Experimental and numerical study of water flow in soil under irrigation in northern Senegal:...

Experimental and numerical study of water flowin soil under irrigation in northern Senegal:evidence of air entrapment

C. H AMMECKERa , A . C . D . ANTONINO

b, J. L. MAEGHTa & P. BOIVIN

c,d

aInstitut de Recherche pour le Developpement, UR 67, route des peres maristes, BP 1386 Dakar, Senegal, bDepartamento de Energia

Nuclear, Universidade Federal de Pernambuco, Avenida Professor Luiz Freire 1000, Cidade Universitaria, Recife, PE 50740-540,

Brazil, cInstitut de Recherche pour le Developpement, UR 67, BP 5045, 34032 Montpellier Cedex 1, France, and dEcole Polytechnique

Federale de Lausanne, IATE-Pedologie, 1015 Lausanne, Switzerland

Summary

Irrigation by surge flooding does not always wet the soils thoroughly, and we have investigated the

reasons for this on an irrigated plot in northern Senegal by monitoring the water budget during a rice

cropping season (100 days). The amount of water added during each irrigation event was measured, and

evapotranspiration and infiltration were estimated with lysimeters and Muntz infiltration rings, respect-

ively. At the same time, piezometric levels, neutron probe values and water tension data were recorded at

two stations in the plot. These measurements showed unusual results: infiltration rate was less than

1� 10�6 mm s�1 (less than 0.1mm a day), there was a constant water deficit during the entire irrigation

period, around 50 cm deep, and tensiometers at 40 cm reacted very slowly to water infiltration. The water

fluxes in the vadose zone derived from these data showed clearly a discrepancy between fluxes calculated

from hydraulic gradients and fluxes calculated from mass conservation. The hydraulic gradients sug-

gested a zero flux plane at 40 cm below the surface, but the calculated values of the fluxes overestimated

by several orders of magnitude the infiltration rates determined on the plot, whereas fluxes determined

from mass conservation matched far better. These results show that air was entrapped between the

shallow water table and the wetting front, and this inhibited water infiltration. Modelling water flow

down the soil profile with a computer program for simulating one-dimensional water movement

(Hydrus) confirmed that single-phase models cannot describe imbibition in this situation. Simple infiltra-

tion models based on a modified Green–Ampt equation accounting for air compression and air counter-

flow, however, fit experimental infiltration data much better. We demonstrated that where surge flooding

is associated with a shallow water table, as in many large irrigation schemes, one must take into account

the presence of air to quantify the flow of water into the soil.

Introduction

The infiltration of water into soil has been much studied and

quantified, especially through the Darcy equation extended to

non-saturated porous media by Richards (1931). Many com-

puter models quantifying water flow and water budget in soil

profiles are now available. However, most of them are designed

to quantify single-phase flow, namely only water flow, on the

assumption that air escapes freely and does not affect the infil-

tration of water into soil. This assumption is valid for a wide

variety of situations encountered in the field. For surge flooding

in irrigated paddy fields and under intense rain (Jarett et al.,

1980), the assumption of free air escape is no longer valid,

especially when the water table is close to the surface. Under

these conditions air is trapped and compressed. The conse-

quences of this on infiltration have been evaluated theoretically

and in laboratory experiments on soil monoliths by Adriani &

Franzini (1966), Vachaud et al. (1974), Touma & Vauclin

(1986), Jalali-Farahani et al. (1993), Grismer et al. (1994), Latifi

et al. (1994) and Wang et al. (1998). The most important effect

of air compression is a sharp decrease in infiltration rate. Several

authors observed and measured the air compression in the field

Paper given at the Michel Rieu Memorial Colloquium, 8–10 October

2001, in Paris.

Correspondence: C. Hammecker, IRD-MSEM, 300 av. Emile

Jeanbreau, 34095 Montpellier Cedex, France. E-mail:

[email protected]

Received 13 November 2001; revised version accepted 7 May 2002

European Journal of Soil Science, September 2003, 54, 491–503

# 2003 Blackwell Publishing Ltd 491

and quantified the decrease of infiltration rate (Bianchi &

Haskell, 1966; Dixon & Linden, 1972; Linden et al., 1977).

Others, such as Starr et al. (1978), have shown that flow is

unstable and that fingering arises from air’s becoming com-

pressed during infiltration. Otherwise little is known of the

entrapment of air in the field and its effect on infiltration under

crops. This phenomenon is of particular interest in flooded rice

cropping in arid regions where there is serious risk of salinization

because of the evaporative demands and lack of leaching.

We have studied the effect of air compression both directly

and indirectly, while quantifying the water budget under irri-

gated rice in northern Senegal, and we report the results below.

Experimental data of water infiltration and tensiometric pro-

files are used to show air entrapment. The comparison between

field experimental data and simulations by a traditional model

for single-phase flow, namely Hydrus (Simunek et al., 1998), is

used to quantify the importance of air entrapment. Finally,

infiltration is simulated with a Green–Ampt type equation,

adapted for air compression and counter-flow, and simulation

results are discussed.

Theory

The effect of air compression in front of a progressing wetting

front has been studied by Bouwer (1964), Morel-Seytoux &

Khanji (1974) and Wang et al. (1997), who established analyt-

ical infiltration equations accounting for air compression and

air counter-flow derived from the Green & Ampt (1911) infil-

tration equation:

iw ¼ �Ksðhwf � zÞ � h0

z; ð1Þ

where iw is the rate of water infiltration [LT�1], Ks is the

saturated hydraulic conductivity [LT�1], hwf is the soil water

pressure head [L] at the wetting front, z is the depth of the

wetting front [L], and h0 is the pressure head of water at the

surface [L]. Capillary pressure is defined as the pressure differ-

ence between the non-wetting fluid and the wetting fluid. Hence

in this case the water pressure head near the wetting front is

hwf ¼ ha � hc;

with ha and hc being, respectively, the air and the capillary

pressure heads. Whereas the air pressure depends on the pro-

gression of the wetting front, the water pressure depends itself

on the pore geometry according to Laplace’s law. When the

wetting front progresses and the air underneath cannot escape,

its pressure will increase until the capillary pressure and the

infiltration rate iw tends towards 0:

iw ¼ Kzþ h0 þ hc � ha

z

� �: ð2Þ

However, Wang et al. (1998) demonstrated experimentally that

air escapes when it reaches a pressure called air breaking

pressure, Hb, defined as

Hb ¼ h0 þ zþ hab; ð3Þ

where hab is the air-bubbling pressure of the soil. After the air

has escaped, the pressure decreases until it reaches the air-

closing value Hc:

Hc ¼ h0 þ zþ hwb; ð4Þ

where hwb is the water-bubbling pressure of the soil. Wang

et al. (1997) defined these two pressure values as the inflection

point on the drying and wetting retention curve of the soil,

and, assuming the applicability of the van Genuchten (1980)

model, they suggested their evaluation:

hab ¼ 1

�d

and

hwb ¼ 1=�wt � �; ð5Þ

where �¼ 0* 2 for sandy soils, �¼ 2* 5 for loamy soils, and

�¼ 5* 8 for clay soils. The subscripts d and wt stand, respect-

ively, for the drying and wetting scanning curve. When the

wetting curve is not available, it is usually admitted that

�wt¼ 2�d (Kool & Parker, 1987; Nielsen & Luckner, 1992).

We adopted this procedure in our study.

If the air behaves like a perfect gas then the air pressure can

be calculated according to Boyle’s law:

ha ¼ hatmz

B� z

� �; ð6Þ

where hatm is the atmospheric air pressure (& 1013 cm of

water) and B is the depth of the air-impermeable barrier,

which is usually the water table depth (Figure 1). From

Equations (4) and (5), the capillary pressure at the wetting

front hc is the water-bubbling pressure hwb during the infil-

tration phase. The instantaneous infiltration rate, iw, is then

given by

iw ¼ Kczþ h0 þ hwb � haðzÞ

z: ð7Þ

Here Kc is the saturated hydraulic conductivity for air-confining

conditions and corresponds to the reduction of saturated

hydraulic conductivity by the relative water conductivity krc:

Kc ¼ krcKs:

Experimental results show that 0.5 is a suitable value for

krc (Vachaud et al., 1974; Touma et al., 1984; Wang et al., 1998).

Equation (7) describes infiltration while air pressure

increases below the progressing wetting front, and the time t

when the wetting front reaches z is given by

t ¼ K�1e

ðz

zþ h0 þ hwb � haðzÞdz; ð8Þ

where Ke is the effective hydraulic conductivity, namely:

492 C. Hammecker et al.

# 2003 Blackwell Publishing Ltd, European Journal of Soil Science, 54, 491–503

Ke ¼Kc

f¼ Kc

�ð1� Sw;0 � Snw;cÞ; ð9Þ

where � is the porosity of soil, Sw,0 is initial water saturation

before infiltration, and Snw,c is saturation of air in the

wetted zone. Equation (8) can be evaluated numerically, as

an analytical solution proposed by Wang et al. (1997) is only a

rough approximation.

The infiltration rate reaches zero at specific values for time

and depth, t0 and z0, which are characteristics of soil proper-

ties. At this point air escapes, and ha decreases and starts

an infiltration phase with air counter-flow described by the

following equation (Wang et al., 1997) for t >t0 and z >z0:

iw ¼ Kcðhab � hwbÞ2 z20Keðhab � hwbÞðt� t0Þ� �1=2

; ð10Þ

and the time for the wetting front progression is given by

t ¼ t0 þðz2 � z20Þ

Keðhab � hwbÞ: ð11Þ

Finally after several simplifications exposed and validated in

Wang et al. (1997), an equation aimed to describe the entire

period of infiltration rate iw, taking into account air compres-

sion and vertical air counter-flow, can be written as follows:

iw ¼ 1

2fKc f ðhab � hwbÞg1=2t�1=2: ð12Þ

Note that in this final relation the infiltration is independent

of the ponding pressure head (h0), the air pressure head (ha)

and the depth of the water table (B). Moreover, unlike in the

traditional Philip equation, the infiltration does not reach a

constant value, but continuously decreases with the square

root of time.

This case applies to vertical one-dimensional air counter-

flow with cyclic air pressure release through the bigger

pores, when air pressure reaches the air-bubbling pressure.

However, in many experimental cases studied by Grismer

et al. (1994) on various types of soil, the air pressure reaches

a maximum value and remains constant during infiltration.

Such an infiltration process occurs as preferential flow

through a pore-channel or a fissure opens under air pres-

sure, from where air escapes continuously, to match the

infiltrating of water. This phenomenon can take place only

if the wetted zone desaturates progressively in order to

increase the air permeability as the wetting front depth

progresses, so that a constant air flux can be maintained.

The complete infiltration kinetics can be described as

follows:

haðzÞ < hamax; t ¼ðK�1

c f fzþ h0 þ hwb � haðzÞg�1zdz ð13aÞ

and

haðzÞ � hamax; t ¼ðK�1

c f ðzþ h0 þ hwb � hamaxÞ�1zdz; ð13bÞ

where ha is the air pressure defined in Equation (5) and hamax

is the maximal air pressure.

A second case reported by Grismer et al. (1994) is when

the difference between air pressure and driving pressure

reaches a minimum and remains constant during the

air counter-flow phase. The relation between time and the

depth, t(z), of the wetting front can be expressed as

follows:

t5t0; t ¼ðK�1

c f fzþ h0 þ hwb � haðzÞg�1zdz ð14aÞ

and

t � t0; t ¼ðK�1

c f fzþ hminÞ�1zdz

¼ K�1c f fz� hmin lnðzþ hminÞg; ð14bÞ

where hmin is the minimal capillary pressure head. In this case

air pressure increases linearly with increasing depth and with

no progressive desaturation occurring in the wetted zone. It

corresponds to a continuous leak of air throughout a

constantly saturated layer of soil. In both of these cases, the

flow rate of air is equivalent to that of water infiltration during

the air counter-flow period as described in Equations (13b)

and (14b).

B

hwf

ha(z)

h0

z

ha(z) = hatm ( zB – z)

Figure 1 Schematic representation of the progression of the wetting

front in the soil profile. z is the depth of the progressing wetting front,

h0 is the water pressure head at the soil surface, B is the depth of the

water table, and hwf and ha(z) are, respectively, the soil water pressure

head at the wetting front and the air pressure below the wetting front.

Evidence of air entrapment in irrigated soil 493


Materials and methods

The experimental site

The experiment was done in a 0.3-ha irrigated paddy field in

northern Senegal (16�400N, 15�W), in the middle valley of the

Senegal River. The field was 100m long and 30m wide, within

an irrigation scheme, dedicated mainly to rice cropping. The

soil profile is a 2-m layer of clay overlying a fine sandy sedi-

ment 5–6m thick. The soil itself is a heavy clay Vertisol with

polyhedral and vertic structures (slickensides), and with cracks

that widen and extend downwards from the surface as the soil

shrinks during drying. It contains 65–70% of clay minerals

which are mainly Fe-smectite (Favre et al., 2002) and kaolinite.

The water table is established in the sandy layer. Rice is grown

under flood irrigation, and a superficial pond of 5–25 cm is

maintained during the complete plant growth cycle (about

100 days). At a regional scale, the water table is fed by the

Senegal River, and its depth fluctuates between 2 and 3m

during the dry season. During the wet season when the

water level in the river rises to its maximum height, the piezo-

metric level sometimes reaches the soil surface. Moreover,

these movements of the water table are augmented locally

by leakage from the irrigation canals and by the irrigation

itself.

Experimental device

A complete water budget was computed to quantify the dif-

ferent water fluxes involved during the cropping cycle. Tensio-

metric data were recorded daily at the two sites in the field

(Figure 2) at 0, 20, 40, 60 and 80 cm. The matric tension for

stations 2 and 3 was recorded both manually with a mercury

manometer and continuously with electronic pressure trans-

ducers connected to a datalogger. The water content was meas-

ured at the three experimental stations with a neutron probe

(Nardeux, solo 20), at 10-cm intervals in a 1-m access tube.

The soil water content changes have been evaluated by relative

probe counts (C/C0, where C0 is the number of counts in water

and C is the number of counts in the soil) because the alternate

swelling and shrinking of the soil seriously complicated the

neutron probe calibration with volumetric water content.

Piezometric level was monitored weekly at five places: on

the edge of the irrigation canal, near the two tensiometric sites,

in the middle of the field, and outside the field opposite the

canal (Figure 2).

Water budget and soil water flow

The field was irrigated with siphon tubes running from the

canal to a defined spot at a constant height above ground

level. The water flux in the siphon tubes was calibrated for

different water levels in the canal. For each irrigation, its

duration, the water level in the canal and the number of siphon

tubes were recorded to enable us to calculate the water inputs.

The input flux was calculated by

qe ¼ nðahw þ bÞ; ð15Þ

where n is the number of siphons, hw is the height of the

water in the canal, and a and b are two fitting parameters for

calibration. The volume of water introduced in the field for

each irrigation is

Ve ¼ qeDt; ð16Þ

where Dt represents the duration of irrigation.

Precipitation was recorded with a rain gauge placed in the

middle of the field at 1.75m above the soil surface. Two

lysimeters (0.6m� 0.6m� 0.9m high sunk 0.6m into soil)

and two open Muntz cylinders (1.06m in diameter and 0.5m

high, of which 0.3m was in the soil) were set in the field for

calculating, respectively, evapotranspiration (ET) and infiltra-

tion rate (I) by monitoring water level in both devices, thus:

ET ¼ dhlysi

dt; ð17aÞ

and

I ¼ dhcyl

dt� ET: ð17bÞ

At each irrigation event, water was introduced in the device

through lateral holes, which were otherwise blocked with rub-

ber stoppers. The variation in water content (DS) in soil

profile to a depth Z, during a given time interval (t1� t0),

corresponds to the variation of the water content down the

soil profile. It can also be defined as the algebraic sum of the

inputs (irrigation or precipitation or both) P, the evapotran-

spiration ET, and the bottom flow (drainage or capillary rise

from a water table) Fb:

DS ¼ðð�t1 � �t0Þdz ð18aÞ

PlotDikeIrrigation

canal Piezometer

Clayey soil

Sandy soil

Distance from canal /m

Hei

ght /

m

P.aP.1 P.2 P.3

P.b P.cSt. 3St. 2

050 100 150 200

2

4

6

Figure 2 Schematic representation of the studied plot with the transect

of piezometers (P.a, P.1, P.2, P.3, P.b, P.c) and two measurement

stations St. 2 and St. 3.



and

DS ¼ P� ET þ Fb: ð18bÞ

The amount of water leaving through the bottom of the profile

is given by Fb¼ qinfDt, where qinf is the flux there. The water

flux can be calculated at any depth z in the profile with the

Darcy equation:

qz ¼ �Kzð�ÞðrHÞz; ð19Þ

which in one dimension (vertical) is

qz ¼ �Kzð�ÞdH

dz

� �z

; ð20Þ

where Kz is the hydraulic conductivity at depth z, and (dH/dz)zis the hydraulic gradient at this depth. The sign of q indicates

the direction of the water flow: negative values indicate a

downward flow and positive values upward flow. The quantity

Kzþ1/2 is the geometric mean of Kz and Kzþ1, respectively the

hydraulic conductivity values at depth z and z þ 1.

The principle of continuity imposes

q�qt

¼ �rq: ð21Þ

In a soil profile with one-dimensional flow the variation in

water content (D�) at a depth zi, between the depths zi�1/2 and

ziþ1/2 and during a time interval Dt of Equation (21), becomes

D�Dt

� �i

¼qiþ1=2 � qi�1=2

ziþ1=2 � zi�1=2

� �; ð22Þ

where qi�1/2 et qiþ1/2 corresponds to water fluxes at the two

limits of the soil layer.

Unsaturated hydraulic properties of the soil profile

The chief unsaturated hydraulic properties were determined partly

in situ, down the soil profile, and partly at the laboratory.

Hydraulic conductivity was determined with a disc permeameter

(Perroux&White, 1988; Smettem&Clothier, 1989) every 20 cm in

a 1-m deep pit. Four cylinders of soil (diameter of 5 cm and length

of 6 cm) were sampled at each infiltration measurement point so

that we could determine the water retention curve and for particle-

size analysis. The retention curves were determined on cylindrical

soil samples by a method similar to that of Wind (1968). We

recorded simultaneously the shrinkage of the soil sample, and the

characteristic mass-wetness (�) against apparent density (�a) was

established (Braudeau et al., 1999). It was then possible to deter-

mine the relationship of actual water content (�) against pressure

head (h), despite the swelling and shrinking properties of this soil.

The unsaturated soil hydraulic parameters (van Genuchten,

1980) were determined by fitting models to experimental data

with the RETC code of van Genuchten et al. (1991). The

unsaturated soil hydraulic parameters were fitted to the clas-

sical van Genuchten functions (van Genuchten, 1980) for the

retention curve:

�ðhÞ ¼ ð�s � �rÞf1þ ð�hÞngm þ �r

and

Kð�Þ ¼ KsSlef1� ð1� S1=m

e Þmg2;

where � is the volumetric water content, h is the pressure head

[L], �s and �r are, respectively, the saturated and residual water

contents, and � [L�1], n and m are fitting parameters. Usually

m is considered as m ¼ 1� 1/n (Mualem, 1976). The saturated

hydraulic conductivity is Ks, and l is a fitting parameter found

to be equal to 0.5 for most soils (Mualem, 1976). The effective

saturation is defined as

Se ¼�ðhÞ � �s�s � �r

:

Hydraulic conductivity for the sandy soil in the aquifer was

measured in situ by the slug-test method (Bouwer & Rice,

1976), and the retention curve was derived from the particle-

size distribution (Arya et al., 1999).

The modelling

To quantify the effect of the presumed air compression on

infiltration, the experimental data were compared with numer-

ical simulations done with a single-phase one-dimensional

water flow model. The Hydrus model (Simunek et al., 1998)

employed for this calculation uses a numerical finite element

procedure to solve the Richards equation:

q�wqt

¼ qqz

Kqhqz

þ cos �

� �� S;

where �w is the volumetric water content, t is the time [T], h is

the pressure head [L], K is the hydraulic conductivity [LT�1], z

is the depth [L], � is the angle with a vertical axis, and S is a

sink or source term. The model was used (i) directly in forward

simulation with previously determined unsaturated hydraulic

parameters, and (ii) inversely to find out the best fitting par-

ameters. We did the actual fitting with Hydrus-2D (Simunek

et al., 1999), following the minimization of an objective func-

tion with a Marquardt–Levenberg algorithm. The considered

domain is a 3-m deep profile (2m of clayey soil and 1m of

aquifer), where the boundary conditions are both Dirichlet

conditions, namely the upper limit given by the ponding

water level in the plot and the lower level given by the depth

of the water table.

Results

Experimental data

Water budget. Recordings of the water inputs during the

cropping season, i.e. the precipitation and the irrigation

events, show that the total amount of water introduced in



the field was 3600m3, corresponding to 1.10m of water. Meas-

urements of the cumulative water level in the Muntz rings

show an equivalent amount of water, namely 1.06 and 1.07m

for stations 2 and 3 (Table 2). Despite the potential lateral loss

of water due to leakage throughout the field’s boundaries, the

estimation of the water inputs and the total water consump-

tion due to evapotranspiration and infiltration coincide. Dur-

ing the same period evapotranspiration was 0.95m at station 2

and 1.07m at station 3, corresponding to evaporation rates of

9.3mm day�1 and 10.6mm day�1, respectively, in agreement

with average values measured in this area for rice (Raes et al.,

1995; Boivin et al., 1999). This difference in evaporation rate

for the two stations is systematically recorded every year, and

arises mainly because station 3 is on the boundary of the plot

and of the irrigation scheme. It therefore was a drier and less

sheltered atmosphere than station 2, which is nearer to the

canal and in the centre of the plot. Infiltration was calculated

by integration of Equation (17b). Cumulative infiltration

reached 0.11m at station 2 and 0.0022m at station 3, over

the cropping season. Considering the accuracy of the measure-

ment method, the order of magnitude rather than the actual

value of this latter result has to be considered. The correspond-

ing average infiltration rates are, respectively, 12.8� 10�6 and

less than 1� 10�6mm s�1 (1.1mm day�1 and less than 0.1mm

day�1). These results are inconsistent with the order of magni-

tude of saturated hydraulic conductivity measured independ-

ently which ranged from 10�2 to 10�4mm s�1 (Table 1).

Piezometric results. The water table rose continuously during

the irrigation (Figure 3), presumably as a result of the water

added at the surface. However, it maintained a constant slope

from the canal towards the uncultivated area of about 1%.

This suggests that water table is supplied mainly by leaks from

the bottom of the canal.

Water content profile. The soil at station 1, near the irriga-

tion canal, and at station 2 in the middle of the field (Figure 4a)

filled with water rapidly; after 1week of irrigation the soil

profiles became uniformly saturated (C/C0¼ 0.65) at these latter

stations. At station 3 the water content was distinctly depleted

at 50 cm (C/C0< 0.58) for 70days of the cropping season

(Figure 4b). At the end of the cropping season, when the super-

ficial layers had dried, the water profile became homogeneous.

The previously unsaturated zone at 50 cm depth saturated to a

C/C0 value of 0.62. This indicates a substantial retardation in

the water infiltration down the profiles because the wetting

front was blocked at around 50 cm.

Tensiometric data. During the irrigation the water tension in

the soil profile at station 2 developed as expected: the tension

decreased sharply in the upper part of the profile for each

depth as the wetting front progressed with time (Figure 5a)

until saturation was reached. There was a short drought

20 days after the first irrigation, which corresponds to a halt

in the irrigation for application of fertilizer. Figure 5(b) shows

a similar behaviour at station 3, where the tensiometers at 10

and 20 cm follow the same pattern. However, at 40 cm the

tension decreased slowly in two stages: in the first 35 days the

tension decreased from 600 hPa to 100 hPa and it took a

further 50 days to reach 20 hPa. The tension in the two deeper

tensiometers remained constant during the entire experiment.

If we consider the hydraulic gradient and corresponding

hydraulic conductivity we can calculate the potential flux

between each instrumented node from Equation (20). The

results displayed in Figure 6(a) show that for the upper layers

(10–20 and 20–40 cm) water descended, whereas in the lower

ones (40–60 and 60–80 cm) it ascended or did not flow, in the

first 30 days after the beginning of irrigation. Consequently, a

zero-flux plane probably existed near 40 cm, where upward

and downward flows converge. Moreover, the flux in the

lower layers also equals zero as the tension at 60 and 80 cm

remained constant at 200 hPa during the irrigation. Below

40–50 cm the suction seems to have been unaffected by the

infiltration, unlike at station 2.

Potential fluxes derived from unsaturated soil parameters

and hydraulic gradients have values of up to 40 cmday�1

(4.63� 10�3mm s�1) for downward flow, and 10 cmday�1

Table 1 Unsaturated soil hydraulic parameters for the profile. �r repre-

sents the residual water content, �s is the saturated water content, �

and n are fitting parameters, Ks is the saturated hydraulic conductivity,

and d is the apparent soil density

a Ks d

Depth �r �s /hPa�1 n /mm s�1 /g cm�3

Surface 0 0.43 4.34� 10�3 1.22 3.80� 10�3 1.76

20 cm 0 0.39 1.25� 10�3 1.53 1.24� 10�3 1.72

40 cm 0 0.33 1.15� 10�3 2.65 0.349� 10�3 1.72

60 cm 0 0.34 1.24� 10�3 2.19 0.151� 10�3 1.74

80 cm 0 0.36 1.92� 10�3 1.13 0.464� 10�3 1.73

Aquifer 0.01 0.25 10� 10�3 1.54 50.0� 10�3 1.55

Table 2 Water budget at stations 2 and 3

Cumulative ET þ infiltration Cumulative ET Cumulative infiltration Average ET rate Average infiltration rate

/mm /mm s�1

Station 2 1061 949 111.6 107 � 10�6 12.8 � 10�6

Station 3 1072 1070 2.2 121 � 10�6 0.231 � 10�6



(1.16� 10�3mm s�1) for upward flow. Previous infiltration

results make these potential flux values unrealistic, especially

when the increase in water content is taken into account.

Considering that flux is zero at the bottom of the profile, we

have derived fluxes for the upper layers from mass conserva-

tion with Equation (22), as represented in Figure 6(b). The

assumption of a zero flux lower limit is consistent with the flux

values determined from the hydraulic gradients. The results

obtained with mass conservation agree better with global

water balance results, as the average descending flux is

0.2mmday�1 (2.32� 10�6mm s�1) for the upper layers, and

zero for the lower ones.

Fluxes calculated with hydraulic gradient are potential only,

because they do not actually take place. They are probably

impeded by some other phenomenon, such as the presence of

compressed air, exerting a counter-pressure to imbibition.

Modelling

Single-phase modelling. The flow of water down the soil

profile was simulated with unsaturated soil hydraulic param-

eters determined down the soil profile (Table 1) and with

the previously defined Dirichlet boundary conditions. The

results depicted in Figure 7(a) show a rapid infiltration into

the soil; they conform to evolution of the tensiometric profile

at station 2 where the profile is completely saturated a few

hours after the beginning of irrigation. The match between

simulation results and evolution of tension measured at station

3 is poor, however. We know from our earlier tests that the

model for simulating various conditions of unsaturated single-

phase one-dimensional infiltration is sound, and so the poor

fitting in this instance may have two potential sources: (i) the

unsaturated hydraulic parameters were not determined prop-

erly, or (ii) the model is not adapted to simulate the observed

conditions, namely when air compression interferes with the

simple water infiltration. To test the first hypothesis, we did an

inverse modelling with Hydrus-2D to fit unsaturated soil

hydraulic parameters to the experimental data. The parameters

were evaluated for two layers (0–25 cm and 25 cm�2m) on the

assumption that the saturated and residual water contents were

known. The best fit was obtained with R2¼ 0.81 on 115

observed data; the results are depicted in Figure 7(b), and the

parameters are listed in Table 3. The simulated infiltration fitted

only roughly the evolution of the tension at 40 cm, because the

model could not reproduce suitably the regular decrease of

water tension. The fitted unsaturated soil hydraulic parameters

show only slight differences from the previously determined

ones, except for saturated conductivity of the second layer

where an unlikely value of 0.25mmday�1 (2.9� 10�6 mms�1)

was recorded. This very small value has indeed no real physical

0 days

Soil surface

Hei

ght /

m

7 days14 days35 days49 days70 days

98 days

00

3

4

5

6

2

50 100

Distance from canal /m

150 200

Figure 3 Evolution of the water

table during the cropping season.



significance, as it is two orders of magnitude less than the

previously determined value, but must rather be seen as a fitting

parameter in this case.

Two-phase modelling. To test the possibility of air compression

during infiltration, simple two-phase flow models based on the

Green–Ampt infiltration equation were used. Several of the

equations presented previously were used to describe the

different stages, and four different cases have been considered:

1 the general infiltration (G) described by Equation (12),

2 the two stages of infiltration with vertical intermittent air

escape (TS) of Equations (7) and (10),

3 the two stages of infiltration with maximal air pressure

(TSmax) for constant air release with desaturation, Equation

(13), and

4 the two stages of infiltration with a minimal capillary pres-

sure head (TSmin).

We calculated the infiltration with air compression and air

counter-flow over a depth of 1m, assuming an impermeable

barrier at 1.50m. We calculated the depth of the barrier to air

flow from an average water table level over the irrigation

period. Because these equations were defined for a homoge-

neous soil, with constant unsaturated soil hydraulic param-

eters down the profile, we used the geometric means for Kc

and Ke, and the arithmetic means for hw and ha for the clayey

horizon (Table 4).

Evolution with time of infiltration rate and wetting front are

represented in Figures 8(a) and (b), respectively. They are

compared with the experimental fluxes derived from the calcu-

lation of mass conservation, and the progression of the wetting

front evaluated from the experimental superficial fluxes and

tensiometric data. Infiltration G, calculated with an analytical

relationship, largely overestimates the experimental data as the

values go to 200mmday�1 over the irrigation period. These

larger rates are due mainly to the large tensions for hw and hain the clay. Consequently the difference between hw and ha is

also large, and drives infiltration, Equation (12). Infiltration

TS shows a rapid decrease of infiltration rate, while air pres-

sure accumulates beneath the wetting front, until reaching a

minimum value around 0.1mmday�1 (1.16� 10�6mm s�1)

after 2.28 days. When air escapes, the infiltration rate increases

drastically to 100mmday�1 (1.16� 10�3mm s�1) before

decreasing slowly with the same kinetics as infiltration in G.

The first part of infiltration in TS accords with experimental

data, but the second part, describing infiltration with air

counter-flow, also overestimates experimental values. The

minimal infiltration rate from this calculation can be seen as

biased by the numerical procedure, depending on the incre-

ment dz, as the minimal infiltration rate is zero when dz tends

towards 0. The calculations presented here were done with a dz

increment of 0.5mm, representing 1/2000 of the infiltration

depth, which can reasonably be considered as suitably small.

However, the calculated minimal infiltration rate is obtained at

depth z0 of 372mm and after a period t0 of 2.287days. These

results match the experimental data, especially with the tensio-

metric measurements, showing a blockage of infiltration at 40 cm.

For infiltration TSmax, a maximal air pressure head hamax

had to be defined in Equation (13). This value was evaluated

by a best fitting procedure on experimental data, and 3342mm

for hamax was found. The infiltration rate decreases steadily

until reaching a minimum of 0.01mm day�1 after 40 days of

irrigation. A substantial increase in infiltration rate occurs

afterwards as the driving pressure head (zþ h0þ hw) rises in

the profile. The overall result for infiltration shows a much

better agreement with experimental data, but it does not

describe the entire infiltration phase satisfactorily.

Figure 4 Evolution of relative neutron probe counts in station 2 and

station 3.



1000

800

600

400

200

0

–200

Tens

ion

/hP

a

1000

800

600

400

200

0

–200

Tens

ion

/hP

a

10 cm

20 cm

40 cm

60 cm

80 cm

10 cm

20 cm

40 cm

60 cm

80 cm

0 20 40 60 80 100

0 20 40 60 80 100

Time /days

(a)

(b)

Figure 5 Evolution of the tensionwith duration

of irrigation (a) at station 2 and (b) at station 3

versus the number of days after irrigation.



Finally for infiltration TSmin, the first stage of infiltration

is equivalent to the first stage of TS, but when reaching its

minimum the infiltration rate stays constant. Conformity with

experimental data is notably better for this infiltration procedure,

although it does not describe the phenomena perfectly.

Figure 6 Water fluxes calculated with (a) hydraulic gradient and (b)

mass conservation method, at station 3.

Figure 7 (a) Direct one-dimensional single-phase water flow modelling

and (b) best fit for inverse modelling.

0–0.25m 0.25–2m

�

/hPa�1 n

Ks

/mm s�1

�

/hPa�1 n

Ks

/mm s�1

Value 8.7 � 10�3 1.14 57 � 10�6 2.56� 10�3 3.09 2.9 � 10�6

Lower (95%) 7.4 � 10�3 1.09 36 � 10�6 1.83� 10�3 2.20 1.5 � 10�6

Upper (95%) 9.9 � 10�3 1.19 78 � 10�6 3.3� 10�3 3.99 4.4 � 10�6

Table 3 Results for unsaturated soil hydraulic

parameter evaluation by inverse modelling. �

and n are fitting parameters and Ks is the

saturated hydraulic conductivity



We also calculated the progressing of the wetting front with

these four models. Models G and TS show poor agreement

with experimental data as the calculated wetting front reaches

100 cm deep after only 2 or 3 days of irrigation. Model TSmax

fits the experimental data well for the first 50 days of irriga-

tion, but then diverges completely. The best conformity is

obtained for model TSmin, which fits the experimental data

adequately during the entire irrigation period.

Discussion

Our results recorded during the irrigation show that infiltra-

tion was very slow at station 2 and is at the limit of precision

of our measurements at station 3 (< 10� 10�6mm s�1). The

water content profile and tensiometric data at station 2 accord

with theoretical infiltration models, but at station 3 they

diverge thoroughly. The constant decrease in water content

around 50 cm and the unusual behaviour of the tensiometer

at 40 cm confirm a blocking of infiltration observed at this

latter station. Moreover, this feature is attested by the discre-

pancy between the two methods used for the calculation of the

infiltration fluxes because only the method based on mass

conservation gives consistent results, whereas hydraulic gradi-

ents show clearly the existence of a zero flux plane at 40 cm.

Modelling with Hydrus, taking into account the independently

determined unsaturated hydraulic parameters as well as the

boundary and initial conditions, also shows inconsistency with

experimental data. On the other hand inverse modelling could

not fit properly experimental tensiometric measurements, and

even with the best fit obtained, unrealistic values for saturated

hydraulic conductivity were obtained. This combination of

results shows that, at least at station 3, the presence of

entrapped air dominates the kinetics of infiltration, and that

the usual models of water flow cannot simulate the processes

occurring at this site. Much better agreements are obtained

with simple two-phase flow models based on the Green–Ampt

equation of infiltration, in which a sharp wetting front is

assumed. However, models involving intermittent vertical

escape of air always overestimate the actual experimental infil-

tration rates. In fact, we saw no free release of air bubbles

from the soil surface during the cropping season. Nevertheless,

when we poked a stick into the soil air bubbles rose to the

surface. Moreover, the cracks close rapidly at the soil surface

during irrigation (less than 4 hours), as described by Favre

et al. (1997) in similar soil; they do not contribute to the escape

of air.

The model TSmin, in which there is a constant minimal

tension, i.e. a constant difference between the driving pressure

and the air pressure beneath the wetting front, showed the best

results. A consequence is that air has to escape freely at a

constant rate in order to maintain the rate at which water

infiltrates. As apparently air does not escape vertically, it can

probably escape laterally throughout the clay layer towards

the uncultivated zone where the soil remains unsaturated,

depending on the air hydraulic conductivity as depicted in

Figure 9. This interpretation of lateral escape of air agrees

with the piezometric results. In the inner part of the scheme,

Table 4 Average unsaturated hydraulic soil parameters for the two-

phase flow model. For explanation of terms see text

Kc Ke hw ha B

/mm s�1 /cm

0.345 � 10�3 1.25 � 10�3 282 548 150

Figure 8 Calculated water infiltration rate (a) and progression of

wetting front (b) for two-phase flow infiltration model. 1: G model;

2: TS model; 3: TSmax model; 4: TSmin model.



i.e. far from unsaturated soil borders, we saw no evidence of

air bubbling. The very fine texture of the soil probably keeps

the soil saturated and prevents the air from escaping vertically.

Conclusion

A complete set of measurements taken at various scales and with

several techniques showed that water infiltration into soil is

governed chiefly by the presence of air trapped between two wet-

ting fronts, namely irrigation in the upper part and the water table

at the lower limit. These results were confirmed indirectly by for-

ward and inverse modelling for water flow with a single-phase

model (Hydrus). We showed that a simple model based on a

Green–Ampt infiltration equation taking into account air

compression greatly improves the fit between calculated and

measured data. The best fit was found for the theoretical case

where infiltration reaches a minimal capillary pressure, where the

difference between water tension and the air pressure remains

constant. The rate at which water infiltrates corresponds to the

flux of escaping air. We saw no air bubbles released at the surface,

andwe therefore suggest that airmight escape laterally through the

uncultivated soil.A two-dimensional two-phase flowmodel should

be developed and tested to validate this hypothesis.

Our study shows the crucial importance of air compression on

infiltration into soil in flood irrigation, especially when the water

table is near the surface. Similar hydraulic conditions are probably

common in large irrigation schemes where surge flooding is used.

This phenomenon will also strongly influence soil conservation, as

leaching towards the water table is prevented and irrigation water

concentrates superficially with the risk of salt accumulation. It

should therefore be considered as paramount in large flooded-

rice schemes where there is a serious risk of salinization.

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