Horton‘s method and infiltration indices

There are so many empirical infiltration equation like as,

• Horton's Equation 
• Kostiakov Equation 
• Philip's Equation
• Green Ampt Equation 

Horton's Equation :

By using the time as an exponential decay Horton expressed the decay of infiltration capacity.   

fp = fc + (f0 – fc) e^{- kt}

^Where, 

fp = the infiltration capacity (depth/time) at some time t

fc  = a final or equilibrium capacity

fo  = the initial infiltration capacity

k  = a Horton's decay coefficient representing the rate of decrease in f capacity

 Horton's decay coefficient which depends upon soil characteristics and vegetation cover

 If the initial rainfall is less than fp in that the behaviour of infiltration capacity can be understood by, 

We  known that in the initial phase the infiltration capacity is more, because more water is required to fill the pores and as the pores fill with the water infiltration capacity reduces.

It indicates that if the rainfall supply exceeds the infiltration capacity, infiltration tends to decrease in an exponential manner. Although simple in form, difficulties in determining useful values for fo and k restrict the use of this equation. The area under the curve for any time interval represents the depth of water infiltrated during that interval. The infiltration rate is usually given in inches per hour and the time t in minutes, although other time increments are used and the coefficient k is determined accordingly.

Infiltration Indices : 

The average value of infiltration is called infiltration index.

Two types of infiltration indices

• φ - index
• w –index

φ index:

It is the average rainfall above which the rainfall volume is equal to the runoff volume. The φ index is derived from the rainfall hyetograph with the knowledge of the resulting runoff volume. 

 

w index:

It is the average infiltration rate during the time rainfall intensity exceeds the capacity rate. simply initial losses are separated from the total abstraction and average value of infiltration rate called w index.

 

Where,

P = total precipitation

R = Total runoff

Ia = Initial losses

te = The total time