Set-membership approach for identification of the uncertainty in power-law relationships: the case of sediment yield

Power laws are used to describe a large variety of natural and man-made phenomena. Consequently, they are used in a wide range of scientific research and management applications. In this paper, we focus on the identification of uncertainty bounds on a power law relationship from experimental data, using a bounded-error characterization. These bounds can subsequently be used as constraints in e.g. optimization and scenario studies. The basic so-called set-membership approach involves outlier identification and removal, feasible parameter set estimation, evaluation of the feasible model output set and tuning of the error bounds. As an example we examine scattered sediment yield versus catchment (or watershed) area data of Wasson, (1994). The key result of this is an appropriate unfalsified relationship between sediment yield and catchment area with uncertainty bounds.