Analysis
of
Water Flow
under
Trickle Irrigation:
I.
Theory
and
Numerical Solution
F. Lafolie, R. Guennelon, and M. Th. van Genuchten*
ABSTRACT
Estimating the size of the ponded surface area is a major source
of error in modeling water movement under trickle irrigation. After
reviewing available approaches and models for simulating water flow
under trickle irrigation, we present a new numerical solution of the
governing partial differential equations that improves the prediction
of the size of the ponded area at the soil surface. A common for-
mulation could be used for both Cartesian and axicylindrical flow
geometries. The spatial operator was approximated using finite dif-
ferences, and time integration was performed with an implicit
method. Nonlinearity was treated by means of a fixed point iterative
algorithm. The proposed model is applicable to saturated-unsatu-
rated flow in layered soils having anisotropic hydraulic properties.
Accuracy and stability of the solution are checked and comparisons
made with previous numerical solutions for several trickle irrigation
and other unsaturated flow problems.
I
NCREASED IRRIGATION EFFICIENCY, reduced water
stress, ease of automation, the ability to apply fer-
tilizers and other chemicals with irrigation water, and
low economic cost are some of the factors that have
contributed to the increased popularity of trickle ir-
rigation over the last few decades (Bucks et al., 1982).
Trickle irrigation is now applied to a wide variety of
crops grown on soils with a broad range in soil texture,
soil structure, and hydraulic
properties. Notwith-
standing its popularity, surprisingly little attention has
been paid to estimating soil water distributions during
trickle irrigation under
realistic field
conditions. Lack
of understanding of how soil water content distribu-
tions are affected by the unsaturated soil hydraulic
properties has sometimes resulted in suboptimal man-
agement and low water-use efficiency (Hillel, 1985).
The shape and total volume of the wetted soil region
below a trickle emitter varies widely with irrigation
and soil hydraulic parameters. Using the number of
drippers, the discharge rate, and the irrigation fre-
quency as adjustable parameters, a trickle irrigation
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 au-
thor.
Published in Soil Sci. Soc. Am. J. 53:1310-1318 (1989).
system should be designed such that the wetted soil
volume matches as closely as possible the crop rooting
pattern.
Soil hydraulic properties usually exhibit consider-
able spatial variability at the field scale. An important
task in the design of a drip irrigation network is to
evaluate how spatial variability affects water content
distributions in the field. Particularly useful would be
a sensitivity analysis which shows how deterministic
soil water contents are affected by variations in rele-
vant model parameters. One application of modeling