Applied Geostatistics Miles Logsdon mlogu.washington.edu Mimi DIorio mimidu.washington.edu

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Applied GeostatisticsMiles Logsdonmlog_at_u.washin
gton.eduMimi DIoriomimid_at_u.washington.edu
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• An Introduction to Applied Geostatistics by
  Edward H. Isaaks and R. Mohan Srivastava Oxford
  University Press 1989.
• Spatial Data Analysis Theroy and Practice by
  Robert Haining Cambridge University Press 1993.
• Statistics for Spatial data by Noel a. c.
  Cressie Wiley  Sons Inc. 1991. 

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Introduction to Geostatistics

• D is the spatial domain or area of interest
• s contains the spatial coordinates
• Z is a value located at the spatial coordinates

• Z(s) s D
• Geostatistics Z random D fixed infinite
  continuous
• Lattice Models Z random D fixed finite
  (ir)regular grid
• Point Patterns Z 1 D random finite

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GeoStatistics

• A way of describing the spatial continuity as an
  essential feature of natural phenomena.
• The science of uncertainty which attempts to
  model order in disorder.
• Recognized to have emerged in the early 1980s
  as a hybrid of mathematics statistics and
  mining engineering.
• - Now extended to spatial pattern description

• Univariate
• Bivariate
• Spatial Description

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Univariate

• One Variable
• Frequency (table)
• Histogram (graph)
• Do the same thing (i.e count of observations in
  intervals or classes
• Cumulative Frequency (total below cutoffs)

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Summary of a histogram

• Measurements of location (center of distribution
• mean (m µ x )
• median
• mode
• Measurements of spread (variability)
• variance
• standard deviation
• interquartile range
• Measurements of shape (symmetry length
• coefficient of skewness
• coefficient of variation

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Bivariate
Scatterplots
Correlation
Linear Regression
slope constant
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Autocorrelation

• Values at locations that are near to each other
  are more similar than values at locations that
  are farther apart.

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Spatial Description
- Data Postings symbol maps (if only 2 classes
indicator map - Contour Maps - Moving Windows
gt heteroscedasticity (values in some region
are more variable than in others) - Spatial
Continuity (h-scatterplots
Spatial lag h (01) same x y1
h(00) h(03) h(05)
correlation coefficient (i.e the correlogram
relationship of p with h
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Lags

• Variograms How do we estimate them

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Binning Lags

• Variograms How do we estimate them

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Lets review
Geostatistics
Univariate - Bivariate - Spatial Description -
VECTOR OR RASTER

• Data Postings gt symbol maps
• Contour Maps
• Moving Windows gt heteroscedasticity
• Spatial Continuity h-scatterplots

Lag bins
Spatial Lag h distance
Values at locations that are near to each other
are more similar than values at locations that
are farther apart. Autocorrelation
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Definitions

• Variograms What are they

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• Correlogram p(h) the relationship of the
  correlation coefficient of an h-scatterplot and h
  (the spatial lag)
• Covariance C(h) the relationship of the
  coefficient of variation of an h-scatterplot and
  h
• Semivariogram variogram moment of
  inertia

OR half the average sum difference between the x
and y pair of the h-scatterplot OR for a h(00)
all points fall on a line xy OR as h
points drift away from xy
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Isotropy

• Variograms What are their features

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Anisotropy

• Variograms What are their features

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Anisotropy

• Variograms What are their features

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Anisotropy

• Variograms What are their features

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Structured Process in Geostatistics
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Physiognomy / Pattern / structure

• Composition The presence and amount of each
  element type without spatially explicit measures.
• Proportion richness evenness diversity
• Configuration The physical distribution in
  space and spatial character of elements.
• Isolation placement adjacency
• some metrics do both

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Types of Metics

• Area Metrics
• Patch Density Size and Variability
• Edge Metrics
• Shape Metrics
• Core Area Metrics
• Nearest-Neighbor Metrics
• Diversity Metrics
• Contagion and Interspersion Metrics

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Shape Metricsperimeter-area relationships

• Shape Index (SHAPE) -- complexity of patch
  compared to standard shape
• vector uses circular raster uses square
• Mean Shape Index (MSI) perimeter-to-area ratio
• Area-Weighted Mean Shape Index (AWMSI)
• Landscape Shape Index (LSI)
• Fractal Dimension (D) or (FRACT)
• log P 1/2Dlog A P perimeter A area
• P sq.rt. A raised to D and D 1 (a line)
• as polygons move to complexity P A and D -gt 2
• A few fractal metrics
• Double log fractal dimension (DLFD)
• Mean patch fractal (MPFD)
• Area-weighted mean patch fractal dimension
  (AWMPFD)

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Contagion Interspersion and Juxtaposition

• When first proposed (ONeill 1988) proved
  incorrect Li Reynolds (1993) alternative
• Based upon the product of two (2) probabilities
• Randomly chosen cell belongs to patch i
• Conditional probability of given type i
  neighboring cells belongs to j
• Interspersion (the intermixing of units of
  different patch types) and Juxtaposition (the mix
  of different types being adjacent) index (IJI)

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Changing patterns
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Flying