Furrow Advance‐Rate Solution for Stochastic Infiltration Properties

A flow‐balance equation of surface irrigation is used to solve, section by section, the advance problem on heterogeneous soils. The advance‐linear‐velocity (ALIVE) solution as a function of time is a sum of exponential terms. Within a section, the properties are uniform, and two linear relationships between the advance rate $x\prime \left(t\right)$ and the distance $x\left(t\right)$ result. The inverse problem is solved step by step, identifying the Horton infiltration law of the studied section from the record of the velocity and the knowledge of the infiltration in the previous sections. Theoretical examples and field experiments are compared. When applying a standard evaluation approach, assuming a uniform infiltration function to an heterogeneous soil misleading results can occur. Perturbations in the advance rate can lead to an incorrect infiltration function when using either the standard ALIVE or Kostiakov‐based hydrologic models. However, a nonstandard ALIVE procedure is feasible since the distinction between the sections having different infiltration properties can be detected. To apply the velocity analysis, a high density of advance points is required.