Assessment of indirect estimation methods to extend observed stage-discharge relationships for above-structure-limit conditions at flow-gauging weirs

Abstract

Streamflow is seldom directly measured; instead, the stage (flow depth) is continuously measured and converted into a discharge using a stage-discharge (SD) rating curve (RC) at a flow-gauging weir or specific river section. During flood events, flow-gauging weirs might be flooded with the water level beyond the gauging weir's designed measuring capacity, also referred to as the structural limit of the weir. Subsequently, the standard calibration of the flow-gauging weir will no longer be a true reflection of the actual discharges that occurred during the flood events, and the standard SD RC must then be extended beyond the highest stage reading to reflect these high discharges at above-structure-limit flow conditions. Direct measurements, e.g., conventional current gaugings, are also not always possible owing to various practical constraints associated with these high discharge events. As a result, various indirect methods for extending SD RCs are available; however, the impact of using these different methods varies significantly and highlights the need for a robust and reliable extension method. The overall aim of this research is to assess and compare a selection of indirect extension methods (e.g., hydraulic and one-dimensional modelling methods) with direct extension (benchmark) methods (e.g., at-site conventional current gaugings, hydrograph analyses and level pool routing techniques), in order to establish the best-fit and most appropriate SD extension method to be used in South Africa. As pilot case study, 10 flow-gauging sites in the Free State, Gauteng, KwaZulu-Natal, Limpopo, Mpumalanga, and the Western Cape provinces were selected based on the range of possible site conditions present, e.g., type of flow-gauging weir, at-site and river geometry, flow conditions, type of hydraulics controls, and data availability. The following hydraulic methods were considered and applied at each site: (i) Simple extension (SE), (ii) Logarithmic extension (LE), (iii) Velocity extension simple approach (VE-SA), (iv) Velocity extension hydraulic radius approach (VEHRA), (v) Velocity extension Manning’s approach (VE-MA), (vi) Slope area method (SAM), and (vii) Stepped backwater analysis (SBA). In addition, one-dimensional modelling (1-D) was conducted using the Hydrologic Engineering Centre River Analysis System (HEC-RAS). Data were collected based on the hydrometric and geometric requirements for the extension of SD relationships. The processing of the geometric data, e.g., wetted perimeter, wetted area, and hydraulic radius, was done using the Windows CrossSection Professional (WinXSPRO), which is essentially a channel cross-section analyser. All the SD extensions were executed in the Microsoft Excel environment using semi-automated tools. The indirect extension methods’ results were compared and independently assessed against the direct SD measurements or estimates at each site by using a ranking-based selection procedure based on a selection of goodness-of-fit (GOF) criteria. In considering the overall GOF-based rankings, the SBA, SAM, and 1-D HEC-RAS steady flow modelling were identified as the most appropriate indirect estimation methods to reflect the hydraulic conditions during high discharges at a flow-gauging site. The other indirect extension methods were characterised by larger statistical differences between the at-site benchmark values and the modelled values. The VE-MA and SE methods are regarded as the least appropriate methods. In general, any extension method must be hydraulically correct if it is to be used as a robust approach to extend SD RCs beyond the structural limit. The extension of a RC is significantly more affected by the site (and river reach) geometry, initial hydraulic conditions, flow regimes and level of submergence at high discharges than the actual extension method used. Hence, there is no one-size-fits-all approach available for the extension of SD RCs in South Africa. By improving the quality of all input data and assigning more appropriate roughness coefficients, in conjunction with the implementation of new or alternative SD extension methods, the improved extension of SD RCs is warranted to result in consistent and acceptable results. Consequently, the improved and extended RCs will result in improved hydrological data sets, all of which, will contribute towards enhanced operational water resource planning, management, and allocation in South Africa. The recommendations for future research are towards the review of the current procedures used to estimate roughness coefficients for flash floods, and the consideration of alternative methods to extend SD relationships, e.g., hydrodynamic models, support vector machines (SVMs) and artificial neural network (ANN) methods.