Analysis of Water Flow under Trickle Irrigation: II. Experimental Evaluation
F. Lafolie, R. Guennelon, and M. Th. van Genuchten*
ABSTRACTA numerical solution for predicting soil water content distributions
during trickle irrigation on stratified and anisotropic soils was compared with data from a field experiment carried out on a loamy clay
soil using 24 field plots irrigated at different rates and frequencies.
The unsaturated hydraulic conductivity was estimated from measured soil water retention and saturated hydraulic conductivities. Observed volumetric soil water contents and saturated areas on the soil
surface were compared with model predictions. The effects of anisotropy and soil surface crusting on experimental and calculated soil
water distributions were also investigated. Relatively good agreement was obtained between predicted and measured soil water content distributions vs. depth. The shape of the observed wetted soilvolume was also predicted reasonably well. The effects of possible
errors in the hydraulic characteristics on calculated water content
distributions are discussed.

NCREASED IRRIGATION EFFICIENCY and reduced
Itributed
water stress are some of the factors that have conto the increased popularity of trickle (drip)
irrigation during the last several decades (Bucks et al.,

1982, p. 220-290). A quantitative understanding ofsoil water distributions during trickle irrigation isneeded for optimizing crop production and minimizing deep percolation losses of water. This understanding may be developed through a combination of field
experimentation and numerical modeling.
Until now, most published experimental data forevaluating trickle irrigation models have been for relatively coarse-textured soils, since trickle irrigation initially was developed mainly for this type of soils inarid and semi-arid areas (e.g., Israel and the southwestern U.S.A.). By contrast, experimental data forfine-textured soils are nearly absent (Mostaghimi etal., 1983). The purpose of this work is to describe atrickle irrigation field experiment conducted on a layered clay soil, and to compare the experimental datawith results from a numerical finite difference model
described by Lafolie et al. (1989).
MATERIALS AND METHODS

F. Lafolie and R. Guennelon, Station de Science du Sol, INRA,
Domaine St-Paul, B.P. 91, 84140 Montfavet, France; M.Th. van
Genuchten, USDA-ARS, U.S. Salinity Lab. 4500 Glenwood Drive,
Riverside, CA 92501. Received 2 May 1988. "Corresponding author.

Field Experiments
The experiments were carried out on a 1-ha field at the
INRA station in Montfavet, France. A geostatistical analysis
of observed particle size distributions revealed little variation in surface soil texture across the field. The mean particle
size distribution was found to be 29% clay, 60% silt and 11%

Published in Soil Sci. Soc. Am. J. 53:1318-1323 (1989).

sand. Twenty four equally spaced drippers were located1319

LAFOLIE ET AL.: ANALYSIS OF WATER FLOW UNDER TRICKLE IRRIGATION. II.

30

0

D

10

*

10

20

a

D

.o 40

}

N

Gravimetric
xWater Content

a
O D D
a

t
I

I
mo

O

0

Neutron Probe
?

.

,

,100'

-C

-

1) O

D

[] O

a
-

80D

80-

D

60-

-

Gravimetric_^Bulk Density

D
D
D

D

O

"

\
rj4o|» a n a
gfo

D
-

gj 60

a

O

20-

D

50 R (cm)

30

D

I1 O

D

1 0

D

Zfcm)
I00

l5

12

J4

L6

1.8

BULK DENSITY, P.a (g/crrv1)

Fig. 1. Measured vertical bulk density distributions at selected points
along the trickle irrigation line.

along a 70-m-long trickle line. The discharge rates of thedrippers were all approximately 4L/h as measured before
and after each irrigation. For time and technical reasons, theexperiments were conducted successively on sets of, at most,
five drippers. Each plot corresponding to a single dripper
was first carefully leveled and then irrigated following aschedule that involved cycles of approximately 4 h of irrigation and close to 20 h of redistribution.
Four vertical neutron-probe access tubes were installed atregular intervals along the trickle line for the purpose of
estimating soil bulk density profiles by neutron scattering.
Another bulk density profile was obtained gravimetricallyby sampling successive soil cores between 0 and 130 cm.
Results are plotted in Fig. 1. Notice a relatively sharp transition zone in bulk density at around the 30-cm depth, especially for the gravimetric sampling. The transition is lessapparent for the neutron method, since sharp changes withthis method are smoothed by averaging over relatively large
volumes of soil. Because of the observed bulk density change
at 30 cm, the soil profile was assumed to consist of twolayers, each having its own hydraulic properties.
Data Recorded for Each Plot
Initial water-content profiles were obtained by taking coresamples adjacent to each plot at 10-cm intervals until adepth of 1 m. Photographs of the soil surface under eachdripper taken at the end of the last irrigation were used toestimate both the saturated and unsaturated wetted areas at
the soil surface. The photographs were also used to verify
the shape of the ponded areas (circular or otherwise).
A large number of data was recorded at several sampling
locations (Fig. 2), 2 to 5 h after the end of the last irrigation.
First, the axis of symmetry of each plot was established (usually just below the dripper), at which location a soil bulkdensity profile between 25- and 45-cm depth at 3-cm intervals was measured by gamma-ray transmission. Next, a vertical trench was carefully cut through the axis of symmetry,and samples taken for gravimetric soil water content measurements. Figure 2 shows the location of these water-content

Fig. 2. Sampling locations for soil bulk density and gravimetric watercontent measurements in a vertical cross section under the dripper(D).

measurements, i.e., along a vertical line below the dripper
between the gamma-ray access tubes, along vertical lines 40
cm away from the dripper, and also along a horizontal line
at 40-cm depth. The data were used to estimate spatial distributions of the water content, and to assess the dimensionsof the wetted soil volume.
Determination of the Soil Hydraulic Characteristics
The soil water content (0)-pressure head (i/-) relationshipin the range of 0 to — 150 m was obtained using pressure
cells. One field plot was equipped with five tensiometers at
depths of 20, 40, 60, 80 and 100 cm, and with a neutronprobe access tube for water content measurements. The
field-measured soil water retention curve between 0 and— 800 cm was in good agreement with the laboratory measured curve. No significant differences between the gravimetric retention curves were found for the surface and subsurface horizons. Attempts to fit the analytical expressionsof Brooks and Corey (1964) or van Genuchten (1980) to theobserved data were not very successful. Consequently, wesmoothed the data with a cubic spline function and used
the resulting curve to generate a vector of 200 retention
points at intervals (A0) of 0.0025. The derivative of the
spline function was used to generate corresponding soil
water capacities. Linear interpolation between the entries of
the water retention vector was used during the numericalsimulations.
The saturated hydraulic conductivity, Ks, was measured
at seven regularly spaced locations along the trickle irrigation line for the upper layer, and at five locations for thesecond layer. Measurements were made on soil cores (15cm diam., 7-cm height) taken immediately after the last irrigation. The cores were taken with metal cylinders that were
driven into the wetted zone under the emitters. The twoends of the samples were then carefully smoothed while, atthe same time, avoiding any slaking of the soil. In the laboratory, these samples were slowly wetted from below to
reduce air entrapment. Once saturated, different positive total pressure heads in the range of 0.1 to 5 cm were imposedat the bottom of the sample. After establishing steady-state
flow, the corresponding flow rates were recorded. A linear
regression between the measured fluxes and potential dif-

1320

SOIL SCI. SOC. AM. J., VOL. 53, SEPTEMBER-OCTOBER 1989

Table 1. Measured saturated conductivities, Ks, of the surface andsubsurface soil layers.
Surface layer(0-30 cm)
Site no.

Subsurface layer(>30 cm)
Site no.

Ks
1

2

3

14.7

1
2
3

4

2.95
24.5

4
5

5
6
7

-10000.

K,

m d~'

md"
3.14
3.64

1

-100000.

0.86
0.95
0.09
2.94
0.29

2.75
3.09

ferences gave the global resistance of the system consistingof the soil sample plus attached permeameter. Subtracting
the known resistance of the permeameter gave the resistanceof the soil, and hence the hydraulic conductivity as the inverse of the resistance. The linear regressions over seven oreight points were always excellent, giving intercepts thatwere generally very close to zero. Values for Ks measured inthis manner are listed in Table 1. Notice that, except for two
samples that probably contained some macropores, Ks forthe surface layer remained in a relatively narrow range between 2.7 and 3.7 m/d. By comparison, results for the second layer were more scattered. Having data for the soil water
retention curve and Ks, the predictive pore size distribution
model of Mualem (1976) was subsequently used to estimate
the unsaturated hydraulic conductivity curve, K(\{/), for thetwo soil layers. For each simulation, we always used themeasured conductivity value of the nearest sampling site.
Modification of the Predicted Hydraulic Conductivity
Curve
Figure 3 shows that the measured soil water retention
curve decreases very quickly between saturation and the firstmeasured data point less than saturation. Because of this,Mualem's model generated a AT(^)-curve which decreased
very sharply when \l/ became <0. For example, between \l/= 0 and —15 cm, the hydraulic conductivity decreased bya factor of 104 (Fig. 4). For similar reasons, the soil water
capillary capacity, d6/d\l/, close to saturation was also veryhigh. Simulations made with these hydraulic curves resulted
in water content profiles with extremely large gradients(sharp moisture fronts) which did not agree with the observed field data (results not shown here). These large gradients also persisted between individual irrigations, again
being contrary to our observations. Because of the above
inconsistencies, we decided to modify the Mualem-predicted
hydraulic conductivity curve close to saturation. Figure 4
shows a semi-logarithmic plot of K/KS vs. ^. Note that the
curve is more or less linear for \f/ less than — 30 cm. Because
the first observed data point of the 0(\l/) curve less than saturation was at ^ = — 30 cm, we decided to use the predicted
K(\(>) curve only for \j/ values less than — 30 cm. Between 0
and — 30 cm we adopted, rather arbitrarily, an exponential
relation of the form K = Ks exp(/3i£), where ft was calculated
to keep continuity at $ = — 30 cm (see the dashed line in
Fig. 4). No independent laboratory data were available tosupport this modification, and hence the accuracy of themodified curve could not be further assessed.
RESULTS AND DISCUSSION
Figure 5 compares calculated and observed verticalwater content distributions immediately under thedripper, and at a radial distance of 40 cm. Similar. -1000.

'Cubic Spline<
LU-Observed

UJ

cc

-100.

CO
LU

-10.

.15

.25

.35

.45

.55

WATER CONTENT, 9 fcm'/cm")
Fig. 3. Observed and cubic spline soil water retention curves, $(0),for the surface soil layer, 0 to 30 cm.

-120

Fig. 4. Semi-logarithmic plot of the relative hydraulic conductivity,
KIKa vs. pressure head, ^, as predicted with Mualem's model(solid line) and interpolated from saturation to the first data pointof the measured soil water retention curve (dashed line).
horizontal distributions at 40-cm depth are given in
Fig. 6. Observed results are averages of four or five
replicates, with the bar through each data point indicating the range of observed values. The data weretaken after 66 (top), 92 (middle) and 165 (bottom)
hours of irrigation, corresponding to total amounts ofapplied water of 56, 64, and 107 L, respectively. The
extremely low initial water contents near the soil surface corresponded to a pressure head of less than-100 m.
The calculated water content distributions in Fig. 5
and 6 (solid lines) were obtained with the numericalmodel of Lafolie et al. (1989). Numerical results wereobtained for a domain extending 75 cm radially and
130 cm vertically. Vertical increments of the finite difference grid increased from 2 cm at the soil surface to
4 cm at the bottom of the domain, while the radial

1321

LAFOLIE ET AL.: ANALYSIS OF WATER FLOW UNDER TRICKLE IRRIGATION. II.

.15

.25

WATER CONTENT (cmVcm").35_____.15
.25
.35

.45

Table 2. Measured and calculated saturated radius, Rs, for isotropic
and anisotropic soil crusting conditions.
CalculatedTime

Measuredf

Isotropic

Anisotropic

66

9,11,9,1092
165

16, 16, 18
19, 20, 27, 27

7.8
8.0
8.2

16.0
17.5
17.0

t Values of replicates.
0.40

Q20

0—————02—————04

0.6

RADIAL DISTANCE (cm)Fig. 6. Measured and calculated horizontal water content distributions at the 40-cm depth. Calculations are for an isotropic andanisotropic conductivity tensor.

UNDER EMITTERLATERAL PROFILE
Fig. 5. Measured and calculated water content distributions under
the dripper (left) and at a radial distance of 40 cm away from thedripper (right), after application of 56 (a,b), 64 (c,d) and 107 L(e,f) of water. Calculations are for an isotropic and anisotropic
conductivity tensor.

increments were 3 cm. The time step varied from 1 s
to 1 h. The simulations were initially carried out with
an isotropic hydraulic conductivity tensor. Figure 5
and 6 show reasonable agreement between the fieldmeasured data and the simulated results. However,some systematic discrepancies existed. For example,
the calculated vertical water content distributions at
a radial distance of 40 cm were always lower thanthose measured in both the extreme top and bottom
parts of the soil profile (Fig. 5b,d,f). The same is true
for the water content in the bottom of the profile justbelow the dripper (Fig. 5a,c,e).
Several factors probably contributed to these deviations. For example, the experimental water content
distributions were derived from observed gravimetricvalues using measured bulk densities (pd) at the corresponding depths, whereas a constant pd was assumed
for each of3 the two layers in the simulations (1.33 and1.54 g/cm for the surface and subsurface layers, respectively). Measured pd at depths greater than 90 cm
always exceeded 1.6, resulting in local errors in watercontents up to about 6%. We also noticed an increasein pd of the top layer during the experiments as a function of the amount of applied water. Gamma-probe
data recorded for each plot showed that, at the end of
the experiments, the average dry pd had increased toabout 1.45 in the surface layer. This caused additional
deviations of up to about 10% in the calculated watercontent.
Table 2 compares observed and predicted values ofthe saturated radius, Rs, at the soil surface. Except for
the first sampling at t = 66 h, calculated results forthe isotropic case severely underpredicted the measured values. We believe that these deviations between
observed and predicted Rs values, as well as those between the observed and predicted water content in
Fig. 5 are caused primarily by the relatively poor characterization of the soil hydraulic properties.

1322

SOIL SCI. SOC. AM. J., VOL. 53, SEPTEMBER-OCTOBER 1989
RADIAL DISTANCE (cm)20

40

Fig. 7. Effect of the saturated hydraulic conductivity, Ks, of thesurface horizon on calculated water-content distributions during
trickle irrigation.

Several factors, in addition to those mentioned
above, likely played a role. We initially hypothesizedthat the saturated conductivity, Ks, of the surface layer
might have been overestimated during at least part ofthe experiments. To test the effect of changes in Ks of
the surface layer, we carried out several simulations.
Figure 7 presents the results obtained for a 4-h trickle
irrigation with the same soil as before, but now for a
uniform initial pressure head of — 500 cm. Results arefor two values of Ks of the surface horizon, 3 and 9
m/day, leading to saturated radii of 7.2 and 4.0 cm,
respectively. As expected, the smaller K^ value resulted in a larger wetted radius, Rs. However, thewater content distributions inside the profile were
only marginally affected by the change in Ks of thesurface layer. This is especially true for the water contents in the deeper soil layers. Similar effects were
found when the entire experiment, as in Fig. 5, wassimulated. Hence, improved water content distributions in the soil profile could not be obtained by simply changing the saturated hydraulic conductivity ofthe surface layer.
During the field experiments, we observed the formation of a thin soil surface crust that more or lessfollowed the ponded area on the soil surface below thedripper. Formation of a soil crust is presumablycaused by particle dispersion and/or soil swelling during saturated or near-saturated flow, and will result in
lower porosities and hydraulic conductivities, especially for fine-textured soils (Shainberg and Shalhevet,1984). The main effect of soil crust formation in our
experiments was to increase the saturated (ponded)area with each irrigation cycle, as indeed shown by
the data in Table 2. Similar effects of soil sealing andpossibly compaction were noted by Jury and Earl

(1977) during a series of field experiments on a sandy
loam soil. These authors also found that successive
laboratory measurements of A^s tended to give lower
values, further indicating that pore geometry waschanging with time.
Another factor which may have caused a discrepancy between observed and predicted water contents
is anisotropy in the hydraulic conductivity tensor. In
situ observations of the wetted soil profile along thewalls of open soil trenches indicated the presence ofpreferential flow paths in the soil. Preferential flow
paths were especially visible in the well-structured
subsurface horizon at depths greater than 30 cm. As
shown by Wang and Narasimhan (1985), gravity induced preferential flow may occur in a structured soil,
even when water contents are slightly less than saturation. One way to numerically account for preferential flow in a structured soil is to assume an anisotropic hydraulic conductivity tensor in which thesaturated hydraulic conductivity in the vertical direction (KVJ is larger than the horizontal saturated hydraulic conductivity (Kh s).
In order to test the above assumptions, we incorporated provisions for surface crusting and soil anisotropy into the numerical model. The time-dependent nature of the soil-crusting process at the soil
surface was approximated by multiplying Ks of thesurface 2 mm of soil under the dripper by a "soilcrusting factor" (cf) of 0.2 once the soil became saturated. In accordance with field observations, only thesaturated soil surface was assumed to be affected bysoil crusting. The value of cf = 0.2 was chosen suchthat it reduced Ks significantly from its original value,
while still yielding values that are considerably higher
than KS values typical for fully developed soil crusts(Shainberg and Shalhevet, 1984). Anisotropy in thehydraulic conductivity was approximated by increasing Kv s of the second (subsurface) layer by 50%.
Numerical results for the anisotropic soil-crustingcase are also shown in Fig. 5. Predictions of the watercontents in the subsurface layer were improved, although discrepancies remained in the deeper layers
away from the axis of symmetry (Fib. 5b,d). Note thatwater contents of the surface horizon immediately below the emitter were essentially unaffected by surface
crusting (Fig. 5a,c,d), whereas surface water contents
at a radial distance of 40 cm from the dripper werehigher. These higher water contents at r = 40 cm resulted from the larger ponded radii (Table 2) causedby soil crusting. The above effects of soil crusting andsoil anisotropy can only be approximated because of
inaccurate and incomplete data of the soil hydraulicproperties in time and space. However, they do accurately reflect the qualitative effects of the crustingand preferential flow phenomena.
SUMMARY AND CONCLUSIONSA previously proposed numerical model for predicting soil profile water content distributions during
trickle irrigation on stratified and anisotropic soils(Lafolie et al., 1989) was used to analyze a field trickle
irrigation experiment. The experiments were carriedout on a loamy clay soil using 25 field plots irrigatedNASSAR & HORTON: WATER TRANSPORT IN UNSATURATED NONISOTHERMAL SALTY SOIL: I.

at different rates and frequencies. Results for a typicalset of experiments involving cycles of 4 h of irrigationand 20 h of redistribution are presented in this paper.
While the observed water contents were simulated
reasonably well with the model, a number of systematic discrepancies were noted. Most of these could be
related to inadequate characterization of the unsaturated soil hydraulic conductivity. In our study, thissoil property was estimated from the field-measured
soil water retention curve using the predictive modelof Mualem (1976). The estimated hydraulic conductivity curve was modified in the vicinity of saturation
to allow for realistic predictions of the measured soil
water contents. Other problems involving the hydraulic properties were related to the heterogeneous
behavior of the fine-textured soil. For example, particle dispersion and/or soil swelling probably contributed to the formation of a thin soil crust on the soil
surface under the emitter. As shown by numericalsimulations, the associated reductions in porosity andhydraulic conductivity help to explain the larger than
predicted saturated (ponded) areas observed on thesoil surface during the experiments. Soil heterogeneity
was also related to preferential flow in the well-structured subsurface horizon at depths greater than 30 cm.
Preferential flow was accounted for by assuming ananisotropic hydraulic conductivity tensor which favors water flow in the vertical direction.
Inclusion of soil crusting and soil anisotropy re-1323

sulted in improved predictions of soil water contents,and especially of the ponded area at the soil surface.
We conclude that accurate descriptions of the soil hydraulic properties are crucial for reliable prediction ofsoil water contents during trickle irrigation. Accurate
descriptions of the hydraulic properties appear especially important when calculated water fluxes are later
used for predicting solute transport during trickle irrigation.