1. Future Directions of Map Analysis and GIS Modeling: …where we are headed and how we get there Presentation by Joseph K. Berry Adjunct Faculty in Natural Resources, Warner College of Natural Resources, Colorado State University Adjunct Faculty in Geosciences, Department of Geography, University of Denver Principal, Berry & Associates // Spatial Information Systems Email: jberry@innovativegis.com — Website: www.innovativegis.com/basis This PowerPoint with notes and online links to further reading is posted at www.innovativegis.com/basis/Present/CentroidCSU2014/ Presentation Premise: There is a “map-ematics” that extends traditional math/stat concepts and procedures for the quantitative analysis of map variables (digital maps) “They who don’t know, don’t know they don’t know” Presentation Premise: There is a “map-ematics” that extends traditional math/stat concepts and procedures for the quantitative analysis of map variables (digital maps) …three major considerations will influence map analysis/modeling future development— Mathematical Framework, Data Structure and Educational Approach GIS Centroid Seminar — Colorado State University September 19, 2014 Basis

2. Mapping vs. Ana lyzing (Processing Mapped Data) Global Positioning System (locate and navigate) Remote Sensing (measure and classify) Geographic Information Systems (map and analyze) GPS/GIS/RS (Berry) … GIS is a Technological Tool involving — −Mapping that creates a spatial representation of an area −Display that generates visual renderings of a mapped area −Geo-query that searches for map locations having a specified classification, condition or characteristic “Map” (Descriptive Mapping) “Analyze” …and an Analytical Tool involving — −Spatial Mathematics that applies scalar mathematical formulae to account for geometric positioning, scaling, measurement and transformations of mapped data −Spatial Analysis that investigates the contextual relationships within and among mapped data layers −Spatial Statistics that investigates the numerical relationships within and among mapped data layers (Prescriptive Modeling) (Biotechnology)(Nanotechnology)

3. GIS as a Technological Tool (Critical Technological Frontiers) (Berry) -- highly detailed 3D city models provide entirely new perspectives and realism supporting greater intuitive interaction with maps and improved understanding of spatial context. Intelligent 3D Models through the combination of GIS, CAD and BIM (Building Information Management) enabled by greater interoperability of data formats will be extended to other applications, such as forestry and natural resources management thereby translating the “What and Where” information into a seamless whole. -- the ever expanding sensor web provides the foundation for real-time GIS. Emergency response and military geospatial intelligence offer “situational awareness” for fast and effective response. Real-time GIS-enabled instruments are being coupled with automated devices, such as water levee gates and earthquake warning broadcast systems, for near instantaneous response. Incorporating the multiple data streams from live video, ground sensors, tracking devices, drone aircraft and space-based instruments within a GIS framework enable both Intelligent Agents (automated devices) and decision makers to “see What is Happening Where” and respond events as they unfold. -- Temporal GIS incorporates the X, Y and Z dimensions as well as time for a 4D representation that introduces the time element to geospatial data to account for changes over time (in-situ evolution as well as positioning displacement of moving elements). Inroads have been made to display time series animation of spatial data (such as the Doppler Radar Images of a moving storm front), but the move toward fully integrated and comprehensive temporal GIS is hindered by the enormous amount of data needed to bring about the vision. However, the algorithms and methods for basic Change Detection in multiple images of the same scene taken at different times has greatly matured but need to be easier to use and more intuitive. Tomorrow’s Cyber Farmer (Precision Agriculture/Conservation example) Tomorrow’s Cyber Farmer (Precision Agriculture/Conservation example) …to pull off these amazing technological feats, significant advances in Map Analysis/Modeling capabilities and acceptance are needed. However, for the most part, there’s a big disconnect between maps as interface and the rich understanding that can be had by thinking “map-ematically”. …based on Matt Ball's blog at http://www.sensysmag.com/spatialsustain/what-are-some-of-the-technological-frontiers-for-gis-advancement.htmlhttp://www.sensysmag.com/spatialsustain/what-are-some-of-the-technological-frontiers-for-gis-advancement.html Three major considerations will influence map analysis/modeling future development— Mathematical Framework, Data Structure and Educational Approach. 3D Integration Real-Time GIS Temporal GIS

4. Spatial Statistics Operations Spatial Analysis Operations “Map-ematics” Map Stack Maps as Data, not Pictures Vector & Raster — Aggregated & Disaggregated Qualitative & Quantitative A Mathematical Structure for Map Analysis/Modeling Technological Tool Mapping/Geo-Query (Discrete, Spatial Objects) Geotechnology  RS – GIS – GPS Grid-based Map Analysis Toolbox (Berry) Esri Spatial Analyst operations …over 170 individual “tools” (Continuous, Map Surfaces ) Map Analysis/Modeling Analytical Tool Geo-registered Analysis Frame …organized set of numbers  Matrix of Numbers www.innovativegis.com/basis/BeyondMappingSeries/www.innovativegis.com/basis/BeyondMappingSeries/, Book IV, Topic 9 for more discussion A Map-ematical Framework Traditional math/stat procedures can be extended into geographic space to support Quantitative Analysis of Mapped Data “…thinking analytically with maps”

5. Spatial Analysis Operations (Geographic Context) Spatial Analysis extends the basic set of discrete map features (points, lines and polygons) to map surfaces that represent continuous geographic space as a set of contiguous grid cells (matrix), thereby providing a Mathematical Framework for map analysis and modeling of the Contextual Spatial Relationships within and among grid map layers (Berry) GIS as “Technical Tool” (Where is What) vs. “Analytical Tool” (Why, So What and What if) Map StackGrid Layer Map Analysis Toolbox Basic GridMath & Map Algebra ( + - * / ) Advanced GridMath (Math, Trig, Logical Functions) Map Calculus (Spatial Derivative, Spatial Integral) Map Geometry (Euclidian Proximity, Effective Proximity, Narrowness) Plane Geometry Connectivity (Optimal Path, Optimal Path Density) Solid Geometry Connectivity (Viewshed, Visual Exposure) Unique Map Analytics (Contiguity, Size/Shape/Integrity, Masking, Profile) Mathematical Perspective: Unique spatial operations

6. The integral calculates the area under the curve for any section of a function. Curve Map Calculus — Spatial Derivative, Spatial Integral Advanced Grid Math — Math, Trig, Logical Functions Spatial Integral Surface COMPOSITE Districts WITH MapSurface Average FOR MapSurface_Davg MapSurface_D avg …summarizes the values on a surface for specified map areas (Total= volume under the surface) Slope draped over MapSurface 0% 65% Spatial Derivative …is equivalent to the slope of the tangent plane at a location SLOPE MapSurface Fitted FOR MapSurface_slope Fitted Plane Surface 500’ 2500’ MapSurface Advanced Grid Math Surface Area …increases with increasing inclination as a Trig function of the cosine of the slope angle S_Area= Fn(Slope) Spatial Analysis Operations (Math Examples) D z xy Elevation S_area= cellsize / cos(D z xy Elevation) ʃ Districts_Average Elevation Curve The derivative is the instantaneous “rate of change” of a function and is equivalent to the slope of the tangent line at a point (Berry)

7. Seen if new tangent exceeds all previous tangents along the line of sight Tan = Rise/Run Rise Run Viewshed Splash Solid Geometry Connectivity Spatial Analysis Operations (Distance Examples) (Berry) Map Geometry — (Euclidian Proximity, Effective Proximity, Narrowness) Plane Geometry Connectivity — (Optimal Path, Optimal Path Density) Solid Geometry Connectivity — (Viewshed, Visual Exposure) Euclidean Proximity …from a point to everywhere… Highest Weighted Exposure Sums Viewer Weights   Counts # Viewers 270/621= 43% of the entire road network is connected Visual Exposure Distance Shortest straight line between two points… Travel-Time Surface Effective Proximity …not necessarily straight lines (movement) HQ (start) On Road 26.5 minutes …farthest away by truck Off Road Absolute Barrier On + Off Road 96.0 minutes …farthest away by truck, ATV and hiking Off Road Relative Barriers Plane Geometry Connectivity …like a raindrop, the “steepest downhill path” identifies the optimal route (Quickest Path) Farthest (end) HQ (start) Truck = 18.8 min ATV = 14.8 min Hiking = 62.4 min

8. Spatial Statistics Operations (Numeric Context) (Berry) Spatial Statistics seeks to map the variation in a data set instead of focusing on a single typical response (central tendency), thereby providing a Statistical Framework for map analysis and modeling of the Numerical Spatial Relationships within and among grid map layers GIS as “Technical Tool” (Where is What) vs. “Analytical Tool” (Why, So What and What if) Map StackGrid Layer Map Analysis Toolbox Basic Descriptive Statistics (Min, Max, Median, Mean, StDev, etc.) Basic Classification (Reclassify, Contouring, Normalization) Map Comparison (Joint Coincidence, Statistical Tests) Unique Map Statistics (Roving Window and Regional Summaries) Surface Modeling ( Density Analysis, Spatial Interpolation) Advanced Classification ( Map Similarity, Maximum Likelihood, Clustering) Predictive Statistics (Map Correlation/Regression, Data Mining Engines) Statistical Perspective: Unique spatial operations

9. Spatial Statistics (Linking Data Space with Geographic Space) Continuous Map Surface Spatial Distribution Surface Modeling techniques are used to derive a continuous map surface from discrete point data– fits a Surface to the data (maps the variation). Geo-registered Sample Data Discrete Sample Map Spatial Statistics Histogram 7060504030 20 100 80 In Geographic Space, the typical value forms a horizontal plane implying the average is everywhere X= 22.6 (Berry) …lots of NE locations exceed Mean + 1Stdev X + 1StDev = 22.6 + 26.2 = 48.8 Unusually high values +StDev Average Standard Normal Curve Average = 22.6 Numeric Distribution StDev = 26.2 (48.8) Non-Spatial Statistics In Data Space, a standard normal curve can be fitted to the data to identify the “typical value” (average) Roving Window (weighted average)

10. Slope (Percent) Map Clustering: Elevation (Feet) Advanced Classification (Clustering) X axis = Elevation (0-100 Normalized) Y axis = Slope (0-100 Normalized) Elevation vs. Slope Scatterplot Data Space Slope draped on Elevation Slope Elev Entire Map Extent Spatially Aggregated Correlation Scalar Value – one value represents the overall non-spatial relationship between the two map surfaces …where x = Elevation value and y = Slope value and n = number of value pairs r = …1 large data table with 25rows x 25 columns = 625 map values for map wide summary Cluster 1 Cluster 2 (Berry) Spatial Statistics Operations (Data Mining Examples) “data pair” of map values + “data pair” plots here in… Data Space Predictive Statistics (Correlation) Map Correlation: Slope (Percent) Elevation (Feet) Roving Window Localized Correlation Map Variable – continuous quantitative surface represents the localized spatial relationship between the two map surfaces …625 small data tables within 5 cell reach = 81map values for localized summary r =.432 Aggregated Geographic Space + Geographic Space …as similar as can be WITHIN a cluster …and as different as can be BETWEEN clusters Map of the Correlation

11. Grid-based Map Data Structur e (geo-registered matrix of map values) (Berry) …the bottom line is that… All spatial topology is inherent in the grid. Conceptual Spreadsheet (73 x 144) #Rows= 73 #Columns= 144 = 10,512 grid cells …each 2.5 0 grid cell is about 140mi x 140mi 18,735mi 2 …from Lat/Lon “ crosshairs to grid cells ” that contain map values indicating characteristics or conditions at each grid location Lat/Lon The easiest way to conceptualize a grid map is as an Excel spreadsheet with each cell in the table corresponding to a Lat/Lon grid space (location) and each value in a cell representing the characteristic or condition (information) of a mapped variable occurring at that location. …maximum Lat/Lon decimal degree resolution is a four-inch square anywhere in the world The Latitude/Longitude grid forms a continuous surface for geographic referencing where each grid cell represents a given portion of the earth’ surface. 30 0 Grid Lines 9090 2.5 0 Latitude/Longitude Grid (140mi grid cell size) Coordinate of first grid cell is 90 0 N 0 0 E Analysis Frame (grid “cells”)

12. Database Table Geographic Space Grid Space “Where” RDBMS Organization Data Space Each column (field) represents a single map layer with the values in the rows indicating the characteristic or condition at each grid cell location (record) “What” … Spatially Keyed data in the cloud are downloaded and configured to the Analysis Frame defining the Map Stack Universal Database K ey (moving Lat/Lon from crosshairs to grid cells) Lat/Lon as a Universal Spatial Key Once a set of mapped data is stamped with its Lat/Lon “Spatial Key,” it can be linked to any other database table with spatially tagged records without the explicit storage of a fully expanded grid layer— all of the spatial relationships are implicit in the relative Lat/Lon positioning. (Berry) Conceptual Organization Elevation Surface Spreadsheet 30m Elevation ( 99 columns x 99 rows) Wyoming’s Bighorn Mts. Spatially Keyed data in the cloud Lat/Lon serves as a Universal dB Key for joining data tables based on location Keystone Concept Each of the conceptual grid map spreadsheets (matrices) can be converted to interlaced RDBMS format with a long string of numbers forming the data field (map layer) and the records (values) identifying the information at each of the individual grid cell locations. 2D Matrix  1D Field

13. What (Value) …value indicates characteristic or condition at a location Spatially Aware Database (XY, Value) Where (XY) …Lat/Lon coordinates identify earth position of a dB record 5-step Process for Unlocking the Universal Spatial Db Key Step 2. User specifies the cell size of the analysis window. …e.g., 100m Analysis Frame (grid map layer) Longitude Latitude Step 3. Computer determines the Lat/Lon ranges defining each grid cell ( cutoffs ) and the centroid location. …defines the Analysis Frame 1 6 3 0 7 16 5 11 8 4 11 9 13 6 15 7 4 9 2 2 20 12 4 0 1 13 3 7 10 0 3 1 7 2 6 Step 4. Computer determines the appropriate grid cell for each database record that falls within the analysis frame’s geographic extent based on its Lat/Lon coordinates… then repeats for all selected dB records. … but Lat/Lon grid cells are only square at the equator— so is the entire idea a bust? (Berry) Hint: spatial resolution of the analysis frame is key Step 1. User identifies the geographic extent of the analysis window. Step 5. Computer summarizes the values if more than one value “falls” into an individual grid cell-- result is a “ Grid Map Layer ” for inclusion in a map stack for subsequent map analysis. Shish Kebab of numbers Map Stack

14. GIS Evolution The Early Years Revisit Analytics (2020s) GIS Development Cycle (…where we’re heading) Map Analysis (1990s) Computer Mapping (1970s) Spatial dB Mgt (1980s) The Early Years Contemporary GIS GeoWeb (2000s) Revisit Geo-reference (2010s) Future Directions Mapping focus Data/Structure focus Analysis focus …about every decade Cube (6 squares) 3D Solid (X,Y,Z Data) Future Directions Square (4 sides) 2D Planar (X,Y Data) Cartesian Coordinates (Berry) Hexagon (6 sides) Today Future Pentagonal Dodecahedral (12 pentagons) Today Future

15. The lion’s share of the growth has been GIS’s ever expanding capabilities as a “ technical tool ” for corralling vast amounts of spatial data and providing near instantaneous access to remote sensing images, GPS navigation, interactive maps, asset management records, geo-queries and awesome displays. However, GIS as an “ analytical tool ” hasn’t experienced the same meteoric rise— in fact it can be argued that the analytic side of GIS has somewhat stalled… partly because of… (Berry) …but modern digital “maps are numbers first, pictures later” and we do mathematical and statistical things to map variables that moves GIS from— “Where is What” graphical inventories, to a “Why, So What and What If” problem solving environment— “thinking analytically with maps” GIS Education (shifting the current Technical focus to a Pedagogical focus)

16. Technology Experts “-ists” Domain Experts “-ologists” The “-ists” and the “-ologists” (Berry) Solution Space Together the “-ists” and the “-ologists” frame and develop the Solution for an application. …understand the “tools” that can be used to display, query and analyze spatial data Data and Information focus …understand the “science” behind spatial relationships that can be used for decision-making Knowledge and Wisdom focus The “-ists ” The “-ologists ” — and — Why, So What, What If Spatial Reasoning Where is What GIS Expertise

17. “Public” …under Stakeholder, Policy & Public auspices “Policy Makers” The “-ists” and the “-ologists” (toward a much bigger tent) “Stakeholders” “Decision Makers” Technology Experts “-ists” Domain Experts “-ologists” Solution Space Application Space Geotechnology’s Core …Decision Makers utilize the Solution… (Berry) Spatial Reasoning GIS Expertise We are simultaneously trivializing … …and complicating GIS Technology

18. Conclusions/Upshot (moving away from your grandfather's map) (Berry) – automated the cartographic process where points, lines and areas (spatial objects) defining geographic features on a map are represented as an organized set of X,Y coordinates. – linked computer mapping capabilities with traditional database management capabilities by assigning an ID# to each spatial object that serves as a common database key between a spatial table (Where) and an attribute table (What). – developed a comprehensive theory of map analysis where spatial information is represented numerically as continuous spatial distributions (raster), rather than in graphic fashion as discrete spatial objects (vector) identified by inked lines on a map. These digital maps are frequently conceptualized as a set of "floating maps" with a common registration, allowing the computer to "look" down and across the stack of digital maps to characterize spatial relationships of the mapped data that can be summarized (database queries) or mathematically manipulated (analytic processing). – the Internet has moved maps and mapping from a “down the hall and to the right” specialist’s domain, to everyone’s desktop, notebook and mobile device. While the bulk of these applications involve navigation, mapping and geo-query (technological), they have fully established the digital map beachhead that sees “maps as data, not just images.” Tomorrow’s GIS arena will be radically different from the past four decades… In the future, Geotechnology will fully exploit its numerical character by extending… 1) Scientific Use of Spatial Data – SpatialSTEM education will infuse science with “analytical tools” for unlocking radically new understandings of spatial patterns and relationships in their research. 2) Spatial Solutions to Devices – “map-ematical solutions” will be directly tied to automated devices through continued coupling of RS, GIS, GPS and robotics. 3) Spatial Reasoning and Dialog – GIS models will enable decision-makers to interactively investigate and better communicate “Why, So What and What If” of the probable spatial outcomes/impacts of critical decisions. See http://www.innovativegis.com/basis/BeyondMappingSeries/BeyondMapping_I/Epilog/BM_I_Epilog.htm for more discussionhttp://www.innovativegis.com/basis/BeyondMappingSeries/BeyondMapping_I/Epilog/BM_I_Epilog.htm … quantitative mapped data analysis and modeling completely changes our perspective of “what a map is (and isn’t)” Computer Mapping (1970 to 1980) Spatial Database Management Systems (1980 to 1990) Map Analysis and GIS Modeling (1990 to 2000) GeoWeb and Mobile Devices (2000 to 2010) Ag & NR considerations …next time

19. So Where to Head from Here? Joseph K. Berry Joseph K. Berry jberry@innovativegis.com jberry@innovativegis.com eMail Contact Online Materials (www.innovativegis.com/Basis/Courses/SpatialSTEM/) ) This PowerPoint with notes and online links to further reading is posted at www.innovativegis.com/basis/Present/CentroidCSU2014/ Website (www.innovativegis.com) For more papers and presentations on Geotechnology For more papers and presentations on Geotechnology www.innovativegis.com For more papers and presentations on Geotechnology For more papers and presentations on Geotechnology www.innovativegis.com Beyond Mapping Compilation Series …nearly 1000 pages and more than 750 figures in the Series provide a comprehensive and longitudinal perspective of the underlying concepts, considerations, issues and evolutionary development of modern geotechnology (RS, GIS, GPS).