An alternative approach to sediment source identification: uncertainty analysis and sample number optimization

Identifying sediments sources is an important branch of catchment erosion modeling that uses multiple tracers in a robust set of statistical analysis techniques commonly known as the “fingerprinting approach”. The techniques employed in the fingerprinting approach follow two distinct stages of multivariate statistical analysis: discrimination and classification. The first one refers to determining the best set of tracers that have the potential to be selected as a tracer. The second stage consists of classifying the eroded sediment samples in the n-dimensional space defined by the tracer properties. In this step, the relative contribution of each source to the composition of the suspended sediment is calculated. One of the challenges for improving the “fingerprinting approach” is estimating the uncertainties of the results. In this sense, defining the number of samples used to characterize sources and eroded sediments is considered an important issue in terms of costs and source of uncertainties. Therefore, the main objective of this work is to present an alternative modeling with a focus on uncertainty analysis and sample number optimization based on the model developed by Clarke and Minella (2016). The advantages of the proposed model include 1) the calculus of the source apportionments, making it possible to evaluate the effects of reducing the sample number on the uncertainties; 2) takes account the collinearity between the tracers adding the variance-covariance matrix applied into the generalized least squares (GLS) method; and 3)  adds the calculus of uncertainty associated with the number of samples (sediment sources and the  sediments. To demonstrate the usefulness of the model, we used a dataset available from the Arvorezinha experimental catchment located in southern Brazil. The implementation of this model was carried out in the Phyton®, so that any user can evaluate the uncertainties in the reduction of the number of samples as well as the importance of collinearity in the set of available tracers. The results confirmed the assumption the increased uncertainty as the number of samples decreases in the sources or eroded sediment samples. Moreover, the addition of the variance-covariance matrix in the solution of the overdetermined system allows to take into account the deleterious effects of collinearity in the fingerprinting approach. With this tool, new perspectives are opened to systematically improve the definition of the number of samples needed based on the uncertainty analysis of the set of samples available, fundamental to the advancement of research in the area of environmental monitoring and modeling, as well as for the management of water resources and soil management in agricultural catchments.