River stage or flow rates are required for the design and evaluation of hydraulic structures. Most river reaches are ungauged and a methodology is needed to estimate the stages, or rates of flow, at specific locations in streams where no measurements are available. Flood routing techniques are utilised to estimate the stages, or rates of flow, in order to predict flood wave propagation along river reaches. Models can be developed for gauged catchments and their parameters related to physical characteristics such as slope, reach width, reach length so that the approach can be applied to ungauged catchments in the region. The objective of this study is to assess Muskingum-based methods for flow routing ill ungauged river reaches, both with and without lateral inflows. Using observed data, the model parameters were calibrated to assess performance of the Muskingum flood routing procedures and the Muskingum-Cunge method was then assessed using catchment derived parameters for use in ungauged river reaches. The Muskingum parameters were derived from empirically estimated variables and variables estimated from assumed river cross-sections within the selected river reaches used. Three sub-catchments in the Thukela catchment in KwaZulu-Natal, South Africa were selected for analyses, with river lengths of 4, 21 and 54 km. The slopes of the river reaches and reach lengths were derived from a digital elevation model. Manning roughness coefficients were estimated from field observations. Flow variables such as velocity, hydraulic radius, wetted perimeters, flow depth and top flow width were determined from empirical equations and cross-sections of the selected rivers. Lateral inflows to long river reaches were estimated from the Saint-Venant equation. Observed events were extracted for each sub-catchment to assess the Muskingum-Cunge parameter estimation method and Three-parameter Muskingum method. The extracted events were further analysed using empirically estimated flow variables. The performances of the methods were evaluated by comparing both graphically and statistically the simulated and observed hydrographs. Sensitivity analyses were undertaken using three selected events and a 50% variation in selected input variables was used to identify sensitive variablesThe performance of the calibrated Muskingum-Cunge flood routing method using observed hydrographs displayed acceptable results. Therefore, the Muskingum-Cunge flood routing method was applied in ungauged catchments, with variables estimated empirically. The results obtained shows that the computed outflow hydrographs generated using the Muskingum-Cunge method, with the empirically estimated variables and variables estimated from cross-sections of the selected rivers resulted in reasonably accurate computed outflow hydrographs with respect to peak discharge, timing of peak flow and volume. From this study, it is concluded that the Muskingum-Cunge method can be applied to route floods in ungauged catchments in the Thukela catchment and it is postulated that the method can be used to route floods in other ungauged rivers in South Africa. / Thesis (M.Sc.)-University of KwaZulu-Natal, Durban, 2005.