GIST 4302/5302: Spatial Analysis and Modeling...Peters projection mentioned in the video Equal-area...
Transcript of GIST 4302/5302: Spatial Analysis and Modeling...Peters projection mentioned in the video Equal-area...
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GIST 4302/5302: Spatial Analysis and ModelingLecture 2: Review of Map Projections and Intro to Spatial Analysis
Guofeng Caowww.myweb.ttu.edu/gucao
Department of Geosciences
Texas Tech University
Spring 2015
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Review of Map Projections
Map projections
• Elements in map projectionsI Datum (e.g., WGS84∼NAD 83, NAD 27)I Developable surfacesI Projection
• DistortionsI shape (comformal), distance, area (equivalent), directionI distortions magnitude varies across a mapI be careful of what you want to preserve
Great instructions on map projections: http:
//www.progonos.com/furuti/MapProj/CartIndex/cartIndex.html
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Mercator Projection
• One of the most commonly used map projections in wall maps
• Which of the following operations is/are suitable in Mercatorprojection?
1. navigation2. distance measuring3. nearest neighbors
• Why the air flight traces are not straight lines on a map?
• What would it really look like if drawing a line on a map withMercator projection?
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Distortions of Mercator Projection
• It usually leads to distortions in terms of shape and area
• Online map websites (e.g., Google Maps, ArcGIS online) use WebMercator, a variant of Mercator projection
• Mercator puzzle: http://gmaps-samples.googlecode.com/svn/
trunk/poly/puzzledrag.html
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Mercator Projection
• Africa in Mercator projection
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Mercator Projection
• In fact, area of Africa is about 14 times of Greenland
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Mercator Projection
• In fact, Africa is as big as the United States, China, India, Japanand all of Europe combined
Figure : Image courtesy: Kai Krause
• Scene in TV show West Wing :https://www.youtube.com/watch?v=n8zBC2dvERM
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Gall-Peters Projection
• Peters projection mentioned in the video
• Equal-area
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Other Commonly Used Projections
• UTM (Universal Traverse Mercator)
• Gnomonic (great circles as straight lines)
• Equal-area (e.g.,Lambert, Albers)
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Cartogram
• County map of 2004 US presidential election result
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Cartogram
• Equal-density cartogram of 2004 US presidential election result
Figure : Image courtesy: Gastner, Shalizi,and Newman
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Cartogram
• Equal-density: cartogram of world population in the year of 2000
Figure : Image courtesy: ESRI
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Measures and Map Projections
• Comparing results of volume measures (e.g., length and area) indifferent map projections http:
//servicesbeta.esri.com/demos/compareMeasurements.html
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Maps Lie
Maps lie, be citical when reading them!!
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Introduction to Spatial Analysis and Modeling
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Introduction to Spatial Analysis and Modeling
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Scope of Spatial Analysis and Modeling
• Data do not equal information
• Analysis of spatial data (geospatial data in particular)I Spatial data manipulation (in GIS)
I Spatial query, measurements, transformation, network analysis,location analysis (spatial optimization) . . .
I Spatial data analysisI Exploratory spatial analysisI Visual analyticsI Data-driven, let data speak themselves
I Spatial statisticsI An extension of traditional statistics into a spatial settings to
determine whether or not data are typical or unexpectedI Geostatistics: Quantify the spatial relationships between observations
of different locations for estimation of unknown locationsI Spatial modeling
I Involves constructing models to predict spatial outcomesI Only focus on spatial statistical modeling
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Topics
• Spatial data representation and manipulationI Buffer, spatial query, overlay analysis (lab 2-3)I Surface analysis and map algebra (lab 6)
• Point pattern analysis (lab 4)
• Spatial statisticsI Spatial autocorrelation (lab 5)I Spatial regression (lab 8)
• Spatial interpolationI Deterministic interpolation (lab 6)I Kriging (lab 7)
• Spatial uncertainty
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Characteristics of (Geographic) Spatial Data
1. Spatial (and temporal) Context: “Everything is related to everythingelse, but near things are more related than distant things”
I Waldo Toblers First Law (TFL) of geographyI nearby things are more similar than distant thingsI phenomena vary slowly over the Earth’s surfaceI Compare time series
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Characteristics of (Geographic) Spatial Data
• Implication of Tobler’s First Law (TFL)I We can do samplings and fill the gap using estimation procedures
(e.g. weather stations)I Spatial patternsI Image a world without TFL:
I White noiseI No lines, polygons or geometry (how to draw a polygon on a white
noise map?)
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Characteristics of (Geographic) Spatial Data
2. Spatial heterogeneityI “Second law of geography” (Goodchild, UCGIS 2003)I Earths surface is non-stationaryI Laws of physical sciences remain constant, virtually everything else
changesI Elevation,I Climate, temperaturesI Social conditions
I ImplicationsI Global model might be inconsistent with regional modelsI Spatial Simpsons Paradox (a special case of modified areal unit
problem, which we will discuss more in the later of this class)
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Characteristics of (Geographic) Spatial Data
Side note: example of Simpson’s paradox
• Simpson’s paradox usually fools us on tests of performance in real life
• The following is a real life example. Comparison of recovery ratesbetween a new treatment and a traditional treatment for kidneystones.
New Treatment Traditional TreatmentSmall Stones 93%(81/87) 87%(234/270)Large Stones 73%(192/263) 69%(55/80)
All 78%(273/350) 83%(289/350)
• Comparison of batting average of two baseball players:
1996 1997 CombinedDerek Jeter 25.0%(12/48) 31.4%(183/582) 31.0%(195/630)
David Justice 25.3%(104/411) 32.1%(45/140) 27.0%(149/551)
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Characteristics of (Geographic) Spatial Data
• In a spatial settings, it is related to modified areal unit problem(MAUP) or omitted variable problem, which will discuss more in thelater of this class
Figure : Image Courtesy of OpenShaw
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Characteristics of (Geographic) Spatial Data
3. Fractal behaviorI What happens as scale of map changes?I Coast of Maine
• ImplicationsI Scale is critical for the problem of studyI Volume of geographic features tends to be underestimated
I length of linesI area of polygons
I Think of the difference of distances that an ant and elephant neededto travel from where I stand to the center of memorial circle
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Microscale or Macroscale
Please try to tell whether the following maps are micro- ormacro-scale:
• http://www.smithsonianmag.com/science-nature/
macro-or-micro-test-your-sense-of-scale-2208824/
?no-ist=
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Characteristics of (Geographic) Spatial Data
Summary: three interrelated characteristics of spatial data
• Spatial context/spatial pattern/spatial structure/spatialdependence/spatial texture..
• Spatial heterogeneity/locality
• Fractal behaviors/scaling effects
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Elements of Spatial Data
Elements
• Georeferenced measurements (point or area/region specific samples)Spatial arrangement: regular or irregular (gridded or scatteredsampling locations)
• variables/attributes: continuous or discrete (e.g., chemicalconcentration, soil types, disease occurrences)
• auto- and cross-correlation endemic to spatial data (Toblers first lawof Geography)
Types of spatial data
• Point pattern data
• Areal data
• Geostatisticla data
• Spatial interaction or network data
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Types of Spatial Data: Geostatistical Data
Geostatistical data
• Attributes vary continuously in space, e.g., temperature, rainfall,elevation
• Measurements of nominal scale (e.g., soil types), or interval/ratioscale (e.g., depth of boreholes)
• Sampling only at fixed set of locations
• Occurs often in physical-related sciences
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Types of Spatial Data: Geostatistical Data
Example: 300 randomly placed points
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Types of Spatial Data: Geostatistical Data
Objective
• Mapping spatial variations of regional variables
• Make estimation at unsampled locations
Example: elevation surface generated from 300 points
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Types of Spatial Data: Areal Data
Areal (lattice) data
• attributes take values only at fixed set of areas or zones, e.g.,administrative districts, pixels of satellite images
• Attributes distribute homogeneously within a region
• Lattice or uniform raster data could be taken as a special case ofthis type of data
Example:
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Types of Spatial Data: Areal Data
Objective
• Detect and model spatial patterns or trends in areal values
• Use covariates or relationships with adjacent areal values forinference (e.g., disease rates in light of socioeconomic variables)
Example:
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Types of Spatial Data: Areal Data
Example 2: find the correlation among maps
• It is analog to the cases in traditional statistics, but each variable is(multidimensional) ‘maps’ instead of single ’numbers’
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Types of Spatial Data: Point Pattern Data
Point pattern data
• series of point locations with recorded events, e.g., locations oftrees, epic centers, disease or crime incidents
• attribute values also possible at same locations, e.g., tree diameter,magnitude of earthquakes (marked point pattern)
Example
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Types of Spatial Data: Point Pattern Data
Objective
• detect clustering or regularity, as opposed to complete randomness,of event locations (in space and time)
• If abnormal clustering detected, investigate possible relations withpotential factors, e.g., density of disease occurrences withsocio-economic status
• Difference with geostatistical point data
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Types of Spatial Data: Point Pattern Data
Example:
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Types of Spatial Data: Spatial Interaction or Network Data
Spatial interaction or network data
• Topological space (not Euclidean space )
• Attributes relate to pairs of points or areas: flows from origins todestinations, e.g., population migrating from CA to TX
• Mostly interested in spatial patterns of aggregate interaction, ratherthan individuals themselves
• Not a major topic of this class
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Types of Spatial Data: Spatial Interaction or Network Data
Objective
• Modeling of flow patterns
• Mostly interested in spatial patterns of aggregated interaction,rather than individual behaviors
Example
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Types of Spatial Data: Spatial Interaction or Network Data
Example
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Types of Spatial Data: Summary
Summary
• Geostatistical data
• Spatial point pattern
• Areal (lattice) data
• Spatial interaction/network data
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Representation of Spatial Data
Spatial datatase
• Before we could conduct any analysis on these data, we need to firstunderstand
I how these data are represented in GIS databases (e.g., shape files)I how to to query what are needed from the databases
Guofeng Cao, Texas Tech GIST4302/5302, Lecture 2: Review of Map Projections and Intro to Spatial Analysis 41/41