“…Schematic showing a half-furrow and the implementation of a special boundary condition accounting for variable water depth in the furrow (Q p is the irrigation water supply rate, c p is the solute concentration in the incoming irrigation water, Q in is the water infiltration rate from the furrow into the soil profile across the furrow walls, c is the solute concentration in the furrow water and in the infiltration water, S is the volume of water in the half-furrow, h w is the water level in the furrow, α is the angle defining the slope of the ridge side, a is the half-width of the bottom of the furrow, b is the half-width of the water surface, and P and E are precipitation and evaporation fluxes, respectively) 1 3 transverse dispersivities were set at 10 and 1 cm that is at one-tenth and one-hundreds of the depth of the soil profile (Beven et al 1993), respectively. Note that no reactions are considered in (4) so it can only be used to describe the transport of nonreactive solutes such as chloride and nitrate.…”