phytotoxicity of salt and plant salt uptake: modeling ecohydrological feedback mechanisms

Phytotoxicity of salt and plant salt uptake: Modeling

ecohydrological feedback mechanisms

Peter Bauer-Gottwein,1 Nikolaj F. Rasmussen,1 Dagmar Feificova,2 and Stefan Trapp1

Received 28 March 2007; revised 1 September 2007; accepted 14 December 2007; published 12 April 2008.

[1] A new model of phytotoxicity of salt and plant salt uptake is presented and is coupledto an existing three-dimensional groundwater simulation model. The implementation ofphytotoxicity and salt uptake relationships is based on experimental findings from willowtrees grown in hydroponic solution. The data confirm an s-shaped phytotoxicityrelationship as found in previous studies. Uptake data were explained assuming steadystate salt concentration in plant roots, passive salt transport into the roots, and activeenzymatic removal of salt from plant roots. On the one hand, transpiration stronglydepends on groundwater salinity (phytotoxicity); on the other hand, transpirationsignificantly changes the groundwater salinity (uptake). This feedback loop generatesinteresting dynamic phenomena in hydrological systems that are dominated bytranspiration and are influenced by significant salinity gradients. Generic simulations areperformed for the Okavango island system and are shown to reproduce essentialphenomena observed in nature.

Citation: Bauer-Gottwein, P., N. F. Rasmussen, D. Feificova, and S. Trapp (2008), Phytotoxicity of salt and plant salt uptake:

Modeling ecohydrological feedback mechanisms, Water Resour. Res., 44, W04418, doi:10.1029/2007WR006067.

1. Introduction

[2] Salinization of soils and shallow groundwater insemiarid and arid regions is one of today’s major environ-mental problems. Presently, about 831 million hectares ofthe world’s approximately 5 billion hectares of agriculturalland are affected by salinization [e.g., Rengasamy, 2006].Because elevated salinity levels inhibit plant growth, soilsalinization is a serious threat to agricultural productivityand global food security. Phytotoxicity of salt and salttolerance mechanisms of plants have been thoroughlyinvestigated over past decades, both on the macroscopiclevel [e.g., Ayers et al., 1952; Curtin et al., 1993; Maas,1986] and the molecular level [e.g., Blumwald, 2000;Maathuis and Amtmann, 1999; Maser et al., 2002; Serranoet al., 1999; Tyerman and Skerrett, 1999; Volkmar et al.,1998]. Hydrological research has at the same time focusedon the quantitative description of water flow and salinitytransport in partially and fully saturated soils. Severalnumerical simulation tools have been developed for vadosezone water flow and salinity transport, including HYDRUS[Simunek et al., 1998, 1999] and LEACHM [Hutson andWagenet, 1992]. For groundwater systems, the MOD-FLOW/MT3DMS/SEAWAT family of codes has becomethe standard tool used in quantitative description andevaluation of flow and salinity transport problems [Guoand Langevin, 2002; Harbaugh and McDonald, 1996a,1996b; Zheng and Wang, 1999].

[3] While physical flow and transport processes havebeen a focus of hydrological research and modeling fordecades, two feedback mechanisms between plants andhydrological systems have received little attention to date:phytotoxicity of salt and plant salt uptake. Because salt hasa toxic effect on plants, elevated salt concentrations willreduce the transpiration rate, which in turn will change theflow field. At the same time, plants act as sinks for salt,because they take up dissolved ions. However, uptaketypically occurs at lower concentrations than ambient con-centrations in the surrounding soil or groundwater (ions areactively excluded from uptake water by enzymatic removal),which leads to accumulation of dissolved solids in theresidual water (S. Trapp, D. Feificova, N. F. Rasmussen,and P. Bauer-Gottwein, ‘‘Plant uptake of NaCl in relation toenzyme kinetics and toxic effects,’’ submitted to Environ-mental and Experimental Botany, 2008). While phytotoxic-ity of salinity is taken into account in most standard models(e.g., HYDRUS), a systematic quantitative treatment ofmacroscopic plant salt uptake based on empirical studiesis missing. However, particularly in shallow groundwatersystems in the semiarid and arid regions, plant salt uptakeand consequent salt accumulation in the residual water is akey ecohydrological feedback mechanism.[4] On the basis of experimental results for phytotoxicity

and plant uptake of NaCl, a new quantitative process modelfor plant/water/salinity dynamics was developed. The modelwas coupled to a standard groundwater simulation tool.While the identified phytotoxicity and salt uptake relation-ships should be valid in the unsaturated zone too, imple-mentation is presented here for the pure groundwater caseby limiting the analysis to phreatophytic plants that usegroundwater as a primary water source. Conceptual andnumerical difficulties related to salt transport and geochem-ical reactions in the unsaturated zone can thus be avoided.

1Department of Environmental Engineering, Technical University ofDenmark, Kongens Lyngby, Denmark.

2Institute of Chemical Technology, Prague, Czech Republic.

Copyright 2008 by the American Geophysical Union.0043-1397/08/2007WR006067

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WATER RESOURCES RESEARCH, VOL. 44, W04418, doi:10.1029/2007WR006067, 2008

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Presently, the proposed relationships are based on growthexperiments with willow trees in NaCl solution of varyingconcentration. Further experimental work is required toconfirm the general applicability of the model. Nonetheless,the application of the model to the Okavango Delta islandproblem [Bauer et al., 2006c] demonstrates that the modelidentifies essential feedback mechanisms that are required inorder to reproduce observed natural system behavior.

2. Methods

[5] In this section, the standard implementation of phy-totoxicity of salt and plant salt uptake relationships as usedin common groundwater simulation tools is reviewed.Subsequently, a new model of these processes is developedon the basis of experimental findings. In the standardimplementation, evaporation and transpiration are combinedinto one single process; however, the new implementationtreats them separately.

2.1. Standard Implementation of Evapotranspirationand Salt Uptake in Groundwater Models

[6] In standard groundwater models (e.g., USGS-MODFLOW) [Harbaugh and McDonald, 1996a, 1996b],transient groundwater flow is described with a diffusionequation for the hydraulic head [e.g., Bear, 1979; Domenicoand Schwartz, 1998]:

Ss@h

@t¼ @

@xiKij

@h

@xj

� �þ q; ð1Þ

In this formula, Ss (m�1) is the specific storage of theaquifer. The symbol h denotes the piezometric head (mabove datum). The symbol Kij denotes the hydraulicconductivity tensor (m s�1) and q (m3 m�3 s�1) representsany source and sink terms. Indices i and j in this andsubsequent formulas indicate coordinate directions andEinstein’s summation convention is used. If densitydifferences due to variable concentration are significant,fluid potential will not only depend on piezometric head butalso on concentration, thus introducing a nonlinear couplingbetween water flow and salinity transport [e.g., Herbert etal., 1988]. The contribution of transpiration to q, is ofparticular interest in this analysis. In groundwater models,transpiration and evaporation are commonly lumped intoone single process, evapotranspiration (ET). The standardparameterization of the evapotranspiration term assumesthat the evapotranspiration rate depends only on thepiezometric head. Some frequently used evapotranspirationparameterizations in groundwater models are a linear and anexponential dependence on depth to groundwater:

qET x; y; hð Þ ¼ �qET ;max x; yð Þ � fET hð Þ:

[7] The factor fET is a dimensionless head-dependentreduction factor, which is of the form

fET hð Þ ¼ 1 for h � ES

fET hð Þ ¼ 1� ES � hd

for ES � d � h < ES; and

fET hð Þ ¼ 0 for h � ES� d

ð2aÞ

for the linear dependence and

fET hð Þ ¼ 1 for h � ES; and

fET hð Þ ¼ exp � ES � hd

� �for h < ES

ð2bÞ

for the exponential dependence.[8] The term qET is the evapotranspiration sink term

(m3 m�3 s�1), qET,max is the maximum evapotranspirationrate for unlimited water supply (m3 m�3 s�1), ES (m abovedatum) and d (m) are the elevation of the evapotranspirationsurface and the extinction depth, respectively.[9] The salinity transport in groundwater is typically

simulated as an advective-dispersive process, obeying thegoverning equation [e.g., Bear, 1979; Zheng and Wang,1999]

@ qcð Þ@t

¼ @

@xiqDij

@c

@xj

� �� @

@xiqvicð Þ þ m: ð3Þ

[10] The symbol q denotes the effective porosity (�),Dij is the diffusion/dispersion tensor (m2 s�1), whichdepends on the pore velocity [e.g., Bear, 1979], vi is thepore velocity vector (m s�1) and m (kg m�3 s�1) representsany mass source/sink terms present in the domain. Thecontribution to m of interest in this study is the salt uptakeby plants. The sink term due to evapotranspiration (mET) isof the form

mET ¼ �qET x; y; h; cð Þ � cET ; ð4Þ

where cET (kg m�3) is the uptake concentration oftranspiration, i.e., the concentration of the water removedfrom the aquifer by evapotranspiration.[11] The concentration cET is generally smaller than the

aquifer concentration, which leads to salinity accumulation inthe aquifer. The standard implementation of cET used inMT3DMS [Zheng andWang, 1999] and SEAWAT [Langevinand Guo, 2006] is the following:

cET ¼ c for c < �

cET ¼ m for c � �;ð5Þ

where m is a threshold concentration (kg m�3). Theevapotranspiration process is thus assumed to take up alldissolved solids present in the aquifer up to a certainthreshold concentration. Beyond that threshold, cET issmaller than the aquifer concentration c and the ET processthus starts accumulating salinity in the groundwater. Nojustification was found in the literature for this form of therelationship between cET and c (equation (5)). Experimentswith willow trees in hydroponic solution indicated adifferent relationship (Trapp et al., submitted manuscript,2008), which will be described in the subsequent section.

2.2. Novel Implementation of Phytotoxicity and PlantSalt Uptake in Groundwater Models

2.2.1. Review of Results FromWillow Tree Experiments[12] A number of laboratory growth experiments with

willow trees were performed to determine the relationship

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W04418 BAUER-GOTTWEIN ET AL.: SALT AND PLANT SALT UPTAKE W04418

between external NaCl concentration, plant uptake concen-tration and salt toxicity (Trapp et al., submitted manuscript,2008). Genetically identical willow cuttings were grownunder constant, identical conditions over periods of up to10 d in Erlenmeyer flasks closed with cork stoppers aroundthe stem. NaCl concentrations in distilled water ranged from0.1 to 20 kg m�3. Evapotranspiration was monitored dailyby weighing the system. The concentration of ions insolution was estimated using measurements of electricalconductivity. Inhibition of transpiration, normalized to theinitial transpiration (before addition of NaCl) and transpi-ration of controls, was used as toxicity criterion. The massbalance for NaCl was established and a mathematical modeldescribing salt uptake was developed. The willow treetoxicity test was described in detail by Trapp et al. [2000]and has been used in a number of studies on phytotoxicity[Larsen et al., 2005; Trapp et al., 2004; Ucisik and Trapp,2006; Yu et al., 2005].[13] The relationship between external water NaCl con-

centration and NaCl concentration in uptake water is non-linear and is shown in Figure 1. Basically, the uptakeconcentration remains very small up to a ‘‘breakthroughpoint.’’ Below that point, enzymatic reactions pump salt outof plant root cells, beyond that point, uptake concentrations

increase almost linearly, which indicates passive salt uptake.The breakthrough concentration depends on the length ofthe growing period but, after about 160 h, it has reached anasymptotic value (Trapp et al., submitted manuscript, 2008).Results for a 240 h growing period can thus be consideredrepresentative of long-term behavior.[14] The phytotoxicity of salt was expressed as normal-

ized relative transpiration (NRT), i.e., the transpiration ofthe tree sample relative to the transpiration of a control treesample growing at c = 0 kg m�3. Raw NRT data werecollected for time intervals of 24, 48, 72, 96, 168, 192 and240 h. The data were normalized to 240 h using break-through concentration ratios observed at each time interval.

NRT240 ¼ NRTobs �BTPobs

BTP240

: ð6Þ

In this equation, NRT240 (�) is the normalized NRT for the240h growing period, NRTobs (�) is the observed NRT forany growing period (NRT of controls is 1 (100%)), BTPobs

(kg m�3) is the observed breakthrough point for anygrowing period and BTP240 (kg m�3) is the breakthroughpoint for the 240 h period. The resulting NRT240 values areshown in Figure 2 as a function of the concentration. Thedata clearly follow an s-shaped toxicity curve. All data fallon a similar curve, except the 24-h series.2.2.2. Modeling of Phytotoxicity andUptake Relationships[15] The evapotranspiration flux qET is separated into a

contribution by evaporation, qE, and a contribution bytranspiration, qT. While the evaporation flux is independentof the salinity and is implemented according to equation (2)the transpiration rate strongly depends on the groundwatersalinity. The transpiration term (qT) must therefore bereformulated as

qT x; y; h; cð Þ ¼ �qT ;max x; yð Þ � fT hð Þ � gT cð Þ: ð7Þ

Figure 1. The relationship between salt uptake by plantsand water salinity: concentration in the water taken up bythe willow trees (cT in kg m�3) as a function of the waterconcentration (c in kg m�3) for different growing periods.Multiple symbols of the same kind indicate multiple growthexperiments under the same conditions. Results fromequation (10) are indicated as solid black lines. R2 =0.9353, and root-mean-square error (RMSE) is 1.479 kgm�3. Data from Trapp et al. (submitted manuscript, 2008).

Figure 2. The reduction of transpiration with increasingsalinity. NRT240 is plotted as a function of NaCl concentra-tion in water. Data from the 24-h observation period werenot used for fitting. Multiple symbols indicate multipleexperiments. R2 = 0.9356, and RMSE is 6.61%.

W04418 BAUER-GOTTWEIN ET AL.: SALT AND PLANT SALT UPTAKE

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In this formula, qT (m s�1) is the actual transpiration rate,qT,max (m s�1) is the maximum or potential rate, fT (�) is thehead-dependent reduction factor and gT (�) is the salinity-dependent reduction factor. The exact form of gT(c) is basedon experimental results and will be developed below (seealso Trapp et al., submitted manuscript, 2008). Implement-ing the transpiration rate as a function of the saltconcentration requires that salinity transport is simulatedsimultaneously along with water flow and that theintroduced coupling mechanism between the two processesis taken into account. As a numerical tool for such coupledsimulations, the SEAWAT code [Langevin and Guo, 2006]for variable density groundwater flow, based on USGS-MODFLOW, was used in this study.[16] Phytotoxicity of salt was implemented as an s-

shaped toxicity curve as a function of the salt concentration.The following functional relationship was used:

gT cð Þ ¼ NRT ¼ 1� 1

1þ t=c; ð8Þ

where NRT denotes the normalized transpiration (�), c isthe NaCl concentration in kg m�3 and t (kg m�3) is a fittingparameter. This formulation is similar to other salt toxicityresponse curves used in the literature [e.g., van Genuchtenand Hoffmann, 1984]. Using the data from Trapp et al.(submitted manuscript, 2008), presented in Figure 2, t wasfitted to the value of 0.39 (kgm�3). The achieved fit is excellent(R2 = 0.9356, RMSE (root-mean-square error) = 6.61%).The 95% confidence interval for t is 0.36–0.42 (kg m�3).The 24-h series was excluded from the fit.[17] The measured relationship between uptake concen-

tration and water concentration was interpreted with adynamic model of the salt mass balance in plant roots,accounting for passive uptake of NaCl and enzymaticremoval. Enzymatic removal from roots was assumed tobe governed by Michaelis-Menten-type kinetics [Larsen etal., 2005]. The mass balance for salt uptake into roots

consists of the influx of salt with water into the roots, theoutflux of salt from the roots to the plant body, and anenzymatic removal term to account for sodium pumps inroot cell biomembranes. The model is identical to a modeldeveloped for cyanide uptake of plant roots [Larsen et al.,2005]:

dmR

dt¼ c � qT � cR �

qT

KRW

� vmax cR

KM þ cR�MR; ð9Þ

where mR (kg) is the salt mass in the roots and cR (kg kg�1

root mass) is the salt concentration in the root tissue. Thesymbol KRW denotes the root-water distribution coefficient(m3 kg�1),MR is the root mass (kg m�3), KM (kg kg�1) is thehalf-saturation constant and vmax (kg kg�1 root mass d�1) isthe maximum enzymatic removal rate. Assuming that the saltconcentration in the plant roots is steady state gives aquadratic relationship between the uptake concentration andthe water concentration [Larsen and Trapp, 2006; Trapp etal., submitted manuscript, 2008]:

dmR

dt¼ 0 ¼ qT � c� qT � cT � vmax � KRW � cT

KM þ KRW � cT�MR

cT cð Þ ¼ 1

KRW

�b �ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffib2 � 4ag

p2a

a ¼ � qT ;max

MRKRW

b ¼ cqT ;max

MR

� KM

qT ;max

MRKRW

� vmax

g ¼ cKM

qT ;max

MR

:

ð10Þ

In this derivation, it is assumed that the toxic effect on thetranspiration rate is the same as on the active root mass. Withrising water salinity, transpiration and active root mass arereduced by the same factor, which can therefore be cancelledfrom equation (10). This assumption is made to keepdevelopment simple and may be relaxed as more experi-mental data become available.[18] The half-saturation constant and maximum enzymatic

removal rate were determined by fitting the observed data ofTrapp et al. (submitted manuscript, 2008), to the model(Figure 1). The fit resulted in a value of 0.0001 kg kg�1 forKM and 0.02 kg kg�1 d�1 for vmax. The fit is excellent (R

2 =0.9353, RMSE (root-mean-square error) = 1.479 kg m�3).However, the model underpredicts cT for high concentrationsbecause the model assumes a constant enzymatic removalrate vmax over the entire concentration range. In the experi-ment, the trees do not survive treatment with very highconcentrations and vmax decreases to zero. The relationshipbetween cT and c therefore approaches the 1:1 line for veryhigh concentrations.

3. Results

3.1. Zero-Dimensional Box Modeling of anAquifer Under Continued Transpiration

[19] We consider a highly simplified box model of anaquifer under phreatic transpiration as depicted in Figure 3.We assume instantaneous replenishment of the aquifer fromboundaries with fixed concentration cin and perfect, instan-taneous mixing within the aquifer. There are no water sinks

Figure 3. Conceptual box model of an aquifer underphreatic transpiration. The aquifer is recharged fromboundaries, and the inflowing water is taken up by phreatictranspiration.

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or boundary outflows in the domain except phreatic tran-spiration. The mass balance for the groundwater compart-ment can be written as

dc

dt¼ qT � A

V� cin � cTð Þ; ð11Þ

where A is the surface area of the box and V is its volume.A unit box of volume 1 m3 with a surface area of 1 m2 wasconsidered. The initial concentration was set equal to theboundary concentration. Model parameters were chosen inaccordance with experimental results from Trapp et al.(submitted manuscript, 2008) (Table 1). The ordinarydifferential equation (equation (11)) was solved usingMATLAB’s ‘‘ode45’’ solver. This solver uses a one-stepexplicit Runge-Kutta formula [Dormand and Prince, 1980].The evolution of concentration over time was calculated

with the standard implementation and with the newimplementation of phytotoxicity and plant salt uptake.Simulation results are shown in Figure 4 and results of aparameter sensitivity analysis are summarized in Figure 5.Because the enzymatic removal rate (vmax) and the rootmass (MR) only appear as a product in equation (10), theirsensitivity is the same. While the concentration riseslinearly with time over the entire simulation period for thestandard implementation, a steady state concentration isreached in the new implementation.[20] Steady state concentrations and transpiration rates

are plotted in Figure 6 as functions of the prescribedboundary concentration. Note that steady state in thissystem is reached once the uptake concentration (cT) isequal to the boundary concentration. Whether sustainedplant growth is possible in the system or not thus dependson the salinity of the boundary water supply. Solving

Table 1. Base Case Parameters for the Zero-Dimensional Box Model of an Aquifer Under Continued Phreatic Transpiration

Parameter Description Unit Value in Base Case Source

V box volume m3 1 Authors’ choiceA box surface area m2 1 Authors’ choiceqT,max transpiration rate m d�1 0.01 Trapp et al. (submitted manuscript, 2008)MR specific root mass kg m�2 1 Trapp et al. (submitted manuscript, 2008)cin boundary concentration kg m�3 0.1 Authors’ choicet toxicity parameter kg m�3 0.39 Trapp et al. (submitted manuscript, 2008)vmax naximum enzymatic removal rate kg kg�1 d�1 0.02 Trapp et al. (submitted manuscript, 2008)KM half-saturation constant kg kg�1 0.0001 Trapp et al. (submitted manuscript, 2008)KRW root-water distribution coefficient m3 kg�1 0.001 Trapp et al. (submitted manuscript, 2008)

Figure 4. Concentration versus time and transpiration versus time in the base case box model. In thestandard implementation, m = 0 is assumed. In the standard implementation of phytotoxicity and saltuptake, the concentration increases linearly with time, whereas in the novel implementation, a steady stateis reached. The transpiration rate is constant over time in the standard implementation and is reducedsignificantly in the novel implementation because of phytotoxicity.


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equation (11) for the steady state concentration in thegroundwater, we derive

c1 ¼ S � cin

S ¼ vmaxmRKRW þ KM þ cinKRWð ÞqT ;max

KM þ cinKRWð ÞqT ;max

;ð12Þ

where c1 (kg m�3) is the steady state groundwaterconcentration in the aquifer. The steady state concentrationin the aquifer is thus directly proportional to both theenzymatic activity of the roots and the ratio of the root massto the transpiration rate. Figure 4 shows that simulationresults for the new implementation of phytotoxicity and saltuptake differ widely from results for the standard imple-mentation. In the standard implementation, the groundwaterconcentration increases linearly and the transpiration ratestays constant. Steady state is never reached in the system.

3.2. Spatially Distributed Modeling of anAquifer Under Continued Transpiration

[21] The SEAWAT package [Guo and Langevin, 2002;Langevin and Guo, 2006] was modified in order to take intoaccount identified ecohydrological feedback mechanisms.An additional flow package was implemented for transpi-ration (TPT package). The TPT package is analogous to theevapotranspiration (EVT) package. An additional inputparameter field was used to supply the toxicity parameter t.

The parameter t can thus vary in space and time in thedomain. The actual transpiration rate was implementedaccording to equation (7). The head-dependent reductionfactor, fT(h), was assumed to be of the same form as fET(h)in the EVT package (equation (2)). The salinity-dependentreduction factor, gT(c), was implemented according toequation (8).[22] SEAWAT’s SSM (source-sink mixing) package was

modified in order to implement the relationship betweenuptake concentration and groundwater concentration. Addi-tional input parameter fields were used to supply the uptakeparameters vmax, KM, MR and KRW. All these parameters canthus vary in space and time. The relationship betweenuptake concentration and groundwater concentration wasimplemented according to equation (10). The modifiedSEAWAT code is available as online auxiliary material.1

[23] The implementation was tested by comparison withbox model results obtained from MATLAB’s ordinarydifferential equation solver. A one-cell model was set upin SEAWAT and the resulting concentrations with respect totime were compared with results from the MATLAB code.No appreciable differences were found between solutionsproduced by the MATLAB solver and solutions producedby the modified SEAWAT version.

Figure 5. Sensitivity analysis for the base case box model. The sensitivities of the concentration c andthe salinity-dependent reduction factor gT are shown. Sensitivities are displayed as composite scaled

sensitivities for a parameter change of +20%, i.e., CSS(c) = 1T

Pt¼T

t¼0

cchange � cbasecbase

� 10:2 and CSS(gT) =

1T

Pt¼T

t¼0

gT ;change�gT ;basegT ;base

� 10:2.

1Auxiliary materials are available in the HTML. doi:10.1029/2007WR006067.

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3.3. Application: The Okavango Island Case Example

[24] Islands in the Okavango Delta wetland are exemplarynatural groundwater systems, where the described feedbackmechanisms are of relevance. The Okavango Delta is a large(30000 km2) terminal alluvial fan, located in Botswana,Southern Africa [McCarthy et al., 1998, 2000; McCarthyand Ellery, 1994]. The approximate location of theOkavango Delta is 22�E to 24�E, 18� to 20�S. The averageinflow to the system is about 300 m3 s�1, of which almost100% is lost by evapotranspiration [Bauer et al., 2006a;Dincer et al., 1987; Gieske, 1997]. Because almost 100% ofthe water is consumed by the evapotranspirative demand ofsurface wetlands and adjacent shallow groundwater sys-tems, about 300,000 tons of dissolved solutes are accumu-lated in the Okavango Delta every year. Islands in theOkavango Delta are slightly elevated areas that are sur-rounded by open water surfaces. Because the islands’topographic elevation is higher than the maximum floodlevel, vegetation growth and transpiration establish a con-centric flow pattern. Over time, continuous inflow as well asevaporative and transpirative water loss lead to rising saltconcentrations in groundwater and plants die off in succes-sion, starting from the centre of the island (Figure 7) [Baueret al., 2004, 2006b, 2006c; Ellery et al., 1993; Gieske, 1996;McCarthy et al., 1993].[25] One particular island, Thata Island [Bauer et al.,

2006c; McCarthy et al., 1991], has been studied extensivelyover the past years. In one study, major ion concentrationsin groundwater were sampled at multiple points in space

and time and the groundwater salinity distribution in thesubsurface was mapped using geophysical techniques.Temporal changes in water levels on and around the islandwere monitored over a period of 1 year. The results of theseinvestigations are documented by Bauer et al. [2004,2006c]. Here, the Thata Island case example is used as atest case for the investigation of feedback mechanismsbetween groundwater flow and salinity transport. The time-scales of salinity accumulation on the islands are rather long(on the order of thousands of years) and direct observationof the entire process is not feasible. However, spatialpatterns of concentration and transpiration can be comparedto model results at various time steps to check the validity ofthe chosen modeling approach (Figure 8).[26] A three-dimensional finite difference groundwater

flow and salinity transport model was set up for ThataIsland. The modified version of SEAWAT, described inprevious sections, was used. The model is a highly simpli-fied representation of a naturally complex situation. Thesurrounding swamps are represented as fixed head/fixedconcentration cells. Transpiration and evaporation are activeon the island. The evaporation surface (ESE) was set to thetopographic surface [from Gumbricht et al., 2005] andevaporation was assumed to depend exponentially on depthto water table with an extinction depth of DE = 2 m(equation (2)). The transpiration surface (EST) was set farbelow the topographic surface because of the assumption thattranspiration is never limited bywater availability. Themodeldomain is shown in Figure 8 and model parameters are

Figure 6. Steady state concentration c1 in the groundwater and steady state salinity-dependentreduction factor gT,1 as a function of the boundary concentration cin. Simulation results are displayed forthe box model base case.


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summarized in Table 2. A horizontal grid cell size of 5 m 5 m was used, while the vertical discretization was 3 m. Thetotal simulation period was 800 years and the simulationstarted with a uniform concentration of 0.1 kg m�3 in theentire domain. In all simulations, an upstream finite differ-ence scheme was used for the advective transport terms[Zheng and Wang, 1999]. Bauer-Gottwein et al. [2007]found that in order to limit numerical diffusion and toachieve a grid-convergent solution, grid cell sizes of abouthalf the dispersivity were required for the simulation of theOkavango islands. This fine resolution is prohibitivelyexpensive in terms of CPU time for fully three-dimensionalsimulations. Calculation of the 3D Thata Island modelwould require about 60 d of CPU time on a modern PC.The primary effect of numerical diffusion in this system isto artificially delay the onset of density fingering instabil-

ities in the centre of the island. Density fingering is,however, not the focus of this study, and the use of acoarser spatial grid resolution that reduces the computation-al load to a manageable level is reasonable.[27] Two simulation runs were performed. In the first run

(run A), the new implementation of phytotoxicity of salt andsalt uptake was used. The salinity-dependent reductionfactor for transpiration (gT) was implemented with theparameters listed in Table 2. The head-dependent reductionfactor for transpiration (fT) was set to 1 and the head-dependent reduction factor for evaporation (fE) was imple-mented with the parameters listed in Table 2. The secondrun (run B) was performed with the standard implementa-tion of evapotranspiration. Evaporation and transpirationwere lumped into one process and were assumed to beindependent of salinity. The head-dependent reduction

Figure 7. Typical Okavango Delta island. TDS, total dissolved solids; s, groundwater electricalconductivity. The vegetation along the island’s fringes consists of tall evergreen trees. Moving toward theisland’s center, the riverine forest is successively replaced by palm trees and a salt-tolerant grass,Sporobolus spicatus. For details on the vegetation distribution on the Okavango islands, see Gumbricht etal. [2004].

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Table 2. SEAWAT Model Parameters for Thata Island Simulations

Parameter Description Unit Value Source

X domain size in x direction m 400 Bauer et al. [2006c]Y domain size in y direction m 700 Bauer et al. [2006c]Z domain size in z direction m 30 thickness of freshwater aquifer

Bauer et al. [2006c]dx horizontal cell size m 5 authors’ choicedy horizontal cell size m 5 authors’ choicedz vertical cell size m 3 authors’ choiceKh horizontal hydraulic conductivity m s�1 10�6 Bauer et al. [2004]Kv vertical hydraulic conductivity m s�1 10�6 Bauer et al. [2004]Ss specific storage m�1 10�4 Bauer et al. [2004]Sy specific yield � 0.2 Bauer et al. [2004]q effective porosity � 0.25 Bauer et al. [2004]qE,max maximum evaporation rate m s�1 3.5 10�8 Bauer et al. [2004]DE evaporation extinction depth m 2 estimated on the basis of

Bauer et al. [2004]ESE evaporation surface m above datum topography authors’ choiceqT,max maximum transpiration rate m s�1 3.5 10�8 estimated on the basis of

Bauer et al. [2004]DT transpiration extinction depth m irrelevantEST transpiration surface m above datum far below topography authors’ choicet toxicity parameter kg m�3 0.39 Trapp et al. (submitted manuscript, 2008)MR specific root mass kg m�2 0.3 same ratio qT,max/MR as in work by Trapp et al.

(submitted manuscript, 2008)cin boundary concentration kg m�3 0.1 Bauer et al., 2006cvmax maximum enzymatic removal rate kg kg�1 d�1 0.02 Trapp et al. (submitted manuscript, 2008)KM half-saturation constant kg kg�1 0.0001 Trapp et al. (submitted manuscript, 2008)KRW root-water distribution coefficient m3 kg�1 0.001 Trapp et al. (submitted manuscript, 2008)Dm effective molecular diffusion coefficient m2 s�1 10�8 Bauer-Gottwein et al. [2007],

Bauer et al. [2006c]aL longitudinal dispersivity m 1 Bauer-Gottwein et al. [2007],

Bauer et al. [2006c]aT transverse dispersivity m 1 Bauer-Gottwein et al. [2007],

Bauer et al. [2006c]

Figure 8. Field evidence from Thata Island. (left) Airborne photo of the island showing the vegetationdistribution with dense vegetation (dark) on the island’s fringes and bare soil/salt crust in the island’scenter (bright). (right) The sampled shallow groundwater electrical conductivity (in mS cm�1) issuperimposed on the satellite image. Groundwater salinity clearly correlates with the vegetationdistribution. Sampling points are shown as white dots along with an interpolated surface. The modelboundary is indicated as a red line.


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factor for evapotranspiration (fET) was implemented usingthe same parameters as used for fE in run A. Simulationresults are summarized in Figures 9 and 10.[28] In run A, spatial concentration patterns after 800 years

show accumulation zones of very high concentrationaround the topographic depressions (Figure 9). The rest ofthe domain is in quasi-steady state and salt inflow fromboundaries is compensated for by plant salt uptake. In runB, the domain is salinized much more uniformly, becauseevapotranspiration rates are not limited by rising salinitylevels. In both runs, concentrations are eventually stabilizedby density-driven vertically downward flow in the centre ofthe accumulation zones [Bauer et al., 2006c; Zimmermann

et al., 2006]. Concentration patterns produced by run A arein better agreement with field observations than the onesproduced by run B. In reality, high salinities are onlyobserved near topographic depressions (pans), while low-salinity conditions prevail in the rest of the island [Bauer etal., 2006c].[29] The salinity-dependent reduction factor gET is 1 all

over the domain in run B and varies according to the salinitydistribution in run A. In run A, transpiration rates are verylow in large parts of the domain. Vigorous vegetation isonly encountered along the fringe of the island. This is inexcellent agreement with observed vegetation patterns(Figure 7). The head-dependent reduction factor fE/fETreflects the importance of evaporation compared to transpi-ration. Evaporation is generally high where the topographicelevation is depressed. The closer the water table is to thetopographic surface, the closer fE/fET is to one. Significantevaporation fluxes are simulated around the central pan onthe island, which is in agreement with field observations ofefflorescent salt crusts in these areas. The factor fE/fET isgenerally lower in run B than in run A, since higherevapotranspiration rates in run B result in lower groundwa-ter levels all over the domain.[30] Time series of concentration, gT and fE/fET for runs A

and B are shown in Figure 10 for two specific locations inthe domain. Concentrations generally increase much fasterin run B because of higher evapotranspiration rates. Thetranspiration reduction factor (gT) stabilizes asymptoticallyin run A (i.e., the trees die off), while it is equal to 1 for theentire simulation period in run B. The evaporation reductionfactor (fE/fET) is stable at low values or slowly decreasing inrun B but shows interesting dynamics in run A: Because ofreduced transpiration rates (phytotoxicity), trees successivelydie off on the island, which leads to rising water tables andhigher evaporation rates. Over time, the water balance shiftsfrom transpiration dominated to evaporation dominated.Steady state is never reached in this system, in either run Aor run B.[31] Run A reproduces a characteristic feature of the

Okavango Delta islands, which cannot be reproduced usingthe standard implementation of phytotoxicity of salt andplant salt uptake. Because of rising salinity, the transpirationrate is successively reduced and drops to values close tozero in the center of the domain (Figure 8). Plant life isessentially restricted to a strip of riverine vegetation alongthe ‘‘shoreline’’ of the island. As can be seen in Figure 7,this is in good agreement with field observations. Thephenomenon can be observed on thousands of individualislands in the Okavango Delta using Google Earth.

4. Discussion

[32] The spatially distributed simulations of the ThataIsland system demonstrate that the proposed model ofphytotoxicity and plant salt uptake can, at least qualitatively,explain phenomena observed in nature. However, thisqualitative comparison cannot be considered a full modelvalidation under field conditions. Several limitations need tobe mentioned and should be investigated further.[33] Toxicity and uptake relationships are expected to be

different for different dissolved solutes. Some ions (e.g.,K+) are essential to plant growth and may even be activelytaken up, while others (e.g., Na+, Al3+) are detrimental and

Figure 9. Results of Thata Island simulations. The saltconcentration c is shown in the top plots. The salinity-dependent reduction factor gT/gET is shown in the middleplots, and the depth to water table–dependent reductionfactor fE/fET is shown in the bottom plots. Simulation resultsare shown for t = 800 years. Results of run A (newimplementation) are shown in the left plots, and results ofrun B (standard implementation) are shown in the rightplots. Location 1 is indicated as a white circle, and location2 is indicated as a white cross. Simulated time series forthese locations are shown in Figure 10. A lower gT/gETfactor implies less transpiration, i.e., less vigorous anddense vegetation. The concentration and vegetation patternsproduced by run A are in much better agreement with thefield observations (Figure 8) than the results of run B.

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are actively excluded [Glass, 1989; Marschner, 1995;Mengel and Kirkby, 2001]. The relationships used in thisarticle are based on data for NaCl only. Other solutes needto be investigated to ensure wider applicability for a range ofnaturally occurring salinity compositions. The MODFLOW/MT3DMS/SEAWAT family of codes has the capability ofsimulating multispecies reactive transport and has recentlybeen coupled to the geochemical modeling tool PHREEQC[Zheng and Wang, 1999, Prommer et al., 2003]. However,extension to multiple species simulation is limited bylimited availability of representative macroscopic uptakeand toxicity relations for different solutes.[34] Moreover, toxicity and uptake relationships are

expected to vary from one plant species to another [Liethand Mochtchenko, 2003; Maas, 1986; Marschner, 1995;Shani et al., 2007]. Here, only willow trees were tested and,in the Okavango island simulation, it was assumed that allplants are similar to willow trees. In any real-world appli-cation, however, the natural vegetation cover is a mosaic ofvarious species and toxicity and uptake relationships shouldreflect this diversity. To a certain degree, the vegetationcover will adjust to changing salinity levels; more salt-tolerant species will replace less salt-tolerant species inareas affected by salinization, as has been documented forthe Okavango islands by Ellery et al. [1993]. For example,

preliminary unpublished data from experiments with barley(Hordeum vulgare), a comparatively salt-tolerant grassspecies [Maser et al., 2002], indicate that the toxicityparameter t in equation (8) is much higher (� 3 kg m�3)for this plant species than for willow trees (0.39 kg m�3).[35] The reduction of the transpiration rate with increas-

ing groundwater salinity cannot be explained by the reduc-tion of total water potential difference between leaves andgroundwater; instead, it is a toxic effect of the salt. The totalpotential of water in the soil-plant system is [Hillel, 1998]

hT ¼ hz þ hp þ hs; ð13Þ

where hT (m) is the water potential in weight units, i.e.,energy per weight. The quantity hz is the elevationcontribution to the potential, hp is the pressure contributionto the potential and hs is the osmotic contribution to thepotential:

hz ¼ z

hp ¼p

rg

hs ¼cRT

rg;

ð14Þ

Figure 10. Results of Thata Island simulations. Simulated time series of the salt concentration c, thesalinity-dependent reduction factor gT/gET, and the depth to water table–dependent reduction factor fE/fETshown in Figure 9 for locations 1 (white circle) and 2 (white cross). The factors gT/gET and fE/fET aredefined in equation (7).


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where r is density of water (1000 kg m�3), g isgravitational acceleration (9.81 m s�2), p is capillarypressure (N m�2), c is the molar concentration (mol m�3),R is the universal gas constant (=8.31 J mol�1 K�1) andT is the temperature (K).[36] Assuming that the reduction of transpiration is a

purely physical effect, the transpiration flux would beproportional to the total potential difference Dh betweenthe plant leaves and the soil water solution. Capillarysuction by plants is limited to a certain value (the so-calledpermanent wilting point, hpwp ffi �153 m [Hillel, 1998]).Assuming that the elevation difference between the ground-water and the leaves is small, we can write for the totalpotential difference:

4h ¼ hsoil � hleaf

¼ hp;soil � hp;leaf þ hs;soil � hs;leaf þ hz;soil � hz;leaf

¼ �hp;leaf þ hs;soil � hs;leaf : ð15Þ

[37] This implies that the transpiration flux will dependlinearly on salinity and decrease to zero once the osmoticpotential is equal to the permanent wilting point. Theconcentration clim for which the transpiration decreases tozero can be calculated (assuming a temperature of 293 K):

clim ¼ � hpwprgRT

¼ � 153m � rgRT

¼ 616mol

m3: ð16Þ

[38] For NaCl, this corresponds to 18 kg m�3 (molecularweight of NaCl is 58.5 g/mol and 1 mol NaCl produces2 mol ions). This value is much higher than the observedtranspiration reduction threshold seen in the experiments(�1 kg m�3). We therefore conclude that the observedtranspiration reduction is not due to physical effects butdue to toxic effects. The toxicity threshold varies from oneplant species to another, which further supports the argu-ment for a toxic effect and not a universal physical effect.[39] Finally, the relationships used here are based on

laboratory growth experiments in hydroponic solution.While we do not expect the fundamental behavior of plantcells to be different in natural soils, geochemical reactionsmay be important in soil systems. Moreover, preliminaryresults show higher toxicity of salt in soil culture. This maybe due to reduced mixing (slower diffusion in porousmedia) and consequently higher local concentrations inthe immediate vicinity of the roots. Growth experimentsin porous media instead of hydroponic solution are thelogical next step.[40] Supporting evidence comes from molecular research

on ion transport channels in the plant cell membranes:Active exclusion of Na+ is commonly seen in many plantspecies [Maser et al., 2002], and the responsible transportenzymes have actually been identified [Maser et al., 2002],most of them located in roots. Interestingly, the half-saturation constant for sodium determined for the Na+

symporter in the plasmamembrane [Maathuis and Amtmann,1999] matches the macroscopic half-saturation constantfound by Trapp et al. (submitted manuscript, 2008).[41] Simulation of the Okavango Delta island system

shows that observed concentration patterns and vegetationdynamics in this system can be explained with the new

implementation of phytotoxicity and plant salt uptake, whilethe standard implementation of these processes fails toreproduce observed system behavior. In the absence ofdetailed quantitative data on different dissolved solids anddifferent plant species, the new model already generates thecorrect system response, at least qualitatively. In order tocheck if the simulated system response is robust withrespect to highly variable toxicity and uptake parameters,a sensitivity analysis was carried out with the spatiallydistributed model. The three most important model param-eters (t, vmax and KM) were changed by 20% each and thesimulated concentration and transpiration distribution wascompared with the base run (Figure 11). While the generalpattern (salinity accumulation and breakdown of transpira-tion in the center of the island) remains stable, very highsensitivities result in the area around the topographicdepressions. This is due to the delicate interplay of transpi-ration and evaporation, which are simulated as two separateprocesses in the novel implementation. A slightly highertoxicity parameter t, for instance, leads to higher sustainedtranspiration rates around the topographic depressions and,consequently, lower groundwater tables and lower evapora-tion rates. Less evaporation leads to less evapoconcentrationand consequently to higher sustained transpiration rates,closing the positive feedback loop. The highly nonlinearfeedback mechanisms introduced into the flow transportsystem in the novel implementation therefore lead to dif-ferent kinds of dynamic phenomena. More data fromlaboratory and field experiments is required to parameterizethese processes.

5. Conclusions

[42] A new dynamic model for phytotoxicity of salt andplant salt uptake was implemented into a standard ground-water modeling tool. The dynamic model is based onexperimental data from laboratory growth experiments withwillow trees. While the plant salt uptake and toxicity modelrequires further confirmation with additional experimentaldata, it already offers some interesting insights into vegeta-tion/water/salinity dynamics both in natural and agriculturalecosystems. Correct parameterization of phytotoxicity ofsalt and plant salt uptake will be important in any hydro-logical system, where transpiration contributes significantlyto the water balance and salinity displays significant vari-ability. It is particularly important in terminal systems,where all inflowing water is taken up by evapotranspiration.In such systems, plants, by growing, are actually diggingtheir own graves because salinity accumulation inhibitstranspiration and long-term survival. Simulation resultsindicate that any transpiration-dominated terminal systemwill move into a steady state with respect to salinity, wheresalt inflow from the boundaries is compensated for by saltuptake by plants. Conversely, in systems with significantevaporation, the salt concentration will continuously in-crease and will be eventually limited by density-driven flowphenomena and mineral precipitation.[43] Given the importance of soil and groundwater sali-

nization for global agricultural productivity and food secu-rity, reliable and accurate simulation tools for soil water andsalt budgets are essential to support natural resource man-agement. A more realistic and accurate representation of

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phytotoxicity of salt and plant salt uptake will enhancemodel reliability and predictive capacity and thus improveour ability to analyze and solve one of today’s majorenvironmental problems.

[44] Acknowledgments. We thank the Department of Water Affairs,Government of Botswana, and the Institute of Environmental Engineering,ETH Zurich, for sharing data and expertise on the Okavango Delta islands.

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Figure 11. Sensitivity pattern of the concentration c and the salinity-dependent reduction factor gT withrespect to the toxicity parameter t, the enzymatic removal rate vmax, and the half-saturation constant KM.

The plotted quantities are CSS(c) =cchange tendð Þ � cbase tendð Þ

cbase tendð Þ � 1Dp=p and CSS(gT) =

gT ;change tendð Þ � gT ;baseðtendÞgT ;base tendð Þ � 1

Dp=p,

with tend = 800 years and Dp/p = 0.2. The region of highest sensitivities is the area around thetopographic depressions, where both transpiration and evaporation are significant.


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��P. Bauer-Gottwein, N. F. Rasmussen, and S. Trapp, Department of

Environmental Engineering, Technical University of Denmark, DK-2800Kongens Lyngby, Denmark. ([email protected])

D. Feificova, Institute of Chemical Technology, Technicka 5, 166 28Prague, Czech Republic.

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phytotoxicity of salt and plant salt uptake: modeling ecohydrological feedback mechanisms

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