Soil water dynamics under surface trickle irrigation as affected by soil hydraulic properties, discharge rate, dripper spacing and irrigation duration

IRRIGATION AND DRAINAGE

Irrig. and Drain. 59: 254–263 (2010)

Published online 9 January 2009 in Wiley InterScience (www.interscience.wiley.com) DOI: 10.1002/ird.471

SOIL WATER DYNAMICS UNDER SURFACE TRICKLE IRRIGATION ASAFFECTED BY SOIL HYDRAULIC PROPERTIES, DISCHARGE RATE,

DRIPPER SPACING AND IRRIGATION DURATIONy

S. ELMALOGLOU* AND E. DIAMANTOPOULOS

Department of Natural Resources Management and Agricultural Engineering, Agricultural University of Athens, Athens, Greece

ABSTRACT

This study was carried out to determine the effects of discharge rate, irrigation duration and inter-emitter distances

on the wetting front advance patterns and on deep percolation under surface trickle irrigation. For this purpose a

cylindrical flow model incorporating evaporation and water extraction by roots, was used in order to optimize the

use of irrigation water. The mathematical model was applied to two different soil types: loamy sand and silt. Two

irrigation depths (18 and 30mm), two spaces between the emitters (80 and 60 cm) and two discharge rates (2 and

4 l h�1) were used. The initial condition for the two involved soils was that of uniform initial moisture content.

From the analysis of the different numerical experiments, it is concluded that for the same irrigation depth, the

same dripper spacing and the same soil (for time t� ti) the vertical component of the wetted zone is greater for a

smaller discharge rate than for a higher one. It was noticed that there was a faster overlapping of the wetted bulbs in

the fine-grained soil and that deep percolation seems to be lower in the fine-grained soil than in the coarse-grained.

Deep percolation increases as applied irrigation depth increases. Copyright # 2009 John Wiley & Sons, Ltd.

key words: point source; mathematical modelling; water extraction; evaporation; trickle irrigation duration; average water content;coefficient of uniformity; irrigation efficiency

Received 13 August 2008; Revised 31 October 2008; Accepted 31 October 2008

RESUME

La presente etude a ete consacree a la determination des effets du debits des goutteurs, des durees d’irrigation et des

ecartements de goutteurs, sur l’avancement du front d’humectation, l’efficience de l’irrigation et les pertes d’eau

par percolation profonde. Dans ce but, un modele mathematique de l’ecoulement axisymetrique de l’eau, qui prend

en compte l’evaporation et l’extraction racinaire, a ete utilise pour optimiser l’usage de l’eau d’irrigation. Ce

modele a ete applique a deux differents types de sol: sablo-limoneux et silt. Deux doses d’irrigation (18 et 30mm),

deux ecartements entre les rampes de goutteurs et les goutteurs 80 et 60 cm et deux debits pour chacun 2 et 4 l h�1

ont ete appliques. La condition initiale pour les deux sols impliques dans cette etude est une teneur en eau initiale

uniforme.

A partir de l’analyse de differents essais numeriques, il a ete conclu que pour la meme dose d’irrigation, le meme

sol et le meme ecartement, pour les temps plus petits ou egaux a la duree d’irrigation, la composante verticale du

front d’humectation est plus grande pour le plus petit debit (Q¼ 2 l h�1). Pour un temps egal a la periode d’arrosage

(temps total de chaque simulation) la percolation profonde est plus petite sur sol fin et augmente tant que la dose

d’irrigation augmente. Aussi pour le meme debit de goutteurs, la meme dose et le meme sol, en diminuant

*Correspondence to: S. Elmaloglou, Department of Natural Resources Management & Agricultural Engineering, Agricultural University ofAthens, 11855 Athens, Greece. E-mail: [email protected] dynamique de l’eau dans le sol sous irrigation localisee affectee par les propretes hydrauliques du sol, le debit, l’espacement des goutteurs etla duree d’irrigation.

Copyright # 2009 John Wiley & Sons, Ltd.

SOIL WATER DYNAMICS UNDER SURFACE TRICKLE IRRIGATION 255

l’ecartement des goutteurs et par consequence en diminuant la duree d’irrigation nous constatons une augmentation

de l’efficience d’irrigation. Copyright # 2009 John Wiley & Sons, Ltd.

mots cles: goutteur; modelisation mathematique; extraction racinaire; evaporation; duree d’irrigation localisee ponctuelle; teneur en eaumoyenne; coefficient d’uniformite!!efficience de l’irrigation

INTRODUCTION

Drip irrigation as a method of irrigating large fields has become quite common practice in the last three decades.

The reasons for the growing popularity of drip irrigation are several. Drip irrigation offers improved yields, requires

less water and decreases the cost of tillage. Because drip irrigation makes it possible to place water precisely where

it is needed and to apply it with a high degree of uniformity at low flow rates, it lessens both surface runoff and deep

percolation. These features make drip irrigation potentially much more efficient than other irrigation methods,

which can translate into significant water savings.

The soil water flow under drip irrigation is strongly dependent on the soil type, dripper spacing, dose

combinations and rates of water application. For effective design and use of drip systems there is a need to predict

soil water dynamics taking into account all these parameters. Soil water flow may be described by analytical or

numerical solutions of the governing flow equations for specific initial and boundary conditions. In order to achieve

an analytical solution, many simplifying assumptions are required, which limit their applicability to real field

conditions. Many researches have proposed the use of analytical solutions for design purposes considering various

source configurations (Bresler, 1978; Amoozegar-Fard et al., 1984; Philip, 1984; Warrick, 1986; Risse and

Chesness, 1989; Revol et al., 1997a, b; Thorburn et al., 2003).

The choice of inter-emitter distances depends on several factors such as discharge rate, crop, and soil hydraulic

properties (Karmeli and Keller, 1975; Bresler, 1978; Clothier and Smettem, 1990). The typical inter-emitter

distance is in the range 0.30–1m.

The present study is a numerical experiment that may provide detailed information on the effect of soil type,

dripper spacing and discharge rate on the wetting front advance patterns and on water losses by deep percolation,

under drip irrigation. Several combinations of inter-emitter distances, irrigation duration and discharge rate were

studied. Two dripper spacings of 60� 60 and 80� 80 cm were chosen, because they are currently used in trickle

irrigated soils. The current discharge rates in drip irrigation were applied (2 and 4 l h�1). Also the alternating

direction implicit finite difference method is used in order to solve the mathematical model which describes the

axisymmetric infiltration from surface drippers.

METHODOLOGY

Soil physical characteristics

The loamy sand and the silt from the Rosetta database (Schaap and Leij, 1998) were selected and the class

average values of the water retention Q(H) and unsaturated hydraulic conductivity K(H) according to van

Genuchten (1980) were used (Elmaloglou and Malamos, 2006). The values of parameters included in van

Genuchten’s equations are summarized in Table I.

The physical and mathematical model

The physical and mathematical models used in this simulation are described in detail by Elmaloglou and

Malamos (2006). For more details on evaporation and transpiration, the reader should refer to Elmaloglou and

Diamantopoulos (2007).

Table I. Values of the saturated (Qs) and residual (Qr) water contents, hydraulic conductivities (Ks) for the two soils under study(Schaap and Leij, 1998)

Soil Qs (cm3 cm�3) Qr (cm

3 cm�3) Ks (cm h�1)

Loamy sand 0.390 0.049 4.383Silt 0.489 0.05 1.819

Copyright # 2009 John Wiley & Sons, Ltd. Irrig. and Drain. 59: 254–263 (2010)

DOI: 10.1002/ird

Table II. Combinations of discharge rate, dripper spacing and irrigation duration

Discharge rate (l h�1) Dripper spacing (cm) Irrigation duration, ti (h) Irrigation depths (mm)

2 80� 80 9.60 302 60� 60 5.40 304 80� 80 4.80 304 60� 60 2.70 302 80� 80 5.76 182 60� 60 3.24 184 80� 80 2.88 184 60� 60 1.62 18

256 S. ELMALOGLOU AND E. DIAMANTOPOULOS

The root depth was taken as 48 cm. The values of initial volumetric water content Qi were 0.1641 and

0.1979 cm3 cm�3 for the loamy sand and the silt, respectively. The above values were chosen so that for time t¼ 0,

both soils had the same value of effective saturation.

Irrigation simulations were selected to represent typical drip irrigation systems. Several combinations of

discharge rate, irrigation durations and inter-emitter distances were tested (Table II). To evaluate and compare the

different treatments, some parameters such as bulb extension, average water content, soil moisture uniformity and

irrigation efficiency were used.

RESULTS AND ANALYSIS

Wetted soil volume (or bulb) extension

The bulb extension parameter allows us to verify if the supplied water has been stored in the root zone and is,

therefore, available to the plant. An increase in soil water content of zones near the dripper was observed at the

beginning of the irrigation. Thereafter, the wet front extended laterally and in depth. At the end of the irrigation

time, a wetted disc around the dripper was observed. A part of this wetted disc is saturated and the radius of the

saturated zone depends directly on the applied discharge rate and the soil type (Bresler, 1978).

Figures 1 and 2 show the evolution of the wetting fronts under two neighbouring drippers at three different times

(ti=2; ti; 24 h), for both the loamy sand and silt soils, for the two discharge rates (2 and 4 l h- 1) and for the two

dripper spacings 80� 80 and 60� 60 cm. The irrigation duration ti varies according to the dripper spacing and

inversely with the discharge rate (Table II). An overlapping of the wetted bulbs was observed during the simulation

experiments. For the same discharge rate, irrigation depth and dripper spacing, a faster overlapping in the fine-

grained soil was observed (Figures 1(a, b)–2(a, b), 1(c, d)–2(c, d), 1(e, f)–2(e, f), 11(g, h)–2(g, h).

Also, from the same figures, it is concluded that for the same irrigation depth, dripper spacing and soil (for t� ti),

the vertical component of the wetted zone is deeper for a slower discharge rate than for a faster one. This is in

accordance with the findings of the Bresler et al. (1971) model without considering water extraction by roots and

evaporation.

For both the spacing and the discharge rates, the draining water depth as a percentage of the applied irrigation

depth is given in Table III. Deep percolation seems to be lower in the fine-grained soil (silt) than in the coarse-

grained (loamy sand). Also, deep percolation increases as applied irrigation depth increases.

Average of volumetric soil water content

The average volumetric soil water content Qav is calculated for the inter-dripper root zone. To illustrate our

approach, we divide the flow domain into a network of rectangles, where each point on the grid is designated by two

subscripts, i and j, indicating that the point is located at the coordinates ri and zj. The value Q(i,j) is assumed to be


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Figure 1. The evolution of the wetting front for the loamy sand soil, for 80� 80 cm dripper spacing: (a, b) applied irrigation depth of 30mm;(c, d) applied irrigation depth 18mm. The evolution of the wetting front for the loamy sand soil, for 60� 60 cm dripper spacing: (e, f) applied

irrigation depth of 30mm; (g, h) applied irrigation depth 18mm


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Figure 2. The evolution of the wetting front for the silt soil, for 80� 80 cm dripper spacing: (a, b) applied irrigation depth of 30mm;(c, d) applied irrigation depth 18mm. The evolution of the wetting front for the silt soil, for 60� 60 cm dripper spacing: (e, f) applied irrigation

depth of 30mm; (g, h) applied irrigation depth of 18mm


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Table III. Deep percolation depth as a percentage of applied irrigation depth

Discharge rate (l h�1) Dripper spacing (cm) Applied irrigation depth,30mm

Applied irrigation depth,18mm

Loamy sand Silt Loamy sand Silt

2 80� 80 25.2 13.0 14.3 6.32 60� 60 23.4 13.0 12.0 6.94 80� 80 27.0 14.4 14.2 5.14 60� 60 23.9 14.1 10.9 5.5


constant in a volume of soil (Surf ði; jÞ � Dz). The average soil water content is calculated from

Figuresoil; (c

Copyri

Qav ¼

PNk¼1

Qði; jÞ � Surf ði; jÞ � Dz

p � S2f � Zr

(1)

where N is the total number of the computing nodes in the root zone and Surf(i, j) is the area including each node

(i, j).

3. (a, b) Average water content in the inter-dripper root zone for spacing 80� 80 cm, with discharge rate 2 and 4 l/h, for the loamy sand, d) Average water content in the inter-dripper root zone for spacing 60� 60 cm, with discharge rate 2 and 4 l/h, for the loamy sand soil.

This figure is available in colour online at www.interscience.wiley.com/journal/ird

ght # 2009 John Wiley & Sons, Ltd. Irrig. and Drain. 59: 254–263 (2010)

DOI: 10.1002/ird

Figure 4. (a, b) Average water content in the inter-dripper root zone for spacing 80� 80 cm, with discharge rate 2 and 4 l/h, for the silt soil; (c, d)Average water content in the inter-dripper root zone for spacing 60� 60 cm, with discharge rate 2 and 4 l/h, for the silt soil. This figure is

available in colour online at www.interscience.wiley.com/journal/ird


At the end of the irrigation durations the inter-dripper root zone had an average water content of 19.5–22.4 and

22.9–25.9%.

The average water content within the root zone is dependent on the discharge rate and the dripper spacing.

Figures 3 and 4 show the progress of the average water content for several combinations of discharge rate, irrigation

duration and inter-emitter distances for the loamy sand and silt respectively.

The time intervals between successive irrigations depend on the applied irrigation depth, and these periods were

sufficient to return the average soil moisture in the root zone to its initial state (Figures 3 and 4).

Coefficient of uniformity

The Christiansen uniformity coefficient (CUC) proposed first for sprinkle irrigation (Christiansen, 1942) was

used to evaluate the moisture uniformity in the irrigated field (Kang et al., 1999;Wu and Gitlin, 1983) and is defined

as follows:

Copyri

CUC ¼ 100� 1�

PNk¼1

Qði; jÞ �Qavj j

NQav

2664

3775 (2)

ght # 2009 John Wiley & Sons, Ltd. Irrig. and Drain. 59: 254–263 (2010)

DOI: 10.1002/ird

Figure 5. (a, b) Coefficient of uniformity in the inter-dripper root zone for spacing 80� 80 cm, with discharge rate 2 and 4 l/h, for the loamy sandsoil; (c, d) Coefficient of uniformity in the inter-dripper root zone for spacing 60� 60 cm, with discharge rate 2 and 4 l/h, for the loamy sand soil.

This figure is available in colour online at www.interscience.wiley.com/journal/ird

Figure 6. (a, b) Coefficient of uniformity in the inter-dripper root zone for spacing 80� 80 cm, with discharge rate 2 and 4 l/h, for the silt soil;(c,d) Coefficient of uniformity in the inter-dripper root zone for spacing 60� 60 cm, with discharge rate 2 and 4 l/h, for the silt soil. This figure is

available in colour online at www.interscience.wiley.com/journal/ird


DOI: 10.1002/ird



Initially, the coefficient of uniformity was 100%. From the start of the irrigation, a diminution of the coefficient

of uniformity was observed (Figures 5 and 6). This indicates a kind of heterogeneity due to the partial wetting of

regions near the drippers. A minimum value, depending on the spacing–discharge rate combination, was reached,

indicating maximum spatial variation of the water content in the root zone. The latter is reached, also for the same

soil and the same amount of irrigation water, too quickly using a smaller spacing and/or a greater discharge rate

(Figures 5 and 6).

Thereafter, an increase of the coefficient of uniformity indicating an improvement of the bulb moisture

distribution was noted. At the end of the irrigation durations the inter-dripper root zone had a coefficient of

uniformity of 65–70 and 67–73% for the loamy sand and silt, respectively. The uniformity coefficient reached a

value of 92–99% just at the end of the different numerical experiments.

Irrigation efficiency

The irrigation efficiency is defined as the ratio of the average depth of irrigation water that is beneficially used to

the average depth of irrigation water applied (On-Farm Irrigation Committee, 1978).

For the two dripper spacings 80� 80 and 60� 60 cm and for the two discharge rates (2 and 4 l h�1) the irrigation

efficiency percentage at the total simulation time is given in Table IV.

An analysis of the four parameters (bulb extension, average of volumetric water content, moisture uniformity and

irrigation efficiency) has allowed us to optimize the use of irrigation water.

Table IV. Irrigation efficiency percentage for the different numerical experiments

Applied irrigation depth 30mm (loamy sand)

Discharge rate (l h�1) Dripper spacing (cm)

80� 80 60� 60

2 64.8 66.64 63.5 65.2

Applied irrigation depth 18mm (loamy sand)


80� 80 60� 60

2 74.4 76.74 73.6 75.1

Applied irrigation depth 30mm (silt)


80� 80 60� 60

2 79.0 79.34 76.6 78.8

Applied irrigation depth 18mm (silt)


80� 80 60� 60

2 86.6 86.84 84.9 86.2


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CONCLUSION

Given the importance of water in arid and semi-arid countries, water saving for the different systems of irrigation

represents the main objective of theoretical and experimental studies carried out all over the world.

The drip irrigation system is considered to be one of the most economical irrigation techniques. In the selection

of discharge rate, irrigation duration and dripper spacing, a certain amount of empiricism is involved. Thus, it was

important to approach this problem from a theoretical point of view.

From the analysis of the different numerical experiments, it is concluded that for the same irrigation depth,

dripper spacing and soil (for time t� ti) the vertical component of the wetted zone is deeper for a slower discharge

rate than for a faster one. This is in accordance with the findings of the Bresler et al. (1971) model without

considering water extraction by roots and evaporation. Also it was noted that there was a faster overlapping of the

wetted bulbs in the fine-grained soil and that deep percolation seems to be lower in the fine-grained soil (silt) than in

the coarse-grained (loamy sand). Deep percolation increases as applied irrigation depth increases.

It is also noted that for the same discharge rate, applied irrigation depth and soil type, decreasing the dripper

spacing and as a consequence decreasing the irrigation duration, an increase of the irrigation efficiency is obtained.

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Documents

Soil water dynamics under surface trickle irrigation as affected by soil hydraulic properties, discharge rate, dripper spacing and irrigation duration