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Local Polynomial Interpolation, Moving Window Kriging and Radial Basis Functions

Husam Jubeh
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Local Polynomial Interpolation, Moving Window Kriging and Radial Basis Functions Tools

Local Polynomial Interpolation

How to use Local Polynomial Interpolation Tool in ArcToolbox ArcMap ArcGIS??

Local Polynomial Interpolation Tool
Local Polynomial Interpolation

Path to access the tool

:

Local Polynomial Interpolation Tool, Interpolation Toolset, Geostatistical Analyst Tools Toolbox

 

Local Polynomial Interpolation

Fits the specified order (zero, first, second, third, and so on) polynomial, each within specified overlapping neighborhoods, to produce an output surface.

1.    Input features

The input point features containing the z-values to be interpolated.

2.    Z value 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 z-values or m-values.

3.    Output geostatistical layer (optional)

The geostatistical layer produced. This layer is required output only if no output raster is requested.

4.    Output raster (optional)

The output raster. This raster is required output only if no output geostatistical layer is requested.

5.    Output 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.

6.    Order of polynomial (optional)

The order of the polynomial.

7.    Search neighborhood (optional)

Defines which surrounding points will be used to control the output. Standard is the default.

Standard

  • Major semiaxis—The major semiaxis value of the searching neighborhood.

    1. Minor semiaxis—The minor semiaxis value of the searching neighborhood.
    2. Angle—The angle of rotation for the axis (circle) or semimajor axis (ellipse) of the moving window.
    3. Maximum neighbors—The maximum number of neighbors that will be used to estimate the value at the unknown location.
    4. Minimum neighbors—The minimum number of neighbors that will be used to estimate the value at the unknown location.
    5. Sector type—The geometry of the neighborhood.
      • One sector—Single ellipse.
      • Four sectors—Ellipse divided into four sectors.
      • Four sectors shifted—Ellipse divided into four sectors and shifted 45 degrees.
      • Eight sectors—Ellipse divided into eight sectors.

      Smooth

      1. Major semiaxis—The major semiaxis value of the searching neighborhood.
      2. Minor semiaxis—The minor semiaxis value of the searching neighborhood.
      3. Angle—The angle of rotation for the axis (circle) or semimajor axis (ellipse) of the moving window.
      4. Smoothing factor—The Smooth Interpolation option creates an outer ellipse and an inner ellipse at a distance equal to the Major Semiaxis multiplied by the Smoothing factor. The points that fall outside the smallest ellipse but inside the largest ellipse are weighted using a sigmoidal function with a value between zero and one.

      Standard Circular

      1. Radius—The length of the radius of the search circle.
      2. Angle—The angle of rotation for the axis (circle) or semimajor axis (ellipse) of the moving window.
      3. Maximum neighbors—The maximum number of neighbors that will be used to estimate the value at the unknown location.
      4. Minimum neighbors—The minimum number of neighbors that will be used to estimate the value at the unknown location.
      5. Sector type—The geometry of the neighborhood.

      • One sector—Single ellipse.
      • Four sectors—Ellipse divided into four sectors.
      • Four sectors shifted—Ellipse divided into four sectors and shifted 45 degrees.
      • Eight sectors—Ellipse divided into eight sectors.

      Smooth Circular

      1. Radius—The length of the radius of the search circle.
      2. Smoothing factor—The Smooth Interpolation option creates an outer ellipse and an inner ellipse at a distance equal to the Major Semiaxis multiplied by the Smoothing factor. The points that fall outside the smallest ellipse but inside the largest ellipse are weighted using a sigmoidal function with a value between zero and one.

    8.    Kernel function (optional) 

    The kernel function used in the simulation.

    1. EXPONENTIAL—The function grows or decays proportionally.
    2. GAUSSIAN—Bell-shaped function that falls off quickly toward plus or minus infinity.
    3. QUARTIC—Fourth-order polynomial function.
    4. EPANECHNIKOV—A discontinuous parabolic function.
    5. POLYNOMIAL5—Fifth-order polynomial function.
    6. CONSTANT—An indicator function.

    9.    Bandwidth (optional)

    Used to specify the maximum distance at which data points are used for prediction. With increasing bandwidth, prediction bias increases and prediction variance decreases.

    10. Use spatial condition number threshold (optional)

    Option to control the creation of prediction and prediction standard errors where the predictions are unstable. This option is only available for polynomials of order 1, 2, and 3.

    1. Unchecked—Predictions will be created everywhere, including areas where the predictions are unstable. This is the default.
    2. Checked—Prediction and prediction standard errors will not be created where the predictions are unstable.

    11. Spatial condition number threshold (optional)

    Every invertible square matrix has a condition number that indicates how inaccurate the solution to the linear equations can be with a small change in the matrix coefficients (it can be due to imprecise data). If the condition number is large, a small change in the matrix coefficients results in a large change in the solution vector.

    12. Weight field (optional)

    Used to emphasize an observation. The larger the weight, the more impact it has on the prediction. For coincident observations, assign the largest weight to the most reliable measurement.

    13. Output surface type (optional)

    Surface type to store the interpolation results.

    1. PREDICTION—Prediction surfaces are produced from the interpolated values.
    2. PREDICTION_STANDARD_ERROR— Standard Error surfaces are produced from the standard errors of the interpolated values.
    3. CONDITION_NUMBER—The Spatial condition number surface indicates the stability of calculations at a particular location. The larger the condition number, the more unstable the prediction, so locations with large condition numbers may be prone to artifacts and erratic predicted values.

    Moving Window Kriging

    How to use Moving Window Kriging Tool in ArcToolbox ArcMap ArcGIS??

    Moving Window Kriging Tool
    Moving Window Kriging

    Path to access the tool

    :

    Moving Window Kriging Tool, Interpolation Toolset, Geostatistical Analyst Tools Toolbox

     

    Moving Window Kriging

    Recalculates the Range, Nugget, and Partial Sill semivariogram parameters based on a smaller neighborhood, moving through all location points.

    1.    Input geostatistical model source

    The geostatistical model source to be analyzed.

    2.    Input dataset(s)

    The name of the input datasets and field names used in the creation of the output layer.

    When checked, the Always reset input datasets when the geostatistical model source changes parameter ensures that when a different geostatistical model source is specified, its associated datasets are automatically inserted into the tool. If unchecked and the geostatistical model source is changed, the displayed input datasets remain unchanged. This can lead to problems if the model is incompatible with the dataset; for example, a model was created to predict temperature, and a new dataset with rainfall data is specified.

    3.    Input point observation locations

    Point locations where predictions will be performed.

    4.    Maximum neighbors to include

    Number of neighbors to use in the moving window.

    5.    Output feature class

    Feature class storing the results.

    6.    Output 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.

    7.    Output surface raster (optional)

    The prediction values in the output feature class are interpolated onto a raster using the Local polynomial interpolation method.

    Radial Basis Functions

    How to use Radial Basis Functions Tool in ArcToolbox ArcMap ArcGIS??

    Radial Basis Functions Tool
    Radial Basis Functions

    Path to access the tool

    :

    Radial Basis Functions Tool, Interpolation Toolset, Geostatistical Analyst Tools Toolbox

     

    Radial Basis Functions

    Uses one of five basis functions to interpolate a surfaces that passes through the input points exactly.

    1.    Input features

    The input point features containing the z-values to be interpolated.

    2.    Z value 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 z-values or m-values.

    3.    Output geostatistical layer (optional)

    The geostatistical layer produced. This layer is required output only if no output raster is requested.

    4.    Output raster (optional)

    The output raster. This raster is required output only if no output geostatistical layer is requested.

    5.    Output 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.

    6.    Search neighborhood (optional)

    Defines which surrounding points will be used to control the output. Standard is the default.

    Standard

    1. Major semiaxis—The major semiaxis value of the searching neighborhood.
    2. Minor semiaxis—The minor semiaxis value of the searching neighborhood.
    3. Angle—The angle of rotation for the axis (circle) or semimajor axis (ellipse) of the moving window.
    4. Maximum neighbors—The maximum number of neighbors that will be used to estimate the value at the unknown location.
    5. Minimum neighbors—The minimum number of neighbors that will be used to estimate the value at the unknown location.
    6. Sector type—The geometry of the neighborhood.
    • One sector—Single ellipse.
    • Four sectors—Ellipse divided into four sectors.
    • Four sectors shifted—Ellipse divided into four sectors and shifted 45 degrees.
    • Eight sectors—Ellipse divided into eight sectors.

    Smooth

    1. Major semiaxis—The major semiaxis value of the searching neighborhood.
    2. Minor semiaxis—The minor semiaxis value of the searching neighborhood.
    3. Angle—The angle of rotation for the axis (circle) or semimajor axis (ellipse) of the moving window.
    4. Smoothing factor—The Smooth Interpolation option creates an outer ellipse and an inner ellipse at a distance equal to the Major Semiaxis multiplied by the Smoothing factor. The points that fall outside the smallest ellipse but inside the largest ellipse are weighted using a sigmoidal function with a value between zero and one.

    Standard Circular

    1. Radius—The length of the radius of the search circle.
    2. Angle—The angle of rotation for the axis (circle) or semimajor axis (ellipse) of the moving window.
    3. Maximum neighbors—The maximum number of neighbors that will be used to estimate the value at the unknown location.
    4. Minimum neighbors—The minimum number of neighbors that will be used to estimate the value at the unknown location.
    5. Sector type—The geometry of the neighborhood.

    • One sector—Single ellipse.
    • Four sectors—Ellipse divided into four sectors.
    • Four sectors shifted—Ellipse divided into four sectors and shifted 45 degrees.
    • Eight sectors—Ellipse divided into eight sectors.

    7.    Radial basis function (optional)

    There are five radial basis functions available.

    1. THIN_PLATE_SPLINE—Thin-plate spline function
    2. SPLINE_WITH_TENSION— Spline with tension function
    3. COMPLETELY_REGULARIZED_SPLINE— Completely regularized spline function
    4. MULTIQUADRIC_FUNCTION— Multiquadric spline function
    5. INVERSE_MULTIQUADRIC_FUNCTION—Inverse multiquadric spline function

    8.    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 small-scale variation of the surface. The (optimal) parameter is determined by finding the value that minimizes the root mean square prediction error (RMSPE).

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