Future Directions of Map Analysis and GIS Modeling
2014 Manitoba GIS User Group
Fall Conference | October 1, 2014 | Winnipeg, Manitoba, Canada
Premise: There are three major forces driving map analysis/modeling— establishing a
Premise: There
are three
major forces driving
map
analysis/modeling—
a
map-ematical
framework
(SpatialSTEM)
, utilizing
a Universal
Spatial establishing
Database Key
map-ematical framework
(SpatialSTEM)
utilizing a
Universal
Spatial Database Key
and radical
changes in, Raster
Data
Structure
and radical changes in Raster Data Structure
This PowerPoint with notes and online links to further reading is posted at
www.innovativegis.com/basis/Present/Manitoba2014/
Presented by
Joseph K. Berry
Adjunct Faculty in Geosciences, Department of Geography, University of Denver
Adjunct Faculty in Natural Resources, Warner College of Natural Resources, Colorado State University
Principal, Berry & Associates // Spatial Information Systems
Email: jberry@innovativegis.com — Website: www.innovativegis.com/basis
Mapping vs. Analyzing (Processing Mapped Data)
…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
…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
“Analyze”
“Map”
(Descriptive Mapping)
Geographic Information
Systems
(Prescriptive Modeling)
(map and analyze)
Remote
Sensing
Global Positioning
System
(locate and navigate)
(Biotechnology)
GPS/GIS/RS
(measure and classify)
(Nanotechnology)
(Berry)
A Mathematical Structure for Map Analysis/Modeling
Technological Tool
Mapping/Geo-Query
Geotechnology
(Discrete, Spatial Objects)
 RS – GIS – GPS
(Continuous, Map Surfaces)
Analytical Tool
Map Analysis/Modeling
Geo-registered
Analysis Frame  Matrix
Map Stack
“Map-ematics”
of Numbers
Maps as Data, not Pictures
Vector & Raster — Aggregated & Disaggregated
Qualitative & Quantitative
…organized set of numbers
Grid-based
Spatial Analysis
Operations
Map Analysis
Toolbox
Spatial Statistics
Operations
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”
ArcGIS Spatial Analyst operations
www.innovativegis.com/basis/BeyondMappingSeries/, Book IV, Topic 9 for more discussion
…over 170 individual “tools”
(Berry)
Spatial Analysis Operations (Geographic Context)
GIS as “Technical Tool” (Where is What) vs. “Analytical Tool” (Why, So What and What if)
Grid Layer
Map Stack
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
Map Analysis Toolbox
Unique spatial
operations
Mathematical Perspective: Classes of mathematical operations
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)
(Berry)
Spatial Analysis Operations (Math Examples)
Advanced Grid Math — Math, Trig, Logical Functions
Map Calculus — Spatial Derivative, Spatial Integral
Spatial Derivative
MapSurface
2500’
…is equivalent to the slope
of the tangent plane
at any grid location
Slope draped over
MapSurface
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
500’
Surface
3D
Fitted Plane
65%
Curve
SLOPE MapSurface Fitted
FOR MapSurface_slope
0%
2D
Dzxy Elevation
ʃ Districts_Average Elevation
Advanced Grid Math
Spatial Integral
…summarizes the values on a
surface for specified map areas
(Total= volume under the surface)
Surface Area
S_Area=
Fn(Slope)
…increases with
increasing inclination
as a Trig function of
the cosine of
the slope
angle
COMPOSITE Districts WITH MapSurface
Average FOR MapSurface_Davg
MapSurface_Davg
S_area= cellsize / cos(Dzxy Elevation)
Surface
3D
The integral calculates the
area under the curve for any
section of a function.
Curve
2D
(Berry)
Spatial Analysis Operations (Distance Examples)
Pythagoras
500 BC
96.0 minutes
Map Geometry — (Euclidian Proximity, Effective Proximity, Narrowness)
Plane Geometry Connectivity — (Optimal Path, Optimal Path Density)
Solid Geometry Connectivity — (Viewshed, Visual Exposure)
Distance
Proximity
…farthest away by truck,
ATV and hiking
Effective Proximity
Off Road
Relative Barriers
HQ (start)
On Road
26.5 minutes
Off Road
Absolute Barrier
…farthest away
by truck
On + Off Road
Travel-Time
Surface
Splash Algorithm
2000 AD
Farthest
(end)
Shortest straight line between
two points (S,SL,2P)…
…from a point to
everywhere (S,SL)…
…not necessarily straight
lines (S movement)
Connectivity
HQ
Truck = 18.8 min
ATV = 14.8 min
Hiking = 62.4 min
(start)
…like a raindrop, the
“steepest downhill
path” identifies the
optimal route
Solid Geometry Connectivity
Rise
Run
Visual Exposure
(Quickest)
Tan = Rise/Run
Seen if new tangent exceeds
all previous tangents
along the line of sight
Plane Geometry
 Counts
# Viewers
Sums
Viewer
Weights 
Splash
Viewshed
270/621= 43% of the entire
road network is connected
Highest
Weighted
Exposure
(Berry)
Spatial Statistics Operations (Numeric Context)
GIS as “Technical Tool” (Where is What) vs. “Analytical Tool” (Why, So What and What if)
Grid Layer
Map Stack
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
Map Analysis Toolbox
Unique spatial
operations
(Berry)
Statistical Perspective:
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)
Spatial Statistics (Linking Data Space with Geographic Space)
Geo-registered Sample Data
Roving Window (weighted average)
#1 = 4
Spatial Distribution
Spatial
Statistics
#1 = 4
Discrete Sample Map
#1 = 4
Non-Spatial Statistics
Continuous Map Surface
Surface Modeling techniques are used to derive a continuous map surface
from discrete point data– fits a Surface to the data (maps the variation).
Standard Normal Curve
Average = 22.6
In Geographic Space, the typical value
forms a horizontal plane implying
the average is everywhere
StDev =
26.2
Histogram
(48.8)
10
20
30
40
X + 1StDev
= 22.6 + 26.2
=
In Data Space, a
standard normal curve can
be fitted to the data to identify
the “typical value” (average)
0
…lots of NE locations
exceed Mean + 1Stdev
50
Numeric Distribution
60
70
80
Unusually
high
values
48.8
X= 22.6
+StDev
Average
(Berry)
Spatial Statistics Operations (Data Mining Examples)
Map Clustering:
Elevation vs. Slope Scatterplot
Data Pairs
Cluster 2
Plots here in…
High,High
Data
Space
Elevation
Geographic
Space
(Feet)
Slope
+
Slope
(Percent)
Cluster 1
Low,Low
Elev
X axis = Elevation (0-100 Normalized)
Y axis = Slope (0-100 Normalized)
Advanced Classification (Clustering)
Map Correlation:
+
Slope draped
on Elevation
Geographic Space
Data Space
Spatially Aggregated Correlation
Scalar Value – one value represents the overall non-spatial relationship
between the two map surfaces
Roving Window
…1 large data table
Entire Map
Extent
Elevation
(Feet)
Slope
(Percent)
r = .432 Aggregated
with 25rows x 25 columns =
625 map values for map wide summary
r=
…where x = Elevation value and y = Slope value
and n = number of value pairs
…625 small data tables
within 5 cell reach =
81map values for localized summary
Localized Correlation
Predictive Statistics (Correlation)
Map Variable – continuous quantitative
surface represents the localized spatial
relationship between the two map surfaces
(Berry)
Grid-based Map Data (geo-registered matrix of map values)
2.50 Latitude/Longitude Grid
(140mi grid cell size)
90
Analysis
Frame
(Matrix)
300
Coordinate of first grid cell is 900 N 00 E
#Rows= 73 #Columns= 144
Conceptual Spreadsheet (73 x 144)
The Latitude/Longitude grid forms a
continuous surface for geographic referencing
where each grid cell represents a given
portion of the earth’ surface.
-------------------------------------------------------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.
Lat/Lon
…each 2.50 grid cell is
about 140mi x 140mi
18,735mi2
…maximum Lat/Lon
decimal degree resolution
is a four-inch square
anywhere in the world
…from Lat/Lon
“crosshairs
to grid cells”
that contain map
values indicating
characteristics or
conditions at each
location
(Berry)
Universal Spatial Db Key (developing spatially-aware databases)
…Spatially Keyed data in the cloud are
downloaded and configured to the
Analysis Frame defining the Map Stack
…like a faucet
spewing data
Lat/Lon serves as a Universal dB Key
Spatially Keyed
for joining data tables based on location
data in the cloud
“What” = Data Value
“Where” = Lat/Lon cell
Conceptual Organization
RDBMS Organization
Spreadsheet
30m Elevation
(99 columns x 99 rows)
“Where”
Geographic
Space
Grid
Space
2D Matrix 1D Field
Database Table
Keystone
Concept
Once a set of mapped data is
stamped with its Lat/Lon
“Spatial Db 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
in the raster grid.
(Berry)
Lat/Lon as a
Universal
Spatial Key
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”
GIS Development Cycle (…where we’re heading)
Radically new
Data Structures & Analytics
GIS Evolution
Revisit Analytics
(2020s)
Future Directions
2D Planar
3D Solid
(X,Y Data)
(X,Y,Z Data)
Cartesian Coordinates
GeoWeb
(2000s)
Revisit Geo-reference
(2010s)
Square
(4 sides)
Cube
(6 squares)
Hexagon
(6 sides)
Pentagonal
Dodecahedral
(12 pentagons)
Contemporary GIS
Spatial dB Mgt (1980s)
Map Analysis
…about every decade
(1990s)
The Early Years
Mapping focus
Data/Structure focus
Analysis focus
Computer Mapping
(1970s)
(Berry)
So Where to Head from Here?
Website (www.innovativegis.com)
Online Materials
(www.innovativegis.com/Basis/Courses/SpatialSTEM/)
For more papers and presentations
on Geotechnology
)
www.innovativegis.com
This PowerPoint with notes and online links to further reading is posted at
www.innovativegis.com/basis/Present/Manitoba2014/
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).
eMail Contact
Joseph K. Berry
jberry@innovativegis.com