Estimation of Time Parameter Proportionality Ratios in Large Catchments: Case Study of the Modder-Riet River Catchment, South Africa

Abstract

Catchment response time parameters such as the time of concentration (TC), lag time (TL) and time to peak (TP) are fundamental to design flood estimation in ungauged catchments; hence, errors in time parameter estimates directly impact on design flood estimates. As much as 75% of the total error in design peak discharge estimates in ungauged catchments could be ascribed to errors in the estimation of catchment response time. The seven different time parameter definitions available in hydrological literature are interchangeably used when time parameters are obtained from observed rainfall and streamflow data, respectively. As a result, time intervals from various points during a storm extracted from a hyetograph (e.g. effective rainfall centroid, end of effective rainfall, and/or maximum rainfall intensity) to various points on the resultant hydrograph (e.g. peak discharge, inflection point on recession limb, and centroid of direct runoff) are often misinterpreted as TC, TL and/or TP. Due to the difficulty in estimating the centroid values from above-mentioned hyetographs and hydrographs, other TL estimation techniques have been proposed in literature. Instead of using TL as an input for design flood estimation methods, it is rather used as input to the computation of TC. In using TL defined as the time from the centroid of effective rainfall to the centroid of direct runoff, TC and TL are normally related by TC = 1.417TL. In TL defined as the time from the centroid of effective rainfall to the time of the peak discharge, the proportionality ratio increases to 1.667. However, in contradiction, Schultz (1964) established that for small catchments in Lesotho and South Africa, TL  TC. In addition, Gericke and Smithers (2016; 2017) also showed that TP  TC at medium to large catchment scales in South Africa, but the relevance of the TL proportionality ratio (x = 1.667), i.e. TL = 0.6TC, was not established. The overall purpose of this study is thus to investigate and establish the suitability of the currently recommended time parameter definitions and proportionality ratios for small catchments in larger sub-catchment areas (exceeding 50 km²) of the Modder-Riet River Catchment in South Africa. The focus is on the estimation of time parameter proportionality ratios from observed rainfall and streamflow data using a simplified convolution process and the seven different time parameter definitions currently recognised in hydrological literature. The time parameters TC, TL and TP were individually estimated using the various time variables obtained from observed hyetographs and hydrographs to establish average time parameter proportionality ratios at a catchment level. The time parameter estimates proved to be highly variable due to the spatial and temporal distribution of rainfall events, variation in peak discharges and the distance of the rainfall events from the catchment outlet. However, the variability in the average estimated time parameter proportionality ratios proved to be less significant. In this study, where TL is defined as the time from the centroid of effective rainfall to the peak discharge, TC and TL proved to be related by TC = 1.003TL and where TL is defined as the time from the centroid of effective rainfall to the centroid of direct runoff, the proportionality ratio reduced to 0.992. In all the sub-catchments under consideration, the preliminary findings of Gericke and Smithers (2014; 2016; 2017), i.e. TP  TC  TL, were confirmed. In other words, it highlighted that the proportionality ratios currently proposed for small catchments, i.e. TC = 1.417TL and TC = 1.667TL, are not applicable at larger catchment levels. Building upon the critical assessment of the available time parameter definitions and proportionality ratios, it is envisaged that the implementation and expansion of both the identified research values and adopted methodology to other catchments in South Africa and internationally, will ultimately contribute towards improved time parameter estimations at a catchment level. Consequently, the improved time parameter estimations will also result in improved design flood estimations.