The isometric log-ratio (ilr)-ion plot: A proposed alternative to the Piper diagram

Abstract

The Piper diagram has been a staple for the analysis of water chemistry data since its introduction in 1944. It was conceived to be a method for water classification, determination of potential water mixing between end-members, and to aid in the identification of chemical reactions controlling a sample set. This study uses the information gleaned over the years since the release of the Piper diagram and proposes an alternative to it, capturing the strengths of the original diagram while adding new ideas to increase its robustness. The new method uses compositional data analysis to create 4 isometric log-ratio coordinates for the 6 major chemical species analyzed in the Piper diagram and transforms the data to a 4-field bi-plot, the ilr-ion plot. This ilr-ion plot conveys all of the information in the Piper diagram (water mixing, water types, and chemical reactions) while also visualizing additional data, the ability to examine Ca2+/Mg2+ versus Cl-/SO42−. The Piper and the ilr-ion plot were also compared using multiple synthetic and real datasets in order to illustrate the caveats and the advantages of using either diagram to analyze water chemistry data. Although there are challenges with using the ilr-ion plot (e.g., missing or zero values zeros in the dataset must be imputed by positive real numbers), it appears that the use of compositional data analysis coupled with the ilr-ion plot provides a more in-depth and complete analysis of water quality data compared to the original Piper diagram.