Calculate contamination plume stability statistics in Surfer

In the article "A Practical Method to Evaluate Ground Water Contaminant Plume Stability", Joseph A. Ricker proposes a method of determining plume stability by comparing several calculated characteristics over time. The primary characteristics of interest are volume, planar area, average concentration, contaminant plume mass, and center of mass.  Step by step instructions for performing each of the required calculations in Surfer are outlined below.

Grid the concentration data

It is quite common for concentration data sets to contain very high values surrounded by low values or undetectable values.  This distribution of data can lead to artificially high results after interpolation.  To prevent high concentration values from having an outsized impact on the surrounding areas, the log of the concentration data should be used during interpolation.  The Log, save as linear Z transform in Surfer allows you to do this and still obtain a grid with true concentration values.

Since concentration data will never be negative, you can also tell Surfer to set the minimum Z value to zero.  These two settings will improve the accuracy of your results.

  1. Click Home | Grid Data | Grid Data.
  2. In the Grid Data-Select Data dialog,
    1. Click Browse, select your data file, and click Open.
    2. Set the X, Y, and Z variable columns.
    3. Click Kriging in the Gridding Method section.
    4. Click Skip to End.
  3. In the Grid Data - Kriging - Output dialog, 
    1. In the Grid Z Limits section, click in the Minimum field, select Custom and enter 0.
    2. Click in the Z Transform field and select Log, save as linear.
    3. Verify the Grid Report option is checked. 
      The grid report provides valuable information about data distribution and how the grid was created that ensures all results can be checked for quality and repeated as needed.
    4. Set any other options you'd like, and then click Finish to create the grid.
Ricker Method Contour Map.png
Surfer map illustrating the input data as a post layer and the gridded contamination plume data as a contour layer.

 

Calculate the area and volume of the plume

To determine the volume and area of a plume, you must know the accepted safe level of the contaminant in question.  For the purposes of this example, the accepted safe concentration will be 10 µg/L

  1. Click the Grids | Calculate | Volume command.
  2. In the Grid Volume dialog,
    1. Click Grid File in the Upper Surface section.
    2. If you created a map from the grid file, click <None> and select the appropriate map layer. 
      If you did not create a map from the grid, click Browse, select the contaminant concentration grid file, and click Open.
    3. Click Constant in the Lower Surface section and enter 10 or the accepted safe concentration.
    4. Click OK to generate a Grid Volume report.

The Grid Volume report will provide several volume and area calculations in the same units as the input grid.  For example, if your XY coordinates are in meters and your concentration is in µg/L then the reported area will be in meters squared and the volume will be in µg/L/m2.

The values we're interested in are the Positive Volume [Cut] and the Positive Planar Area [Cut].  These represent the volume and area inside the plume where the contaminant concentration (upper surface) is above the accepted safe level (lower surface).

Ricker Method Volume Report.png
Surfer Grid Volume Report showing the volume and area results

 

Calculate the plume mass and average concentration

The average plume concentration is calculated by dividing the volume (µg/L*m2) by the planar area (m2)

  1. In the Grid Volume report, make note of the Positive Volume [Cut], which provides the volume above the lower surface (safe concentration).
  2. Make note of the Positive Planar Area [Cut], which provides the area of intersection between the lower surface and upper surface where the concentration is above the defined value.
  3. Divide the Positive Volume by the Positive Planar Area.
    At this point you have the average concentration of the plume where the concentration is above the cutoff concentration.
  4. To get the average concentration of the entire plume, add the cutoff concentration to the above calculated average.

If you know the aquifer thickness and effective porosity then a representative estimate of the plume mass can be calculated using the formula below:

 

Plume mass (kg) = Planar area (m2) x Average concentration (µg/L) x Aquifer thickness (m) x Effective porosity x 1000L/m3 x 1kg/1E+9 µg

 

As noted in Mr. Ricker's article, this plume mass is not exact but it is a useful single value that can be used to indicate plume stability over time.

 

References:

Ricker, J. A. 2008. “A Practical Method to Evaluate Groundwater Contaminant Plume Stability,” Ground Water Monitoring and Remediation 28(4): 85–94.

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