hellip after the rainfall

Interception and depression storage abstractions

Infiltration process

Topics Interception + depression storage

What is an infiltration process

How we can measure infiltration

Which methods are available for calculation of infiltration

What are limits of calculation methods for rainfall-runoff modelling

Application of Green-Ampt infiltration method

Hydrologic Cycle

How does vegetation influence stormwater

(Xiao Q McPherson EG Ustin SL Grismer ME 2000 A new approach to modeling tree rainfall interception Journal of Geographical Research Atmospheres 105 29173-29188)(Chow Applied Hydrology)

∆119878 = 119867119875 minus (119867119876+119867119864119879)

S hellip water storage (mm)HP hellip (total) rainfall depth (mm)HQ hellip runoff depth (mm)HET hellip evapotranspiration (mm)

119867119875 = 119867119878119865 + 119867119879119865+119867119868

HSF hellip stemflow

HTF hellip throughfall(precipitation at forest floor)

HI hellip interception loss

ldquoNet rainfallrdquo or ldquoeffective rainfallrdquo

Balance on natural catchment

Balance of vegetation canopy

interception loss+ depression storage Water retained in vegetation or accumulated in hollows

over the surface

Negligible in a large storms but may reach up to 20 of annual precipitation

Depend on the vegetation (type conditions density) ground surface and rainfall character

Interception Dominant at the beginning of the storm

Important for small rainfall amounts and short rainfalls

Interception capacity renews when water evaporate

Methods of estimation

Empirical value

Regression analysis (measured rainfall in an open area vs under canopy)

Lump subtraction based on vegetation storage capacity ndash (eg 005 ndash 02 cm)

Other methods including temporal variation existhellip (Dohnal et al 2014 JHH 62 p 277-284)

Interception capacity

Depression storage surface detention

SD hellip surface detentionbull Water in excess of depression storage ndash due to flowing waterbull Depends on discharge

DS hellip depression storage (= surface retention dead storage)bull Water stored in surface pits and depressionsbull When water supply rate exceeds infiltrationbull Water subsequently infiltrate or evaporate

Sometimes as a lumped value or

(after Antoine et al 2012 Catena 91 p 10-20)119863119878 = 119878119863(1 minus 119890minus119875119890

1119878119863)

SD hellip max storage capacity Pe hellip rainfall excess (Precipitation ndash Infiltration)

Infiltration process Infiltration is a process during which water on the soil

surface enters the soil profile (generally vertical process)

This process is connected to whole soil profile

Infiltration rate ndash actual amount of water entering the soil profile (units of depth per time ndash LT-1) it is a description of process

Infiltration capacity ndash maximum amount of water which can enter the soil profile (units of depth per time ndash LT-1) it is a property of soil profile

Infiltration process Infiltration rate

dt

tditi

)()(

Total infiltration (cumulative infiltration)

dttitI

t

0

)()( Saturation zone

Wetting zone

Transmission zone

Infiltration process Affected by

Soil properties

Soil horizons

Hydraulic conductivity

Soil surface condition

Vegetation cover

Antecendent soil moisture

hellip

Infiltration measurement 3 main approaches

Ring infiltrometer method Sprinkler method Permeameter method

To obtain Saturated hydraulic conductivity (KS)= ability of soil to conduct water under saturated conditions

or look for temporal changes of infiltration rate

L

hKAQ

Darcyrsquos law

zh

Total hydraulic head

Infiltration measurement -Sprinkler Mostly as I = Rainfall ndash Runoff

where rainfall intensity and duration is set runoff is measured

Difficult to mimic natural rain (intensity raindrop sizes kinetic energy)

Slope is necessary

Representative area can be reached

Technically demanding

Infiltration measurement ndash ring infiltrometer Single or double rings inserted into ground

Shallow ponding

t

Hi

i ndash infiltration rateH ndash decrease of water levelt ndash time step

Infiltration measurement Ponded infiltration is usually measured using double

ring infiltrometer

Infiltration is measured until the infiltration rate is constant

Infiltration measurement Unstaturated flow is more complex process

It can be measured by disc infiltrometers

Infiltration can bemeasured underdifferent suctionpressures conditions

Infiltration measurement Record of infiltration field measurement

Infiltration calculation Different methods are available for infiltration calculation

Richardlsquos equation Hortonlsquos model Philliplsquos model Green-Ampt method Kostiakov equation

Approximation of an exact theory (Richards)

Richardrsquos equation (1D)

Kz

D

Kz

K

z

zKqz

KD

Soil water diffusivityDarcy

K

zD

zz

q

t

Darcy + continuity eq

Green-Ampt method Introduced by Green and Ampt in 1911 This method is based on two main assumptions

Wetting front is sharp defined Depth of ponding (depth of water on the surface pressure

head on the surface) is negligible

(fro

mE

lem

ents

of

Ph

ysic

al

Hyd

rolo

gy

19

98

)

Wetting front depth

Moisture profile in time t

Green-Ampt method Actual infiltration rate

(fro

mA

pp

lied

Hyd

rolo

gy

19

88

)

dt

tdIti

)()(

Darcylsquos law

dz

dhKq

Total infiltration

)()( isfLtI

fLtI )(

Green-Ampt method

(fro

mA

pp

lied

Hyd

rolo

gy

19

88

)

qi

f

f

L

LhKi

))(( 0

h0 is considered to be very small and therefore it is neglected

IL f

I

IKi

Green-Ampt method

tKtI

tI

))(

1ln()(

hellip after solving

I

IK

dt

dI

)1(

I

Ki

(fro

mA

pp

lied

Hyd

rolo

gy

19

88

)

00 z fLz finite difference

KI

K

Green-Ampt method - parameters Best way to get values of Green-Ampt method parameters is

to measure them in the field Hydraulic conductivity porosity wetting front suction head

If no measurement is available the values can be obtained from tables according to soil class

Soil type PorosityEffectiveporosity

Suctionhead

Hydraulicconductivity

- - mm mmh

Sand 0437 0417 495 1178

loamy sand 0437 0401 613 299

sandy loam 0453 0412 1101 109

loam 0463 0434 889 34

silt loam 0501 0486 1668 65

sandy clay loam 0398 0330 2185 15

clay loam 0464 0309 2088 10

silty clay loam 0471 0432 2730 10

sandy clay 0430 0321 2390 06

silty clay 0479 0423 2922 05

clay 0475 0385 3163 03

Hortonlsquos equation Based on the concept introduced by Horton (1933) ndash an

example of infiltration excess approach to direct runoffcalculation

Decreasing infiltration rate in a few hours scale due to soil compaction air entrapment etc

tk

cc eiiiti 0

i(t) ndash infiltration rate at time t (LT-1)ic ndash minimum infiltration rate (infiltration rate after soil saturationor minimum infiltration rate) (LT-1)i0 ndash initial infiltration rate (maximum infiltration rate) (LT-1)k ndash decay constant specific to the soil

tkc

c ek

iititI

10

Philliplsquos equation Two-parameter method introduced by Philip (1957)

TtS

ti 2

1

2

i(t) ndash infiltration rate at time t (LT-1)I(t) ndash cumulative infiltration at time t (L)S ndash sorptivity ndash function of soil suction potential (parameter specificto the soil) (LT-05)T ndash transmisivity (minimum infiltration rate mostly assumed to beclose to saturated hydraulic conductivity) (LT-1)

tTtStI 21

Conclusion The infiltration process is a very complex and can be

described using the models of different complexity and detail

Simple methods involve significant simplifictaion of theprocess as well as the soil profile

Saptial and temporar variability Problematic input data for distributed models

Topics Interception + depression storage

What is an infiltration process

How we can measure infiltration

Which methods are available for calculation of infiltration

What are limits of calculation methods for rainfall-runoff modelling

Application of Green-Ampt infiltration method

Hydrologic Cycle

How does vegetation influence stormwater

(Xiao Q McPherson EG Ustin SL Grismer ME 2000 A new approach to modeling tree rainfall interception Journal of Geographical Research Atmospheres 105 29173-29188)(Chow Applied Hydrology)

∆119878 = 119867119875 minus (119867119876+119867119864119879)

S hellip water storage (mm)HP hellip (total) rainfall depth (mm)HQ hellip runoff depth (mm)HET hellip evapotranspiration (mm)

119867119875 = 119867119878119865 + 119867119879119865+119867119868

HSF hellip stemflow

HTF hellip throughfall(precipitation at forest floor)

HI hellip interception loss

ldquoNet rainfallrdquo or ldquoeffective rainfallrdquo

Balance on natural catchment

Balance of vegetation canopy

interception loss+ depression storage Water retained in vegetation or accumulated in hollows

over the surface

Negligible in a large storms but may reach up to 20 of annual precipitation

Depend on the vegetation (type conditions density) ground surface and rainfall character

Interception Dominant at the beginning of the storm

Important for small rainfall amounts and short rainfalls

Interception capacity renews when water evaporate

Methods of estimation

Empirical value

Regression analysis (measured rainfall in an open area vs under canopy)

Lump subtraction based on vegetation storage capacity ndash (eg 005 ndash 02 cm)

Other methods including temporal variation existhellip (Dohnal et al 2014 JHH 62 p 277-284)

Interception capacity

Depression storage surface detention

SD hellip surface detentionbull Water in excess of depression storage ndash due to flowing waterbull Depends on discharge

DS hellip depression storage (= surface retention dead storage)bull Water stored in surface pits and depressionsbull When water supply rate exceeds infiltrationbull Water subsequently infiltrate or evaporate

Sometimes as a lumped value or

(after Antoine et al 2012 Catena 91 p 10-20)119863119878 = 119878119863(1 minus 119890minus119875119890

1119878119863)

SD hellip max storage capacity Pe hellip rainfall excess (Precipitation ndash Infiltration)

Infiltration process Infiltration is a process during which water on the soil

surface enters the soil profile (generally vertical process)

This process is connected to whole soil profile

Infiltration rate ndash actual amount of water entering the soil profile (units of depth per time ndash LT-1) it is a description of process

Infiltration capacity ndash maximum amount of water which can enter the soil profile (units of depth per time ndash LT-1) it is a property of soil profile

Infiltration process Infiltration rate

dt

tditi

)()(

Total infiltration (cumulative infiltration)

dttitI

t

0

)()( Saturation zone

Wetting zone

Transmission zone

Infiltration process Affected by

Soil properties

Soil horizons

Hydraulic conductivity

Soil surface condition

Vegetation cover

Antecendent soil moisture

hellip

Infiltration measurement 3 main approaches

Ring infiltrometer method Sprinkler method Permeameter method

To obtain Saturated hydraulic conductivity (KS)= ability of soil to conduct water under saturated conditions

or look for temporal changes of infiltration rate

L

hKAQ

Darcyrsquos law

zh

Total hydraulic head

Infiltration measurement -Sprinkler Mostly as I = Rainfall ndash Runoff

where rainfall intensity and duration is set runoff is measured

Difficult to mimic natural rain (intensity raindrop sizes kinetic energy)

Slope is necessary

Representative area can be reached

Technically demanding

Infiltration measurement ndash ring infiltrometer Single or double rings inserted into ground

Shallow ponding

t

Hi

i ndash infiltration rateH ndash decrease of water levelt ndash time step

Infiltration measurement Ponded infiltration is usually measured using double

ring infiltrometer

Infiltration is measured until the infiltration rate is constant

Infiltration measurement Unstaturated flow is more complex process

It can be measured by disc infiltrometers

Infiltration can bemeasured underdifferent suctionpressures conditions

Infiltration measurement Record of infiltration field measurement

Infiltration calculation Different methods are available for infiltration calculation

Richardlsquos equation Hortonlsquos model Philliplsquos model Green-Ampt method Kostiakov equation

Approximation of an exact theory (Richards)

Richardrsquos equation (1D)

Kz

D

Kz

K

z

zKqz

KD

Soil water diffusivityDarcy

K

zD

zz

q

t

Darcy + continuity eq

Green-Ampt method Introduced by Green and Ampt in 1911 This method is based on two main assumptions

Wetting front is sharp defined Depth of ponding (depth of water on the surface pressure

head on the surface) is negligible

(fro

mE

lem

ents

of

Ph

ysic

al

Hyd

rolo

gy

19

98

)

Wetting front depth

Moisture profile in time t

Green-Ampt method Actual infiltration rate

(fro

mA

pp

lied

Hyd

rolo

gy

19

88

)

dt

tdIti

)()(

Darcylsquos law

dz

dhKq

Total infiltration

)()( isfLtI

fLtI )(

Green-Ampt method

(fro

mA

pp

lied

Hyd

rolo

gy

19

88

)

qi

f

f

L

LhKi

))(( 0

h0 is considered to be very small and therefore it is neglected

IL f

I

IKi

Green-Ampt method

tKtI

tI

))(

1ln()(

hellip after solving

I

IK

dt

dI

)1(

I

Ki

(fro

mA

pp

lied

Hyd

rolo

gy

19

88

)

00 z fLz finite difference

KI

K

Green-Ampt method - parameters Best way to get values of Green-Ampt method parameters is

to measure them in the field Hydraulic conductivity porosity wetting front suction head

If no measurement is available the values can be obtained from tables according to soil class

Soil type PorosityEffectiveporosity

Suctionhead

Hydraulicconductivity

- - mm mmh

Sand 0437 0417 495 1178

loamy sand 0437 0401 613 299

sandy loam 0453 0412 1101 109

loam 0463 0434 889 34

silt loam 0501 0486 1668 65

sandy clay loam 0398 0330 2185 15

clay loam 0464 0309 2088 10

silty clay loam 0471 0432 2730 10

sandy clay 0430 0321 2390 06

silty clay 0479 0423 2922 05

clay 0475 0385 3163 03

Hortonlsquos equation Based on the concept introduced by Horton (1933) ndash an

example of infiltration excess approach to direct runoffcalculation

Decreasing infiltration rate in a few hours scale due to soil compaction air entrapment etc

tk

cc eiiiti 0

i(t) ndash infiltration rate at time t (LT-1)ic ndash minimum infiltration rate (infiltration rate after soil saturationor minimum infiltration rate) (LT-1)i0 ndash initial infiltration rate (maximum infiltration rate) (LT-1)k ndash decay constant specific to the soil

tkc

c ek

iititI

10

Philliplsquos equation Two-parameter method introduced by Philip (1957)

TtS

ti 2

1

2

i(t) ndash infiltration rate at time t (LT-1)I(t) ndash cumulative infiltration at time t (L)S ndash sorptivity ndash function of soil suction potential (parameter specificto the soil) (LT-05)T ndash transmisivity (minimum infiltration rate mostly assumed to beclose to saturated hydraulic conductivity) (LT-1)

tTtStI 21

Conclusion The infiltration process is a very complex and can be

described using the models of different complexity and detail

Simple methods involve significant simplifictaion of theprocess as well as the soil profile

Saptial and temporar variability Problematic input data for distributed models

Hydrologic Cycle

How does vegetation influence stormwater

(Xiao Q McPherson EG Ustin SL Grismer ME 2000 A new approach to modeling tree rainfall interception Journal of Geographical Research Atmospheres 105 29173-29188)(Chow Applied Hydrology)

∆119878 = 119867119875 minus (119867119876+119867119864119879)

S hellip water storage (mm)HP hellip (total) rainfall depth (mm)HQ hellip runoff depth (mm)HET hellip evapotranspiration (mm)

119867119875 = 119867119878119865 + 119867119879119865+119867119868

HSF hellip stemflow

HTF hellip throughfall(precipitation at forest floor)

HI hellip interception loss

ldquoNet rainfallrdquo or ldquoeffective rainfallrdquo

Balance on natural catchment

Balance of vegetation canopy

interception loss+ depression storage Water retained in vegetation or accumulated in hollows

over the surface

Negligible in a large storms but may reach up to 20 of annual precipitation

Depend on the vegetation (type conditions density) ground surface and rainfall character

Interception Dominant at the beginning of the storm

Important for small rainfall amounts and short rainfalls

Interception capacity renews when water evaporate

Methods of estimation

Empirical value

Regression analysis (measured rainfall in an open area vs under canopy)

Lump subtraction based on vegetation storage capacity ndash (eg 005 ndash 02 cm)

Other methods including temporal variation existhellip (Dohnal et al 2014 JHH 62 p 277-284)

Interception capacity

Depression storage surface detention

SD hellip surface detentionbull Water in excess of depression storage ndash due to flowing waterbull Depends on discharge

DS hellip depression storage (= surface retention dead storage)bull Water stored in surface pits and depressionsbull When water supply rate exceeds infiltrationbull Water subsequently infiltrate or evaporate

Sometimes as a lumped value or

(after Antoine et al 2012 Catena 91 p 10-20)119863119878 = 119878119863(1 minus 119890minus119875119890

1119878119863)

SD hellip max storage capacity Pe hellip rainfall excess (Precipitation ndash Infiltration)

Infiltration process Infiltration is a process during which water on the soil

surface enters the soil profile (generally vertical process)

This process is connected to whole soil profile

Infiltration rate ndash actual amount of water entering the soil profile (units of depth per time ndash LT-1) it is a description of process

Infiltration capacity ndash maximum amount of water which can enter the soil profile (units of depth per time ndash LT-1) it is a property of soil profile

Infiltration process Infiltration rate

dt

tditi

)()(

Total infiltration (cumulative infiltration)

dttitI

t

0

)()( Saturation zone

Wetting zone

Transmission zone

Infiltration process Affected by

Soil properties

Soil horizons

Hydraulic conductivity

Soil surface condition

Vegetation cover

Antecendent soil moisture

hellip

Infiltration measurement 3 main approaches

Ring infiltrometer method Sprinkler method Permeameter method

To obtain Saturated hydraulic conductivity (KS)= ability of soil to conduct water under saturated conditions

or look for temporal changes of infiltration rate

L

hKAQ

Darcyrsquos law

zh

Total hydraulic head

Infiltration measurement -Sprinkler Mostly as I = Rainfall ndash Runoff

where rainfall intensity and duration is set runoff is measured

Difficult to mimic natural rain (intensity raindrop sizes kinetic energy)

Slope is necessary

Representative area can be reached

Technically demanding

Infiltration measurement ndash ring infiltrometer Single or double rings inserted into ground

Shallow ponding

t

Hi

i ndash infiltration rateH ndash decrease of water levelt ndash time step

Infiltration measurement Ponded infiltration is usually measured using double

ring infiltrometer

Infiltration is measured until the infiltration rate is constant

Infiltration measurement Unstaturated flow is more complex process

It can be measured by disc infiltrometers

Infiltration can bemeasured underdifferent suctionpressures conditions

Infiltration measurement Record of infiltration field measurement

Infiltration calculation Different methods are available for infiltration calculation

Richardlsquos equation Hortonlsquos model Philliplsquos model Green-Ampt method Kostiakov equation

Approximation of an exact theory (Richards)

Richardrsquos equation (1D)

Kz

D

Kz

K

z

zKqz

KD

Soil water diffusivityDarcy

K

zD

zz

q

t

Darcy + continuity eq

Green-Ampt method Introduced by Green and Ampt in 1911 This method is based on two main assumptions

Wetting front is sharp defined Depth of ponding (depth of water on the surface pressure

head on the surface) is negligible

(fro

mE

lem

ents

of

Ph

ysic

al

Hyd

rolo

gy

19

98

)

Wetting front depth

Moisture profile in time t

Green-Ampt method Actual infiltration rate

(fro

mA

pp

lied

Hyd

rolo

gy

19

88

)

dt

tdIti

)()(

Darcylsquos law

dz

dhKq

Total infiltration

)()( isfLtI

fLtI )(

Green-Ampt method

(fro

mA

pp

lied

Hyd

rolo

gy

19

88

)

qi

f

f

L

LhKi

))(( 0

h0 is considered to be very small and therefore it is neglected

IL f

I

IKi

Green-Ampt method

tKtI

tI

))(

1ln()(

hellip after solving

I

IK

dt

dI

)1(

I

Ki

(fro

mA

pp

lied

Hyd

rolo

gy

19

88

)

00 z fLz finite difference

KI

K

Green-Ampt method - parameters Best way to get values of Green-Ampt method parameters is

to measure them in the field Hydraulic conductivity porosity wetting front suction head

If no measurement is available the values can be obtained from tables according to soil class

Soil type PorosityEffectiveporosity

Suctionhead

Hydraulicconductivity

- - mm mmh

Sand 0437 0417 495 1178

loamy sand 0437 0401 613 299

sandy loam 0453 0412 1101 109

loam 0463 0434 889 34

silt loam 0501 0486 1668 65

sandy clay loam 0398 0330 2185 15

clay loam 0464 0309 2088 10

silty clay loam 0471 0432 2730 10

sandy clay 0430 0321 2390 06

silty clay 0479 0423 2922 05

clay 0475 0385 3163 03

Hortonlsquos equation Based on the concept introduced by Horton (1933) ndash an

example of infiltration excess approach to direct runoffcalculation

Decreasing infiltration rate in a few hours scale due to soil compaction air entrapment etc

tk

cc eiiiti 0

i(t) ndash infiltration rate at time t (LT-1)ic ndash minimum infiltration rate (infiltration rate after soil saturationor minimum infiltration rate) (LT-1)i0 ndash initial infiltration rate (maximum infiltration rate) (LT-1)k ndash decay constant specific to the soil

tkc

c ek

iititI

10

Philliplsquos equation Two-parameter method introduced by Philip (1957)

TtS

ti 2

1

2

i(t) ndash infiltration rate at time t (LT-1)I(t) ndash cumulative infiltration at time t (L)S ndash sorptivity ndash function of soil suction potential (parameter specificto the soil) (LT-05)T ndash transmisivity (minimum infiltration rate mostly assumed to beclose to saturated hydraulic conductivity) (LT-1)

tTtStI 21

Conclusion The infiltration process is a very complex and can be

described using the models of different complexity and detail

Simple methods involve significant simplifictaion of theprocess as well as the soil profile

Saptial and temporar variability Problematic input data for distributed models

How does vegetation influence stormwater

(Xiao Q McPherson EG Ustin SL Grismer ME 2000 A new approach to modeling tree rainfall interception Journal of Geographical Research Atmospheres 105 29173-29188)(Chow Applied Hydrology)

∆119878 = 119867119875 minus (119867119876+119867119864119879)

S hellip water storage (mm)HP hellip (total) rainfall depth (mm)HQ hellip runoff depth (mm)HET hellip evapotranspiration (mm)

119867119875 = 119867119878119865 + 119867119879119865+119867119868

HSF hellip stemflow

HTF hellip throughfall(precipitation at forest floor)

HI hellip interception loss

ldquoNet rainfallrdquo or ldquoeffective rainfallrdquo

Balance on natural catchment

Balance of vegetation canopy

interception loss+ depression storage Water retained in vegetation or accumulated in hollows

over the surface

Negligible in a large storms but may reach up to 20 of annual precipitation

Depend on the vegetation (type conditions density) ground surface and rainfall character

Interception Dominant at the beginning of the storm

Important for small rainfall amounts and short rainfalls

Interception capacity renews when water evaporate

Methods of estimation

Empirical value

Regression analysis (measured rainfall in an open area vs under canopy)

Lump subtraction based on vegetation storage capacity ndash (eg 005 ndash 02 cm)

Other methods including temporal variation existhellip (Dohnal et al 2014 JHH 62 p 277-284)

Interception capacity

Depression storage surface detention

SD hellip surface detentionbull Water in excess of depression storage ndash due to flowing waterbull Depends on discharge

DS hellip depression storage (= surface retention dead storage)bull Water stored in surface pits and depressionsbull When water supply rate exceeds infiltrationbull Water subsequently infiltrate or evaporate

Sometimes as a lumped value or

(after Antoine et al 2012 Catena 91 p 10-20)119863119878 = 119878119863(1 minus 119890minus119875119890

1119878119863)

SD hellip max storage capacity Pe hellip rainfall excess (Precipitation ndash Infiltration)

Infiltration process Infiltration is a process during which water on the soil

surface enters the soil profile (generally vertical process)

This process is connected to whole soil profile

Infiltration rate ndash actual amount of water entering the soil profile (units of depth per time ndash LT-1) it is a description of process

Infiltration capacity ndash maximum amount of water which can enter the soil profile (units of depth per time ndash LT-1) it is a property of soil profile

Infiltration process Infiltration rate

dt

tditi

)()(

Total infiltration (cumulative infiltration)

dttitI

t

0

)()( Saturation zone

Wetting zone

Transmission zone

Infiltration process Affected by

Soil properties

Soil horizons

Hydraulic conductivity

Soil surface condition

Vegetation cover

Antecendent soil moisture

hellip

Infiltration measurement 3 main approaches

Ring infiltrometer method Sprinkler method Permeameter method

To obtain Saturated hydraulic conductivity (KS)= ability of soil to conduct water under saturated conditions

or look for temporal changes of infiltration rate

L

hKAQ

Darcyrsquos law

zh

Total hydraulic head

Infiltration measurement -Sprinkler Mostly as I = Rainfall ndash Runoff

where rainfall intensity and duration is set runoff is measured

Difficult to mimic natural rain (intensity raindrop sizes kinetic energy)

Slope is necessary

Representative area can be reached

Technically demanding

Infiltration measurement ndash ring infiltrometer Single or double rings inserted into ground

Shallow ponding

t

Hi

i ndash infiltration rateH ndash decrease of water levelt ndash time step

Infiltration measurement Ponded infiltration is usually measured using double

ring infiltrometer

Infiltration is measured until the infiltration rate is constant

Infiltration measurement Unstaturated flow is more complex process

It can be measured by disc infiltrometers

Infiltration can bemeasured underdifferent suctionpressures conditions

Infiltration measurement Record of infiltration field measurement

Infiltration calculation Different methods are available for infiltration calculation

Richardlsquos equation Hortonlsquos model Philliplsquos model Green-Ampt method Kostiakov equation

Approximation of an exact theory (Richards)

Richardrsquos equation (1D)

Kz

D

Kz

K

z

zKqz

KD

Soil water diffusivityDarcy

K

zD

zz

q

t

Darcy + continuity eq

Green-Ampt method Introduced by Green and Ampt in 1911 This method is based on two main assumptions

Wetting front is sharp defined Depth of ponding (depth of water on the surface pressure

head on the surface) is negligible

(fro

mE

lem

ents

of

Ph

ysic

al

Hyd

rolo

gy

19

98

)

Wetting front depth

Moisture profile in time t

Green-Ampt method Actual infiltration rate

(fro

mA

pp

lied

Hyd

rolo

gy

19

88

)

dt

tdIti

)()(

Darcylsquos law

dz

dhKq

Total infiltration

)()( isfLtI

fLtI )(

Green-Ampt method

(fro

mA

pp

lied

Hyd

rolo

gy

19

88

)

qi

f

f

L

LhKi

))(( 0

h0 is considered to be very small and therefore it is neglected

IL f

I

IKi

Green-Ampt method

tKtI

tI

))(

1ln()(

hellip after solving

I

IK

dt

dI

)1(

I

Ki

(fro

mA

pp

lied

Hyd

rolo

gy

19

88

)

00 z fLz finite difference

KI

K

Green-Ampt method - parameters Best way to get values of Green-Ampt method parameters is

to measure them in the field Hydraulic conductivity porosity wetting front suction head

If no measurement is available the values can be obtained from tables according to soil class

Soil type PorosityEffectiveporosity

Suctionhead

Hydraulicconductivity

- - mm mmh

Sand 0437 0417 495 1178

loamy sand 0437 0401 613 299

sandy loam 0453 0412 1101 109

loam 0463 0434 889 34

silt loam 0501 0486 1668 65

sandy clay loam 0398 0330 2185 15

clay loam 0464 0309 2088 10

silty clay loam 0471 0432 2730 10

sandy clay 0430 0321 2390 06

silty clay 0479 0423 2922 05

clay 0475 0385 3163 03

Hortonlsquos equation Based on the concept introduced by Horton (1933) ndash an

example of infiltration excess approach to direct runoffcalculation

Decreasing infiltration rate in a few hours scale due to soil compaction air entrapment etc

tk

cc eiiiti 0

i(t) ndash infiltration rate at time t (LT-1)ic ndash minimum infiltration rate (infiltration rate after soil saturationor minimum infiltration rate) (LT-1)i0 ndash initial infiltration rate (maximum infiltration rate) (LT-1)k ndash decay constant specific to the soil

tkc

c ek

iititI

10

Philliplsquos equation Two-parameter method introduced by Philip (1957)

TtS

ti 2

1

2

i(t) ndash infiltration rate at time t (LT-1)I(t) ndash cumulative infiltration at time t (L)S ndash sorptivity ndash function of soil suction potential (parameter specificto the soil) (LT-05)T ndash transmisivity (minimum infiltration rate mostly assumed to beclose to saturated hydraulic conductivity) (LT-1)

tTtStI 21

Conclusion The infiltration process is a very complex and can be

described using the models of different complexity and detail

Simple methods involve significant simplifictaion of theprocess as well as the soil profile

Saptial and temporar variability Problematic input data for distributed models

∆119878 = 119867119875 minus (119867119876+119867119864119879)

S hellip water storage (mm)HP hellip (total) rainfall depth (mm)HQ hellip runoff depth (mm)HET hellip evapotranspiration (mm)

119867119875 = 119867119878119865 + 119867119879119865+119867119868

HSF hellip stemflow

HTF hellip throughfall(precipitation at forest floor)

HI hellip interception loss

ldquoNet rainfallrdquo or ldquoeffective rainfallrdquo

Balance on natural catchment

Balance of vegetation canopy

interception loss+ depression storage Water retained in vegetation or accumulated in hollows

over the surface

Negligible in a large storms but may reach up to 20 of annual precipitation

Depend on the vegetation (type conditions density) ground surface and rainfall character

Interception Dominant at the beginning of the storm

Important for small rainfall amounts and short rainfalls

Interception capacity renews when water evaporate

Methods of estimation

Empirical value

Regression analysis (measured rainfall in an open area vs under canopy)

Lump subtraction based on vegetation storage capacity ndash (eg 005 ndash 02 cm)

Other methods including temporal variation existhellip (Dohnal et al 2014 JHH 62 p 277-284)

Interception capacity

Depression storage surface detention

SD hellip surface detentionbull Water in excess of depression storage ndash due to flowing waterbull Depends on discharge

DS hellip depression storage (= surface retention dead storage)bull Water stored in surface pits and depressionsbull When water supply rate exceeds infiltrationbull Water subsequently infiltrate or evaporate

Sometimes as a lumped value or

(after Antoine et al 2012 Catena 91 p 10-20)119863119878 = 119878119863(1 minus 119890minus119875119890

1119878119863)

SD hellip max storage capacity Pe hellip rainfall excess (Precipitation ndash Infiltration)

Infiltration process Infiltration is a process during which water on the soil

surface enters the soil profile (generally vertical process)

This process is connected to whole soil profile

Infiltration rate ndash actual amount of water entering the soil profile (units of depth per time ndash LT-1) it is a description of process

Infiltration capacity ndash maximum amount of water which can enter the soil profile (units of depth per time ndash LT-1) it is a property of soil profile

Infiltration process Infiltration rate

dt

tditi

)()(

Total infiltration (cumulative infiltration)

dttitI

t

0

)()( Saturation zone

Wetting zone

Transmission zone

Infiltration process Affected by

Soil properties

Soil horizons

Hydraulic conductivity

Soil surface condition

Vegetation cover

Antecendent soil moisture

hellip

Infiltration measurement 3 main approaches

Ring infiltrometer method Sprinkler method Permeameter method

To obtain Saturated hydraulic conductivity (KS)= ability of soil to conduct water under saturated conditions

or look for temporal changes of infiltration rate

L

hKAQ

Darcyrsquos law

zh

Total hydraulic head

Infiltration measurement -Sprinkler Mostly as I = Rainfall ndash Runoff

where rainfall intensity and duration is set runoff is measured

Difficult to mimic natural rain (intensity raindrop sizes kinetic energy)

Slope is necessary

Representative area can be reached

Technically demanding

Infiltration measurement ndash ring infiltrometer Single or double rings inserted into ground

Shallow ponding

t

Hi

i ndash infiltration rateH ndash decrease of water levelt ndash time step

Infiltration measurement Ponded infiltration is usually measured using double

ring infiltrometer

Infiltration is measured until the infiltration rate is constant

Infiltration measurement Unstaturated flow is more complex process

It can be measured by disc infiltrometers

Infiltration can bemeasured underdifferent suctionpressures conditions

Infiltration measurement Record of infiltration field measurement

Infiltration calculation Different methods are available for infiltration calculation

Richardlsquos equation Hortonlsquos model Philliplsquos model Green-Ampt method Kostiakov equation

Approximation of an exact theory (Richards)

Richardrsquos equation (1D)

Kz

D

Kz

K

z

zKqz

KD

Soil water diffusivityDarcy

K

zD

zz

q

t

Darcy + continuity eq

Green-Ampt method Introduced by Green and Ampt in 1911 This method is based on two main assumptions

Wetting front is sharp defined Depth of ponding (depth of water on the surface pressure

head on the surface) is negligible

(fro

mE

lem

ents

of

Ph

ysic

al

Hyd

rolo

gy

19

98

)

Wetting front depth

Moisture profile in time t

Green-Ampt method Actual infiltration rate

(fro

mA

pp

lied

Hyd

rolo

gy

19

88

)

dt

tdIti

)()(

Darcylsquos law

dz

dhKq

Total infiltration

)()( isfLtI

fLtI )(

Green-Ampt method

(fro

mA

pp

lied

Hyd

rolo

gy

19

88

)

qi

f

f

L

LhKi

))(( 0

h0 is considered to be very small and therefore it is neglected

IL f

I

IKi

Green-Ampt method

tKtI

tI

))(

1ln()(

hellip after solving

I

IK

dt

dI

)1(

I

Ki

(fro

mA

pp

lied

Hyd

rolo

gy

19

88

)

00 z fLz finite difference

KI

K

Green-Ampt method - parameters Best way to get values of Green-Ampt method parameters is

to measure them in the field Hydraulic conductivity porosity wetting front suction head

If no measurement is available the values can be obtained from tables according to soil class

Soil type PorosityEffectiveporosity

Suctionhead

Hydraulicconductivity

- - mm mmh

Sand 0437 0417 495 1178

loamy sand 0437 0401 613 299

sandy loam 0453 0412 1101 109

loam 0463 0434 889 34

silt loam 0501 0486 1668 65

sandy clay loam 0398 0330 2185 15

clay loam 0464 0309 2088 10

silty clay loam 0471 0432 2730 10

sandy clay 0430 0321 2390 06

silty clay 0479 0423 2922 05

clay 0475 0385 3163 03

Hortonlsquos equation Based on the concept introduced by Horton (1933) ndash an

example of infiltration excess approach to direct runoffcalculation

Decreasing infiltration rate in a few hours scale due to soil compaction air entrapment etc

tk

cc eiiiti 0

i(t) ndash infiltration rate at time t (LT-1)ic ndash minimum infiltration rate (infiltration rate after soil saturationor minimum infiltration rate) (LT-1)i0 ndash initial infiltration rate (maximum infiltration rate) (LT-1)k ndash decay constant specific to the soil

tkc

c ek

iititI

10

Philliplsquos equation Two-parameter method introduced by Philip (1957)

TtS

ti 2

1

2

i(t) ndash infiltration rate at time t (LT-1)I(t) ndash cumulative infiltration at time t (L)S ndash sorptivity ndash function of soil suction potential (parameter specificto the soil) (LT-05)T ndash transmisivity (minimum infiltration rate mostly assumed to beclose to saturated hydraulic conductivity) (LT-1)

tTtStI 21

Conclusion The infiltration process is a very complex and can be

described using the models of different complexity and detail

Simple methods involve significant simplifictaion of theprocess as well as the soil profile

Saptial and temporar variability Problematic input data for distributed models

interception loss+ depression storage Water retained in vegetation or accumulated in hollows

over the surface

Negligible in a large storms but may reach up to 20 of annual precipitation

Depend on the vegetation (type conditions density) ground surface and rainfall character

Interception Dominant at the beginning of the storm

Important for small rainfall amounts and short rainfalls

Interception capacity renews when water evaporate

Methods of estimation

Empirical value

Regression analysis (measured rainfall in an open area vs under canopy)

Lump subtraction based on vegetation storage capacity ndash (eg 005 ndash 02 cm)

Other methods including temporal variation existhellip (Dohnal et al 2014 JHH 62 p 277-284)

Interception capacity

Depression storage surface detention

SD hellip surface detentionbull Water in excess of depression storage ndash due to flowing waterbull Depends on discharge

DS hellip depression storage (= surface retention dead storage)bull Water stored in surface pits and depressionsbull When water supply rate exceeds infiltrationbull Water subsequently infiltrate or evaporate

Sometimes as a lumped value or

(after Antoine et al 2012 Catena 91 p 10-20)119863119878 = 119878119863(1 minus 119890minus119875119890

1119878119863)

SD hellip max storage capacity Pe hellip rainfall excess (Precipitation ndash Infiltration)

Infiltration process Infiltration is a process during which water on the soil

surface enters the soil profile (generally vertical process)

This process is connected to whole soil profile

Infiltration rate ndash actual amount of water entering the soil profile (units of depth per time ndash LT-1) it is a description of process

Infiltration capacity ndash maximum amount of water which can enter the soil profile (units of depth per time ndash LT-1) it is a property of soil profile

Infiltration process Infiltration rate

dt

tditi

)()(

Total infiltration (cumulative infiltration)

dttitI

t

0

)()( Saturation zone

Wetting zone

Transmission zone

Infiltration process Affected by

Soil properties

Soil horizons

Hydraulic conductivity

Soil surface condition

Vegetation cover

Antecendent soil moisture

hellip

Infiltration measurement 3 main approaches

Ring infiltrometer method Sprinkler method Permeameter method

To obtain Saturated hydraulic conductivity (KS)= ability of soil to conduct water under saturated conditions

or look for temporal changes of infiltration rate

L

hKAQ

Darcyrsquos law

zh

Total hydraulic head

Infiltration measurement -Sprinkler Mostly as I = Rainfall ndash Runoff

where rainfall intensity and duration is set runoff is measured

Difficult to mimic natural rain (intensity raindrop sizes kinetic energy)

Slope is necessary

Representative area can be reached

Technically demanding

Infiltration measurement ndash ring infiltrometer Single or double rings inserted into ground

Shallow ponding

t

Hi

i ndash infiltration rateH ndash decrease of water levelt ndash time step

Infiltration measurement Ponded infiltration is usually measured using double

ring infiltrometer

Infiltration is measured until the infiltration rate is constant

Infiltration measurement Unstaturated flow is more complex process

It can be measured by disc infiltrometers

Infiltration can bemeasured underdifferent suctionpressures conditions

Infiltration measurement Record of infiltration field measurement

Infiltration calculation Different methods are available for infiltration calculation

Richardlsquos equation Hortonlsquos model Philliplsquos model Green-Ampt method Kostiakov equation

Approximation of an exact theory (Richards)

Richardrsquos equation (1D)

Kz

D

Kz

K

z

zKqz

KD

Soil water diffusivityDarcy

K

zD

zz

q

t

Darcy + continuity eq

Green-Ampt method Introduced by Green and Ampt in 1911 This method is based on two main assumptions

Wetting front is sharp defined Depth of ponding (depth of water on the surface pressure

head on the surface) is negligible

(fro

mE

lem

ents

of

Ph

ysic

al

Hyd

rolo

gy

19

98

)

Wetting front depth

Moisture profile in time t

Green-Ampt method Actual infiltration rate

(fro

mA

pp

lied

Hyd

rolo

gy

19

88

)

dt

tdIti

)()(

Darcylsquos law

dz

dhKq

Total infiltration

)()( isfLtI

fLtI )(

Green-Ampt method

(fro

mA

pp

lied

Hyd

rolo

gy

19

88

)

qi

f

f

L

LhKi

))(( 0

h0 is considered to be very small and therefore it is neglected

IL f

I

IKi

Green-Ampt method

tKtI

tI

))(

1ln()(

hellip after solving

I

IK

dt

dI

)1(

I

Ki

(fro

mA

pp

lied

Hyd

rolo

gy

19

88

)

00 z fLz finite difference

KI

K

Green-Ampt method - parameters Best way to get values of Green-Ampt method parameters is

to measure them in the field Hydraulic conductivity porosity wetting front suction head

If no measurement is available the values can be obtained from tables according to soil class

Soil type PorosityEffectiveporosity

Suctionhead

Hydraulicconductivity

- - mm mmh

Sand 0437 0417 495 1178

loamy sand 0437 0401 613 299

sandy loam 0453 0412 1101 109

loam 0463 0434 889 34

silt loam 0501 0486 1668 65

sandy clay loam 0398 0330 2185 15

clay loam 0464 0309 2088 10

silty clay loam 0471 0432 2730 10

sandy clay 0430 0321 2390 06

silty clay 0479 0423 2922 05

clay 0475 0385 3163 03

Hortonlsquos equation Based on the concept introduced by Horton (1933) ndash an

example of infiltration excess approach to direct runoffcalculation

Decreasing infiltration rate in a few hours scale due to soil compaction air entrapment etc

tk

cc eiiiti 0

i(t) ndash infiltration rate at time t (LT-1)ic ndash minimum infiltration rate (infiltration rate after soil saturationor minimum infiltration rate) (LT-1)i0 ndash initial infiltration rate (maximum infiltration rate) (LT-1)k ndash decay constant specific to the soil

tkc

c ek

iititI

10

Philliplsquos equation Two-parameter method introduced by Philip (1957)

TtS

ti 2

1

2

i(t) ndash infiltration rate at time t (LT-1)I(t) ndash cumulative infiltration at time t (L)S ndash sorptivity ndash function of soil suction potential (parameter specificto the soil) (LT-05)T ndash transmisivity (minimum infiltration rate mostly assumed to beclose to saturated hydraulic conductivity) (LT-1)

tTtStI 21

Conclusion The infiltration process is a very complex and can be

described using the models of different complexity and detail

Simple methods involve significant simplifictaion of theprocess as well as the soil profile

Saptial and temporar variability Problematic input data for distributed models

Interception Dominant at the beginning of the storm

Important for small rainfall amounts and short rainfalls

Interception capacity renews when water evaporate

Methods of estimation

Empirical value

Regression analysis (measured rainfall in an open area vs under canopy)

Lump subtraction based on vegetation storage capacity ndash (eg 005 ndash 02 cm)

Other methods including temporal variation existhellip (Dohnal et al 2014 JHH 62 p 277-284)

Interception capacity

Depression storage surface detention

SD hellip surface detentionbull Water in excess of depression storage ndash due to flowing waterbull Depends on discharge

DS hellip depression storage (= surface retention dead storage)bull Water stored in surface pits and depressionsbull When water supply rate exceeds infiltrationbull Water subsequently infiltrate or evaporate

Sometimes as a lumped value or

(after Antoine et al 2012 Catena 91 p 10-20)119863119878 = 119878119863(1 minus 119890minus119875119890

1119878119863)

SD hellip max storage capacity Pe hellip rainfall excess (Precipitation ndash Infiltration)

Infiltration process Infiltration is a process during which water on the soil

surface enters the soil profile (generally vertical process)

This process is connected to whole soil profile

Infiltration rate ndash actual amount of water entering the soil profile (units of depth per time ndash LT-1) it is a description of process

Infiltration capacity ndash maximum amount of water which can enter the soil profile (units of depth per time ndash LT-1) it is a property of soil profile

Infiltration process Infiltration rate

dt

tditi

)()(

Total infiltration (cumulative infiltration)

dttitI

t

0

)()( Saturation zone

Wetting zone

Transmission zone

Infiltration process Affected by

Soil properties

Soil horizons

Hydraulic conductivity

Soil surface condition

Vegetation cover

Antecendent soil moisture

hellip

Infiltration measurement 3 main approaches

Ring infiltrometer method Sprinkler method Permeameter method

To obtain Saturated hydraulic conductivity (KS)= ability of soil to conduct water under saturated conditions

or look for temporal changes of infiltration rate

L

hKAQ

Darcyrsquos law

zh

Total hydraulic head

Infiltration measurement -Sprinkler Mostly as I = Rainfall ndash Runoff

where rainfall intensity and duration is set runoff is measured

Difficult to mimic natural rain (intensity raindrop sizes kinetic energy)

Slope is necessary

Representative area can be reached

Technically demanding

Infiltration measurement ndash ring infiltrometer Single or double rings inserted into ground

Shallow ponding

t

Hi

i ndash infiltration rateH ndash decrease of water levelt ndash time step

Infiltration measurement Ponded infiltration is usually measured using double

ring infiltrometer

Infiltration is measured until the infiltration rate is constant

Infiltration measurement Unstaturated flow is more complex process

It can be measured by disc infiltrometers

Infiltration can bemeasured underdifferent suctionpressures conditions

Infiltration measurement Record of infiltration field measurement

Infiltration calculation Different methods are available for infiltration calculation

Richardlsquos equation Hortonlsquos model Philliplsquos model Green-Ampt method Kostiakov equation

Approximation of an exact theory (Richards)

Richardrsquos equation (1D)

Kz

D

Kz

K

z

zKqz

KD

Soil water diffusivityDarcy

K

zD

zz

q

t

Darcy + continuity eq

Green-Ampt method Introduced by Green and Ampt in 1911 This method is based on two main assumptions

Wetting front is sharp defined Depth of ponding (depth of water on the surface pressure

head on the surface) is negligible

(fro

mE

lem

ents

of

Ph

ysic

al

Hyd

rolo

gy

19

98

)

Wetting front depth

Moisture profile in time t

Green-Ampt method Actual infiltration rate

(fro

mA

pp

lied

Hyd

rolo

gy

19

88

)

dt

tdIti

)()(

Darcylsquos law

dz

dhKq

Total infiltration

)()( isfLtI

fLtI )(

Green-Ampt method

(fro

mA

pp

lied

Hyd

rolo

gy

19

88

)

qi

f

f

L

LhKi

))(( 0

h0 is considered to be very small and therefore it is neglected

IL f

I

IKi

Green-Ampt method

tKtI

tI

))(

1ln()(

hellip after solving

I

IK

dt

dI

)1(

I

Ki

(fro

mA

pp

lied

Hyd

rolo

gy

19

88

)

00 z fLz finite difference

KI

K

Green-Ampt method - parameters Best way to get values of Green-Ampt method parameters is

to measure them in the field Hydraulic conductivity porosity wetting front suction head

If no measurement is available the values can be obtained from tables according to soil class

Soil type PorosityEffectiveporosity

Suctionhead

Hydraulicconductivity

- - mm mmh

Sand 0437 0417 495 1178

loamy sand 0437 0401 613 299

sandy loam 0453 0412 1101 109

loam 0463 0434 889 34

silt loam 0501 0486 1668 65

sandy clay loam 0398 0330 2185 15

clay loam 0464 0309 2088 10

silty clay loam 0471 0432 2730 10

sandy clay 0430 0321 2390 06

silty clay 0479 0423 2922 05

clay 0475 0385 3163 03

Hortonlsquos equation Based on the concept introduced by Horton (1933) ndash an

example of infiltration excess approach to direct runoffcalculation

Decreasing infiltration rate in a few hours scale due to soil compaction air entrapment etc

tk

cc eiiiti 0

i(t) ndash infiltration rate at time t (LT-1)ic ndash minimum infiltration rate (infiltration rate after soil saturationor minimum infiltration rate) (LT-1)i0 ndash initial infiltration rate (maximum infiltration rate) (LT-1)k ndash decay constant specific to the soil

tkc

c ek

iititI

10

Philliplsquos equation Two-parameter method introduced by Philip (1957)

TtS

ti 2

1

2

i(t) ndash infiltration rate at time t (LT-1)I(t) ndash cumulative infiltration at time t (L)S ndash sorptivity ndash function of soil suction potential (parameter specificto the soil) (LT-05)T ndash transmisivity (minimum infiltration rate mostly assumed to beclose to saturated hydraulic conductivity) (LT-1)

tTtStI 21

Conclusion The infiltration process is a very complex and can be

described using the models of different complexity and detail

Simple methods involve significant simplifictaion of theprocess as well as the soil profile

Saptial and temporar variability Problematic input data for distributed models

Depression storage surface detention

SD hellip surface detentionbull Water in excess of depression storage ndash due to flowing waterbull Depends on discharge

DS hellip depression storage (= surface retention dead storage)bull Water stored in surface pits and depressionsbull When water supply rate exceeds infiltrationbull Water subsequently infiltrate or evaporate

Sometimes as a lumped value or

(after Antoine et al 2012 Catena 91 p 10-20)119863119878 = 119878119863(1 minus 119890minus119875119890

1119878119863)

SD hellip max storage capacity Pe hellip rainfall excess (Precipitation ndash Infiltration)

Infiltration process Infiltration is a process during which water on the soil

surface enters the soil profile (generally vertical process)

This process is connected to whole soil profile

Infiltration rate ndash actual amount of water entering the soil profile (units of depth per time ndash LT-1) it is a description of process

Infiltration capacity ndash maximum amount of water which can enter the soil profile (units of depth per time ndash LT-1) it is a property of soil profile

Infiltration process Infiltration rate

dt

tditi

)()(

Total infiltration (cumulative infiltration)

dttitI

t

0

)()( Saturation zone

Wetting zone

Transmission zone

Infiltration process Affected by

Soil properties

Soil horizons

Hydraulic conductivity

Soil surface condition

Vegetation cover

Antecendent soil moisture

hellip

Infiltration measurement 3 main approaches

Ring infiltrometer method Sprinkler method Permeameter method

To obtain Saturated hydraulic conductivity (KS)= ability of soil to conduct water under saturated conditions

or look for temporal changes of infiltration rate

L

hKAQ

Darcyrsquos law

zh

Total hydraulic head

Infiltration measurement -Sprinkler Mostly as I = Rainfall ndash Runoff

where rainfall intensity and duration is set runoff is measured

Difficult to mimic natural rain (intensity raindrop sizes kinetic energy)

Slope is necessary

Representative area can be reached

Technically demanding

Infiltration measurement ndash ring infiltrometer Single or double rings inserted into ground

Shallow ponding

t

Hi

i ndash infiltration rateH ndash decrease of water levelt ndash time step

Infiltration measurement Ponded infiltration is usually measured using double

ring infiltrometer

Infiltration is measured until the infiltration rate is constant

Infiltration measurement Unstaturated flow is more complex process

It can be measured by disc infiltrometers

Infiltration can bemeasured underdifferent suctionpressures conditions

Infiltration measurement Record of infiltration field measurement

Infiltration calculation Different methods are available for infiltration calculation

Richardlsquos equation Hortonlsquos model Philliplsquos model Green-Ampt method Kostiakov equation

Approximation of an exact theory (Richards)

Richardrsquos equation (1D)

Kz

D

Kz

K

z

zKqz

KD

Soil water diffusivityDarcy

K

zD

zz

q

t

Darcy + continuity eq

Green-Ampt method Introduced by Green and Ampt in 1911 This method is based on two main assumptions

Wetting front is sharp defined Depth of ponding (depth of water on the surface pressure

head on the surface) is negligible

(fro

mE

lem

ents

of

Ph

ysic

al

Hyd

rolo

gy

19

98

)

Wetting front depth

Moisture profile in time t

Green-Ampt method Actual infiltration rate

(fro

mA

pp

lied

Hyd

rolo

gy

19

88

)

dt

tdIti

)()(

Darcylsquos law

dz

dhKq

Total infiltration

)()( isfLtI

fLtI )(

Green-Ampt method

(fro

mA

pp

lied

Hyd

rolo

gy

19

88

)

qi

f

f

L

LhKi

))(( 0

h0 is considered to be very small and therefore it is neglected

IL f

I

IKi

Green-Ampt method

tKtI

tI

))(

1ln()(

hellip after solving

I

IK

dt

dI

)1(

I

Ki

(fro

mA

pp

lied

Hyd

rolo

gy

19

88

)

00 z fLz finite difference

KI

K

Green-Ampt method - parameters Best way to get values of Green-Ampt method parameters is

to measure them in the field Hydraulic conductivity porosity wetting front suction head

If no measurement is available the values can be obtained from tables according to soil class

Soil type PorosityEffectiveporosity

Suctionhead

Hydraulicconductivity

- - mm mmh

Sand 0437 0417 495 1178

loamy sand 0437 0401 613 299

sandy loam 0453 0412 1101 109

loam 0463 0434 889 34

silt loam 0501 0486 1668 65

sandy clay loam 0398 0330 2185 15

clay loam 0464 0309 2088 10

silty clay loam 0471 0432 2730 10

sandy clay 0430 0321 2390 06

silty clay 0479 0423 2922 05

clay 0475 0385 3163 03

Hortonlsquos equation Based on the concept introduced by Horton (1933) ndash an

example of infiltration excess approach to direct runoffcalculation

Decreasing infiltration rate in a few hours scale due to soil compaction air entrapment etc

tk

cc eiiiti 0

i(t) ndash infiltration rate at time t (LT-1)ic ndash minimum infiltration rate (infiltration rate after soil saturationor minimum infiltration rate) (LT-1)i0 ndash initial infiltration rate (maximum infiltration rate) (LT-1)k ndash decay constant specific to the soil

tkc

c ek

iititI

10

Philliplsquos equation Two-parameter method introduced by Philip (1957)

TtS

ti 2

1

2

i(t) ndash infiltration rate at time t (LT-1)I(t) ndash cumulative infiltration at time t (L)S ndash sorptivity ndash function of soil suction potential (parameter specificto the soil) (LT-05)T ndash transmisivity (minimum infiltration rate mostly assumed to beclose to saturated hydraulic conductivity) (LT-1)

tTtStI 21

Conclusion The infiltration process is a very complex and can be

described using the models of different complexity and detail

Simple methods involve significant simplifictaion of theprocess as well as the soil profile

Saptial and temporar variability Problematic input data for distributed models

Infiltration process Infiltration is a process during which water on the soil

surface enters the soil profile (generally vertical process)

This process is connected to whole soil profile

Infiltration rate ndash actual amount of water entering the soil profile (units of depth per time ndash LT-1) it is a description of process

Infiltration capacity ndash maximum amount of water which can enter the soil profile (units of depth per time ndash LT-1) it is a property of soil profile

Infiltration process Infiltration rate

dt

tditi

)()(

Total infiltration (cumulative infiltration)

dttitI

t

0

)()( Saturation zone

Wetting zone

Transmission zone

Infiltration process Affected by

Soil properties

Soil horizons

Hydraulic conductivity

Soil surface condition

Vegetation cover

Antecendent soil moisture

hellip

Infiltration measurement 3 main approaches

Ring infiltrometer method Sprinkler method Permeameter method

To obtain Saturated hydraulic conductivity (KS)= ability of soil to conduct water under saturated conditions

or look for temporal changes of infiltration rate

L

hKAQ

Darcyrsquos law

zh

Total hydraulic head

Infiltration measurement -Sprinkler Mostly as I = Rainfall ndash Runoff

where rainfall intensity and duration is set runoff is measured

Difficult to mimic natural rain (intensity raindrop sizes kinetic energy)

Slope is necessary

Representative area can be reached

Technically demanding

Infiltration measurement ndash ring infiltrometer Single or double rings inserted into ground

Shallow ponding

t

Hi

i ndash infiltration rateH ndash decrease of water levelt ndash time step

Infiltration measurement Ponded infiltration is usually measured using double

ring infiltrometer

Infiltration is measured until the infiltration rate is constant

Infiltration measurement Unstaturated flow is more complex process

It can be measured by disc infiltrometers

Infiltration can bemeasured underdifferent suctionpressures conditions

Infiltration measurement Record of infiltration field measurement

Infiltration calculation Different methods are available for infiltration calculation

Richardlsquos equation Hortonlsquos model Philliplsquos model Green-Ampt method Kostiakov equation

Approximation of an exact theory (Richards)

Richardrsquos equation (1D)

Kz

D

Kz

K

z

zKqz

KD

Soil water diffusivityDarcy

K

zD

zz

q

t

Darcy + continuity eq

Green-Ampt method Introduced by Green and Ampt in 1911 This method is based on two main assumptions

Wetting front is sharp defined Depth of ponding (depth of water on the surface pressure

head on the surface) is negligible

(fro

mE

lem

ents

of

Ph

ysic

al

Hyd

rolo

gy

19

98

)

Wetting front depth

Moisture profile in time t

Green-Ampt method Actual infiltration rate

(fro

mA

pp

lied

Hyd

rolo

gy

19

88

)

dt

tdIti

)()(

Darcylsquos law

dz

dhKq

Total infiltration

)()( isfLtI

fLtI )(

Green-Ampt method

(fro

mA

pp

lied

Hyd

rolo

gy

19

88

)

qi

f

f

L

LhKi

))(( 0

h0 is considered to be very small and therefore it is neglected

IL f

I

IKi

Green-Ampt method

tKtI

tI

))(

1ln()(

hellip after solving

I

IK

dt

dI

)1(

I

Ki

(fro

mA

pp

lied

Hyd

rolo

gy

19

88

)

00 z fLz finite difference

KI

K

Green-Ampt method - parameters Best way to get values of Green-Ampt method parameters is

to measure them in the field Hydraulic conductivity porosity wetting front suction head

If no measurement is available the values can be obtained from tables according to soil class

Soil type PorosityEffectiveporosity

Suctionhead

Hydraulicconductivity

- - mm mmh

Sand 0437 0417 495 1178

loamy sand 0437 0401 613 299

sandy loam 0453 0412 1101 109

loam 0463 0434 889 34

silt loam 0501 0486 1668 65

sandy clay loam 0398 0330 2185 15

clay loam 0464 0309 2088 10

silty clay loam 0471 0432 2730 10

sandy clay 0430 0321 2390 06

silty clay 0479 0423 2922 05

clay 0475 0385 3163 03

Hortonlsquos equation Based on the concept introduced by Horton (1933) ndash an

example of infiltration excess approach to direct runoffcalculation

Decreasing infiltration rate in a few hours scale due to soil compaction air entrapment etc

tk

cc eiiiti 0

i(t) ndash infiltration rate at time t (LT-1)ic ndash minimum infiltration rate (infiltration rate after soil saturationor minimum infiltration rate) (LT-1)i0 ndash initial infiltration rate (maximum infiltration rate) (LT-1)k ndash decay constant specific to the soil

tkc

c ek

iititI

10

Philliplsquos equation Two-parameter method introduced by Philip (1957)

TtS

ti 2

1

2

i(t) ndash infiltration rate at time t (LT-1)I(t) ndash cumulative infiltration at time t (L)S ndash sorptivity ndash function of soil suction potential (parameter specificto the soil) (LT-05)T ndash transmisivity (minimum infiltration rate mostly assumed to beclose to saturated hydraulic conductivity) (LT-1)

tTtStI 21

Conclusion The infiltration process is a very complex and can be

described using the models of different complexity and detail

Simple methods involve significant simplifictaion of theprocess as well as the soil profile

Saptial and temporar variability Problematic input data for distributed models

Infiltration process Infiltration rate

dt

tditi

)()(

Total infiltration (cumulative infiltration)

dttitI

t

0

)()( Saturation zone

Wetting zone

Transmission zone

Infiltration process Affected by

Soil properties

Soil horizons

Hydraulic conductivity

Soil surface condition

Vegetation cover

Antecendent soil moisture

hellip

Infiltration measurement 3 main approaches

Ring infiltrometer method Sprinkler method Permeameter method

To obtain Saturated hydraulic conductivity (KS)= ability of soil to conduct water under saturated conditions

or look for temporal changes of infiltration rate

L

hKAQ

Darcyrsquos law

zh

Total hydraulic head

Infiltration measurement -Sprinkler Mostly as I = Rainfall ndash Runoff

where rainfall intensity and duration is set runoff is measured

Difficult to mimic natural rain (intensity raindrop sizes kinetic energy)

Slope is necessary

Representative area can be reached

Technically demanding

Infiltration measurement ndash ring infiltrometer Single or double rings inserted into ground

Shallow ponding

t

Hi

i ndash infiltration rateH ndash decrease of water levelt ndash time step

Infiltration measurement Ponded infiltration is usually measured using double

ring infiltrometer

Infiltration is measured until the infiltration rate is constant

Infiltration measurement Unstaturated flow is more complex process

It can be measured by disc infiltrometers

Infiltration can bemeasured underdifferent suctionpressures conditions

Infiltration measurement Record of infiltration field measurement

Infiltration calculation Different methods are available for infiltration calculation

Richardlsquos equation Hortonlsquos model Philliplsquos model Green-Ampt method Kostiakov equation

Approximation of an exact theory (Richards)

Richardrsquos equation (1D)

Kz

D

Kz

K

z

zKqz

KD

Soil water diffusivityDarcy

K

zD

zz

q

t

Darcy + continuity eq

Green-Ampt method Introduced by Green and Ampt in 1911 This method is based on two main assumptions

Wetting front is sharp defined Depth of ponding (depth of water on the surface pressure

head on the surface) is negligible

(fro

mE

lem

ents

of

Ph

ysic

al

Hyd

rolo

gy

19

98

)

Wetting front depth

Moisture profile in time t

Green-Ampt method Actual infiltration rate

(fro

mA

pp

lied

Hyd

rolo

gy

19

88

)

dt

tdIti

)()(

Darcylsquos law

dz

dhKq

Total infiltration

)()( isfLtI

fLtI )(

Green-Ampt method

(fro

mA

pp

lied

Hyd

rolo

gy

19

88

)

qi

f

f

L

LhKi

))(( 0

h0 is considered to be very small and therefore it is neglected

IL f

I

IKi

Green-Ampt method

tKtI

tI

))(

1ln()(

hellip after solving

I

IK

dt

dI

)1(

I

Ki

(fro

mA

pp

lied

Hyd

rolo

gy

19

88

)

00 z fLz finite difference

KI

K

Green-Ampt method - parameters Best way to get values of Green-Ampt method parameters is

to measure them in the field Hydraulic conductivity porosity wetting front suction head

If no measurement is available the values can be obtained from tables according to soil class

Soil type PorosityEffectiveporosity

Suctionhead

Hydraulicconductivity

- - mm mmh

Sand 0437 0417 495 1178

loamy sand 0437 0401 613 299

sandy loam 0453 0412 1101 109

loam 0463 0434 889 34

silt loam 0501 0486 1668 65

sandy clay loam 0398 0330 2185 15

clay loam 0464 0309 2088 10

silty clay loam 0471 0432 2730 10

sandy clay 0430 0321 2390 06

silty clay 0479 0423 2922 05

clay 0475 0385 3163 03

Hortonlsquos equation Based on the concept introduced by Horton (1933) ndash an

example of infiltration excess approach to direct runoffcalculation

Decreasing infiltration rate in a few hours scale due to soil compaction air entrapment etc

tk

cc eiiiti 0

i(t) ndash infiltration rate at time t (LT-1)ic ndash minimum infiltration rate (infiltration rate after soil saturationor minimum infiltration rate) (LT-1)i0 ndash initial infiltration rate (maximum infiltration rate) (LT-1)k ndash decay constant specific to the soil

tkc

c ek

iititI

10

Philliplsquos equation Two-parameter method introduced by Philip (1957)

TtS

ti 2

1

2

i(t) ndash infiltration rate at time t (LT-1)I(t) ndash cumulative infiltration at time t (L)S ndash sorptivity ndash function of soil suction potential (parameter specificto the soil) (LT-05)T ndash transmisivity (minimum infiltration rate mostly assumed to beclose to saturated hydraulic conductivity) (LT-1)

tTtStI 21

Conclusion The infiltration process is a very complex and can be

described using the models of different complexity and detail

Simple methods involve significant simplifictaion of theprocess as well as the soil profile

Saptial and temporar variability Problematic input data for distributed models

Infiltration process Affected by

Soil properties

Soil horizons

Hydraulic conductivity

Soil surface condition

Vegetation cover

Antecendent soil moisture

hellip

Infiltration measurement 3 main approaches

Ring infiltrometer method Sprinkler method Permeameter method

To obtain Saturated hydraulic conductivity (KS)= ability of soil to conduct water under saturated conditions

or look for temporal changes of infiltration rate

L

hKAQ

Darcyrsquos law

zh

Total hydraulic head

Infiltration measurement -Sprinkler Mostly as I = Rainfall ndash Runoff

where rainfall intensity and duration is set runoff is measured

Difficult to mimic natural rain (intensity raindrop sizes kinetic energy)

Slope is necessary

Representative area can be reached

Technically demanding

Infiltration measurement ndash ring infiltrometer Single or double rings inserted into ground

Shallow ponding

t

Hi

i ndash infiltration rateH ndash decrease of water levelt ndash time step

Infiltration measurement Ponded infiltration is usually measured using double

ring infiltrometer

Infiltration is measured until the infiltration rate is constant

Infiltration measurement Unstaturated flow is more complex process

It can be measured by disc infiltrometers

Infiltration can bemeasured underdifferent suctionpressures conditions

Infiltration measurement Record of infiltration field measurement

Infiltration calculation Different methods are available for infiltration calculation

Richardlsquos equation Hortonlsquos model Philliplsquos model Green-Ampt method Kostiakov equation

Approximation of an exact theory (Richards)

Richardrsquos equation (1D)

Kz

D

Kz

K

z

zKqz

KD

Soil water diffusivityDarcy

K

zD

zz

q

t

Darcy + continuity eq

Green-Ampt method Introduced by Green and Ampt in 1911 This method is based on two main assumptions

Wetting front is sharp defined Depth of ponding (depth of water on the surface pressure

head on the surface) is negligible

(fro

mE

lem

ents

of

Ph

ysic

al

Hyd

rolo

gy

19

98

)

Wetting front depth

Moisture profile in time t

Green-Ampt method Actual infiltration rate

(fro

mA

pp

lied

Hyd

rolo

gy

19

88

)

dt

tdIti

)()(

Darcylsquos law

dz

dhKq

Total infiltration

)()( isfLtI

fLtI )(

Green-Ampt method

(fro

mA

pp

lied

Hyd

rolo

gy

19

88

)

qi

f

f

L

LhKi

))(( 0

h0 is considered to be very small and therefore it is neglected

IL f

I

IKi

Green-Ampt method

tKtI

tI

))(

1ln()(

hellip after solving

I

IK

dt

dI

)1(

I

Ki

(fro

mA

pp

lied

Hyd

rolo

gy

19

88

)

00 z fLz finite difference

KI

K

Green-Ampt method - parameters Best way to get values of Green-Ampt method parameters is

to measure them in the field Hydraulic conductivity porosity wetting front suction head

If no measurement is available the values can be obtained from tables according to soil class

Soil type PorosityEffectiveporosity

Suctionhead

Hydraulicconductivity

- - mm mmh

Sand 0437 0417 495 1178

loamy sand 0437 0401 613 299

sandy loam 0453 0412 1101 109

loam 0463 0434 889 34

silt loam 0501 0486 1668 65

sandy clay loam 0398 0330 2185 15

clay loam 0464 0309 2088 10

silty clay loam 0471 0432 2730 10

sandy clay 0430 0321 2390 06

silty clay 0479 0423 2922 05

clay 0475 0385 3163 03

Hortonlsquos equation Based on the concept introduced by Horton (1933) ndash an

example of infiltration excess approach to direct runoffcalculation

Decreasing infiltration rate in a few hours scale due to soil compaction air entrapment etc

tk

cc eiiiti 0

i(t) ndash infiltration rate at time t (LT-1)ic ndash minimum infiltration rate (infiltration rate after soil saturationor minimum infiltration rate) (LT-1)i0 ndash initial infiltration rate (maximum infiltration rate) (LT-1)k ndash decay constant specific to the soil

tkc

c ek

iititI

10

Philliplsquos equation Two-parameter method introduced by Philip (1957)

TtS

ti 2

1

2

i(t) ndash infiltration rate at time t (LT-1)I(t) ndash cumulative infiltration at time t (L)S ndash sorptivity ndash function of soil suction potential (parameter specificto the soil) (LT-05)T ndash transmisivity (minimum infiltration rate mostly assumed to beclose to saturated hydraulic conductivity) (LT-1)

tTtStI 21

Conclusion The infiltration process is a very complex and can be

described using the models of different complexity and detail

Simple methods involve significant simplifictaion of theprocess as well as the soil profile

Saptial and temporar variability Problematic input data for distributed models

Infiltration measurement 3 main approaches

Ring infiltrometer method Sprinkler method Permeameter method

To obtain Saturated hydraulic conductivity (KS)= ability of soil to conduct water under saturated conditions

or look for temporal changes of infiltration rate

L

hKAQ

Darcyrsquos law

zh

Total hydraulic head

Infiltration measurement -Sprinkler Mostly as I = Rainfall ndash Runoff

where rainfall intensity and duration is set runoff is measured

Difficult to mimic natural rain (intensity raindrop sizes kinetic energy)

Slope is necessary

Representative area can be reached

Technically demanding

Infiltration measurement ndash ring infiltrometer Single or double rings inserted into ground

Shallow ponding

t

Hi

i ndash infiltration rateH ndash decrease of water levelt ndash time step

Infiltration measurement Ponded infiltration is usually measured using double

ring infiltrometer

Infiltration is measured until the infiltration rate is constant

Infiltration measurement Unstaturated flow is more complex process

It can be measured by disc infiltrometers

Infiltration can bemeasured underdifferent suctionpressures conditions

Infiltration measurement Record of infiltration field measurement

Infiltration calculation Different methods are available for infiltration calculation

Richardlsquos equation Hortonlsquos model Philliplsquos model Green-Ampt method Kostiakov equation

Approximation of an exact theory (Richards)

Richardrsquos equation (1D)

Kz

D

Kz

K

z

zKqz

KD

Soil water diffusivityDarcy

K

zD

zz

q

t

Darcy + continuity eq

Green-Ampt method Introduced by Green and Ampt in 1911 This method is based on two main assumptions

Wetting front is sharp defined Depth of ponding (depth of water on the surface pressure

head on the surface) is negligible

(fro

mE

lem

ents

of

Ph

ysic

al

Hyd

rolo

gy

19

98

)

Wetting front depth

Moisture profile in time t

Green-Ampt method Actual infiltration rate

(fro

mA

pp

lied

Hyd

rolo

gy

19

88

)

dt

tdIti

)()(

Darcylsquos law

dz

dhKq

Total infiltration

)()( isfLtI

fLtI )(

Green-Ampt method

(fro

mA

pp

lied

Hyd

rolo

gy

19

88

)

qi

f

f

L

LhKi

))(( 0

h0 is considered to be very small and therefore it is neglected

IL f

I

IKi

Green-Ampt method

tKtI

tI

))(

1ln()(

hellip after solving

I

IK

dt

dI

)1(

I

Ki

(fro

mA

pp

lied

Hyd

rolo

gy

19

88

)

00 z fLz finite difference

KI

K

Green-Ampt method - parameters Best way to get values of Green-Ampt method parameters is

to measure them in the field Hydraulic conductivity porosity wetting front suction head

If no measurement is available the values can be obtained from tables according to soil class

Soil type PorosityEffectiveporosity

Suctionhead

Hydraulicconductivity

- - mm mmh

Sand 0437 0417 495 1178

loamy sand 0437 0401 613 299

sandy loam 0453 0412 1101 109

loam 0463 0434 889 34

silt loam 0501 0486 1668 65

sandy clay loam 0398 0330 2185 15

clay loam 0464 0309 2088 10

silty clay loam 0471 0432 2730 10

sandy clay 0430 0321 2390 06

silty clay 0479 0423 2922 05

clay 0475 0385 3163 03

Hortonlsquos equation Based on the concept introduced by Horton (1933) ndash an

example of infiltration excess approach to direct runoffcalculation

Decreasing infiltration rate in a few hours scale due to soil compaction air entrapment etc

tk

cc eiiiti 0

i(t) ndash infiltration rate at time t (LT-1)ic ndash minimum infiltration rate (infiltration rate after soil saturationor minimum infiltration rate) (LT-1)i0 ndash initial infiltration rate (maximum infiltration rate) (LT-1)k ndash decay constant specific to the soil

tkc

c ek

iititI

10

Philliplsquos equation Two-parameter method introduced by Philip (1957)

TtS

ti 2

1

2

i(t) ndash infiltration rate at time t (LT-1)I(t) ndash cumulative infiltration at time t (L)S ndash sorptivity ndash function of soil suction potential (parameter specificto the soil) (LT-05)T ndash transmisivity (minimum infiltration rate mostly assumed to beclose to saturated hydraulic conductivity) (LT-1)

tTtStI 21

Conclusion The infiltration process is a very complex and can be

described using the models of different complexity and detail

Simple methods involve significant simplifictaion of theprocess as well as the soil profile

Saptial and temporar variability Problematic input data for distributed models

Infiltration measurement -Sprinkler Mostly as I = Rainfall ndash Runoff

where rainfall intensity and duration is set runoff is measured

Difficult to mimic natural rain (intensity raindrop sizes kinetic energy)

Slope is necessary

Representative area can be reached

Technically demanding

Infiltration measurement ndash ring infiltrometer Single or double rings inserted into ground

Shallow ponding

t

Hi

i ndash infiltration rateH ndash decrease of water levelt ndash time step

Infiltration measurement Ponded infiltration is usually measured using double

ring infiltrometer

Infiltration is measured until the infiltration rate is constant

Infiltration measurement Unstaturated flow is more complex process

It can be measured by disc infiltrometers

Infiltration can bemeasured underdifferent suctionpressures conditions

Infiltration measurement Record of infiltration field measurement

Infiltration calculation Different methods are available for infiltration calculation

Richardlsquos equation Hortonlsquos model Philliplsquos model Green-Ampt method Kostiakov equation

Approximation of an exact theory (Richards)

Richardrsquos equation (1D)

Kz

D

Kz

K

z

zKqz

KD

Soil water diffusivityDarcy

K

zD

zz

q

t

Darcy + continuity eq

Green-Ampt method Introduced by Green and Ampt in 1911 This method is based on two main assumptions

Wetting front is sharp defined Depth of ponding (depth of water on the surface pressure

head on the surface) is negligible

(fro

mE

lem

ents

of

Ph

ysic

al

Hyd

rolo

gy

19

98

)

Wetting front depth

Moisture profile in time t

Green-Ampt method Actual infiltration rate

(fro

mA

pp

lied

Hyd

rolo

gy

19

88

)

dt

tdIti

)()(

Darcylsquos law

dz

dhKq

Total infiltration

)()( isfLtI

fLtI )(

Green-Ampt method

(fro

mA

pp

lied

Hyd

rolo

gy

19

88

)

qi

f

f

L

LhKi

))(( 0

h0 is considered to be very small and therefore it is neglected

IL f

I

IKi

Green-Ampt method

tKtI

tI

))(

1ln()(

hellip after solving

I

IK

dt

dI

)1(

I

Ki

(fro

mA

pp

lied

Hyd

rolo

gy

19

88

)

00 z fLz finite difference

KI

K

Green-Ampt method - parameters Best way to get values of Green-Ampt method parameters is

to measure them in the field Hydraulic conductivity porosity wetting front suction head

If no measurement is available the values can be obtained from tables according to soil class

Soil type PorosityEffectiveporosity

Suctionhead

Hydraulicconductivity

- - mm mmh

Sand 0437 0417 495 1178

loamy sand 0437 0401 613 299

sandy loam 0453 0412 1101 109

loam 0463 0434 889 34

silt loam 0501 0486 1668 65

sandy clay loam 0398 0330 2185 15

clay loam 0464 0309 2088 10

silty clay loam 0471 0432 2730 10

sandy clay 0430 0321 2390 06

silty clay 0479 0423 2922 05

clay 0475 0385 3163 03

Hortonlsquos equation Based on the concept introduced by Horton (1933) ndash an

example of infiltration excess approach to direct runoffcalculation

Decreasing infiltration rate in a few hours scale due to soil compaction air entrapment etc

tk

cc eiiiti 0

i(t) ndash infiltration rate at time t (LT-1)ic ndash minimum infiltration rate (infiltration rate after soil saturationor minimum infiltration rate) (LT-1)i0 ndash initial infiltration rate (maximum infiltration rate) (LT-1)k ndash decay constant specific to the soil

tkc

c ek

iititI

10

Philliplsquos equation Two-parameter method introduced by Philip (1957)

TtS

ti 2

1

2

i(t) ndash infiltration rate at time t (LT-1)I(t) ndash cumulative infiltration at time t (L)S ndash sorptivity ndash function of soil suction potential (parameter specificto the soil) (LT-05)T ndash transmisivity (minimum infiltration rate mostly assumed to beclose to saturated hydraulic conductivity) (LT-1)

tTtStI 21

Conclusion The infiltration process is a very complex and can be

described using the models of different complexity and detail

Simple methods involve significant simplifictaion of theprocess as well as the soil profile

Saptial and temporar variability Problematic input data for distributed models

Infiltration measurement ndash ring infiltrometer Single or double rings inserted into ground

Shallow ponding

t

Hi

i ndash infiltration rateH ndash decrease of water levelt ndash time step

Infiltration measurement Ponded infiltration is usually measured using double

ring infiltrometer

Infiltration is measured until the infiltration rate is constant

Infiltration measurement Unstaturated flow is more complex process

It can be measured by disc infiltrometers

Infiltration can bemeasured underdifferent suctionpressures conditions

Infiltration measurement Record of infiltration field measurement

Infiltration calculation Different methods are available for infiltration calculation

Richardlsquos equation Hortonlsquos model Philliplsquos model Green-Ampt method Kostiakov equation

Approximation of an exact theory (Richards)

Richardrsquos equation (1D)

Kz

D

Kz

K

z

zKqz

KD

Soil water diffusivityDarcy

K

zD

zz

q

t

Darcy + continuity eq

Green-Ampt method Introduced by Green and Ampt in 1911 This method is based on two main assumptions

Wetting front is sharp defined Depth of ponding (depth of water on the surface pressure

head on the surface) is negligible

(fro

mE

lem

ents

of

Ph

ysic

al

Hyd

rolo

gy

19

98

)

Wetting front depth

Moisture profile in time t

Green-Ampt method Actual infiltration rate

(fro

mA

pp

lied

Hyd

rolo

gy

19

88

)

dt

tdIti

)()(

Darcylsquos law

dz

dhKq

Total infiltration

)()( isfLtI

fLtI )(

Green-Ampt method

(fro

mA

pp

lied

Hyd

rolo

gy

19

88

)

qi

f

f

L

LhKi

))(( 0

h0 is considered to be very small and therefore it is neglected

IL f

I

IKi

Green-Ampt method

tKtI

tI

))(

1ln()(

hellip after solving

I

IK

dt

dI

)1(

I

Ki

(fro

mA

pp

lied

Hyd

rolo

gy

19

88

)

00 z fLz finite difference

KI

K

Green-Ampt method - parameters Best way to get values of Green-Ampt method parameters is

to measure them in the field Hydraulic conductivity porosity wetting front suction head

If no measurement is available the values can be obtained from tables according to soil class

Soil type PorosityEffectiveporosity

Suctionhead

Hydraulicconductivity

- - mm mmh

Sand 0437 0417 495 1178

loamy sand 0437 0401 613 299

sandy loam 0453 0412 1101 109

loam 0463 0434 889 34

silt loam 0501 0486 1668 65

sandy clay loam 0398 0330 2185 15

clay loam 0464 0309 2088 10

silty clay loam 0471 0432 2730 10

sandy clay 0430 0321 2390 06

silty clay 0479 0423 2922 05

clay 0475 0385 3163 03

Hortonlsquos equation Based on the concept introduced by Horton (1933) ndash an

example of infiltration excess approach to direct runoffcalculation

Decreasing infiltration rate in a few hours scale due to soil compaction air entrapment etc

tk

cc eiiiti 0

i(t) ndash infiltration rate at time t (LT-1)ic ndash minimum infiltration rate (infiltration rate after soil saturationor minimum infiltration rate) (LT-1)i0 ndash initial infiltration rate (maximum infiltration rate) (LT-1)k ndash decay constant specific to the soil

tkc

c ek

iititI

10

Philliplsquos equation Two-parameter method introduced by Philip (1957)

TtS

ti 2

1

2

i(t) ndash infiltration rate at time t (LT-1)I(t) ndash cumulative infiltration at time t (L)S ndash sorptivity ndash function of soil suction potential (parameter specificto the soil) (LT-05)T ndash transmisivity (minimum infiltration rate mostly assumed to beclose to saturated hydraulic conductivity) (LT-1)

tTtStI 21

Conclusion The infiltration process is a very complex and can be

described using the models of different complexity and detail

Simple methods involve significant simplifictaion of theprocess as well as the soil profile

Saptial and temporar variability Problematic input data for distributed models

Infiltration measurement Ponded infiltration is usually measured using double

ring infiltrometer

Infiltration is measured until the infiltration rate is constant

Infiltration measurement Unstaturated flow is more complex process

It can be measured by disc infiltrometers

Infiltration can bemeasured underdifferent suctionpressures conditions

Infiltration measurement Record of infiltration field measurement

Infiltration calculation Different methods are available for infiltration calculation

Richardlsquos equation Hortonlsquos model Philliplsquos model Green-Ampt method Kostiakov equation

Approximation of an exact theory (Richards)

Richardrsquos equation (1D)

Kz

D

Kz

K

z

zKqz

KD

Soil water diffusivityDarcy

K

zD

zz

q

t

Darcy + continuity eq

Green-Ampt method Introduced by Green and Ampt in 1911 This method is based on two main assumptions

Wetting front is sharp defined Depth of ponding (depth of water on the surface pressure

head on the surface) is negligible

(fro

mE

lem

ents

of

Ph

ysic

al

Hyd

rolo

gy

19

98

)

Wetting front depth

Moisture profile in time t

Green-Ampt method Actual infiltration rate

(fro

mA

pp

lied

Hyd

rolo

gy

19

88

)

dt

tdIti

)()(

Darcylsquos law

dz

dhKq

Total infiltration

)()( isfLtI

fLtI )(

Green-Ampt method

(fro

mA

pp

lied

Hyd

rolo

gy

19

88

)

qi

f

f

L

LhKi

))(( 0

h0 is considered to be very small and therefore it is neglected

IL f

I

IKi

Green-Ampt method

tKtI

tI

))(

1ln()(

hellip after solving

I

IK

dt

dI

)1(

I

Ki

(fro

mA

pp

lied

Hyd

rolo

gy

19

88

)

00 z fLz finite difference

KI

K

Green-Ampt method - parameters Best way to get values of Green-Ampt method parameters is

to measure them in the field Hydraulic conductivity porosity wetting front suction head

If no measurement is available the values can be obtained from tables according to soil class

Soil type PorosityEffectiveporosity

Suctionhead

Hydraulicconductivity

- - mm mmh

Sand 0437 0417 495 1178

loamy sand 0437 0401 613 299

sandy loam 0453 0412 1101 109

loam 0463 0434 889 34

silt loam 0501 0486 1668 65

sandy clay loam 0398 0330 2185 15

clay loam 0464 0309 2088 10

silty clay loam 0471 0432 2730 10

sandy clay 0430 0321 2390 06

silty clay 0479 0423 2922 05

clay 0475 0385 3163 03

Hortonlsquos equation Based on the concept introduced by Horton (1933) ndash an

example of infiltration excess approach to direct runoffcalculation

Decreasing infiltration rate in a few hours scale due to soil compaction air entrapment etc

tk

cc eiiiti 0

i(t) ndash infiltration rate at time t (LT-1)ic ndash minimum infiltration rate (infiltration rate after soil saturationor minimum infiltration rate) (LT-1)i0 ndash initial infiltration rate (maximum infiltration rate) (LT-1)k ndash decay constant specific to the soil

tkc

c ek

iititI

10

Philliplsquos equation Two-parameter method introduced by Philip (1957)

TtS

ti 2

1

2

i(t) ndash infiltration rate at time t (LT-1)I(t) ndash cumulative infiltration at time t (L)S ndash sorptivity ndash function of soil suction potential (parameter specificto the soil) (LT-05)T ndash transmisivity (minimum infiltration rate mostly assumed to beclose to saturated hydraulic conductivity) (LT-1)

tTtStI 21

Conclusion The infiltration process is a very complex and can be

described using the models of different complexity and detail

Simple methods involve significant simplifictaion of theprocess as well as the soil profile

Saptial and temporar variability Problematic input data for distributed models

Infiltration measurement Unstaturated flow is more complex process

It can be measured by disc infiltrometers

Infiltration can bemeasured underdifferent suctionpressures conditions

Infiltration measurement Record of infiltration field measurement

Infiltration calculation Different methods are available for infiltration calculation

Richardlsquos equation Hortonlsquos model Philliplsquos model Green-Ampt method Kostiakov equation

Approximation of an exact theory (Richards)

Richardrsquos equation (1D)

Kz

D

Kz

K

z

zKqz

KD

Soil water diffusivityDarcy

K

zD

zz

q

t

Darcy + continuity eq

Green-Ampt method Introduced by Green and Ampt in 1911 This method is based on two main assumptions

Wetting front is sharp defined Depth of ponding (depth of water on the surface pressure

head on the surface) is negligible

(fro

mE

lem

ents

of

Ph

ysic

al

Hyd

rolo

gy

19

98

)

Wetting front depth

Moisture profile in time t

Green-Ampt method Actual infiltration rate

(fro

mA

pp

lied

Hyd

rolo

gy

19

88

)

dt

tdIti

)()(

Darcylsquos law

dz

dhKq

Total infiltration

)()( isfLtI

fLtI )(

Green-Ampt method

(fro

mA

pp

lied

Hyd

rolo

gy

19

88

)

qi

f

f

L

LhKi

))(( 0

h0 is considered to be very small and therefore it is neglected

IL f

I

IKi

Green-Ampt method

tKtI

tI

))(

1ln()(

hellip after solving

I

IK

dt

dI

)1(

I

Ki

(fro

mA

pp

lied

Hyd

rolo

gy

19

88

)

00 z fLz finite difference

KI

K

Green-Ampt method - parameters Best way to get values of Green-Ampt method parameters is

to measure them in the field Hydraulic conductivity porosity wetting front suction head

If no measurement is available the values can be obtained from tables according to soil class

Soil type PorosityEffectiveporosity

Suctionhead

Hydraulicconductivity

- - mm mmh

Sand 0437 0417 495 1178

loamy sand 0437 0401 613 299

sandy loam 0453 0412 1101 109

loam 0463 0434 889 34

silt loam 0501 0486 1668 65

sandy clay loam 0398 0330 2185 15

clay loam 0464 0309 2088 10

silty clay loam 0471 0432 2730 10

sandy clay 0430 0321 2390 06

silty clay 0479 0423 2922 05

clay 0475 0385 3163 03

Hortonlsquos equation Based on the concept introduced by Horton (1933) ndash an

example of infiltration excess approach to direct runoffcalculation

Decreasing infiltration rate in a few hours scale due to soil compaction air entrapment etc

tk

cc eiiiti 0

i(t) ndash infiltration rate at time t (LT-1)ic ndash minimum infiltration rate (infiltration rate after soil saturationor minimum infiltration rate) (LT-1)i0 ndash initial infiltration rate (maximum infiltration rate) (LT-1)k ndash decay constant specific to the soil

tkc

c ek

iititI

10

Philliplsquos equation Two-parameter method introduced by Philip (1957)

TtS

ti 2

1

2

i(t) ndash infiltration rate at time t (LT-1)I(t) ndash cumulative infiltration at time t (L)S ndash sorptivity ndash function of soil suction potential (parameter specificto the soil) (LT-05)T ndash transmisivity (minimum infiltration rate mostly assumed to beclose to saturated hydraulic conductivity) (LT-1)

tTtStI 21

Conclusion The infiltration process is a very complex and can be

described using the models of different complexity and detail

Simple methods involve significant simplifictaion of theprocess as well as the soil profile

Saptial and temporar variability Problematic input data for distributed models

Infiltration measurement Record of infiltration field measurement

Infiltration calculation Different methods are available for infiltration calculation

Richardlsquos equation Hortonlsquos model Philliplsquos model Green-Ampt method Kostiakov equation

Approximation of an exact theory (Richards)

Richardrsquos equation (1D)

Kz

D

Kz

K

z

zKqz

KD

Soil water diffusivityDarcy

K

zD

zz

q

t

Darcy + continuity eq

Green-Ampt method Introduced by Green and Ampt in 1911 This method is based on two main assumptions

Wetting front is sharp defined Depth of ponding (depth of water on the surface pressure

head on the surface) is negligible

(fro

mE

lem

ents

of

Ph

ysic

al

Hyd

rolo

gy

19

98

)

Wetting front depth

Moisture profile in time t

Green-Ampt method Actual infiltration rate

(fro

mA

pp

lied

Hyd

rolo

gy

19

88

)

dt

tdIti

)()(

Darcylsquos law

dz

dhKq

Total infiltration

)()( isfLtI

fLtI )(

Green-Ampt method

(fro

mA

pp

lied

Hyd

rolo

gy

19

88

)

qi

f

f

L

LhKi

))(( 0

h0 is considered to be very small and therefore it is neglected

IL f

I

IKi

Green-Ampt method

tKtI

tI

))(

1ln()(

hellip after solving

I

IK

dt

dI

)1(

I

Ki

(fro

mA

pp

lied

Hyd

rolo

gy

19

88

)

00 z fLz finite difference

KI

K

Green-Ampt method - parameters Best way to get values of Green-Ampt method parameters is

to measure them in the field Hydraulic conductivity porosity wetting front suction head

If no measurement is available the values can be obtained from tables according to soil class

Soil type PorosityEffectiveporosity

Suctionhead

Hydraulicconductivity

- - mm mmh

Sand 0437 0417 495 1178

loamy sand 0437 0401 613 299

sandy loam 0453 0412 1101 109

loam 0463 0434 889 34

silt loam 0501 0486 1668 65

sandy clay loam 0398 0330 2185 15

clay loam 0464 0309 2088 10

silty clay loam 0471 0432 2730 10

sandy clay 0430 0321 2390 06

silty clay 0479 0423 2922 05

clay 0475 0385 3163 03

Hortonlsquos equation Based on the concept introduced by Horton (1933) ndash an

example of infiltration excess approach to direct runoffcalculation

Decreasing infiltration rate in a few hours scale due to soil compaction air entrapment etc

tk

cc eiiiti 0

i(t) ndash infiltration rate at time t (LT-1)ic ndash minimum infiltration rate (infiltration rate after soil saturationor minimum infiltration rate) (LT-1)i0 ndash initial infiltration rate (maximum infiltration rate) (LT-1)k ndash decay constant specific to the soil

tkc

c ek

iititI

10

Philliplsquos equation Two-parameter method introduced by Philip (1957)

TtS

ti 2

1

2

i(t) ndash infiltration rate at time t (LT-1)I(t) ndash cumulative infiltration at time t (L)S ndash sorptivity ndash function of soil suction potential (parameter specificto the soil) (LT-05)T ndash transmisivity (minimum infiltration rate mostly assumed to beclose to saturated hydraulic conductivity) (LT-1)

tTtStI 21

Conclusion The infiltration process is a very complex and can be

described using the models of different complexity and detail

Simple methods involve significant simplifictaion of theprocess as well as the soil profile

Saptial and temporar variability Problematic input data for distributed models

Infiltration calculation Different methods are available for infiltration calculation

Richardlsquos equation Hortonlsquos model Philliplsquos model Green-Ampt method Kostiakov equation

Approximation of an exact theory (Richards)

Richardrsquos equation (1D)

Kz

D

Kz

K

z

zKqz

KD

Soil water diffusivityDarcy

K

zD

zz

q

t

Darcy + continuity eq

Green-Ampt method Introduced by Green and Ampt in 1911 This method is based on two main assumptions

Wetting front is sharp defined Depth of ponding (depth of water on the surface pressure

head on the surface) is negligible

(fro

mE

lem

ents

of

Ph

ysic

al

Hyd

rolo

gy

19

98

)

Wetting front depth

Moisture profile in time t

Green-Ampt method Actual infiltration rate

(fro

mA

pp

lied

Hyd

rolo

gy

19

88

)

dt

tdIti

)()(

Darcylsquos law

dz

dhKq

Total infiltration

)()( isfLtI

fLtI )(

Green-Ampt method

(fro

mA

pp

lied

Hyd

rolo

gy

19

88

)

qi

f

f

L

LhKi

))(( 0

h0 is considered to be very small and therefore it is neglected

IL f

I

IKi

Green-Ampt method

tKtI

tI

))(

1ln()(

hellip after solving

I

IK

dt

dI

)1(

I

Ki

(fro

mA

pp

lied

Hyd

rolo

gy

19

88

)

00 z fLz finite difference

KI

K

Green-Ampt method - parameters Best way to get values of Green-Ampt method parameters is

to measure them in the field Hydraulic conductivity porosity wetting front suction head

If no measurement is available the values can be obtained from tables according to soil class

Soil type PorosityEffectiveporosity

Suctionhead

Hydraulicconductivity

- - mm mmh

Sand 0437 0417 495 1178

loamy sand 0437 0401 613 299

sandy loam 0453 0412 1101 109

loam 0463 0434 889 34

silt loam 0501 0486 1668 65

sandy clay loam 0398 0330 2185 15

clay loam 0464 0309 2088 10

silty clay loam 0471 0432 2730 10

sandy clay 0430 0321 2390 06

silty clay 0479 0423 2922 05

clay 0475 0385 3163 03

Hortonlsquos equation Based on the concept introduced by Horton (1933) ndash an

example of infiltration excess approach to direct runoffcalculation

Decreasing infiltration rate in a few hours scale due to soil compaction air entrapment etc

tk

cc eiiiti 0

i(t) ndash infiltration rate at time t (LT-1)ic ndash minimum infiltration rate (infiltration rate after soil saturationor minimum infiltration rate) (LT-1)i0 ndash initial infiltration rate (maximum infiltration rate) (LT-1)k ndash decay constant specific to the soil

tkc

c ek

iititI

10

Philliplsquos equation Two-parameter method introduced by Philip (1957)

TtS

ti 2

1

2

i(t) ndash infiltration rate at time t (LT-1)I(t) ndash cumulative infiltration at time t (L)S ndash sorptivity ndash function of soil suction potential (parameter specificto the soil) (LT-05)T ndash transmisivity (minimum infiltration rate mostly assumed to beclose to saturated hydraulic conductivity) (LT-1)

tTtStI 21

Conclusion The infiltration process is a very complex and can be

described using the models of different complexity and detail

Simple methods involve significant simplifictaion of theprocess as well as the soil profile

Saptial and temporar variability Problematic input data for distributed models

Richardrsquos equation (1D)

Kz

D

Kz

K

z

zKqz

KD

Soil water diffusivityDarcy

K

zD

zz

q

t

Darcy + continuity eq

Green-Ampt method Introduced by Green and Ampt in 1911 This method is based on two main assumptions

Wetting front is sharp defined Depth of ponding (depth of water on the surface pressure

head on the surface) is negligible

(fro

mE

lem

ents

of

Ph

ysic

al

Hyd

rolo

gy

19

98

)

Wetting front depth

Moisture profile in time t

Green-Ampt method Actual infiltration rate

(fro

mA

pp

lied

Hyd

rolo

gy

19

88

)

dt

tdIti

)()(

Darcylsquos law

dz

dhKq

Total infiltration

)()( isfLtI

fLtI )(

Green-Ampt method

(fro

mA

pp

lied

Hyd

rolo

gy

19

88

)

qi

f

f

L

LhKi

))(( 0

h0 is considered to be very small and therefore it is neglected

IL f

I

IKi

Green-Ampt method

tKtI

tI

))(

1ln()(

hellip after solving

I

IK

dt

dI

)1(

I

Ki

(fro

mA

pp

lied

Hyd

rolo

gy

19

88

)

00 z fLz finite difference

KI

K

Green-Ampt method - parameters Best way to get values of Green-Ampt method parameters is

to measure them in the field Hydraulic conductivity porosity wetting front suction head

If no measurement is available the values can be obtained from tables according to soil class

Soil type PorosityEffectiveporosity

Suctionhead

Hydraulicconductivity

- - mm mmh

Sand 0437 0417 495 1178

loamy sand 0437 0401 613 299

sandy loam 0453 0412 1101 109

loam 0463 0434 889 34

silt loam 0501 0486 1668 65

sandy clay loam 0398 0330 2185 15

clay loam 0464 0309 2088 10

silty clay loam 0471 0432 2730 10

sandy clay 0430 0321 2390 06

silty clay 0479 0423 2922 05

clay 0475 0385 3163 03

Hortonlsquos equation Based on the concept introduced by Horton (1933) ndash an

example of infiltration excess approach to direct runoffcalculation

Decreasing infiltration rate in a few hours scale due to soil compaction air entrapment etc

tk

cc eiiiti 0

i(t) ndash infiltration rate at time t (LT-1)ic ndash minimum infiltration rate (infiltration rate after soil saturationor minimum infiltration rate) (LT-1)i0 ndash initial infiltration rate (maximum infiltration rate) (LT-1)k ndash decay constant specific to the soil

tkc

c ek

iititI

10

Philliplsquos equation Two-parameter method introduced by Philip (1957)

TtS

ti 2

1

2

i(t) ndash infiltration rate at time t (LT-1)I(t) ndash cumulative infiltration at time t (L)S ndash sorptivity ndash function of soil suction potential (parameter specificto the soil) (LT-05)T ndash transmisivity (minimum infiltration rate mostly assumed to beclose to saturated hydraulic conductivity) (LT-1)

tTtStI 21

Conclusion The infiltration process is a very complex and can be

described using the models of different complexity and detail

Simple methods involve significant simplifictaion of theprocess as well as the soil profile

Saptial and temporar variability Problematic input data for distributed models

Green-Ampt method Introduced by Green and Ampt in 1911 This method is based on two main assumptions

Wetting front is sharp defined Depth of ponding (depth of water on the surface pressure

head on the surface) is negligible

(fro

mE

lem

ents

of

Ph

ysic

al

Hyd

rolo

gy

19

98

)

Wetting front depth

Moisture profile in time t

Green-Ampt method Actual infiltration rate

(fro

mA

pp

lied

Hyd

rolo

gy

19

88

)

dt

tdIti

)()(

Darcylsquos law

dz

dhKq

Total infiltration

)()( isfLtI

fLtI )(

Green-Ampt method

(fro

mA

pp

lied

Hyd

rolo

gy

19

88

)

qi

f

f

L

LhKi

))(( 0

h0 is considered to be very small and therefore it is neglected

IL f

I

IKi

Green-Ampt method

tKtI

tI

))(

1ln()(

hellip after solving

I

IK

dt

dI

)1(

I

Ki

(fro

mA

pp

lied

Hyd

rolo

gy

19

88

)

00 z fLz finite difference

KI

K

Green-Ampt method - parameters Best way to get values of Green-Ampt method parameters is

to measure them in the field Hydraulic conductivity porosity wetting front suction head

If no measurement is available the values can be obtained from tables according to soil class

Soil type PorosityEffectiveporosity

Suctionhead

Hydraulicconductivity

- - mm mmh

Sand 0437 0417 495 1178

loamy sand 0437 0401 613 299

sandy loam 0453 0412 1101 109

loam 0463 0434 889 34

silt loam 0501 0486 1668 65

sandy clay loam 0398 0330 2185 15

clay loam 0464 0309 2088 10

silty clay loam 0471 0432 2730 10

sandy clay 0430 0321 2390 06

silty clay 0479 0423 2922 05

clay 0475 0385 3163 03

Hortonlsquos equation Based on the concept introduced by Horton (1933) ndash an

example of infiltration excess approach to direct runoffcalculation

Decreasing infiltration rate in a few hours scale due to soil compaction air entrapment etc

tk

cc eiiiti 0

i(t) ndash infiltration rate at time t (LT-1)ic ndash minimum infiltration rate (infiltration rate after soil saturationor minimum infiltration rate) (LT-1)i0 ndash initial infiltration rate (maximum infiltration rate) (LT-1)k ndash decay constant specific to the soil

tkc

c ek

iititI

10

Philliplsquos equation Two-parameter method introduced by Philip (1957)

TtS

ti 2

1

2

i(t) ndash infiltration rate at time t (LT-1)I(t) ndash cumulative infiltration at time t (L)S ndash sorptivity ndash function of soil suction potential (parameter specificto the soil) (LT-05)T ndash transmisivity (minimum infiltration rate mostly assumed to beclose to saturated hydraulic conductivity) (LT-1)

tTtStI 21

Conclusion The infiltration process is a very complex and can be

described using the models of different complexity and detail

Simple methods involve significant simplifictaion of theprocess as well as the soil profile

Saptial and temporar variability Problematic input data for distributed models

Green-Ampt method Actual infiltration rate

(fro

mA

pp

lied

Hyd

rolo

gy

19

88

)

dt

tdIti

)()(

Darcylsquos law

dz

dhKq

Total infiltration

)()( isfLtI

fLtI )(

Green-Ampt method

(fro

mA

pp

lied

Hyd

rolo

gy

19

88

)

qi

f

f

L

LhKi

))(( 0

h0 is considered to be very small and therefore it is neglected

IL f

I

IKi

Green-Ampt method

tKtI

tI

))(

1ln()(

hellip after solving

I

IK

dt

dI

)1(

I

Ki

(fro

mA

pp

lied

Hyd

rolo

gy

19

88

)

00 z fLz finite difference

KI

K

Green-Ampt method - parameters Best way to get values of Green-Ampt method parameters is

to measure them in the field Hydraulic conductivity porosity wetting front suction head

If no measurement is available the values can be obtained from tables according to soil class

Soil type PorosityEffectiveporosity

Suctionhead

Hydraulicconductivity

- - mm mmh

Sand 0437 0417 495 1178

loamy sand 0437 0401 613 299

sandy loam 0453 0412 1101 109

loam 0463 0434 889 34

silt loam 0501 0486 1668 65

sandy clay loam 0398 0330 2185 15

clay loam 0464 0309 2088 10

silty clay loam 0471 0432 2730 10

sandy clay 0430 0321 2390 06

silty clay 0479 0423 2922 05

clay 0475 0385 3163 03

Hortonlsquos equation Based on the concept introduced by Horton (1933) ndash an

example of infiltration excess approach to direct runoffcalculation

Decreasing infiltration rate in a few hours scale due to soil compaction air entrapment etc

tk

cc eiiiti 0

i(t) ndash infiltration rate at time t (LT-1)ic ndash minimum infiltration rate (infiltration rate after soil saturationor minimum infiltration rate) (LT-1)i0 ndash initial infiltration rate (maximum infiltration rate) (LT-1)k ndash decay constant specific to the soil

tkc

c ek

iititI

10

Philliplsquos equation Two-parameter method introduced by Philip (1957)

TtS

ti 2

1

2

i(t) ndash infiltration rate at time t (LT-1)I(t) ndash cumulative infiltration at time t (L)S ndash sorptivity ndash function of soil suction potential (parameter specificto the soil) (LT-05)T ndash transmisivity (minimum infiltration rate mostly assumed to beclose to saturated hydraulic conductivity) (LT-1)

tTtStI 21

Conclusion The infiltration process is a very complex and can be

described using the models of different complexity and detail

Simple methods involve significant simplifictaion of theprocess as well as the soil profile

Saptial and temporar variability Problematic input data for distributed models

Green-Ampt method

(fro

mA

pp

lied

Hyd

rolo

gy

19

88

)

qi

f

f

L

LhKi

))(( 0

h0 is considered to be very small and therefore it is neglected

IL f

I

IKi

Green-Ampt method

tKtI

tI

))(

1ln()(

hellip after solving

I

IK

dt

dI

)1(

I

Ki

(fro

mA

pp

lied

Hyd

rolo

gy

19

88

)

00 z fLz finite difference

KI

K

Green-Ampt method - parameters Best way to get values of Green-Ampt method parameters is

to measure them in the field Hydraulic conductivity porosity wetting front suction head

If no measurement is available the values can be obtained from tables according to soil class

Soil type PorosityEffectiveporosity

Suctionhead

Hydraulicconductivity

- - mm mmh

Sand 0437 0417 495 1178

loamy sand 0437 0401 613 299

sandy loam 0453 0412 1101 109

loam 0463 0434 889 34

silt loam 0501 0486 1668 65

sandy clay loam 0398 0330 2185 15

clay loam 0464 0309 2088 10

silty clay loam 0471 0432 2730 10

sandy clay 0430 0321 2390 06

silty clay 0479 0423 2922 05

clay 0475 0385 3163 03

Hortonlsquos equation Based on the concept introduced by Horton (1933) ndash an

example of infiltration excess approach to direct runoffcalculation

Decreasing infiltration rate in a few hours scale due to soil compaction air entrapment etc

tk

cc eiiiti 0

i(t) ndash infiltration rate at time t (LT-1)ic ndash minimum infiltration rate (infiltration rate after soil saturationor minimum infiltration rate) (LT-1)i0 ndash initial infiltration rate (maximum infiltration rate) (LT-1)k ndash decay constant specific to the soil

tkc

c ek

iititI

10

Philliplsquos equation Two-parameter method introduced by Philip (1957)

TtS

ti 2

1

2

i(t) ndash infiltration rate at time t (LT-1)I(t) ndash cumulative infiltration at time t (L)S ndash sorptivity ndash function of soil suction potential (parameter specificto the soil) (LT-05)T ndash transmisivity (minimum infiltration rate mostly assumed to beclose to saturated hydraulic conductivity) (LT-1)

tTtStI 21

Conclusion The infiltration process is a very complex and can be

described using the models of different complexity and detail

Simple methods involve significant simplifictaion of theprocess as well as the soil profile

Saptial and temporar variability Problematic input data for distributed models

Green-Ampt method

tKtI

tI

))(

1ln()(

hellip after solving

I

IK

dt

dI

)1(

I

Ki

(fro

mA

pp

lied

Hyd

rolo

gy

19

88

)

00 z fLz finite difference

KI

K

Green-Ampt method - parameters Best way to get values of Green-Ampt method parameters is

to measure them in the field Hydraulic conductivity porosity wetting front suction head

If no measurement is available the values can be obtained from tables according to soil class

Soil type PorosityEffectiveporosity

Suctionhead

Hydraulicconductivity

- - mm mmh

Sand 0437 0417 495 1178

loamy sand 0437 0401 613 299

sandy loam 0453 0412 1101 109

loam 0463 0434 889 34

silt loam 0501 0486 1668 65

sandy clay loam 0398 0330 2185 15

clay loam 0464 0309 2088 10

silty clay loam 0471 0432 2730 10

sandy clay 0430 0321 2390 06

silty clay 0479 0423 2922 05

clay 0475 0385 3163 03

Hortonlsquos equation Based on the concept introduced by Horton (1933) ndash an

example of infiltration excess approach to direct runoffcalculation

Decreasing infiltration rate in a few hours scale due to soil compaction air entrapment etc

tk

cc eiiiti 0

i(t) ndash infiltration rate at time t (LT-1)ic ndash minimum infiltration rate (infiltration rate after soil saturationor minimum infiltration rate) (LT-1)i0 ndash initial infiltration rate (maximum infiltration rate) (LT-1)k ndash decay constant specific to the soil

tkc

c ek

iititI

10

Philliplsquos equation Two-parameter method introduced by Philip (1957)

TtS

ti 2

1

2

i(t) ndash infiltration rate at time t (LT-1)I(t) ndash cumulative infiltration at time t (L)S ndash sorptivity ndash function of soil suction potential (parameter specificto the soil) (LT-05)T ndash transmisivity (minimum infiltration rate mostly assumed to beclose to saturated hydraulic conductivity) (LT-1)

tTtStI 21

Conclusion The infiltration process is a very complex and can be

described using the models of different complexity and detail

Simple methods involve significant simplifictaion of theprocess as well as the soil profile

Saptial and temporar variability Problematic input data for distributed models

Green-Ampt method - parameters Best way to get values of Green-Ampt method parameters is

to measure them in the field Hydraulic conductivity porosity wetting front suction head

If no measurement is available the values can be obtained from tables according to soil class

Soil type PorosityEffectiveporosity

Suctionhead

Hydraulicconductivity

- - mm mmh

Sand 0437 0417 495 1178

loamy sand 0437 0401 613 299

sandy loam 0453 0412 1101 109

loam 0463 0434 889 34

silt loam 0501 0486 1668 65

sandy clay loam 0398 0330 2185 15

clay loam 0464 0309 2088 10

silty clay loam 0471 0432 2730 10

sandy clay 0430 0321 2390 06

silty clay 0479 0423 2922 05

clay 0475 0385 3163 03

Hortonlsquos equation Based on the concept introduced by Horton (1933) ndash an

example of infiltration excess approach to direct runoffcalculation

Decreasing infiltration rate in a few hours scale due to soil compaction air entrapment etc

tk

cc eiiiti 0

i(t) ndash infiltration rate at time t (LT-1)ic ndash minimum infiltration rate (infiltration rate after soil saturationor minimum infiltration rate) (LT-1)i0 ndash initial infiltration rate (maximum infiltration rate) (LT-1)k ndash decay constant specific to the soil

tkc

c ek

iititI

10

Philliplsquos equation Two-parameter method introduced by Philip (1957)

TtS

ti 2

1

2

i(t) ndash infiltration rate at time t (LT-1)I(t) ndash cumulative infiltration at time t (L)S ndash sorptivity ndash function of soil suction potential (parameter specificto the soil) (LT-05)T ndash transmisivity (minimum infiltration rate mostly assumed to beclose to saturated hydraulic conductivity) (LT-1)

tTtStI 21

Conclusion The infiltration process is a very complex and can be

described using the models of different complexity and detail

Simple methods involve significant simplifictaion of theprocess as well as the soil profile

Saptial and temporar variability Problematic input data for distributed models

Hortonlsquos equation Based on the concept introduced by Horton (1933) ndash an

example of infiltration excess approach to direct runoffcalculation

Decreasing infiltration rate in a few hours scale due to soil compaction air entrapment etc

tk

cc eiiiti 0

i(t) ndash infiltration rate at time t (LT-1)ic ndash minimum infiltration rate (infiltration rate after soil saturationor minimum infiltration rate) (LT-1)i0 ndash initial infiltration rate (maximum infiltration rate) (LT-1)k ndash decay constant specific to the soil

tkc

c ek

iititI

10

Philliplsquos equation Two-parameter method introduced by Philip (1957)

TtS

ti 2

1

2

i(t) ndash infiltration rate at time t (LT-1)I(t) ndash cumulative infiltration at time t (L)S ndash sorptivity ndash function of soil suction potential (parameter specificto the soil) (LT-05)T ndash transmisivity (minimum infiltration rate mostly assumed to beclose to saturated hydraulic conductivity) (LT-1)

tTtStI 21

Conclusion The infiltration process is a very complex and can be

described using the models of different complexity and detail

Simple methods involve significant simplifictaion of theprocess as well as the soil profile

Saptial and temporar variability Problematic input data for distributed models

Philliplsquos equation Two-parameter method introduced by Philip (1957)

TtS

ti 2

1

2

i(t) ndash infiltration rate at time t (LT-1)I(t) ndash cumulative infiltration at time t (L)S ndash sorptivity ndash function of soil suction potential (parameter specificto the soil) (LT-05)T ndash transmisivity (minimum infiltration rate mostly assumed to beclose to saturated hydraulic conductivity) (LT-1)

tTtStI 21

Conclusion The infiltration process is a very complex and can be

described using the models of different complexity and detail

Simple methods involve significant simplifictaion of theprocess as well as the soil profile

Saptial and temporar variability Problematic input data for distributed models

Conclusion The infiltration process is a very complex and can be

described using the models of different complexity and detail

Simple methods involve significant simplifictaion of theprocess as well as the soil profile

Saptial and temporar variability Problematic input data for distributed models