Geostatistical modelling of Arsenic in groundwater

Arsenic in groundwater is largely the result of minerals dissolving from weathered rocks and soils. Arsenic is found naturally in rocks in the earth’s crust and it is recognized as a poison and a carcinogen substance. It occurs within organic compounds (combined with hydrogen and carbon), and within inorganic compounds (combined within sulphur, chlorine or oxygen). In water, arsenic has no smell or taste and can only be detected through a chemical analysis.

The concentration of arsenic in ground waters in the Duero river basin is relatively low, usually ranging from 0.01 to 0.02 milligrams per litre (mg/L). Sample data (arsenic_sample.shp) for this example comes from the central region of the Duero basin, where a recent investigation has shown increasing concentrations of Arsenic in various linked primarily to illegal agricultural practices.

By using ArcGIS Geostatistical Analyst, we are going to perform a prediction model for the data. In this case the geostatistical method that best suits the spatial variability of the data is the Kriging, which is an stochastic method.

A comparison of the different methods (deterministic and stochastic) can be found in the following document:

Open ArcMap. In the menu bar click on Customize > Extensions… and activate Geostatistical Analyst extension. Click close.

In the Geostatistical Analyst toolbar, click on “Launch Geostatistical Analyst Wizard” button. This will prompt the following window:

Methods: We must select the method by which you want to analyze the data, in this case is Kriging.
Source dataset: the shapefile on which we are going to carry out the modelling. In this case, we select “arsenic_sample”.
Data Field: The field you want to perform the analysis. In this case, the concentration levels of Arsenic in mg per litre (“AS_”).

Click next. If you get a message saying that two or more sample point exist at the same location, select the option “Use Mean”. The following window will appear:

In Kriging type, select “Ordinary Kriging”. Select “Prediction” as the output type.
In Transformation, select “Log”, since is necessary for the data to apply a logarithmic transformation.
In Order of trend removal, select “First”. To find out which order of trend removal is necessary for a given dataset, check this link:

Click Next.  The following window allows us to find out whether the data have directional anisotropy present or not. If the surface resemble a circle, there is no directional anisotropy. If there is anything like the figure, the data have directional anisotropy.

In the next window, we choose the following options:

Model: 1. Type = “Spherical”.
Anisotrophy = “True”.
Show Search Direction = “True”.

Now we must change the angle until the blue line that comes from the center of the Semivariogram Map match with the direction of the major axis of the ellipse, as shown in the figure:

Click Next. In the next window, we change the Maximum Neighbours to 12 and Minimum Neighbours to 6. As sampled locations get farther from the prediction location, their influence on the prediction location decreases. So, to speed up interpolation calculations, we can ignore those far-off sampled points.

Click Next. The Cross Validation window will appear. You can see a table showing a the model’s predicted data compared with the measured values, along with the Standard error.

On the lower-right side of the window you can see the prediction errors:

  • Root-Mean-Square: 7.356
  • Average Standard Error: 10,836.42
  • Mean Standardized: 0.002047
  • Root-Mean-Square Standardized: 0.0161

Click Finish. A report summary of the selected method will appear.

The final result is as shown below:

In the final result, we can see how there is a growing gradient in Arsenic concentration from East to West. Note the area colored in red, where the predicted concentration of Arsenic is greater than 15,3 mg/L, which in 300 times higher than the legal limit.

Anyway, we can try to refine the model by changing the model parameters. The lower the Root-Mean-Square (RMS), the better our prediction map is. To compare two models, we can right-click on the model in the table on contents and go to “Compare…”

Additionally, we can calculate the Standard Error Map. A Standard Error Map quantifies the uncertainty of our predictions. The larger the standard errors, the more uncertain are our predictions.


About Sergio Perez
An environmental scientist passionate for the world of Geographical Information Systems and its application to the field of hydrological management.

One Response to Geostatistical modelling of Arsenic in groundwater

  1. Pingback: Semivariogram – example of the XY graph | Tabagus - The Web and Data Portal

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