Label | Explanation | Data Type |

Input point features | The input point features containing the z-values to be interpolated into a surface raster. | Feature Layer |

Z value field | The field that holds a height or magnitude value for each point. This can be a numeric field or the Shape field if the input point features contain z-values. | Field |

Output surface raster | The output interpolated surface raster. It is always a floating-point raster. | Raster Dataset |

Semivariogram properties | The Semivariogram model to be used. There are two methods for kriging: Ordinary and Universal. Ordinary kriging can use the following semivariogram models: - Spherical—Spherical semivariogram model. This is the default.
- Circular—Circular semivariogram model.
- Exponential—Exponential semivariogram model.
- Gaussian—Gaussian or normal distribution semivariogram model.
- Linear—Linear semivariogram model with a sill.
Universal kriging can use the following semivariogram models: - Linear with Linear drift—Universal Kriging with linear drift.
- Linear with Quadratic drift—Universal Kriging with quadratic drift.
There are options available via the Advanced Parameters dialog box. These parameters are: - Lag size—The default is the output raster cell size.
- Major range—Represents a distance beyond which there is little or no correlation.
- Partial sill—The difference between the nugget and the sill.
- Nugget—Represents the error and variation at spatial scales too fine to detect. The nugget effect is seen as a discontinuity at the origin.
| KrigingModel |

Output cell size (Optional) | The cell size of the output raster that will be created. This parameter can be defined by a numeric value or obtained from an existing raster dataset. If the cell size hasn't been explicitly specified as the parameter value, the environment cell size value will be used if specified; otherwise, additional rules will be used to calculate it from the other inputs. See the usage section for more detail. | Analysis Cell Size |

Search radius (Optional) | Defines which of the input points will be used to interpolate the value for each cell in the output raster. There are two options: Variable and Fixed. Variable is the default. - Variable
Uses a variable search radius in order to find a specified number of input sample points for the interpolation. - Number of points—An integer value specifying the number of nearest input sample points to be used to perform interpolation. The default is 12 points.
- Maximum distance—Specifies the distance, in map units, by which to limit the search for the nearest input sample points. The default value is the length of the extent's diagonal.
- Fixed
Uses a specified fixed distance within which all input points will be used for the interpolation. - Distance—Specifies the distance as a radius within which input sample points will be used to perform the interpolation.
The value of the radius is expressed in map units. The default radius is five times the cell size of the output raster. - Minimum number of points—An integer defining the minimum number of points to be used for interpolation. The default value is 0.
If the required number of points is not found within the specified distance, the search distance will be increased until the specified minimum number of points is found. When the search radius needs to be increased it is done so until the Minimum number of points fall within that radius, or the extent of the radius crosses the lower (southern) and/or upper (northern) extent of the output raster. NoData is assigned to all locations that do not satisfy the above condition.
- Distance—Specifies the distance as a radius within which input sample points will be used to perform the interpolation.
| Radius |

Output variance of prediction raster (Optional) | Optional output raster where each cell contains the predicted variance values for that location. | Raster Dataset |

Available with Spatial Analyst license.

Available with 3D Analyst license.

## Summary

Interpolates a raster surface from points using kriging.

The Empirical Bayesian Kriging tool provides enhanced functionality or performance.

## Usage

Kriging is a processor-intensive process. The speed of execution is dependent on the number of points in the input dataset and the size of the search window.

Low values within the optional output variance of prediction raster indicate a high degree of confidence in the predicted value. High values may indicate a need for more data points.

The Universal kriging types assume that there is a structural component present and that the local trend varies from one location to another.

The Semivariogram properties allow control of the semivariogram used for kriging. A default value for Lag size is initially set to the default output cell size. For Major range, Partial sill, and Nugget, a default value will be calculated internally if nothing is specified.

The optional output variance of prediction raster contains the kriging variance at each output raster cell. Assuming the kriging errors are normally distributed, there is a 95.5 percent probability that the actual z-value at the cell is the predicted raster value, plus or minus two times the square root of the value in the variance raster.

The Output cell size parameter can be defined by a numeric value or obtained from an existing raster dataset. If the cell size hasn’t been explicitly specified as the parameter value, it is derived from the Cell Size environment if it has been specified. If the parameter cell size or the environment cell size have not been specified, but the Snap Raster environment has been set, the cell size of the snap raster is used. If nothing is specified, the cell size is calculated from the shorter of the width or height of the extent divided by 250 in which the extent is in the output coordinate system specified in the environment.

If the cell size is specified using a numeric value, the tool will use it directly for the output raster.

If the cell size is specified using a raster dataset, the parameter will show the path of the raster dataset instead of the cell size value. The cell size of that raster dataset will be used directly in the analysis, provided the spatial reference of the dataset is the same as the output spatial reference. If the spatial reference of the dataset is different than the output spatial reference, it will be projected based on the selected Cell Size Projection Method value.

Some input datasets may have several points with the same x,y coordinates. If the values of the points at the common location are the same, they are considered duplicates and have no effect on the output. If the values are different, they are considered coincident points.

The various interpolation tools may handle this data condition differently. For example, in some cases, the first coincident point encountered is used for the calculation; in other cases, the last point encountered is used. This may cause some locations in the output raster to have different values than what you might expect. The solution is to prepare your data by removing these coincident points. The Collect Events tool in the Spatial Statistics toolbox is useful for identifying any coincident points in your data.

For data formats that support Null values, such as file geodatabase feature classes, a Null value will be ignored when used as input.

## Parameters

arcpy.ddd.Kriging(in_point_features, z_field, out_surface_raster, semiVariogram_props, {cell_size}, {search_radius}, {out_variance_prediction_raster})

Name | Explanation | Data Type |

in_point_features | The input point features containing the z-values to be interpolated into a surface raster. | Feature Layer |

z_field | The field that holds a height or magnitude value for each point. This can be a numeric field or the Shape field if the input point features contain z-values. | Field |

out_surface_raster | The output interpolated surface raster. It is always a floating-point raster. | Raster Dataset |

semiVariogram_props kriging_model | The Semivariogram model to be used. There are two models for kriging: Ordinary and Universal. The Ordinary model has five types of semivariograms available. The Universal model has two types of semivariograms available. Each semivariogram has several optional parameters that can also be set. - Ordinary model semivariograms
- Spherical—Spherical semivariogram model. This is the default.
- Circular—Circular semivariogram model.
- Exponential—Exponential semivariogram model.
- Gaussian—Gaussian (or normal distribution) semivariogram model.
- Linear—Linear semivariogram model with a sill.
- Universal model semivariograms
- LinearDrift—Universal Kriging with linear drift.
- QuadraticDrift—Universal Kriging with quadratic drift.
- After the semivariogram model is defined, the remaining parameters are common between Ordinary and Universal kriging. These include the following:
- Lag size—The default is the output raster cell size.
- MajorRange—Represents a distance beyond which there is little or no correlation.
- PartialSill—The difference between the nugget and the sill.
- Nugget—Represents the error and variation at spatial scales too fine to detect. The nugget effect is seen as a discontinuity at the origin.
The form of the semivariogram is a text string: "{semivariogramType},{lagSize},{majorRange},{partialSill},{nugget}" For example: "Circular, 2000, 2.6, 542" | KrigingModel |

cell_size (Optional) | The cell size of the output raster that will be created. This parameter can be defined by a numeric value or obtained from an existing raster dataset. If the cell size hasn't been explicitly specified as the parameter value, the environment cell size value will be used if specified; otherwise, additional rules will be used to calculate it from the other inputs. See the usage section for more detail. | Analysis Cell Size |

search_radius (Optional) | Defines which of the input points will be used to interpolate the value for each cell in the output raster. There are two ways to specify the searching neighborhood: Variable and Fixed. Variable uses a variable search radius in order to find a specified number of input sample points for the interpolation. Fixed uses a specified fixed distance within which all input points will be used. Variable is the default. The syntax for these parameters are: - Variable, number_of_points, maximum_distance, where
- number_of_points—An integer value specifying the number of nearest input sample points to be used to perform interpolation. The default is 12 points.
- maximum_distance—Specifies the distance, in map units, by which to limit the search for the nearest input sample points. The default value is the length of the extent's diagonal.
- Fixed, distance, minimum_number_of_points, where
- distance—Specifies the distance as a radius within which input sample points will be used to perform the interpolation. The value of the radius is expressed in map units. The default radius is five times the cell size of the output raster.
- minimum_number_of_points—An integer defining the minimum number of points to be used for interpolation. The default value is 0.
If the required number of points is not found within the specified distance, the search distance will be increased until the specified minimum number of points is found. When the search radius needs to be increased it is done so until the minimum_number_of_points fall within that radius, or the extent of the radius crosses the lower (southern) and/or upper (northern) extent of the output raster. NoData is assigned to all locations that do not satisfy the above condition.
| Radius |

out_variance_prediction_raster (Optional) | Optional output raster where each cell contains the predicted variance values for that location. | Raster Dataset |

### Code sample

This example inputs a point shapefile and interpolates the output surface as a Grid raster.

```
import arcpy
from arcpy import env
env.workspace = "C:/data"
arcpy.Kriging_3d("ca_ozone_pts.shp", "OZONE", "c:/output/krigout",
"Spherical", 2000, "Variable 12")
```

This example inputs a point shapefile and interpolates the output surface as a Grid raster.

```
# Name: Kriging_3d_Ex_02.py
# Description: Interpolates a surface from points using kriging.
# Requirements: 3D Analyst Extension
# Import system modules
import arcpy
from arcpy import env
# Set environment settings
env.workspace = "C:/data"
# Set local variables
inFeatures = "ca_ozone_pts.shp"
field = "OZONE"
outRaster = "C:/output/krigoutput02"
cellSize = 2000
outVarRaster = "C:/output/outvariance"
kModel = "CIRCULAR"
kRadius = 20000
# Execute Kriging
arcpy.ddd.Kriging(inFeatures, field, outRaster, kModel,
cellSize, kRadius, outVarRaster)
```

## Environments

## Licensing information

- Basic: Requires 3D Analyst or Spatial Analyst
- Standard: Requires 3D Analyst or Spatial Analyst
- Advanced: Requires 3D Analyst or Spatial Analyst