Development and assessment of regionalised approaches to design flood estimation in South Africa.

Abstract

Engineers rely on design hydrological information for the design of hydraulic structures, such as dams, bridges, and drainage culverts. No single Design Flood Estimation (DFE) method has been identified internationally as the most appropriate method to use and, in many texts and manuals, the use of a combination of these are recommended. In South Africa, some of the currently recommended and widely used methods were developed outside of South Africa with little or no local adaptation or assessment, and most of the recommended methods were developed prior to 1990. The development of new and updated methods can therefore benefit from the use of much longer observed data sets and new and innovative approaches applied internationally. Four Regional Flood Frequency Analysis (RFFA) approaches widely adopted internationally are direct quantile estimation methods, Probabilistic Rational Method (PRM), Index Flood (IF), and Regional Growth Curve (RGC) methods. The Standard Design Flood (SDF) method is a locally developed PRM. However, the method has been recommended for review in a number of studies, and the IF has been shown to have potential for implementation at a national scale in South Africa. The aim of this study was to develop and assess RFFA approaches for the estimation of design flood quantiles within South Africa utilising the currently available data. This process required the compilation of a hydrological descriptors database, including quality controlled gauged flow data. This data was then utilised to identify a suitable probability distribution for FFA in South Africa, which can be applied at a regional scale through the identification of homogeneous flood producing regions and regional flood models. DFE methods require a range of catchment descriptors to be determined for use in models. Considering the literature reviewed and the available datasets, 17 catchment descriptors were selected for inclusion in the study. The descriptors range from geographic and catchment descriptors to design rainfall quantiles. After data screening, a total of 383 stations were utilised, in the study. The available record lengths and number of gauges were compared to prominent studies undertaken previously and was found to be comparative to the data availability in Australia and the United Kingdom. Linear moments (LM) were adopted for the estimation of the distribution parameters. Five distributions were selected for evaluation based on local recommendations as well as recent international developments: (i) General Extreme Value (GEV), (ii) Generalised Pareto (GPA), (iii) 3-parameter Kappa (KAP3), (iv) Log Pearson Type III (LP3) and (v) Pearson Type III (PE3). The evaluation process relied on an iterative elimination approach, reviewing graphical fits to theoretical distributions, Goodness-of-fit (GoF) criteria, model fit criteria and model uncertainty to identify the most suitable distribution. The graphical fit favoured the GPA, KAP3 and LP3 distributions equally, with the GoF methods ranking LP3 as the most suitable method. Conversely, the GPA was ranked highest for the model fit criterion and displayed the least model uncertainty and is thus recommended as the most suitable distribution for general FFA in South Africa. Two regionalisation approaches were considered to undertake the formation of the pooling groups, i.e. Clustering, and Region of Influence (RoI). For each regionalisation approach the hydrological descriptors were grouped into parameter sets, that constituted all potential descriptor combinations, which were tested for homogeneity as a selection criterion. Using the RoI approach, a maximum of 51% of the regions identified were relatively homogeneous. The super region approach was also applied to identify five dominant regions within which the RoI was applied in an attempt to refine the RoI approach. Using the combination of super regions and RoI provided little additional benefit, increasing the percentage of relatively homogeneous regions identified to only 52.6%. Conversely, the Clustering approach was able to identify 42 relatively homogeneous clusters in South Africa. To assess the suitability of Quantile Regression Technique (QRT) and Parameter Regression Technique (PRT) models in South Africa, four models were developed: (i) a QRT model, (ii) IF with equal station weighting (IF1), (iii) IF with station weighting applied (IF2) and (iv) PRM. Regression models were developed at two scales to estimate the required Scaling Factors, i.e. national and regional, with regional models performing best based on the Nash- Sutcliffe model Efficiency (NSE) coefficient. Six key performance indicators were utilised to assess the quantile estimation of the developed models: (i) NSE, (ii) Relative Error (RE), (iii) Root Mean Square Error (RMSE), (iv) Relative RMSE (RMSEr), (v) BIAS, and (iii) BIASr. The models that performed best in the RE assessment were the IF1 for both regionalisation schemes and the IF2 and PRM models using the RoI. When comparing the BIAS and RMSE of the four best performing clustering and RoI based models, the IF1 and QRT using Clustering models are the dominant models when considering both the RMSEr and the BIASr, the models improved on the results of the remaining models by up to a factor of two. The IF1 and QRT using Clustering models are therefore the best performing models on a national scale. The IF1 however has the added advantage of being able to estimate the entire growth curve as to the predefined QRT models. The IF1 is therefore the recommended model at a national scale, however cognisance needs to be taken when applying the model on the eastern coast due to poor BIASr performance. The new knowledge generated by the study can be divided into data, in the form of potentially the largest database of design flood specific descriptors concentrating on South Africa, and theoretical applications thereof. The theoretical knowledge generated ranges from the investigation into the most suitable frequency distribution to use for FFA in South Africa, to the application of multi-variate regionalisation approaches, which have not been applied in South Africa before. However, one of the key contributions was the development and performance assessment of four DFE models at multiple scales for South Africa for the estimation of peak design flood values.