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8 INFILTRATION AND SOIL MOISTURE

8.1 Infiltration When rain falls upon the ground it first of all wets the vegetation or the bare soil. When the surface cover is completely wet, subsequent rain must either penetrate the surface layers if the surface is permeable, or run off the surface towards a stream channel if the surface is impermeable. The infiltration characteristics of soil constitute an important variable that influences the absorption of the part of rainwater in the soil medium and the consequent runoff of the rest to streams.

If the surface layers are porous and have minute passages available for the passage of water droplets, the water infiltrates into the sub surface soil. The downward flow of water through the surface layers of the soil (profile) is called infiltration. Once infiltration water has passed through the surface layers, it percolates downward under the influence of gravity until it reaches the zone of saturation at the phreatic surface.

Infiltration is a typical example of non-steady flow of water. The driving force for the water entry is the gradient of the pressure head between the wetting front, the soil surface and gravity. The gradient of the pressure head decreases with time, because of the advancing wetting front. When applied at the soil surface, water changes over time the distribution of water content in the soil profile. The following zones (Bodman and Coleman, 1944) can be distinguished in the soil profile as shown in Fig 8.1.

The saturated zone is a very thin zone of the soil surface and extends to a depth of a few millimetres.

The transition zone represents a rapid decrease in water content between the saturated zone and the nearly saturated transmission zone. Its thickness ranges between few millimeters to a few centimeters.

The transmission zone is the conveyance zone for the infiltrating water. In this zone there is little change in water content. This is a lengthening unsaturated zone with nearly uniform water content. Here the suction gradients are negligible and water movement is primarily due to gravity.

The wetting zone is a thin zone where water content changes from its initial value to the value of the transmission zone. The wetting front is the visible limit of water penetration, where the gradient of the pressure head is very large. It forms a sharp boundary between wet and dry soil.

The volume of water that has infiltrated into the soil, called cumulative infiltration, I, when the volume fraction passes from i to is of the form:

Where s is the distance in the direction of flow and the integration is done from 0 to infinity. As a result of decreasing pressure head with time, the rate of infiltration decreases monotonically, up to an asymptotic value, called steady state infiltration rate. The only driving force is then only gravity. The infiltration rate may be expressed as:

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Fig 8.1 The four zones of the infiltration profile

Source: (Bodman, Coleman, 1944)

Generally, under ponded conditions, the infiltration is at a high rate at the beginning, decreasing rapidly and then more slowly until it approaches a constant rate as shown in Fig 8.2. As water moves deeper into the soil, filling the pores, the hydraulic rate goes on decreasing and hence the infiltration rate. The dispersion of aggregates, blocking of the cracks and channels, swelling of the colloids also reduce the infiltration rate. Soil pores are also blocked and the infiltration rate is reduced significantly, when water is turbid.

Fig 8.2 Rate of infiltration as a function of time under ponded conditions

Source: (Ghildyal and Tripathi, 2005) In the general progression of the hydrological cycle beginning with atmospheric water vapour and ensuring precipitation, the top layers of material near the land surface provide the first of the subsurface

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storages. Under soil moisture, consideration is given to water in those layers of the soil near the surface that contain the rooting zone of vegetation.

The study of soil moisture is of vital interest to the agriculturalist, especially in those countries where irrigation can improve the yield of food or cash crop. More recently, the role played by soil moisture content in the management of greater yields and flood control is being more fully appreciated.

8.2 Infiltration Capacity The intake rate or infiltration capacity of a soil is a measure of its capacity to take and absorb the ponded water or the water applied. Different types of soil allow water to infiltrate at different rates. Each soil has a different infiltration capacity, i, measured in mm/h or in/h. For example, rain falling on a gravelly or sandy soil will rapidly infiltrate and provide the phreatic surface below the ground surface, even heavy rain will not produce runoff. However a clayey soil will resist infiltration and the surface will become covered with water even in light rains. The rainfall rate affects how much rain will infiltrate and how much will run off. Infiltration capacity is usually designated fc and actual rate of infiltration can be expressed as;

i=ic when I ≥ ic

i=I when I ≤ ic

8.2.1 Factors affecting Infiltration Rate The infiltration rate of a soil is the sum of percolation and water entering storage above the groundwater table. The infiltration capacity of a soil is affected by surface sealing caused by;

i. Formation of a thin contact layer on the soil surface ii. Soil compaction formed due to plough pan

iii. Soil cracking due to drying of soil iv. Crop rotation v. Tillage operation

vi. Presence of salts in soil vii. Soil erosion which exposes either the less permeable or the more permeable soil from beneath the

ground surface and viii. Variations in temperature of soil.

8.2.2 Other Factors which Affect the Infiltration Capacity K is a function of surface texture: if vegetation is present K is small, while a smoother surface texture such as bare soil will yield larger values. io and ic are functions of both soil type and cover. For example a bare, sandy or gravelly soil will have high values of io and ic, and a bare clayey soil will have low values of io and ic, but both values will increase for both soils if they are turfed, ic is a function of:

i. Slope- up to a limiting value (varying between 16% and 24%) after which there is little variation,

ii. Initial Moisture Content- the drier the soil initially, the larger ic will be, but the variation may be comparatively small, and

iii. Rainfall Intensity- if the intensity is increased, then ic. will increase. This parameter has greater effect on ic than any other variable

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Infiltration rate appears to be largely controlled by the surface pores. Even just a small increase in the hydrostatic head over these pores results in an increase in the flow through the soil surface. The hydrostatic head over the smallest cross-section of a pore continues to increase with the rainfall intensity until a limiting value is reached, where runoff prevents any further increase. However, it seems unlikely that this limiting condition is often reached in natural conditions.

Exposed soil can be rendered almost impermeable by the compacting impact of large drops coupled with the tendency to wash very fine particles into the voids. The surface tends to become ‘puddled’ and the fc value drops sharply. Similarly, compaction due to man or animals treading the surface or to vehicular traffic can severely reduce infiltration capacity.

Dense vegetal cover such as grass or forest tends to promote high value of fc. The dense root systems, all providing ingress to the subsoil, the layer of organic debris forming a sponge–like surface, burrowing animals and insects opening up ways into the soil cover preventing compaction and the vegetations transpiration removing soil moisture, all tend to help the infiltration process.

Generally it can be said that infiltration rate is affected by radial moisture content, condition of soil surface, hydraulic conductivity of soil profile, texture, porosity, vegetative cover as well as degree of swelling of soil colloids and organic matter.

Other effects that marginally affect infiltration rate are frost heave, leaching out of soluble salts and drying cracks which increase fo and the entrapping of interstitial air, which affects viscosity and has a direct effect on resistance to flow. Other things being equal fo and fc will have higher value during the warmer seasons of the year. The fluid characteristics also come into play; water entering the soil could contain impurities. Its turbidity is also an important factor since the suspended particles tend to block the pores and reduce the amount of infiltration. The water temperature affects its viscosity and therefore the amount of water infiltrating.

8.2.3 Variation of Infiltration Capacity with Time Figure 8.3 shows the relationship between the infiltration capacity of three different types of soil and time. It represents the instantaneous rate of water (cm/hr) entering the soil medium, after the start of rainfall or application of water with respect to time lapsed. The intake rate declines with time.

Fig 8.3 Relationship between the intake rate of soil and time Source: (USDA, 1964)

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8.2.4 Variation of Total Intake with Time The relationship between the total intake of soil with time for three different types of soil is shown in Fig. 8.4. It is an expression of the time required for a soil to absorb a specified amount of water. It helps to determine the speed at which the wet front advances in a field.

Fig 8.4 Relationship between the cumulative intake and time for three soils

Source: (USDA, 1964).

8.3 Methods of Determining Infiltration 8.3.1 Infiltration Indices i) The Φ–index, defined as the average rate of loss such that the volume of rainfall in excess of that rate will be equal to the volume of direct runoff rate, which the rainfall volume equals the volume of runoff, is one of the more commonly used method for approximation of infiltration losses. The method assumes a constant value for the intake rate of rainwater into the soil for the full duration of the rainfall.

Another method known as W-Index considers the initial abstraction, but since determination of the initial values of abstraction is difficult, this method is not popular. The Φ-index is always equal (for uniform rain) or greater than the W–Index.

ii) The W-index is the average rate of infiltration during the period when the rainfall intensity exceeds the infiltration rate and is given by;

ft

SRPIndexW ( 8.1)

where P = total storm precipitation (cm), R = total surface runoff (cm), S = depression and interception losses (cm), tf = time period (in hours) during which the rainfall intensity exceeds infiltration rate; sometimes, it is taken equal to the rainfall period, and W = average rate of infiltration (cm/hr).

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The W-index is more accurate than the Φ-index because it excludes the interception and depression losses which are considered as a part of infiltration in the latter. Thus W-index is always less than Φ-index. Wmin index, the minimum values of W-index is called Wmin index is obtained, when the soil is very wet. At that stage, because the effect of the depression storage and interception losses is negligible, W-index and Q index are approximately equal. It may be noted that both W-index and Φ-index vary from storm to storm even for the same basin (Arora, 2007). The Φ index gives the average infiltration of rainwater. The remaining volume of rainfall, which flows out as surface runoff is called the excess rainfall volume and is considered to be equal to the excess rainfall runoff volume i.e. the excess runoff volume of a storm hydrograph after separation of the base flow from it. The time period during which the excess rainfall occurs is called the effective time period (tc)

Procedure for Determination of the Φ–Index

i. Draw the hyetograph of the storm rainfall and compute the total volume of rainfall ii. Compute the excess runoff volume from the storm hydrograph by separating the base flow from it

iii. Subtract (ii) from (i) to determine the total intake of rainwater into the soil iv. Divide the value at (iii) with the effective rainfall period to get the Φ–index (cm/hr)

Therefore;

)(infinf

)(infintint)/(

c

c

tperiodallraEffectiveoccursrainexcessnowhenperiodduringonInfiltratiiltrationTotal

tperiodallraEffectivesoiltheowaterofakeTotalhrcmindex

Example 8.1

A storm with 13cm precipitation produced a direct runoff of 6.0cm. The time distribution of the storm is as given in the Table 8.1. Estimate the -index of the catchment..

Table 8.1 Time Distribution of the Storm Time from start of storm 1 2 3 4 5 6 7 8 Incremental rainfall in each hour 0.45 0.70 1.83 2.50 3.36 2.70 0.97 0.59

Solution Plot the rainfall hyetograph as in Fig 8.5.

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0.00

0.50

1.00

1.50

2.00

2.50

3.00

3.50

4.00

1 2 3 4 5 6 7 8

Phi-index = 1.076

Time, h

Rainfallintensity,cm/h

Fig 8.5 Rainfall Hyetograph

Total precipitation P = 13.1 cm Total Runoff Q = 6.0 cm

hrcmt

QPWr

index

/89.08

61.13

Since the –index should be more than 0.75 (non-uniform rainfall). The rainfall in the first second and eighth hour is ineffective in producing excess rain. Therefore the effective time period, te = 8 – 3= 5 hrs.

076.1538.5

559.07.045.089.08

inf

xt

periodallraeffectiveduringonInfiltratiindexe

Check

The –index is marked off on the hyetograph as shown above. The area of the hatched area above the –index line should equal to the given runoff.

= (1.83 – 1.076) + (2.5 – 1.076) + (3.36 – 1.076) + (2.7 –1.076) = 6 cm which is as given

Example 8.2

A catchment area of 25km2 has one recording gauge. During a storm, the mass curve of the rainfall was recorded in Table 8.2 as follows:

Table 8.2 Mass Curve of Rainfall Time from start of storm 0 3 6 9 12 15 18 21

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Accumulated rainfall 0 10 21 39 50 65 79 100

If the volume of rainfall due to the storm is 1.5 x 106 m3, estimate the –index of the catchment.

Solution Total runoff volume 36105.1 m

Catchment area 225km

mmmmxmx

areaCatchmentvolumerunoffTotaldepthrunoffTotalQ

6006.01025105.1

26

36

Total Precipitation, P = 90mm

Total Infiltration mmQP 4060100

hrmm

hrmmt

QPindexWr

/9048.1

/2140

2160100

Since the Φ–index should be greater than the W-index, the Φ–index is a little more than 1.9048mm/hr, therefore causing infiltration to the ground every three- hour interval, more than 3 x 1.9048 = 5.714 mm.

Incremental rainfalls are worked out in the Table 8.3. From the values of incremental rainfall calculated it can be observed that, no excess rainfall occurred in two out of seven (those values less than 5.714- the average value of infiltration in three hours). Hence the excess rain must have fallen in 5 x 3 = 15hours. Hence the effective time period, te = 15hrs.

Table 8.3 Incremental Rainfall Time from start of storm Accumulated Rainfall (mm) Incremental rainfall in each interval

0 0 - 3 3 3* 6 8 5* 9 26 18

12 50 24 15 70 20 18 89 19

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21 100 11

hmmindexWhrmm

index

/9048.1/133.215

3215

3540

Example 8.3

The following mass curve shown in Table 8.4 was obtained for a 21 hour effective rainfall period that occurred on the catchment area of 40 km2. Calculate the ordinates of the effective rainfall hyetograph and the runoff volume, when the – index is 0.5cm/hr.

Table 8.4 Mass Curve of rainfall Time from start of storm (h) 0 3 6 9 12 15 18 21

Accumulated rainfall 0 1.5 4.0 6.0 6.5 9.0 12.0 14.0

Solution

A tabular solution of the problem is given Table 8.5. First the incremental rainfall in a time, t is calculated. The infiltration losses in a given interval are obtained by multiplying the –index with the corresponding time interval. The hyetograph ordinates are then obtained by subtracting the infiltration losses from the corresponding incremental rainfall in a time t. The ordinates of the rainfall intensity are obtained by dividing by the time interval.

Table 8.5 Determination of Infiltration Parameters Time interval (h)

Accumulated Rainfall (cm)

Rainfall in Time (cm)

Infiltration Losses –x (cm)

Hyetograph Ordinate(cm)

Rainfall Intensity (cm/hr)

0-0 0.0 0.0 0.0 0.0 0.00 0-3 1.5 1.5 1.5 0.0 0.00 3-6 4.0 2.5 1.5 1.0 0.33 6-9 6.0 3.5 1.5 2.0 0.67 9-12 6.5 3.0 1.5 1.5 0.50

12-15 9.0 6 1.5 4.5 1.50 15-18 12 6 1.5 4.5 1.50 18-21 14 8 1.5 6.5 2.17

Direct runoff volume from the catchment = summation of volumes of runoff during each time period, from the catchment

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= Area of the hyetograph bars x catchment area Area of hyetograph bars = 3hr (0.33+0.67+0.50+1.5+1.5+2.17) cm/h = 20.01cm = 0.2001m Catchments area = 40km2 = 40x106 m2 Therefore volume of direct runoff = (0.2001x40x106) m3 = (8.004x106) m3 8.3.2 Infiltrometers In this method characteristics of a soil are determined by ponding the water in a metal cylinder after installing it on the ground surface and then measuring the rate of absorption of ponded water into the ground surface by registering the fall of water level in the cylinder.

An infiltrometer is a wide diameter, short tube surrounding an area of soil. One ring (infiltrometer) may be used but this gives a high degree of variability in the measured data due to uncontrolled lateral movement of water from the cylinder after the wetting front reaches the cylinder bottom. For this reason, two rings are usually used to minimise the above limitation. This is achieved by ponding water in buffer area around the first cylinder by providing a concentric cylinder of larger diameter, which also acts as a guard cylinder. The measurement by cylinder infiltrometers is affected by the thickness of the cylinder material, the type of beveling of the cylinder bottom, the method of driving the cylinder into the soil and the depth of cylinder installation.

Method of Measurement

Two concentric cylinders of rolled steel 2mm thick, 25cm height and of diameters 30mm and 50mm are driven into the ground up to a depth of 15cm with a wooden mallet. A point gauge is fixed on the inner cylinder for measurement of the depth of water in it as shown in Fig. 8.6.

Fig 8.6 Concentric ring infiltrometers installed in the field. A measured quantity of water is added to the inner cylinder up to the desired level. To prevent any puddling or sealing of the ground surface inside the inner cylinder, a jute matting is recommended to be placed while pouring water. After the cylinder is filled to three-quarters of the height from the ground surface, the matting is removed. The buffer area between the two cylinders is also filled with water and the level of water is maintained approximately at the same level in both cylinders. The water depth is measured at regular intervals and infiltration is calculated for each interval. Care is taken to add water after each reading in order to maintain a constant head in the inner cylinder, for infiltration. Samples of the recorded results are shown in Table 8.6.

15cm 30 cm 10 cm

6 to 12 cm GSL

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Table 8.6 Results from Infiltrometer Measurements

The infiltration rate of the soil for an area is computed by taking measurements at different points of the soil and then averaging the data collected. Care should be taken to avoid points where there are abnormalities in the soil like soil crackling, plant roots, surface sealing, etc in the soil.

Such tests give useful comparative results but they do not simulate real conditions and have been largely replaced by sprinkler test of larger areas. Here the sprinkler simulates rainfall, and runoff from the plot is collected and measured as well as inflow. The difference is assumed to have infiltrated.

Though rain simulating sprinklers are a good deal more realistic than flooded rings, there are still limitations to the reliability of results thus obtained, which give higher values of infiltration than natural conditions do.

8.3.3 Other Methods for Determining Infiltration Capacity i. Observation from infiltration pits and ponds: By noting the depression in the level of water in the

pits and ponds and deducting the loss due to evaporation, an idea about the infiltration rates in such soils can be obtained.

ii. Artificial rain simulators on a small area of land of 0.1 to 50m2, water is applied by artificial

showers at a uniform rate. The resulting surface runoff is measured and the infiltration capacity of the soil is determined (Raghunath, 2006).

8.3.4 Infiltration Models The methods explained below fall into three main categories and are considered easy to use and yield scientifically based estimates using soil hydraulic and climatic parameters representative of the prevailing conditions. The categories are; i) Richards’s Equation Models, ii) Empirical Models and iii) Green Ampt Models. i) Richards Equation For flow in a porous medium, part of the cross-sectional area A is occupied by soil or rock strata, so the ratio Q/A does not equal the actual fluid velocity, but defines a volumetric flux, q, called the Darcy flux. Darcy’s law for flow in a porous medium is written as;

fKSqAQ

(8.2)

where K is the hydraulic conductivity of the medium.

Elapsed time (min)

Water surface distance from a Reference level

Infiltration during elapsed time

Before filling (cm)

After filling (cm)

Depth (cm)

Average (cm/h)

Accumulated Depth (cm)

0 0 10.0 - - - 5 8.3 10.0 1.7 20.4 1.7

10 9.0 10.0 1.0 12.0 2.7

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In the above equation, Darcy’s law was developed to relate the Darcy flux, q, to the rate of head loss per unit length of medium Sf. Consider flow in the vertical direction and denote the total head of the flow by h; then

zhS f / where the negative sign indicates that the total head is decreasing in the direction of flow because of friction. Darcy’s law is then expressed as;

zhKq

(8.3)

Darcy’s law applies to a cross section of the porous medium found by averaging over an area that is large compared with the cross section of individual pores and grains of the medium. At this scale, Darcy’s law describes a steady uniform flow of constant velocity, in which the net force on any fluid element is zero. For unconfined saturated flow the suction force binding water to soil particles through surface tension must also be included. For unsaturated conditions, Darcy’s law is;

dzdhKq

(8.3a)

The head h of the water is measured in dimensions of height but can also be thought of as the energy per unit weight of the fluid. In an unsaturated porous medium, the part of the total energy possessed by the fluid due to the soil suction forces is referred to as the suction head . It is therefore evident that the suction head will vary with the moisture content of the medium. The total head h is the sum of the suction and gravity heads

zh (8.4) No term is included for the velocity head of the flow because the velocity is so small that its head is negligible. Substituting for h in (8.3)

z

zKq

(8.5)

1z

Kq (8.6)

Equation 8.6 is sufficient to describe the steady flow of soil moisture.

1z

K

1z

DK (8.6a)

where D is the soil water diffusivity dd / which has dimensions TL /2 .

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A part of the voids is occupied by water and the remainder by air, the volume occupied by water being measured by the soil moisture content defined as;

volumetotalwaterofvolume

(8.7)

Then below is the continuity equation for one-dimensional unsteady unsaturated flow in a porous medium.

0

zq

t

(8.8)

The continuity equation is applicable to flow at shallow depths below the land surface. At greater depth, such as in deep aquifers, changes in the water density and in the porosity can occur as the result of changes in fluid pressure and these must also be accounted for in developing the continuity equation. Substituting eqn. (8.6a) into the continuity equation (8.8) gives;

1

zDK

zt

(8.9)

which is a one-dimensional form of Richard’s equation, the governing equation for unsteady unsaturated flow in a porous medium, first presented by Richards (1931). Example 8.4 (Adopted from Hornberger et al, 1998) Consider that moisture content in a fine sand is measured to be 0.25 at an elevation 3m above the local water table and to be 0.15 at an elevation of 3.5m above the water table. Estimate the direction of flow and magnitude of the flux for the specified soil profile given that the hydraulic relationships for this particular sand are as follows: For a moisture content of 0.25, the capillary pressure head is about -0.42m For a moisture content of 0.15, the capillary pressure head is about -0.45m K (θ=0.25) = 5100.5 x ; K (θ=0.15) = 6100.5 x ; K(θ=0.20)= 5100.2 x

Note: Assume steady flow conditions. Solution For Direction of flow;

From Equation 8.5a, if dzdh >0, the flow will be downward (because the calculated specific

discharge zq will be negative). Conversely, if dzdh <0, the flow will be upward. This is in

reiteration of the main point of Darcy’s law that water flows down a gradient in hydraulic head.

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To calculate dzdh , we know that zh Therefore;

m

mz

hhdzdh

5.00.35.3

)0.35.3(35.335.3

But 5.3 = -0.45 and 42.03

Thus 94.05.0

47.05.0

)42.0(0.3)45.0(5.3

dzdh

Since the calculated hydraulic gradient is positive (dzdh >0), the water flow is downward.

The specific discharge can be estimated from, Equation 8.5a,

dzdhKqz .

The hydraulic gradient varies with moisture content over the interval 3m to 3.5m. The “average” value of hydraulic conductivity can be determined in two ways;

(i) Getting the average of K (θ=0.25) and K (θ=0.15) (Hydraulic conductivity values at height 3m and 3.5m)

(ii) Using the value of K(θ=0.20)

Going by the first method, K= (21 5100.5 x + 6100.5 x ) = 51075.2 x ms-1

Thus specific discharge 155 10585.2)94.0(1075.2 msxxqz One of the goals of infiltration research is to develop models, which accurately describe the infiltration process. Several mathematical expressions describe infiltration into soils. Some are based on the physics of flow through porous medium while others are empirical. Physically based models are numerical computer models, meaning that finite difference or finite element methods are used to solve the Richards’ type partial differential flow equation. a) Physical based models Horizontal infiltration: Boltzmann Transformation The cumulative infiltration as a function of time may be measured in the field. But such experiments will not provide information about (s,t). To get such information the Richards equation should be solved. Due to non-linearity, general analytical solutions of such an equation are unfortunately unavailable. The equation is only solved using numerical approximations. For the case of infiltration from a thin layer of water into an homogeneous soil with uniform initial fraction of water, the initial and boundaries conditions are:

= i for s > 0 and t = 0 = i for s tending to infinity and t >= 0

= 0 for s = 0 and t >= 0 (0 the volume fraction of water at the soil surface). In the case of horizontal infiltration, z/s = 0, therefore the general flow equation takes the form:

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sD

st

(8.10)

This equation may be transformed into an ordinary differential equation by introducing a variable = st -

½. This is known as the Boltzmann Transformation. The flow equation then becomes:

ddD

dd

dd

(8.11)

and the boundaries conditions:

= i, for = o, for = 0

This equation can be solved analytically if D is assumed constant. The result is;

212D

erfcIoI

(8.12)

Where erfc stand for the complementary error function b)Vertical Infiltration (Philip Model 1957) During vertical infiltration, the influence of gravity becomes more important as time progresses. Then the Richard flow equation, including the gravitational term should be solved. The solution takes the form;

..., 24321

23

21

tatatatats (8.13)

Where a1 , a2, . . ., are function of . These coefficients can be evaluated by numerical methods using D() and k() functions. The cumulative infiltration obtained by the above technique is given by;

… + tA +tA +t A + St = I 2321

23

21

(8.14)

The infiltration rate can be derived from the above equation with respect to time;

… + tA +tAA + St =i 23

21

21

32121 (8.15)

I and i are usually truncated after the two terms, because for not too large t these series converge rapidly. In that case,

t1A + St =I 21

and 121 A + St =i 2

1 (8.16)

Other equations which provide solutions to Richard’s equation include Philip1969, Knight 1973, Parlange 1975, Brutesaert 1977, Collis-George 1977, Swartzendruber and Clauge 1989. They are quite restrictive

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since they only describe infiltration from a water ponded surface into a semi finite, homogenous soil with a uniform antecedent water content (USEPA, 1998). ii) Empirical Models Empirical models are usually in the form of simple equations, the parameters of which are derived by means of curve fitting the equation to the actual measurements of the cumulative water infiltration. The equations provide estimates of cumulative infiltration and infiltration, without providing estimates of water content distribution. a) Kostiakov Model This Kostiakov (1932) proposed the following equation model and has the form,

I = t-n (8.17) where I is the infiltration rate at time t and (>0) and n (0<n<1) are empirical constants depending on the soil. The constants and n can be determined by curve fitting Eqn 8.17 to experimental data for cumulative infiltration I. Kostiakov’s equation describes the infiltration quite well at smaller times but becomes less accurate at larger times (Philip, 1957). b) Horton’s Equation Horton (1940) proposed an infiltration equation to represent the generally observed decrease of infiltration rate with time, tending to a steady-state value. Although Chow et al, (1988) reported that Horton’s equation can be derived from Richards equation, it can be seen that f is non zero as t approaches infinity. It does not adequately represent the rapid decrease of f from very high values at small t.

For water supply rate in excess of infitration capacity, refer to Fig 8.7

dkt

cc tteiiii 0)( 0 (8.18)

c

co

Iiik

i = Infiltration rate of at anytime t (mm/hr) from start of the rainfall ic = Final steady state value of infiltration capacity (mm/hr) io = Initial infiltration capacity at t =0 (mm/hr) t = Time from the start of the rainfall (min) td = Total duration of rainfall (min) Ic= shaded area in Fig 8.7. k = Constant depending on a particular soil and surface cover (min-1)

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cI

Time

io

ciiInfil

tratio

n ra

te

Fig 8.7 Infiltration curve (Horton) The determination of io and ic is tedious and difficult although the method has been widely used by hydrologists, but in practice the equation tends to underestimate the usually very rapid initial decrease of infiltration rate with time. An example is given below.

Example 8.5 The infiltration capacities of an area at different intervals of time are indicated in Table 8.7. Find the equation for the infiltration capacity in the exponential form.

Table 8.7: Infiltration Capacities Time in hours 0 0.25 0.50 0.75 1.00 1.25 1.50 1.75 2.00 Infiltration capacity,i (cm/h) 10.4 5.6 3.2 2.1 1.5 1.2 1.1 1.0 1.0 Solution Using the general curve equation, Kt

cc eiiii )( 0

This is also expressed as ektii

ii

co

c1010 loglog

Hence )(loglog

1)(loglog

110

1010

10coc ii

ekii

ekt

and the separate infiltration parameters are

plotted in Table 8.8.

Table 8.8 Infiltration Parameters T (h) 0 0.25 0.5 0.75 1 1.25 1.5 1.75 2 i (cm/h) 10.4 5.6 3.2 2.1 1.5 1.2 1.1 1.0 1.0

i-ic 9.4 4.6 2.2 1.1 0.5 0.2 0.1 0.0 0.0

Log10(i-ic) 0.97 0.66 0.34 0.04 -0.30 -0.70 -1.00 - -

A graph of Time vs cii 10Log is plotted in Fig 8.8

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Fig 8.8 A Plot of Time vs Log10 (i-ic) ic = 1.0

The slope of the line = ek 10log

1 = -0.754

k = 3.05 Hence the equation for Infiltration capacity curve is given as;

tei 05.3)0.14.10(0.1 tei 05.34.90.1

c) Holtan’s Equation

Holtan (1961) developed an empirical infiltration model on experimental data collected at USDA. The model is based on storage concepts. In fact, the infiltration rate is expressed as a function of the available storage above an impending layer and a final steady state. This model is given as:

nc IMaii (8.19)

where M is the storage potential of the soil above the impending layer, and I the cumulative infiltration, a and n are constant depending on the soil type, surface, and cropping conditions. Holtan found that n is almost 1.4.This model has been found suitable for catchment modeling because of soli water dependence. d) Huggins and Monke Equation Huggins and Monke (1967) modified the Holtan model to give:

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n

P

ac M

IMaii

(8.20)

where Ma is the available storage in the control zone and Mp is the total void volume of the control zone. Huggins and Monke indicated that a was 5 to 6 times the saturated hydraulic conductivity and n could be approximated by 0.65.

iii) The Green and Ampt Models Green and Ampt (1911) proposed an approximated method for the calculation of the vertical infiltration. It was the first physically based infiltration equation and has been the subject of considerable developments in soil physics and hydrology because of its simplicity and satisfactory performance over a wide range of hydrological problems. In its development, the following assumptions are made. See Fig.8.9.

the soil is homogeneous; at the start of the infiltration, the soil moisture is uniformly distributed;

iz 0, with (z,0) the moisture content at level z at time t = 0 and i the initial moisture content;

the infiltration creates a sharply defined infiltration front; above the infiltration front, the water content is uniformly distributed (near saturation);

(z,t) = s stz , with s the water content above the wetting front.

SATURATED

UNSATURATED

PONDING

Infiltration- front

Zf

H

s

i

z

0

Fig 8.9 The Green and Ampt method

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Under these assumptions, the infiltration rate may be calculated - based on Darcy's law as;

(t)L(t)L + + H K = i(t)

f

f0 (8.21)

where i(t) = the infiltration rate (mm/h); K = the hydraulic conductivity (m/h); H0 = the ponding height (m); Φ = the suction head at the wetting front (m); Lf = the depth of the infiltration front (m). Defining isM and fMLI = the cumulative infiltration amount and neglecting the ponding height, the equation may be rearranged:

) I(t)M + 1 ( K = i(t)

(8.22)

Integration over time - accounting that I(0) = 0 – yields;

)ln M

I(t) + 1 ( M t K = I(t)

(8.23)

The method is applicable for relatively coarse soils that are initially dry. Green-Ampt Parameters The model contains 4 parameters: K, , s and i. Typical values of Ks, e and are given in Table.8.9. The value of i will strongly depend on the antecedent rainfall conditions. The moisture content above the wetting front is limited to the effective porosity of the soil, e. Full saturation will however seldom be observed in the field, due to air entrapment.

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Table 8.9 Typical values of Green-Ampt infiltration parameters (after Rawls et al., 1983) e

( - )

(cm)

Ks (cm/h)

Sand 0.42 5.0 11.78 loamy sand 0.40 6.1 2.99 sandy loam 0.41 11.0 1.09 Loam 0.43 8.9 0.34 silt loam 0.49 16.7 0.65 sandy clay loam 0.33 21.9 0.15 clay loam 0.31 20.9 0.10 silt clay loam 0.43 27.3 0.10 sandy clay 0.32 23.9 0.06 silty clay 0.42 29.2 0.05 Clay 0.38 31.6 0.03 For the same reason, the value of the hydraulic conductivity above the wetting front, K, is often set to 0.66 Ks, where Ks represents the conductivity at saturation. The Brooks-Corey (1964) equation may be used to calculate ;

where a and b are parameters, depending on the soil characteristics; r is the residual moisture content of the soil, after it has been thoroughly drained.

a) The Mein and Larson Model The Green and Ampt equation allows for the calculation of the infiltration rate, provided that ponding occurs, i.e.. under the condition that the rainfall intensity is larger than the infiltrability rate. The method has been extended by Mein and Larson (1973) to account for ponding conditions. Basically, Mein and Larson make a distinction between periods with ponding and periods without ponding:

during periods without ponding, all the rainfall will infiltrate: during periods with ponding, the Green and Ampt equations are used

Ponding will occur when the potential infiltration rate is less than or equal to the rainfall intensity. A scheme for the application of the method under variable rainfall input is given as in the Fig. 8.10.

e

rb - =a )( (8.24)

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Fig 8.10 The Mein and Larson Model Application Source: (Mein and Larson, 1973)

8.3.5 Recent Studies in Uganda Recent studies on infiltration rate in Uganda provide some interesting results. Infiltration data were collected from the upper, middle and lower side of the Kyetume ridge at Kabanyolo, Makerere University and six infiltration models, Green Ampt, Horton, Kostiakov, Philip, Holtan and Collis George tested. The steady state infiltration, sorptivity, transmissivity and the infiltration decay rates varied considerably, but infiltration data fitted the Horton, Kostiakov and Collis George within 5%. The Philip model fits the data for small times, while the Green and Ampt and Holtan did not fit the infiltration data. A modified Holtan tested on the three soils was similar to three best fit models in terms of bias, but more accurate than Kostiakov and Collis and George (Majaliwa and Tenywa, 1998). Other studies (Tenywa et al, 2000) on the hydrological properties on soils along a slope cleared by heavy machinery and subsequently cropped by two seasons, show that water infiltration was higher at the upper slope and decreased in lower slope positions, with more negative impacts of continuous cultivation on water infiltration of the middle and upper segments along the slope. The Kostiakov model gave comparatively better prediction of infiltration rates than the Green & Ampt and Philip models used in the study.

At t=0, F=0

At t, F(t) is known

Calculate f(t) from F(t) using GA

Ponding throughout interval. Calculate F(t+dt) by GA

No ponding at beginning of interval. Calculate tentative values F’(t+dt) = F(t) + i(t)dt f’(t+dt) from F’(t+dt) using GA

Ponding starts during interval. Calculate F(p) from i(t); find dt’=(F(p)-F(t)) / i(t). Calculate F(t+dt) from F(p) and dt’ by GA

f’(t+dt)<=i(t)

f(t) <= i(t) yes no

yes

No ponding throughout interval. F(t+dt)=F’(t+dt)

no

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8.4 Soil Moisture

8.4.1 Soil Structure and Composition The structure and composition of the soil (Fig. 8.11) will, to a great extent determine the amount of moisture a soil can hold. Thus it is important to appreciate the concepts of soil structure and composition.

The original parent material of soil is the soil rock of the earth’s outer skin. Weathering and erosion break down the surface layers of the soil geological strata and in many areas large quantities of unconsolidated material (soil) have been deposited.

Fig 8.11 Soil structure and composition Thus soil may be a direct product of underlying weathered rocks or may be formed from loose deposits unrelated to the rock below, but deposited by wind, water, ice etc. Soil deposits and their composition can therefore be very variable. Another most important constituent of a soil especially in the upper layers is the organic material derived from decomposition of living plants and other organisms.

8.4.2 Water in the Soil. Most of the content of a soil comes from rainfall or melting snow infiltrating as seepage water moving by gravity and surface tension through the pore spaces. Its pathways are smoothed by a thin film of hygroscopic water, held tightly by electrostatic forces on each of the soil particles and is not easily moved by other forces including plant roots.

Below the percolating flow, the voids in the soil are filled with air and /or water vapour. This layer is a zone of aeration with a complex mixture of solids, liquids and gases. With increase in depth, the aeration zone gives way to a layer of saturated soil with all the pore spaces occupied by water and the saturated capillary zone water is held by capillary forces between the soil particles and is at a pressure less than atmospheric. At greater depths in the same zone, the pressure exceeds atmospheric pressure. The surface over which the pressure equals atmospheric pressure is defined as the water table. The extent of the capillary zone is dependant on the soil composition and packing of soil particles.This topic is discussed further under Section 14.1.1. The wetness of the soil can be assessed in the following terms:

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i. Water Content

s

Wm m

m (8.25)

ii. Water Content,( volume fraction)

t

W

VV

(8.26)

The volume fraction θ is equivalent to the depth ratio of soil water, that is, the equivalent depth of free water relative to the depth of soil for a unit plan area. This is useful in relating soil moisture to precipitation and evaporation depths.

iii. Degree of Saturation.

voids

w

gw

w

VV

VVV

S

(8.27)

8.4.3 Soil Water Potential The mineral and organic compounds of soil form a solid (though not rigid) matrix, the interstices which consist of irregularly shaped pores with a geometry defined by the boundaries of the matrix (Fig.8.12). The pore space, in general, is filled partly with soil air and liquid vapour and partly with the liquid phase of soil water.

Fig 8.12 Soil moisture within and suspended between adjacent soil aggregates Soil serves as the storage reservoir for water. Only the water stored in the root zone of a crop can be utilized by it for its transpiration and build-up of plant tissues. When ample water is in the root zone, plants can obtain their daily water requirements for proper growth and development. Attraction forces

where mw = mass of water in soil sample ms = mass of dry solids in the soil Vw = Volume of water in the soil Vs = Volume of solids in soil sample Vg = Volume of gas in soil sample

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between the soil and moisture molecules, keep the soil and water together. These include surface tension when soil is wet and adsorption when dry. Surface tension can be defined as the force of attraction that tends to keep the liquid surface intact by making it as small as possible. This is the degree of firmness with, which water or moisture is held in the soil; ultimately it is the force per unit area used to extract water from soil. It is normally influenced by surface tension and adhesion. The energy of water tension depends greatly on specific surface and structure of the soil as well as the dissolved salt content. The smaller the pores, the greater the attraction between the hygroscopic water and the soil particles and the lesser the free energy. Also the more the dissolved solutes, the less the free energy. Consequently the retention and movement of water in soil is largely dependent on energy effects (Ghildyal and Tripathi, 2005). Apart from considering soil water in terms of relative masses or volumes, it can be considered in terms of the amount of energy needed for its movement (kinetic) or for its retention in the soil (potential). Potential energy however is the dominant influence (since kinetic energy is very small because water moves very slowly through a soil) and results from gravity, capillary and adsorptive forces. Hence, the soil water potential represents the work (energy) required to overcome the forces acting on the soil water if referred from a given datum to the point of interest. If this energy is represented in terms of energy per unit volume (j/m3) then;

Total Potential = Gravity potential + capillary potential.

pgt (8.28)

The gravity potential is given by gz wg where z is the height or the point of interest above some

arbitrary datum as in Fig. 8.13. w is the density of water, and g the gravitational acceleration .The capillary potential is exemplified in the Fig 8.14 showing a rise of water in a capillary tube to a height of above the surrounding water level. Above the meniscus at A, the pressure is atmospheric but just below

the meniscus, the pressure in the water is gw . This is the energy per unit volume at A due to

capillary p i.e. the capillary potential p . Thus the total potential at A is:

gzggz wwwt gh w (8.29)

z

h Datum

z

gwp

p = 0

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Fig 8.13 Soil Water Potential Source: (Shaw, 1994)

Where h, in Fig 8.13 is the height of the water surface above the datum for z in the static water situation

of the figure )( z is constant (at h) for all points in the water, there are no water movements if there are no differences in total potential. Water will move through a soil between points of different total potential. The latter is often written as t ⁄w g or the equivalent height of water (energy per unit weight). The

negative capillary pressure potential gw is usually called the suction pressure or tension pressure.

The capillary water potential, p , is of significant importance in the assessment of soil moisture. Here, it is assumed a sample of non-shrinking (constant –volume) soil is saturated and at stage 1 is covered by a

layer of water. The hydrostatic pressure at the soil surface is given by gw and therefore p at or near the soil surface is greater than atmospheric pressure. In the case of a thin soil, increases in are small to points within the soil and thus it can be assumed that the soil water pressure is at same positive

potential p . When water is withdrawn from the soil, the water level falls until it reaches the soil surface at stage 2. At this point the head of water has disappeared and the soil water pressure at and near the soil surface is zero, although the soil is still saturated. Further withdrawal of water can only take place when suction pressure is applied and the air-water interface takes on the form of the line of stage 3 with solid particles in contact with the air. The soil water then experiences surface tension forces seeking to prevent its removal and the soil water pressure is therefore negative in relation to the atmospheric pressure. With increased suction, the surface tension in the large pores is overcome, further water will be withdrawn from the soil at stage 4 and air enters the emptied pores (Shaw, 1994).

Water content,

Pore water pressure, p

Clay Soil

Sandy Soil

Water content,

Pore water pressure, p

Sorption

Desorption (Drying)

(Wetting)

Fig 8.14a: Soil water retention with increasing suction

Fig 8.14b: Wetting and drying curves The’ Hysterisis Effect’

Source: (Ghildyal and Tripathi, 2005)

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The relationship between soil water content and water pressure in the pores is shown for contrasting soils in figure 8.14a. The finely saturated clay soil has higher initial water content owing to a higher porosity, but with small or moderate soil water tensions, the sandy soil will release more water from its larger pores. The withdrawal of water from a soil due to increasing tension (the drying process) is called desorption. The reverse wetting process, the addition of water to an unsaturated soil is called sorption. The wetting curve does not follow the same relationship as the drying curve as shown in Fig 8.14b. The water content – pore water pressure relationship can be very complex and a family of curves may be obtained for varying initial states of the soil. The effect is caused by the interaction of the soil pores, the influence of entrapped air and the changing of soil volume due to shrinking and swelling.

Thus in determining the state of water in the soil, the soil water content and the soil water tension p should be determined, since there is no single unique relationship between these two variables.The soil moisture characteristic exhibits hysteresis- a non-unique relationship which depends on the previous history of wetting and drying. The Hysteresis Effect A major factor in the explanation of hysteresis is the so-called ‘’ink-bottle’’ effect, which arises due to the fact that many pores have relatively narrow inlets as shown in Fig 8.15.

r1

r2

Fig 8.15 The’ ink bottle’ effect

Source: (Ghildyal and Tripathi, 2005)

To empty such a pore, suction has first to overcome surface tension at the narrow throat

1

2r

. There will

then be a discontinuity as the larger pore empties. If suction is reduced, the water surface has to be drawn up by surface tension. But to fill the pore, the surface has to rise through the widest part of the pore. To

allow this, suction must be reduced to a value corresponding to

2

2r

, where r2 > r1.

Hence a given water content is achieved at a lower suction on re-wetting.

Air entrapment may also affect the desorption-sorption characteristic. In the sorption phase, for complete re-wetting to occur, all air must be removed from the pore space. In practise, some will remain trapped and this can lead to a failure to ‘’close’’ the hysteresis loop.

A further contribution to hysteresis is the effect of water movement on the angle of contact ( ) of the meniscus. Although approaching zero for a clean glass surface, for a rough or coated surface, >0. When water is withdrawn, tends to decrease and when water rises, tends to increase. These effects reinforce hysteresis. Finally, hysteresis may occur due to a change of state of a shrinking and/or swelling soil (Ghildyal and Tripathi, 2005).

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8.4.4 Soil Moisture Characteristics

Moisture in a soil is dependent mostly on texture, soil structure and it can be seen that sandy soils drain faster at low tension where as clay soil retain moisture a lot more even at high tension such that it is not available for plants to use. The Fig 8.16 shows moisture available to plants at different tensions.

Fig 8.16 Typical moisture characteristics curves of clay, loam and sandy soils

Source: after (USDA, 1964)

i) Soil Moisture Stress It is defined as the combination of soil moisture tension and osmotic pressure. Osmotic pressure is the pressure with which water moves across membranes from an area of higher salts concentration to an area of lower concentration. Osmotic pressure hinders the use of soil moisture by plants. The higher the osmotic pressure, the harder it is for the plants to extract the water from the soil.

The rooting characteristics such as depth to which the plant roots extend as well as the proliferation/ density of the roots determine to a large extent the amount of water taken up from the soil by the plant in addition to other factors such as soil moisture characteristics. The deeper the roots can go the more access to soil moisture, therefore during favourable growing periods, roots often elongate to deeper levels in order to be able to use some of the reserved moisture down below during drought periods. Plant roots vary from species to species for example an annual plant must extend its roots down into the soil to make available water for its use where as perennial plants already have elongated roots.

Apart from rooting characteristics, other factors also limit the amount of moisture available to the plant for example high water table, shallow soils, impermeable formation near the surface, fertility and soil salinity status as well as crop management practices. ii) Rooting Characteristics and Moisture Use of Crops The amount of moisture available to crops is dependent on the depth to which plant roots reach, their ability to spread out in terms of depth and lateral extent sometimes reffered to as their density. The best way to ensure that plants have enough water/ moisture available to them during their life period is to alter

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their root system such that the roots can reach as far down into the soil layers as possible. This will ensure that even during the dry periods, the crops can still access the water in the deeper layers of the soil. Some cultivation practices can be used to alter the root systems for example cutting the top growth at different physiological stages as well as the cultivation and cutting of surface roots. The soil pattern of an area is also known to affect the root characteristics for example maize crop has been found to extend as deep as 1.5 meters in medium to coarse soils while in fine soils roots are shallow. Effective Root Zone is the depth at which the roots of average mature plants are capable of reducing soil moisture to the extent that it is replaced by irrigation.This is shown in Table 8.10 for some common crops.

Table8.10: Effective root zone depth of some common crops (grown on very deep, well drained soils)

Source: Gandhi, et al, 1970

Shallow rooted Moderately deep rooted Deep rooted Very deep rooted Depth of root zone 60cm 90cm 120cm 180cm Rice Wheat Maize Sugarcane Potato Tobacco Cotton Citrus Cauliflower Castor Sorghum Coffee Cabbage Groundnut Pearl millet Apple Lettuce Muskmelon Soyabean Grapevine Onion Carrots Sugar beet Safflower Pea Tomato Lucerne Bean Chilli

iii) Soil Moisture Capacities a) Field Capacity: Is the water content of soil (volume fraction) after the saturated soil has drained under gravity to equilibrium; (usually for about 2 days). When the soil is saturated, it will hold no more water. After rainfall ceases, saturated soil relinquishes water and becomes unsaturated until it can just hold a certain amount against the forces of gravity. At this point, the larger pores are filled with air and the smaller pores are filled with water and the drainage is slow. It can be determined by ponding the soil surface and allowing it to drain for three days and then measuring the moisture content of the soil.

b) Soil Moisture Deficit: is the extent to which water is drier than the Field Capacity; difference between the amount of water in a soil when saturated and the amount of water when drier. A Soil Moisture Deficit of 40 mm implies that 40 mm of water are required to bring it to Field Capacity.

c) Permanent wilting point: Is the volume of water content of the drying soil beyond which a wilting plant will not recover when provided again with humid conditions. At this point the water films around the soil are held so tightly that the plant roots cannot remove a sufficient enough amount of water to prevent wilting unless more water is added to the soil.

There is much less water available at field capacity in a sandy soil that drains quickly, compared to loam or clay soil. The higher the clay content of a soil, the greater its retention capability. At the permanent

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wilting point, a clay soil will still contain a significant amount of water, but it is a finely divided state, held under high tension in the minute pores and absorbed to the surface of the clay particles.Fig 8.17 shows water at different stages in the soil:

Oven dry

Ultimatewilting point

wilting pointPermanent

Field capacity

Available moisturefor sandy loam

Saturation

Unavailable for plants

Available for survival

Available for plant

Limited amountavailable

growth

HYGROSOPIC WATER

CAPILLARY WATER

GRAVITATIONAL ORFREE W ATER

Sandy loam

Silt loam

Fig 8.17: Water at Different Stages in Soil Source: (USDA, 1964)

iv) Methods of measuring Soil water Content (Volumetric Fraction)

a) Gravimetric Determination

A soil sample of known volume (Vt) is removed from the soil with a soil auger. The sample is weighed (mt) and then dried in a special oven at temperatures between 100 and 110C until the weight is constant (ms). The gravimetric water content is obtained from;

s

st

s

wm m

mmmm

Calculating the bulk density tsb Vm and knowing w (1 g/cm3), the volumetric water

content, can be found from: w

bm

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This method can be reliable and accurate if measurements are made precisely. However it is destructive of the soil. A new sample must be taken for another measurement and all subsequent samples should be similar to the original sample, thus a large enough sampling area with homogeneous soil must be selected when siting the sampling points. The main disadvantages are that it is time consuming and laboratory equipment is required.

b) Neutron Scattering

The technique gives a direct measurement of the volumetric soil moisture content in the field. A radioactive source is lowered into an augered hole in the soil; the first neutrons emitted are impeded by the hydrogen nuclei of soil water. The collisions with the hydrogen nuclei (in the water) cause a scatter of slowed nuclei and a detector senses the density of these, dependent on the number of hydrogen nuclei present. A reading of the detector of the slow neutrons gives a measure of the amount of water present in the soil. A compact portable instrument was developed by a special research team of the Institute of Hydrology. The neutron source and detector are mounted in the probe, which is lowered down an access tube previously set in the ground at a selected sampling point. Measurements are made at various depths in the soil so that a water content profile is obtained. The instrument must be calibrated for different soil types and each site should have its own probe. The technique is ideal for catchment areas where soil moisture measurements are required on a regular basis.

v) Methods of measurement of Soil water Potential

a) The Tensiometer

Tensiometers provide a direct measure of the tenacity with which water is held by soils. They measure the matric or capillary potential. They can also be used to estimate the soil moisture content. The tensiometer consists of a porous ceramic cup filled with water which is buried in the soil at any desired depth and connected to a water filled tube to a manometer or vacuum gauge (Fig. 8.18). When the Tensiometer is placed in the soil where the tension measurements are to be made, the bulk water inside the porous cup comes into hydraulic contact and tends to equilibrate with soil water through the pores in the ceramic cup. When initially placed in the soil, water contained in the tensiometer is generally at atmospheric pressure. Soil water, being generally at sub-atmospheric pressure, exercises a suction which draws out a certain amount of water from the rigid and airtight tensiometer, thus causing a drop in its hydrostatic pressure. This pressure is indicated by the manometer or vacuum gauge. An increase in soil-water content reduces tension and lowers the reading.

The main limitation in the use of tensiometers is the fact that at suctions of about 1 bar, air dissolved in the water comes out of solution and the water column in the tensiometer breaks. Therefore in practice, tensiometers are only useful up to suctions of about 0.85 bars, which is comparatively low tension for soils with high clay content. As an irrigation guide therefore, tensiometers are helpful for crops needing nearly saturated soils and crops grown in sandy or light loamy soils in which there is little water left when the pore pressures approach this limit.

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Gla s s t u b e

Me r c u r y c u p

Co n n e c t in gt u b e

Po r o u s c e r a micc u p

So il s u r f a c e

Op e n in g t o f il lwit h wa t e r

Fig 8.18 A Tensiometer connected to a mercury manometer

b) Electrical Resistance blocks

These are simple, inexpensive instruments used for measuring soil water potential. A porous block of gypsum with a pair of electrodes (Fig. 8.19) embedded is buried in the soil. Water from the soil seeps in to the gypsum until the pore pressures in the soil and block reach equilibrium. Then the water content of the block is measured by the electrical resistance between the electrodes. A direct relationship is obtained between the electrical resistance and the water content, which is dependent on the soil water potential. Electrical resistance blocks are made commercially and are a useful indicator of irrigation need in crop production. One of the disadvantages of this method is that the block has a long response time and is dependent on continuous close contact with the soil. There is also a hysteresis effect between the wetting and drying curve relationships between electrical resistance and soil moisture tension, but calibration data are usually given for the drying curve. Gypsum blocks are not long lasting since they are solution effects and they soon deteriorate in wet soils. Field instruments developed for the measurement of moisture tension can also be connected to recorders and thus make valuable monitoring devices for continuous assessment of soil conditions, but many of them are not accurate and are therefore more adapted to agricultural and engineering requirements rather than to scientific research of hydrological process.

Fig 8.19 An electrical resistance block

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c) Pressure membrane and plate technique The apparatus consists of pressure plates contained in an air-tight metallic chamber (Fig. 8.20). The plates are saturated and soil placed on them and also saturated. The plates are then placed in the metallic chambers, sealed tightly and a controlled pressure is applied. After a while, water starts to drip out of soil until equilibrium against the applied pressure is achieved. The moisture content of the soil sample is then measured at different pressures. The moisture contents can be plotted against the pressures to obtain soil moisture characteristic curves.

Fig 8.20 Pressure plate apparatus

Summary The movement of water within the soil is commonly referred to as Infiltration. There are a number of factors that will influence the process of infiltration and in turn its rate. The soil moisture for any soil is dependent on this process. Researchers have investigated the variation of infiltration capacity over time and different methods of determination of infiltration of a soil. These methods include infiltrometers and infiltration models. This chapter discusses soil moisture, describing the different levels of water stored in soil such as wilting point and field capacity. The study of such water aspects is important in relation to the hydrological cycle, agriculture and flood control. References

1. Arora, K. R. Irrigation, Water Power and Water Resources Engineering, Standard Paublishers, 2007, New Dehli, India.

2. Bodman, G.B., Coleman, E.A., Moisture and Energy Conditions during downward entry of Water into Soils, 1944, 8 pp116-122 Proceedings Soil Science Society of America,

3. Brooks R.H., Corey A.T., Hydraulic Properties of Porous Media, Hydrology Papers No 3 Colorado State University, 1964, Fort Collins, Colorado, USA.

4. Chow V.T., Maidment, D.R. , Mays L.W., Applied Hydrology, McGraw Hill, 1988 New York,USA. 5. Ghandi,R.T., Gupta P.C., Joseph A.P., Rege N.D., Coover J.R., Jones D. F., Phelan J.T. Pope E.J.,

Handbook on Irrigation Water Requirements,1970, Water Management Division, Department of Agriculture, Ministry of Agriculture, New Dehli, India.

6. Ghildyal B.P., Tripathi R.P. Soil Physics, New Age Publishers Ltd, 2005, New Dehli, India.

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7. Holtan, R.E., A Concept for Infiltration Estimates in Watershed Engineering, USDA,1961, ARS 41-51

8. Hornberger, G.M., Raffensperger, J.P., Wiberg, P.L., Eshelman, K.N., Elements of Physical Hydrology, The Johns Hopkins University Press, 1998, USA.

9. Horton R. E., Analysis of Runoff Plant Experiments with varying Infiltration Capacity,Trans American Geophysics Union, 1939,Vol 20 pp693-711.

10. Huggins L.F., Monke E.J. The Mathematical Simulation of the Hydrology of Small Watersheds, Tech Report 1, Purdue University Water Resources Centre, 1967, Lafayette, Indiana, USA.

11. Kostaikov,A.N., On the dynamics of the Coefficient of Water Percolation in Soils and on the necessity of Studying if from a Dynamic Point of View for Purposes of Amelioration, Translated 6th Communique International Soil Science, 1932, Part A, pp17-21.

12. Majaliwa, J.G.M., Tenywa, M.M. Infiltration Characteristics of Soils of the Kyetume Ridge, Kabanyolo, Uganda, Makerere University Agricultural Research Institute, Kabanyolo (MUARIK), Vol 1 pp 57-65,1998.

13. Mein R.G., Larson, C.L. Modeling Infiltration during a Steady Rain, Water Resources Research, 1973, Vol 9, No2 pp384-394.

14. Michael, A.M. Irrigation Theory and Practice, Vikas Publishing House PVT Ltd, 2003, New Delhi, India.

15. Philip. J.R. The Theory of Infiltration in Advances in Hydroscience 1969 ed. Chow,V.T. vol 5 pp215-296.

16. Raghunath H.M. Hydrology, Principles, Analysis, Design, New Age International Publishers, 2006, India.

17. Ravi, V., Williams, J.R., Burden, D.S.,Estimation of Infiltration Rate in the Vadose Zone: Compilation of Simple Mathematical Models, United States Environment Protection Agency, 1998 Ohio, USA

18. Rawls,W.J, Brakensheik, D.L. Miller N., Green- Ampt Infiltration Parameters from Soils Data, Journal Hydraulic Division, ASCE,1983, Vol 109, No 1 pp 62-70.

19. Richards, L.A., Capillary Conduction of Liquids through Porous Media, Physics,1931, Vol 1pp 318-333.

20. Shaw E.M. Hydrology in Practice, Chapman and Hall, 1994, London, UK. 21. Tenywa, M.M., Zake, J.Y.K., Ssessanga, S., Majaliwa,J.G.M., Kawongolo J.B., Bwamiki, D.,

Changes in Water Infiltration along a Catena prior to Mechanised Clearing Operations and after Two Cropping Seasons, African Crop Science Journal, 2000, Vol 8 No 3 pp233-242.

22. Viessman,Jr.W., Lewis G.L, Introduction to Hydrology, Fourth Edition, Harper Collins College Publishers, 1996, Florida USA.

23. United States Department of Agriculture, National Engineering Handbook, Section 15. Ch. 1 , Soil Plant Water Relationships. USDA, SCS, 1960, Washington D.C. USA.

24. United States Department of Agriculture, National Engineering Handbook, Section 15. Ch. 1 , Soil Plant Water Relationships. USDA, SCS, 1964, Washington D.C. USA.

Further Reading

1. Ayoade J.O., Tropical Hydrology and Water Resources, Macmillan, 1998, London, UK. 2. Garg S.K. Hydrology and Water Resources Engineering, Khanna Publishers, 1998, Dehli, India. 3. Subramanya, K. Engineering Hydrology, 2nd Edition, Tata McGraw-Hill Publishing, 2001. 4. Wilson, E.M Engineering Hydrology, 4th Edition, Macmillan, 1996, London, UK.

Questions 1. What is infiltration capacity? 2. What are the factors that affect the infiltration capacity of a soil?

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3. Describe two methods of determining the infiltration capacity of a soil? 4. What do you understand by the terms?

i) Field Capacity ii) Soil Moisture deficit iii) Root Constant? iv) Permanent Wilting Point

5 a) Distinguish between i) -index and W-index ii) Infiltration capacity and Infiltration rate b) The average rainfall over 45 ha of watershed for a particular storm was as follows:

Time (hr) 0 1 2 3 4 5 6 7 Rainfall (cm) 0.00 0.50 1.00 3.25 2.50 1.50 0.50 0.00 The volume of runoff from this storm was determined as 2.25 ha-m. Establish the -index. 6. An infiltration experiment was carried out on a small plot having sandy soil. The resulting

infiltration data was given in the table belowas: Time (h) 1 2 3 4 5 6 7 9 11 13 15 17 19 21 Infiltration Capacity, f (cm/h)

3.3

2.9

2.5

2.1

1.9

1.6

1.5

1.42

1.31

1.24

1.23

1.2

1.18

1.18

a) Derive and plot the infiltration curve b) Derive the equation for the curve in a) above

7. Distinguish between the sorption and desorption process in the relationship of soil water content

and pore water pressure of a soil. Explain the difference between a sandy and clayey soil. 8. Define soil moisture tension and soil moisture stress. Indicate the relationship between them and

how they affect plant growth. 9. Describe briefly one method of measuring:

i) Soil moisture content ii) Soil water Potential

10. Describe the Pressure membrane and plate technique for determining soil moisture potential. 11. (a) Explain the factors that affect the infiltration capacity of a soil.

(b) When two tensiometers were installed at 0.4m and 0.5m above the water table in a uniform sandy soil, the readings indicated capillary pressure heads of -0.45m and -0.6m respectively. Assuming that the moisture characteristic and hydraulic conductivity curves for this particular sand show the following relationship;

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Volumetric Moisture Content (θ) 0.05 0.1 0.14 0.18 0.25 0.28 0.36 0.4 0.55

Hydraulic Conductivity,

K (ms-1) 6x10-8 0.3x10-6 5x10-6 1.5x10-5 5x10-5 0.4x10-4 2x10-4 2x10-4 2x10-4

Capillary Pressure head (Ψm) -0.60 -0.48 -0.45 -0.43 -0.42 -0.408 -0.36 -0.36 -0.36

(i). What is the direction of water movement between the two tensiometers? (ii). Estimate the magnitude of the specific discharge between the two tensiometers.

12. Discuss the zones of the infiltration profile 13. What are the assumptions for the following types of infiltration models below: i) Richard’s Equation ii) Empirical models iii) Green-Ampt models