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# Operators and functions of Spatial Analyst

Release 9.3

Print all topics in : "Performing analysis in Spatial Analyst"

Note: This topic was updated for 9.3.1.

The functions associated with raster cartographic modeling can be divided into five types:

• Those that work on single cell locations (local functions)
• Those that work on cell locations within a neighborhood (focal functions)
• Those that work on cell locations within zones (zonal functions)
• Those that work on all cells within the raster (global functions)
• Those that perform a specific application (for example, hydrologic analysis functions)

Each of these categories can be influenced by, or based on, the spatial or geometric representation of the data and not solely on the attributes that the cells portray. For example, a function that adds two layers together (via single cell locations) is dependent on the cell's location and the value of its counterpart in the second layer. Functions applied to cell locations within neighborhoods or zones rely on the spatial configuration of the neighborhood or zone as well as the cell values in the configuration.

Local functions

Local functions, or per-cell functions, compute a raster output dataset where the output value at each location (cell) is a function of the value associated with that location on one or more raster datasets. That is, the value of the single cell, regardless of the values of neighboring cells, has a direct influence on the value of the output. A per-cell function can be applied to a single raster dataset or to multiple raster datasets. For a single dataset, examples of per-cell functions are the trigonometric functions (for example, sin) or the exponential and logarithmic functions (for example, exponential log).

Examples of local functions that work on multiple raster datasets are functions that return the minimum, maximum, majority, or minority value for all the values of the input raster datasets at each cell location.

Focal functions

Focal, or neighborhood, functions produce an output raster dataset in which the output value at each cell location is a function of the input value at a cell location and the values of the cells in a specified neighborhood around that location. A neighborhood configuration determines which cells surrounding the processing cell should be used in the calculation of each output value.

Neighborhood functions can return the mean, standard deviation, sum, and range of values within the immediate or extended neighborhood.

Zonal functions

Zonal functions compute an output raster dataset where the output value for each location depends on the value of the cell at the location and the association that location has within a cartographic zone. Zonal functions are similar to focal functions except that the definition of the neighborhood in a zonal function is the configuration of the zones or features of the input zone dataset, not a specified neighborhood shape. However, zones do not necessarily have any order or specific shapes. Each zone can be unique. Zonal functions return the mean, sum, minimum, maximum, or range of values from the first dataset that fall within a specified zone of the second.

Global functions

Global, or per-raster, functions compute an output raster dataset in which the output value at each cell location is potentially a function of all the cells combined from the various input raster datasets. There are two main groups of global functions: Euclidean distance and weighted distance.

### Euclidean distance global functions

Euclidean distance global functions assign to each cell in the output raster dataset its distance from the closest source cell (a source may be the location from which to start a new road). The direction of the closest source cell can also be assigned as the value of each cell location in an additional output raster dataset.

### Weighted distance global functions

A global weighted-distance function determines the cost of moving from a destination cell (the location where you want to end the road) to the nearest source cell (the location where you want to start the road) over a cost surface (cost being determined by cost schema, such as cost of construction). To take this one step further, the shortest or least-cost path over a cost surface can be calculated over a non networked surface from a source cell to a destination cell using the global least-cost path function. In all the global calculations, knowledge of the entire surface is necessary to return the solution.

Application functions

There are a wide series of cell-based modeling functions developed to solve specific applications. An application function performs an analysis that is specific to a discipline. For example, hydrology functions create a stream network and delineate a watershed. The local, focal, zonal, and global functions are general functions and are not specific to any application. There is some overlap in the categorization of an application function and the local, focal, zonal, and global functions (such as the fact that even though slope is usually used in the application of analyzing surfaces, it is also a focal function). Some of the application functions are more general in scope, such as surface analysis, while other application functions are more narrowly defined, such as the hydrologic analysis functions. The categorization of the application functions is an aid to group and understand the wide variety of Spatial Analyst operators and functions. You may find that a specific application function can manipulate cell-based data for an entirely different application from its category. For example, calculating slope is a surface analysis function that can be useful in hydrologic analysis as well.

Application functions include the following:

• Density analysis
• Surface generation
• Surface analysis
• Hydrologic analysis
• Geometric transformation
• Generalization
• Resolution altering

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