Infiltration Capacity Decay Horton Calculator
Our hydrology & water resources calculator computes infiltration capacity decay horton accurately. Enter your values for instant results.
Reviewed by Daniel Agrici, Founder & Lead Developer
Formula
f(t) = fc + (f0 - fc) x e^(-kt)
Horton's equation f(t) = fc + (f0 - fc) x e^(-kt) describes how soil infiltration capacity decays exponentially over time. f0 is the initial (maximum) infiltration rate when soil is dry, fc is the final steady-state rate when soil is fully saturated, k is the decay constant (min⁻¹) controlling how quickly capacity drops, and t is elapsed time in minutes. The result f(t) gives instantaneous infiltration capacity in mm/hr, used to determine when rainfall intensity exceeds soil absorption and surface runoff begins.
Worked Examples
Example 1: Sandy Loam After Dry Spell
Problem:f0 = 200 mm/hr, fc = 25 mm/hr, k = 0.35 min⁻¹, t = 30 min
Solution:f(30) = 25 + (200 - 25) × e^(-0.35×30) = 25 + 175 × e^(-10.5) = 25 + 0.05 ≈ 25.05 mm/hr
Result:f(30 min) ≈ 25 mm/hr — nearly at steady state after 30 minutes
Example 2: Clay Soil During Storm
Problem:f0 = 40 mm/hr, fc = 3 mm/hr, k = 0.08 min⁻¹, rainfall intensity = 25 mm/hr
Solution:f(20) = 3 + (40-3)×e^(-0.08×20) = 3 + 37×0.202 = 3 + 7.47 = 10.47 mm/hr > 25 mm/hr? No — rainfall exceeds f at t>0, so runoff begins immediately
Result:f(20 min) = 10.5 mm/hr; since rainfall (25) > f(20), runoff = 25 − 10.5 = 14.5 mm/hr
Frequently Asked Questions
What is Horton\'s infiltration capacity decay model?
Robert Horton (1940) observed that soil infiltration capacity starts high when soil is dry and declines exponentially to a steady final rate as pores saturate: f(t) = fc + (f0 − fc) × e^(−kt). f0 is the initial rate, fc is the final (saturated) rate, k is the decay constant, and t is time. It remains one of the most widely used infiltration models in hydrological practice.
How do I calibrate Horton\'s parameters from field data?
Conduct a double-ring infiltrometer test, recording infiltration rate at regular intervals (e.g., every 5 minutes). Plot rate vs. time on a semi-log scale: the intercept at t = 0 gives f0 and the asymptote gives fc. Fit the exponential curve to estimate k. Alternatively, linearize by computing ln[f(t) − fc] and regressing against time to find k as the negative slope.
What is the difference between Horton and Green-Ampt infiltration models?
Horton\'s model is empirically fitted to observed rate data without explicit physical parameters. Green-Ampt uses a piston-flow assumption with physically measurable inputs: saturated hydraulic conductivity, wetting front suction, and initial water deficit. Green-Ampt is preferred when soil texture data are available; Horton is convenient when time-series rate data are available but soil physical properties are not.
How is Horton\'s infiltration used in stormwater runoff modeling?
HEC-HMS and similar models use Horton infiltration to separate rainfall into runoff-producing excess and infiltration loss. The model integrates f(t) over the storm duration to find total infiltrated depth, then subtracts from rainfall to get direct runoff. Accurate f0, fc, and k values are critical: overestimating fc underestimates peak flood flow in design events.
References
Reviewed by Daniel Agrici, Founder & Lead Developer · Editorial policy