Comparing different error structures in MixSIAR analysis using artificial mixtures from real sediment sources

Within a catchment context, statistical models are widely used to predict the load of pollutants (i.e. fine sediments, chemicals compounds) from potential sources around it, into a main channel (mixture). MixSIAR is a Bayesian mixing model framework that has been used in many environmental studies. As with other models, it presents some assumptions that might be assessed before its use. In this study, a set of artificial mixtures (from real sources) were created using four different catchment sediment sources (Channel Bank; Cultivated land; Pasture and Road Material). The material collected from each source was sieved (<63um) then analysed via WD-XRF for elemental composition. The data collected from this analysis was used to test and assess the main model parameters within an experimental context. A simple range test was performed to initially select tracers that were potentially good predictors. In the end, the model was structured with 43 tracers (elements) using the mean and standard deviation among 10 replicates. Furthermore, it was run using 10^6 iterations (length of the chain) and two different error structures to be compared (residual vs multiplicative error). The results demonstrated the accuracy of the MixSIAR approach to get the real composition in different mixture combinations using a large number of tracers, although in some mixtures a statistically different value was observed where the source term with highest internal variability was present in larger proportion (frequently when %CB >10%). The most precise and reliable results based on convergence were those using the “Residual error” structure, where the value of each mixture was closer to the real and model convergence was achieved more easily. On the other hand, “Multiplicative error” structure led to longer model run times (due to its complexity) and in most cases the model did not converge as for the “Residual error” structure when using the full set of tracers. To mitigate this problem, a posterior tracer selection based on diagnostic information was devised which made it  possible to increase dramatically the convergence of the predicted parameters without a significant difference in the result. Although the “Residual error” structure showed to be the most convenient for further analysis, the technique applied for “Multiplicative error” structure can be used as a potential solution to achieve model convergence while reducing model runtime.