Raster Analysis and Terrain Analysis Chapter 10 Part 2 & 11 Raster Analysis Lecture 11

Scope: Neighborhood operations Vector neighborhoods are not well-defined and depends upon the size and shape of the feature and neighboring feature, Raster neighborhood is better defined. Lecture 11

Neighborhood Operations Moving Windows (Windows can be any size; often odd to provide a center) Lecture 11

Kernels vs. Moving Window Lecture 11

Neighborhood Operations: Separate edge kernals can be used

Neighborhood Operations Lecture 11

Example:Identifying spatial differences in a raster layer This is an edge detection operation – The first kernel amplifies differences in the x direction the second amplifies differences in the y direction.

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 Lecture 11

Zonal Functions Zonal operations apply functions based on defined regions or zones.

Scope: Global operation Global operations can be useful for continuous data like temperature and rainfall. You want to find global maximums. Lecture 11

ArcMap’s Raster Calculator                                                                            Raster Calculator tool dialog box example Xor is an exclusive OR – exactly one of the operands is true "ceil" returns the smallest integer (represented as a double precision number) that is greater than or equal to "x". In mathematics and computer science, the floor and ceiling functions map a real number to the next smallest or next largest integer. More precisely, floor(x) = ⌊x⌋ is the largest integer not greater than x and ceiling(x) = ⌈x⌉ is the smallest integer not less than x.[1] From ArcGIS Help Files Lecture 11

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 Lecture 11

A cost surface is based on a fixed cost such as miles per gallon. Lecture 11

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 Lecture 11

Friction Surface Lecture 11 Variable cost Total distance is 22.4/ 4 segments = 5.6 Lecture 11

Chapter 10 Assignment Read Ch. 10 Problems: 2, 4, 6, 8, 12, 14, 16,19, 22, 23 Lecture 11

Terrain Analysis Lecture 11

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. Lecture 11

Lecture 11

Digital Elevation Models Terrain Analysis Slope and Aspect Used for: hydrology, conservation, site planning, other infrastructure development. Watershed boundaries, flowpaths and direction, erosion modeling, and viewshed determination 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) Lecture 11

Slope (continued)

Measured in the steepest direction of elevation change 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 3rd Order Finite Difference Lecture 11

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: Lecture 11

Slope (continued) for Zo ΔZ/Δx = (49 – 40)/20 = 0.45 ΔZ/Δy = (45 – 48)/20 = -0.15 Lecture 11

Slope (continued) Generalized formula for ΔZ/Δx and ΔZ/Δy ΔZ/Δx = (Z5 – Z4)2* ΔZ/Δy = (Z2 – Z7)2* Using the four nearest cells for Zo ΔZ/Δx = (49 – 40)/20 = 0.45 ΔZ/Δy = (45 – 48)/20 = -0.15 * = times cell width Slope calculation base on cells adjacent to the center cell The distance is from cell center to cell center Lecture 11

Slope (continued) Multiply (kernal, cell by cell) Add (results) Divide by #cells x cell width Use slope formula Kernal for ΔZ/Δx Kernal for ΔZ/Δy ΔZ/Δx = (49 – 40)/20 = 0.45 ΔZ/Δy = (45 – 48)/20 = -0.15 Lecture 11

Multiply (kernal, cell by cell) Add (results) Divide by #cells x cell width Use slope formula Lecture 11

Slope in ArcGIS 10 From ArcGIS 10 Help Lecture 11

Aspect Lecture 11

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 3rd-order finite difference methods Lecture 11

Aspect in ArcGIS 10 From ArcGIS 10 Help Lecture 11

Curvature Lecture 11

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 Lecture 11

Lecture 11

Lecture 11

Shaded Relief Surfaces Lecture 11

Flow Direction From ArcGIS 10 Desktop Help Lecture 11

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 Lecture 11

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 Lecture 11

35.7

Watershed Drainage network 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 Lecture 11

Lecture 11

Routing and Allocation 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 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) Lecture 11

Assignments for Chapter 11 Read chapter 11. Problems: 3, 4, 6, 8, 22 Lecture 11