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V. Soil-Water Regime during Trickle Infiltration

V. Soil-Water Regime during Trickle Infiltration

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368



ESHEL BRESLER



it into the air, instantaneously. The soil-water content immediately beneath the

ponded area, A = n p 2 , is equal to the water content at saturation, OS. This

saturated area, the size of which is-a function of time, is the only place where

water can infdtrate into the soil from the surface.

Figure 5 shows the calculated vertical water flux at the surface across the

saturated water entry zone, as a function of infiltration time ( t ) and distance

from the center of source. Since 0 = 0, in the interval 0 < x < p(t), the hydraulic

conductivity of the saturated zone is constant and equal to the saturated

conductivity. Thus, the decrease in vertical water flux with time (Fig. 5) is due

only to the decrease in negative value of the vertical hydraulic gradient at the

.Of -



.O i



2 cm



o=o.ge3 crn' cm-' min-'



.o 6



-.o :



.

C



'i



-



.O.c



x



3



2.03



.O i



.o 1

0



I

200



400



I

600



eoo



I



I



I



I



I



I



1



1000



1200



1



1x10



.01 --K@s)



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TRICKLE-DRIP IRRIGATION



369



saturated zone. Within the time considered, the hydraulic gradient has always

been less than unity (the vertical flux of Fig. 5 is always greater than K,) but

tends to approach a limit. The limiting value of the hydraulic gradient and the

length of time involved in obtaining it depends on both the distance from the

trickle source and its rate of discharge (Fig. 5). The larger the trickle discharge

and the smaller the distance from the source, the faster the hydraulic gradient as

a function of time approaches its limiting value. If a value of 1 to this limit were

approached throughout the whole ponded area, then we would have from Eq.

(170 p(t

m) + [Q/K(0,)n]'/2. However, since at finite value of time, the

limiting hydraulic gradient is less than 1, then p ( f ) < (Q/nK,)'12 in cylindrical

flow [p(t) < Q/(2K,) in plane flow], if evaporation is not too significant. (If

evaporation is important, then p(t)< {Q/[K,n

+ E ] "2.),Neglectingevaporation

the difference between p ( t ) and [Q/(K,n)]'/2 [or Q/(2K,)] depends on the

average vertical water pressure gradient at z = 0 over the interval 0 G r (or x) <

p ( t ) [Eq. (29)]. Since the rate of change of this average value decreases with

time (Fig. S), the rate of growth of the saturated water entry zone also decreases

with time, as shown in Fig. 6. From this figure one can see that at a relatively

large infiltration time ( t ) , the radius of the saturated water entry zone ( p ) is

much less than [Q/K,n)] ' I 2 (see Table I1 for values of K,). Figure 6 further

indicates that the radius of the saturated water entry zone will always be larger

as K , decreases and Q increases. This fact has a very important practical

implication (see Section VII).

-+



I



-"E



0.4

0=20

liter/hour

liter/hour



-



I



____-----



-



0



0



50

100 150 200

i0

INFILTRATION TIME, t (minutes)



FIG. 6. Radius of the saturated water entry zone p ( t ) as a function of infiltration time

( t ) for two soils and two discharge rates (Q). After Bresler (1977).



3 70



ESHEL BRESLER



Q.0.983 cm3 cm-l min"

HORIZONTAL DISTANCE X, cm

32

LO

0

8

16

24

32 40



Q.0.495 cm3 cm-' min-'



0



8



16



24



I



48



8



-



16



-



-



FIG, 7. Water content filed as a function of cumulative infiltration ( V = 4')for two cases

of discharge (Q). The numbers labeling the curves indicate water content (0). After Brandt

et al. (1971).



TRICKLE-DRIP 1RRIGATlON



371



B. WATER-CONTENT DISTRIBUTION



T o illustrate the water-content distribution, the plane flow model is considered. Examples of water-content distribution for two cases of trickle discharge

(Q), expressed in terms of discharge per unit length, are given in Fig. 7, which

shows how the soil-water content changes with time and position during trickle

infiltration. The illustration also shows the effect of trickle discharge on the

water-content field. The saturated water-entry zone is shown by the particular

line of saturated water content at the surface, where B s = 0.44. This zone is

larger as the rate of trickle discharge increases. In the vicinity of the source (x =

0, z = 0 in Fig. 7), the moisture gradients increase when the rate of discharge

decreases. These gradients can be calculated from the distances between lines of

equal water content. This condition is reversed as the wetting front is approached. The overall shape of the wetted zone also depends on the trickle

discharge. The vertical component of the wetted zone becomes larger and the

horizontal component narrower as the rate of discharge decreases.



C. WETTING FRONTS



The wetting front is an important factor in trickle infiltration because it

indicates the boundaries of the irrigated soil volume. Figure 8 shows the location

of the wetting front, as a function of the space coordinates (Y,z) and the total

amount of infiltrated water, for two different trickle discharges and two soils

differing in their hydraulic characteristics (Table I1 and Fig. 1-3 of Bresler et al,

RADIAL DISTANCE, r ( c r n )



40



Q=4

(2.20 Iiter/hour

I



N



30



FIG. 8. Wetting front position as a function of infiltration time and cumulative infiltration water (in liters) indicated by the numbers labeling the lines, for two soils and two d i s

charges. After Bresler (1977).



372



ESHEL BRESLER



1971). The total amount of infiltrated water (in liters) is indicated on the

wetting front lines appearing in the figure. The trickle discharge, Q, in terms of

volume per unit time, and the soil textures, are also indicated in the figure.

The data presented in Fig. 8 demonstrate clearly that the rate of trickle

discharge and the hydraulic properties of the soil have a remarkable effect on the

shape of the wetted soil zone. Increasing the rate of discharge and decreasing the

saturated conductivity result in an increase in the horizontal component of the

wetted area and a decrease in the vertical component of the wetted soil depth.

This is probably affected by the changes in the size of the water-entry saturated

zone for each soil type and rate of discharge (Fig. 6). This ponded zone becomes

larger as the soil becomes less permeable and as the trickle rate increases.

The possibility of controlling the wetted volume of any particular soil, and the

water content distribution within its boundaries, by regulating the trickle discharge according to the hydraulic properties of the soil (Figs. 7 and 8), is of

practical interest in the design of field irrigation systems (see Section VII).



D. EFFECT OF SURFACE EVAPORATION



A possible effect of soil-water evaporation, which occurs simultaneously with

infiltration, on the water distribution pattern can also be tested by numerical

models (Brandt ef al., 1971; Bresler, 1975). The results of water distribution

data, using the numerical procedure of Hanks er a/. (1969) to evaluate evaporation as a function of soil-water content E(B), as well as a high potential

evaporation value of E, = 10 mm/day, remain essentially the same as if

evaporation were completely neglected. It appears, therefore, that generally

water evaporation which takes place during infiltration is not an important

factor in infiltration from a trickle source. This is so because usually free water

evaporation rate (E,) is on the order of 1 cm day-’ or less and K , of many

“normal” soils is on the order of 1 cm hour-’, so that E,/K, is generally less

than 0.04. The net water flux into the soil anywhere in the saturated water entry

zone is given by qnet = K,(dH/dz) -E,. Since during trickle infiltration the value

of dH/dz is generally less than -1, the ratio between outward flow due to

evaporation and gross inward infiltration flow is, in most practical cases, less

than 4%.However, under very dry conditions where E, is extremely high, and in

a soil of very low permeability where K , is extremely low, the effect of

evaporation during infiltration from a trickle source may be important.



VI. Solute Distribution during Infiltration



As mentioned before (Section III,B), the accumulation of salt between emitters may be a serious problem for crops irrigated by trickling. Control of soil



TRICKLE-DRIP IRRIGATION



373



salinity regime is therefore essential to the permanent operation of a trickle

irrigation system. In addition, since fertilization simultaneously with irrigation

seems to be a good practice, optimizing the nutritional regime in the root zone

depends on the possibility of controlling the fertilizer salts in the wetted soil

volume. Salt distribution in the soil under trickle irrigation will be demonstrated

here by an example involving the case of low concentrated inflow solution in the

irrigation water that miscibly displaces a highly concentrated solution originally

present in the soil. Interactions between the solute and the soil matrix are

ignored. Two soil media with widely different hydraulic properties and salt

dispersion characteristics are discussed.

The results presented in Figs. 9 and 10 were obtained from the cylindrical flow

model when the hydraulic soil functions K(e) and p ( 8 ) were those of Gilat

(loam) and Nahal Sinai (sand) soils (Bresler et ul., 1971, Figs. 1, 2, and 3). The

soil diffusion coefficient was taken as D p ( 0 ) = 0.004 exp (loo), and the

dispersivities were chosen to be AL = 0.2 cm, and AT = 0.01 cm [Eq. (9)] .The

soils are assumed to have initially uniform water contents and solution concentration [c,(r,z) = 52.35 meqbiter and 0,(r,z) = 0.213 for Gilat; c,(r,z) = 300

meq/liter and 0,(r,z) = 0.0375 for Nahal Sinai] with 0, = 0.265 and 0, = 0.44

for Nahal Sinai and Gilat, respectively. The “water capacity” (0, - O n = 0.227),

the initial volumetric salt content (cnO, = 11.25 meq/liter soil), and COO,,which

is the minimum possible volumetric salt content at the soil inlet, are taken to be

the same for the two soils. [Inlet salt concentration was C,(t) = 5 meq/liter for

Nahal Sinai and C,(t) = 3.0 meq/liter for Gilat soil.] Two cases of constant

trickle discharge, Ql = 4 liters/hour and Q , = 20 liters/hour, are considered.

The general pattern of salt distribution in the two soils and for the two trickle

discharges is demonstrated in Figs. 9 and 10. In Fig. 9 the salt concentration

field is expressed in terms of salt concentration in the soil solution (as meq/liter

bulk soil). Both figures show how the position of the dissolved salt field in the

cylindrical flow pattern is influenced by the trickle discharge and the hydraulic

properties of the two soils (Bresler et ul., 1971).

The fact that the water capacity (0, - On), the initial volumetric salt content

(c,0,), and the minimum inlet salt content (COO,) are identical in the two soils,

makes it possible to compare the salt distribution data (Figs. 9 and 10) of these

two soils. To be able to compare the effect of trickle discharges and to place the

two different rates on an equal basis, the results are compared for an identical

amount of cumulative infiltration (12 liters) and not for an equal time allowed

for the irrigation. It should be noted that the values of OS, O n , c,, C,, Q and

total infiltration used in the examples, are in the range of practical and actual

field conditions.

Figure 9 demonstrates the shape of the actual salt-concentration distribution.

In both soils and with both trickle discharges, the solution concentration of the

saturated water entry zone is identical to that of the infiltrated water. The

concentration rises as the wetting front is approached and reaches its initial value



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