Lecture-9_Bb_1SlidePerPage - Spatial Analysis III Spatial...

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Unformatted text preview: Spatial Analysis III Spatial Analysis III Density Estimation Measurements Descriptive Summaries Density Estimation Densit Spatial Interpolation’s Cousin Spatial Interpolation creates interpolated points from known samples. Density Estimation does this also. Estimation does this also How do they differ? Spatial Interpolation strives to fill in the Interpolation strives to fill in the _______ of a continuous field • e.g. a point upon a hillside that has not been directly observed Density estimation, on the other hand, creates a _______ from _______ objects. • The field’s value at any point is an _______ of the _______ of discrete objects at that point. Density Estimation Densit A continuous field measured at eight irregularly spaced sample points 75 75 54 72 69 OR… 73 Eight discrete objects with nothing but nothing but empty space between them. 68 57 66 Density Estimation Densit Appropriate Application Spatial Interpolation techniques should not Interpolation techniques should not be applied to _______ objects. Similarly, Density Estimation techniques should not be applied to should not be applied to _______ fields. fields Consider the techniques you have learned in the past for mapping density (Population, for example) (P Dot Density Mapping • Effective, but your objects remain _______ Choropleth Mapping • Though your mapping units may be _______, they remain _______. • Internal _______ within your (arbitrary) mapping unit is _______ by the areal averaging process! Density Estimation Densit Removal of _______ is the last thing that we would want when searching for a geographic _______! Fortunately, thanks to GIS, we are not thanks to GIS we are not confined to these parameters. While Choropleth maps have always been popular due to their relative ease of preparation, GIS has permitted us to map density upon more localized scale density upon a more localized scale. • We are no longer forced to describe density upon a arbitrary (national/state/county) scale! Density Estimation Densit Thus, rather than discussing Population Density in the th traditional sense, we should discuss the Population density of discuss the Population density of varying varying _______ __________ Consider Palm Beach County: Palm Beach County: • Land Area – 2,023 mi2 • Population – 1,287,987 people • Population Density = 637 people/mi2 – Does this adequately describe the distribution of people within our county? – It would be far superior to analyze density at a greatly reduced _______ __________ Density Estimation Densit These reduced spatial resolutions are computed as a ______ ______ about the discrete point. The shape of the th kernel is dependant upon a _______ parameter. • Increasing the distance produces a broader, broader, flatter shape These kernels are A typical kernel function then then _______ to produce to produce a composite _______ Density Estimation Densit The __________ of the resulting field depends on the width of the field depends on the width of the kernel kernel The kernels should _______ together to produce a continuous surface (right) If the distance parameter is too low, the kernels will remain di discrete objects (below) (b Density Estimation Densit In ArcMap, Spatial Analyst, Density Density Density Estimation Densit Calculating Density with Spatial Analyst As you can see, Spatial Analyst permits either Simple or Kernel permits either ‘Simple’ or ‘Kernel’ density calculations Density Estimation Densit Calculating Density with Spatial Analyst __________ density • Points or lines that li th fall within the search area are summed, then th divided by the search area size to get each cell's density value. Density Estimation Densit Calculating Density with Spatial Analyst Analyst _______ density • The values associated with each point are spread out, starting from the point location, to the specified radius. • The density is greatest at the point location and diminishes to zero when reaching the specified radius. Measurements Many tasks require measurement from maps maps Measurement of distance, area Such measurements are tedious and measurements are tedious and inaccurate if made by hand Measurement using GIS tools and Measurement using GIS tools and digital digital databases is _______, _______, and _______ It was this ability that led the Canadian government to fund the development of the world first GIS CGIS in mid world’s first GIS, CGIS, in mid-1960s Measurements Measurement of Length _______ • A rule for determining distance between points in space. Pythagorean/Straight-line Metric: • Simplest Metric • The shortest distance between two points (x1, y1) and (x2,y2) on flat plane is the (x1, y1) and (x2,y2) on a flat plane is the hypotenuse of a right-angled triangle: D= – (The square of the hypotenuse is equal to the sum of the squares of the other two sides) Measurements Measurement of Length (Cont.) Pythagorean/Straight-line Metric: • This is only suitable when working with a _______ projection projection. – i.e. the surface of the Earth is NOT accounted for. Network distance: • Most trips do not occur upon a straight line basis. • Thus, the _______ distance of network segments along a travel route must be calculated travel route must be calculated • Each segment is calculated using the Pythagorean metric. Measurements Measurement of Length (Cont.) The Great Circle metric: • Gives the _________ ___________ (the Great Circle distance) between two points on spherical globe distance) between two points on a spherical globe. Decimal Degrees: r * acos[sin(lat1) * sin(lat2) + cos(lat1) * cos(lat2) * cos(lon2 - lon1)] r=6378.7 (kilometers); r=3963.0 (normal miles) (http://www.meridianworlddata.com/Distance(http://www.meridianworlddata.com/Distance-Calculation.asp) Measurements Issues with Length Measurement The abstracted Polyline is never a perfect representation of the real world equivalent. It will always tend to cut _______ will always tend to cut The length of a Polyline tends to be ______ than the length of the object it represents • The exception to this rule are those cases where the object truly is _______ : Surveyed Features (Buildings, roads, parcel boundaries) Measurements Issues with Length Measurement Measurements in GIS will usually be based upon 2-D features. • In these cases, an _________ surface will NOT be accounted for. • Thus the measurement reported may be substantially _______ than reality Measurements Measurement of Area Measuring area is superficially obvious but difficult in practice In GIS, it is based on coordinates of polygon vertices • Breaks _______ shapes into a series of trapezia • The area of these is area of these is then calculated and summed. Measurements Measurement of Shape Shape is a property of many objects of interest in geography • CBD, electorate district, habitat patch, etc. The description of which may be verbal… Measurements Shape & Gerrymandering The 12th Congressional District of NC was drawn in 1992 using a GIS, Designed to be majority Designed to be a majority-minority district: with a district: with majority of African American voters, expected to return an African American to Congress. This objective was achieved at the cost of a very contorted shape contorted shape. The U.S. Supreme Court eventually rejected the design. Measurements Measurement of Shape A common measurement is: S = P/ 3.54 x SQRT(A) where, P- perimeter, A- area • Normalized, the compactness of a circle is _____ • The more contorted more contorted the area, the ______ the shape measure Descriptive Summaries Descri Attempt to summarize useful properties of data sets in one or properties of data sets in one or two two statistics Descriptive summaries can borrow summaries can borrow many concepts and techniques from non-spatial statistics • especially when they are used for non-spatial attributes when they are used for non attributes However, caution should be applied when using them for spatial attributes attributes • For example, many statistical techniques are designed to make inferences about a larger population based upon the assumption that you are working with a _______ and _______ sample. • However, most geographic data sets are neither of these Descriptive Summaries Descri The Centroid or Mean Center The point at which an imaginary, flat, weightless, and rigid map would _______ perfectly if weights of if weights of identical value were placed on it so that each weight represented the location of a single entity within a population. Descriptive Summaries Descri The Centroid or Mean Center Found for a point set by taking the weighted ______ of coordinates coordinates • Each enumeration unit has a Centroid with an x,y coordinate • Each of these is weighted by of these is weighted by the population in question • The mean of these weights is then achieved by dividing by the sum of the weights. While a single centroid may seem boring, a set of centroids may provide useful insights. i ht Florida’s Hispanic Population Centroid Florida’s Total Population Centroid Descriptive Summaries Descri The Point of Minimum Aggregate Travel (MAT) (MAT) MAT point minimizes the sum of _______ from each point to the center (MAT point) from each point to the center (MAT point) MAT point may be a good candidate point to _______ any _______ service, • e.g. schools, hospitals, stores, fire stations, government centers No simple mathematical expression for MAT • It must be found by a trial-and-error process of iteration: • An initial guess is successively improved using a suitable algorithm Descriptive Summaries Descri Dispersion Used to measure the _______ of points around a center. • i.e. The antithesis to clustering. Mean distance from the centroid is a simple measure of dispersion in 2-D di Descriptive Summaries Descri Measures of Pattern The distribution of points may be either: • _______ – Points are located independently, and all locations are equally likely. • _______ – Some locations are more likely than others, and the presence of one point may _______ others to its vicinity vicinity. – Identification of clustering is the necessary first step prior to the isolation of a _______ for clustering. – e.g. The spread of some disease, The spread of some disease Symbiotic organisms Descriptive Summaries Descri Measures of Pattern Distribution of points may be either (Cont.): • _______ – The presence of one point may make others _______ likely in its vicinity. – Such patterns are commonly the result of patterns are commonly the result of _________ for space. – i.e. The presence of one population inhibits the presence of another. presence of another. – Organisms, retail outlets, etc. These patterns can be identified th through various statistical methods statistical methods Descriptive Summaries Descri Fragmentation Statistics Measure the degree of fragmentation of spatial data sets Useful in landscape ecology, forestry in landscape ecology forestry etc. • Habitat fragmentation affects the success of certain species (particularly major predators) • Plant/animal populations are less likely to _______ in highly fragmented landscapes that have potentially _________ regions in between habitable _______ in between habitable Various Indices of Fragmentation: • Number of patches • Size distribution • Average shape of patches (for each class) Descriptive Summaries Descri Fragmentation Statistics Three images of part of the state of Rondonia in the state of Rondonia in Brazil, for 1975, 1986, and 1992. Note the increasing fragmentation of the natural habitat as natural habitat as a result of settlement. ...
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