Uncertainty modelling and analysis of environmental systems: a river sediment yield example

Abstract: Throughout the last decades uncertainty analysis has become an essential part of environmental model building (e.g. Beck 1987; Refsgaard et al., 2007). The objective of the paper is to introduce stochastic and setmembership uncertainty modelling concepts, which basically differ in the assumptions that are made with respect to the uncertainty characterization. Stochastic uncertainty modelling is most frequently applied and is characterized by probability density functions (pdf’s) or simply by means and (co)variances. Typical approaches are the Bayesian and the Monte Carlo Markov Chain methods. Alternatively, a set-membership or bounded-error characterization, as opposed to a stochastic characterization, is favoured when assumptions about distribution or estimates of mean and covariance cannot be satisfactorily tested, as with small data sets or heavily structured (modelling) errors. The bounded-error characterization is in essence deterministic. Both approaches, using tools as DREAM, GLUE, exact and approximate bounding, MCSM and a pavement-based technique, were tested on a real-world example. The example, based on Wasson’s (1994) sediment yield – area data and after a log-log transformation of the data, is a linear static problem with two parameters