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Quickly and Easily Create Class Piper Plots in Grapher Using the Class Ternary Plots

In the fields of hydrogeology and groundwater analysis, piper plots (piper trilinear diagrams or groundwater piper diagrams) are very powerful tools for visualizing the relative abundance of common ions in water samples. Although there are other plot types that can show abundance of ions in groundwater, this plot type is especially useful because it allows you to plot multiple samples on the same plot, thus allowing for grouping water samples by groundwater facies and other criteria. In this day and age when groundwater is so closely monitored, it is especially important to have a plot type like the piper plot that makes it easy to determine whether it is suitable for human use.

A piper plot is comprised of three components: a ternary (trilinear) diagram in the lower left representing cations (magnesium, calcium, and sodium plus potassium), a ternary diagram in the lower right representing anions (chloride, sulfate, and carbonate plus bicarbonate), and a diamond plot in the middle which is a matrix transformation of the two ternary diagrams. Each sample is normalized to 100 (sum of cations = 100 and sum of anions = 100), so the relative concentrations are on a percentage basis.

The three components of the piper plot. Bottom left is a ternary plot of the cations, bottom right is a ternary plot of the anions, and top is a diamond plot of a projection from the other two plots.

 

The diamond plot then can be analyzed to tell you what kind of groundwater you’re looking at. Samples in the top quadrant are calcium sulfate waters, samples in the left quadrant are calcium bicarbonate waters, samples in the right quadrant are sodium chloride waters, and samples in the bottom quadrant are sodium bicarbonate waters.

Interpretation of the diamond plot (modified from http://inside.mines.edu/~epoeter/_GW/18WaterChem2
/WaterChem2pdf.pdf
). Samples in the top quadrant are calcium sulfate waters, which are typical of gypsum ground water and mine drainage. Samples in the left quadrant are calcium bicarbonate waters, which are typical of shallow fresh ground water. Samples in the right quadrant are sodium chloride waters, which are typical of marine and deep  ancient ground water. Samples in the bottom quadrant are sodium bicarbonate waters, which are typical of deep ground water influenced by ion exchange.

 

Using different symbols in a piper plot is typical to show different collection areas or to demonstrate differences in total dissolved solids amongst the samples. In previous versions of Grapher, in order to create a piper plot you had to use a combination of ternary diagrams, so to modify your symbols you had to add a symbol column to your data file and go through a workaround to display these custom symbols. Grapher 11 though has introduced a classed ternary diagram, so it’s easier than ever to create your piper plot with symbol classes! To do so:

  1. Download the attached zip file containing the template files.
  2. Unzip the file to extract the GRF Grapher file and the XLSX data file. The data file displays class name, cations, anions, and two combined columns. The cations and anions should all be normalized to add up to 100%. Additionally there are three extra columns at the end of the file for custom axes labels.
  3. Open Grapher 11. In the Welcome dialog click Open Document.
  4. In the Open dialog, navigate to the XLSX data file, select it, and click Open. The data file opens in Grapher’s worksheet.
  5. Replace data in Cols B-G with your own normalized cation and anion concentrations.
  6. Go to Cells | Data | Transform. Change First row to 2 and then type Transform equation: I=G+F. Click OK.

The Transform dialog showing the transform used to calculate the x component for the diamond plot.

 

  1. Go to Cells | Data | Transform. Change First row to 2 and then type Transform equation: J=B-sin(D2R(30))*I. Click OK.

The Transform dialog showing the transform used to calculate the y component for the diamond plot.
Note that the D2R here is important because it converts the 30 (degrees) to radians.

 

  1. Use File | Save to save the data file to the same name, or File | Save As to save to your own name.
  2. Click File | Open.
  3. In the Open dialog navigate to the GRF file that came in the ZIP file you downloaded in step 1. Select it and click Open.
  4. If you saved your data to a new name, click on Class Scatter Plot 1 under Piper Points in the Object Manager.
  5. In the Plot tab of the Property Manager, change the Worksheet to your new data file.
  6. Repeat steps 11 and 12 for Ternary Class Plot 1 under Right Class Ternary and Left Class Ternary.

 

Now you have a piper plot of your own data using custom symbol classes. In just a few short minutes you’ve plotted a visually-appealing, completely customizable piper plot which will wow your audience and quickly inform them of what the groundwater has to offer.

 

Updated February 16, 2017

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