A method to track the flow of plasma in the Earth's ionosphere is presented. This takes maps of total electron content (TEC) at various times, and by comparing them derives a map of bulk velocities. The method is a modification of the Horn-Schunck scheme used in computer vision, whereby the aperture problem (caused by the scalar input field not containing enough information to uniquely constrain the vector output field) is overcome by making pragmatic assumptions about the divergence and rotation of the flow. The continuity equation linking plasma velocity and density is given source terms constrained by models of plasma generation and recombination. This can be used to mitigate solar terminator effects, where the close proximity of daytime plasma generation and nighttime recombination causes the impression of plasma flow. The method successfully reconstructs the behavior of test data. It also gives plausible results with real electron density maps from the 2003 Halloween Storms.