Statistical process control in assessing production and dissolution rates of biogenic silica in marine environments

This paper provides pieces of advice on the practices of quality assurance and quality control in assessing production and dissolution rates of biogenic silica in marine waters with stable isotope techniques. The objective is to make a rigorous contribution to the interpretation of 30Si isotopic measurements including modelling and uncertainty analyses. The results are illustrated with real data taken from Beucher et al. [Beucher, C., Tréguer, P., Corvaisier, R., Hapette, A/-M., Elskens, M., 2004a. Production and dissolution of biogenic silica in a coastal ecosystem of western Europe. Marine Ecology Progress Series 267:57–69.]. Prior to the flux rate assessment, there are a number of analytical considerations required for screening between optimal and defective experimental conditions. Three indexes were proposed to check the relevance of underlying assumptions when dealing with 30Si tracer enrichment and dilution techniques. Afterwards for extracting rate values from measurements, it is necessary to postulate a model, and if required an optimization method. Various models and formulae were compared for their precision and accuracy. It was shown that oversimplified models risk bias when their underlying assumptions are violated, but overly complex models can misinterpret part of the random noise as relevant processes. Therefore, none of the solutions can a priori be rejected, but each should statistically be assessed with hypothesis testing. A weighted least squares regression strategy combining an analysis of the standardized residuals and cost function (sum of the weighted least squares residuals) was used to select optimal solution subsets corresponding to a given data set, i.e. the solution that uses the most relevant processes and which was tested for the presence of outliers (observations or measurements with undue influence in the flux rate assessment).