Lal R., Shukla M.K. Principles of Soil Physics
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50 5.4 1 15 4.4 21.6 0.046 0.141 0.293
65 5.5 1 15 4.5 26.1 0.038 0.124 0.300
85 5.6 1 20 4.6 30.7 0.033 0.108 0.230
115 6.8 1 30 5.8 36.5 0.027 0.093 0.193
145 6.5 1 30 5.5 42 0.024 0.083 0.183
180 7 35 6 48 0.021 0.075 0.171
(d) The parameters of the Philip equation are obtained by plotting column (8) and (9) and
fitting a linear relationship:
S=2.66; and A=0.11
(e) The parameters of the Green–Ampt equation are obtained by plotting column (7) and
(9) and fitting a linear regression line
i
c
=0.22; b=1.74
Example 14.2
Use the same data as given in Example 14.1 and calculate the parameters of the
Kostiakov and Horton infiltration equations.
Solutions
The parameters of the Kostiakov equation: B=1.387 and n=0.397 The parameters of
the Horton equation: i
c,
=0.239 cm min−
1
, i
0
= 1.068 cm min
−1
, and k=0.08.
PROBLEMS
1. Consider the following data from the double ring inflltrometer test conducted in
plow till vs. no-till experiments over a 3-hr period. Fit Green and Ampt, Philip,
Kostiakov, Mezencev, Horton, and Holtan models to these data, and compute the
parameters of these equations.
Cumulative infiltration (cm)
Cumulative Infiltration (cm)
Time (min) Plow till No-till Time (min) Plow till No-till
0 0 0 100 64.6 137.1
10 9.2 21.6 110 68.5 148.8
20 19.6 39.2 120 74.4 158.6
30 27.4 54.8 130 78.3 166.4
Principles of soil physics 404
40 32.2 68.5 140 82.2 178.2
50 39.2 82.2 150 86.2 186.0
60 45.0 94.0 160 90.1 193.8
70 49 105.7 170 94.0 201.7
80 54.8 115.5 180 97.9 209.5
90 58.7 127.3
2. Horizontal infiltration test was conducted in a tube of 50 cm
2
cross-sectional are.
After 10 minutes, the cumulative infiltration was 1.2 ml. Calculate the expected
cumulative infiltration and infiltration rate after 30 min, 1 hr, 3 hrs, and 6 hrs. Use Philip
equation and calculate S for the given time intervals.
3. Infiltration rate monitored as a function of cumulative rainfall was found to be 25
mm h
−1
when a total of 80 mm of water had infiltrated. If final steady state of infiltration
is 4 mm h
−1
, calculate infiltration rate at a cumulative infiltration of 150 and 300 mm.
4. Using the necessary data from Problem 3, calculate how much water can be
delivered to the root zone of a crop without exceeding the soil’s infiltrability if the
sprinkler irrigation rate is 20 and 25 mm h
−1
. What will be the highest steady state
infiltration rate for 250 mm depth of irrigation in the shortest possible time?
5. A double ring infiltrometer study yielded the following results.
Cumulative infiltration (mm) Infiltration rate (mm h−1)
50 10
100 6
Use the Green and Ampt equation and compute infiltration rate corresponding to a
cumulative infiltration of 400 mm. Assume that the steady rate of infiltration is 2 mm h
−1
.
6. Using the information in Problem 5, calculate the amount of water provided to the
root zone of a strawberry crop being irrigated with an overhead sprinkling irrigation
system at the rate of 10 mm h
−1
. At what rate should the irrigation be supplied to provide
200 mm of water in the shortest time?
7. Assuming the K
s
of soil used in Problem 2 to be 1 cmh−
1
, estimate cumulative
infiltration and infiltration rate for a vertical column at the end of time intervals given in
Problem 2.
8. Refer to Problems 2 and 7 above and assume that the soil characteristics defined
above are applicable under field conditions with a natural slope of 5%. How much runoff
will occur in storms with constant rainfall intensities of 20 and 50 mm h−1 for 15
minutes and 1 h each?
Water infiltration in soil 405
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incipient ponding. Soil Sci. Soc. Am. Proc. 28:614–619.
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Water infiltration in soil 407
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Principles of soil physics 408
15
Soil Water Evaporation
Soil water evaporation is an important component of surface energy balance. The rate and
quantity of evaporation from a soil surface is a complicated process affected by many soil
characteristics, tillage, and environmental interactions. Evaporation also affects plant
available water content of soil and causes salinization in irrigated lands. It is known that
energy and water availability largely dominate the process of evaporation, thus on an
average these broad principles can be used to estimate direct soil water evaporation.
15.1 INTRODUCTION
Evaporation is the process of change of the state of water from a liquid to gaseous phase.
It is a principal process of water cycling in the hydrosphere. Evaporation from a
landscape may occur from plant canopies, free water surface, or soil surface. Evaporation
of water from bare soil (i.e., in the absence of vegetation) is the process by which water is
lost from the soil to the atmosphere. If the evaporation process is not controlled, a
considerable amount of water can be lost from an irrigated or a rainfed cropland.
Evaporation takes place from plowed land, shallow farmland, from soil between tree and
row crops, and agricultural lands with no vegetation.
During planting and germination period, evaporation can reduce soil water content
significantly and can hamper plant growth.
There are four conditions for evaporation from soil to occur. One, the evaporation
from a bare soil takes place continuously, provided there is a continuous supply of
energy. The amount of energy required is the latent heat of water for evaporation, which
is about 590 cals/g of water evaporated at 15°C. The soil body itself, which gets cooler
after rather than before evaporation, can supply this energy. Alternately, it can come from
the advected or radiated energy from the surroundings. The second and third physical
conditions for evaporation from bare soils are: the vaporpressure gradient between the
soil and the atmosphere, and the transport of vapor away from soil by diffusion and/or
convection. The energy for evaporation and vapor removal are generally external to the
evaporating soil and are greatly influenced by meteorological factors (i.e., air
temperature, humidity, wind velocity, and radiation). The evaporation rate is determined
by the external evaporativity or water conductivity of the soil. The fourth condition is that
there is a continuous supply of water within the soil body to the evaporating surface. This
condition depends on both physical and conductance properties of soil. Some of them are:
water content of soil body, soil water potential, hydraulic conductivity of soil, texture,
compaction, soil horizonation or layering, and depth to the water table.
An important condition in poorly drained soils is evaporation in presence of a shallow
ground water table. The evaporation occurs at a nearly steady state level and water
content of profile remains almost the same. In the absence of a water table, the
evaporation will dry the topsoil and the process is mostly in an unsteady state. The flow
domains during the evaporation process may be one-dimensional or three-dimensional.
The flow processes may be isothermal or non-isothermal and there may be the
interactions between liquid flow and temperature gradients, conduction of heat, and vapor
in the soil domain. The cracks inside the soil matrix form the secondary evaporation
planes. The evaporation also depends upon the environmental conditions, which can be
regular (i.e., diurnal, seasonal) or irregular (i.e., spells of cool and warm weather and of
rewetting and drying). The presence of surface mulch, depth of soil, and degree of
homogeneity of soil also alter evaporation from the soil surface.
15.2 THE EVAPORATION PROCESS
Following three processes summarize the evaporation of water from soil surface.
15.2.1 Transport of Water to the Soil Surface
As the evaporation process begins at the soil surface, a suction gradient is established
between the surface soil and the layer beneath. This gradient forces the water to move
upwards through capillary rise and supplies the water to the soil surface. This process
continues as long as the soil underneath has enough water storage. The transfer of water
from soil underneath is facilitated easily and for a much longer duration immediately
after irrigation or a rainfall event, when soil water content is high.
15.2.2 Uninterrupted Supply of Heat to Change the State of Water
Solar energy is the most predominant source of heat for water evaporation. There are
other minor sources of energy also, e.g., exothermic reactions, microbial activity, etc. The
energy balance of the soil depends on physical and thermal properties. The latent heat of
vaporization changes the water from a liquid to vapor state.
15.2.3 Transfer of Water Vapor from Soil Surface to Atmosphere
The vapor pressure immediately above the evaporating soil surface is lower than the
vapor pressure inside the soil. This differential pressure creates a vapor pressure gradient,
which enables water vapor to escape from soil to the atmosphere through the process of
convection and diffusion.
15.3 SOIL DRYING DURING EVAPORATION
Principles of soil physics 410
Evaporation leads to the loss of water, with attendant drying and depletion of the soil
moisture reserves. This process of soil drying occurs in three distinct stages (Fig. 15.1)
(Fisher, 1923; Pearse et al., 1949).
15.3.1 Initial Stage
When soil is very wet, evaporation of soil water is governed by external atmospheric
conditions rather than soil properties. The soil has enough water, therefore, conductivity
and supply of water to soil surface are at the potential rate. The evaporation rate during
this stage is denoted as “potential evaporation.” This stage is sustained over time because
as the water content of soil profile decreases the hydraulic conductivity also decreases.
However, hydraulic gradient increases and compensates for the reduction in hydraulic
conductivity. This situation is analogous to the
FIGURE 15.1 Three stages of
evaporation during simultaneous
drainage and evaporation from initially
saturated profiles of sand, silt, and
clay. (Modified from Hillel and van
Bavel, 1976.)
flux-controlled stage of water infiltration into soil. Some soil properties, which influence
the meteorological or atmospheric factors, include soil surface reflectance, mulch, ground
cover, etc. The duration of the first stage of the drying process is lower for coarse-
textured than fine-textured soils because fine-textured soils retain high water content and
have more conductivity than coarse-textured soils. Figure 15.1 shows that the duration of
the first stage of drying is in the order clay > loam > sand. The duration for first stage is
also lower for a structureless than for a structured soil. Mulching increases the water
content profile but shortens the duration of first stage of drying (Fig. 15.1). The duration
of first stage is inversely proportional to soil water diffusivity (D
0
).
15.3.2 Intermediate Stage
Soil water evaporation 411
The evaporation rate during this stage is no longer at the potential rate but starts
decreasing gradually with time. Soil starts to heat up and is not able to conduct water to
the surface at the potential rate. The water content of the soil profile is decreased further
as is the hydraulic conductivity. The hydraulic gradient can no longer increase
significantly because the soil water pressure head is close to the partial water vapor
pressure. The time at which the decrease in hydraulic conductivity is not compensated by
hydraulic gradient denotes the end of first stage of drying. The depth of dry zone
increases as does the hydraulic resistance of soil to water transport. The rate of
evaporation during this stage is directly proportional to soil water diffusivity.
15.3.3 The Final Stage
The evaporation rate during this stage is relatively steady at a low rate and can continue
up to several days. During this stage the liquid-water conductance totally ceases. This
stage is also known as the vapor diffusion stage, since water transmission is primarily due
to a slow process of vapor diffusion. The evaporation rate is determined by soil properties
(affinity of the soil for water) rather than the evaporative demand of the atmosphere.
15.4 THEORY OF EVAPORATION
Specific processes of evaporation depend upon the presence of the water table at shallow
depth, horizonation, and soil temperature region.
15.4.1 Steady Evaporation in the Presence of a Water Table
The essential and necessary condition for steady state flow is that the rate of change of
flux density with depth is zero (dq/dz=0). Moore (1939) first studied the vertical steady
state flow of water from a water table through soil profile during evaporation. Philip
(1957), Gardner (1958), Ripple et al. (1972) discussed theoretical solutions for steady
state evaporation. Mathematically, the steady upward flow can be described by the
Darcy– Buckingham equation, for boundary condition z=0, Φm=0 and z is positive
upward from the ground water table. The steady state upward flow or evaporation (q
e
)
can be expressed as follows [see also Darcy law for unsaturated flow] and see Eq. (13.3):
(15.1)
In terms of soil-water diffusivity [see Eq. (13.24)], the steady state evaporation is given
by
(15.2)
where D(θ) is hydraulic diffusivity, θ is water content, K(θ) is hydraulic conductivity, z is
height above the water table, and Φ
m
is suction head. Eq. (15.1) shows that for dΦ
m
/dz=1,
q=0. Eq. (15.1) can be rearranged as follows
Principles of soil physics 412
(15.3)
separation of variables results in
(15.4)
Integrating Eq. (15.4) to depths between 0 to z and suction gives the following expression
in terms of depth of soil profile
(15.5)
Similarly, Eq. (15.2) can be integrated for depths between 0 to z and following
relationship in terms of z is obtained
(15.6)
Solutions of Eqs. (15.5) and (15.6) require prior knowledge of the functional
relationships between K(Φ
m
) and Φ
m
and K(θ) and D(θ). For solving Eq. (15.5), Gardner
(1958) proposed following relationship between Φ
m
and K:
(15.7)
where parameters a, b, and n are constants and are functions of type of soil. These
parameters are soil-specific and need to be determined for each soil separately.
Transferring Eq. (15.7) into Eq. (15.1) gives the following equation for evaporation rate
(e) estimation
(15.8)
Transferring Eq. (15.7) into (15.5) gives the following equation, which provides the
suction distribution with depth of soil for different fluxes
(15.9)
Steady rate of upward flow and evaporation rate from water table as a function of the
suction prevailing at the soil surface for a sandy loam soil with n=3 is presented in Fig.
15.2 (Gardner, 1958). Fig. 15.2 shows that a
Soil water evaporation 413