Geographic Information Systems: Map Algebra

Two Types of Grids

• Floating Point Grids: Used for continuous values such as elevation, slope, and distance; lack an attribute table due to the wide range of values.
• Integer Grids: Utilized for discrete values with an attribute table; pixels are assigned integers denoting feature classes.

Map Algebra Definition

• A specialized analysis language founded on concepts by Dr. Dana Tomlin, documented in "Geographic Information Systems and Cartographic Modeling."
• Enables cartographic spatial analysis via raster data, applying mathematical operations to rasters that function as geographically referenced numerical arrays.

Map Algebra Operators

• Arithmetic Operators: Addition, subtraction, multiplication, and division.
• Relational Operators: Comparison functions such as greater than and equality checks.
• Boolean Operators: Logical functions including AND, OR, and NOT.
• Logical Values: Utilizes binary digits (1 for true, 0 for false).

Key Operational Tool of Map Algebra

• Raster Calculator: Essential for performing calculations involving raster data layers.

Vector to Raster Conversion

• Feature to Raster: Common tool for converting vector data to raster format; multiple methods exist.
• Importance of setting the processing extent to prevent system crashes during conversion.

Classification of Raster Data

• Reclassify Tool: Assigns specific values to classify raster data, with NoData designated as 0.

Proximity Information Tool

• Euclidean Distance: Calculates proximity, analogous to the "buffer" function in vector models.

Displaying Solar Radiation Data

• Area Solar Radiation Tool: Analysis tool for solar radiation values.
• Base Surface Model: Created using tools like "Surface" or "Spline of Spots," dependent on initial data inputs.

Satellite Image Classification

• Iso Cluster Unsupervised Classification: Classifies satellite images, including building detection, using ISODATA (Iterative Self-Organizing Data Analysis).

Minimizing Classification Errors

• Using streets and large parcels to refine building classifications through techniques like Buffering, Attribute Selection, and UNION to exclude irrelevant data.

Special Issues with Raster Data

• Grids must share the same spatial processing extent and grid cell size for compatibility and accuracy in analysis.

Fundamental Types of Raster Analysis

• Vertical (Spatial Coincidence): Rapidly combines layers using map algebra, applicable in Boolean overlay for spatial suitability.
• Horizontal (Neighborhood Analysis): Analyzes cell characteristics based on neighboring cells; classified into ZONAL (calculations for cell groups with the same value) and FOCAL functions (calculates based on input grid cells within a defined focus).

Logical Values Tracking

• Logical values represent true (1) and false (0) conditions; for example, slopes greater than 15 degrees are marked true.

Raster Merging Operators

• MERGE Function: Used to join discrete rasters where overlaps exist.
• MOSAIC Function: Employed for continuous rasters, eliminates surplus values upon joining.

Types of Raster-Based Models

• Include deterministic models, interpolation models, flow models, cellular automata models, and probability/statistical models.