Inverse Distance Weighted Gridding Advanced Options (Multiple Channels)

Use the IDW Gridding Advanced Options dialog to specify advanced Inverse Distance Weighted gridding options.

IDW Gridding Advanced Options

Weighting power

Modifies the shape of the weighting function. See “The Inverse-Distance Weighting Function: Defining the Weighting Slope and Power” below.

Specify a value greater than or equal to zero.

Script Parameter: IDW_GRIDDING.WEIGHT_POWER (Default: 2)

Weighting slope

Modifies the steepness of the inverse distance-weighting function. See “The Inverse-Distance Weighting Function: Defining the Weighting Slope and Power” below.

Script Parameter: IDW_GRIDDING.WEIGHT_SLOPE (Default: 1)

Search radius

For each grid centre point, all values within the search radius are included in the weighted average yielding the value at that point. The default is determined based on the number of cells in X and Y, and is at least 4 times the cells size. If no value is entered, the calculated default is used.

Script Parameter: IDW_GRIDDING.SEARCH_RADIUS

Blanking distance

The blanking distance controls how far the grid is extrapolated away from the nearest data point. All values at distances greater than the blanking distance are set to dummy. It only makes sense to define a blanking distance less than the search radius, since any grid cell location farther than the search radius from the nearest data point is by definition not valued. If no blanking distance is defined, then during calculation it is set to be 4 times the cell size. (If the vertical and horizontal cell size differ this obtained by taking the square root of the cell area times four).

Script Parameter: IDW_GRIDDING.BLANKING_DISTANCE

Cells to extend beyond data

If set to zero, the grid extent is limited to just overlapping the most extreme data value locations in X and Y. Set this to a positive number to allow the grid to be extrapolated beyond the data edges. The actual extrapolation distance is determined by the search radius, and limited by the blanking distance, and cells extended beyond this distance will remain dummies in the output grid.

Script Parameter: IDW_GRIDDING.CELLS_TO_EXTEND (Default: 0)

Log option

Select to grid your data in "log" or "log-linear" space and save the data in the transformed state or as raw data (linear). By default, the data is gridded "as is".

For log gridding, the log (base 10) of the data value is used and any values less than the supplied log minimum are replaced by the log minimum.

For log-linear gridding, values are first transformed as follows:

Z < -log_minimum: Z - log10( -z / log_minimum )

-log_minimium <= Z <= log_minimum: Z

Z > log_minimum : Z + log10( z ./ log_minimum )

This has the effect of treating large positive or negative values like logarithms, but gives a linear transform for values around zero.

Script Parameter: IDW_GRIDDING.LOG_OPTION
linear: 0
log, save as linear: -1
log-linear, save as linear: -2
log, save as log: 1
log-linear, save as log: 2

Log minimum

Specify the log minimum.

Script Parameter: IDW_GRIDDING.LOG_MINIMUM (Default: 1)

Application Notes

Anti-aliasing

Prior to gridding (and after any log or log-linear transformation), data is pre-processed using an anti-aliasing technique. All values falling inside any single grid cell are averaged, and the data is then represented by the single averaged value at the grid cell centre. Any error in the spatial representation of features introduced by this step will never exceed one-quarter of the Nyquist wavelength, which is equal to 2 cell sizes.

The Inverse Distance Weighting Function: Defining the Weighting Slope and Power

The inverse distance weighting function assigns averaging weights based on distance, out to the defined search radius:

1 / (distance^power + 1/slope)

Where distance is in multiples of the horizontal cell size.

Using the default of 2 for the power, and 1 for the slope produces a bell-shaped weighting function. Requiring a slope > 0 ensures that the weight remains finite at zero distance. Decreasing the slope tends to flatten the bell, resulting in greater weighting of points away from the grid cell, and hence greater smoothing. Choosing a power less than 2, or a slope less than one, may result in over-smoothing the data.

The following table shows the effect of various slopes on the weighting given at various distances away from the centre cell. The weights have been normalized so the weight at the cell centre is equal to 1.

 

weighting of centre cell

weighting 1 cell away

weighting 2 cells away

weighting 3 cells away

weighting 4 cells away

P = 2, S = 0.2

1

0.83

0.55

0.36

0.24

P = 2, S = 0.5

1

0.67

0.33

0.18

0.11

P = 2, S = 1

1

0.5

0.2

0.1

0.56

P = 2, S = 2

1

0.33

0.11

0.053

0.03

Clearly, as the slope increases, the weighting is more tightly concentrated about the centre cell. The search radius should also be chosen based on the fall-off of the weighting function. Increasing the search radius beyond where the weighting function is significant will have little effect on the results, and may result in large increases in processing time, since the processing time varies in proportion to the cube of the search radius. (Remember that the search radius is specified in ground units, not as a multiple of cell sizes.)

  • The yellow asterisk icon () displayed in front of a parameter name indicates that this parameter is required.

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