifer scenarios, respectively,however, remain also then mostly close to 1, implying rela-tively small temporal randomness effects, except for theCyprus case study. Specifically, at the time (t = 19.5 yr) ofthe greatest temporal fluctuation in expected/deterministicsalinity in the Cyprus case (Fig. 4c), the expected salinityE[CST] is only 0.4 of E[CS] in the heterogeneous aquifer

scenario, while E[CT] is only 0.2 of CD in the homogeneousaquifer scenario. Generally, for all three investigated aqui-fer cases, the effect of temporal randomness on expectedsalinity is smaller for heterogeneous (E[CST]/E[CS]) thanfor homogeneous (E[CT]/CD) aquifer conditions.

Fig. 6 illustrates the effects of temporal hydrologicalrandomness on the resulting salinity fluctuations among dif-ferent, equally probable spatio-temporal field realizations,as quantified by the resulting salinity CV value. Specifically,Fig. 6 shows the resulting relative effects in terms of the ra-tio CV[CST]/CV[CS] for combined spatio-temporal fluctua-tions, and the ratio CV[CT]/CV[CS] for only temporalfluctuations, in comparison to the salinity fluctuations ob-tained from only spatial heterogeneity (CV[CS]). In the Israeland Rhodes case studies, the ratio CV[CT]/CV[CS] is smallerthan 1 over the entire simulation period, while for Cyprus itis mostly greater than 1. This means that for both Israel andRhodes, the salinity fluctuation effect of temporal random-ness is smaller than that of spatial randomness, even for thegenerally small spatial heterogeneity (logK variance of 0.5)considered here, whereas the opposite applies to the Cypruscase. As a consequence, the salinity fluctuation effect ofcombined spatio-temporal randomness expressed by the ra-tio CV[CST]/CV[CS] is relatively small in the Israel andRhodes aquifer cases (CV[CST]/CV[CS] mostly close to 1),and much greater in the Cyprus case (CV[CST]/CV[CS] oftenmuch greater than 1), relative to the salinity fluctuation ef-fects of only spatial heterogeneity.

Figs. 7a and b further show that the considerably morepronounced effect of temporal randomness on the salinityCV in the Cyprus case, compared to the Israel and Rhodescases, cannot be explained by the input statistics of randomtemporal fluctuations in either relative terms (consideringaverage CV of NR + QINF over the 20-year simulation period,CV[NR + QINF]

aver), or absolute terms (average standard devi-ation of NR + QINF over the 20-year simulation period,SD[NR + QINF]

aver). Specifically, Figs. 7a and b illustrate theresulting 20-year average CV of CT, CV[CT]aver (scenario B,Table 1, which depends on temporal randomness only),against the input statistics CV[NR + QINF]

aver (Fig. 7a) andSD[NR + QINF]

aver (Fig. 7b) for all aquifer cases, showing norelationship between CV[CT]aver and these input randomnessmeasures. Fig. 7c, however, indicates that CV[CT]aver is in-stead related to aquifer depth, which thus provides a possi-ble explanation for the generally greater impact oftemporal randomness in the Cyprus case study (Figs. 5 and6) that has a considerably shallower aquifer than the Israeland Rhodes cases (Fig. 1).

In principle, many different site conditions and modelparameter choices could affect CV[CT]aver, besides aquiferdepth H, and one may choose a sensitivity analysis investi-gation approach to investigate selected individual effectsof different model conditions and parameters by makinghypothetical changes of conditions and parameters in a sin-gle aquifer case. The investigation approach chosen here,however, is instead a comparative multiple-case investiga-tion of several (even though limited to three) different real-istically parameterized aquifer cases, including all the sitecondition differences that exist and we can quantify be-tween these different cases. The aim of this comparativemultiple-case investigation was to identify possible generaldominant controls and effects of temporal hydrological

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Figure 5 Relative effect of temporal randomness on expected salinity in pumped groundwater, expressed in terms of expectedsalinity ratio E[CT]/CD for homogeneous aquifer (scenarios A and B, Table 1) and E[CST]/E[CS] for heterogeneous aquifer (scenarios Cand D, Table 1) for: (a) the Israel case study, (b) the Rhodes case study, and (c) the Cyprus case study. E[CT] and E[CST] are theexpected salinity in pumped groundwater resulting from the homogeneous and heterogeneous temporally random scenarios B and D(Table 1), and CD and E[CS] are the corresponding salinity results from the temporally deterministic base scenarios A and C (Table 1)shown in Fig. 4.


randomness within the complex interplay of multiple pro-cess and parameter effect interactions that may vary be-tween real aquifer system cases. Our mere three-casenumerical simulation investigation is of course too limitedto yield alone conclusive general results for all possibleaquifer system configurations, but the identification of aqui-fer depth H as a possible main control of resulting predictionuncertainty in salinity of pumped groundwater due to tem-poral randomness still takes one step forward in providing,not proof, but a potentially useful indication for furtherinvestigation efforts to test and support, modify or falsify.

For our own problem and results understanding, wehave also complemented our various CV[CT]aver relationinvestigations with sensitivity analyses where differentmodel parameters were changed from their consideredrealistic range in the different aquifer cases (Berglundet al., 2000; Koussis, 2001). Fig. 7c includes such a sensi-tivity analysis example for CV[CT]aver under a hypotheticalparameterization of the Israel case study with an aquiferdepth H = 55 m instead of its base value H = 125 m. Thischange scenario follows also the obtained inverse relationbetween CV[CT]aver and aquifer depth H. No one of our

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Figure 6 Relative effect of temporal randomness on the salinity coefficient of variation, expressed in terms of ratio CV[CST]/CV[CS], which relates the combined spatial–temporal randomness effects to those from pure spatial randomness, and CV[CT]/CV[CS], which relates the pure temporal randomness effects to those from pure spatial randomness, for: (a) the Israel case study, (b)the Rhodes case study, and (c) the Cyprus case study. CV[CST] is the coefficient of variation of salinity in pumped groundwaterresulting from the temporally random, heterogeneous aquifer scenario D (Table 1); CV[CT] from the temporally random,homogeneous aquifer scenario B (Table 1); and CV[CS] from the heterogeneous base scenario C (Table 1) as shown in Fig. 4.


relation and sensitivity investigations indicated a similarlyclear and robust CV[CT]aver relation as that betweenCV[CT]aver and aquifer depth H in Fig. 7c. For comparisonwith the obtained CV[CT]aver relation to H, Fig. 8 alsoexemplifies the CV[CT]aver relation to the vertical distanceof the pumping well from sea level (ZP) in the differentaquifer cases. An apparently similar relation was obtainedbetween CV[CT]aver and ZP as that between CV[CT]aver andH in Fig. 7c. However, in contrast to the latter relation’sinsensitivity to the exemplified hypothetical change of Hin the Israel case from H = 125 m to H = 55 m (Fig. 7c),the former relation was quite offset by a similar hypothet-

ical change of the Cyprus case ZP value from ZP = 28 m toZP = 13 m.

Discussion and conclusions

We have investigated the influence of temporal hydrologicalrandomness on saltwater intrusion, by consideration ofthree different aquifer case studies, modeled on availabledata for three coastal aquifer zones on the MediterraneanSea. These case studies represent quite different systemcombinations of temporal inflow statistics, with regard tonatural groundwater recharge and upstream boundary

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Figure 7 Relation of the resulting 20-year average salinity coefficient of variation, CV[CT]aver, from pure temporal randomness(scenario B, Table 1) to: (a) the 20-year average coefficient of variation, CV[NR + QINF]

aver, of temporally random inflows NR + QINF,(b) the 20-year average standard deviation, SD[NR + QINF]

aver, of temporally random inflows NR + QINF, and (c) aquifer depth, H. Aconsiderable, inverse relation is found only for aquifer depth, H, for which the illustrated regression line (dashed) isCV[CT]aver = �0.002 Æ H + 0.375 [R2 = 0.93]. This relation is not changed by introduction of a new point (Scenario 1) for a hypotheticalparameterization of the Israel case study with an aquifer depth H = 55 m instead of its base value H = 125 m. NR and QINF are definedas in Fig. 3.


inflow, and other case conditions and parameter values.Nevertheless, all three case studies exhibit similarly a rela-tively small (less than a factor 2) effect of temporal ran-domness on expected salinity in pumped groundwater,with occasional exceptions at times of large fluctuationsin both expected and deterministic salinity. In all threeinvestigated aquifer cases, the temporal randomness effecton expected salinity is further more pronounced in a homo-geneous than in a heterogeneous aquifer scenario, with ran-dom spatial variability being explicitly considered in thelatter.

We have also quantified prediction uncertainty aroundexpected salinity in terms of resulting salinity coefficientof variation, CV[CT] due to temporal randomness alone,and CV[CST] due to combined temporal and spatial random-ness. Our results indicate that, for the aquifer cases inves-tigated here, the magnitude of CV[CT] and the temporalrandomness contribution to CV[CST] do not primarily relateto input temporal fluctuation statistics, but rather to aqui-fer depth, H.

Specifically, CV[CT] exhibits a clear inverse relationshipwith H, thus identifying aquifer depth as a possible main

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Figure 8 Relation of the resulting 20-year average salinity coefficient of variation, CV[CT]aver, from pure temporal randomness(scenario B, Table 1) to the vertical distance of the pumping well from sea level, ZP, for all three main investigated aquifer basecases, a hypothetical parameterization of the Israel case study with aquifer depth H = 55 m and ZP = 40 m (Scenario 1), and ahypothetical parameterization of the Cyprus case study with ZP = 13 m instead of its base value ZP = 28 m (Scenario 2).


indicator for resulting prediction uncertainty in salinity ofpumped groundwater due to temporal randomness. This re-sult indicates as a testable hypothesis, for further investiga-tions to support or falsify, that temporal randomnesseffects on salinity prediction uncertainty may in practicebe negligible for deep aquifers, but significant in shallowones.

The found relatively small temporal randomness effectson groundwater salinity are consistent with results fromprevious numerical experiments of subsurface flow and sol-ute transport dynamics in integrated unsaturated–satu-rated subsurface water systems (Foussereau et al., 2001).Temporal fluctuations around mean precipitation and asso-ciated infiltration and solute transport through the soil sur-face and shallow unsaturated zone may be large. However,the results of Foussereau et al. (2001) show that these fluc-tuations are dampened considerably as the water and solutetransport front and plume movement is traced furtherdownstream through the unsaturated zone and into andthrough the groundwater system. Resulting temporal fluctu-ations in downstream groundwater flow and tracer transportmay thus be relatively small even for temporally high-vari-able water and tracer inputs at the soil surface.

The sources of temporal flow randomness are also in thepresent study at the soil surface and the upstream inlandboundary, i.e., upstream of the coastal groundwater pump-ing locations, for which the salinity in pumped groundwateris quantified. By analogy with previous subsurface flow andtransport results (Foussereau et al., 2001), the temporalfluctuations at these upstream water inflow boundariesshould be attenuated as the water flows downstreamthrough the unsaturated zone and groundwater system to-wards the coast. The present numerical findings of rela-tively small effects of upstream temporal inflowrandomness on downstream coastal groundwater flow andsalinity dynamics are thus physically reasonable.

Furthermore, in contrast to temporal inflow randomness,spatial heterogeneity exists and causes both deterministicand random flow and transport fluctuation componentsthroughout the entire subsurface system. It is therefore alsophysically reasonable for upstream, near-surface temporalinflow variability and randomness to yield smaller relative

effects on downstream coastal groundwater flow and salin-ity in heterogeneous than in homogeneous aquifer cases, asfound in the present study. Deeper aquifers may furtherhave a greater fraction of total groundwater flow with far-field recharge origin than shallower aquifers. This impliesgreater downstream attenuation of temporal fluctuation ef-fects and thus smaller such fluctuation components in thedeeper than in the shallower aquifers, as is also indicatedby the aquifer-depth dependence of temporal randomnesseffects in the present results.

The numerically based hypothesis that temporal random-ness effects on salinity prediction uncertainty may be negli-gible for relatively deep aquifers is thus physically possibleand worthy of further investigation and testing. Its practicalimplications are that complex observations and simulations,accounting for temporal hydrological randomness and itspossible effects, may not be needed for relevant predictionsof expected future salinity fluctuations in pumped ground-water from deeper coastal aquifers, even through theymay be essential for more shallow ones. The computation-ally expensive simulation of complex groundwater–seawa-ter interaction dynamics in coastal aquifers would furthergreatly benefit from new adaptive numerical techniques.Such techniques could in future investigations allow forgreater computational flexibility and improved stability inall space–time statistics details, and thus for both morecomprehensive and better resolved analysis of combinedspatial–temporal variability and randomness effects on sea-water intrusion dynamics.

Acknowledgements

This work was funded by the Swedish Research Council(VR) and the WASSER project of the European Commis-sion’s Directorate General for Research (DG12) under con-tract ENV4-CT97-0459. We gratefully acknowledge thecontribution of Hrvoje Gotovac in the original stochasticmodelling set-up, and of the whole WASSER consortiumto the conceptualization and data support of the threecase studies.


Appendix

Figs. A1–A3 show the geographic location and currentpumping location conditions of each case study. The coastalregion considered in the Israel case study (Fig. A1) is the16 km wide Nitzanim area (Strips 8–11, with boundaries in

Figure A1 Map of the modelled Nitzanim a

Figure A2 Map of the Tsairi basin in the island of Rhodes (Grecatchment areas: the so-called inland and coastal zones.

Strips 7 and 12). The modelled area in the Rhodes case studyis 2.5 km wide and comprises the coastal and inland zonespresented in Fig. A2. The area modelled in the Cyprus casestudy is the Zakaki area, located in the Eastern part of theAkrotiri aquifer, which extends 4 km along the coastline(Fig. A3).

rea in the coastal plain aquifer of Israel.

ece), showing the location of active wells and modelled sub-

Figure A3 Map of the Akrotiri aquifer in the island of Cyprus, showing the location of active wells and the modelled Zakaki area.


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