Stable or unstable wetting fronts in water repellent

soils ± effect of antecedent soil moisture content

Coen J. Ritsemaa,*, John L. Nieberb, Louis W. Dekkera, T.S. Steenhuisc

a DLO Winand Staring Centre for Integrated Land, Soil and Water Research, Section Soil Physical Transport Phenomena, P.O. Box 125,

6700 AC Wageningen, The Netherlandsb University of Minnesota, Department of Biosystems and Agricultural Engineering, Eckles Ave. 1390, St. Paul, MN 55108, USA

c Cornell University, Department of Agricultural and Biological Engineering, Riley-Robb Hall, Ithaca, NY 14853-5701, USA

Abstract

Dry water repellent soils are known to inhibit water in®ltration, ultimately forcing water to ¯ow via preferential paths through

the vadose zone. To study water ¯ow and transport in a water repellent sandy soil, a bromide tracer experiment had been

carried out, which started in the fall after winter wheat had been sown. Despite the uniform tracer application, soil core

sampling indicated that bromide concentrations varied largely from place to place. Wetter sites in the experimental ®eld

received more bromide, due to lateral transport through a thin top layer. Wetting fronts in®ltrated deeper here, leading to

perturbed wetting fronts in the experimental ®eld. In contrast to what was expected, the wetting front perturbations did not

grow to ®ngers. Numerical results indicate that this was attributed to the relatively high soil water contents during the

experiment, which caused the soil to be wettable instead of water repellent. The water-entry capillary pressure of the

secondary wetting branch exceeds the air-entry capillary pressure of the primary drainage branch in this case. In the opposite

situation, with the water-entry capillary pressure of the secondary wetting branch beneath the air-entry capillary pressure of

the primary drainage branch, perturbations would have grown to ®ngers. Such a situation occurs during in®ltration in initially

dry, water repellent soil. The results presented illustrate the effect of antecedent moisture conditions on the formation of stable

and unstable wetting fronts, and its relation to the moment of tracer application. # 1998 Published by Elsevier Science B.V.

All rights reserved.

Keywords: Water repellency; Unstable wetting; Preferential ¯ow; Critical soil moisture content

1. Introduction

Simulation models are widely used for predicting

water and solute transport through soils. Over the last

decade it has become increasingly evident that models

based on Darcy's law and the general convection±

dispersion equation are often not capable to simulate

actual water ¯ow and transport processes (Gee et al.,

1991; Jury and FluÈhler, 1992). The main reason is the

occurrence of preferential ¯ow. Preferential ¯ow can

be found in a variety of soils. First, preferentially

moving water is often encountered in clay and peat

soils, due to the presence of shrinkage cracks and/or

biopores (Bouma and Dekker, 1978; Beven and

Germann, 1982). Second, development of unstable

Soil & Tillage Research 47 (1998) 111±123

*Corresponding author. Tel.: 0031 317 474266; fax: 0031 317

424812; e-mail: c.j.ritsema@sc.dlo.nl

0167-1987/98/$19.00 # 1998 Published by Elsevier Science B.V. All rights reserved.

P I I S 0 1 6 7 - 1 9 8 7 ( 9 8 ) 0 0 0 8 2 - 8

wetting fronts in soils may cause water to move

preferentially along vertical ®ngers toward the

groundwater. Unstable wetting fronts may be induced

if (i) the soil hydraulic conductivity increases with

depth, which is found in ®ne over coarse textured soils

(Hillel and Baker, 1988; Baker and Hillel, 1990) and

in dense over loosely packed soils (Ritsema and

Dekker, 1994a), (ii) soils are water repellent (Ritsema

et al., 1993; Ritsema and Dekker, 1994b), and (iii) if

air entrapment occurs (Glass et al., 1990).

Recently, Ritsema and Dekker (1995) demonstrated

that surface-applied bromide tracers in two water

repellent sandy soils distributed laterally through

the very thin top layer of these soils toward places

where vertical in®ltration dominated. This caused

some places to receive relatively large quantities of

water and solutes and others small ones, leading to

perturbations at the in®ltrating wetting front. The

perturbations propagated to form ®ngers in the

grass-covered water repellent sandy soil at Ouddorp

(Fig. 1(A)), whereas no distinct ®ngered ¯ow patterns

developed in the arable water repellent sandy soil at

Vredepeel (Fig. 1(B)). The mechanism leading to the

formation of the ®ngered ¯ow patterns in the Ouddorp

experimental ®eld has been discussed previously

(Ritsema et al., 1993; Ritsema and Dekker, 1994a;

Ritsema et al., 1998), while the origin of the wavy-like

wetting fronts at the Vredepeel site (Fig. 1(B)) have

not yet been described and explained. Therefore, the

objectives of the present study are (i) to highlight the

¯ow and transport mechanism in the water repellent

sandy soil at Vredepeel, based upon the results of a

detailed bromide tracer experiment, (ii) to describe

and explain the origin of the wavy-like wetting fronts

on basis of measurements and numerical results, and

(iii) to indicate the in¯uence of soil water content on

the occurrence of water repellency.

2. Materials and methods

2.1. Site and soil

The ®eld experiment was carried out at experimen-

tal farm `Vredepeel' in the southeastern part of the

Netherlands. The experimental ®eld was 54 m�80 m.

The soil has been classi®ed as a mesic Typic Hapla-

quod (De Bakker, 1979), and consists of a 30 cm dark

colored sandy topsoil overlying non-calcareous aeo-

lian sand. The organic matter content of the topsoil is

approximately 4.8%, and of the underlying sand

around 0.2%. The clay content of the soil is less than

3%. According to the classi®cation previously used by

Dekker and Ritsema (1994), the topsoil is extremely

water repellent (with Water Drop Penetration Times of

more than 3 h for samples oven-dried at 658C),

whereas the subsoil is wettable.

2.2. Tracer experiment

On 22 November 1990, potassium bromide was

sprayed on the soil surface, with an average bromide

application of 11.1 g mÿ2 (standard deviation

1.0 g mÿ2). To determine the variation in tracer appli-

cation, 48 small petri-dishes were randomly placed on

the soil surface of the experimental ®eld. Shortly

Fig. 1. Fingered flow pattern in a grass-covered water repellent

sandy soil near Ouddorp (A), and a wavy-like wetting front in the

water repellent sandy soil with winter wheat at the Vredepeel

experimental field (B).

112 C.J. Ritsema et al. / Soil & Tillage Research 47 (1998) 111±123

before spraying, winter wheat was sown. The wheat

crop was harvested in August 1991.

The ®eld was divided into sixteen plots, each

10 m�27 m. After 1, 22, 42, 103, 214 and 278 days,

sixteen soil columns with a diameter of 10 cm and a

length of 150 cm were taken (one from each plot) and

sliced into layers. Each sample was used to determine

its volumetric soil water content (oven-drying), dry

bulk density, and bromide concentration. Bromide was

extracted with demineralized water and the extracts

were analyzed using high pressure liquid chromato-

graphy (HPLC).

Groundwater tubes were installed in all sixteen

plots, with ®lters at 0.8±1.0 m, 1.2±1.4 m and 1.9±

2.1 m depth. On each sampling date, groundwater

samples were taken from the tubes situated below

the groundwater level. The groundwater level was

recorded continuously at two spots in the ®eld. Rain-

fall at the experimental ®eld was recorded with a rain

gauge whose rim was ¯ush with the soil surface. A

summary of daily rainfall, potential evaporation and

groundwater tables is shown in Fig. 2.

Additionally, during the tracer experiment, inten-

sive soil samplings were carried out to determine the

short-distance variation of soil water content and the

shape of the in®ltrating wetting front. This type of

measurement has proven to be very useful to detect

preferential ¯ow paths (Ritsema and Dekker, 1996).

Here, 25 samples, each 100 cm3 in volume, were taken

adjacently at depths 10±15, 20±25, 30±35, 40±45, 50±

55 and 60±65 cm yielding a total of 150 samples for

each transect. The water content distributions in the

transects were visualized by contour plots generated

by a spatial interpolation program.

2.3. Laboratory experiments

Soil samples for determination of soil hydraulic

properties were taken in duplicate in the water repel-

lent topsoil (10±18 cm) and in the wettable subsoil

(45±53 cm). The hysteretic soil water retention curves

were measured using the hanging water column

method (Stolte et al., 1992). With this method, the

primary drainage and a secondary wetting branch

were determined. The primary wetting branch of

the soil water retention characteristic was measured

following the capillary rise method. The Wind method

(Boels et al., 1978) was used to determine the water

retention and the unsaturated hydraulic conductivity

characteristics simultaneously. Saturated hydraulic

conductivity was measured using the constant head

method, as described by Klute (1986).

The `critical soil moisture content', as previously

de®ned by Dekker and Ritsema (1994), refers to the

level of soil water content above which the soil is

wettable and below which it is water repellent. The

Fig. 2. Daily precipitation, potential evaporation, and groundwater

level during the tracer experiment.

C.J. Ritsema et al. / Soil & Tillage Research 47 (1998) 111±123 113

soil is called water repellent in case three water drops

placed on its surface with a medicine dropper remain

there for more than 5 s. Critical soil moisture contents

could be derived for each soil layer by repeatedly

applying the WDPT-test on drying, initially ®eld-

moist, soil samples. After a sample was classi®ed

water repellent, the sample was oven-dried at 658Cto determine its critical soil moisture content. Per soil

layer, the critical soil moisture content was determined

by, at least, three samples. Absence of water repel-

lency when water contents are higher than the critical

soil moisture content is ascribed to molecular con-

formational changes of the organic substances respon-

sible for the water repellency (Ma'shum et al., 1988;

Wallis et al., 1990).

2.4. Numerical simulations

Numerical simulations of the Richards equation and

the convection±dispersion equation were derived for

both an initially dry and initially ®eld-moist Vredepeel

site. The purpose for deriving these solutions was to

demonstrate the effect of antecedent soil moisture

content on the ¯ow of water and transport of solutes

in the soil pro®le. The ¯ow and transport simulations

were produced by a ®nite element solution of the

Richards equation and the convection±dispersion

equation described by Nieber (1996) and Ritsema

et al. (1998). The method uses quadrilateral elements

with a specialized downstream weighting of the hy-

draulic conductivities between adjacent node points.

The convection±dispersion process was solved using a

particle tracking-random walk method (PTRW)

described by Abulaban et al. (1998). 50,000 particles

were used to represent the solute mass.

3. Results

3.1. Variation in soil water content, dry bulk density

and bromide concentration

Mean volumetric soil water contents varied between

14.1% and 32.6% on day 1, between 13.1% and 32.1%

on day 22, between 17.8% and 30.6% on day 42,

between 16.6% and 36.0% on day 103, between 3.9%

and 34.4% on day 214 and between 5.7% and 30.5%

on day 278. Standard deviations varied between 0.1%

and 6.9%, and coef®cients of variation ranged

between 0.2% and 82.1%. During the experiment,

variation in soil water content was relatively high in

the humous topsoil and in the upper part of the

wettable subsoil, resulting in high standard deviations

and coef®cients of variation in this zone. Measured

soil water contents and calculated means versus depth

are shown in Fig. 3 for all sampling days.

Mean dry bulk densities varied between

1.12 g cmÿ3 and 1.73 g cmÿ3 during the experiment.

The initially low dry bulk densities of the topsoil were

due to ploughing and subsequent sowing of winter

wheat just before the start of the experiment. The

mean dry bulk density of the topsoil became increas-

ingly higher during the course of the experiment.

Standard deviations decreased with depth, and gen-

erally ranged between 0.12 g cmÿ3 and 0.20 g cmÿ3

in the 0±4 cm layer and between 0.02 g cmÿ3 and

0.03 g cmÿ3 at the 120 to 127.5 cm depth. Coef®cients

of variation ranged between 3.9% and 16.6% for the

30 cm thick topsoil, and between 0.4% and 8.7% for

the underlying subsoil.

On day 1, bromide was present in the 0±4 cm layer

only. On day 22, after 37.3 mm of rain, the bromide

peak protruded between the 15 to 22.5 cm depth. On

day 42, after another 84.3 mm of rain, the bromide

peak was found in the 37.5±52.5 cm layer. On day 103,

after another 59.4 mm of rain, the bromide peak was

found at 75±82.5 cm depth, and on day 214, after

another 123.9 mm rain, it was found in the 97.5±

105 cm layer. On day 278, with an additional

115.2 mm of rain after day 214, no clear bromide

peak could be distinguished anymore. The standard

deviation in measured bromide concentration was

high at the start of the experiment and decreased with

time. Measured bromide concentrations and calcu-

lated mean are shown versus depth in Fig. 4 for all

sampling days. The total amount of bromide recovered

in the soil pro®le to 90 cm depth, calculated on the

basis of the 16 soil cores taken on each sampling day,

equaled 97.3% for day 1, 96% for day 22, 101.5% for

day 42, 80.3% for day 103, 51.5% for day 214 and

40.1% for day 278.

3.2. Origin of the perturbed wetting front

Of the sixteen soil cores sampled on day 1, eleven

cores contained signi®cantly less or signi®cantly more

114 C.J. Ritsema et al. / Soil & Tillage Research 47 (1998) 111±123

Fig

.3.

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mea

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C.J. Ritsema et al. / Soil & Tillage Research 47 (1998) 111±123 115

Fig

.4.

Bro

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116 C.J. Ritsema et al. / Soil & Tillage Research 47 (1998) 111±123

bromide than could be expected on basis of the tracer

application distribution. The lower and upper 95%

con®dence limits of the tracer application distribution

equaled 9.1 g mÿ2 and 13.2 g mÿ2, respectively, while

the mean application rate amounted to 11.1 g mÿ2. On

day 1, ®ve of the sixteen soil cores sampled contained

more bromide than the upper con®dence limit,

whereas six cores contained less bromide than the

lower con®dence limit. In all soil cores, bromide was

con®ned to the 0±4 cm soil layer, and no drainage to

deeper layers had occurred. Bromide recovery of the

16 soil cores sampled on day 1 equaled almost 100%.

The large variation in total bromide amounts recov-

ered in the soil cores can only be caused by the

occurrence of distribution ¯ow, as explained in detail

previously by Ritsema and Dekker (1995). Distribu-

tion ¯ow is referred to as the lateral transport of water

and solutes through a very thin layer at the top of the

soil pro®le. The data indicate that cores with more

bromide than the upper con®dence limit possessed

higher mean volumetric water contents than cores with

less bromide than the lower con®dence limit (Ritsema

and Dekker, 1995). Similar results were found for the

soil cores sampled on days 22 and 42 (Ritsema and

Dekker, 1995). This demonstrates that the distribution

¯ow was directed from the relatively drier locations

within the experimental ®eld toward the wetter areas.

At the wetter places within the experimental ®eld,

wetting fronts protruded slightly deeper than at other

places, leading to perturbed wetting fronts in the upper

part of the soil pro®le (see Fig. 1(B)). The spatial

water content distribution shown in Fig. 5, which is

based upon 75 soil water content measurements in a

1.4 m long and 0.3 m deep transect, clearly illustrates

the shape of such a perturbed wetting front.

3.3. The fate of the perturbed wetting front

In order to investigate if the wetting front perturba-

tions would grow to form ®ngers during further in®l-

tration into the pro®le, several 1.4 m long and 0.65 m

deep transects were dug by taking 150 (100 cm3, 5 cm

wide and 5 cm high) samples to determine their spatial

water content distributions. A typical example with a

wavy-like wetting front is shown in Fig. 6. In the other

trenches sampled, wetting patterns were alike, and no

indications of ®ngered ¯ow were found.

The measured bromide concentrations obtained at

the Vredepeel site did not show evidence of ®ngered

¯ow either. On sampling day 1, the bromide front in all

sixteen soil cores was located in the 0±4 cm layer. On

the basis of the sixteen soil cores sampled on day 22, it

could be calculated that the bromide front protruded to

an average depth of 28.6 cm, with a standard deviation

of 4.4 cm only. At day 42, the bromide front reached

an average depth of 62.8 cm, with a standard deviation

Fig. 5. Two-dimensional soil water content distribution in the water repellent topsoil at Vredepeel, elucidating a perturbed wetting front.

C.J. Ritsema et al. / Soil & Tillage Research 47 (1998) 111±123 117

of 6.4 cm. A few days later, bromide was detected in

the groundwater tubes for the ®rst time all over the

®eld at a concentration level of around 2 mg lÿ1. The

similar concentrations all over the ®eld point to homo-

geneous ¯ow, and it supports the previous results that

®ngered ¯ow did not occur during the experiment. It

might be noticed here that, during another bromide

tracer experiment executed on a water repellent sandy

soil at Ouddorp, ®ngered ¯ow did occur (Ritsema

et al., 1993; see Fig. 1(A)). At this site, bromide

arrival at the groundwater took place at once, too.

However, bromide concentrations varied here between

0.2 m glÿ1 and 160 mg lÿ1 due to the ®ngered ¯ow

process.

To conclude, despite the water repellent character of

the sandy topsoil at Vredepeel, measurements

revealed that ®ngered ¯ow was not a process of

signi®cance during the bromide tracer experiment.

In the next section it is explained why this was the

case.

3.4. Dissipation of wetting front perturbations ±

causes and numerical results

Measured hysteretic water retention functions of the

water repellent topsoil and the wettable subsoil are

shown in Fig. 7. The primary drainage and wetting

branches and a secondary wetting curve are shown.

The capillary pressure is de®ned as the difference

between the air pressure and the water pressure,

and, therefore, in an unsaturated soil the capillary

pressure is generally positive. For the water repellent

topsoil, the water-entry capillary pressure at the pri-

mary wetting branch is lower than the air-entry capil-

lary pressure at the primary drainage branch. In

contrast to the water repellent topsoil, the water-entry

capillary pressure at the primary wetting branch of the

wettable subsoil exceeds the air-entry capillary pres-

sure of the primary drainage branch. Besides the

primary wetting and drainage branches, a secondary

wetting branch for both soil layers is shown, too

(Fig. 7). For both the water repellent topsoil and the

wettable subsoil, the water-entry capillary pressure at

the secondary wetting branch exceeds the air-entry

capillary pressure at the primary drainage branch.

Recently, Nieber (1996) and Ritsema et al. (1998)

showed that the water-entry and air-entry capillary

pressures are of crucial importance with respect to the

possible formation of ®ngers. Especially, in situations

with the water-entry capillary pressure below the air-

entry capillary pressure, ®ngers might form.

In Figs. 8 and 9 numerical results are shown on the

evolution of a perturbed wetting front and an applied

bromide pulse in an initially ®eld-moist (wettable) and

an initially dry (water repellent) Vredepeel soil,

respectively. A two-dimensional ®nite element water

Fig. 6. Two-dimensional soil water content distribution in a trench at Vredepeel, illustrating the stable, wavy-like character of the infiltrating

wetting front at depth during the bromide experiment.

118 C.J. Ritsema et al. / Soil & Tillage Research 47 (1998) 111±123

¯ow and transport model, including hysteresis in the

water retention characteristics, was used for this pur-

pose (Nieber, 1996; Ritsema et al., 1998). The ¯ow

domain was 50 cm wide and 70 cm deep. The topsoil

and subsoil were 30 and 40 cm thick, respectively. For

both the initially ®eld-moist and initially dry Vrede-

peel soil the rainfall was set at a constant intensity of

1.8 mm dayÿ1. The initial conditions were similar in

both cases, except that for the initially dry case a wavy

perturbation in the water content distribution in the

upper 5 cm of the soil was imposed, according to what

was observed in the ®eld (Fig. 1(B)). For solute

transport, an instantaneous pulse of bromide was

imposed at the top of the ¯ow domain at the initiation

of rainfall. The solute was applied at a rate of

5.05 gm mÿ2. In the simulations local dispersivities

were set to 0.001 m for the longitudinal and 0.0002 m

for the transverse. The bottom boundary condition

used in the simulations was free drainage, i.e. unit

hydraulic gradient. In the simulations, measured soil

physical properties of both the water repellent topsoil

and the wettable subsoil were used.

For the initially ®eld-moist Vredepeel soil, com-

puted soil water distributions in the 70 cm soil pro®le

are shown for different times in Fig. 8(A). The pro-

gression of the wetting front is visible in these dia-

Fig. 7. Hysteretic water retention curves of the water repellent topsoil (A) and the wettable subsoil (B) at Vredepeel.

C.J. Ritsema et al. / Soil & Tillage Research 47 (1998) 111±123 119

grams, but the maximum saturations are quite low

(maximum of 0.26) because of the low imposed rain-

fall intensity. It is observed that under these condi-

tions, the wetting front progresses downward in a

stable form. The transport of bromide is shown in

Fig. 8(B). The distribution of the bromide in the

direction of ¯ow indicates a Gaussian spreading, as

would be expected under stable ¯ow conditions. The

breakthrough curve for the solute at the bottom of the

¯ow domain is illustrated in Fig. 10. The shape of this

breakthrough curve indicates that the dispersion pro-

cess produces a gaussian distribution of the solute.

For the initially dry Vredepeel soil, simulated soil

water distributions in the soil pro®le are shown in

Fig. 8. Numerical results showing the formation of a stable wetting front (A) and the uniform transport of bromide (B) during infiltration in an

initially field-moist Vredepeel soil.

120 C.J. Ritsema et al. / Soil & Tillage Research 47 (1998) 111±123

Fig. 9(A) for different times. The wavy distribution of

soil water content in the top 5 cm of the soil pro®le is

clearly visible for the distribution at t�0 days. In the

domain above the wavy boundary the soil is wet

enough to be water wettable, while below this bound-

ary and above the interface between the two soil layers

the soil is water repellent. Following the initiation of

rainfall, the upper part of the pro®le wets up until it

becomes saturated. The water does not readily enter

the underlying water repellent soil, and will not enter it

until the water pressure reaches the water entry value

of the water repellent soil. Once the water pressure at

the wavy boundary reaches the water entry value, the

front progresses downward at the troughs of the

Fig. 9. Numerical results showing the growth of fingered flow pathways (A) and the heterogeneous transport of bromide (B) during infiltration

in initially dry Vredepeel soil.

C.J. Ritsema et al. / Soil & Tillage Research 47 (1998) 111±123 121

boundary, forming ®ngers. The ®ngers continue to

progress downward until they reach the water wettable

bottom layer, at which point they rapidly drain into

that layer. Much water is stored in the ®ngers and in

the upper part of the top layer prior to the ®ngers

reaching the bottom layer. So once they reach that

layer the movement is rapid. Steady-state ¯ow is

achieved within 1 or 2 days after the ®ngers reach

the water wettable layer. The distribution of solute

through the initially dry Vredepeel soil is illustrated in

Fig. 9(B). Here it is seen that the solute transport is not

Gaussian, but instead there is a signi®cant tailing of

the solute distribution. An interesting feature of the

solute distribution is the amount of solute that is

trapped in the upper part of the domain in the vicinity

of where the water enters the ®ngers. This solute is in a

low velocity zone and moves out very slowly. The

reader should note that the velocities obtained for the

®nite element solution used here are quite poor

approximations, and if more accurate velocities were

obtained (with mixed ®nite elements for instance) the

amount of `trapped' solute might be signi®cantly less.

The breakthrough curve for the unstable case (initially

dry soil) is displayed in Fig. 10 along with that for the

stable case (initially ®eld-moist soil). The break-

through curve is much sharper for the unstable case,

and there is signi®cant tailing due to the slow release

of the solute that is trapped. For the unstable case,

bromide arrival at the bottom of the ¯ow domain was

much quicker than computed for the stable ¯ow

situation (Fig. 10). This means that when adsorbing

compounds are surface-applied on an initially dry

Vredepeel topsoil, not only travel times of these

compounds to the groundwater will be much faster

than when applied on an initially ®eld-moist topsoil,

but the receiving dose of these compounds at the

groundwater will be much higher as well due to the

fact that signi®cant parts of the topsoil (i.e. buffering

capacity!) will be bypassed by the ®ngered ¯ow path-

ways.

To conclude, the numerical results clearly indicate

that the perturbations at the proceeding wetting front

can either propagate or dissipate, depending on the

antecedent soil water content. Finger formation occurs

during in®ltration into the initially dry water repellent

topsoil when the water-entry capillary pressure of the

wetting branch is lower than the air-entry capillary

pressure of the primary drainage branch. No ®ngers

are formed in the topsoil at higher initial soil water

contents. The soil physical properties of the wettable

subsoil preclude formation of ®ngers under any cir-

cumstances. This indicates that, at least from a soil

protection and soil management point of view, it

would be advisable to avoid extreme drying of water

repellent soils, for instance by use of sprinkler irriga-

tion, in order to prevent the formation of ®ngers during

subsequent rain events. In this way, accelerated down-

ward transport of water and solutes will be restrained

and minimized.

Acknowledgements

This work was carried out within the Environment

and Climate Research Programme of the EU within

framework of project EV5V-CT94-0467 `Analysis and

Improvement of Existing Models of Field-Scale

Solute Transport through the Vadose Zone of Differ-

ently Textured Soils with Special Reference to Pre-

ferential Flow'. We would like to thank W.

Hamminga, L.J.T. van der Pas and J.H. Smelt for their

assistance in sampling and data collection. The

authors greatly acknowledge the ®nancial support of

the NATO Collaborative Research Grant No. 960704,

and the SHELL for providing a travel grant to present

this work at the 16th World Congress of Soil Science,

Aug. 1998, Montpellier, France.

Fig. 10. Computed bromide breakthrough curves at 70 cm depth

(bottom flow domain) for the stable (initially field-moist) and

unstable (initially dry) flow cases.

122 C.J. Ritsema et al. / Soil & Tillage Research 47 (1998) 111±123

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