The Interpolate Points tool takes point data with values at each point and uses an interpolation method, that accounts for the error in estimating the underlying semivariogram through repeated simulations, to produce rasters of predicted and prediction error values.

The outputs are hosted imagery layers.

Learn how empirical Bayesian kriging works

## Examples

Example applications of this tool include the following:

- An air quality management district has sensors at some locations that measure pollution levels. This tool can be used to predict pollution levels at locations that don't have sensors, such as locations with at-risk populations—schools or hospitals, for example.
- Predict heavy metal concentrations in crops based on samples taken from individual plants.
- Predict soil nutrient levels (nitrogen, phosphorus, potassium, and so on) and other indicators (such as electrical conductivity) to study their relationships to crop yield and prescribe precise amounts of fertilizer for each location in the field.
- Meteorological applications include prediction of temperatures, rainfall, and associated variables (such as acid rain).

## Usage notes

Interpolate Points includes configurations for input layers, interpolation settings, and result layers.

### Input layers

The Input layers group includes the following parameters:

Input Point Features identifies the features to interpolate. For feature inputs, a count of features is displayed below the layer name. The count includes all features in the layer, except features that have been removed using a filter. Environment settings, such as Processing extent, are not reflected in the feature count.

Interpolate field is the data values to interpolate. The field must be numeric.

### Interpolation settings

The Interpolation settings group includes the following parameters:

Optimize for specifies whether the interpolation will be optimized for speed, accuracy, or a combination of both.

This tool uses the Empirical Bayesian Kriging geoprocessing tool to perform the interpolation. The parameters that are supplied to the Empirical Bayesian Kriging tool are controlled by the Optimize for parameter. More accurate predictions will take longer to calculate. The following options are available:

- Speed—The interpolation model will be optimized for faster calculations by using the fewest number of simulations and employing the most efficient options and configurations.
- Balance—The interpolation model will be balanced between speed and accuracy by using typical options and configurations. This is the default.
- Accuracy—The interpolation model will be optimized for accurate and precise calculations by using the largest number of simulations and the most complicated options and configurations.

The following table lists the parameter values used in the Empirical Bayesian Kriging tool for each option:

Parameter Speed Balance Accuracy Data transformation type

NONE

NONE

EMPIRICAL

Semivariogram model type

POWER

POWER

K_BESSEL

Maximum number of points in each local model

50

75

200

Local model area overlap factor

1

1.5

3

Number of simulated semivariograms

30

100

200

Search neighborhood (Min neighbors)

8

10

15

Search neighborhood (Max neighbors)

8

10

15

Output Cell Size is the cell size of the output raster.

The available units are feet, miles, meters, and kilometers.

Transform Data specifies whether the data will be transformed to a normal distribution before performing analysis. If the data values do not appear to be normally distributed (bell shaped), it is recommended that you perform a transformation.

- Unchecked—No transformation will be applied. This is the default
- Checked—A transformation to the normal distribution will be applied.

Size of Local Models is the number of points in each local model.

A larger value will make the interpolation more global and stable, but small-scale effects may be missed. Smaller values will make the interpolation more local, so small-scale effects are more likely to be captured, but the interpolation may be unstable.

Number of Neighbors is the number of neighbors that will be used when calculating the prediction at a particular raster cell.

### Result layers

The Result layers group includes the following parameters:

Output raster name is the name of the output raster layer that will be created and added to the map.

The name must be unique. If a layer with the same name already exists in your organization, the tool will fail and you will be prompted to use a different name.

Output prediction error specifies whether a raster of the standard errors of the interpolated predictions will be created. Prediction errors are useful because they provide information about the reliability of the predicted values. This parameter is optional.

If a raster of standard errors for the interpolated predictions is requested, it will have the same name as the Output raster value, but with the word Errors appended to it.

- Output layer type specifies the type of raster output that will be created. The output can be either a tiled imagery layer or a dynamic imagery layer.
- Save in folder specifies the name of a folder in My content where the result will be saved.

## Environments

Analysis environment settings are additional parameters that affect a tool's results. You can access the tool's analysis environment settings from the Environment settings parameter group.

This tool honors the following analysis environments:

- Output coordinate system
- Processing extent
##### Note:

The default processing extent in Map Viewer is Full extent. This default is different from Map Viewer Classic in which Use current map extent is enabled by default.

- Snap raster
- Cell size
- Mask

## Credits

This tool consumes credits.

Use Estimate credits to calculate the number of credits that will be required to run the tool. For more information, see Understand credits for spatial analysis.

## Outputs

This tool includes the following outputs:

A raster layer of predictions calculated using an empirical semivariogram distribution that is generated by merging the individual semivariograms from the semivariogram distributions in the point's neighborhood.

A raster layer of standard errors of the interpolated predictions.

- A common rule is that the true value will fall within two standard errors of the predicted value 95 percent of the time. For example, a new location has a predicted value of 50 and a standard error of 5.
- This means that the best estimate of the true value at that location is 50, but it reasonably could be as low as 40 or as high as 60.
- To calculate this range of reasonable values, multiply the standard error by 2, add this value to the predicted value to get the upper end of the range, and subtract it from the predicted value to get the lower end of the range.

## Usage requirements

This tool requires the following user type and configurations:

- Professional or Professional Plus user type
- Publisher, Facilitator, or Administrator role, or an equivalent custom role with the Imagery Analysis privilege

## References

- Chilès, J-P., and P. Delfiner (1999). Chapter 4 of Geostatistics: Modeling Spatial Uncertainty. New York: John Wiley & Sons, Inc.
- Krivoruchko, K. (2012). "Empirical Bayesian Kriging," ArcUser Fall 2012.
- Krivoruchko, K. (2012). "Modeling Contamination Using Empirical Bayesian Kriging,"
*ArcUser Fall 2012*. - Krivoruchko, K., and A. Gribov (2014). "Pragmatic Bayesian kriging for non-stationary and moderately non-Gaussian data," Mathematics of Planet Earth. Proceedings of the 15
^{th}Annual Conference of the International Association for Mathematical Geosciences, Springer 2014, pp. 61-64. - Krivoruchko, K., and A. Gribov (2019). "Evaluation of empirical Bayesian kriging," Spatial Statistics Volume 32. https://doi.org/10.1016/j.spasta.2019.100368.
- Pilz, J., and G. Spöck (2007). "Why Do We Need and How Should We Implement Bayesian Kriging Methods," Stochastic Environmental Research and Risk Assessment 22 (5):621–632.

## Resources

Use the following resources to learn more:

- What is Empirical Bayesian kriging?
- Interpolate Points in ArcGIS REST API
- interpolate_points in ArcGIS API for Python
- Empirical Bayesian Kriging in ArcGIS Pro with the Geostatistical Analyst extension