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SURFACE WATER HYDROLOGY (CE547)

Definition of terms used to describe water movement in the

unsaturated zone


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DEFINITIONS

Infiltration: the movement of water from soil surface into

the soil

Redistribution: the subsequent movement of infiltrated

water in the unsaturated zone of soil

Exfiltration: evaporation from the upper layer of the soil

Capillary Rise: the movement from the saturated zone

upward into the unsaturated zone due to surface tension

Recharge: the movement of percolating water from the

unsaturated zone to the subjacent saturated flow

Percolation: downward flow in the unsaturated zone


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Material Properties of Soil

Pore size and its distribution indicated by grain size distribution

(accumulative frequency plot of grain diameter (log scale) Vs Weight

fraction of grains with smaller diameter


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Material Properties of Soil (contd)

Particle Density (m) is the weighted average density of

the mineral grains up a soil

Bulk Density (b) is the dry density of the soil

Porosity,, is the proportion of pore spaces in a volume

of soil

m

mmV

m m

bs a w m

M M

V V V V

1 b

m


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SOIL-WATER STORAGE

Volumetric water content (or simply water content), , is

the ratio of water volume to soil volume

Measurement: The representative soil sample of known

volume is first weighed, then at 105oC the sample is dried

in oven, reweighed and calculated as

m

s

VV

are the weights before and after drying, respectively

swet sdry

w s

swet sdry

M M

V

Here M and M


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SOIL-WATER STORAGE (contd)

Degree of Saturation or Wetness, S, is the proportion of

pores that contain water

Total Soil-Water storage is expressed as a depth [L]

(volume per unit area), which is the product of the

volumetric water content times the thickness of the layer

w

a w

VS

V V


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Ranges of porosities, field capacities, and permanent wilting

points for soils of various textures.


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SOIL-WATER FLOW

Darcys Law:

x

-1

, q is the volumetric flow rate in the x-direction per unit

cross sectional area of medium (LT ),

z is the elevation above an arbitrary datum (L)

p is the water p

x h

h

d z pq K

dx

d pdzK

dx dx

where

-2

-1

h

ressure (FL )

K is the hydraulic conductivity of the medium LT


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SOIL-WATER FLOW (contd)

Pressure Head,

Darcys Law for vertical unsaturated flow

The relations between pressure and water content [()] and

between hydraulic conductivity and water content [Kh()] are

crucial determinants of unsaturated flow in soils

has dimensions Lw

p

1

z h

h

d zq K

dz

dK

dz


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Hydraulic Conductivity, Kh[LT-1], is the rate (volume per

unit time per unit area) at which water moves through a

porous medium under a unit potential-energy gradient.

Hydraulic-Conductivity-Water-Content Relations: For a

given soil, unsaturated hydraulic conductivity is very low

at low to moderate water contents; it increases

nonlinearly to its saturated value, Kh*, as the water

content increases to saturation.



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Soil-Water Pressure:

The water table is the surface at which pressure (p) is

equal to zero (at atmospheric pressure)

Negative pressure is often called tension or suction and

is called tension head, matric potential, or martic suctionwhen p


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Pressure-Water-Content Relations Moisture-Characteristics curve is the relation between pressure

head,, (often plotted on a logarithmic scale) and water content,,

for a given soil



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Analytical Approximations ofand KhRelations


*

*

ae

b

b

ae

c

h h

c

h h

S S

K S K S

K K


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Hysteresis in the ()

relation for Rubicon sandy

loam


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Soil Water pressure (tension), , Vs. degree of saturation, S, for soils

of three different textures


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Representative Values of parameters


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Factors Affecting Infiltration

Gravity:The greater the depth of water over the

surface, the greater is the hydrostatic head orthe gravitational force.

Existing Soil Moisture: Dry Soil: Creates a strong capillary potential in the

capillary size pores between soil grains. The capillary

force is strongest just under the dry ground surface. Wet Soil: Wetness in the soil creates resistance to

infiltration


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Soils at surface: A loosened soil in a newly ploughedfield will infiltrate rainfall rapidly, but as the rain continues,

the soil is compacted and the infiltration rate is reduced.

Inwash of Fine Material: reduces the size of pore

openings, reducing infiltration.

Compaction by man and animals: Reduction ininfiltration results.

Natural processes:Burrowing by animals and insects,

provides additional openings for water to penetrate the soil.

Factors Affecting Infiltration (contd...)


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Vegetative Cover: provides protection for the

soil from compaction by rain mixed effect!!

Temperature: Viscosity of water increases with

decrease in temperature decrease in infiltration

Measurement Error: may occur due to the

entrapped air in the soil.

Factors Affecting Infiltration (contd...)


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Designation of hydrologic soil-profile horizons. Note that this figure is idealized

and that one or more of these horizons may be absent in a given situation


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Hydrologic Horizons: For describing water

movement in soils, a set of horizons are definedbased on the range of water contents and the soil-

water pressure. The depths of loaction and thethicknesses of these hydrologic horizons vary both

in space and time


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Groundwater Zone (Phreatic Zone):

Saturated, Pressure head in positive

If no groundwater flow, only hydrostatic pressure

Water table is at atmospheric pressure.

The level at which water would stand in a well

Fluctuations of water table seasonal climatic

variations

Recharge due to individual storm events is possible


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Tension-saturated zone (capillary fringe):

Entire zone of negative pressures (tension) above the

water table is known as vadose zone

Lowest portion of this Vadose zone is nearlysaturated, due to capillary effect. Surface tension

forces draw the water into the spaces above the

water table, creating the tension-saturated zone orcapillary fringe.

Here, the pressure is hydrostatic

Pressure at the top of this zone is ae= height of thecapillary rise in the soil


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Intermediate zone:

Enters through percolation from above and leaves by gravity

drainage.

Tension in this zone depends on soil texture, water content.

Most of the soil profile is occupied by this zone Root Zone (soil moisture zone):

Zone from which plant roots can extract water during

transpiration

Its upper boundary is the soil surface, while its lower boundary is

indefinite and irregular

Water enters by infiltration and leaves by transpiration,

evaporation and gravity drainage. Water content is usually above

PWP

May approach saturation following intense infiltration events, but

would be below field capacity most of the times, between events.


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Typical moisture profile development with a constant rainfall rate


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Infiltration rate versus time for a given rainfall intensity


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Infiltration curves for several rainfall intensities


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Quantitative Modeling of Infiltration at a Point

Analysis applies to representative soil volumes that are

large relative to the typical pore size

Water is assumed to move only in the liquid state and its

movement is not significantly affected by the flow of air in

the soil pores or by temperature or by osmotic gradients

Water is assumed to move vertically through inter-

connected inter-grain pores that are randomly distributed

throughout a quasi-homogeneous soil


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Richards Equation

Darcy's law for vertical unsaturated flow is combined with

conservation of mass to obtain the Richards equation, which

is the basic theoretical equation for infiltration into a homogeneous

porous medium.

h

Non-linear, No closed form anlytical solutions, except for highly

simplified - and K relations and boundary conditions.

Ri h d E ti ( td )


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The Richards equation can be used as a basis for numerical

modeling of infiltration, exfiltration, redistribution, by specifying

appropriate boundary conditions and initial conditions, dividing

the soil into thin layes, and applying the equation to each layer

sequentially at small increments of time.

The predictions from the numerical models are found to have

reasonably good agreement with laboratory and field measurement.

Richards Equation (contd...)

Richards Equation (contd )


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However, numerical solutions may not be directly useful in providing

conceptual overview of the ways in which various factors influence

infiltration

They are generally too computationally intensive for inclusion in

operational hydrologic models.

Thus there have been a number of attempts to develop approximate

analytical solutions to the Richards equation, for situations such as

infiltration.

Richards Equation (contd...)


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Soil Water Diffusivity

h

h h

KD K

2L T

b

ae

C

h hK K

3 2b bh ae hD b K

0 0ae hand D

Since

and


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Richards Equation

Recall

Darcys Law

Total head

So Darcy becomes

Continuity becomes

z

h

Kqz

zh

z

zq K

z

K Kz

D K

z

D K

Soil water diffusivity

Kz

Dzz

q

t

zq K Kz


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Infiltration

General Process of water

penetrating from groundinto soil

Factors affecting

Condition of soil surface,vegetative cover, soilproperties, hydraulicconductivity, antecedentsoil moisture

Four zones

Saturated, transmission,wetting, and wetting front

depth

Wetting Zone

Transmission

Zone

Transition Zone

Saturation Zone

Wetting Front


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Infiltration

Infiltration rate

Rate at which water enters the soil at the surface (in/hr or

cm/hr)

Cumulative infiltration

Accumulated depth of water infiltrating during given time

period

t

dftF0

)()(

)(tf

dt

tdFtf

)()(

Eq. 1

Eq. 2


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Hortonian Infiltration

Recall Richards Equation

Assume K and D are

constants, not a function oforz

Solve for moisture diffusion

at surface

Kz

Dzt

z

K

zDt

2

2

02

2

zD

t

ktcc effftf

)()( 0

f0initial infiltration rate, f

cis constant rate and k is decay constant

Eq. 3


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Hortons Infiltration curve and hyetograph


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Hortonian Infiltration

0

0.5

1

1.5

2

2.5

3

3.5

0 0.5 1 1.5 2

Time

Infiltra

tion

rate,

k1

k3

k2

k1 < k2 < k3

fc

f0


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Green-Ampt Model

Physically based

Original proposition in 1911 by Green and Ampt

Subsequent development: Mein and Larson (1973)

Applies Darcys law and principle of conservation of

mass

In a finite difference formulation that allows view of the

infiltration process.

Good performance when compared with numerical

solutions of the Richards equation.

Idealized Conditions


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Idealized Conditions

Z : vertical axis (upward)

Z` : downward direction along the z-axis

f(t) : infiltration time at t [LT-1]

F(t): total amount of water infiltrated upto time t [L]

Consider a block of soil homogeneous to an infinite depth

Horizontal surface at which there is no ET

Initial water contentois invariant and


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Green Ampt Infiltration

Wetted Zone

Wetting Front

Ponded Water

Ground Surface

Dry Soil

0h

L

i

z

LLtF i )()(

dt

dL

dt

dFf

zh

Kz

Kf

fz

hKqz

MoistureSoilInitial

FrontWettingtoDepth

i

L


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(Cont.)

Apply finite difference to thederivative, between

Ground surface

Wetting front

Kz

Kf

Wetted Zone

Wetting Front

Ground Surface

Dry Soil

L

i

z0,0 z

fLz ,

KL

KKz

KKz

Kf f

0

0

FL

LtF )(

1

FKf

f

Kz

Kf

Eq. 4


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1

LK

dt

dL f

1

FKf

f

dt

dLf


(Cont.)

LtF )(

Wetted Zone

Wetting Front

Ground Surface

Dry Soil

L

i

z

L

dLdLdt

K

f

f

CLLtK

ff )ln(

Integrate

Evaluate the constant of integration

)ln( ffC

0@0 tL

)ln(L

LKtf

ff

Eq. 5


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Green Ampt Infiltration (Cont.)

)ln(

L

LKt

f

ff

)1ln(f

fF

KtF

1

FKf f

Wetted Zone

Wetting Front

Ground Surface

Dry Soil

L

i

z

See: htt ://www.ce.utexas.edu/ rof/mckinne /ce311k/Lab/Lab8/Lab8.html

Eq. 6

Eq. 7

Given K, t, ,and , a trial value of F is substituted on the right-hand side (agood trial value is F=Kt), and a new value of F calculated on the left-hand side,

which is substituted as a trail value on the right-hand side, and so on, until the

calculated values of F converge to a constant. The final value of cumulative

infiltration F is substituted into Eq. 7 to determine the corresponding potential

infiltration ratef.

Iterative solution


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Soil Parameters

Green-Ampt model requires

Hydraulic conductivity, Porosity, Wetting Front Suction

Head

Brooks and Corey

Soil Class Porosity Effective

Porosity

Wetting

Front

Suction

Head

Hydraulic

Conductivity

n e K(cm) (cm/h)

Sand 0.437 0.417 4.95 11.78

Loam 0.463 0.434 9.89 0.34

Clay 0.475 0.385 31.63 0.03

e r

(1 )i e es

e

res

Effective saturation

Effective porosity


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Ponding time

Elapsed time between the time rainfall begins

and the time water begins to pond on the soilsurface (tp)

Ponding Time


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Ponding Time

Up to the time of ponding, all rainfall hasinfiltrated (i= rainfall rate)

if ptiF *

1F

Kf f

1

* p

f

ti

Ki

)( KiiKt

fp

Potential

Infiltration

Actual Infiltration

Rainfall

Accumulated

RainfallInfiltration

Time

Time

In

filtrationrate,

f

Cumulative

Infiltration,

F

i

pt

pp tiF *

Eq. 8


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ln fP f pf P

FF F K t t

F

Eq. 9

Eq. 9 can be used to calculate the depth of infiltration after ponding, and

then Eq. 7 can be used to obtain the infiltration ratef.

Actual Infiltration Rate


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Example

Silty-Loam soil, 30%

effective saturation,

rainfall 5 cm/hr intensity

30.0

/65.0

7.16

486.0

e

e

s

hrcmK

cm

340.0)486.0)(3.01()1( ees 340.0*7.16

hr17.0

))(65.00.5(0.5

68.565.0

)(

KiKii

Kt f

p