Two models, KINEROS2 and EUROSEM, that simulate hydrologic event erosion on small catchments as a distributed, dynamic convective transport process are described briefly. Each employs a numerical solution of the mass balance equation, and uses time distributed rainfall rates as input. The equations for convective transport of sediment are quite similar to the kinematic equation for hydrologic response of a surface or channel. The features of the models are outlined, and the areas where research is needed are indicated. An example of simulation of rainfall plot test data is shown, demonstrating the practical value of dealing with particle size distribution, and an example is given of the value of these models in developing improved slope length factors in lumped models.