Summary: A new method for departure point determination on Cartesian grids, the semi-analytical upwind path line tracing (SUT) method, is presented and compared to two typical departure point determination methods used in semi-Lagrangian advection schemes, the Euler method and the four-step Runge-Kutta method. Rigorous comparisons of the three methods were conducted for a severely curving hypothetical flow field and for advective transport in the rotation of a Gaussian concentration hill. The SUT method was shown to have equivalent accuracy to the Runge-Kutta method but with significantly improved computational efficiency. Depending on the case being simulated, the SUT method provides either far greater or equivalent computational efficiency and more certain accuracy than the Euler method.