DU Mini-Workshops on GIS Modeling -- Surface Modeling/Analysis Introduction to GIS Modeling Week 5 — Summarizing Neighborhoods GEOG 3110 –University of Denver Presented by Joseph K. Berry W. M. Keck Scholar, Department of Geography, University of Denver Calculating slope, aspect and profile maps; Applying spatial differentiation and integration; "Roving window" summary operations; Characterizing edges and complexity Joseph K. Berry, Keck Visiting Scholar

Class Logistics and Schedule DU Mini-Workshops on GIS Modeling -- Surface Modeling/Analysis Lessons Learned Grading Thoughts— … thoughts about the “red” …are any of the comments useful? …if so, which ones? …also—distinction among Numerical, Geographical and Display Data Types Teams for Exercise #5 New teams? …or same as Exercise #1&2 ...or, same as Exercises 3&4 Midterm Study Questions (and student answer outlines) …posted now ; if useful I will coordinate posting of group answers on Monday and Wednesday Midterm Exam …you will download and take the 2-hour exam online (honor system) sometime between 8:00 am Friday February 11 and 5:00 pm Wednesday February 16 Exercise #6 (mini-project, example) — you will form your own teams (2 to 4 members) and tackle one of eight projects; posted now but we will discuss all aspects of the project “opportunities” next week …assigned Thursday, February 11 and final report due 5:00 pm Sunday, February 21 No Exercise Week 7 — pause …a moment for a group “dance of joy” Exercises #8 and #9 — to tailor your work to your interests, you can choose to not complete either or both of these standard exercises; in lieu of an exercise, however, you must submit a short paper (4-8 pages) on a GIS modeling topic of your own choosing Berry Joseph K. Berry, Keck Visiting Scholar

Quick Review (Simple proximity) DU Mini-Workshops on GIS Modeling -- Surface Modeling/Analysis Quick Review (Simple proximity) Simple Proximity surfaces can be generated for groups of points, lines or polygons …sets of Points Lines Areas Accumulation surfaces of ever-increasing distance away from a starting location(s) Berry Joseph K. Berry, Keck Visiting Scholar

Quick Review (Effective proximity) DU Mini-Workshops on GIS Modeling -- Surface Modeling/Analysis Quick Review (Effective proximity) Effective Proximity surfaces are generated by considering absolute and relative barriers to movement …sets of Points Water Absolute Barrier Lines Slope Relative Barrier Areas Water & Slope Absolute & Relative Berry Joseph K. Berry, Keck Visiting Scholar

Quick Review (Simple & Effective Proximity comparisons) DU Mini-Workshops on GIS Modeling -- Surface Modeling/Analysis Quick Review (Simple & Effective Proximity comparisons) Simple Proximity …sets of Points Water Absolute Barrier Lines Slope Relative Barrier Areas Water & Slope Absolute & Relative Effective Proximity Berry Joseph K. Berry, Keck Visiting Scholar

Measuring Distance as “Waves” (Splash) DU Mini-Workshops on GIS Modeling -- Surface Modeling/Analysis Measuring Distance as “Waves” (Splash) (See recommended reading on the CD “Calculating Effective Distance” for an in-depth discussion) (Berry) Joseph K. Berry, Keck Visiting Scholar

Simple Proximity (Euclidean Distance) DU Mini-Workshops on GIS Modeling -- Surface Modeling/Analysis Simple Proximity (Euclidean Distance) Starters S1 Proximity 25,1 Close to S1 … a Starter location is selected … Proximity from the location to all other locations is computed Starters S2 Proximity Close to S2 1,25 …repeat for another starter location Shortest Proximity Close Shortest Proximity Working Map Shortest Proximity Close to S2 to S1 … the computed Proximity values are compared to the current shortest proximity values … smaller values replace larger ones … repeat for next starter location Shortest Proximity Updated …compare proximity surfaces …store smallest value at each location Berry Joseph K. Berry, Keck Visiting Scholar

Effective Proximity (Intervening Conditions) DU Mini-Workshops on GIS Modeling -- Surface Modeling/Analysis Starters Values on this map identify locations for measuring proximity; values can be used to indicate movement weights (characteristics weight) S1 S2 Movement Type Movement propagates from a starter location in waves; step distance can be orthogonal or diagonal (geographic distance) Friction Relative ease of movement is represented as Absolute and relative barriers; steps incur the relative impedance of the location it is passing through (conditions impedance) Effective Proximity (S1) Minimize (Weight * Distance * Impedance) Effective Proximity (S2) Effective Proximity (Overall) COMPARE— store Minimal Effective Distance …repeat for all other Starter locations Minimize (Effective Distance from different starters) Berry Joseph K. Berry, Keck Visiting Scholar

Basic and Advanced Distance Operations DU Mini-Workshops on GIS Modeling -- Surface Modeling/Analysis Basic and Advanced Distance Operations Basic Operations (Static) — Simple Proximity as the crow “flies” counting cell lengths as it moves out as a wave front (Simple– starts counting at 1) Effective Proximity as the crow “walks” in not necessarily straight lines that respect absolute/ relative barriers (Thru– absolute and relative barriers) Advanced Operations— …based on differences in the nature of the movement (Static): Guiding Surface (Up/Down/Across) Stepped-accumulation (continuing distance) Gravity Model (movement weights) Back Link (starter ID# for identifying closest starter location) …based on differences in the intervening conditions (Dynamic): Accumulation (Total accumulation) Momentum (Net accumulation) Direction (Look-up table) www.innovativegis.com/basis/MapAnalysis/Topic25/Topic25.htm Berry Joseph K. Berry, Keck Visiting Scholar

Basic and Advanced Distance Operations DU Mini-Workshops on GIS Modeling -- Surface Modeling/Analysis Basic and Advanced Distance Operations Effective Proximity Minimize (Distance * Impedance) Friction Relative ease of movement is represented as Absolute and relative barriers; steps incur the relative impedance of the location it is passing through (Conditions Impedance) Extension uses 5) a look-up table to update the friction surface based on the nature of the movement (direction, accumulation, momentum) Movement Type Movement propagates from a starter location in waves; step distance can be orthogonal or diagonal (Geographic Distance) Starters Values on this map identify locations for measuring proximity. Extensions include using the starter value to 1) indicate movement weights, 2) indicate starting distance value and 3) starter location ID# Guiding Surface Extension considers 4) whether a step is uphill, downhill or across based on guiding surface configuration Berry Joseph K. Berry, Keck Visiting Scholar

Connectivity Operations DU Mini-Workshops on GIS Modeling -- Surface Modeling/Analysis Connectivity Operations Optimal Path Density counts the number of optimal paths passing through each map location (Drain) Optimal Path Connectivity— Optimal Path identifies the steepest downhill path over a surface identifying the flow path if a terrain surface, or the optimal path if a proximity surface (Stream) Visual Connectivity— Viewshed results in a binary map identifying locations that are 1= seen and 0= not seen from at least one viewer location (Simple) Visual Exposure counts the number of viewer cells connected to each map location (Completely) Weighted Visual Exposure weights the number of connections based on viewer cell importance (Weighted) Visual Prominence records the largest exposure angle to viewer cells (Degrees) <ScreenHeights> <TargetHeights> <ViewerHeight> Berry Joseph K. Berry, Keck Visiting Scholar

Classes of Spatial Analysis Operators DU Mini-Workshops on GIS Modeling -- Surface Modeling/Analysis Classes of Spatial Analysis Operators …all spatial analysis involves changing values (numbers) on a map(s) as a mathematical or statistical function of the values on that map or another map(s) (See MapCalc Applications, “Cross-Reference” for a cross reference of MapCalc operations and those of other systems)) (Berry) Joseph K. Berry, Keck Visiting Scholar

Neighborhood Operations DU Mini-Workshops on GIS Modeling -- Surface Modeling/Analysis Neighborhood Operations ORIENT -- Creates a map indicating aspect along a continuous surface. PROFILE -- Creates a map indicating the cross-sectional profile along a continuous surface. SCAN -- Creates a map summarizing the values that occur within the vicinity of each cell. SLOPE -- Creates a map indicating the slope (1st derivative) along a continuous surface. INTERPOLATE -- Creates a continuous surface from point data (uses IDW or Nearest neighbor). (Berry) Joseph K. Berry, Keck Visiting Scholar

Characterizing Neighborhoods DU Mini-Workshops on GIS Modeling -- Surface Modeling/Analysis Characterizing Neighborhoods (Berry) Joseph K. Berry, Keck Visiting Scholar

DU Mini-Workshops on GIS Modeling -- Surface Modeling/Analysis Calculating Slope (max, min, median, average) At a location, the eight individual slopes can be calculated for the elevation values in a 3x3 window… then summarized for the maximum, minimum, median and average slope. The Maximum, Minimum, Median and Average slopes can be calculated using all eight individual slopes in the window or just the four corner slopes. For example, the calculated Average slope using the four corners is 29%; using all eight is 59% . Slope = Rise/Run (*100 for %) ( ArcTan for Degrees) (Berry) Joseph K. Berry, Keck Visiting Scholar

DU Mini-Workshops on GIS Modeling -- Surface Modeling/Analysis Calculating Slope (fitted using least squares & vector algebra) “Fitted slope” considers the overall slope within the window by least square fitting a plane to the nine elevation values …orientation of the fitted plane identifies the Aspect/Azimuth (Berry) Joseph K. Berry, Keck Visiting Scholar

DU Mini-Workshops on GIS Modeling -- Surface Modeling/Analysis Calculating Slope (fitted using least squares & vector algebra) “Fitted slope” considers the overall slope within the window by least square fitting a plane to the nine elevation values or by the closure of the vector sum of the eight individual slopes …orientation of the fitted plane or direction of resultant vector identifies the Aspect/Azimuth (Berry) Joseph K. Berry, Keck Visiting Scholar

DU Mini-Workshops on GIS Modeling -- Surface Modeling/Analysis Creating a Profile Map (Set of cross-sections) The value assigned to each cell identifies the profile class of the side slope through the cell. (Berry) Joseph K. Berry, Keck Visiting Scholar

Neighborhood Techniques DU Mini-Workshops on GIS Modeling -- Surface Modeling/Analysis Neighborhood Techniques Calculating Slope and Aspect… Use Slope to create maps of Slope_fitted, Slope_max, Slope_min and Slope_avg Use Compute to calculate difference surfaces between Slope_max minus Slope_min. and Slope_max minus Slope_fitted Use Orient to create aspect maps in octants and degrees azimuth Develop a binary model that identifies map locations that are fairly steep (1-20 percent slope) AND southerly oriented (135-245 degrees azimuth) (Exercise 5, Part 1, Questions 1-3) (Berry) Joseph K. Berry, Keck Visiting Scholar

DU Mini-Workshops on GIS Modeling -- Surface Modeling/Analysis Classes of Neighborhood Operations Two broad classes of neighborhood analysis— Characterizing Surface Configuration Summarizing Map Values (Berry) Joseph K. Berry, Keck Visiting Scholar

DU Mini-Workshops on GIS Modeling -- Surface Modeling/Analysis Creating a Crime Risk Density Surface Crime Incident Reports Crime Incident Locations Grid Incident Counts Geo-Coding Vector to Raster Calculates the total number of reported crimes within a roving window– crime density Density Surface Totals Roving Window 2D perspective display of crime density contours 3D surface plot 91 Crime Risk Map Classified Crime Risk Classify Counts the number of incidences (points) within in each grid cell 2D grid display of discrete incident counts Berry Joseph K. Berry, Keck Visiting Scholar

DU Mini-Workshops on GIS Modeling -- Surface Modeling/Analysis Roving Window Total (Density Surface) # of Customers Customer Density Berry Joseph K. Berry, Keck Visiting Scholar

DU Mini-Workshops on GIS Modeling -- Surface Modeling/Analysis Roving Window Average (Simple Average) Average = Total / #cells = 91 / 110 = 0.83 Berry Joseph K. Berry, Keck Visiting Scholar

DU Mini-Workshops on GIS Modeling -- Surface Modeling/Analysis Distance-Weighted Decay Functions Weighted Average of values in the “roving window” Standard mathematical decay functions where weights (Y) decrease with increasing distance (X) Berry Joseph K. Berry, Keck Visiting Scholar

DU Mini-Workshops on GIS Modeling -- Surface Modeling/Analysis Roving Window Decay Functions (Spatial Filters) Example spatial filters depicting the fall-off of weights (Z) as a function of geographic distance (X,Y) Berry Joseph K. Berry, Keck Visiting Scholar

DU Mini-Workshops on GIS Modeling -- Surface Modeling/Analysis Roving Window Data Summary (Weighted Average) Comparison of simple average (Uniform weights) and weighted average (Linear weights) smoothing results Berry Joseph K. Berry, Keck Visiting Scholar

Neighborhood Techniques DU Mini-Workshops on GIS Modeling -- Surface Modeling/Analysis Neighborhood Techniques Roving Windows Data Summaries… Use Scan to create a map of Housing Density Use Scan to create a map of the “coefficient of variation” in slope Covertype Diversity Use Scan to identify the neighborhood proportion that has the same cover type Develop a binary model to identify locations that have high diversity and low proportion similar (Exercise 5, Part 2, Questions 4-6) (Berry) Joseph K. Berry, Keck Visiting Scholar

DU Mini-Workshops on GIS Modeling -- Surface Modeling/Analysis Creating a Housing Density Map The TOTAL number of houses within 500 meters is calculated for each map location Note: Density Analysis and Spatial Interpolation are not the same thing (Berry) Joseph K. Berry, Keck Visiting Scholar

DU Mini-Workshops on GIS Modeling -- Surface Modeling/Analysis Iterative Smoothing The AVERAGE housing density value is successively calculated to smooth the Housing_density surface (seeking the geographic trend) (Berry) Joseph K. Berry, Keck Visiting Scholar

DU Mini-Workshops on GIS Modeling -- Surface Modeling/Analysis Coefficient of Variation Map The COFFVAR of the elevation values within 500 meters is calculated. Coffvar= (Stdev/Mean) * 100 What information do you think a Coffvar map of crop yield would contain? How might it be used? (Berry) Joseph K. Berry, Keck Visiting Scholar

DU Mini-Workshops on GIS Modeling -- Surface Modeling/Analysis Creating a Covertype Diversity Map …a DIVERSITY map indicates the number of different map values that occur within a window… e.g., cover types. As the window is enlarged, the diversity increases. (Berry) Joseph K. Berry, Keck Visiting Scholar

DU Mini-Workshops on GIS Modeling -- Surface Modeling/Analysis Characterizing “Edginess” A simple “Edginess” model for the meadow involves assigning 1 to the meadow (Renumber) then calculating the total values within a 3x3 window for just the meadow area (Around) (Berry) Joseph K. Berry, Keck Visiting Scholar

…questions cover Class/Lab material and Reading assignments to date Pop Quiz Possibility …questions cover Class/Lab material and Reading assignments to date — you reviewed the previous class material and did the required reading for this class as well as, right? (Berry)