Raster Analysis and Terrain Analysis Chapter 10 & 11 Raster Analysis

Raster Data Model Raster cells store data (nominal, ordinal, interval/ratio) Forest 1,…9, Excellent for terrain and hydrological modeling Complex constructs built from raster data -Connected cells can be formed in to networks -Related cells can be grouped into neighborhoods or regions

Examples of Raster Analysis Predict fate of pollutants in the atmosphere The spread of disease Animal migrations Crop yields EPA - hazard analysis of urban superfund sites Market analysis Watershed analysis Terrain analysis

Map algebra Concept introduced and developed by Dana Tomlin and Joseph Berry (1970’s) Cell by Cell combination of raster data 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 such as addition, subtraction and multiplication

Scope: Local operations

Many Local Functions (page 412 of text)

Logical Operations AND Non-zero values are “true”, zero values are “false” N = null values

Logical Operations OR Non-zero values are “true”, zero values are “false” N = null values

Logical Operations NOT

More Local Functions – logical comparisons

An Example of a Logical Operation

Reclassification

Conditional Function

Nested Functions

Overlay

Raster Clip Operation

Raster Addition

Be Careful of Ambiguity

Raster Overlay in Idrisi

First * Second 0*0=0 0*1=0 1*1=1

First + Second 0+0=0 0+1=1 1+1=2

Scope: Neighborhood operations

Neighborhood Operations Moving Windows (Windows can be any size; often odd to provide a center)

Kernels vs. Moving Window

Neighborhood Operations: Separate edge kernals can be used

Neighborhood Operations

Example:Identifying spatial differences in a raster layer

Raster Analysis Moving windows and kernals can be used with a mean kernal to reduce the difference between a cell and surrounding cells. (done by average across a group of cells) Raster data may also contain “noise”; values that are large or small relative to their spatial context. (Noise often requiring correction or smooth(ing)) Know as “high-pass” filters The identified spikes or pits can then be corrected or removed by editing

Zonal Functions

Scope: Global operation

ArcMap’s Raster Calculator Raster Calculator tool dialog box example From ArcGIS Help Files

Cost Surface The minimum cost of reaching cells in a layer from one or more sources cells “travel costs” Time to school; hospital; Chance of noxious foreign weed spreading out from an introduction point Units can be money, time, etc. Distance measure is combined with a fixed cost per unit distance to calculate travel cost If multiple source cells, the lowest cost is typically placed in the output cell

Friction Surface (version of a Cost Surface) The cell values of a friction surface represent the cost per unit travel distance for crossing each cell – varies from cell to cell Used to represent areas with variable travel cost. Notes: Barriers can be added. Multiple paths are often not allowed Cost and Friction Surfaces are always related to a source cell(s); “from something” The center of a cell is always used the distance calculations

Friction Surface

Terrain Analysis

Digital Elevation Models (DEM)/Terrain Analysis Terrain determines the natural availability and location of surface water, and hence soil moisture and drainage. Water quality through control of sediment entrainment and transport, slope steepness and direction defines flood zones, watershed boundaries and hydrologic networks. Terrain also strongly influences location and nature of transportation networks or the cost and methods of house and road construction.

Digital Elevation Models Terrain Analysis Slope and Aspect Used for: hydrology, conservation, siteplanning, other infrastructure development. Watershed boundaries, flowpaths and direction, erosion modeling, and viewsheddetermination all use slope and/or aspect data as input. Slope is defined as the change is elevation (a rise) with a change in horizontal position (a run). Slope is often reported in degrees (0° is flat, 90° is vertical)

Slope (continued)

Measured in the steepest direction of elevation change Often does not fall parallel to the raster rows or columns Which cells to use? Several different methods: Four nearest cells 3 rd Order Finite Difference

Slope (continued) Elevation is Z Using a 3 by 3 (or 5 by 5) moving window Each cell is assigned a subscript and the elevation value at that location is referred to by a subscripted Z value The most common formula:

Slope (continued) for Z o ΔZ/Δx = (49 – 40)/20 = 0.45 ΔZ/Δy = (45 – 48)/20 = -0.15

Slope (continued) Slope calculation base on cells adjacent to the center cell The distance is from cell center to cell center for Z o ΔZ/Δx = (49 – 40)/20 = 0.45 ΔZ/Δy = (45 – 48)/20 = Generalized formula for ΔZ/Δx and ΔZ/Δy ΔZ/Δx = (Z 5 – Z 4 )2* ΔZ/Δy = (Z 2 – Z 7 )2* Using the four nearest cells * = times cell width

Slope (continued) ΔZ/Δx = (49 – 40)/20 = 0.45ΔZ/Δy = (45 – 48)/20 = Kernal for ΔZ/ΔxKernal for ΔZ/Δy Multiply (kernal, cell by cell) Add (results) Divide by #cells x cell width Use slope formula

Multiply (kernal, cell by cell) Add (results) Divide by #cells x cell width Use slope formula

Slope in ArcGIS 10 From ArcGIS 10 Help

Aspect

The orientation (in compass angles) of a slope Calculation: Aspect = tan -1 [ -(ΔZ/Δy)/(ΔZ/Δx)] As with slope, estimated aspect varies with the methods used to determine ΔZ/Δx and ΔZ/Δy Aspect calculations also use the four nearest cell or the 3 rd -order finite difference methods

Aspect in ArcGIS 10 From ArcGIS 10 Help

Curvature

Viewshed The viewshed for a point is the collection of areas visible from that point. Views from any non-flat location are blocked by terrain. Elevations will hide a point if they are higher than the viewing point, or higher than the line of site between the viewing point and target point

Shaded Relief Surfaces

From ArcGIS 10 Desktop Help Flow Direction

Raster Analysis High pass filters Return: Small values when smoothly changing values. Large positive values when centered on a spike Large negative values when centered on a pit

High Pass Filter Raster data may also contain “noise”; values that are large or small relative to their spatial context. A mean kernal is used to reduce the difference between a cell and surrounding cells. (done by average across a group of cells) The identified spikes or pits can then be corrected or removed by editing

35.7

Watershed An area that contributes flow to a point on the landscape Water falling anywhere in the upstream area of a watershed will pass through that point. Many be small or large Identified from a flow direction surface Drainage network A set of cells through which surface water flows Based on the flow direction surface

Routing and Allocation Routing – Finding the shortest path between any nodes in a network – Optimal path Each link in the net can also be assigned an impedance value Using an accumulated distance and the impedance factor – Most efficient route can be found, rather than just the shortest – Nodes can also be coded with stops and barriers Preventing movement and forcing traffic along another path – Although routing can be done in raster, it is much easier if performed in a vector system

Routing and Allocation Allocation – Process used to define the areal extent of services areas – Service areas are defined around a site Region is formed that includes a defined area – Location/allocation model (optimizes network efficiency) Technique for the evaluation of multiple facility locations – Determining the configuration of facilities (location) – Assigning demand for the facilities (allocation)