Presentation by Joseph K. Berry W.M. Keck Scholar in Geosciences, University of Denver Adjunct Faculty in Natural Resources, Colorado State University Principal, Berry & Associates // Spatial Information Systems — Website: Over 35 years of teaching graduate courses and professional workshops in grid-based map analysis and modeling has lead me to believe that there is… a “map-ematics” that extends traditional math/stat concepts and procedures for quantitative analysis of mapped data …that enhances our understanding of spatial patterns and relationships needed in more effective solutions and decision-making. This presentation addresses that contention. Map Analysis and Modeling in Forestry’s Future: …where we are headed and how we can get there Plenary presentation at Esri Forestry GIS Solutions Conference, May 1-3, 2012, Redlands, CA Note: this PowerPoint with notes and online links to further reading is posted at

Making a Case for SpatialSTEM 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. In just forty years GIS has morphed from boxes of cards passed through a window to a megabuck mainframe that generated page-printer maps, to today’s sizzle of a 3D fly-through rendering of terrain anywhere in the world with back-dropped imagery and semi-transparent map layers draped on top— all pushed from the cloud to a GPS enabled tablet or smart phone. What a ride! (Berry) Over 35 years of teaching graduate courses and professional workshops in grid-based map analysis and modeling has lead me to believe that there is… a “map-ematics” that extends traditional math/stat concepts and procedures for quantitative analysis of mapped data. The premise is that “maps are numbers first, pictures later” and we do mathematical things to mapped data that moves GIS from “Where is What” graphical inventories to a “Why, So What and What If” problem solving environment— “Thinking with Maps” However, GIS as an “analytical tool” hasn’t experienced the same meteoric rise — in fact it might be argued that the analytic side of GIS has somewhat stalled over the last decade.

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

“Policy Makers” The “-ists” and the “-ologists” (a bigger tent) “Stakeholders” …under Stakeholder, Policy & Public auspices “Decision Makers” TechnologyExperts “-ists” DomainExperts “-ologists” SolutionSpace Application Space Geotechnology’s Core Decision Makers utilize the Solution (Berry) Spatial ReasoningGIS Expertise We are simultaneously trivializing ……and complicating GIS Technology

Spatial Analysis Operations (Geographic Context) GIS as “Technical Tool” ( Where is What ) vs. “Analytical Tool” ( Why, So What and What if ) Reclassify (Position, Value, Size, Shape, Contiguity) Overlay (Location-specific, Region-wide, Map-wide) Distance (Distance, Proximity, Movement, Optimal Path, Visual Exposure) Neighbors (Characterizing Surface Configuration, Summarizing Values) GIS Perspective: Map Analysis Toolbox Basic GridMath & Map Algebra ( + - * / ) Advanced GridMath (Math, Trig, Logical Functions) Map Calculus (Spatial Derivative, Spatial Integral) Map Geometry (Euclidian Proximity, Narrowness, Effective Proximity) 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: (Berry) Map StackGrid Layer

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_Davg …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 MapSurface Advanced Grid Math Surface Area …increases with increasing inclination as a Trig function of the cosine of the slope angle SArea= Fn(Slope) Spatial Analysis Operations (Math Examples) (Berry) D z xy Elevation 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

Spatial Analysis Operations (Distance Examples) (Berry) Map Geometry — (Euclidian Proximity, Narrowness, Effective Proximity) Plane Geometry Connectivity — (Optimal Path, Optimal Path Density) Solid Geometry Connectivity — (Viewshed, Visual Exposure) Euclidean Proximity …from a point to everywhere… Highest 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) Seen if new tangent exceeds all previous tangents along the line of sight Tan = Rise/Run Rise Run Viewshed Splash

Spatial Statistics Operations (Numeric Context) GIS as “Technical Tool” ( Where is What ) vs. “Analytical Tool” ( Why, So What and What if ) Surface Modeling (Density Analysis, Spatial Interpolation, Map Generalization) Spatial Data Mining (Descriptive, Predictive, Prescriptive) GIS Perspective: 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: (Berry) Map StackGrid Layer

Spatial Statistics (Linking Data Space with Geographic Space) Continuous Map Surface Geographic 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 Roving Window (weighted average) Spatial Statistics Histogram In Geographic Space, the typical value forms a horizontal plane implying the average is everywhere to form a horizontal plane X= 22.6 (Berry) …lots of NE locations exceed Mean + 1Stdev X + 1StDev = = 48.8 Unusually high values +StDev Average Standard Normal Curve Average = 22.6 Numeric Distribution StDev = 26.2 Non-Spatial Statistics In Data Space, a standard normal curve can be fitted to the data to identify the “typical value” (average)

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 Entire Map 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 X axis = Elevation (SNV Normalized) Y axis = Slope (SNV Normalized) Elevation vs. Slope Scatterplot Slope draped on Elevation Data Space Cluster 1 Cluster 2 Cluster 3 Two Clusters Three Clusters Cluster 1 Cluster 2 Geographic Space (Berry) Spatial Statistics Operations (Data Mining Examples)

Future Directions:  Social Acceptability as 3 rd filter/rail The Softer Side of GIS (The NR Experience) Podium Historically Ecosystem Sustainability and Economic Viability have dominated Natural Resources discussion, policy and management. But Social Acceptability has become the critical third filter needed for successful decision-making. Spatial Reasoning, Dialog and Consensus Building (Berry) Increasing Social Science & Public Involvement 1970s2010s Inter-disciplinary Science Team Table “-ists”“-ologists”

(Berry) So What’s the Point? 3) Grid-based map analysis and modeling involving Spatial Analysis and Spatial Statistics is in large part, simply extensions of traditional mathematics and statistics. 1)Current GIS education in NR for the most part insists that non-GIS students interested in understanding map analysis and modeling must be tracked into general GIS courses that are designed for GIS specialists, and that the material presented primarily focus on commercial GIS software mechanics that GIS-specialists need to know to function in the workplace. 4) The recognition by the GIS community that quantitative analysis of maps is a reality and the recognition by the STEM community that spatial relationships exist and are quantifiable should be the glue that binds the two perspectives. 2) However, solutions to complex spatial problems need to engage “domain expertise” in GIS– outreach to other disciplines to establish spatial reasoning skills needed for effective solutions that integrate a multitude of disciplinary and general public perspectives. Online Presentation Materials and References Joseph K. Berry — Handout, PowerPoint and Online References Handout, PowerPoint and Online References …also see online book Beyond Mapping III …also see online book Beyond Mapping III Handout, PowerPoint and Online References Handout, PowerPoint and Online References …also see online book Beyond Mapping III …also see online book Beyond Mapping III Handout

Slide 1, Title – This PowerPoint with notes and live links is posted online at— The following links are to the online book Beyond Mapping III posted at  Slide 2, Making a Case for SpatialSTEM – Making a Case for SpatialSTEM; A Multifaceted GIS Community; GIS Education’s Need for “Hitchhikers”; Overview of Spatial Analysis and StatisticsMaking a Case for SpatialSTEMA Multifaceted GIS CommunityGIS Education’s Need for “Hitchhikers”Overview of Spatial Analysis and Statistics  Slide 3, The “-ists” and the “-ologists” and Slide 4, (A Larger Tent) – Melding the Minds of the “-ists” and “-ologists”; The Softer Side of GIS; Fitting Square Pegs in Round GIS Education HolesMelding the Minds of the “-ists” and “-ologists”The Softer Side of GISFitting Square Pegs in Round GIS Education Holes  Slide 5, Spatial Analysis Operations (Geographic Context) – Simultaneously Trivializing and Complicating GIS; SpatialSTEM Has Deep Mathematical Roots; Understanding Grid-based Data; Suitability ModelingSimultaneously Trivializing and Complicating GIS SpatialSTEM Has Deep Mathematical RootsUnderstanding Grid-based DataSuitability Modeling  Slide 6, (Math Examples) – Map-ematically Messing with Mapped Data; Characterizing Micro-terrain Features; Reclassifying and Overlaying MapsMap-ematically Messing with Mapped DataCharacterizing Micro-terrain FeaturesReclassifying and Overlaying Maps  Slide 7, (Distance Examples) – Calculating Effective Distance and Connectivity; E911 for the Backcountry; Routing and Optimal Paths; Deriving and Using Travel-Time Maps; Deriving and Using Visual Exposure Maps; Creating Variable-Width Buffers; Applying Surface AnalysisCalculating Effective Distance and ConnectivityE911 for the BackcountryRouting and Optimal PathsDeriving and Using Travel-Time MapsDeriving and Using Visual Exposure MapsCreating Variable-Width BuffersApplying Surface Analysis  Slide 8, Spatial Statistics Operations (Numeric Context) – Infusing Spatial Character into Statistics; Paint by Numbers Outside the Traditional Statistics BoxInfusing Spatial Character into StatisticsPaint by Numbers Outside the Traditional Statistics Box  Slide 9, (Linking Data Space with Geographic Space) – Spatial Interpolation Procedures and Assessment; Linking Data Space and Geographic Space;Spatial Interpolation Procedures and AssessmentLinking Data Space and Geographic Space  Slide 10, (Data Mining Examples) – Characterizing Patterns and Relationships; Analyzing Map Similarity and ZoningCharacterizing Patterns and RelationshipsAnalyzing Map Similarity and Zoning  Slide 11, The Softer Side of GIS (The NR Experience) – GIS’s Supporting Role in the Future of Natural Resources; Human Dimensions of GISGIS’s Supporting Role in the Future of Natural ResourcesHuman Dimensions of GIS  Slide 12, So What’s the Point? – Is GIS Technology Ahead of Science?; GIS Evolution and Future Trends; Spatial Modeling in Natural ResourcesIs GIS Technology Ahead of Science?GIS Evolution and Future TrendsSpatial Modeling in Natural Resources _______________________ Additional References: (Links are posted at “Papers” item)  An Analytical Framework for GIS Modeling — white paper presenting a conceptual framework for map analysis and GIS ModelingAn Analytical Framework for GIS Modeling  GIS Modeling and Analysis— book chapter on grid-based map analysis and modelingGIS Modeling and Analysis  A Brief History and Probable Future of Geotechnology — white paper on the evolution and future directions of GIS technologyA Brief History and Probable Future of Geotechnology Additional Information (live links by slide #)