Lava flows as kinematic waves

A recently proposed model for the emplacement of lava flows is reinterpreted as a kinematic wave theory for the depth of the flow. Explicit kinematic wave solutions and their properties are derived for three time-dependent boundary conditions of practical interest. These boundary conditions correspond to effusion rates that decrease, increase, and crest and broadly reflect types of eruption behavior documented in the geologic literature. Particular attention is given to the way source behavior propagates along the flow in relation to the advance of the flow itself.