V. SoilWater Regime during Trickle Infiltration
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368
ESHEL BRESLER
it into the air, instantaneously. The soilwater 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 isa 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
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TRICKLEDRIP 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).
+
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0.4
0=20
liter/hour
liter/hour

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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 cml min"
HORIZONTAL DISTANCE X, cm
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16
24
32 40
Q.0.495 cm3 cm' min'
0
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16
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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).
TRICKLEDRIP 1RRIGATlON
371
B. WATERCONTENT DISTRIBUTION
T o illustrate the watercontent distribution, the plane flow model is considered. Examples of watercontent 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 soilwater content changes with time and position during trickle
infiltration. The illustration also shows the effect of trickle discharge on the
watercontent field. The saturated waterentry 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. 13 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 waterentry 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 soilwater 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 soilwater 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
TRICKLEDRIP 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 saltconcentration 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