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Impact of soil water flux on vadoze zone solutetransport parametersXiaomin Chen a , M. Vanclooster b & Genxing Pan aa College of Resources and Environmental Sciences , Nanjing Agricultural University ,Nanjing, 210095, People's Republic of Chinab Department of Environmental Sciences and Land Use Planning , Université Catholiquede Louvain , Louvain-la-Neuve, B-1348, BelgiumPublished online: 05 Feb 2007.

To cite this article: Xiaomin Chen , M. Vanclooster & Genxing Pan (2002) Impact of soil water flux on vadoze zone solutetransport parameters, Communications in Soil Science and Plant Analysis, 33:3-4, 479-492, DOI: 10.1081/CSS-120002758

To link to this article: http://dx.doi.org/10.1081/CSS-120002758

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IMPACT OF SOIL WATER FLUX ONVADOZE ZONE SOLUTE TRANSPORT

PARAMETERS

Xiaomin Chen,1 M. Vanclooster,2 and Genxing Pan1

1College of Resources and Environmental Sciences,

Nanjing Agricultural University, Nanjing 210095,

People’s Republic of China2Department of Environmental Sciences and Land Use

Planning, Universite Catholique de Louvain,

B-1348 Louvain-la-Neuve, Belgium

ABSTRACT

The transport processes of solutes in two soil columns filled with

undisturbed soil material collected from a unsaturated sandy

aquifer formation in Belgium subjected to a variable upper

boundary condition were identified from breakthrough curves

measured by means of time domain reflectometry (TDR). Solute

breakthrough was measured with 3 TDR probes inserted into each

soil column at three different depths at a 10 min time interval. In

addition, soil water content and pressure head was measured at 3

different depths. Analytical solute transport models were used to

estimate the solute dispersion coefficient and average pore-water

velocity from the observed breakthrough curves. The results

showed that the analytical solutions were suitable in fitting the

observed solute transport. The dispersion coefficient was found to

be a function of the soil depth and average pore-water velocity,

imposed by the soil water flux. The mobile moisture content on the

479

Copyright q 2002 by Marcel Dekker, Inc. www.dekker.com

COMMUN. SOIL SCI. PLANT ANAL., 33(3&4), 479–492 (2002)

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other hand was not correlated with the average pore-water velocity

ðR2 ¼ 0:0684Þ and the dispersion coefficient ðR2 ¼ 0:0873Þ:

INTRODUCTION

Appropriate management of the soil and water resources requires a good

knowledge of the transport processes and fate of dissolved chemicals in the soil

water. Water flow imposes a convective movement on the dissolved chemicals,

while local variations in the flow velocity induces hydrodynamical dispersion.

The process of diffusion, induced by the differences in the solute concentration,

enhances solute displacement. Dissolved chemicals in the soil water are further

subjected to chemical and physical interactions between the soil fluid

phase and the soil matrix, either enhancing or retarding the transfer of the

substances dissolved in the water phase (1). Therefore, the characterization of the

chemical solute transport in the soil has become an active field of environmental

research.

Given the intrinsic variability of the soil physical parameters, the

characterization of solute transport at the field scale is a complicated task. In

recent years, the time domain reflectometry (TDR) has been widely used in

soil physical research. It has been considered as an attractive tool with a

wide range of applications since it is nondestructive, highly accurate and

low in labor requirement compared other methods (2,3). In addition, the

TDR allows to measure two important soil physical state variables: the soil

moisture content and the total electrical conductivity, both with a high

spatio-temporal resolution. TDR technology allows therefore to measure the

water transport and solute breakthrough at the time the experiment is being

conducted and does not require assumptions about the local flux density of

water (4).

The use of TDR in the estimation of the concentrations of conservative

solutes was initiated by Dalton et al. (5). Their approach was based on signal

attenuation of a voltage pulse propagating along the transmission line, which

serves as a measure of electrical conductivity in a bulk soil. Vanclooster et al. (6)

and Mallants et al. (7) used horizontally installed TDR probes in laboratory

column experiments taken along a field transect. Horizontal positioning of the

TDR probes enables the sampling of a larger area perpendicular to the mean

direction of flow. This is an advantage for estimating solute fluxes, especially in

multilayered heterogeneous soils where horizontal flow at the microscopic scale

might influence longitudinal solute dispersion. In addition, the horizontal

configuration allows measuring solute breakthrough at different depths, which is

a prerequisite for identifying the governing solute transport mechanism (8).

When solute velocities are independent of solute depth, full mixing of solutes in

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the complete pore water domain occurs. In this case, the convective dispersive

transport model is appropriate, and solute dispersion remains constant with depth.

However, if solute velocities vary with the soil depth, a stream-tube concept will

be more appropriate for describing the transport. The identification of the

governing solute transport can be estimated from solute breakthrough curves (the

correlation curve between solute relative concentration with time) measured at

different depths, as presented by Vanclooster et al. (1), Vanderborght et al. (9,10).

However, few studies have been reported so far about the impact of the flow

condition on the governing solute transport concept.

The objective of the present study was to determine the governing transport

processes as solutes move through undisturbed soil columns and to analyze the

dependence of the solute transport parameters upon water flux density and soil

moisture.

MATERIALS AND METHODS

Theory

Measurement of Solute Breakthrough by Means of TDR

As shown by several researchers (4,11), solute breakthrough curves may be

established from TDR-based estimates of the bulk soil electrical conductivity’s

(ECb) during steady state solute transport experiments with salty tracers. A linear

relationship is generally observed between the resident solute concentration of a

salty tracer, Cr, and ECb for constant water contents ranging from relatively low

to saturation and for salinity levels ranging from 0 to approximately 50 dS m21

(12). The linear relationship may be express as:

Cr ¼ aþ bECb ð1Þ

where a and b are calibration constants. ECb (dS m21) can be related to

the impedance, Z(V), of an electromagnetic wave that travels through the soil

(13):

ECb ¼Kc

Z 2 Zcable

ð2Þ

where Kc is the cell constant of the TDR probe (m21), and Zcable (V) is the

resistance associated with cable, connectors, and cable tester. Relative solute

concentration, C (x, t ), can be expressed as

Cðx; tÞ ¼Cr 2 Ci

C0 2 Ci

ð3Þ

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where C0 is a reference concentration such as the input concentration during

miscible displacement, and Ci is the background concentration. Combining

Eqs. (1) to (3), we could get

Cðx; tÞ ¼Z21

x;t 2 Z21i

Z210 2 Z21

i

ð4Þ

where Zi is the impedance before application of the tracer solution, and Z0 is the

impedance associated with the reference concentration, C0. Eq. (4) shows that,

under steady flow conditions (i.e., constant soil water content) the relative solute

concentration, C(x, t ), at a particular depth, x, and time, t, can be derived from the

measured impedance, Zx, t, if appropriate values of Zi and Z0 are available. The

values for Z0 have been discussed by Mallants et al. (14).

Estimating Solute Transport Parameters

Analytical solutions of the governing steady state solute transport models

may be used in an inverse way to estimate the solute transport parameters (15).

Using inverse procedures, breakthrough curves drawn by the observed laboratory

or field data are matched to the analytical solutions. Computer codes such as

CXTFIT 2.0 (15) are ready available to predict solute distributions in time and

space for specified model parameters and to estimate solute parameters in an

inverse way.

The convection–dispersion equation of the CXTFIT model allows

simulating one-dimensional transport of solutes, subject to adsorption, first-

order degradation, and zero-order production, in a homogeneous soil. The model

is formalized as:

›

›tðuCr þ rbCcÞ ¼

›

›xuD

›Cr

›x2 JwCr

� �2 umlCr 2 rbmsCc

þ uglðxÞ þ rbgsðxÞ ð5Þ

where Cr is the volume-averaged or resident concentration of the liquid

phase(g L21); Cc is the concentration of the adsorbed phase (g L21); D is the

dispersion coefficient (cm2 h21); u is the volumetric water content (cm3 cm23); Jw is

the volumetric water flux density (cm h21); rb is the soil bulk density (g cm23); ml

andms are the first-order decay coefficients for degradation of the solute in the liquid

and adsorbed phases, respectively;gl (mol cm23 h21) and gs (mol cm23 h21) are the

zero-order production terms for the liquid and adsorbed phases, respectively; x is the

distance (cm); and t is the time (h). We assumed that m could not be negative. The

production functions are given as a function of distance.

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Solute adsorption by the solid phase is described with a linear sorption

isotherm as

Cc ¼ KdCr ð6Þ

where Kd is an empirical distribution constant. Using Eq. (6) and assuming

steady-state flow in a homogenous soil, Eq. (5) may be rewritten as

Fr

›Cr

›t¼ D

›2Cr

›x22 n

›Cr

›x2 mCr þ gðxÞ ð7Þ

where nð¼ Jw=uÞ is the average pore-water velocity, Fr is the retardation factor

given by

Fr ¼ 1 þrbKd

uð8Þ

and m and g are, respectively, combined first- and zero-order rate coefficients:

m ¼ ml þrbKdms

uð9Þ

gðxÞ ¼ glðxÞ þrbgsðxÞ

uð10Þ

When the first-order degradation coefficients in the liquid (ml) and

adsorbed (ms) phases are identical, Eq. (9) becomes

m ¼ mlFr ð11Þ

Experimental Approach

The transport processes of solute in the vadoze zone were examined in two

undisturbed soil columns. The experimental soil (Table 1) was classified as a

Fimic Anthrosol (FAO–UNESCO) and was collected from a sandy aquifer. The

two soil columns have a total length of 30 cm and a diameter of 15 cm.

The soil columns were put on filter. A 0.05-m high supporting reservoir was

put under the filter layer. A 1.5-cm-diameter drainage tube was embedded in

water layer and connected to a water column. The soil columns created a negative

pressure head at the bottom of soil column and unsaturated flow conditions. Soil

water contents, u, and bulk soil electrical conductivities, ECb, were monitored by

means of TDR probes installed at 10 cm, 20 cm and 30 cm depths. Measurements

were made with a Tektronix cable tester (Tektronix 1502C, Beaverton, OR).

Prior to the installation, the TDR probes were calibrated in the laboratory for

moisture and impedance measurements. In addition to the TDR probes, three

tensiometers were also inserted horizontally at the same depths as TDR probes.

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The soils were saturated with tap water before the experiments. As the

impedance of distilled water was higher than 1 kV, which is beyond the measuring

range of the cable tester, normal tap water ðelectrical conductivity ¼ 0:75 dS m21Þ

was used. A constant flux of water was established by means of a syringe peristaltic

pump. Three different flux densities (2.11, 3.59, and 4.61 cm h21) in soil column 1

and two different flux densities (2.14 and 3.58 cm h21) in the soil column 2 were

applied. After establishing steady-state saturated flow using tap water, a solute

solution containing 1000 mg kg21 Ca(NO3)2 was added continuously to keep the

soil columns in a state of C ¼ C0: Solute application time (t0) ranged from 4 h to 7 h.

After saturated state conditions were reached, the tap water was applied again until

solutes completely leached out of the soil columns. Values of the total resistance or

impedance, Z, of soils were obtained from 3 TDR probes inserted into the soil

column at three depths of 10, 20, and 30 cm. The travel time of the electromagnetic

wave and the impedance were taken from the screen of the cable tester.

Impedance of the soil, soil water content, and pressure head at the 3

different depths were measured every 10 minutes. Topp’s equation was used to

calibrate TDR for soil moisture. The indirect calibration procedure described by

Mallants et al. (14) was used to calculate relative solute concentration. The

observed breakthrough curves were modelled by means of the convection–

dispersion equation available in CXTFIT 2.0.

RESULTS AND DISCUSSION

The measured impedance variations with the time after adding Ca(NO3)2 to

the soil column 1 are shown in Fig. 1. At time = 0 the impedance was about 260V

at the depth of 10 cm in the soil column 1 when the solution flux was 3.59 cm h21

and dropped to about 180V about 1 hour after Ca(NO3)2 was added. The value of

impedance remained fairly constant around 180V during about 4.5 hours,

indicating that the TDR signal was not affected by the location of the solute mass

within the transmission (probe) length. Some minor variations in impedance were

measured, but the variations were much smaller than the impedance increase

after 4.5 hours.

The impedance of middle soil layer dropped to 170V about 2 hours after

Ca(NO3)2 was added, while that of the bottom layer decreased to 170V about

3 hours after. Similar results were obtained by the other fluxes in two soil

columns. However, the higher the solute flux, the lower the impedance was. The

flux increased which resulted in the solute concentration rise. Therefore the

impedance of solution decreased.

The value of impedance for almost all the TDR probes did not return

exactly to the original value before Ca (NO3)2 was added. After 10 hours of the

experiment, the final impedance was slightly higher than the initial impedance

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value. This suggested that the addition of the solute pulse had in some way altered

the baseline ECb (4). In soils where the original solute concentrations are high,

the final impedance readings may be higher than the initial readings because of

leaching in the soil. The magnitude of the error will depend on the initial solute

concentrations of the soil and the leaching water.

Figure 2 shows the soil water distribution in soil column during the

leaching experiment. Steady state flow was obtained as observed from the steady-

state moisture contents. The vertical distribution of the water in the soil columns

was not uniform during the leaching experiments. Near the reservoir, the

horizontal TDR lines gave water contents about 0.4 cm3 cm23. The distribution

of the moisture content tended to be low in soil surface and high in the bottom of

the soil column due to the hysteresis, caused by the different moisture contents of

the three layers at the beginning of the experiment (18) and the influence of

gravitational potential on the water movement.

The CXTFIT model (15) was used to analyze the solute transport behaviors

based on the one-dimensional convection-dispersion equation (Eq. (5)) under

various boundary conditions. The model was used to optimize pore water velocity

and dispersion coefficient from observed breakthrough curves. Figure 3 shows the

experimental data and the analytical data with CXTFIT of the two undisturbed sandy

soil columns. Good agreement could be seen between the measured and simulated

breakthrough curves of relative concentrations of solute with time. A perfect

convergence of breakthrough curves in the two soil columns could be found. This

study demonstrated that the CXTFIT model was suitable for fitting the observed

solute transport. However, this does not mean that the convection dispersion model

is the governing transport mechanism, since this can only be proofed by analyzing

the travel depth dependency of the solute transport parameters (8).

Figure 1. Relationship between soil impedance and time after adding Ca(NO3)2 in soil

column 1.

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Estimated transport parameters for three solute fluxes in the soil column 1

and the two solute fluxes in the soil column 2 are given in Table 2. A good fit

between the experimental data and the data of analytical model, CXTFIT, could

be obtained, as shown by the high R 2 values.

In the soil column 1, as shown in Fig. 4, the dispersion coefficient of solute

decreased with the soil depth, and regression analysis indicated that the

correlation between the dispersion coefficient and depth was significant at the 5%

probability level. The equation is Y ¼ 2310:36X 1:98 ðr ¼ 20:8477; n ¼ 9Þ;where X is the soil depth (cm) and Y is the dispersion coefficient (cm2 h21). The

decrease of the dispersion coefficient with depth may indicate that stable solute

flow was not reached in the topsoil layer.

In the soil column 2, the relationship of the dispersion coefficient of solute

with soil depth could not be found to have any regularity (Fig. 4). Especially, the

dispersion coefficient increased at the bottom soil layer, which might be

attributed to the difference of texture between top and bottom soils.

Figure 2. Relationship between moisture distribution in the soil column and time

measured by TDR.

Figure 3. Measured and simulated breakthrough curves of relative solute concentrations

(C/C0) in relation to time in the two undisturbed soil columns.

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These observations show that the adopted size of the experimental device

may be critical in obtaining solute transport parameters. This is suggested by the

depth decrease of the hydrodynamic dispersion coefficient in the first column,

suggesting unstable flow conditions; and sudden depth increase of the

hydrodynamic dispersion coefficient in the second column suggesting structural

heterogeneity. We therefore recommend increasing the sampling size of the soil

columns in future solute transport studies.

Average velocities of pore water in the soil columns were calculated by

dividing the Darcian flux by the average measured volumetric moisture content.

The relationships of pore-water velocities with the soil depths in the two soil

columns are shown in Fig. 5. The pore-water velocities were also affected by

gravitational potential in homogeneous soils. It was indicated that the pore-water

velocities decreased with the soil depth.

By regression analysis, a significantly positive correlation at the 5%

probability level could be found between the average pore-water velocity and the

Table 2. Characteristics of Solute Breakthrough Curves for Two Undisturbed Soil

Columns

Soil Column

Fluxa

(cm h21)

Depthb

(cm)

uc

(cm3 cm23)

nd

(cm h21)

De

(cm2 h21) R2

1 3.59 10 0.2967 15.71 30.12 0.8654

20 0.3055 12.02 3.50 0.9533

30 0.4222 10.21 1.80 0.9259

2.11 10 0.2773 8.56 9.90 0.9719

20 0.2954 7.39 4.70 0.9539

30 0.4173 6.28 2.30 0.8631

4.61 10 0.2738 34.89 52.86 0.9144

20 0.2907 18.00 9.34 0.9144

30 0.4277 14.89 6.06 0.8509

2 2.14 10 0.2846 8.32 3.22 0.9583

20 0.3028 6.46 2.44 0.9259

30 0.3963 6.39 9.14 0.9615

3.58 10 0.2547 9.49 4.69 0.9493

20 0.3025 8.99 1.95 0.9429

30 0.3785 8.71 9.35 0.9695

a Flux is flux density controlled by a syringe peristaltic pump.b Depth is the distance from soil surface to the place of TDR installed.c u is moisture content.d n is average pore-water velocity.e D is dispersion coefficient. The cm h21 means cm per hour.

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dispersion coefficient of solute in the soil column 1 (Fig. 6). But such a correlation

could not be found in the soil column 2, because the dispersion coefficient in the

bottom soil layer suddenly increased due to native heterogeneity of the soil.

CONCLUSIONS

The results of this investigation indicated that the flux dependency of the

vadoze zone solute transport parameters by modeling the TDR measured

breakthrough curves in undisturbed small soil cores. Solute transport parameters

were inferred by inverting the analytical solution of the governing classical

convection dispersion equation.

Notwithstanding the concern about the adopted sample size in our study,

clear linear relationships between the solute dispersion coefficient and the pore

water velocity were identified. However, more experimental studies should,

Figure 5. Relationships between the pore-water velocities (n ) and the soil depths in the

soil column 1 (Ex 1) and soil column 2 (Ex 2) at different solute fluxes.

Figure 4. Variations of dispersion coefficient (D ) of solute with the depth in the two soil

columns.

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Figure 6. Correlations between average pore-water velocities (n ) and dispersion

coefficients (D ) in the soil column 1 at solute fluxes of 3.59 cm h21 (A), 2.11 cm h21 (B),

and 4.61 cm h21 (C).

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therefore, be carried out at the larger scales to further explore the relationships

between solute transport parameters and water flow regime imposed by the

surface boundary conditions.

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