As defined by Fread (1981) and Linsley et al. (1982), flood routing is a mathematical method for predicting the changing magnitude and celerity of a flood wave as it propagates down rivers or through reservoirs. Numerous flood routing techniques, such as the Muskingum flood routing methods, have been developed and successfully applied to a wide range of rivers and reservoirs (France, 1985). Generally, flood routing methods are categorised into two broad, but somewhat related applications, namely reservoir routing and open channel routing (Lawler, 1964). These methods are frequently used to estimate inflow or outflow hydrographs and peak flow rates in reservoirs, river reaches, farm ponds, tanks, swamps, and lakes (NRCS, 1972; Viessman et al., 1989; Smithers and Caldecott, 1995).
Flood routing is important in the design of flood protection measures in order to estimate how the proposed measures will affect the behaviour of flood waves in rivers so that adequate protection and economic solutions can be found (Wilson, 1990). In practical applications, the prediction and assessment of flood level inundation involves two steps. A flood routing model is used to estimate the outflow hydrograph by routing a flood event from an upstream flow gauging station to a downstream location. Then the flood hydrograph is input to a hydraulic model in order to estimate the flood levels at the downstream site (Blackburn and Hicks, 2001).
Flood routing procedures may be classified as either hydrological or hydraulic (Choudhury et al., 2002). Hydrological methods use the principle of continuity and a relationship between discharge and the temporary storage of excess volumes of water during the flood period (Shaw, 1994). Hydraulic methods of routing involve the numerical solutions of either the convective diffusion equations or the one-dimensional Saint-Venant equations of gradually varied unsteady flow in open channels (France, 1985).
Several factors should be considered when evaluating which routing method is the most appropriate for a given situation. According to the US Army Corps of Engineers (1994a), the factors that should be considered in the selection process include, inter alia, backwater effects, floodplains, channel slope, hydrograph characteristics, flow network, subcritical and supercritical flow. The selection of a routing model is also influenced by other factors such as the required accuracy, the type and availability of data, the available computational facilities, the computational costs, the extent of flood wave information desired, and the familiarity of the user with a given model (NERC, 1975; Fread, 1981).
The hydraulic methods generally describe the flood wave profile more adequately when compared to hydrological techniques, but practical application of hydraulic methods are restricted because of their high demand on computing technology, as well as on quantity and quality of input data (Singh, 1988). Even when simplifying assumptions and approximations are introduced, the hydraulic techniques are complex and often difficult to implement (France, 1985). Studies have shown that the simulated outflow hydrographs from the hydrological routing methods, always have peak discharges higher than those of the hydraulic routing methods (Haktanir and Ozmen, 1997). However, in practical applications, the hydrological routing methods, are relatively simple to implement and reasonably accurate (Haktanir and Ozmen, 1997). An example of a simple hydrological flood routing technique used in natural channels is the Muskingum flood routing method (Shaw, 1994).
Among the many models used for flood routing in rivers, the Muskingum model has been one of the most frequently used tools, because of its simplicity (Tung, 1985). As noted by Kundzewicz and Strupczewski (1982), the Muskingum method of flood routing has been extensively applied in river engineering practices since its introduction in the 1930s. The modification and the interpretation of the Muskingum model parameters, in terms of the physical characteristics, extends the applicability of the method to ungauged rivers (Kundzewicz and Strupczewski, 1982). Most catchments are ungauged and thus a methodology to compute the flood wave propagation down a river reach or through a reservoir is required. One option is to develop models for gauged catchments and relate their parameters to physical characteristics (Kundzewicz, 2002). The approach for flood routing then can be applied to ungauged catchments in the region (Kundzewicz, 2002).
In this study, the Muskingum-Cunge method is adopted to estimate the model parameters because of its simplicity as well as its ability to perform flood routing in ungauged catchments by estimating the model parameters from flow and channel characteristics. The Muskingum-Cunge parameter estimation method utilises catchment variables such as flow top width (W), slope (S), average velocity (Vav), discharge (Q0), celerity (Vw), and catchment length (L) to estimate the parameters of the Muskingum method.
When performing flood routing in ungauged catchments, the model parameters have to be estimated without observed hydrographs. The inflow hydrograph could be generated using a hydrological model such as the ACRU model (Schulze, 1995). For this study, the observed hydrographs are used to simulate an outflow hydrograph.
The objectives of this study are thus to:
(i) Assess the performance of the Muskingum method, both with and without lateral inflow, using calibrated parameters, and
(ii) Assess the performance of the Muskingum-Cunge method in ungauged catchments using derived parameters,derived by:
(a) using variables estimated from empirical equations developed for different river reaches, and
(b) using variables estimated from assumed cross-sections within the river reach.
To understand the Muskingum flood routing methods, relevant literature was reviewed and is presented in Chapter 2. The literature review contained in Chapter 2 includes the basic Muskingum method, the Muskingum-Cunge method, the Three-Parameter Muskingum method, the Non-Linear Muskingum method, and the SCS Convex method as well as channel discharge relationships. Catchment selection and location, gauge selection, catchment descriptions and flow data analyses are included in Chapter 3. Details of assumptions made in the flow analysis, calculation steps to estimate the Muskingum flood routing parameters and methodology adopted in the study are contained in Chapter 4. The performance of the Muskingum method, both with calibrated parameters and in ungauged river reaches, and the sensitivity of the Muskingum flood routing parameters to different catchment variables are presented in Chapter 5. Discussion of the different Muskingum flood routing methods and conclusions are contained in Chapter 6. Finally, recommendations for further research are presented in Chapter 7.