Relative variation of ionic composition in a karstic lake under the theory of unweighted vs weighted logratio analysis

Abstract

The use of logratio analysis in limnological studies has proved to be effective for solving the problems of the constrained nature of compositional data. The method offers a graphical tool, the relative variation biplot, to explore relative changes of the ions. However, recent methodological developments have shown that the results can be perturbed by low-valued ions with high variances and proposed downweighting their influences as in correspondence analysis. Additional to all properties of the unweighted version, this weighted logratio analysis extends the previous work and has the advantage of the principle of distributional equivalence. As a motivating application, we chose a karstic lake with dominating ions calcium and sulphate causing other ions to be present relatively in low absolute levels. Besides, one of the collected compositional samples was suspected to be unusual which, in part, contributes to high relative variances. This paper is therefore concerned with the choice of the best method for the analysis of such extremely saline water systems by comparing performances of both unweighted and weighted logratio analyses. We concluded that introducing weights captured more features of ionic relationships with almost all compositional variability explained. We observed that the ratio of calcium to sulphate, ammonium or phosphorus (to a lesser extent) was particularly valuable in understanding the natural chemical process of the lake. A constant log-contrast model based on calcium, ammonium, nitrate and total soluble phosphorus appeared as an equilibrium equation.