Piper diagrams using Gnuplot or Veusz

Piper diagrams are used by geochemists to describe and clasify natural groundwaters, see for example Wikipedia.

A Piper diagram consists of two ternary plots and a central diamond plot. They can be plotted on Cartesian coordinates as described in:

• Peeters, L. (2014). A background color scheme for Piper plots to spatially visualize hydrochemical patterns. Groundwater Vol.52, pp.2–6.

Many computer programs allow plotting data in Cartesian coordinades. Two such open-source programs are Gnuplot (Wikipedia, official website) and Veusz (Wikipedia, official website). Files needed to plot Piper diagrams using either Gnuplot or Veusz are available here. They have been made for Gnuplot version 5.2 and Veusz version 3.0.1.

Download

See the releases section.

Get going

The zip-file contains two folders, one for Gnuplot and the other for Veusz. For each program there are input text files to draw the axes and the grids (both files are equal for the two programs). An example data file is also included with several sets of chemical compositions of natural waters (this input text file is also equal for both programs).

• Gnuplot: The script Piper.gpl is used to create the Piper diagram by using the command "load". This is a text file. Before using it, you must change the line: wf = 'C:\Piper\Gnuplot' (at the beginning of the script) so that it points to your working folder. At the beginning of the script there is section named #--- Graphic output; uncomment the two lines indicated to generate a SVG-file (instead of displaying the diagram in a screen window). You may easily change the axes labels, for example add electric charges as in: set label 41 "Ca^{2+}"...; or move labels around, etc, but be aware that the SVG output is not exactly equivalent to what you will see on the screen.

• Veusz: The Veuz file (Piper-Veusz.vsz) is used with the menu "File / Open". This is a text file. Before using it you will need to change the following line: AddImportPath(u'C:\\Piper\\Veusz') (at the top of the file) so that it points to the location of your working folder. In the menu "Edit / Custom definitions" of Veusz check that the variable "xOffset" is defined, otherwise load the file Offset.vsz.

The files for both programs have been prepared to create text labels large enough for diagrams 7x8 cm in size.

Input data

• The input data file Piper-data.csv is a text file where data are separated by semicolons (;). You may change this in both Gnuplot and Veusz.

• Comments start with the symbol "#". You may change this in both Gnuplot and Veusz.

• Each row contains a water sample: the name of the sample, followed by the concentrations of Ca, Mg, Na, K, HCO3 (alkalinity), Cl and SO4. All concentrations must be in mol/L. However, you may use milli mol/L or micro mol/L as long as all the values for a given water sample (that is, for a given row in the data file) have equal units.

• Groups of data:

  • in Gnuplot water samples are separated into groups by introducing two empty lines. The "plot" command in Gnuplot uses the "index" option to select a group of data (starting at index zero). The first row of each group contains its name in column one; this name is used in the key (legend). An alternative would be to use a different input file for each group of data, but the provided script uses a single input data file.

  • In Veusz data may be divided into groups by adding new x-y plots (menu "Insert / Add xy" when the Piper diagram widget is selected) and then defining the plotted interval for the X and Y data, in the format x_cat[37:112] (starting with zero). An alternative would be to use a different input file for each group of data, but the provided Veusz file uses a single input data file.

    Three x-y plots are needed for each group of data: a left ternary plot, using the calculated "x_cat" and "y_cat" values, the right ternary plot, using the "x_an" and "y_an" values, and the diamond plot, using the "x_d" and "y_d" values. If you add data, or change it, you must manually modify the data ranges in each of the three x-y plots, as indicated in the example Veusz file. You must also select (for each of these three plots) the same marker and color, as indicated in the provided Veusz file. The key text for each group of data, displayed in the legend, is entered (manually) only for the left ternary plot, see the provided Veusz file.

• First row:

  • in Gnuplot the first row of each data group contains the name of the group in column one. The contents of the following columns in that row are not used. In the following rows, column one contains the name of each sample (not used).

  • Veusz will use a name above a column to specify what the dataset name should be. In the provided Veusz file, the first non-comment row of the data file must contain: any text (the name of the first data group), followed by the texts: Ca_mol/L; Mg_mol/L; Na_mol/L; K_mol/L; HCO3_mol/L; Cl_mol/L; SO4_mol/L (the delimiter is ";" but it may be changed in the Veusz file). The dataset-names Ca_mol/L etc are hard-wired in defined functions in the provided Veusz file (Piper-Veusz.vsz). You may if you wish add a name for each group of data in column one of the first row of that group of data, as long as the rest of the line is empty (as in the provided data file Piper-data.csv). If you add additional texts in the following columns, for example:

    Smith et al 1980; all data in mmol/L

    the provided Veusz file (Piper-Veusz.vsz) in such a case will not work.

Output

Publication-quality output is obtained with SVG files, which may later be edited using Inkscape (Wikipedia, official website). The two output files generated by the provided Gnuplot script and the Veusz file are seen below, at the top and bottom, respectively.

Axes and grids

The axes and grids are plotted in the Cartesian coordinates, similarly to the description provided here. The width of the ternary plots is 1 (corresponding to 100 %), and the spacing between the two ternary plots is 0.4, so that the left bottom edge of the ternary plot on the right is at 1.4 (this is the variable xOffset) and its right edge is at 2.4. The coordinates of the axes and grids, stored in files Piper-axes.csv and Piper-grid.csv have been calculated based on this. The "tick" labels and axes labels are calculated and placed in the Piper diagram when it is being drawn.