--- jupytext: text_representation: extension: .md format_name: myst format_version: 0.13 jupytext_version: 1.11.5 kernelspec: display_name: Python 3 language: python name: python3 --- # Focal Operation ## Focal Operations * Operations: * Local, focal and global operations based on the spatial scope of neighborhood * Neighborhood relation operations * 3 kinds of mapping/analysis units: * Cells * Raster zones * Features | Mapping Units | Neighborhood Relation: Local | Neighborhood Relation: Focal | Neighborhood Relation: Global | | :--- | :--- | :--- | :--- | | **Cells** | Local | Focal | Global | | **Raster zones** | Local | | | | **Features (vectors)** | Local | | | ## Topics * Focal operations with raster map * Moving-window, distance/direction based, irregular weighted neighborhoods * Focal operations with vector map * Buffer * Domain-based focal neighborhoods * Watershed * Types of focal operations ## Focal Operations * Compute for each output MU with the neighbors of its focal neighborhood * Cells, raster zones, vector features as MUs * Data manipulation within MU's focal neighborhood ## Focal Neighborhood * A set of locations that has a certain relationship with a MU * Beyond the MU itself (vs local neighborhood) * Represents interactional relationship between a MU and other locations * Exchange of matter, energy, and information * The MU is also referred to as the neighborhood focus * The related locations are referred to as the neighbors ## Characterizing Focal Neighborhoods * Two ways to characterize focal neighborhoods: * Based on distance and direction * Moving-window (raster), Buffer (vector/raster) * Based on domain knowledge/processes * Watershed, viewshed, network, etc. ## Moving-Window Neighborhoods * Neighborhood defined by a "window" of a specific shape and size * The window "moves" from cell to cell * Neighborhood is same for all cells (relative to the focus) * Types: * Square (3x3, 5x5, etc.) * Circle * Plus (rook's case) ## Focal Statistics * Calculate a statistic for the values within the moving window * Common statistics: * **FocalSum**: Total value (e.g., total biomass) * **FocalMean**: Average value (smoothing) * **FocalMax/FocalMin**: Range or edge detection * **FocalVariety**: Number of unique values (diversity) ## Examples of Moving-Window Operations * **Smoothing**: Use FocalMean to reduce noise in data * **Edge Detection**: Use FocalMax - FocalMin to find where values change rapidly * **Focal Variety**: Useful for identifying boundaries between different land cover types ## Morphology/Shape Analysis * Use Focal operations to analyze the shape of features * **Erosion**: Using FocalMinimum on a binary map * Removes outer layer of pixels * **Expansion/Dilation**: Using FocalMaximum on a binary map * Adds an outer layer of pixels ## Morphology/Shape Analysis (cont.) * **Inner Boundaries**: Identify cells that are part of the feature but touch the background * **Outer Boundaries**: Identify background cells that touch the feature * Combined boundaries provide detailed structural analysis ## Distance/Direction-Based Neighborhoods * Neighborhood defined by specific distance and directional parameters * Neighborhoods in ArcGIS: * Rectangle, circle, annulus (donut), or wedge (a slice of a circle) ## Finding Appropriate Wind Farm Sites * Selection criteria: * **Wind speed**: Higher elevation generally equals higher speed (Elevation >= 1000m) * **Aspect**: Facing the prevailing wind direction * **Wind exposure**: Not blocked by nearby hills in the prevailing wind direction * Data needed: * Prevailing wind direction (e.g., 225° to 315°) * Digital Elevation Model (DEM) * **Wedge neighborhood**: Used to check for obstructions in the specific wind direction ## Types of Focal Operations * **Simple Focal Operations**: Neighborhood is predefined (shape/size) * Example: Moving window * **Irregular/Weighted Focal Operations**: Neighbors have different "weights" or importance * Example: Gravity model, Kernel density estimation * **Process-based Focal Operations**: Neighborhood is defined by a physical process * Example: Watershed (defined by terrain/gravity) ## Irregular Weighted Neighborhood * Neighborhood and weights are defined by a matrix * 0s indicate a location is not a neighbor * Other values represent weight (neighbor relation property) * Matrix can be stored as a neighborhood text file * Kernel file in ArcGIS * All cells use the same neighborhood structure * Operation: **Weighted Summary** * Get the neighbor value from the input map * Summarize (weight * value) ## Weighted Moving-Average (Smoothing) * Weights are inversely proportional to distance * The weight for the focus MU is typically the largest * Used to reduce noise while preserving more detail than a simple mean ## Kernel Density Estimation (KDE) * Neighborhood is a circle with a radius (bandwidth) * Weights are defined by a continuous kernel function * Weight is highest at the center and decreases to zero at the boundary * Operations: 1. Calculate weighted value for each neighbor (Weight * Value) 2. Sum all weighted values 3. Normalize (optional) ## Process-Based Focal Neighborhoods * Neighborhood is defined by a physical or social process * Examples: * **Watershed**: Neighborhood defined by terrain and gravity (flow of water) * **Viewshed**: Neighborhood defined by line-of-sight and topography * **Service Area**: Neighborhood defined by travel time on a road network ## Watershed as a Focal Neighborhood * A watershed is a neighborhood where all locations drain to a common outlet (focus) * Interaction: Water, sediment, and pollutants move from neighbors to the focus * Neighborhood is irregular and varies from location to location ## Types of Focal Operations (Based on Output) * Three types of focal operations based on what the output value represents: 1. Characterize focal neighborhood 2. Compare focus MU and its neighbors 3. Predict attribute at the focus MU ## Type 1: Characterize Focal Neighborhood * The output value summarizes the attributes within the neighborhood * Focal Statistics: * **FocalSum**: Total amount * **FocalMean**: Average intensity/density * **FocalMax/FocalMin**: Extremes * **FocalVariety**: Diversity/Heterogeneity * **FocalMajority**: Dominant type ## Type 2: Compare Focus MU and Neighbors * The output value represents the relationship or contrast between the focus and its surrounding area * Operations: * **ContrastLocation**: Distance to specific neighbors * **ContrastValue**: Difference between focus value and neighborhood mean * **FocalPercentage**: Percentage of neighbors with values equal to the focus * **FocalPercentile**: Percentage of neighbors with values less than the focus ## ContrastValue Operation Examples * **FocalPercentage**: * Measures the homogeneity of the focus relative to its neighbors * **FocalPercentile**: * Identifies if a focus MU is a local peak (high percentile) or local pit (low percentile)