In the mix

Stiff water quality diagrams are a useful tool in helping to understand groundwater chemistry. Their use is described in Hem, 1985. They are generally used to show the most abundant cations and anions plotted as a graph of two line plots, with the cations on the left and anions on the right. Figure 1 shows a typical Stiff diagram, and Figure 2 shows an example of the scale display for the diagram.

Figure 1 - Example of a single Stiff diagram

In a Stiff diagram, the distance from the centerline is proportional to the concentration (in millequivalents, which is the concentration by weight divided by the ionic weight) of each ion. Values for ions that were not detected are plotted as the detection limit, or zero if no detection limit was reported. The standard diagram shows two cations, potassium and sodium, in the upper left corner and one ion each in the other positions. This display of the major ion chemistry is useful for delimiting subsurface water populations in many situations. Different chemical constituents can be chosen to highlight other groundwater issues. Using other constituents for investigating various relationships between major ions, trace elements, constituents of concern, physical measurements such as pH or temperature and non-chemical values such as water level can create interesting displays.

Figure 2 - Stiff diagram scale display

Plots from several different samples can be posted on a map, and the relationships between the samples can be viewed qualitatively. Most programs for creating Stiff diagrams draw the diagram for the data from one sample which must then be pasted onto a map. Software that posts the diagrams for all of the wells automatically on the map can eliminate the manual-pasting step.

There are a number of setup parameters that determine how the Stiff diagrams are to be displayed. These include the chemical constituents to be drawn and the way the diagrams are to be displayed. Figure 3 shows an example of a screen to select the chemical constituents to be displayed and their location on the diagram.

Figure 3 - Screen for selecting chemical consituents to be displayed

Figure 4 shows a screen for selecting the Stiff diagram display parameters, including the pens and fonts to be used and the annotations for each diagram. Sometimes it is useful to display high concentration waters, such as oilfield brines or seawater, at a different scale from the groundwater or to display the high concentration waters in a different color. In the screen shown, the software has been told to display all the diagrams at the same scale, but to show the more concentrated waters in a different color.

Figure 4 - Screen for entering parameters

Figure 5 shows an example of several stiff diagrams drawn on a map. Each polygon represents a water sample at the specific location (well) where it is drawn. It is possible to make some interesting interpretations based on this figure. At the top (north) end of the figure is a well with a relatively high chemical concentration. The software has colored it magenta because the concentration of total dissolved solids has exceeded a user-defined cutoff of 1500 milligrams per liter (mg/l). To the south are two stations that also have high concentrations. You can identify the higher concentrations by the greater width of the symbols compared to some of the lower concentration values in the center of the map, as well as by the color. The high concentration value to the north is associated with an industrial facility, while the southern values are near a residential area, which is not visible, but is off the map to the southeast. It might be reasonable to infer that the high values to the south were caused by pollu tion from the industrial facility. The Stiff diagrams tell a different story.

Figure 5 - Stiff water quality diagram displayed on a map

There are two lines of evidence that suggest that the high concentration in the water to the south is unrelated to the water to the north. The first is the shape of the Stiff diagrams. The water to the north is high in calcium and sulfate, while the waters to the south are lower in those ions and higher in sodium/potassium and bicarbonate. This can be seen from the shapes of the curves and suggests a different source for the water in the south. Also, it is clear from the Stiff diagrams that the wells in the middle of the figure are relatively low in all ions, and their shape -- while subdued due to their low concentration -- does not look very much like the waters to the north or the south. This is another piece of evidence that the two areas of high concentration are unrelated. The information provides a fairly complete picture of the relationship between the three water populations -- the conclusion being drawn that the high concentration waters to the south are not related to the water to the north.

In order to draw valid conclusions from the Stiff diagrams, it is important to have confidence in the numbers that went into drawing them. Figure 6 shows the raw data and calculations for the Stiff diagrams for two wells. Two things to look at are the charge balance error and the reported vs. calculated values for total dissolved solids (TDS). For the two samples shown, the charge balance is within about one and a half millequivalent units of neutral, for samples where the total charge is over thirty. This is within approximately five percent, acceptable for this use. Looking at the TDS values, the comparison of reported and calculated concentrations for the first sample is within five percent, but for the second there is a greater gap. For this display it is likely still acceptable, but looking at a different time period might strengthen the validity of this interpretation.

Figure 6 - Raw data and calculations accompanying Stiff water quality diagram

Stiff diagrams should not be used as the sole tool for interpretation. In this case, a potentiometric surface map (a contour map of the hydrodynamic gradient) could also be of value, and this is shown in Figure 7. In fact, this contour map, if used without the Stiff diagrams, does suggest that the groundwater could be flowing from the north to the south, and the information from the water chemistry is needed for the correct interpretation. A study of the distribution of the constituents of concern, and perhaps trace elements in the water, could provide additional information to be used in the interpretation. Stiff diagrams on maps can be a very valuable tool for understanding subsurface waters (or surface water for that matter), and when used as part of a complete study, can provide an understanding of the water in question that is difficult to obtain using other visualization methods.

Figure 7 - Potentiometric surface added to Stiff diagram

The figures in this paper were created with Enviro Spase, an environmental geographic information system (GIS), from Geotech Computer Systems Inc., ( and are presented with permission.


Hem, John D., 1985 - Study and interpretation of the chemical characteristics of natural water, U.S. Geological Survey Water-Supply Paper 2254, Third Edition, p. 263.

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Dr. David Rich is president of Geotech Computer Systems Inc., Englewood, Colo. He can be reached via e-mail at

This article originally appeared in the 12/01/2000 issue of Environmental Protection.