A new version of the Langelier-Ludwig square diagram under a compositional perspective

Abstract

The Langelier-Ludwig square diagram is a commonly used diagnostic tool in groundwater chemistry. Suitable groupings of cations and anions are selected and plotted as percentages of milliequivalents with the sums of the selected cations and anions plotted on the y- and x-axes, respectively. It displays relative ratios rather than absolute concentration whereby each axis ranges from 0 to 50 meq%. However, the sample space in which data are represented in a Langelier-Ludwig square diagram is indeed given by the simplex. Incorrect conclusions may be drawn when the compositional nature of compositional data is not taken into account, i.e., a change in one value in one component changes all other values due to due to the constant sum constraint of the measured chemical elements. Correlations are thus influenced by the presence of negative bias in the covariance structure and linear or nonlinear patterns on the square diagram can be misinterpreted. A new version of the Langelier-Ludwig square diagram based on a well-chosen coordinate representation of cations and anions is proposed. The advantage of the revised diagram is that all the information is contained in the log-ratios describing the intricate relationship between chemical species in aqueous solutions. It is shown that the geochemical interpretation of this new diagram – based on the relative dominance of major ions and distance from the (robust) barycenter of the data – provides a better and unbiased understanding of water-environment interactions. To further aid interpretation, (robust) tolerance ellipses show the correlation structure in the new version of the Langelier-Ludwig square diagram, and clustering algorithms can be applied to divide the data into groups beforehand. A bunch of different plotting options and interactive representations complete the implementation in free open-source software. It is recommended to replace the classic Langelier-Ludwig diagram with the new version.