This thesis concerns general improvements to rainfall runoff models and focuses on two particular aspects, namely flood-wave routing in the main channel and consistent parameterisation of the rainfall-runoff process under different degrees of discretization of the catchment. The primary goal is to: 1) describe a general methodology for parameterisation of a rainfall runoff model so that the parameters are consistent across catchments modelled at different discretization scales and 2) develop an improved channel routing technique which takes proper account of the effects of all characteristics of wave motions in the channels. The first of these concerns methods for removing the inconsistency of parameterisation that results from different catchment discretizations in rainfall-runoff models. A stochastic Tokunaga network is developed for dealing with the scaling inconsistence. The problem of network embedding is also discussed. The second is a relatively simple method for the solution of the full dynamic wave equations for one-dimensional channel flow, which accurately simulates the effects of shocks. / PhD Doctorate