Application of the meta-channel concept. Construction of the meta-channel hydraulic geometry for a natural catchment

This is the second in a series of three papers about the meta-channel concept which illustrates the derivation of the principles behind the concept, the construction of the hydraulic geometry and the application of the concept to flood routing, respectively. It was shown in the first of these that a channel network in a catchment can be conceptualized into a single 'effective channel' representation: a meta-channel. This study uses this conceptualization to show how such a meta-channel can be constructed. The techniques derived are applied to one catchment in New Zealand. We derive hydraulic geometries expressed as functions of flow distance throughout this catchment based on the Leopold and Maddock power laws. This derivation uses classical published values for hydraulic geometry coefficients and exponents, regional parameterization of the index flood relationship for New Zealand as a whole, together with local knowledge regarding the order of magnitude of the channel roughness. Conservation principles derived from the continuity and mechanical energy balance equations are used to construct the hydraulic geometry of the meta-channel of this catchment. A meta-channel long profile is established and compared against the mainstream long profile. The effectiveness of the Leopold and Maddock power law assumptions is tested by comparing the derived hydraulic geometry against available field cross-sectional data for the gauging site at the outlet of the catchment.