ALIVE (Advance Linear Velocity): Surface Irrigation Rate Balance Theory

Previously, surface irrigation hydraulic models used the principle of mass conservation to simulate the advance of water along the field and to solve the inverse problem of finding the infiltration function from measurements of advance. A flow rate rather than a volume balance theory, in combination with an advance function that is more physically realistic than the usual power function, is introduced, in which the Horton equation is used to describe infiltration, $Q_{\mathrm{in}}={\mathrm{Ax}}^{\prime }\left(t\right)+{\int }_0^{t}I(t-u)x^{\prime }\left(u\right)\mathrm{du}\text{.}$ In this equation, $Q_{\mathrm{in}}$ is the inflow rate per furrow or per unit width of border; A is the average cross‐sectional area of the stream; $x^{\prime }\left(t\right)$ is advance rate at irrigation time t; I is infiltration rate from Horton's equation; u is advance time to position x; and $t-u$ is intake‐opportunity time at x. An exponential advance rate function emerges from the solution of the flow rate equation. Furthermore, the inverse problem is solved in the same manner, a given exponential advance rate function leads to the determination of a Horton law infiltration function. The resulting advance rate, if expressed as a function of distance $[x^{\prime }=f(x\left)\right]\text{,}$ shows two distinctive linear decreasing parts from which infiltration parameters as well as surface storage emerge.