GIS Functions and Operators The functions associated with raster cartographic

modeling can be divided into five types: Those that work on single cell locations (local functions

or operators) 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)

Map Algebra Map algebra is a language specifically designed for

geographic cell-based systems and provides the basis for cartographic modeling.

Based on concepts originally presented by Joe Berry and C. Dana Tomlin.

Map algebra provides a language to conveying logic constructs while maintaining the power of the mathematical base underlying the cell-based structure.

Map Algebra operators and functions apply mathematical computations on a raster “map” vs. matrix algebra.

Local Functions Local functions apply their calculations to a single cell location before

calculating the next location, until all cells have been processed. To perform the calculation, the local function only needs to know the values at the location for a single raster or for multiple rasters, as well as, in some cases, a comparison value.

Operations or functions can be applied on single or multiple grids:

output = (inlayer1 + inlayer2) / 2

output = sin(inlayer1)

output = min(inlayer1, inlayer2, inlayer3)

Operators and Functions

There are three types of operations: Arithmetic operators: *, /, -, + Boolean operators: And, Or, Xor, Not Relational operators: ==, >, <, <>,

>=, <=

2/])2[]1([ InlayerInlayerOutput

Operators and Functions

Mathematical functions are applied to the values in a single input raster. There are four groups of mathematical functions Logarithmic Arithmetic Trigonometric Powers

Other local functions compute statistics, combine, or other operations from a list of multiple inlayers.

Output = min(Inlayer1, Inlayer2, Inlayer3)

Focal Functions

Focal (or neighborhood) functions compute an output grid in which the output value at each cell location is a function of the input cells in the specified neighborhood “around” each output (or target) location.

Neighborhoods can be different sizes and geometries.

Different arithmetic and statistical functions can be applied to summarize a neighborhood values.

Example:

Output = focalsum (Input, rectangle, 3,3)

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.

Output = zonalsum(inlayer, zonelayer)

Output = zonalgeometry(zonelayer, all)

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.

Output from the Euclidean distance function, each cell contains the shortest distance to any input point.

Application Functions

There are a wide series of cell-based modeling functions developed to solve specific applications.

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).

Application functions include the following: Density analysis Surface generation Surface analysis Hydrologic analysis Geometric transformation Generalization Resolution altering

Lab 2 Part 1: Examine Grids

Compute Slope and look at the statistics Reclass Slope and compute the area in

Zone 5 Part 2: Locating a Watch Tower (Iron

Age II) Jordan Highlands – Dr. Christopherson

PhD research site We will attempt to identify the “watch

tower” based on three factors Must be “In View” of the Fort and the

Largest City Must be located in the highest elevation

zone Must have either a rectangular or circular

structure Will Intersect on the three factors to narrow

the search