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    SURFACE WATER HYDROLOGY (CE547)

    Definition of terms used to describe water movement in the

    unsaturated zone

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    SURFACE WATER HYDROLOGY (CE547)

    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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    SURFACE WATER HYDROLOGY (CE547)

    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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    SURFACE WATER HYDROLOGY (CE547)

    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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    SURFACE WATER HYDROLOGY (CE547)

    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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    SURFACE WATER HYDROLOGY (CE547)

    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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    SURFACE WATER HYDROLOGY (CE547)

    Ranges of porosities, field capacities, and permanent wilting

    points for soils of various textures.

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    SURFACE WATER HYDROLOGY (CE547)

    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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    SURFACE WATER HYDROLOGY (CE547)

    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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    SURFACE WATER HYDROLOGY (CE547)

    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.

    SOIL-WATER FLOW (contd)

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    SURFACE WATER HYDROLOGY (CE547)

    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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    SURFACE WATER HYDROLOGY (CE547)

    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

    SOIL-WATER FLOW (contd)

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    SURFACE WATER HYDROLOGY (CE547)

    Analytical Approximations ofand KhRelations

    SOIL-WATER FLOW (contd)

    *

    *

    ae

    b

    b

    ae

    c

    h h

    c

    h h

    S S

    K S K S

    K K

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    SURFACE WATER HYDROLOGY (CE547)

    Hysteresis in the ()

    relation for Rubicon sandy

    loam

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    SURFACE WATER HYDROLOGY (CE547)

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

    of three different textures

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    SURFACE WATER HYDROLOGY (CE547)

    Representative Values of parameters

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    SURFACE WATER HYDROLOGY (CE547)

    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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    SURFACE WATER HYDROLOGY (CE547)

    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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    SURFACE WATER HYDROLOGY (CE547)

    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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    SURFACE WATER HYDROLOGY (CE547)

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    SURFACE WATER HYDROLOGY (CE547)

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    SURFACE WATER HYDROLOGY (CE547)

    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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    SURFACE WATER HYDROLOGY (CE547)

    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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    SURFACE WATER HYDROLOGY (CE547)

    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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    SURFACE WATER HYDROLOGY (CE547)

    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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    SURFACE WATER HYDROLOGY (CE547)

    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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    SURFACE WATER HYDROLOGY (CE547)

    Typical moisture profile development with a constant rainfall rate

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    SURFACE WATER HYDROLOGY (CE547)

    Infiltration rate versus time for a given rainfall intensity

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    SURFACE WATER HYDROLOGY (CE547)

    Infiltration curves for several rainfall intensities

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    SURFACE WATER HYDROLOGY (CE547)

    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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    SURFACE WATER HYDROLOGY (CE547)

    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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    SURFACE WATER HYDROLOGY (CE547)

    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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    SURFACE WATER HYDROLOGY (CE547)

    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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    SURFACE WATER HYDROLOGY (CE547)

    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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    SURFACE WATER HYDROLOGY (CE547)

    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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    SURFACE WATER HYDROLOGY (CE547)

    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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    SURFACE WATER HYDROLOGY (CE547)

    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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    SURFACE WATER HYDROLOGY (CE547)

    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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    SURFACE WATER HYDROLOGY (CE547)

    Hortons Infiltration curve and hyetograph

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    SURFACE WATER HYDROLOGY (CE547)

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    SURFACE WATER HYDROLOGY (CE547)

    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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    SURFACE WATER HYDROLOGY (CE547)

    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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    SURFACE WATER HYDROLOGY (CE547)

    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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    SURFACE WATER HYDROLOGY (CE547)

    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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    SURFACE WATER HYDROLOGY (CE547)

    Green Ampt Infiltration

    (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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    SURFACE WATER HYDROLOGY (CE547)

    1

    LK

    dt

    dL f

    1

    FKf

    f

    dt

    dLf

    Green Ampt Infiltration

    (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

    [email protected] tL

    )ln(L

    LKtf

    ff

    Eq. 5

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    SURFACE WATER HYDROLOGY (CE547)

    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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    SURFACE WATER HYDROLOGY (CE547)

    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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    SURFACE WATER HYDROLOGY (CE547)

    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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    SURFACE WATER HYDROLOGY (CE547)

    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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    SURFACE WATER HYDROLOGY (CE547)

    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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    SURFACE WATER HYDROLOGY (CE547)

    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