*2.1. The Kinematic Wave Model*

The kinematic wave model considers that, in the Barré de Saint-Venant momentum equation, the inertial and pressure terms are negligible with respect to the friction and gravity terms [2]:

$$\frac{\partial \mathbf{A}}{\partial \mathbf{t}} + \frac{\partial \mathbf{Q}}{\partial \mathbf{x}} = -\mathbf{W} \tag{1}$$

$$\mathbf{S\_f} = \mathbf{S\_0} \tag{2}$$

where A = A(x,t) is the hydraulic area (L2); Q = Q(x,t) is the flow (L3T−1); W is the infiltrated volume per unit of furrow length in unit time (L3T−1); t is the time (T); So is the slope of the bottom of the furrow (LL<sup>−</sup>1); and Sf is the friction slope (LL<sup>−</sup>1).

#### *2.2. Green and Ampt Equations*

The Green and Ampt model [20] is established from the continuity equation and Darcy's law, with the following hypotheses: (a) the initial moisture profile in a soil column is uniform θ = θo; (b) water pressure at the soil surface is hydrostatic: ψ ≥ 0, where h is the water depth; (c) there is a well-defined wetting front characterized by negative pressure: ψ = −hf < 0, where hf is the suction at the wetting front; and (d) the region between the soil surface and the wetting front is completely saturated (plug flow)): θ = θ<sup>s</sup> and K = Ks, where Ks is the hydraulic saturation conductivity, that is, the value of the hydraulic conductivity of Darcy's law corresponding to the volumetric saturation content of water. The resulting ordinary differential equation is as follows:

$$\mathbf{V\_{I}} = \frac{\mathbf{dI}}{\mathbf{d}t} = \mathbf{K\_{t}} \left( \mathbf{1} + \frac{\mathbf{h} + \mathbf{h\_{f}}}{\mathbf{z\_{f}}} \right) \mathbf{I(t)} = \mathbf{z\_{f}} \Delta \boldsymbol{\theta}(\mathbf{t}) \tag{3}$$

where Δθ = θ<sup>s</sup> − θ<sup>o</sup> is the storage capacity; I is the accumulated infiltrate volume per unit of soil surface or infiltrated depth; and zf is the position of the wetting front.
