Evaluation of procedures and development of statistical models for determining frequency of floods with special reference to Southern Africa

The selection of a suitable flood frequency procedure to model flood flows for a given region is one of the important problems in hydrology. This study investigates the performance of commonly used procedures in order to develop suitable frequency models that can be used in the design of civil engineering works in Southern Africa. The development of the frequency models is based on regional flood frequency approach. This approach is of particular interest in those regions where the availability of flood data is limited or missing. The methodology used to carry out the research involved the following steps: data screening, delineation of Southern Africa into homogeneous regions, identification of the underlying statistical distributions of flood flows, selection of appropriate frequency estimation procedures and development of relationships to predict mean annual floods (MAF) or index floods. The data for the analysis comprised of annual maximum discharge series from eleven countries of Southern Africa, namely, Angola, Botswana, Lesotho, Malawi, Mozambique, Namibia, South Africa, Swaziland, Tanzania, Zambia and Zimbabwe. The data were screened for discordance, autocorrelation and cross-correlation. All the stations that were found to be discordant, auto correlated and cross-correlated were excluded from detailed analysis. The exercise to delineate Southern Africa into homogeneous regions involved grouping together basins which were considered to have similar hydrological, climatic and physiographic characteristics. This was to allow the extrapolation of records in a region with more precision and use of regression equations to predict hydrologic variables in terms of catchment characteristics with greater confidence. Once a homogeneous region was delineated the next step was to search for a suitable frequency distribution to model flood flows for that particular region. Two approaches i.e. L-moment ratio diagram and the regional behaviour of statistics were applied to search for a suitable statistical distribution to model flood flows for the delineated homogeneous regions in Southern Africa. The selection of the suitable flood estimation procedures for the delineated homogeneous regions was implemented by evaluating the performance of different procedures by doing Monte Carlo simulation. Predictive ability test indicators, i.e, the bias, the standard error of estimate, the root mean square error and the expected probability of exceedance were applied to assess the performance of various procedures. The results of the predictive ability tests were consequently used to select the most robust flood estimation procedures for the regions in delineated Southern Africa. In order to extrapolate research results from beyond individual basin boundaries, regression models were developed to predict MAF from catchment characteristics. These relationships can be used to predict MAF to allow transfer of information from gauged to ungauged catchments. Delineation of homogeneous regions was carried out for Malawi, Namibia, South Africa, Tanzania and Zimbabwe. Lesotho and Swaziland were found to comprise as single regions. Lack of adequate data for Angola, Botswana, Mozambique and Zambia did not allow carrying out regional homogeneity analysis. Based on the results obtained from simulation either P3/PWM or LP3/MOM were selected as appropriate procedures to model flood flows in Southern Africa. Some work was carried out also to assess the effect of data and model errors in the estimation of design floods. The effect of this combination of errors was studied by using simulation technique and then applying non-parametric method of estimating the probability density function and consequently obtaining the safety factors for design floods. The study was based on the analysis of annual maximum data from Tanzania only. The results of the study showed that magnitudes of uncertainties in quantile estimates vary with model type and sample size for a particular site. Lastly, a statistical model known as AGREGEE was tested to find out whether it can be applied to predict flood quantiles as an alternative procedure to classical frequency distribution models. The model makes use of a -combination of rainfall, discharge and historical information. The model was tested using data from eight catchments in Tanzania. The quantile estimates obtained from the AGREGEE model were found to be comparable to those obtained from the regional frequency curve developed for a given homogeneous region in Tanzania up to 100 years return period.