The Inverse Distance Weighting (IDW) interpolation method uses a distance weighted average of data points to calculate grid cell values in the output raster surface. This method estimates the unknown cell values in output surface by averaging the values of all input sample data points that lie within the specified search radius.
For example, while interpolating using IDW method, the input data points are individually weighted according to a power weighted distance algorithm. The weighting power of the function controls the rate at which the weighting is applied as the distance from the grid node to the input points increases. As a result, the closer an input-point is to the center of the raster cell being estimated, the more that point value will contribute to the raster cell value. In the example below, the unknown values are estimated using the values of nearby known points.
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Sample Rainfall Data |
Estimated Surface |
The weighting factors declines as distance from the grid cell increases.
Inverse Distance Weighting (IDW) Method Options
- Parameter Unit
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Specifies whether spatial parameters are defined in cell units or distance units.
The search radius defines the maximum distance allowed between a grid cell and the neighboring input data points that will be considered when computing its value. The distance value determines whether these points are considered in the distance weighing average. The search distance radius is measured in increments of the output cell size. For optimum performance, keep the search distance to a value less than or equal to 5x the output cell size.
Distance specifies the spatial parameters in Distance unit. The units supported by MapInfo Pro are US survey feet, yards, rods, chains, miles, nautical miles, millimeters, centimeters, meters, inches, links and kilometers. When you choose Distance, you need to select a distance unit from the Distance Unit drop-down list.
Click More Options to open the following advanced options.
Weighting Model
By default, the weighting of an input data point is inversely proportional to its distance from the grid node. This can be changed by choosing a different Weight Model. MapInfo Pro Advanced supports the following weight models:
- Linear - Each input point’s weight is proportional to its Euclidian distance from the grid node being interpolated. The linear weight model enables the Nugget, Range and Taper parameters to be adjusted in order to vary the weight assignments. At distances less than the Nugget distance the weight model will be 1 – i.e., all data will contribute equally. The Range parameter is used to set the outer distance threshold for which the weight model is applied. Any samples which exceed the Range and are less than the Search Distance will be assigned an equal weight.
- Exponential - Each input point’s weight is proportional to its distance from the grid node being interpolated raised to the specified power. Increasing the power value will cause smaller weights to be assigned to closer points and more distant points to be assigned equal but large weights. Increasing power values will therefore cause each interpolated grid node to more closely approximate the sample values closest to it. As with the Linear model the Nugget and Range properties can be modified to constrain that distance over which the exponential weight model is most effective.
- Power - The default option, each input point’s weight is proportional to the inverse of its distance to the specified Power from the grid node. Increasing the weighting power reduces the influence distant points have on the calculated value of each grid node. Large power values cause grid cell values to approximate the value of the nearest data point, while smaller power values will result in data values being more evenly distributed among neighboring grid nodes. The weighting value defaults to 2 (i.e., the weight of any data point is inversely proportional to the square of its distance from the grid cell) which is appropriate for most situations. If required, the weighting value can be altered to any positive value.
- Gaussian - The weight assigned to each input value is determined according to a 2D Gaussian function centered on the grid node. The shape and standard deviation of the Gaussian function is proportional to the Range with larger values producing a flatter function and a smoother grid.
Parameters
The following table lists the parameters for the weight models:
| Parameter | Description |
|---|---|
| Power | Increasing the power value means assigning larger weights to closer points and equal but small weights to distant points. |
| Nugget | Set the distance. If the distance is less than the Nugget distance the weight model will be 1 – i.e., all data will contribute equally. |
| Range | Set the outer distance threshold for which the weight model is applied. Any samples which exceed the Range and are less than the Search Distance will be assigned an equal weight. |
| Taper |
Click the Taper check-box to display the Taper controls. The Taper controls allow you to apply a taper function to the interpolated value of each grid node based on its distance to the nearest valid sample point. The taper function is applied using a linear weighting model thereby adjusting the expected grid node values towards the background value. Between a distance of zero and the From distance the taper function is assigned a constant value of 1 (i.e., no modification is made to the grid node). Between the From and To distance the taper function is applied as a linear weighting between the grid node value and the background value. Beyond the To distance grid nodes are assigned the background value. |
| Background Value | The background value assigned beyond the range distance. |
Smoothing Method
You can apply smoothing on the gridded data to produce smoother surface. Smoothing is used to enhance the sharpness of an image or improve the appearance of the edges. Select a suitable Smoothing method and level for your data.
Smoothing Level - Move the smoothing slider to set the smoothing level for the output raster. You can set a value between 0 to 6. A value of zero applies no smoothing. A value of 6 applies maximum smoothing.
Clipping
By default the algorithm populates every cell in the raster. You may want to clip the raster to make unconstrained cells invalid. You could do this, for example, by clipping the raster to a boundary polygon. As an alternative, the minimum curvature method provides a fast and simple automated clipping method.
This method allows you to define what an unconstrained cell is by specifying a ‘near’ and ‘far’ distance (as an integer number of cells). Any cell that has a constrained cell inside the ‘near’ distance will be considered constrained. Otherwise, any cell that has constrained cells within the ‘far’ distance on three or more sides will be considered constrained. This method tends to interpolate across voids within the data while terminating on the edges of the data.
- None - No clipping is applied to the raster cells.
- Near Only - The Near value represents the maximum distance from a source input data point for which an interpolated raster cell will be created. Cells in the raster which lie at a distance greater than the Near distance will be assigned a null value. This method has the same effect as applying a distance buffer to the source data points equal to the near distance.
- Near/Far - Interpolated cells in the output raster will be clipped to the near distance if no other data point is found within the Far distance that meet the angular search constraints. Applying both Near and Far clipping can be useful to constrain the interpolated raster to a required distance from the source points, while also permitting larger gaps to be interpolated in irregularly spaced data.
- Polygon - You can provide a TAB file of polygon(s) to clip the output raster to the polygon boundaries. You can specify whether to clip a region outside or inside the raster bounds. However, it does not support polygons with holes.
Coincident Points Method
The Coincident Points drop-down list controls the handling of multiple data points at the same location. For more information see, Coincident Point Methods.
Search Options
- Search Modes
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The search mode defines how the interpolation algorithm searches for input data points within the search neighborhood. The shape of the search neighborhood is dictated by the type and distribution of the input data. The following search modes are available:
- Spherical - Performs an equidistant radial search within the search neighborhood. The search distance is defined by the Major Axis Search parameter, which is defined in Parameter Units. For optimum performance, it is recommended to keep the search distance small. A value less than or equal to 5x of the output cell size is usually sufficient. Spherical search is best applied when the variation in the spatial distribution of the input data is considered isotropic.
- Elliptical - Performs an elliptical search within the specified search neighborhood. The shape of the ellipse is defined by the Major Axis Search and Minor Axis Search parameters. The Major Axis Search defines the maximum width (x axis) of the search ellipse and the Minor Axis Search defines the minimum width (y axis). Major Axis Orientation defines the rotation angle of the ellipses Major search axis, measured clockwise from North (0 degrees). An elliptical search is best applied when some directional anisotropy is known to exist in the spatial distribution of the input data.
A default search radius will be calculated for you. If you wish to enter a specific distance then you can do so by typing the required values into the Major Axis Search box. To apply anisotropic search, choose elliptical search mode and enter a value into the Minor Axis Search and Major Axis Orientation box. The size of the Major axis search must be larger than the minor search axis.
- Apply Sector Support
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The following search modes are available:
- Apply Sector Support - Click this checkbox to apply sector support.
- No of Sectors - Count of sectors to be used, valid values are 1 to 32.
- Minimum Valid Sectors - Minimum number of valid sectors required, valid values are 1 and greater.
- Use Nearest Points - Select this checkbox to use the nearest points.
- Minimum Points/Sectors - Minimum number of points per sector to validate sector.
- Maximum Points/Sectors - Maximum number of points to be used per sector when Use Nearest Points is selected. The valid values are 1 or more.
- Sector Orientation - Starting orientation of sectors in degrees, valid values are 0 to 360. When search sectors are enabled, the sector orientation defines the edge of the first sector, in degrees East of North. For example, if you have an orientation of 0 degrees and two search sectors, then the sectors lie to the West and East of North respectively.
Note: If you use search sectors in conjunction with a search ellipse, you may want to design the sector orientation so that they are aligned with the major axis of the search ellipse. The orientation of the search ellipse does not modify the orientation of the sectors. So, if you have two search sectors and a major axis pointing Northeast (45 degrees), then you will probably want to define the sector orientation as Northwest (315 degrees) so that the search sectors are aligned in the direction of the major axis. As a general rule, if you have two sectors, use the major axis orientation minus 90 degrees. If you have 4 sectors, use the major axis orientation minus 45 degrees.
Raster Geometry
Cell Size
Specify the cell size for the output raster in the Cell Size box. The cell size defines the width and height of a raster cell in distance units. If the raster cells are square both width and height are specified with same value.
By default, Automatic is selected which means will calculate the output raster cell size based on source data points. Click Suggest, to see the calculated cell size value in the box before it is processed. You can modify the cell size value to produce output raster with the desired cell size. The Suggest button is active only when the input data source is in MapInfo native format.
Output Geometry
The Output Geometry allows you to limit the output data points according to specified region (bounds) and ignore all points that lie outside of the specified region. The data within the specified bounds will be written in the output file. To specify the Raster Bounds, enter coordinate values for raster origin and extent.
- Min X - X coordinate of the origin (lower left corner of the cell).
- Min Y - Y coordinate of the origin (lower left corner of the cell).
- Max X - The maximum coordinate value for X (upper right corner of the cell).
- Max Y - The maximum coordinate value for Y (upper right corner of the cell).
The output file will contain data for the specified region only.
If required, click More Options to specify the projection for the output raster. If the input file is a MapInfo .TAB file, projection values are read from the input file, which you can override here.
- Category - The Category drop-down list consists of all projection systems supported by MapInfo Pro. For example, Longitude/Latitude, Universal Transverse Mercator (ED 50), Universal Transverse Mercator (NAD 27 for Canada), etc.
- Sub Category - The Sub Category drop-down list consists of the type of projection based on the selected projection system.