Uses one of five basis functions to process each measured sample value, thus creating an exact interpolation surface
Uses one of five basis functions to process each measured sample value, thus creating an exact interpolation surface.
The smooth search neighborhood is only available for the Inverse multiquadric function.
For all methods except the Inverse multiquadric function, the higher the parameter value, the smoother the surface. The opposite is true for the Inverse multiquadric function.
Parameter  Explanation  Data Type 
in_features

The input point features containing the zvalues to be interpolated. 
Feature Layer 
z_field

Field that holds a height or magnitude value for each point. This can be a numeric field or the Shape field if the input features contain zvalues or mvalues. 
Field 
out_ga_layer
(Optional)

The geostatistical layer produced. This layer is required output only if no output raster is requested. 
Geostatistical Layer 
out_raster
(Optional)

The output raster. This raster is required output only if no output geostatistical layer is requested. 
Raster Dataset 
cell_size
(Optional)

The cell size at which the output raster will be created. This value can be explicitly set under Raster Analysis from the Environment Settings. If not set, it is the shorter of the width or the height of the extent of the input point features, in the input spatial reference, divided by 250. 
Analysis Cell Size 
search_neighborhood
(Optional)

Defines which surrounding points will be used to control the output. Standard is the default. This is a Search Neighborhood class SearchNeighborhoodStandard ,SearchNeighborhoodSmooth, SearchNeighborhoodStandardCircular, and SearchNeighborhoodSmoothCircular. Standard
Smooth
StandardCircular
SmoothCircular

Geostatistical Search Neighborhood 
radial_basis_functions
(Optional)

Available Radial basis functions.

String 
small_scale_parameter
(Optional)

Used to calculate the weights assigned to the points located in the moving window. Each of the radial basis functions has a parameter that controls the degree of smallscale variation of the surface. The (optimal) parameter is determined by finding the value that minimizes the root mean square prediction error (RMSPE). 
Double 
Interpolate point features onto a rectangular raster.
Interpolate point features onto a rectangular raster.
RBF methods are a series of exact interpolation techniques; that is, the surface must pass through each measured sample value. There are five different basis functions:
Each basis function has a different shape and results in a different interpolation surface. RBF methods are a special case of splines.
RBFs are conceptually similar to fitting a rubber membrane through the measured sample values while minimizing the total curvature of the surface. The basis function you select determines how the rubber membrane will fit between the values. The diagram below illustrates conceptually how an RBF surface fits through a series of elevation sample values. Notice in the cross section that the surface passes through the data values.
Being exact interpolators, the RBF methods differ from the global and local polynomial interpolators, which are both inexact interpolators that do not require the surface to pass through the measured points. When comparing an RBF to IDW (which is also an exact interpolator), IDW will never predict values above the maximum measured value or below the minimum measured value as you can see in the cross section of a transect of sample data below.
However, the RBFs can predict values above the maximum and below the minimum measured values as in the cross section below.
Optimal parameters are determined using cross validation in a similar manner as explained for IDW and local polynomial interpolation.
RBFs are used to produce smooth surfaces from a large number of data points. The functions produce good results for gently varying surfaces such as elevation.
However, the techniques are inappropriate when large changes in the surface values occur within short distances and/or when you suspect the sample data is prone to measurement error or uncertainty.
In Geostatistical Analyst, RBFs are formed over each data location. An RBF is a function that changes with distance from a location.
For example, suppose the radial basis function is simply the distance from each location, so it forms an inverted cone over each location. If you take a cross section of the x,z plane for y = 5, you will see a slice of each radial basis function. Now, suppose you want to predict a value at y = 5 and x = 7. The value of each radial basis function at the prediction location can be taken from the figure above, given by the values Φ_{1}, Φ_{2} , and Φ_{3}, which simply depend on the distance from each data location. The predictor is formed by taking the weighted average w_{1}Φ_{1} + w_{2}Φ_{2} + w_{3}Φ_{3} + …
Now the question is how to determine the weights? So far, you have not used the data values at all. The weights w_{1}, w_{2}, w_{3}, and so on, are found by requiring that, when the prediction is moved to a location with a measured value, the data value is predicted exactly. This forms N equations with N unknowns and can be solved uniquely. Thus, the surface passes through the data values, making predictions exact.
The radial basis function in this example is a special case of the multiquadric RBF. Geostatistical Analyst also allows you to use other RBFs such as completely regularized splines, thinplate splines, splines with tension, and inverse multiquadric. Sometimes, the difference between these is not great, but you may have reason to choose one or you can try several and use crossvalidation to select one. Each of the RBFs has a parameter that controls the "smoothness" of the surface.
For all methods except inverse multiquadric, the higher the parameter value, the smoother the map; the opposite is true for inverse multiquadric.
You can link related {{typeName}}
from your personal space to this model item, or you can create a new {{typeName.toLowerCase()}}.
These authorship information will be submitted to the contributor to review.
Comment(s)