Available with Spatial Analyst license.

The easiest way to understand cell-based modeling is from the perspective of an individual cell (the worm's-eye approach), as opposed to the entire raster (the bird's-eye approach) (Tomlin, 1994). Consider a cell in a raster dataset. It represents a location, and it has a value. All Spatial Analyst tools ask the cell to manipulate or retain its value based on a defined series of rules.

## Output value calculation

To calculate an output value for a specified location (cell) using any Spatial Analyst tool, the things you need to know are as follows:

- The value of the specified location (cell)
- The manipulation that will be performed on the value
- Which other cell locations and their values to include in the calculations

## Calculation process for each cell

The calculation process occurs for each location (cell) in the raster dataset in any Spatial Analyst tool. All tools work on a cell-by-cell basis, and each calculation for each cell requires the value of the cell, the manipulation that is being applied, and other cell locations to include in the calculations. The documentation for the tool indicates the logic behind how the value is manipulated.

The tools are grouped into categories based on how they manipulate values, With some tools, the output value is calculated by knowing only the value of your location, such as raising your value by a specified power. With other tools, you can determine the values of other locations in the raster dataset to which your specified location belongs, such as looking in a neighborhood around you (a focal tool) or including cell locations and their values defined by other raster datasets (zonal tools).

For many tools, you can refine how the manipulation (the calculations) will be performed through user-defined parameters. For example, the cells to include in each calculation for a focal tool may vary based on the neighborhood that is defined.

## Calculation processes for specific tools

The following examples demonstrate the calculation process applied to certain tools:

- Power tool—When applying this tool to a raster dataset, you need to know how to take the value of your location's value and raise it to the power defined by the value of the same location the cell represents in the other raster dataset to return an output value for your location.
- Cos tool—When applying this tool to a raster dataset, you must know the value of your specified location and how to take the cosine of that value to return an output value.
- Distance Accumulation tool—When applying this tool, you must know your location and determine how far your location is from the closest source (which is defined by a source dataset) to return an output value for your location.
- Focal Statistics tool—When applying this tool to determine the maximum value within a 3-by-3 neighborhood, you must know your location's value and the values of the eight immediate neighbors around your location. You will calculate a specified statistic for the nine values and apply the resulting value to the output at your location.
- Zonal Statistics tool—When applying this tool with the Mean option, you must know your location's value and take the mean of all the values of the cells that belong to the same zone as your cell, which is defined by a zone raster dataset.

## References

Tomlin, D. 1994, "Map Algebra: one perspective". Landscape and Urban Planning. Vol 30, Issues 1-2.