Development and assessment of an ensemble joint probability event based approach for design flood estimation in South Africa.

Abstract

It has been reported that global climate change has impacted on the frequency as well as severity of flood events. Reliable flood estimates are required for managing and designing hydraulic structures, which is essential under extreme weather regimes in the future. Design flood estimation methods in South Africa are based on statistical analysis of past streamflow data, and rainfall based methods. Rainfall-based methods often have preference over streamflow-based methods for design flood estimation due to longer records of rainfall data that also have a greater spatial and temporal coverage than streamflow records. A key assumption in rainfall based methods for design flood estimation is the assumption regarding the exceedance probability of the estimated flood. It is generally assumed that the return period of the estimated flood will be the same return period as the input rainfall. This equality of rainfall and flood return periods is generally not true given the use of model parameters representing average conditions and the impact of antecedent moisture conditions on hydrological response. Hence, a Joint Probability Approach (JPA) where the key input model parameters, and not only the input design rainfall, are treated probabilistically will overcome the limitations associated with rainfall based design flood estimation. The underlying approach to the JPA is that instead of the use of a single combination of input variables to determine the flood characteristics, the method uses multiple combinations of flood producing parameters to determine the flood characteristics. In this study, a JPA was applied using the SCS-SA model, and the modelling framework used to determine the derived flood frequency curve is based on three principal elements. These include: (i) defining the key model inputs with their respective probability distributions and correlations, (ii) a stochastic model to synthesise sequences of the selected variables, and (iii) selecting an appropriate deterministic hydrological model to simulate the flood generation process, and use of the simulated outputs to derive the flood distribution. To evaluate the performance of the model, the results were compared to observed streamflow data. A statistical analysis was conducted in conjunction with graphs to verify the performance of the model. The Nash-Sutcliff Efficiency (NSE), absolute relative difference and Mean Absolute Relative Error (MARE) were used to evaluate the performance of the model. The results produced from applying the Ensemble SCS-SA model with rainfall that was fitted to the probability distribution of the 1 day design rainfall and sampling from the 90 % prediction intervals for each return period indicates that the model was performing relatively poorly in terms of estimating both the observed design runoff volume and design peak discharge for all the selected test catchments. The incorporation of the correlation between the rainfall depth and rainfall duration using a conditional probability distribution and in conjunction with the probability distributions of the other key input variables in the Ensemble SCS-SA model, resulted in significantly improved estimated runoff volume and peak discharges for all the catchments used. The Ensemble SCS-SA model has also shown potential and flexibility to deal with uncertainty by accounting for the distributed nature of the input variables and taking on values across the full range of their distribution in the modelling process, thus avoiding the potential of bias that can occur when adopting a single set of pre-determined input values. This study has shown the potential and flexibility of the Ensemble SCS-SA model to deal with uncertainty, providing opportunity for the expanded application of the model.