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 UniversityAdjunct 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

Mapping vs. Analyzing (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)

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, suchas 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 decisionmakers 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.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

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-basedMap 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/, 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”

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

The integral calculates the

area under the curve for any section of a function. Curve

Map Calculus — Spatial Derivative, Spatial IntegralAdvanced 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 overMapSurface

0%

65%

Spatial Derivative

…is equivalent to the slope of the tangent plane at a location

SLOPE MapSurface Fitted FOR MapSurface_slope

Fitted PlaneSurface

500’

2500’

MapSurface

Advanced Grid Math

Surface Area

…increases with increasing inclination as a Trig function of the cosine of the slopeangle

S_Area= Fn(Slope)

Spatial Analysis Operations (Math Examples)

Dzxy Elevation

S_area= cellsize / cos(Dzxy 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)

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…

HighestWeightedExposure

SumsViewerWeights

Counts # Viewers

270/621= 43% of the entire road network is connected

Visual Exposure

Distance

Shortest straight line between two points…

Travel-TimeSurface

Effective Proximity

…not necessarily straight lines (movement)

HQ (start)On Road

26.5 minutes

…farthest away by truck

Off RoadAbsolute Barrier

On + Off Road

96.0 minutes

…farthest away by truck, ATV and hiking

Off RoadRelative Barriers

Plane Geometry

Connectivity

…like a raindrop, the “steepest downhillpath” identifies the optimal route(Quickest Path)

Farthest(end)

HQ (start) Truck = 18.8 min

ATV = 14.8 min Hiking = 62.4 min

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

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

SpatialStatistics

Histogram

706050403020100 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)

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

Slo

pe

Elev

Entire MapExtent

Spatially Aggregated CorrelationScalar Value – one value represents the overall non-spatial relationship between the two map surfaces

…where x = Elevation value and y = Slope valueand 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 CorrelationMap 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

Grid-based Map Data Structure (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 2.50 grid cell is about 140mi x 140mi

18,735mi2…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 squareanywhere 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.

300

Grid Lines

90

2.50 Latitude/Longitude Grid (140mi grid cell size)

Coordinate of first grid cell is 900 N 00 E

AnalysisFrame

(grid “cells”)

Database Table

Geographic Space

GridSpace

“Where”

RDBMS Organization

Data SpaceEach 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 Key (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 belinked 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 Surfa

ce

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

What (Value)

…value indicatescharacteristicor 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

11

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1111 8844

1111

99

1313

66

1515 77

4499

22

22

2020

121244

00

11

1313

33

77

101000

33

11 77

2266

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 Kebabof numbers

Map Stack

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

PentagonalDodecahedral(12 pentagons)

Today

Future

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 analyticallywith maps”

GIS Education (shifting the current Technical focus to a Pedagogical focus)

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 “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

“Public”…under Stakeholder,

Policy & Public auspices

“Policy Makers”

The “-ists” and the “-ologists” (toward a much bigger tent)

“Stakeholders”

“Decision Makers”

TechnologyExperts

“-ists”DomainExperts

“-ologists”Solution

Space

Application SpaceGeotechnology’s Core

…Decision Makers utilize

the Solution…

(Berry)

Spatial Reasoning

GIS Expertise

We are simultaneously trivializing… …and complicating GIS Technology

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 discussion

…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

So Where to Head from Here?

Joseph K. Berry Joseph K. Berry jberry@innovativegis.comjberry@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/

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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).