1. GIS Functions and Operators The functions associated with raster cartographic modeling can be divided into five types: 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 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 a neighborhood (focal functions) Those that work on cell locations within zones (zonal functions) Those that work on cell locations within zones (zonal functions) Those that work on all cells within the raster (global functions) Those that work on all cells within the raster (global functions) Those that perform a specific application (for example, hydrologic analysis functions) Those that perform a specific application (for example, hydrologic analysis functions)

2. Map Algebra Map algebra is a language specifically designed for geographic cell-based systems and provides the basis for cartographic modeling. 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. 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 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. Map Algebra operators and functions apply mathematical computations on a raster “map” vs. matrix algebra.

3. 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. 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: Operations or functions can be applied on single or multiple grids: output = (inlayer1 + inlayer2) / 2 output = (inlayer1 + inlayer2) / 2 output = sin(inlayer1) output = sin(inlayer1) output = min(inlayer1, inlayer2, inlayer3) output = min(inlayer1, inlayer2, inlayer3)

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

5. Operators and Functions Mathematical functions are applied to the values in a single input raster. There are four groups of mathematical functions Mathematical functions are applied to the values in a single input raster. There are four groups of mathematical functions Logarithmic Logarithmic Arithmetic Arithmetic Trigonometric Trigonometric Powers Powers Other local functions compute statistics, combine, or other operations from a list of multiple inlayers. Other local functions compute statistics, combine, or other operations from a list of multiple inlayers. Output = min(Inlayer1, Inlayer2, Inlayer3)

6. 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)

7. 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 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)

8. 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. 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.

9. Application Functions There are a wide series of cell-based modeling functions developed to solve specific applications. 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). 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: Application functions include the following: Density analysis Density analysis Surface generation Surface generation Surface analysis Surface analysis Hydrologic analysis Hydrologic analysis Geometric transformation Geometric transformation Generalization Generalization Resolution altering Resolution altering

10. Lab 2 Part 1: Examine Grids Part 1: Examine Grids Compute Slope and look at the statistics Compute Slope and look at the statistics Reclass Slope and compute the area in Zone 5 Reclass Slope and compute the area in Zone 5 Part 2: Locating a Watch Tower (Iron Age II) Part 2: Locating a Watch Tower (Iron Age II) Jordan Highlands – Dr. Christopherson PhD research site Jordan Highlands – Dr. Christopherson PhD research site We will attempt to identify the “watch tower” based on three factors 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 “In View” of the Fort and the Largest City Must be located in the highest elevation zone Must be located in the highest elevation zone Must have either a rectangular or circular structure Must have either a rectangular or circular structure Will Intersect on the three factors to narrow the search Will Intersect on the three factors to narrow the search