Horton Infiltration

Horton's equation

Named after the same Robert E. Horton mentioned above, Horton's equation^[2] is another viable option when measuring ground infiltration rates or volumes. It is an empirical formula that says that infiltration starts at a constant rate, f₀, and is decreasing exponentially with time, t. After some time when the soil saturation level reaches a certain value, the rate of infiltration will level off to the rate f_c.

f_t = f_c + (f₀ − f_c)e ^− kt

Where

f_t is the infiltration rate at time t;

f₀ is the initial infiltration rate or maximum infiltration rate;

f_c is the constant or equilibrium infiltration rate after the soil has been saturated or minimum infiltration rate;

k is the decay constant specific to the soil.

The other method of using Horton's equation is as below. It can be used to find the total volume of infiltration, F, after time t.