Future Directions of Map Analysis and GIS Modeling:
…where we are headed and how we get there
GIS Centroid Seminar — Colorado State University
September 19, 2014
Basis
“They who don’t know, don’t know they don’t know”
There
There is
is a
a “map-ematics”
“map-ematics” that
that extends
extends traditional
traditional math/stat
math/stat concepts
concepts
and
and procedures
procedures for
for the
the quantitative
quantitative analysis
analysis of
of map
map variables
variables (digital
(digital maps)
maps)
Presentation
Presentation Premise:
Premise:
…three major considerations will influence map analysis/modeling future development—
Mathematical Framework, Data Structure and Educational Approach
This PowerPoint with notes and online links to further reading is posted at
www.innovativegis.com/basis/Present/CentroidCSU2014/
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
Mapping vs. Analyzing
…GIS is a Technological
(Processing Mapped Data)
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)
GIS as a Technological Tool (Critical Technological Frontiers)
3D Integration
-- 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.
Real-Time GIS -- 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 -- 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)
…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”. Three major considerations will influence map analysis/modeling
future development— Mathematical Framework, Data Structure and Educational Approach.
…based on Matt Ball's blog at http://www.sensysmag.com/spatialsustain/what-are-some-of-the-technological-frontiers-for-gis-advancement.html
(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”
Esri Spatial Analyst operations
…over 170 individual “tools”
www.innovativegis.com/basis/BeyondMappingSeries/, Book IV, Topic 9 for more discussion
(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:
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 a
location
Slope draped over
MapSurface
500’
Surface
Fitted Plane
65%
SLOPE MapSurface Fitted
FOR MapSurface_slope
0%
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
Dzxy Elevation
ʃ Districts_Average Elevation
Spatial Integral
Advanced Grid Math
…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)
The integral calculates the
area under the curve for any
section of a function.
Surface
Curve
(Berry)
Spatial Analysis Operations (Distance Examples)
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
Euclidean 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
Farthest
(end)
Shortest straight line
between two points…
…from a point to
everywhere…
…not necessarily straight
lines (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
Plane Geometry
Visual Exposure
(Quickest Path)
Tan = Rise/Run
Seen if new tangent exceeds
all previous tangents
along the line of sight
 Counts
# Viewers
Sums
Viewer
Weights 
Splash
270/621= 43% of the entire
Viewshed
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
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)
(Berry)
Spatial Statistics (Linking Data Space with Geographic Space)
Roving Window (weighted average)
Geo-registered Sample Data
Spatial Distribution
Spatial
Statistics
Discrete Sample Map
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
50
Numeric Distribution
(Berry)
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
60
70
80
Unusually
high
values
X= 22.6
+StDev
Average
48.8
Spatial Statistics Operations (Data Mining Examples)
Map Clustering:
Elevation vs. Slope Scatterplot
“data pair”
of map values
“data pair”
plots here in…
Cluster 2
Data
Space
…as similar as can be WITHIN
a cluster …and as different as
can be BETWEEN clusters
Elevation
Geographic
Space
(Feet)
Slope
+
Slope
(Percent)
Slope draped
on Elevation
Elev
X axis = Elevation (0-100 Normalized)
Y axis = Slope (0-100 Normalized)
Advanced Classification (Clustering)
Map Correlation:
+
Cluster 1
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)
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)
(Berry)
Map Variable – continuous quantitative
surface represents the localized spatial
relationship between the two map surfaces
r = .432 Aggregated
Map of the Correlation
Grid-based Map Data Structure
90
(geo-registered matrix of map values)
2.50 Latitude/Longitude Grid
(140mi grid cell size)
Analysis
Frame
300
(grid “cells”)
Grid Lines
Coordinate of first grid cell is 900 N 00 E
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.
…the bottom line is that…
All spatial topology is inherent in the grid.
#Rows= 73 #Columns= 144 = 10,512 grid cells
Conceptual Spreadsheet (73 x 144)
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
grid location
(Berry)
Universal Database Key
…Spatially Keyed data in the cloud
are downloaded and configured to
the Analysis Frame
defining the Map Stack
(moving Lat/Lon from crosshairs to grid cells)
Lat/Lon serves as a Universal dB Key
Spatially Keyed
for joining data tables based on location
data in the cloud
Conceptual Organization
RDBMS Organization
Spreadsheet
30m Elevation
(99 columns x 99 rows)
“Where”
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.
Geographic
Space
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.
Universal
Spatial Key
(Berry)
Grid
Space
Wyoming’s Bighorn Mts.
2D Matrix 1D Field
Database Table
Keystone
Concept
Lat/Lon as a
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”
5-step Process for
Unlocking the Universal Spatial Db Key
Spatially Aware
Database
Step 1. User
identifies the
geographic extent
(XY, Value)
of the analysis
window.
Step 2. User
specifies the cell
size of the analysis
window. …e.g., 100m
3
9
What (Value)
…value indicates
characteristic
or condition
at a location
Where (XY)
3
13
6
0
10
…Lat/Lon coordinates
identify earth position of
a dB record
1
Longitude
Latitude
Step 3. Computer
determines the
Lat/Lon ranges
defining each grid
cell (cutoffs) and
the centroid
location. …defines
the Analysis Frame
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.
Map Stack
…but Lat/Lon grid cells are only square
at the equator—
so is the entire idea a bust?
Hint: spatial resolution of the
analysis frame is key
Shish Kebab
of numbers
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.
(Berry)
GIS Development Cycle (…where we’re heading)
Future Directions
GIS Evolution
Revisit Analytics
(2020s)
Future Directions
2D Planar
3D Solid
(X,Y Data)
(X,Y,Z Data)
Cartesian Coordinates
GeoWeb
(2000s)
Today
Today
Revisit Geo-reference
(2010s)
Square
(4 sides)
Cube
(6 squares)
Contemporary GIS
Spatial dB Mgt (1980s)
Map Analysis
Future
(1990s)
Hexagon
(6 sides)
…about every decade
Future
Pentagonal
Dodecahedral
(12 pentagons)
The Early Years
Mapping focus
Data/Structure focus
Analysis focus
Computer Mapping
(1970s)
(Berry)
GIS Education (shifting the current Technical focus to a Pedagogical focus)
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…
…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”
(Berry)
The “-ists” and the “-ologists”
Together the “-ists” and the “-ologists” frame and develop the Solution for an application.
The
“-ists”
— and —
The
“-ologists”
…understand the “tools” that can
be used to display, query and
analyze spatial data
…understand the “science” behind
spatial relationships that can be
used for decision-making
Data and Information focus
Knowledge and Wisdom focus
Application Space
Geotechnology’s Core
“-ists”
Technology
Experts
Solution
Space
“-ologists”
Domain
Experts
GIS Expertise
Spatial Reasoning
Where is What
Why, So What, What If
(Berry)
The “-ists” and the “-ologists” (toward a much bigger tent)
…Decision Makers utilize
the Solution…
…under Stakeholder,
Policy & Public
auspices
“Public”
“Policy Makers”
“Stakeholders”
“Decision Makers”
Application Space
Geotechnology’s Core
“-ists”
Technology
Experts
Solution
Space
“-ologists”
Domain
Experts
Spatial
Reasoning
GIS
Expertise
…and complicating GIS Technology
We are simultaneously trivializing…
(Berry)
Conclusions/Upshot
(moving away from your grandfather's map)
Tomorrow’s GIS arena will be radically different from the past four decades…
Computer Mapping (1970 to 1980) – 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.
Spatial Database Management Systems
(1980 to 1990)– 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).
Map Analysis and GIS Modeling
(1990 to 2000) – 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).
GeoWeb and Mobile Devices
(2000 to 2010) – 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.”
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.
Solutions to Devices – “map-ematical solutions” will be directly tied to automated devices through
continued coupling of RS, GIS, GPS and robotics.
…next time
Ag & NR considerations
3) Spatial Reasoning and Dialog – GIS models will enable decision-makers to interactively investigate and
2) Spatial
better communicate “Why, So What and What If” of the probable spatial outcomes/impacts of critical decisions.
…quantitative
mapped data analysis and modeling completely changes our perspective of “what a map is (and isn’t)”
See http://www.innovativegis.com/basis/BeyondMappingSeries/BeyondMapping_I/Epilog/BM_I_Epilog.htm for more discussion
(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/CentroidCSU2014/
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