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IV. Water Flow in Agricultural Soils

IV. Water Flow in Agricultural Soils

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which the process is controlled by sorptivity S, the rate at which water is

moved or redistributed away from the surface through the body of the

material. Early attempts at modeling the infiltration process used empirically

derived constants to link I with S (Green and Ampt, 1911). Later Philip

(1 957a,b) provided comprehensive mathematical solutions for idealized

infiltration. At large values of t, cumulative infiltration i was described in

terms of a power series of coefficients derived from K(8) and D(8), the soil

water diffusivity; which is defined as:

D(8) = K(B) d$/d8


where D is the product of K(B) and the reciprocal of the $(8) curve for any

value of 8 and has units of area per unit time (m2/s). For practical purposes

and short time intervals, Philip’s equation can be approximated by

1 = St’i2


The “sorptivity” S is the slope of cumulative infiltration against Jt. It

provides us with a convenient parameter of the soil’s absorption rate in units

of length per square root of time (m s-’”). S varies, however, both with the

initial water content Bi and with surface stability. Indeed, lack of variation inS

in any one soil is an excellent measure of stability. Philip’s work gave

solutions for vertical infiltration in situations where both suction and gravity

were operating. The boundary condition was for ponded water at the soil


More recent theories for nonponding infiltration at a constant rate also

assume a vertically uniform soil with uniform Oi, ignoring the effect of

raindrop impact on soil stability, and hysteretic effects, and assume air ahead

of the wetting front to be at atmospheric pressure. The rainfall rate V, is

assumed to be a constant. The basic assumption is that soil-water flow can be

described in terms of D(8) and K(8):

V(8,t ) = -D(O)(dO/dz

+ KO)


where V(8, t ) is the Darcy velocity of water at some position in the soil where

the water content is 8, at time t.

Because D(8) and K(8) are not easily measured and have high CVs, as we

have seen in Section II,A,3, the more sensible approach, which is now being

used in field conditions, is to simplify the theory and describe D(8) and K ( 8 )

in terms of S and K,. The conversion of K(8) to a scaled value of K, was

suggested by Brooks and Corey (1964):

~ ( 0 =) ~ s C ( e s- ei>/(es (6)

D(8) is expressed in terms of an exponential function of 8 (Brutsaert, 1979):



where y(p) is a function of the slope of the wetting front for which Brutsaert

suggested a value of N 8.0. However, if D(8) is not exponential with water

content, this value is not a constant. In Eqs. (6) and (7) S is measured at initial

water content Oi and after t(O,), while 0, and 8, are the saturated and residual

water contents, respectively, and 8, is separately determined. A recent

treatment of modern infiltration theory which describes these principles in

more detail is given by White et al. (1982). They show that successful

prediction of the movement of the wetting front, the time to incipient

ponding, and the time-dependence of surface 8 can be made for the conditions

of constant-rate rainfall, nonsealing surfaces, and uniform Bi. This is sufficient

where sprinkler irrigation or rainfall simulators are csed to obtain infiltration

characteristics ( I , i, etc.) of a stable, homogeneous soil. Variable-rate rainfall

and sealing surfaces are more complex to treat, although by assuming the

surface to be already sealed, as a layered soil, the latter problem has been

tackled successfully (Section IV,B,l).

1. Field Infiltration Afected by Unstable Structures

In a well-known paper written in 1940, Horton, an engineer and an

experimentalist, placed considerable stress on the physicochemical processes

which accompany rain falling on soil surfaces. He described three “exhaustion phenomena” which lead to a decline in the asymptotic values of i,

including the decrease in effective pore size with soil crumb breakdown and

the puddling of soil, which reduces porosity and “colloidal swelling,” which

also reduces pore space. In addition, he considered the significance of

entrapped air in immiscible displacement ahead of the wetting front and the






















FIG.4. Seasonal variations in infiltration (m/s x

drainage basin (Texas). (Adapted from Horton, 1940).

from the North Condho River



forces associated with rainstorms of different drop dimensions and velocities.

Figure 4 shows his data for the seasonal variation in infiltration capacity for

sandy soils in a Texas drainage basin. He ascribed these differences to the

increased biological activity of the May to October period and, in particular,

to the production of wormholes. Horton suggested that wormholes would

operate before the whole soil was saturated (at suctions equivalent to the

wormhole diameters) because of the development of surface detention in

depressions, which pond before the main extent of the surface becomes

ponded. Many of Horton’s hypotheses have been validated by more recent

work, although current infiltration theory has been able to extend far

beyond his notion of a single controlling factor (soil surface versus soil suction). His emphasis on time and space variables are, however, still as relevant

today as they were 40 years ago.

Prediction of cumulative infiltration and time to ponding in soils which are

prone to structural deterioration and crusting remains a central problem of

applied soil physics and hydrology. Considering infiltration into an existing

crust, Hillel and Gardner (1970) developed a model in which the hydraulic

resistance of the crust was related to the conductivity of the underlying

transmission zone. They later utilized this theory as a method for obtaining

field values of K ( 0 ) and D(0) by deliberately imposing a crust of kaolin,

gypsum, or a porous ceramic plate on the soil and supplying water at a

negligible head to it.

At the scale of field or catchment hydrology infiltration has repeatedly

been modeled using equations based on those of Green and Ampt. However,

most assume a unique, single-value function of K and rl, (or rl, transformed in

terms of 0). Wilson et al. (1982), for example, compared three models of

increasing sophistication, which included increasing numbers of terms for air

resistance and viscous drag. They found that the most complex model

predicted infiltration reasonably well for dry soils, but all three models

overpredicted time to ponding for wet soils. In field validation tests they

found surface sealing occurred early during infiltration with wet soils, which

was not adequately predicted by any of the models.

In soils with roughened or unstable, bare surfaces, an “incipient ponding”

condition often occurs early in a rainstorm in which free water lies in small

depressions or furrows but there is no continuous water film. Surface ponding

(rl, = 0) now occurs if rl, is averaged spatially over large enough unit areas,

though a complete free-water film (overland flow) will not form if transmission pores, fissures, and holes exist which can drain the water at perhaps two

to three orders of magnitude faster than K,. In dried, cracking-clay soils, two

phases of infiltration and profile wetting thus occur (see Section IV,A,2).

It is useful at this juncture to compare the rainfall rates and K values we

may encounter in nature. Table I11 shows in schematic form, some equivalent



Table I11

Comparison of Rainfall and Hydraulic Conductivity Rates

Average rainfall





Equivalent rate

at ground



1 .O








Light rain

Steady rain

Heavy rain



2.8 x

2.8 x

1.4 x

2.8 x

5.6 x

1.4 x 10-5

2.8 x

Approximate K, for

various soils




Massive clays

Cracking clays

Sandy clays


Silt loams

Loamy sands

Fine to medium sands

rates for rainfall and K,, with the rainfall in units of millimeters per hour,

units frequently used in infiltration studies although less widely used in soil

physics or soil-plant water studies since rainfall events are not uniform for

periods of as long as an hour.

Surface sealing is a worldwide problem affecting freshly tilled soils which

are exposed to the full force of growing-season rains. In drier regions the

subsoil may contain little stored water for plant growth at cultivation time,

and sealing can seriously reduce the proportion of total rain stored in the soil

either by run-off (Epstein and Grant, 1967) or by increased soil evaporation

from surface-ponded water (Hamblin, 1984). Infiltration rates may be

reduced by several orders of magnitude in the crust. McIntyre (1958) showed

that crusts characteristically may have a surface “skin” with a very low

conductivity (e.g., K , = 5 x lo-’ m/s) overlying a crust ( K , = 5 x lo-* m/s)

of disaggregated material, while the underlying soil may have a K , value of


The susceptibility of the soil to surface sealing can therefore be determined

by tests such as Emerson’s (1967), but how do such stability tests relate to

rainfall parameters such as storm duration, intensity, and droplet energies?

These forces may be very substantial: Ghadiri and Payne (1981) demonstrated that localized impact stresses from raindrops range from 2 to 6 MPa

in the rebound corona for about 50 ms as a droplet hits a surface. Edwards

(1982) developed empirical functions relating runoff probability to soil

surface condition (crusted or not crusted at start of rain). The probability of

crusting given the particular soil type and rainfall was assessed from the

cumulative rainfall. Uncrusted soils were arbitarily defined as receiving

< 13 mm of rain since the last tillage operation. Observed and predicted

runoff values differed because of the creation, and then destruction, of a crust.



Unfortunately, this method seems limited in general application by the size of

the data base required and the interaction with unpredictable cultural


Whisler et al. (1979) used a modeling technique in which the soil physical

properties of the surface were time dependent, since the soil immediately

starts draining when V, < K,. In their solution they used published values of

K , surface flux, porosity, and Oi, 0,, and 8, for a crust and underlying soil.

They then allowed a finite depth of the soil surface to adjust from bulk soil to

crust values during infiltration, with parameters controlling the rate and

amount by which K , decreased up to, and after, crust formation. Their model,

however, still requires input parameters for the type of crust developing on

each soil. There is a substantial gap in our knowledge of the field behavior of

many soil types to varying rainfall conditions. The Food and Agriculture

Organization (F. A. O., 1979) has used simple textural and organic matter

formulas as crusting indices for global assessment purposes. The ratio of

coarse silt to fine silt plus clay and organic matter was found to be in good

agreement with susceptibility to crusting.

2. Infiltration with Surface-Connected Transmission Pores

It can be argued that, provided Vo is less than K , and the surface of the soil

does not slake and crust, transmission pores take no part in infiltration. This

may apply to coarse-and medium-textured soils, and even in clay soils with

cracks or cultivated shear planes, if V, is substantially less than K , (see

Table 111). Clothier and White (1981) used the scale relationships of D and K

converted to 8 and S, previously referred to in Section IV,A, to compare

constant-flux infiltration at small negative pressures and by conventional

ponded methods to identify the contribution of different-sized pores to the

infiltration of sandy field soils. At a value of -0.4 kPa (ECD = 740 pm) they

found 10-fold smaller values for S than those obtained by the ponding

method. In a further study on the effect of pore geometry on the shape of D(0)

curves, Clothier and White (1982) compared water content profiles from the

same soil before and after disturbance at the same small suction by constantflux infiltration. While the disturbed samples yielded the expected exponential D(8) function, the undisturbed soil had a near linear function (constant

with respect to 8). Similar low dependence of D on 8 has been reported by

Hamblin (1982) for undisturbed sandy loamy and sandy clay loam topsoils

and by Hamblin and Tennant (1981) for a loamy sand. Clothier and White

found their disturbed soil contained far fewer pores greater than 200 pm in

diameter than in the undisturbed soil. They called these “biopores” and

considered them partly responsible for the lower diffusivities of the unm2/s,

disturbed soil. [D* (linear diffusivity) of disturbed soil was 1.3 x



whereas the undisturbed D* = 4.1 x

m2/s]. These results support my

earlier comment that structural alteration changes the material properties of

soils, and hence all their derived functions. They also call into question the

assumption that such functions have a single form [such as an exponential

form for D(O)].

A theoretical treatment of infiltration in which noncapillary transmission

pores are present and operate has been considered by Scotter (1978), Beven

and Germann (1981), and Germann and Beven (1981). Transmission pores

which are open to the soil surface but closed at the base are more common in

nature than was traditionally expected or allowed for in classical soil physics.

This has led to reports in the literature of unexpectedly short response times

to water content changes deep in soil profiles after rain (Nulsen, 1980), even

in circumstances where ponding did not apparently occur first. However, it is

likely that ponding develops transiently and then ceases relatively soon, as

surface flow is channeled into the large (noncapillary) pores.

Beven and Germann (1981) and Bouma et al. (1982) described such

situations theoretically and experimentally. They suggested that K(O) can

increase by as much as four orders of magnitude over a pressure drop of only

10 kPa. Beven and Germann (1982) suggested that, from examples in the

literature, rainfall intensities of 1- 10 mm/h would be sufficient to generate

macropore flow in previously dry soils, but they stressed that antecedent

rainfall, initial soil water content (OJ, and actual storm intensities would give

rise to great variation in response.

Germann and Beven (1981) suggested a statistical approach with their

theory. This would provide field data on the proportion of the saturated

volume flux density contributed by their “macropores” (Qma), where



where c = pg/8p ( p is the density, g is gravity, and p is the viscosity), a

combination of terms for the flow of water in tubes from the Poiseuille

equation [see Eq. (13)], A is the total cross-sectional area containing n

vertical large pores, in which the porosity emais a proportionality constant:

Q ma

= - 2


ema= - Vp



where Vp is the volume of each tube and h is its height. The notion of a

proportionality “constant” still oversimplifies the real situation, and the

authors noted that their exponent (of 2) was only a first approximation and

did not fit published data well.

The volume of “drainage” pores has frequently been measured in the past

as the total porosity minus the water-filled pore space at field capacity.



However, the term “field capacity,” meaning the water content at which

measurable drainage ceases, is woefully inexact and justifiably open to

criticism (Ritchie, 1981). Laboratory estimates of the drained upper limit

taken from both disturbed and undisturbed samples may be seriously in error

because the representative elementary volume (REV) contains transmission

pores which are not included in the sample. Moreover, as we have seen, the

rate at which the soil wets also affects the way it drains, if transmission pores

are a significant feature of the soil. Germann and Beven’s analysis suggests

that a lognormal relationship exists between the proportion of large pores

(ems) and the large-pore volume flux density (Q,,). The proportion of

transmission pores need not necessarily be high to have a marked effect.

Pores greater than 3 mm in diameter in the cases examined by these authors

and by Bouma and Dekker (1978) represented no more than 2 or 3 % of the

total porosity. Studies which have compared near-saturation hydraulic

conductivities of soils with and without the transmission-pore contribution

have shown a velocity ratio for difference in K ( 8 ) of four times (Ritchie et al.,

1972) to several hundred times (Nulsen 1980), depending on Oi, V,, and the

degree of swelling and closure of cracks during the period of measurement.

The work of White et al. (1983) has yielded some interesting considerations

on transmission-pore infiltration. From rapid in situ measurements of S, Bi,

8,, and K O using a rainfall simulator (sprinkling infiltrometer), they found a

marked inflection in the surface-monitored $ / S curve at approximately

-0.35 kPa (equivalent to a mean exclusion value for noncapillary pores).












Chromic Vertisol (Houston Black Clay

with Gilgai)



0.2 m


F luvaquent

(Fine Clavev.

Mixed, Mesic)

FIG.5. Schematic representationsof a cultivated chromatic Vertisol (Houston Black Clay)

[redrawn from Ritchie et al. (1972)l and a Fluvaquent (alluvial clay) [redrawn from Bouma and

Dekker (1976)l demonstrating bi- and triscalar pedality.



There was also a high correlation with the reduction in coefficients of

variation in values of S at = -0.35 kPa, again suggesting that transmission-pore hydraulic behavior is highly variable, being the major component

in the very large CVs for K , and K(8).

Hoogmoed and Bouma (1980) laid stress on a “short-circuiting” process

(Beven and Germann’s “channeling”) during infiltration into cracking clays,

where water moves within an interconnected transmission-pore structure

which is not closed at the base, bypassing the matrix peds, particularly during

high-intensity rainfall events (Bouma et al., 1977). Horizontal infiltration into

peds was predicted to be larger per time increment than vertical movement

m/s compared with 11 x lop6 m/s).

under lower rainfall rates (3 x

Such polymodal soil structures are characteristic of Vertisols and calcareous

clay soils. Typical patterns are shown in Fig. 5 for a Vertisol from Ritchie et

al. (1972) and for a Fluvaquent from Bouma and Dekker (1978). They give

rise to some interesting considerations for water flow for plant roots (Section

V1,A). Note that both examples show a marked discontinuity of the pore

structure in the plough layer, which had a pronounced effect on the hydraulic

conductivity in each case.




Infiltration, particularly into dry soil, is dominated by suction gradients

(capillary potential gradients), but redistribution within the whole volume of

the soil is a consequence of both capillary and gravity forces. Flow equations

thus include both D(8) and K(8). The development of general and specific

forms of the combined Darcy flow and continuity equations and their

translation into diffusion terms is well covered in all recent works on soil

physics (Marshall and Holmes, 1979; Hillel, 1980).

In the case of a fallow soil with no alternative sink by plant roots, the

balance between wetting and draining may be taken as an imaginary plane

through the profile. In soils of higher K(8) values (mainly sands), this plane

remains recognizable but moves down the profile in a wave-like progression.

In slower-draining soils the movement proceeds more uniformly through the

wetted region, resulting in a continually decreasing flux at the transition

plane. The effect of gravity can only be ignored at small length scales (close to

alternative sinks such as the upward flux of water vapor to the soil surface

and to large cracks and the flux of the liquid water to plant roots) or in the

case of small infiltration quantities into some dry soils. Hillel (1977) has

published a number of computer simulations for water redistribution, with

simultaneous evaporation and intermittent rainfall, for typical clay, loam,

and sand soils. The clay soil, as we would expect, redistributes water over the



smallest depth but retains the highest water content in the upper parts of the

profile per unit time. Structural influences on unsaturated redistribution are

most noticeable where there is vertical or areal heterogeneity.

I . Vertical Heterogeneity

The effect of vertical discontinuity on water flow has been studied most in

relation to textural contrasts. For example, Hillel and Taplaz (1977) predicted water movement for sand over clay systems, while Clothier et al. (1978)

discussed the significance of variations in water flow through fine- over

coarse-textured soils. Structural variations which have developed from tillage

operations are not always so easy to distinguish in the field, although

penetrometer readings may identify compacted traffic pans and visual scoring

of changes in structure near the surface can give a surprisingly sensitive

indication of hydraulic behavior. Impedance to vertical water flow results in

perched water tables, abrupt inflections in potential gradients, and anaerobic

zones distinguished by mottling (see Section V,B,2). Such layering of hydraulic properties will nearly always result in some check or stress on crop growth,

either through gross differences in water availability to different parts of the

profile or through differential structures and inhibition of root growth into

discretely segregated parts of the whole soil volume. This increases the risk of

the crop’s inability to adapt to other sudden environmental stresses.

There is conflicting opinion, and a shortage of unambiguous evidence, on

the role of “short-circuiting” or preferred pathway flow in unsaturated soils

in which the pores do not reach the surface. In principle, all pores greater

than 30 pm in diameter should drain above $ = - 10 kPa and, as we recall

from Table 11, pores less than 30pm in diameter are smaller than most

longitudinally continuous holes created by roots, worms, or other biological

agents, Yet, there are occasional examples of very rapid water redistribution

at water contents substantially less than the drained upper limit, which

suggest that quite small vertically continuous pores are filled very rapidly,

perhaps as the result of local ponding of water with pockets of soil. This could

occur at the base of the plough layer, or in sand lenses, or in soils which are

initially moist but with negligible flux gradients. Quisenberry and Phillips

(1976) attempted to identify the contribution of transmission-pore flow to

solute transport and unsaturated water redistribution in a silt loam with an

organic Ap horizon. Figure 6a shows a characteristic redistribution profile

for tracer C1- (with chloride recalculated as concentration in the soil water

rather than total soil content, as shown in the original profile) and Oi,which

was less than the upper limit to available water (ULAW). The equivalent

displacement or piston-flow profile (x,xi),which would have occurred after

one hour’s redistribution if there had been no preferred pathway flow, is



CI‘ Concentration in Soil Water

Water Content (v/v)

0.26 0.34 0.42 0.48

Coefficient of Variation
















; 0.6





F1c.6. (a) Water contents and tracer chloride concentration in the applied water for a

cultivated Huntingdon silt loam, at 1 hr (V) and 30 hr

after application of 178-mm water.

Percentages refer to percentage water and chloride recovered. (Redrawn from Quisenberry and

Phillips, 1976.) (b) Coefficients of variation for Chloride concentration down the profiles on

undisturbed (m) and cultivated (0)Huntingdon silt loam (Quisenberry and Phillips, 1976).


indicated. The applied water and C1- had moved 0.7 m in the first hour, and

most of the applied water had moved through the profile in 36 hr. The effect

of tillage was noticeable as a bulge in water and Cl- profiles at 0.15 to 0.2 m,

quantified by plotting the CVs of Cl- concentration with depth for the tilled

and nontilled soils (Fig. 6b). The tilled surface soil (0.15 m) showed a gradual

increase in CV to the depth of the cultivation but then a sudden jump in CV

(from 60-120%) below that, whereas the untilled soil showed a smaller

increase to 0.1 m and had CVs of only 40% in the subsoil. The authors take

this inflection in CV distribution with depth to indicate changes in pore

continuity, with breaks at 0.15m at the base of the ploughed soil. This

analysis, utilizing the change of CV with depth to identify structural

heterogeneity, is similar to that of White et al. (1983). It offers scope in

identifying the contribution of preferred pathway flow at different values of 8.

It should be more widely used, especially in attempting to distinguish flows

resulting from textural versus structural differences.

Soils having natural differences of either texture or structure with depth are

particularly difficult to manage in relation to their water status for crop

growth. Many agricultural soils have finer-textured subsoils than topsoils,

such as the “textural B horizons” of red brown earths (Haploxeralfs and

Rhodoxeralfs), Pullman clay loams in Texas (Torrenic paleustolls), clay with

flint soils in Europe, and tropical Alfisols (Tropuldalfs). Their subsoil

hydraulic conductivities are frequently too slow for good drainage in wet

environments or for rapid enough redistribution of water in seasonally dry



climates to allow deep root penetration. Roots then become confined to

surface layers, with a host of subsequent problems which give rise to yield

depression or even total crop loss. Land management techniques for reducing

vertical heterogeneity is a practical remedy in these cases.

In drought-stressed environments the relationship between crop growth

and water use may be known well enough for the production value of each

millimeter of soil water to be calculated. Deliberate manipulation of soil

structure by landforming, mulching, subsoiling, or chemical stabilization can

improve water-use efficiency so greatly that it pays for itself. While the use of

gypsum for unstable soils and subsoiling (deep ripping, chiseling) are both

widely used as individual amelioration treatments, a notable example from

the Riverina irrigation district in South Eastern Australia has made simultaneous use of four methods to improve the physical properties of a duplex red

brown earth (Rhodoxeralf) for stone fruit production. These soils are prone

to crusting and have low subsoil conductivities, because of both their high

clay content and low Ca: Mg ratios. Cockcroft and Tisdall(l978) reported a

system of soil improvement in which gypsum was injected into the subsoil

during deep ripping, and the top 0.6 m was then cultivated with incorporated

straw and green manures. The surface between trees was covered with straw

mulch to help suppress weeds, reduce crusting and temperature fluctuations,

and increase earthworm numbers. Tisdall (1978) found the number of

earthworms increased on improved plots from 150 to 2000 per m2, with an

associated four-fold increase in pores emptying at - 4 kPa. Infiltration of

50 mm of sprinkler irrigation water was accomplished in 1 min compared

with 83, and yields of stone fruit increased from 18 to 75 ton/ha. The example

is also interesting in relation to the role of earthworm channels in an

unsaturated water environment. Clearly, the channels functioned despite the

“nonponded” surface. However, the soil was never allowed to dry

beyond - 3.0 kPa, and therefore many of the narrower earthworm holes

could have been filled with water much of the time.

2. Areal Heterogeneity

Areal heterogeneity at scales up to tens of meters occurs in many tropical

and subtropical soils which have developed over prolonged weathering and

erosional sequences on old landforms. They have high CVs (35-100%) for

particle size distribution and depth of horizon (Wilding and Drees, 1978) as a

consequence. Many Alfisols and Ultisols are mosaics of different mechanical

composition (with associated changes in base status, pH, and organic carbon

content), whereas some Vertisols and other Alfisols develop “gilgai” phenomena with regular repeat sequences in relative heights of 0.1 to 0.5 m in a

hummock and depression sequence related to differential swelling and

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IV. Water Flow in Agricultural Soils

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