Raster Analysis Ming-Chun Lee

Raster Analysis Performed on cells and grids. Raster cells store data Nominal – land use Ordinal – street classification Interval/Ratio – temperature, elevation Perform analysis based on manipulations on cell values for a single raster layer or multiple layers. Raster analysis is Performed on cells and grids. Raster cells store data, a single cell contains a value which represents a measurement of a certain phenomenon.. Nominal – land use Ordinal – street classification Interval/Ratio – temperature, elevation Perform analysis based on manipulations on cell values for a single raster layer or multiple layers.

Why use Raster GIS Raster is better suited for spatially continuous data Elevations, pH, air pressure, temperature, salinity Raster is better for creating visualizations and modeling environmental phenomena Raster data is a simplified realization of the world, and allows for fast and efficient processing Why use Raster GIS A quick recap on advantages of raster data model: Raster is better suited for spatially continuous data Elevations, pH, air pressure, temperature, salinity Raster is better for creating visualizations and modeling environmental phenomena Some natural phenomena are hard to visualize as a whole, raster helps us visualize those phenomena over a piece of land.. Raster data is a simplified realization of the world, and allows for fast and efficient processing

Map Algebra Cell by Cell combination of raster data layers using mathematical operations one layer multiple layers Each number represents a value at a raster cell location Simple operations can be applied to each number Raster layers may be combined through operations Addition, subtraction and multiplication Raster analysis is mainly based on so-called map algebra: What is map algebra: Combine raster data layers cell by cell using mathematical operations one layer multiple layers Each number represents a value at a raster cell location Simple operations can be applied to each number Raster layers may be combined through operations Addition, subtraction and multiplication

Map Algebra Raster analysis creates a new layer, or new grid, you didn’t actually change the original layers, what you did is take out values from the original layers and do some kind of manipulation on them, and output a new layer..

Map Algebra 1 4 3 2 5 4 7 6 3 Input 1 2 4 2 1 2 3 6 + 6 3 3 4 2 1 6 2 Input 2 4 6 4 3 1 3 2 4 = 7 7 6 6 7 7 13 5 Output 6 10 8 5 2 5 5 10

Map Algebra The computer will allow you to perform virtually any mathematical calculation beware: some will make sense, others won’t. For example, water = 0, land = 1. Then, you can multiply this grid with an elevation map. The output will include 0’s where water existed (x * 0 = 0), and the original elevation value where land existed (x * 1 = x) Or, you can add the elevations and the grid with 0’s and 1’s together (but, it would be meaningless!) The computer will allow you to perform virtually any mathematical calculation beware: some will make sense, others won’t. For example, water = 0, land = 1. Then, you can multiply this grid with an elevation map. The output will include 0’s where water existed (x * 0 = 0), and the original elevation value where land existed (x * 1 = x) Or, you can add the elevations and the grid with 0’s and 1’s together (but, it would be meaningless!)

Map Algebra Grid1 * Grid2 = Grid3 Grid1 Grid2 1 * = Grid3

Map Algebra Multiple grid themes share the same X, Y coordinate space A single output grid theme is the result of the multiple grids Multiple grid themes share the same X, Y coordinate space When you apply map algebra to multiple layers, those layers have to share the same coordinate system. A single output grid theme is the result of the multiple grids

Map Algebra Mathematical Operators: Arithmetic Boolean Relational +, -, *, / Boolean AND, OR, NOT, XOR Relational =, <, >, ≤, ≥, <> Algebraic Functions Powers & Roots, Trigonometry, Logarithm Those mathematical operations that you can use for rater analysis, can be grouped into four categories: Arithmetic Operators – The Arithmetic operators (*, /, -, +) allow for the addition, subtraction, multiplication, and division of two grid themes. Boolean Operators – The Boolean operators (And, Not, Or, and Xor) use Boolean logic (TRUE or FALSE) on the input values. Output values of TRUE are written as 1 and FALSE as 0. Relational Operators – The Relational operators (<, <=, <>, =, >, and >=) evaluate specific relational conditions. If the condition is TRUE, the output is assigned 1; if the condition is FALSE, the output is assigned 0. Algebraic Functions to a single layer… Powers & Roots, Trigonometry, Logarithm

Mathematical Operator: Arithmetic

Mathematical Operator: Boolean

Mathematical Operator: Relational

Mathematical Operator: Algebraic Functions

Scope of Computations Local Functions Focal/Neighborhood Functions Process cells on a cell-by-cell basis. only use data in a single cell to calculate an output value Focal/Neighborhood Functions Process data for each pixel using the attribute values of the neighboring cells of that pixel. Zonal Functions Process cells on the basis of zones. Global Functions Process data at each pixel on the output grid using entire source grid. Now, we have looked at map algebra, looked at some operations you can apply to raster layers. Now let’s look at Scope of Computations The scope of calculation or operation, can be different depend on your analysis purpose.. Local Functions Process cells on a cell-by-cell basis. only use data in a single cell to calculate an output value Focal/Neighborhood Functions Process data for each pixel using the attribute values of the neighboring cells of that pixel. Zonal Functions Process cells on the basis of zones. Global Functions Process data at each pixel on the output grid using entire source grid.

Local Functions 5 4 7 input 25 49 output = sqr(input) 16 (use only the data at one input data point to determine value at a corresponding output location) Operations that modify a single cell Data type changes Arithmetic operations involving a constant Converting one value to another according to a rule (Recode) Local operations on multiple layers Map algebra (Output = f(Input1, Input2,…) Functions may be mathematical or logical output = sqr(input) 16

Local Functions Operations that modify a cell on a single grid Data type changes Arithmetic operations Converting one value to another according to a rule (Recode) Local operations on multiple layers Map algebra (Output = f(Input1, Input2,…) Functions may be mathematical or logical Operations that modify a cell on a single grid Data type changes Arithmetic operations Converting one value to another according to a rule (Recode) Local operations on multiple layers Map algebra (Output = f(Input1, Input2,…) Functions may be mathematical or logical

Local Functions Single grid Multiple grid (addition)

Focal/Neighborhood Functions 5 4 7 input 11 (data from both an input location plus nearby locations to determine the output value) 16 output = focalsum(input)

Focal/Neighborhood Functions Moving window Assigns the value of a neighborhood of grid cells to one particular grid cell (kernel) Useful for calculating local statistical functions Moving Windows (Windows can be any size; often odd to provide a center)

Neighborhood Functions You may want to study ecosystem, and want to figure out the variety of species for each neighborhoods, where is lacking a variety of animals. Different land cover types,

Zonal Functions Zone Sum 1 9 2 7 5 4 7 input Zone 2 zone Zone 1 output = zonalsum(zone, input) Similar to focal function, but which cells being taken into calculation not depend on neighborhood, but depend on zones, which are usually defined by another layer. 9 7 7 7 Zone Sum 1 9 2 7 9 7 7 7 9 9 9 7 9 9 9 7

Zonal Functions Output value at each location depends on the values of all the input cells in an input value grid that shares the same input value zone Type of complex neighborhood function use complex neighborhoods or zones Output value at each location depends on the values of all the input cells in an input value grid that shares the same input value zone Type of complex neighborhood function use complex neighborhoods or zones

input Input_zone 535.54 127 6280 766.62 160 10800

Global Functions 5 4 7 input 6 7 8 9 5 6 7 8 output = trend(input) 4 5

Global Functions Output value of each location is potentially a function of all the cells in the input grid e.g. distance functions, surfaces, interpolation, etc. Output value of each location is potentially a function of all the cells in the input grid e.g. distance functions, surfaces, interpolation, etc.

Distance to Features Cell value is the Distance from the Cell Center to the Nearest Feature(s) in a Specified Layer Physical distance– equivalent to buffers Cost distance Requires a cost grid as input Cost grid contains costs for unit distance Cost distance between two cells is the average of the two values multiplied by the distance between them Total cost is calculated to source cells. Cell value is the Distance from the Cell Center to the Nearest Feature(s) in a Specified Layer Physical distance– equivalent to buffers Cost distance Requires a cost grid as input Cost grid contains costs for unit distance Cost distance between two cells is the average of the two values multiplied by the distance between them Total cost is calculated to source cells.

Distance to Features

Interpolation Between Features Interpolation predicts values for cells in a raster from a limited number of sample data points. Elevation, rainfall, chemical concentration, noise level Average of Nearby Features’ Values, Weighted by Distance, Regardless of Density Example: Number of Bus Routes Serving a Neighborhood! Average of Nearby Features’ Values, Weighted by Distance, Regardless of Density Example: Number of Bus Routes Serving a Neighborhood! Interpolation predicts values for cells in a raster from a limited number of sample data points.. Elevation, rainfall, chemical concentration, noise level, Visiting every location in a study area to measure is expensive, and sometimes just impossible.. The assumption that makes interpolation a viable option is that spatially distributed objects are spatially correlated. Things that are close together tend to have similar characteristics.

Interpolation Between Features

Density of Features Value Assigned Based on the Neighborhood Density of a Feature Can be Weighted on an Attribute Value Example: Estimate a Population Density Surface Using Census Tract Population Another Example – Bus Service Density Value Assigned Based on the Neighborhood Density of a Feature Can be Weighted on an Attribute Value Example: Estimate a Population Density Surface Using Census Tract Population Another Example – Bus Service Density

Density of Features

Spatial Analyst functions Find Distance Calculate Density Interpolate Surface Derive Slope, Aspect Create Contour Cell Statistics Summarize Zones Tabulate Areas Map Query, Calculator Neighborhood Statistics Reclassify

Raster-based Analysis Finding potential sites for a new school (ESRI: Using ArcGIS Spatial Analyst) Criteria: On flat land Near recreation sites Away from existing schools Land use in terms of cost Agricultural – cheapest Barren land Brush/Transitional Forest Built up – most expensive Finding potential sites for a new school (ESRI: Using ArcGIS Spatial Analyst) Criteria: On flat land Near recreation sites Away from existing schools Land use in terms of cost Agricultural – cheapest Barren land Brush/Transitional Forest Built up – most expensive

Slope

Slope

Distance

Distance

Reclassify

Reclassify

Reclassify

Reclassify Lecture 9

Weighting and Combining Datasets Weights: Dist to Rec_sites: 0.5 Dist to schools: 0.25 Landuse: 0.125 Slope: 0.125

Raster Calculation

Raster Calculation

Result

Finding an Access Road to New Sites

Cost Layer Slope: Land Use: High values (10) to steeper slopes Agricultural: 4 Brush/Transitional: 5 Barren land: 6 Forest: 8 Built up: 9 Water: 10

Cost Layer

Cost Layer

Cost Weighted Distance

Cost Weighted Distance

Shortest Path

Shortest Path

Shortest Path