M
ZSpaƟally Distributed Water Fluxes in an
Andisol under Banana Plants: Experiments
and Three-Dimensional Modeling

S

S

:V

Julie Sansoulet,* Yves-Marie Cabidoche, Philippe Ca an, Stéphane Ruy, and Jirka Šimůnek
Water fluxes in the subsurface of forested and agricultural ecosystems vary spa ally across wide ranges because of several interconnected phenomena. On the one hand, subsurface environments are o en highly heterogeneous. On theother hand, infiltra on water is o en distributed unevenly due to aboveground intercep on and redistribu on of rainfall by the plant canopy. These phenomena have important hydro-ecological consequences because they significantly
aﬀect groundwater recharge and nutrient leaching. Field experiments involving subsurface lysimeters and tensiometers
were performed to quan fy the spa al distribu on of fluxes in an Andisol under a banana plant (Musa acuminata Colla).
Wick lysimeters were installed at a depth of 70 cm at several loca ons with respect to the banana stem to measure the
spa al distribu on of subsurface water fluxes. Collected experimental data were simulated using the HYDRUS so ware
package, which numerically solves the Richards equa on describing three-dimensional variably saturated water flow inthe subsurface. Spa ally distributed drainage fluxes were well reproduced with the numerical model. Due to the impact
of stemflow, drainage volumes under the banana stem were up to six mes higher than in the row downstream fromthe stem, as well as between rows, as these areas were sheltered from direct rainfall by the banana leaves and received
only throughfall.

W

above and in the soil exert a majoreﬀect on solute transport in the subsurface and thus
signiﬁcantly inﬂuence the quality of subsurface water resources.
In the humid tropics, high rainfall amounts signiﬁcantly exceed
the potential evapotranspiration from the soil–plant–atmospheresystem. Consequently, drainage is the main component of thesubsurface water balance. Water ﬂuxes in the subsurface of forested and agricultural ecosystems vary spatially across wide ranges
because of several interconnected phenomena. While on the one
side the subsurface environment is often highly heterogeneous, on
the other side inﬁltration water is often distributed unevenly due
to aboveground interception and redistribution of rainfall by theplant canopy. Part of the rainfall water intercepted by plant leaves

evaporates back to the atmosphere, part falls onto the soil surface
between leaves (throughfall), and part ﬂows around branches andstems downward toward the soil surface (stemﬂow).
Stemﬂow is an important hydro-ecological process in forested and agricultural ecosystems because it results in a spatiallylocalized input of water into the soil at the foot of the plant stemand thus signiﬁcantly inﬂuences groundwater recharge (Taniguchi
et al., 1996). Many catchment and subcatchment studies concerned with the eﬀect of agricultural and forest covers on the
distribution of water at the soil surface have therefore partitioned
the incident gross precipitation into stemﬂow and throughfall at
the plant scale (Levia and Frost, 2003). Due to their large leaves,
banana crops exhibit a strong partitioning of rainfall, resulting
in a high amount of stemﬂow (Bassette and Bussière, 2005). As
a consequence, stemﬂow appears to be the primary cause of thespatial distribution of drainage. Moreover, banana plants are often
locally and intensively fertilized at the foot of the plant stem withup to 400 kg N ha−1 yr−1 and 800 kg K ha−1 yr−1 (Godefroy andDormoy, 1988). Stemﬂow is thus likely to remove large quantities of these nutrients from the root zone and leach them into
the deeper subsurface.
Extensive literature has been produced about rainfall interception in forested ecosystems (Carlyle-Moses and Price, 1999)
and about the spatial variability of subsurface drainage due to different types of irrigation (Young and Wallender, 2002) and plantevapotranspiration (Arya et al., 1975). Still, few studies have been
performed to quantify the eﬀect of stemﬂow on the spatial pattern of drainage and associated solute leaching (Sansoulet et al.,2007). Recent lysimetric data have shown a strong inﬂuence of

J. Sansoulet and Y.-M. Cabidoche, Inst. Na onal de la Recherche
Agronomique, Unité Agropédoclima que de la Zone Caraïbe, Domaine
Duclos, 97170 Pe t-Bourg, Guadeloupe, France; P. Ca an, Centre
Interna onal de Recherche Agronomique pour le Développement, Unité
Systèmes de Culture Bananes, Plantains et Ananas, Sta on Neufchâteau,97130 Capesterre Belle Eau, Guadeloupe, France; S. Ruy, Inst. Na onal dela Recherche Agronomique, Unité Climat-Sol-Environnement, Domaine
Saint-Paul, Site Agroparc, 84914 Avignon, France; J. Šimůnek, Dep. ofEnvironmental Sciences, Univ. of California, Riverside, CA 92521. Received
13 Apr. 2007. *Corresponding author (juliesansoulet@yahoo.fr).
Vadose Zone J. 7:819–829
doi:10.2136/vzj2007.0073© Soil Science Society of America
677 S. Segoe Rd. Madison, WI 53711 USA.
All rights reserved. No part of this periodical may be reproduced ortransmi ed in any form or by any means, electronic or mechanical,
including photocopying, recording, or any informa on storage andretrieval system, without permission in wri ng from the publisher.
www.vadosezonejournal.org · Vol. 7, No. 2, May 2008819

the vegetation structure on gravitational drainage, which occurs
mainly below the stem of a banana crop (Cattan et al., 2007). The
researchers underlined the diﬃculty in measuring drainage using
coupled atmospheric and wick lysimeters. While atmosphericlysimeters exhibit percolation only under saturated conditions,wick lysimeters often overestimate water ﬂuxes because of theinduced suction.
Numerical models have, during the last 25 yr, increased ourunderstanding of drainage processes in soil–plant–atmospheresystems (Jarvis, 1991; Lafolie, 1991; Šimůnek et al., 2006). Twoessential factors must be addressed when modeling water ﬂow
through the soil under banana plants: (i) three-dimensional waterﬂow has to be modeled at the scale of the plant, considering therow and interrow phenomena; and (ii) the spatial distributionof rainfall due to its interception and redistribution under thebanana plant has to be evaluated. It thus appears that a distributed approach with spatially distributed boundary conditions
and soil hydraulic properties is probably the most appropriate toaddress this problem. The use of a distributed model makes it possible to determine the system response at each point of the domain
and to identify the critical areas, such as the domain under thebanana stem, that are likely to contribute most to the drainage.
Models simulating water ﬂow in the vadose zone diﬀer intheir conceptual approach, complexity, and mathematical formulation. For a complete review of water ﬂow models, see Herbst etal. (2005). Among the large number of well-established modeling programs, HYDRUS (Šimůnek et al., 2006) was selected
because it allows application of the diﬀerent boundary conditions required for this problem (e.g., stemﬂow, throughfall, freedrainage, and seepage face), has a sophisticated graphical userinterface that simpliﬁes the design of complicated three-dimensional geometries of the transport domain, enables considerationof diﬀerent soil layers and their inclination, considers root water
uptake, distinguishes between soil evaporation and plant transpiration, and also simulates solute movement. An extensive
literature exists (www.pc-progress.cz/Pg_Hydrus_References.htm;
veriﬁed 8 Apr. 2008) documenting the usefulness of HYDRUS
models (one, two, or three dimensional) to simulate plant water
uptake (Chabot et al., 2002; Sommer et al., 2003), to evaluate
surface runoﬀ (Mertens et al., 2001), to predict groundwatertable ﬂuctuations (Ventrella et al., 2000), to analyze ﬂow in thevadose zone above the groundwater table (Kao et al., 2001), toevaluate pesticide transport through the soil (Persicani et al.,
1995; Pang et al., 2000), to assess the eﬀects of irrigation on thespatial distribution of drainage (Assouline, 2002), and for manyother purposes. Still, no three-dimensional modeling study has
been performed to evaluate the eﬀect of rainfall distribution underplants on water ﬂow in soils.
This study was an extensive ﬁeld study undertaken to evaluate distributed subsurface water ﬂuxes under banana plants and touse the collected data to evaluate and numerically simulate these
distributed water ﬂuxes using the HYDRUS software package.
Hence, the study had several phases: (i) laboratory experiments
to obtain soil hydraulic parameters characterizing the unsaturated hydraulic conductivity function, K(h), and the soil water
retention curve, θ(h); (ii) ﬁeld experiments to measure surface
water ﬂuxes (stemﬂow and throughfall) and subsurface pressure
heads and drainage ﬂuxes; and (iii) numerical modeling using thewww.vadosezonejournal.org · Vol. 7, No. 2, May 2008

HYDRUS model to predict distributed water ﬂuxes and comparethem to the in situ drainage measurements.

Materials and Methods
Field Experiments

In the French West Indies, intensive banana cultivation on volcanic ash soils has been going on since the 1960s(Ndayiragije, 1996). These soils, particularly the Andisols (SoilSurvey Staﬀ, 1996), are well known to have a high inﬁltration
capacity. Consequently, banana plantations represent a large
source of nonpoint-source pollution endangering subsurface
groundwater resources. From 15 June to 29 Nov. 2004 (168 d),ﬁeld experiments with installed lysimeters and tensiometers were
performed to quantify the spatial distribution of drainage ﬂuxes
in an Andisol after rainfall interception by banana plants. The
experiments were performed at the CIRAD research facility in
Guadeloupe (Basse Terre), French West Indies (16°09′ N, 61°16′
W, 250 m above sea level).
The Andisol from the ﬁeld site was described by Ndayiragije(1996). It was formed by weathering of quaternary volcanic ash
deposits. The silty A horizon (0–40 cm) exhibits a medium, clear,friable structure. The soil aggregates are separated by many tubular pores. The B horizon (40–80 cm) has a ﬂuﬀy touch and acontinued macroscopic structure with medium and ﬁne tubularpores. The hydraulic properties of the Andisol were measured in
the ﬁeld as well as in the laboratory. Soil property measurements(organic C, bulk density, and total porosity) were performed at
the laboratory of the INRA Agropedoclimatic Unit, Guadeloupe,
French West Indies.
The experimental ﬁeld was a small watershed of 6000 m2
with an average slope of 12%. Planting of the banana plants(1800 plants ha−1) took place on 2 Apr. 2003. The experimental
period was during the second banana cycle. Rainfall was measured at a 1-min time interval using a tipping bucket rain gauge(ARG100, Campbell Scientiﬁc, Logan, UT) with a sensitivity of
0.2 mm per tipping installed at the bottom of the experimental ﬁeld. The tipping bucket was connected to both a Campbell
CR10 datalogger and a global system for mobile communications(SM TC35T, Campbell Scientiﬁc) for remote transfer of data. An
automated meteorological station was located 500 m from theexperimental plot. Global and net radiation, air temperature, relative humidity, and wind speed and direction were measured every
15 s and then averaged and stored for 5-min intervals.
Collection of leachates at diﬀerent positions relative to thebanana plant aimed at the following two objectives: (i) apprehending local variations of water ﬂuxes relative to the redistribution of
rainfall by banana foliage (stemﬂow and throughfall); and (ii) taking
into account the zone inﬂuenced by the stemﬂow and how the stemﬂow is redistributed with respect to the direction of the slope.
Five experimental plots were instrumented in June 2003.
The ﬁrst site was upslope of the ﬁeld where the A horizon was 10
cm thinner (due to tillage erosion), two were downslope of theﬁeld where the soil accumulated, and two were in the middle ofthe ﬁeld. One of the plots, called the fully equipped plot, was isolated from the neighboring soil with a metal sheet and equippedwith a runoﬀ collector (Fig. 1) and a stemﬂow collector (installedat the stem of the banana plant). While 8% of the stemﬂow ﬂux
was stored in the partitioner, the remaining 92% was reinjected820

(1994) and Lacas et al. (2003). At the time of installation, apit 2 m deep was dug between the plant rows and the sampling container was installed in a 70- by 70-cm horizontal
excavation in the vertical face of the soil 30 cm below the A
horizon. Each lysimeter was set 30 cm back from the verticalface of the pit and kept in contact with the upper soil, withbeams and quoins holding it in place. The soil proﬁle above
the lysimeters, including the banana plants, surface litter, the A
horizon, the tillage pan and the B horizon, was not disturbed.
The wicks were encased in polyethylene pipes set in a trenchwith 2% slope and connected to a collection of jerry cans 15
m from the experimental plot. Thus, water ﬂowing throughthe soil was intercepted by the container, drawn into the wick,and conducted to the sampling cans. After installation, thepit and trench were reﬁlled with the original material (B and
A horizons).
Each experimental site included four lysimeters that intercepted water at diﬀerent positions relative to the stem (Fig.
1). Twenty lysimeters were installed overall. Two lysimeters
were considered to be aﬀected by stemﬂow. Lysimeter 1 waslocated directly below the stem, while Lysimeter 2 was locatedbetween 25 and 70 cm downslope from the stem. The third
lysimeter (Lysimeter 3) was also located in the row of banana
plants between 120 and 165 cm downslope from the stem
under the leaves of a neighboring banana plant. This lysimeter was considered to be aﬀected by throughfall and only toa lesser extent by stemﬂow. The last lysimeter (Lysimeter 4)
was installed between two banana plants between rows, 95 cm
away from the banana stems.
A series of tensiometers (SKT 850, SDEC, Reignac sur
Indre, France), capable of measuring pressure heads between
0 and −99 kPa, were installed in multiple locations at eachexperimental site. In the fully equipped plot, tensiometers
were installed at three depths (6, 25, and 55 cm) above theF . 1. Schema c representa on of the flow domain in the banana planta- four lysimeters and around the banana plant (Fig. 1) and thetime step for measurements was between 10 s (during rainon with indicated loca ons of Lysimeters 1 to 4, tensiometers, and thestemflow collector.
fall) and 15 min (between rainfalls). At other sites, they were
installed at 20-, 40-, and 60-cm depths near the banana stemat the plant stem. The collectors for drainage, runoﬀ, and stemand downslope from the stem in the row in four sets. Pressure
ﬂow at this site were also equipped with pressure transducers thatheads were measured every 30 s, then averaged and stored for
were linked to the Campbell CR10 datalogger. At the other four
15-min intervals. Tensiometers were connected to the sameplots, soil solution samplers were weighed manually after each
Campbell CR10 datalogger as the tipping bucket.
rainfall event.
The topography of the fully equipped plot was measured
Distributed drainage was measured using glass wick lysimusing a Trimble 3300DR tacheometer (Trimble Geomatics,
eters. Wick samplers with a ﬁberglass wick that maintains a ﬁxed
Dayton, OH). To evaluate the water balance, daily evapotranstension are the most appropriate and cost-eﬀective devices forpiration (ET) before and after banana ﬂowering was calculated
collecting the leachate (Boll et al., 1992; Rimmer et al., 1995;
during the 168-d experiment according to (i) Pellerin (1986),
Vandervelde et al., 2005). A 45- by 45- by 5-cm steel plate
who expressed the potential evapotranspiration, ET P, as acontainer was ﬁrst ﬁlled with soil from the B horizon. A 2-cmfunction of the global radiation (i.e., ETP = 0.23 × global
diameter hole was then drilled in a corner of the bottom plateradiation), and (ii) Monteith (1965), who related the actualof the container to insert the 1.45-cm-diameter wick. The upperevaporation to its potential value using the crop coeﬃcientsend of the wick was manually unbraided, frayed, and spreadk (i.e., ET = kETP).
evenly across the soil in the plate. The length of the wick inGoverning Flow Equa oneach lysimeter was calculated according to Lacas et al. (2003).
Thirty centimeters of the wick was placed horizontally on the
Water flow was simulated using the HYDRUS model
plate. The wick terminated 50 cm below the plate, correspond(Šimůnek et al., 2006) to numerically solve the Richards equation
ing to a total height of 55 cm and an air-entry value of −5 kPa(Richards, 1931) describing water movement in three-dimenin the wick material. The hydrodynamic parameters of the wicksional transport domains in variably saturated porous media.
were obtained using the experimental data of Knutson and Selker
The governing water ﬂow equation is written in a mixed form towww.vadosezonejournal.org · Vol. 7, No. 2, May 2008821

ensure excellent mass balances of the numerical solution (Celia
et al., 1990):∂θ=∂t∂ ⎡ ⎜⎛ ∂ h ⎞⎟⎤ ∂ ⎡⎢ ⎛⎜ ∂ h ⎞⎟⎤⎥ ∂ ⎡ ⎛⎜ ∂ h ⎞⎟⎤⎢ K ⎜ ⎟⎥ +⎢ K ⎜ −1⎟⎟⎥ − S
K⎜ ⎟+
⎠⎥⎦
∂ x ⎢⎣ ⎝ ∂ x ⎠⎟⎥⎦ ∂ y ⎢⎢⎣ ⎜⎝ ∂ y ⎠⎟⎟⎥⎥⎦ ∂ z ⎢⎣ ⎝ ∂ z

sured in the ﬁeld using the double-ring inﬁltrometer method(Reynolds et al., 2002) applied to both A and B horizons (fourreplications). From the double-ring experiment, we took the ﬁnal
steady-state inﬁltration ﬂux from the inner ring and declared it
to be Ks. The laboratory evaporation method (e.g., Wind, 1968;
Mohrath et al., 1997; Šimůnek et al., 1998) was used to obtain
the other soil hydraulic parameters (i.e., θr, θs, α, and n). During
the experiment on undisturbed soil samples (15-cm diameterand 7-cm height), pressure head proﬁles (four tensiometers) andmean water contents were periodically measured while water wasallowed to evaporate from the top of the sample. Measurements
were repeated three times on each sample. The four soil retention parameters describing the VG model were then obtained byminimizing the sum of squared diﬀerences between the observedand calculated water contents at each measurement time of thelaboratory evaporation experiment. The soil hydraulic parameters
for both A and B horizons were then used for simulations with
the HYDRUS model.

[1]

where θ is the volumetric water content [L3 L−3], h is the pressure
head [L], S is a sink term accounting for the root water uptake[T−1], z is the vertical coordinate [L], x and y are the horizontal
coordinates [L], t is time [T], and K is the unsaturated hydraulicconductivity [L T−1]. The finite-element method is used in
HYDRUS to numerically solve the governing partial differential equations.
Soil Hydraulic Proper es

HYDRUS, similar to most models that simulate unsaturated water ﬂow in soils, requires knowledge of two nonlinear
functions: the unsaturated hydraulic conductivity function, K(h),and the soil water retention curve, θ(h). Both K(h) and θ(h) areeither unknown, diﬃcult to measure, or relatively uncertain whenestimated indirectly from, for instance, pore or particle size distribution. A widely accepted approach is to measure θ(h) data on
relatively small samples under laboratory conditions and then touse ﬁtted retention curve parameters and the pore-size distribution model to predict K(h).
The relations K(h) and θ(h) are often parameterized using
functions proposed by Mualem (1976) and van Genuchten(1980), which are referred to here as van Genuchten(VG) equations:θs − θrθ (h ) =h <0m + θr[2](1+ α h n )θ (h ) = θ sh≥0

HYDRUS Simula ons

Drainage ﬂuxes calculated using the HYDRUS model werevalidated using the ﬁeld drainage data between 25 Sept. and 9
Nov. 2004 (46 d) and statistically evaluated. The modeling period,
which was shorter than the experimental period, was representative of the wet season during which the main drainage ﬂuxes wererecorded. We chose only 46 d to avoid long simulation times, as threedimensional simulations are still very computationally demanding.
The ﬂow domain and ﬁnite element grid (Fig. 2) were deﬁned
so that boundary and initial conditions reproduced the in situ

[3]

with
m = 1−

1
n

n >1

[4]

and
m ⎤2
⎡
K ( h ) = K s S e l ⎢1−(1− S e1/ m ) ⎥
⎣
⎦
with

Se =

θ − θrθs − θr[5][6]

where θr and θs are the residual and saturated watercontents [L3 L−3], respectively, α is the inverse of the
air-entry value [L−1], n is the pore size distribution index,
Ks is the saturated hydraulic conductivity [L T−1], Se is
the relative water saturation (dimensionless), and l is the
tortuosity factor (dimensionless). An appropriate value forl is still the subject of debate. Earlier studies have set l equal to
0.5 as the best estimate proposed by Mualem (1976).
We used a combination of the ﬁeld and laboratory
experiments to evaluate the soil hydraulic properties. To F . 2. A schema c representa on of the flow domain indica ng (a) surface
be able to account for the eﬀects of soil structure, the boundary condi ons, (b) bo om boundary condi ons, (c) pressure head ini alsoil saturated hydraulic conductivity was directly mea- condi ons, and (d) tetrahedral finite element mesh.
www.vadosezonejournal.org · Vol. 7, No. 2, May 2008822

conditions. Water ﬂow in a three-dimensional ﬂow domain withfour wick lysimeters (Fig. 2b) was ﬁrst simulated using HYDRUS.
Lysimeter 4 is located outside of the area separated by a metal sheet
from the surrounding soil. Since this lysimeter is located exactly inthe middle between two banana rows, however, we could use thesymmetry between two banana rows and move it into our computational domain on the other side of the banana tree (Fig. 2b).
Detailed microtopography measured in the ﬁeld was used to reproduce the surface conditions. The transport domain was considered
to be, on average, 0.7 m deep and the surface area was about 8 m2.
Three diﬀerent materials with diﬀerent soil hydraulic properties
were deﬁned to account for two soil horizons (A and B) and thewicks. Each soil horizon was assumed to have uniform hydraulicproperties. Natural anisotropy was not considered.
Pressure heads measured with tensiometers on 25 Sept. 2004
were used as initial conditions (Fig. 2c). Stemﬂow and throughfall
were used as atmospheric and time-variable ﬂux boundary conditions, respectively, at the soil surface of the domain (Fig. 2a).
Throughfall was implemented in the HYDRUS simulation using
the time-variable ﬂux boundary condition since the code allows
only one atmospheric boundary condition and that one was used
for stemﬂow. It was possible to do that because the new HYDRUS
model separates transpiration from the atmospheric boundary condition, unlike previous versions (e.g., HYDRUS-2D). Stemﬂow
measured with the stemﬂow collector (Fig. 1) was applied on asmall area around the plant stem to ensure the proper volume of
inﬁltrating water. Throughfall was then evaluated as the diﬀerence
between the rainfall volume falling on the area of the fully equipped
plot and measured stemﬂow, divided by the surface area of theplot. As Bassette (2005) has shown, for the banana plants at ourexperimental site, stemﬂow increases the incident rainfall relative
to the throughfall by 18 to 20 times.
The wicks were simulated using a modiﬁed seepage faceboundary condition with a limiting pressure of −55 cm to accountfor the vertical part of the wick. The seepage face is a dynamic
outﬂow boundary condition that changes dynamically according to the ﬂow conditions in the system. HYDRUS assumed auniform pressure head of −55 cm along the active part of the seepage face through which water seeped out of the wick, and thencalculated water ﬂux for this area. Along the inactive segment of
the seepage face where water is held in capillaries and cannot seep,
the ﬂux across the boundary was assumed to be zero, and theboundary pressure head (lower than −55 cm) was calculated. Freedrainage was speciﬁed on the remaining part of the bottom of thetransport domain (Fig. 2b). This boundary condition represents
a unit hydraulic gradient. A zero-ﬂux boundary condition wasapplied to all vertical boundaries.
Transpiration was simulated using the sink term of Eq. [1].
Roots were assumed to be distributed uniformly both under theplant stem and between the rows in the upper 50 cm of the soil
proﬁle (A horizon) according to Lecompte et al. (2003). The
water uptake was reduced from its optimal value due to thedecrease in the calculated pressure heads according to the modelof Feddes et al. (1978).
A ﬁnite-element grid (Fig. 2d) was created by ﬁrst generating
two-dimensional triangular elements in the base surface using an
automatic grid generator. This two-dimensional grid was thenextended in the vertical direction using 20 horizontal layers. The
density of the grid was evaluated and judged suﬃcient when the
www.vadosezonejournal.org · Vol. 7, No. 2, May 2008

numerical solution consistently converged and the water balanceerror was <1%. High grid densities were generated around thestem, close to the soil surface, at the interface between diﬀerent
soil layers, and close to the wick because the hydraulic gradients could be considerable at these locations at various times.
Relatively low grid densities could be used farther away from thewick. The ﬁnite-element grid consisted of a total of 33,090 nodes
and 184,788 ﬁnite elements. Finally, the time discretization wasdeﬁned using the initial time step of 0.0001 d and the minimum
allowed time step of 0.00001 d.
Sta s cal Evalua on

The model performance was evaluated using all measured andsimulated drainage data. The correspondence between observed
and predicted soil water drainage ﬂuxes was statistically evaluated using the coeﬃcient of eﬃciency (E), deﬁned by Nash andSutcliﬀe (1970) as∑ i =1(observed i − predicted i )n2∑ i =1(observed i − mean obs )n

E = 1−

2[7]

While calculating the average drainage ﬂuxes at the bottom of
the soil proﬁle from spatially variable ﬂuxes is straightforward in
the numerical model, it is much more complicated to do fromexperimental data. In the numerical model, in which ﬂuxes at
all locations are known, one can simply add ﬂuxes from diﬀerent parts of the domain and divide them by the surface area ofthe domain. In the experimental ﬁeld, ﬂuxes are measured atonly several locations (i.e., lysimeters) and a procedure needs tobe devised for evaluating the average drainage ﬂux. The mean
drainage ﬂux was calculated in our study from measured ﬂuxes atfour lysimeters as a barycentric average relative to the soil surface(Sansoulet et al., 2007) as follows:
1⎡
1
⎤
[8]
LT = ⎢ L1 + L2 + (L2 + L3 )+ L3 + 4L4 ⎥
⎥⎦
8 ⎢⎣
2
where LT is the average value of drainage (mm ha−1) at the ﬁeld
scale, and L1, L2, L3 (row), and L4 (interrow) are drainage volumes(mm) measured with Lysimeters 1, 2, 3, and 4, respectively.

Results and Discussion
Es ma on of Soil Physical and Hydraulic Proper es

The physical and chemical properties of the Andisol (Table
1) were in the range expected for Andisols containing allophane(Quantin, 1994). Particularly relevant are the very low bulk
density values, the high C content, and the large total porosity considering the large clay content of these soils. Andisols
have a soil structure that reﬂects the abundance of noncrystalT
1. Physical proper es of the Andisol: clay content, bulk density, organic C, and total porosity.
Horizon
A
B

Clay†
%
58.6
63.1

Bulk densityg cm−30.71
0.49

Organic C
%
6.69
3.73

Total porosity
m3 m−30.673
0.665† Clay content was determined by quan ta ve recovery of clay a er sonica on and dispersion with Na+ -saturated resins and before H2O2
oxida on of organic ma er.

823

F . 3. (a) Soil water reten on curves, θ(h), and (b) unsaturated hydraulic conduc vity func ons, K(h), of two Andisol horizons (A and B) andof the wick.

a maximum intensity of 96.7 mm h−1, an average intensity of
34.56 mm h−1, and a mean duration of 3 h 46 min, whereas amedian rain had a lower volume (9.8 mm) and duration (2 h 6line materials (Shoji et al., 1993), and thus the entire particle
size distribution (silt and sand) is not presented here. Figure 3ashows the soil water retention curves, θ(h), for two soil horizons
optimized using data from the laboratory evaporation experiments. Since multiple soil samples were used for the evaporation
experiments to characterize the retention properties of the soil,
several more or less similar retention curves were obtained. A
mean curve was ﬁtted for each soil layer (three replicates). The
coeﬃcient of determination between measured and ﬁtted watercontents ranged between 0.67 and 0.77 for diﬀerent soil samples.
Soil hydraulic parameters for the VG functions for diﬀerent soil
layers are presented in Table 2. Higher variations in retention
properties were obtained for the A horizon than for the B horizon. The unsaturated hydraulic conductivity functions, K(h),were obtained by coupling the results of the laboratory evaporation method and the double-ring inﬁltrometers(Fig. 3b). Speciﬁcally, the Mualem pore size distribution model (Mualem, 1976; van Genuchten,1980) was used to predict K(h) from retention
curves determined from the evaporation experiments and the saturated hydraulic conductivity
determined from the inﬁltration experiments. It
should be noted that the wick could not limit
the ﬂow of water in the soil because its hydraulic conductivity is considerably higher than thehydraulic conductivity of either horizon for allpressure heads.

T
2. Eﬀec ve soil hydraulic parameters† obtained using
the Wind and double-ring infiltrometer methods (direct
measurements).
Material
A horizon
B horizon
Wick

θr

θs

———m3 m−3 ———
0.13
0.75
0.11
0.75
0
0.63

α
m−1
19.0
23.3
0.06

n

Ks

l

1.07
1.05
3.61

m d−1
3
1.06
280

0.5
0.5
0.5

† θ r and θ s, residual and saturated volumetric water contents; α , inverseof the air-entry value; n, pore size distribu on index; Ks, saturated
hydraulic conduc vity; l, tortuosity factor.

Experimental Results

The annual rainfall (6568 mm) and averagetemperature (24.1°C) measured in 2004 werequite diﬀerent from the average values of 3565
mm and 24.4°C collected from 1979 to 1999 by
Météo France (2000). During the 168-d experiment, the cumulative rainfall was 4120 mm, with141 rainfall events with volumes >2 mm. The rain
was considered to be an individual rainfall event
if the amount of water precipitated during thepreceding and following 2 h was <4 mm. The
characteristics of these events, given in terms of F . 4. Box plots characterizing sta s cal proper es of rainfall volume, rainfall dura on,
volume, intensity, and duration, are presented in and maximum and mean rainfall intensi es. Maximum and minimum values as well as
first, second, third, and fourth quar les and mean and median values are plo ed.
Fig. 4. A mean rainfall had a volume of 28.2 mm,
www.vadosezonejournal.org · Vol. 7, No. 2, May 2008824

F . 5. Meanpressure heads(calculated fromfive sets, CV =17%) measured
with tensiometersin the soil (top)at the foot of
the plant stem
(Lysimeter 2) and(bo om) between
rows (Lysimeter4). Precipita on
rates are also
shown in both
figures.

min) and equivalent intensities. The
largest rainfall, which had a volumeof 692 mm, maximum intensity of
312 mm h−1, and maximum duration of 45 h 46 min, occurred at theend of the experimental period in
November 2004 and was not representative of the other rainfall events.
Measured pressure heads below
the plant foot and between the rows
at three depths (6, 25, and 55 cm),as well as daily rainfalls, are represented in Fig. 5. Pressure heads
recorded below the plant foot are,at all depths, on average about
21% higher than pressure heads
recorded between the rows. This ismainly due to higher inﬁltration at
the plant foot because of stemﬂow.
Tensiometers installed closer to thesoil surface reacted faster and to agreater extent than those at deeper
depth. They were more strongly
affected by climatic conditions(rain, evaporation, and transpiration). Pressure heads close to thesurface ﬂuctuated between −3.81
and −0.10 m, with an average valueof −0.77 m. Pressure heads at 25and 55-cm depths varied less (from−2.27 to −0.05 m) and were in general higher than at the soil surface,with an average value of −0.55 m,
a value very close to the suction
exerted by the lysimeter wicks. The
higher the rainfall volume, thehigher the pressure heads measured.
After a rainfall event, the pressure
heads increased on average (30 analyzed periods) by 0.34 m at the soil
surface, 0.25 m at the 25-cm depth,
and 0.16 m at the 55-cm depth.
Small rainfall events inﬂuenced thepressure heads at deeper depths only
very little, explaining why watercontents at deeper depths stayed
relatively constant, apart from thezone aﬀected by stemﬂow. Pressure
heads measured above Lysimeters 1
and 3 (data not shown) were almost
the same as those measured above
Lysimeters 2 and 4, respectively.
The observed pressure heads
made it possible to discriminate
three types of response curves (Fig.
6). The Type 1 curve (not reactive)
exhibited little or no variation ofpressure heads during and after therain. The Type 2 curve (fairly reacwww.vadosezonejournal.org · Vol. 7, No. 2, May 2008

F . 6. Typology ofthe evolu ons ofpressure heads a er
a rainfall; P, volume of the rainfall
event; P1, smallest
rainfalls when P <12 mm; P2, moderate rainfalls when P
is between 12 and
63 mm; P3, highest
rainfalls when P >63 mm. The figure
also shows thefrequency of diﬀerent response curve
types for diﬀerent
depths and rainfall
volumes, where
Type 1 is not reacve, Type 2 is fairly
reac ve, and Type 3
is very reac ve.

825

T
3. Components of the mass balance during the 168-d
experiment and the 46-d simulated period: water fluxes acrossthe surface (evapora on, rainfall, and surface runoﬀ ) and bo omof the soil profile (drainage).
Dura on168 (d)46 (d)

Change instorage————————————— mm —————————————
4120
1808
1709
472
131
1373
539
601
157
76

Rainfall Drainage

Runoﬀ

Evapotranspira on

were tested (27 July–20 Oct. 2004). These data were considered
to be adequate, considering uncertainties related to ﬁeld lysimetermeasurements.
Table 3 summarizes water ﬂuxes at the top (evaporation,
inﬁltration, and runoﬀ) and bottom boundaries (measured drainage) for the 168-d (experimental) and 46-d (computational) time
periods. The remainder of the mass balance (i.e., 131 and 76
mm for the 168- and 46-d time periods, respectively) can be
attributed to changes in soil water storage and errors associatedwith measuring or calculating individual ﬂuxes. The largest error
is probably associated with calculations of the mean drainage(i.e., Eq. [8]).

F . 7. Comparison of the cumula ve rainfall and drainage for fiveexperimental sites. Field = average.

tive) showed only a small increase and then a very gradual (>5min) decrease of pressure heads. Finally, the Type 3 curve (veryreactive) displayed a fast variation (<5 min) of pressure heads.
Type 1 curves made it possible to identify locations or depths
that were not aﬀected by the inﬁltrating water. Type 2 curves
represented locations where water ﬂow demonstrated behavior
HYDRUS Model Simula ons and Mass Balancethat can be described using Darcy’s law (ﬁlling of the Andisol
micropores and their subsequent draining due to capillary and
The total rainfall during the 46-d modeling period was 1367
gravitational forces). The very fast response of pressure heads
mm. Pressure heads illustrating the three-dimensional pattern(Type 3) at some locations was indicative of fast preferential ﬂow
of water ﬂow during a rainfall event under the banana plant arethrough macropores. Histograms (Fig. 6) obtained by analyzshown in Fig. 8. This ﬁgure clearly shows that most of the watering 141 rainfall events show that the majorityof responses by tensiometers closest to the soil
surface followed the Type 3 curve. This could be
partly caused by the disturbance created during
installation of shallow tensiometers. Responses oftensiometers installed at deeper depths (25 and55 cm) usually followed, depending on the rainfall volume, Type 1 and 2 curves. Pressure heads
at a 25-cm depth usually followed the Type 2
curve, while those measured at a 55-cm depth
followed the Type 1 curve. The higher the rainfall
volumes, the more frequent the Type 2 response,and vice versa for the Type 1 response. Type 1
curves appeared mainly in parts of the domain
unaﬀected by stemﬂow and thus fast percolationof inﬁltrating water. Tensiometers installed at
all depths below the plant foot recorded >85%of responses of Types 2 or 3. This was probably
caused by the high amounts of inﬁltrating water
resulting from the stemﬂow.
The correspondence of measurements from
diﬀerent experimental plots is compared for one
time period (27 July–20 Oct. 2004) in Fig. 7. The
analyses of the lysimeter data made it possible toevaluate uncertainties related to calculating the
average drainage using Eq. [8]. Based on theseanalyses, Site 3 (the fully equipped plot) was
considered representative of the average drainage
behavior and was thus subjected to deterministic
modeling. Relative uncertainties of the balanced F . 8. Pressure heads illustra ng the three-dimensional water flow under the banana
average drainage were 13% when the ﬁve sites plant during a rainfall event (total rainfall = 65 mm): (a) 0 d; (b) 1 d; (c) 2 d; (d) 4 d.
www.vadosezonejournal.org · Vol. 7, No. 2, May 2008826

ﬂow is concentrated around the stem of the banana tree,
while reduced ﬂuxes are apparent downstream from thestem in the row and between the rows.
Figure 9 shows the measured and simulated cumulative drainage ﬂuxes from the four lysimeters vs. time.
The mass balance error of the water ﬂow simulation was<1%. Simulations showed that under heavy ﬂuxes, suchas those due to stemﬂow, the wicks reproduced the actualﬁeld drainage reasonably well. Mass transfers across thewick–soil interface are determined by diﬀerences in pressure heads between the wick and the soil. Under the driest
conditions, which corresponded to the lower drainage
volumes, pressure heads in the wick were higher than in
the soil and the drainage ﬂow stopped. When pressure
heads at the bottom of the soil proﬁle decreased below−0.55 m, the ﬂow through the seepage face stopped.
Both measurements and calculations showed relatively fast responses of drainage ﬂuxes in Lysimeters 1 and F . 9. Measured and simulated cumula ve fluxes from four lysimeters.
2 to rainfall events. Although the overall correspondence
between measured and calculated ﬂuxes is very high,the retention curves are relatively steep in this range of pressure
there are some distinct diﬀerences. While measured drainage inhead values, however, these diﬀerences correspond to only small
Lysimeters 1 and 2 continued, although at very small rates, evendifferences in water contents. It should be emphasized thatduring time periods without rainfall, calculated drainage started
numerical simulations were performed using measured values ofand ended rather abruptly and there were long time periods ofsoil hydraulic properties without any additional model calibrano calculated drainage. This is because of the type of boundary
tion. Correspondence between measured and simulated drainage
conditions that were used by the model to represent lysimeters.
ﬂuxes and pressure heads is thus reasonable. Had the numerical
Lysimeters were modeled using the seepage face boundary conmodel been calibrated (which is, due to signiﬁcant computational
dition, which is active when pressure heads exceed the limiting
requirements, still a rather diﬃcult task for problems involving
value (−55 cm) and becomes inactive when pressure heads drop
three-dimensional transport domains), correspondence between
below this value.
The numerical model using the measured hydraulic parameters obtained from laboratory and in situ experiments reproduced
the general trends of distributed drainage measured using lysimeters under the banana plant fairly well (Fig. 9). Indeed, thecomparison of model simulations with ﬁeld experimental results
conﬁrmed that simulated and measured data were quite similar.
The model performance was evaluated by comparing the observed
and predicted cumulative drainage in Lysimeters 1, 2, 3, and 4(Fig. 9), as well as observed and predicted pressure heads (Fig. 10)
at diﬀerent soil depths and locations. The coeﬃcient of eﬃciency(E) ranged from 0.62 to 0.76. The model slightly overestimatedﬂuxes downslope from the plant stem, however. This can be
explained by possibly higher root water uptake from deeper
soil layers than anticipated. Simulations and collected drained
volumes, as well as measured soil pressure heads, demonstrated
that the ﬂow under the banana tree was entirely dominated bystemﬂow and its redistribution in the soil proﬁle. Stemﬂow inﬁltrated directly along the plant stem, but part of it was redirected
downstream from the stem due to the slope. The drained volumes
under the banana stem were six times higher than those downstream from the stem in the row and between the rows since thesezones were sheltered by the banana leaves and received essentiallyonly throughfall. Simulations showed that under heavy ﬂuxes,
such as those due to stemﬂow, the wicks reproduced the actualﬁeld drainage reasonably well.
Figure 10 presents measured and simulated pressure heads
at two locations. While the model described measured pressure
F . 10. Measured and simulated pressure heads (a) under theheads and their dynamics very well in the wet range, there wereplant stem and (b) between the rows.
larger diﬀerences in the drier range of pressure head values. Since
www.vadosezonejournal.org · Vol. 7, No. 2, May 2008827

for simulation of rainfall interception parameters. Agric. For. Meteorol.
129:95–100.
Boll, J., T.S. Steenhuis, and J.S. Selker. 1992. Fiberglass wicks for sampling ofwater and solutes in the vadose zone. Soil Sci. Soc. Am. J. 56:701–707.
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measured and simulated values of drainage ﬂuxes and pressure
heads would probably have been much better.

Conclusions
The numerical model used in this study reproduced thegeneral trends of distributed measured drainage under a banana
plant in an Andisol fairly well. Numerical modeling was probably
successful because of the precise determination of the Andisolhydrologic parameters [i.e., the soil water retention curve θ(h),and the saturated hydraulic conductivity, Ks] by a combinationof laboratory and ﬁeld experiments. Using experimental and calculated drained volumes, as well as soil pressure head data, we
attributed drainage ﬂuxes under the banana stem or immediately
downstream from the stem almost exclusively to the stemﬂow.
The drained volumes under the banana stem were six times higher
than 1.2 m downstream from the stem in the row and between
the rows, since both these zones were sheltered by the banana
leaves and received essentially only throughfall. Simulations
showed that under heavy ﬂuxes, such as those due to stemﬂow,
the wicks reproduced the actual ﬁeld drainage reasonably well.
Under smaller surface ﬂuxes (e.g., throughfall), measured water
ﬂuxes with lysimeters were, on average, 50% underestimatedcompared with simulated water ﬂuxes without lysimeters.
The spatially distributed water ﬂuxes under the banana plantalso considerably inﬂuence solute transport. Our results, i.e., aconcentrated water ﬂow around the plant stem, bring into question the common practice of applying fertilizers and pesticides
at the foot of the plant. Under these conditions, the abundant
stemﬂow may rapidly leach the soluble nutrients or pesticides
from the root zone into deeper horizons, and eventually into
the groundwater. This process will be especially important after
ﬂowering, when rainfall interception is maximal. We therefore
recommend that additional research be conducted to evaluate
how our results can be interpreted in the context of a locallyand intensively fertilized banana plantation. Such research could
provide better guidelines for fertilization practices that would
better protect subsurface water resources.
A
This work has been funded by grants from the Doctoral Schoolof Life Sciences (Institut National Agronomique Paris Grignon), fromthe French Ministry of Ecology, from the European Union, and fromthe French National Programme ECCO-PNRH 2003.2005. We thankthe members of the Hydrus-2D discussion forum (www.hydrus2D.
com) for their valuable advice and support. We wish to express ourappreciation to Jacques André, Philippe Artis, Olivier Hutel, Andèves
Mulciba, Jean-Baptiste Nanette, and Christian Palmier, physical science
technicians, as well as Jennifer Martin, the trainer, for their diligent
and meticulous eﬀorts during the collection and processing of the data
presented here.

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