Technical Abstract: Kinematic-wave models of surface irrigation assume a fixed relationship between depth and discharge (typically, normal depth). When surface irrigation inflow is cut off, the calculated upstream flow depth goes to zero, since the discharge is zero. For short time steps, use of the Kinematic Wave model can create an incorrect water surface profile. Issues include difficulty in solving the continuity equation in the first upstream cell and a calculated adverse water-surface profile. The Kinematic Wave model produces a recession time at the upstream boundary that is too small, which can lead to incorrect calculation of recession times as water continues to recede from the surface. This problem becomes more severe for smaller values of bottom slope. In this paper, we present a zero-inertia approximation to the water surface profile at cutoff, which can be extended to the start of recession, after which calculations continue with the Kinematic-wave model. Introduction