Science
Horton Soil Infiltration Capacity Curve f(t) & Cumulative Depth F(t)
Calculate exponentially decaying storm infiltration capacity f(t) = f_c + (f_0 - f_c) * EXP(-k * t) (mm/hr) and exact integrated cumulative infiltration depth F(t) = f_c * t + ((f_0 - f_c) / k) * (1 - EXP(-k * t)) (mm).
Model how dry soil infiltration saturates down to equilibrium conductivity during a storm!
At the onset of heavy rainfall (t = 0), dry unsaturated topsoil absorbs water rapidly at initial infiltration capacity f_0 (mm/hr). As pore spaces swell and fill, infiltration decays exponentially at decay constant k (1/hr) toward final saturated hydraulic capacity f_c <= f_0 according to Robert Horton's equation: f(t) = f_c + (f_0 - f_c) * EXP(-k * t)!
Integrating f(t) from 0 to elapsed storm duration t (hours) yields exact Cumulative Infiltration Depth F(t) (in mm): F(t) = (f_c * t) + ((f_0 - f_c) / k) * (1 - EXP(-k * t))! Whenever storm rainfall intensity exceeds f(t), the excess becomes overland Hortonian stormwater runoff!
| Elapsed Storm Time t (Sandy Loam: f_0 = 75 mm/hr, f_c = 10 mm/hr, k = 2.0 /hr) | Instantaneous Rate f(t) (mm/hr) | Cumulative Infiltrated F(t) (mm) | Soil Saturation State |
|---|---|---|---|
| Storm Start (t = 0.0 hr) | 75.00 mm/hr (= f_0) | 0.00 mm | Dry capillary suction peak |
| 30 Minutes (t = 0.5 hr) | 33.91 mm/hr | 25.54 mm | Rapid pore-filling transition |
| 2 Hours (t = 2.0 hr) | 11.19 mm/hr (~ f_c) | 51.90 mm | Near-saturated equilibrium |
Horton Instantaneous Infiltration Rate f(t) (mm/hr)
Validates f_0 >= f_c >= 0, k > 0, and t >= 0, then evaluates f_c + (f_0 - f_c) * EXP(-k * t).
=IF(OR(B3 < 0, B2 < B3, B4 <= 0, B5 < 0), "Invalid Horton Soil Parameters", ROUND(B3 + (B2 - B3) * EXP(-B4 * B5), 2))Cumulative Infiltrated Water Depth F(t) (mm)
Evaluates exact integral (f_c * t) + ((f_0 - f_c) / k) * (1 - EXP(-k * t)).
=IF(OR(B3 < 0, B2 < B3, B4 <= 0, B5 < 0), "Invalid Horton Soil Parameters", ROUND((B3 * B5) + ((B2 - B3) / B4) * (1 - EXP(-B4 * B5)), 2))Try the example
Use the original values or change them to test your understanding.