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Predicting the attributes of the unsampled locations by kriging utilizing the ‘gstat’ package

Before proceeding to the example, you must have the following installed on your computer: ####Prerequisites #####ArcGIS 10.3.1 or ArcGIS Pro 1.1 (don't have it? try a 60 day trial)

  1. R Statistical Computing Software, 3.1.0 or later
  • 32-bit version required for ArcMap, 64-bit version required for ArcGIS Pro (Note: the installer installs both by default).
  • 64-bit version can be used with ArcMap by installing Background Geoprocessing and configuring scripts to run in the background.
  1. R ArcGIS Bridge

#####Setup Instructions

#####ArcGIS 10.3.1

  • In the Catalog window, navigate to the folder containing the Python Toolbox, R Integration.pyt. Note: You may have to first add a folder connection to the location that you extracted the files or downloaded via GitHub.
  • Open the toolbox, which should look like this:

figurea

  • Run the Install R bindings script. You can then test that the bridge is able to see your R installation by running the Print R Version and R Installation Details tools.

#####ArcGIS Pro 1.1

  • In the Project pane, either navigate to a folder connection containing the Python toolbox, or right click on Toolboxes > Add Toolbox and navigate to the location of the Python toolbox.
  • Open the toolbox, which should look like this:

figureb

-Run the Install R bindings script. You can then test that the bridge is able to see your R installation by running the Print R Version and R Installation Details tools.

##Term descriptions

###Methods Kriging, also referred to as Gaussian process regression is an effective geostatistical method for interpolating the values that are modeled by a Gaussian process governed by prior covariance, as opposed to a piecewise–polynomial spline chosen to optimize smoothness of the fitted values.

Ordinary kriging is a method associated with linear unbiased estimation, as the estimations are weighed linear combination of available data. It does not take into account of the covariates – it assumes constant unknown mean and helps in minimizing error variance. It is the most commonly used method of kriging.

Universal kriging is similar but it includes a polynomial trend model, assumes covariates for interpolation (kriging under non-stationary conditions, in the presence of drift).

###Data The data used here in this example case is Meuse river data. Meuse dataset comprises the measures of four major heavy metals found in the top soil in a flood plain along the river Meuse, Belgium. This is crucial that the contamination happens just because of the river flow that moves the polluted sediments and deposits close to the river bank. This case makes it explicit for geostatistical analysis of the dataset.

###R-Package Package ‘gstat’ is used here in conjunction with the package ‘sp’. 'gstat’ promotes a range of univariate and multivariate geostatistical modelling, prediction and simulation functions while ‘sp’ helps with class descriptions and methods for importing , exporting and visualizing spatial data.

###How to use ####Kriging In order to use this tool, select the ComKriging script tool from the Interp_simul_tools.tbx toolbox in the ArcGIS environment. As you proceed, you will find this tool popped up as shown below in Figure:1.

Figure:1. #####

Figure:1.

The description of each of the parameters found in this pop-up tool is as follow.

  1. Input feature : Input point feature containing fields of the dependant variable and all explanatory variables.
  2. Prediction location : Input point feature representing locations where you would like to predict the probable values for the presence of dependant variable. These point feature must have certain explanatory variables stored as fields.
  3. Dependent variable : Input string that is a field from the input feature containing the sampled attributes. A particular value gives the strength of the field element at that point.
  4. Using log : Taking logarithmic values for the dependent variable.
  5. Covariate variable : Input string that is a field from the input feature containing independent or explanatory variables. This field is necessary only for Universal kriging. Else it runs ordinary kriging by default.
  6. vgm_model : Input for the vgm expression to fit the variogram (default : vgm(1,"Exp",300,1) - for Universal kriging)
  7. Output krige : Output krige shapefile that contains the predictions of the values of unsampled locations from the Prediction_location dataset.
  8. Output_var : Output variance provides how far the values are deviated from the other and the mean and exports the output as a pdf file.

The datatype "Field" has been avoided while developing the script tool (here for Dep_variable and covariate_variable) as it generates some script error in some cases.

#####Steps to use the tool :

  • The feature layers of meuse dataset is provided in this same repository within the data folder.
  • Click the input_feature file icon and browse for the meuse feature class from meuse.gdb.
  • Click the Prediction location file icon and browse for meuse_grid from the same meuse.gdb.
  • Click the column for dep_variable parameter and type the name of any heavy metal variable from the data (eg. 'zinc') as a string to process prediction.
  • In case, if needed to run universal kriging, then click the column for the covariate parameter, which is optional and type ‘dist’ variable as a string to process prediction. Else, leave the column empty (to run ordinary kriging).
  • If needed, mark the Using_log icon to use the logarithmic values of the Variable.
  • Give the Values for the arguments (Partial_Sill, Model, Range, Nugget) in an expression vgm() to the Variogram model. There is a default expression given as 'vgm(1,"Exp",300,1)', meant for universal kriging.
  • Give output files for Output krige and Output_var (Optional) if you want to change the default file selects. Finally click OK.

####Ordinary kriging Once the inputs are given and if the covariate column is left empty, the tool runs ordinary kriging as shown below in Figure:2 and produces the output krige as a shapefile as shown in Figure:3 and variance-variogram plotted and exported as a pdf file.

Figure:2 #####

Figure:2.

figure:3 #####

Figure:3.

####Universal kriging

Once the inputs are given and if the input variable is given as a string to the covariate column (here, it is 'dist'), the tool runs the universal kriging (with the covariate "sqrt(dist)") as shown below in Figure:5. and produces the output krige as a shapefile as shown in Figure:6. and variance-variogram plotted and exported as a pdf file.

Figure:5. #####

Figure:5.

Figure:6. #####

Figure:6.

###References [1] Pebesma, Edzer J. "Multivariable geostatistics in S: the gstat package."Computers & Geosciences 30.7 (2004): 683-691. [2] Pebesma, Edzer, and Benedikt Gräler. "Spatio-temporal geostatistics using gstat." (2015).