Development and assessment of regionalised areal reduction factors for catchment design rainfall estimation in South Africa

Abstract

Design point rainfall depths converted to an average areal design rainfall depth using Areal Reduction Factors (ARFs) are regarded as fundamental input to various design flood estimation methods. The ARF estimation methods currently used in South Africa are regarded as being outdated and not being developed and/or verified using local data. The primary research objective is to estimate geographically-centred and probabilistically correct ARFs representative of the different rainfall regions associated with the Regional Linear Moment Algorithm and Scale Invariance (RLMA&SI) regionalisation scheme in South Africa. Merging of the 78 homogeneous RLMA&SI rainfall clusters was necessary to increase the size of the clusters and the number of rainfall stations within a particular cluster to meet the minimum required number of rainfall stations/km² criteria. The latter merging resulted in 46 delineated clusters. Long duration geographically-centred and probabilistically correct ARFs were estimated using a total of 2 053 artificial circular catchments and 1 779 daily rainfall stations located within the 46 clusters. Random combinations of the 46 clusters were used in an alternating fashion for calibration and/or verification purposes until all possible combinations were considered. Ultimately, it was noted that whether a dedicated set of clusters or all clusters are assigned to calibration, differences are regarded as insignificant, given that all ARF data sets, whether used for calibration or verification, remain only estimated sample values. Subsequently, five (5) ARF regions were deduced from the 46 clusters and all clusters in a particular ARF region were used for the final derivation of a non-linear (second-order polynomial) log-transformed empirical ARF equation. The new regional ARF equation performed similarly, and as expected, when compared to a selection of geographically-centred ARF estimation methods currently used in local and/or international practice in a range of catchment sizes. The estimated ARFs decreased with an increase in area and increased with an increase in both storm duration and return period. The ARF methodology developed in this research and the subsequent findings are new to the South African flood hydrology research community and practice: (i) ARFs were derived and are based on a regionalisation scheme utilising the daily rainfall data in the Daily Rainfall Extraction Utility (DREU) database, (ii) ARFs are probabilistically correct, i.e., vary with return period, and (iii) a web-based software application was developed to enable the consistent estimation of ARFs within the five (5) ARF regions of South Africa.