Fuzzy set theory based methodology for the analysis of measurement uncertainties in river discharge and stage

The discharge and stage measurements in a river system are characterized by a number of sources of uncertainty, which affects the accuracy of a rating curve established from measurements. This paper presents a fuzzy set theory based methodology for consideration of different sources of uncertainty in the stage and discharge measurements and their aggregation into a combined uncertainty. The uncertainty in individual measurements of stage and discharge is represented using triangular fuzzy numbers, and their spread is determined according to the International Organization for Standardization (ISO) standard 748 guidelines. The extension principle based fuzzy arithmetic is used for the aggregation of various uncertainties into overall stage–discharge measurement uncertainty. In addition, a fuzzified form of ISO 748 formulation is used for the calculation of combined uncertainty and comparison with the fuzzy aggregation method. The methodology developed in this paper is illustrated with a case study of the Thompson River near Spences Bridge in British Columbia, Canada. The results of the case study show that the selection of number of velocity measurement points on a vertical is the largest source of uncertainty in discharge measurement. An increase in the number of velocity measurement points provides the most effective reduction in the overall uncertainty. The next most important source of uncertainty for the case study location is the number of verticals used for velocity measurements. The study also shows that fuzzy set theory provides a suitable methodology for the uncertainty analysis of stage–discharge measurements.