Grain size control of sediment composition variability still not resolved

&amp;lt;p&amp;gt;The compositional data analysis (CoDA), unbiased interpretation of geochemical composition of sediments and soils, must correctly treat several major challenges, well-known to environmental geochemists but still improperly handled. Among them, dilution by autochthonous components, e.g., biogenic carbonates or organic matter, and grain size effects are the most relevant. These effects cannot be eliminated by sample pre-treatment, e.g. by sieving or chemical extraction of diluting components, but they can be handled by implementation of interelement relationships and particle size distribution functions. The challenges of CoDA are principally twofold: geochemical/mineralogical and mathematical/statistical. Geochemical/mineralogical challenge is that complete deciphering of sediment composition would need knowledge of mineral composition (and stoichiometry of individual minerals and their content of major and trace elements) in each grain size fraction. This information can be achieved by analysis of finely divided grain-size fractions of studied sediments, which is enormously demanding, in particular in the silt and clay size fractions; that approach can, however, be found in scientific papers. Mathematical/statistical challenge consists in need to respect nature of compositional data (relative nature, i.e. scale dependence, data closure &amp;amp;#8211; content of each component impacts all other components), polymodal data distributions, including the cases when &amp;amp;#8220;outliers&amp;amp;#8221; (in terms of Gaussian distribution) are a regular part of compositional datasets. Compositional data are best treated using log-ratio methodology and robust algorithms (not based on the least squares fitting methods), which are not familiar to geoscientists.&amp;lt;/p&amp;gt;&amp;lt;p&amp;gt;Most traditional geochemical approaches to CoDA are based on empirical knowledge, models, and assumptions which are hardly proven, e.g. a tracer conservativeness or its grain size invariance, which are not easy tested independently. Most novel mathematical/statistical tools are too abstract and computations too complicate for common geochemists. The bottleneck here is to convert geochemical tasks to formal mathematical/statistical terms and develop novel tools, having chance to become routinely used in future.&amp;lt;/p&amp;gt;&amp;lt;p&amp;gt;We studied composition of 483 sediment samples from floodplain and reservoir impacted by historical pollution from chemical industry in Martktredwitz, Germany. We will demonstrate mathematically/statistically correct routes to (1) distinguishing anthropogenic portion of risk elements in sediments of variable grain size and (2) characterisation of grain size control of sediment composition. Task (1) is best achieved by robust regression with log-ratios of concentrations, which still needs certain a priori geochemical expertise. Task ad (2) is best achieved by the use of a functional analysis of particle size distributions (densities) based on Bayes spaces. To support our recommendations, insufficiency of PCA to solve task (1) will be demonstrated.&amp;lt;/p&amp;gt;