A fuzzy inference system for modelling streamflow: Case of Letaba River, South Africa

Abstract

Streamflow modelling of Letaba River in South Africa is complicated by several factors including the existence of dams and other storage structures whose releases are intermittent and based on rules of thumb depending on the irrigation demands and the need to maintain the flow required in the Kruger National park (KNP). The KNP is located about a hundred kilometres downstream of the main storage and water flows through an alluvial aquifer where complex surface–groundwater interactions occur. Farmers abstract water intermittently along the route directly from the river or indirectly from the alluvial aquifer complicating the flow patterns even more. Consequently, the streamflow series in the river shows very little similarity to what would be considered as natural. The actual abstractions are not measured and only monthly estimates of the abstractions currently exist. Like in many other basins in South Africa, streamflow, groundwater level, rainfall and evaporation data in Letaba is sparse and not very reliable. The Takagi–Sugeno fuzzy inference system using subtractive clustering, an approach which are capable of dealing with vague and inadequate information and data has therefore been used to develop a daily streamflow model for Letaba River. In order to take into account the spatial variability and to maximize the use of the available data, the model is applied in a semi-distributed manner consisting of three river reaches. The shuffled complex evolution (SCE-UA) optimizer has been used to calibrate the model. Six years of data from March 2002 to April 2008 has been used for model calibration and verification. To maximize the Nash-Sutcliffe efficiency, the minimum number of clusters required was found to be 10 for 1000 data points in calibration. An analysis of the location of the cluster centers, the coefficients relating the inputs with the simulated streamflow, and the degrees of membership indicates that no single cluster can be associated to the simulation of a specific hydrologic process or component of the streamflow hydrograph (e.g. high flows or low flows). The fuzzy model does not therefore provide any evidence that it is not a pure black box.The Nash–Sutcliffe efficiency results obtained in calibration and verification showed average values of 0.658 and 0.535 with poor values on the first river reach. Very low percent bias values averaging to −0.4% and −2.7% in calibration and verification are obtained highlighting the model’s potential for applications where mass balance considerations are most important.