What is watershed runoff?

TLDR

The study develops a nonlinear mathematical model that links rainfall and runoff to hydrologic variables and defines an apparent watershed infiltration capacity index for comparing watersheds. Using only storm rainfall, duration, and soil moisture, the model derives an equation with preserved coefficients and strong statistical control, yielding the infiltration capacity index. The model’s coefficients are stable across watershed sizes, shows runoff originates from a small, consistent watershed portion, explains discrepancies between in situ and rainfall‑runoff infiltration measurements, and reveals why storm runoff is often nonlinear with respect to its drivers.

Abstract

A nonlinear mathematical model, starting with the integral of an infiltration capacity function, is developed to analytically equate the difference between rainfall and runoff to hydrologie variables. Only the three independent variables—storm rainfall, duration, and soil moisture—are used, and an equation is evolved in which the identity of the coefficients is kept intact and unusually good statistical control is maintained. The coefficients of the equation appear to be stable over a range of watershed sizes and conditions. The equation strongly indicates that runoff usually originates from a small, but relatively consistent, part of the watershed. The function can be manipulated to show a ‘function of apparent watershed infiltration capacity’ This function characterizes the infiltration capacity of that portion contributing to runoff, on the average, and should prove to be a useful infiltration capacity index with which watersheds can be compared. The equation itself provides insight into why in situ measurements of infiltration capacity seldom agree with the capacity determined from rainfall-runoff data. It also indicates why storm runoff frequently is not linear with respect to causative factors.