Re-evaluation of area reduction factors and their impact on floods in South Africa

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ICWEES2018 & IWFC2018

Re-evaluation of area reduction factors and their impact on floods in South Africa Jakobus Andries Du Plessis 1

&

Wynand Loots 1

Received: 24 October 2018 / Accepted: 9 May 2019 / Published online: 28 May 2019 # Saudi Society for Geosciences 2019

Abstract The hydraulic design of structures depends on rainfall and runoff records to model and predict flood frequency for design purposes. The amount of runoff (and consequently flooding) from a catchment area has a direct relationship to the amount of rainfall in that catchment area, but as the point rainfall in any given area is likely to be more than the representative average rainfall over the entire area, a factor needs to be derived to transform point rainfall to representative areal rainfall. This factor is known as the Area Reduction Factor (ARF) and has been calculated and researched in many previous independent studies. The traditional methods for estimating ARFs are empirical in nature and include methods such as the UK Flood Studies Report (NERC 1975), the US Weather Bureau (USWB 1957), and Alexander (1990). The research presented in this paper focuses on reevaluating ARF’s estimates using the UK Flood Studies Report (NERC 1975) and Alexander’s method (Alexander 1990) by following an analytical approach based on Bell’s method (Bell 1976). This research uses statistical methods to evaluate the validity of previously published ARFs. The results presented in this paper indicate that the empirical methods currently in use (specifically Bell’s nomogram) to derive ARFs may result in conservative estimates of flood peaks. There is ample evidence to suggest that modern analytical techniques can be applied to longer rainfall records in order to make a more accurate estimate of the ARFs. Keywords Floods . Areal reduction factors . Storm rainfall . Areal rainfall

Introduction Precipitation data is used extensively for modelling extreme flood events and for the design of storm water systems (Alexander 2002; Adamson 1981; Smithers 1996; Smithers and Schulze 2004; Van Wageningen and Du Plessis 2007). Accurate data is critical for dam design and operation, public safety, bridges and culvert design, etc. In order to produce usable flood modelling design data, mean point rainfall depths have to be related to a catchment area (Adamson 1981). To This article is part of the Topical Collection on Geo-environmental integration for sustainable development of water, energy, environment and society * Jakobus Andries Du Plessis [email protected] Wynand Loots [email protected] 1

Faculty of Engineering, Department of Civil Engineering, Stellenbosch University, P/Bag X1, Matieland 7602, South Africa

achieve this, a factor needs to be incorporated which can be applied to the point rainfall data. This research establishes the validity of existing methods of Area Reduction Factor (ARF) derivation used in South Africa and assesses the impact of the area and return period (within the context of geographical location) on the ARF, as factors identified by Bell