Future Directions of Map Analysis and GIS Modeling Presented by Joseph K. Berry Adjunct Faculty in...
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Transcript of Future Directions of Map Analysis and GIS Modeling Presented by Joseph K. Berry Adjunct Faculty in...
Future Directions of Map Analysis and GIS Modeling
Presented by
Joseph K. Berry
Adjunct Faculty in Geosciences, Department of Geography, University of DenverAdjunct Faculty in Natural Resources, Warner College of Natural Resources, Colorado State University
Principal, Berry & Associates // Spatial Information Systems
Email: [email protected] — Website: www.innovativegis.com/basis
Premise: There are three major forces driving map analysis/modeling— establishing a map-ematical framework (SpatialSTEM), utilizing a Universal Spatial Database Key
and radical changes in Raster Data Structure
2014 Manitoba GIS User GroupFall Conference | October 1, 2014 | Winnipeg, Manitoba, Canada
This PowerPoint with notes and online links to further reading is posted at
www.innovativegis.com/basis/Present/Manitoba2014/
Premise: There are three major forces driving map analysis/modeling— establishing a map-ematical framework (SpatialSTEM), utilizing a Universal Spatial Database Key
and radical changes in Raster Data Structure
Mapping vs. Analyzing (Processing Mapped Data)
(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)
Global Positioning System
(locate and navigate)
Remote Sensing
(measure and classify)
Geographic Information Systems
(map and analyze)
GPS/GIS/RS
Spatial Statistics Operations Spatial Analysis Operations
“Map-ematics”
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)
ArcGIS 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”
Map Stack
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: Classes of mathematical operations
Unique spatial operations
The integral calculates the
area under the curve for any section of a function.
Curve2D
Map Calculus — Spatial Derivative, Spatial IntegralAdvanced Grid Math — Math, Trig, Logical Functions
Spatial Integral
Surface3D
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 any grid location
SLOPE MapSurface Fitted FOR MapSurface_slope
Fitted Plane
Surface3D
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
Curve2D
The derivative is the instantaneous “rate of change” of a function and is equivalent to the slope of the tangent line at any point along the curve
(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)
Proximity
…from a point to everywhere (S,SL)…
HighestWeightedExposure
SumsViewerWeights
Counts # Viewers
270/621= 43% of the entire road network is connected
Visual Exposure
Distance
Shortest straight line between two points (S,SL,2P)…
Travel-TimeSurface
Effective Proximity
…not necessarily straight lines (S 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)
Farthest(end)
HQ (start) Truck = 18.8 min
ATV = 14.8 min Hiking = 62.4 min
Pythagoras500 BC
Splash Algorithm2000 AD
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)
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)
…lots of NE locations exceed Mean + 1Stdev
X + 1StDev= 22.6 + 26.2
= 48.8
Unusually high
values+StDev
Average
#1 = 4
#1 = 4
#1 = 4
Geographic SpaceX 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 1Low,Low
Cluster 2High,High
(Berry)
Spatial Statistics Operations (Data Mining Examples)
Slope(Percent)
Map Clustering:
Elevation(Feet)
Data Pairs
+
Plots here in…
Data Space
Advanced Classification (Clustering)
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
Predictive Statistics (Correlation)
The Latitude/Longitude grid forms a continuous surface for geographic referencing
where each grid cell represents a given portion of the earth’ surface.
300
90
Grid-based Map Data (geo-registered matrix of map values)2.50 Latitude/Longitude Grid (140mi grid cell size)
Coordinate of first grid cell is 900 N 00 E
AnalysisFrame(Matrix)
(Berry)
Conceptual Spreadsheet (73 x 144)
#Rows= 73 #Columns= 144
…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
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
…Spatially Keyed data in the cloud are downloaded and configured to the
Analysis Frame defining the Map Stack
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”
Universal Spatial Db Key (developing spatially-aware databases)
Lat/Lon as a
Universal Spatial Key
Once a set of mapped data is stamped with its Lat/Lon
“Spatial Db 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
in the raster grid.
(Berry)
Conceptual Organization
Elevation Surfa
ce
Spreadsheet 30m Elevation
(99 columns x 99 rows)
Keystone Concept
2D Matrix 1D Field
Spatially Keyed data in the cloud
Lat/Lon serves as a Universal dB Key for joining data tables based on location
…like a faucet spewing data
“What” = Data Value“Where” = Lat/Lon cell
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)
PentagonalDodecahedral(12 pentagons)
Hexagon(6 sides)
Radically new Data Structures & Analytics
Square(4 sides)
2D Planar(X,Y Data)
Cartesian Coordinates
(Berry)
So Where to Head from Here?
Joseph K. Berry Joseph K. Berry [email protected]@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/Manitoba2014/
Website (www.innovativegis.com)For more papers and presentations on GeotechnologyFor more papers and presentations on Geotechnology
www.innovativegis.comwww.innovativegis.com
For more papers and presentations on GeotechnologyFor more papers and presentations on Geotechnology
www.innovativegis.comwww.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).