Infiltration Capacity Decay Horton Calculator

Horton's equation treats infiltration capacity as a rate that begins at f0, the value a dry profile can accept, and relaxes exponentially toward fc, the rate the soil sustains once wetted. The decline is not one process but several acting together: capillary suction gradients weaken as pore water content rises, raindrop impact breaks surface aggregates and seals the top few millimetres with fines, expansive clays swell shut, and air trapped ahead of the wetting front resists displacement. Because of this, fc converges on the saturated hydraulic conductivity of the limiting horizon and behaves as a soil property, while f0 is strongly condition-dependent. Representative values: sands show f0 of 200 to 500 mm/hr with fc of 25 to 50 mm/hr; clay loams f0 of 50 to 100 mm/hr with fc of 2 to 5 mm/hr; heavy clays fall below 2 mm/hr at steady state. The decay constant k typically lies between 0.02 and 2 per minute, so most of the drop is complete within 30 to 120 minutes. Integrating the rate gives cumulative depth F(T) = fc x T + ((f0 - fc)/k) x (1 - e^(-kT)), which is what runoff models actually need. The chief limitation is that the equation was derived assuming the surface is ponded from t = 0. When rainfall intensity is below capacity, actual infiltration is supply-limited and elapsed clock time overstates the decay, so a time-compression correction that indexes decay to cumulative infiltration rather than to the clock is required. The three parameters are empirical fits with no soil-physics meaning and must be recalibrated for each site and antecedent moisture state.

Robert Elmer Horton (1875-1945) ran a private hydrological consultancy and experimental laboratory at Voorheesville, New York. He set out the infiltration-capacity concept in a 1933 paper in the Transactions of the American Geophysical Union on the role of infiltration in the hydrologic cycle, and gave the exponential decay form its fullest statement in 1940 in the Proceedings of the Soil Science Society of America. His central claim was that a catchment converts rain into storm runoff only where rainfall intensity exceeds infiltration capacity, a mechanism now called infiltration-excess or Hortonian overland flow. Horton himself argued that the decline was driven mainly at the surface, by rain packing and sealing, rather than deep within the profile. The wider mechanism was later contested: field work by Betson in 1964 and by Dunne and Black in 1970 showed that in humid, vegetated catchments storm runoff usually originates from saturated near-channel strips instead, so Hortonian flow is now understood as one of several runoff mechanisms, dominant in arid, crusted, compacted, or paved settings. The equation nevertheless survived because it requires nothing more than a rate-versus-time record, which double-ring infiltrometers readily supply. It was written into the EPA Storm Water Management Model at its first release in 1971 and into the US Army Corps of Engineers HEC series, and it remains a selectable loss method in both SWMM and HEC-HMS alongside the more physically grounded Green-Ampt option.