Hydrological flood routing techniques are widely accepted and extensively used in engineering practice. The ability to predict the changing magnitude and celerity of a flood wave as it propagates along rivers or through reservoirs makes flood routing important in designing hydraulic structures and assessing the adequacy of measures for flood protection. However, in practice, only a limited number of gauging stations are available, and even measured or gauged runoff data are frequently unreliable. Establishing gauging stations is an expensive task, and ongoing maintenance and service costs are significant.
Factors considered when selecting suitable gauging stations for streamflow records include the availability and quality of data, and the suitability of the river reach to estimate flood routing parameters using Muskingum methods. In this study, reaches of different lengths were selected to assess the influence of river length on the application of flood routing methods. Some observed hydrographs had unrealistic records, likely due to technical problems or incorrect data acquisition. Hence, the quality of data was carefully examined before selecting events for calibrating the Muskingum methods of flood routing.
Results from both M-Cal and M-Ma methods displayed reasonably similar volume and shape compared to the observed hydrographs. Since Reach-II and Reach-III are long reaches, lateral inflows were added to the flood routing method. However, the addition of lateral inflow to the computed hydrographs in Reach-II and Reach-III was not sufficient to obtain the observed peaks but resulted in outflow peak discharges larger than the inflow peak discharges, as evident in the observed data. Since the addition of lateral inflow as used in this study considers only flows derived from the same rainfall event that resulted in the hydrographs, the under simulation of lateral inflow may be attributed to inflow from other catchments caused by different rainfall events.
The computed hydrographs using the M-Ma method are a better fit to the observed outflow hydrographs for those with good quality data and a uniformly increasing discharge than the hydrographs computed using the M-Cal method. However, both methods produced acceptable results with errors of less than 20% for most statistics considered. Both methods performed better for shorter reaches where the effect of lateral inflow is not significant. However, the parameters of the M-Ma method are only derived from observed hydrographs, and it is not possible to apply the M-Ma method in ungauged catchments. The parameters of the Muskingum-Cunge method can be derived from reach and flow characteristics. Hence, the Muskingum-Cunge method, with empirically estimated parameters (MC-E), and the Muskingum-Cunge method, with variables estimated from an assumed section (MC-X), were applied in ungauged catchments.
The estimated values of the flow variables in both the MC-E and the MC-X methods were nearly equal in this study, resulting in similar computed outflow hydrographs. The computed outflow hydrographs using both the MC-E and MC-X methods had acceptable errors for peak flow magnitude, peak timing, volume, and small RMSE values. Additionally, the coefficients of model efficiency (E) were also near one in most cases, indicating that the hydrograph shapes were very similar to the observed hydrographs. Hence, it can be concluded that the MC-E and MC-X methods can be applied in ungauged reaches where observed data sets are unavailable.
As noted in the previous sections, the selection of an assumed section requires an in-field inspection to select a representative section for estimating variables in the MC-X method. The selection is a subjective procedure, which could result in different computed hydrographs for different scenarios in the same reach. On the other hand, although the parameters of the MC-E method can be estimated from empirical equations, the methods are not subjective and yield the same computed hydrographs for different scenarios in the same reach. Hence, it is recommended that the MC-E method should be applied to route floods in ungauged catchments.
From the sensitivity analysis, it is evident that the performance of the MC-E method is insensitive to the accurate estimation of the roughness coefficient, and a 50% variation in the roughness coefficient resulted in a change of less than 1% error for all the performance statistics considered. Similarly, the performance was found to be insensitive to channel geometry. Hence, from this study, it can be concluded that the Muskingum-Cunge flood routing method, with parameters estimated using the MC-E method, can be used to route hydrographs in ungauged reaches in the Thukela catchments, and it is postulated that the method can be used to route floods in other ungauged rivers in South Africa.