Infiltration

Accum

ula

ted Infiltra

tion (

mm

)

200

300

400

Infiltration depends on the soil type

Accum

ula

ted Infiltra

tion (

mm

)

100

60 120 180

Time (minutes)

Taylor and Ashcroft, 1972]

But also on other factors such as flux (temperature, viscosity,

hydraulic head) and surface conditions (land use and land

cover).

Rainfall at the soil surface is partitioned into infiltration (I) and surface

runoff(Q).

Experimentally, it is observed that not all the rainfall is able to infiltrate into

the soil... this is due to two main reasons:

1. the rainfall intensity is too high, and the maximum (instantaneous)

Infiltration

1. the rainfall intensity is too high, and the maximum (instantaneous)

infiltration rate is exceeded (Horton mechanism).

2. the cumulated rainfall volume is too high and the soil becomes

completely saturated - there is no room for an increase of the water

storage (Dunne mechanism).

Horton mechanism (Horton, 1945): the soil ischaracterized (at any time instant t) by a maximuminfiltration capacity, f*(t), which depends on the soilmoisture conditions and decreases during a givenevent. Thus we have:

P

P

qo

f

Dunne mechanism: water is infiltrated into the soilunless the soil becomes completely saturated (alower impervious surface below the root zone isassumed). After the saturation all the rainfallbecomes surface runoff.

P

P

Pqo

P

f

• Horton mechanism usually dominates in arid and

semiarid climates, where the storms are concentrated in

short periods and are characterized by large rainfall

heights.

• Hortonian surface runoff is usually widespread in space,

but quite limited and local in time.

Infiltration

• Dunne mechanism usually becomes more important in

humid climates, where rainfall events are characterized

by large annual volumes but lower intensities.

• Dunnian surface runoff could be extended in time (once

that saturation is reached), but is usually limited in

space.

Subsurface stormflow

PP

P

qs

Surface runoff is not the only component

Perched subsurface stormflow

PP

P

qs

Flood hydrograph is usually separated into 3 contributions:

• Baseflow

• Slow component (subsurface flow)

• Fast component (surface runoff)

Hydrograph separation

Hydrograph separation is usually performed in a semi-log plane.

Hydrograph separation

a constant maximum infiltration capacity Φ is assumed.

Infiltration: Φ index model (Horton)

an exponential decrease of infiltration capacity f*

through time is assumed.

Infiltration: Horton model

Infiltration: Horton model

• fc [L/T]: minimum infiltration capacity (proportional to saturated

hydraulic conductivity);

• f0 [L/T]: initial infiltration capacity;

• k [1/T]: coefficient controlling the rate of variation of f through

time.time.

Horton model provides potential infiltration, in other words the

infiltration that is obtained if rainfall is larger than f(t): J(t) > f (t).

This condition is not always satisfied, expecially during the first

part of rainfall events when tipically potential infiltration is high as

a consequence of the low soil water content values.

Infiltration: Horton model

In order to avoid this inconsistency (potential infiltration larger than

precipitation), the horton curve can be shifted horizontally by a

certain time t* until the following conditions are satisfied:

• First condition imposes that in the time interval [0; t0] real

infiltration (obtained from the shifted curve) equals precipitation.

• Second condition imposes that at time t0 rainfall intensity equals

infiltration.

Infiltration: SCS model

Hypothesis

Infiltration: SCS model

Infiltration: SCS model

Infiltration: SCS model

SCS model with spatially variable CN

Catchment subdivided in Np sub-catchments through GIS

analysis. CN and S are constant within the sub-catchment but can

vary betweeen different sub-catchments.

Calibration of SCS model with spatially

variable CN�Unknowns are S and α ;

�α is usually assumed equal to 0.2 ;

�surface runoff volume obtained through hydrograph

decomposition (vs) is assumed equal to that calculated through

the SCS model,

where:

A: catchmet area;

tp: rainfall duration;

N: number of sub-catchments.

Calculation of effective precipitation with SCS

We assume that SCS model can be applied in a continuous way

Precipitation is known at discrete time intervals (aggregation of

precipitation occurred during that particular interval), thus J ∆t isprecipitation occurred during that particular interval), thus Jh,i ∆t is

the precipitation in the interval (i-1)∆t - (i)∆t for the sub-catchment

h. It follows that:

if

Calculation of effective precipitation with SCS

Effective precipitation intensity can be then derived from

cumulative runoff for each sub-catchment h:

Water infiltrating into the soil during the event in the sub-

catchment h is:

np: number of time step intervals in which the rainfall event has

been subdivided np = tp/∆t.

Calculation of subsurface stormflow with SCS

been subdivided np = tp/∆t.

Total infiltration is then provided by:

and then the subsurface partition coefficient can be computed

as:

We can then calculate the average intensity of the lost

infiltration:

where n is the number of time steps for which cumulated

Calculation of subsurface stormflow with SCS

where nh,1 is the number of time steps for which cumulated

rainfall is less than the initial loss.

For each time step we can then calulate the following quantity:

if

otherwise

Effective subsurface infiltration

Calculation of subsurface stormflow with SCS

2003

AfterBorga,2003