Theoretical investigation of the time variation of drainage density

Abstract A theoretical equation was developed to express the time variation of drainage density in a basin or geomorphic surface: magnified image D i ( t , T ) is the drainage density at time T on the i ‐th basin or geomorphic surface, which was formed at time t ; β (τ) is a factor related to the erosional force causing the development of the rivers of the basin or surface at time τ; δ i is the maximum drainage density; and D i is the initial drainage density on the i ‐th geomorphic surface or basin. The equation is based on the assumption that the drainage density increases with time until it reaches a specific upper limit δ i ( t )), the maximum drainage density, which is related to certain physical properties of the basin. The equations for various dated basins or geomorphic surfaces can be combined into one modified equation if the same relative erosional forces have acted on those basins or surfaces (β ( t ) = β ( t ) and if the basins or surfaces have the same physical properties δ i ( t ) = δ i ( t ), ( D i = D 0 ). The application of this equation to coastal terraces and glacial tills shows that the model is compatible with observed drainage densities on various dated basins or surfaces.