Piper diagram

Piper diagram of water samples from the Mtshabezi River, Zimbabwe. Data source:^[1]

A piper diagram is a graphical representation of the chemistry of a water sample or samples.

The cations and anions are shown by separate ternary plots. The apexes of the cation plot are calcium, magnesium and sodium plus potassium cations. The apexes of the anion plot are sulfate, chloride and carbonate plus hydrogen carbonate anions. The two ternary plots are then projected onto a diamond.^[2] The diamond is a matrix transformation of a graph of the anions (sulfate + chloride/ total anions) and cations (sodium + potassium/total cations).^[3]

The required matrix transformation of the anion/cation graph is:

\begin{bmatrix} x' \\ y' \\ 1 \end{bmatrix} = \begin{bmatrix} \cos(\frac{\pi}{2}) & \sin(\frac{\pi}{2}) & 0 \\ -2\sin(\frac{\pi}{2}) & 2\cos(\frac{\pi}{2}) & 0 \\ 0 & 0 & 1 \end{bmatrix} \begin{bmatrix} x \\ y \\ 1 \end{bmatrix}

Software

Grapher Commercial software available from Golden Software, Inc.
AqQA Commercial software available from RockWare, Inc.
AquaChem Commercial software from Schlumberger Water Services
ChemPoint Pro Commercial software from Starpoint software, Inc.
The Geochemist's Workbench Commercial software from Aqueous Solutions LLC
GWB Student Edition Free student edition of the popular geochemical modeling software package.
GW Chart Free software for creating piper diagrams from the United States Geological Survey
RockWorks Utilities Commercial software from RockWare, Inc.
EnviroInsite Commercial software from HydroAnalysis, Inc.
Origin 9.1 commercial software from Originlab can create Piper diagrams from spreadsheet data.
Piper 2.0 in HydroOffice 2012 - commercial tool in HydroOffice software can produce variable types of Piper plots in vector graphics

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↑ Love, D.; Moyce, W.; Ravengai, S. (2006). "Livelihood challenges posed by water quality in the Mzingwane and Thuli river catchments, Zimbabwe" (PDF). 7th WaterNet/WARFSA/GWP-SA Symposium, Lilongwe, Malawi. Retrieved 2008-06-20.
↑ Piper, A.M. (1953). A Graphic Procedure in the Geochemical Interpretation of Water Analysis. Washington D.C.: United States Geological Survey. OCLC 37707555. ASIN B0007HRZ36.
↑ Rao, N. Srinivasa (December 1998). "MHPT.BAS: a computer program for modified Hill–Piper diagram for classification of ground water". Computers & Geosciences 24 (10): 991–1008. Bibcode:1998CG.....24..991R. doi:10.1016/S0098-3004(98)00083-1.

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