geostatistical analyst - an introduction - esri
TRANSCRIPT
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Esri International User Conference | San Diego, CA Technical Workshops |
Geostatistical Analyst - An Introduction
Steve Lynch and Eric Krause Redlands, CA
July 2012
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Presentations of interest…
• EBK – Robust kriging as a GP tool - Tuesday 3:00pm – 3:30pm Demo theater
• Geostatistical Simulations - Tuesday 3:30pm – 4:00pm Demo theater
• Areal Interpolation – Performing polygon-to-polygon predictions - Thursday 9:00am – 9:30am Demo theater
• Surface Interpolation in ArcGIS - Wednesday 1:00pm – 2:00pm Demo theater
• Designing and Updating a Monitoring Network - Thursday 9:30am – 10:00am Demo theater
• Concepts and Applications of Kriging - Tuesday 10:15am – 11:30am 15B
• Creating Surfaces - Wednesday 8:30am – 9:45am 15A
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Outline
• What is • geostatistics? • Geostatistical Analyst?
• New in 10 and 10.1 • Interpolation workflow • Demonstrations • Supplementary information • Questions / Answers
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What is geostatistics ?
Range
Sill
Nugget
The statistics of spatially correlated data
Semivariogram
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Semivariogram
Semivariogram(distance h) = 0.5 * average [ (valuei– valuej)2]
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What is geostatistics ?
The statistics of spatially correlated data
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Geostatistical Analyst - Overview
• Interactive - Exploratory Spatial Data Analysis tools - Variography - Kriging - Other interpolation methods - Cross validation
• Geoprocessing toolbox - Interpolation - Sampling Network Design - Simulation - Utilities - Conversion
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Where is Geostatistical Analyst used?
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Where is Geostatistical Analyst used?
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• 12 independent reputable geostatisticians • Given the same data • Asked to perform the same straightforward estimation • Results were widely different • Different
- data analysis conclusions - variogram models and choice of kriging type - searching neighborhoods.
Experiment conducted by the US EPA 20 years ago Isaaks & Srivastava, 1989. An Introduction to Applied Geostatistics.
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Geostatistical Analyst – Toolbar and Toolbox
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Demonstration
Geostatistical Wizard
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What’s new in 10 – Optimize buttons
• Local Polynomial Interpolation • Kriging
- Nugget, partial sill and other(s), are optimized using cross validation with focus on the estimation of the range parameter.
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What’s new in 10.1
• Areal Interpolation - predictions can be made from one set of polygons to
another set of polygons
• Empirical Bayesian Kriging (EBK) - builds local models on subsets of the data, which are
then combined together to create the final surface.
• Normal Score Transformation - Multiplicative Skewing approximation method
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Interpolation workflow
• Exploratory Spatial Data Analysis (ESDA) • Interpolate
- estimation of values at unsampled locations based on known values
• Goodness of fit
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Exploratory Spatial Data Analysis
• Where is the data located? • What are the values at the data points? • How does the location of a point relate to its value?
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Exploratory Spatial Data Analysis (ESDA)
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Exploratory Spatial Data Analysis (ESDA)
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Kriging
• Concepts and Applications of Kriging - Tuesday 10:15am – 11:30am 15B
• Empirical Bayesian Kriging – Robust kriging as a GP tool - Tuesday 3:00 – 3:30pm Demo theater
Outline • Introduction to kriging • Best practices • Fitting a proper model • Variography, transformations, isotropy, stationarity • Comparing models using cross validation • Interpreting results
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What is kriging?
• It is a geostatistical interpolation technique • that models the spatial correlation of point measurements • to estimate values at unmeasured locations.
• Associates uncertainty with the predictions
Distance
Cor
rela
tion
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Demonstration Kriging
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Empirical Bayesian Kriging (EBK)
• automates the most difficult aspects of building a valid kriging model
• estimates the semivariogram through repeated simulations • can handle non-stationary input data.
Unlike other kriging methods (use weighted least squares), the semivariogram parameters in EBK are estimated using restricted maximum likelihood (REML).
New in ArcGIS 10.1
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For a given distance h, the semivariogram model: γ(h)= Nugget + b|h|α
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Empirical Bayesian Kriging (cont)
• Advantages - Requires minimal interactive modeling - Allows accurate predictions of non-stationary data - More accurate than other kriging methods for small datasets - Geoprocessing tool
• Disadvantages - Processing is slower than other kriging methods. - Cokriging and anisotropy are unavailable.
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Demonstration Empirical Bayesian Kriging
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Goodness of fit / Model acceptance
• Subset Features • Cross Validation
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Cressie, 1990
• Cross validation does not prove that the model is correct,
• merely that it is not grossly incorrect.
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Demonstration Cross validation
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Geostatistical layer
• Method and parameters • Pointer to the data • Dynamic
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Output = Prediction, Prediction SE, Probability, Quantile, Condition number
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Demonstration Geostatistical layer
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Areal Interpolation
• reaggregation of data from one set of polygons to another set of polygons
New in ArcGIS 10.1
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Demonstration Areal Interpolation
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Areal Interpolation Thursday 9:00am – 9:30am
Demo theater
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N = 8 N = 100 N = 500
Simple kriging
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Geostatistical Simulations Tuesday 3:30pm – 4:00pm
Demo theater
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Interpolation with Barriers
• Kernel interpolation • Diffusion interpolation
? Cost Raster
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Create Spatially Balanced Points
Sampling Network Design
• Monitor road pollution • Convert roads to raster • High value = busy road • Low value = quite road
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Create Spatially Balanced Points (cont.)
Sampling Network Design
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Densify Sampling Network
Sampling Network Design
• Used kriging to create: - Prediction surface - Standard error of prediction
• Want to add 2 new sites
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Densify Sampling Network (Cont.)
Sampling Network Design
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Designing and Updating a Monitoring Network Thursday 9:30am – 10:00am
Demo theater
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resources.arcgis.com
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http://esripress.esri.com
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