Fundamentals of creating a raster from a geostatistical layer

Geostatistical layers can be converted into raster format using the GA Layer to Grid geoprocessing tool, which can be invoked directly from the Geostatistical Analyst toolbox (see An overview of the Working with Geostatistical Layers toolset), or by right-clicking on the layer in the ArcMap table of contents and using the Data → Export to Raster option.

Block interpolation is used when creating a raster from a geostatistical layer. Block interpolation is an interpolation method that predicts the average value of a phenomenon within a specified area. The specified area can be an irregularly shaped polygon, such as a forest stand; a more regularly shaped polygon, such as a field; or a series of equally shaped squares, as in the case of a raster.

Block interpolation works by calculating predictions for a number of specified locations within an area; the values are averaged, then the average is assigned as the prediction for the entire area. For example, if you specify 10 locations to be predicted within an area, predictions will be made for each of the 10 locations using an identified interpolation model and the original sample points collected for the phenomenon. The location of these 10 points can be either specified by you or randomly or systematically assigned. Each prediction can be weighted in the averaging process based on the area of influence of the prediction location and the distribution of the prediction points. Those prediction locations without any other prediction locations nearby will be weighted greater than those locations that have several identified prediction locations surrounding them.

When converting a geostatistical layer to a raster, the shapes of the blocks performing the averaging are within individual raster cells. The following diagram shows sample points with the block configuration (the raster) that will be used in the block interpolation.

In the conversion, you specify how many point prediction locations within each cell to use in the averaging. For example, you can specify predictions for two points in the x direction and three points in the y direction for each cell. The prediction points will be distributed within each cell so that they represent (or influence) the same amount of area. Thus, no weighting will occur for any of the prediction points. The prediction points are located in the center of each subunit—in this case, in the center of each of the six blocks.

In the following diagram, the highlighted cell will be used to demonstrate block interpolation for one cell (or block) in the raster. However, this procedure occurs for each cell.

The following diagram is a close-up of the highlighted block in the above diagram. A prediction will be made for each of the six points in the cell using the interpolation model identified in the geostatistical layer and the original sample points. The six predictions will be averaged and assigned to that cell.

If you only specify one point in the x direction and one in the y direction, you will make the prediction for the center of each output cell. Processing times will increase as the number of prediction points increases.

The reason you may have more prediction points in either the x or y direction is to account for directional trends. In the 2-by-3 example above, the spacing of the prediction points in the north–south direction is closer than in the east–west direction. Having more prediction points in the north–south direction increases the sampling in that direction to capture the higher variability. That is, the values of the phenomenon change quicker in the north–south direction than in the east–west direction. To capture this, you will need more sample points in that direction.