Geostatistical Analyst - An Introduction
Esri International User Conference | San Diego, CA Technical Workshops | July 2012
Geostatistical Analyst An Introduction Steve Lynch and Eric Krause Redlands, CA
Presentations of interest… •
EBK – Robust kriging as a GP tool -
•
Geostatistical Simulations -
•
Thursday 9:30am – 10:00am Demo theater
Concepts and Applications of Kriging -
•
Wednesday 1:00pm – 2:00pm Demo theater
Designing and Updating a Monitoring Network -
•
Thursday 9:00am – 9:30am Demo theater
Surface Interpolation in ArcGIS -
•
Tuesday 3:30pm – 4:00pm Demo theater
Areal Interpolation – Performing polygon-to-polygon predictions -
•
Tuesday 3:00pm – 3:30pm Demo theater
Tuesday 10:15am – 11:30am 15B
Creating Surfaces -
Wednesday 8:30am – 9:45am 15A
Outline
• What is • geostatistics? • Geostatistical Analyst? • New in 10 and 10.1 • Interpolation workflow • Demonstrations • Supplementary information • Questions / Answers
What is geostatistics ?
The statistics of spatially correlated data
Semivariogram Sill
Nugget Range
Semivariogram Semivariogram(distance h) = 0.5 * average [ (valuei– valuej)2]
What is geostatistics ?
The statistics of spatially correlated data
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
Where is Geostatistical Analyst used?
Where is Geostatistical Analyst used?
Experiment conducted by the US EPA 20 years ago Isaaks & Srivastava, 1989. An Introduction to Applied Geostatistics.
•
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.
Geostatistical Analyst – Toolbar and Toolbox
Geostatistical Wizard Demonstration
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.
What’s new in 10.1 •
Areal Interpolation -
•
Empirical Bayesian Kriging (EBK) -
•
predictions can be made from one set of polygons to another set of polygons 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
Interpolation workflow •
Exploratory Spatial Data Analysis (ESDA)
•
Interpolate -
•
estimation of values at unsampled locations based on known values
Goodness of fit
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?
Exploratory Spatial Data Analysis (ESDA)
Exploratory Spatial Data Analysis (ESDA)
Kriging •
Concepts and Applications of Kriging -
Tuesday 10:15am – 11:30am 15B
Outline • Introduction to kriging • Best practices • Fitting a proper model • Variography, transformations, isotropy, stationarity • Comparing models using cross validation • Interpreting results
•
Empirical Bayesian Kriging – Robust kriging as a GP tool -
Tuesday 3:00 – 3:30pm Demo theater
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
Correlation
•
Distance
Kriging Demonstration
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
For a given distance h, the semivariogram model: γ(h)= Nugget + b|h|α
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.
Empirical Bayesian Kriging Demonstration
Goodness of fit / Model acceptance
•
Subset Features
•
Cross Validation
Cressie, 1990
•
Cross validation does not prove that the model is correct,
•
merely that it is not grossly incorrect.
Cross validation Demonstration
Geostatistical layer
•
Method and parameters
•
Pointer to the data
•
Dynamic
Output = Prediction, Prediction SE, Probability, Quantile, Condition number
Geostatistical layer Demonstration
Areal Interpolation •
reaggregation of data from one set of polygons to another set of polygons
New in ArcGIS 10.1
Areal Interpolation Demonstration
Demo theater Areal Interpolation Thursday 9:00am – 9:30am
Simple kriging
N = 500 100 8
Demo theater Geostatistical Simulations Tuesday 3:30pm – 4:00pm
Interpolation with Barriers
•
Kernel interpolation
•
Diffusion interpolation
? Cost Raster
Create Spatially Balanced Points •
Monitor road pollution
•
Convert roads to raster
•
High value = busy road
•
Low value = quite road
Sampling Network Design
Create Spatially Balanced Points (cont.)
Sampling Network Design
Densify Sampling Network •
•
Used kriging to create: -
Prediction surface
-
Standard error of prediction
Want to add 2 new sites
Sampling Network Design
Densify Sampling Network (Cont.)
Sampling Network Design
Demo theater Designing and Updating a Monitoring Network Thursday 9:30am – 10:00am
resources.arcgis.com
http://esripress.esri.com
• Thank you for attending • Have fun at UC2012 • Open for Questions • Please fill out the evaluation: www.esri.com/ucsessionsurveys First Offering ID: 637 Second Offering ID: 812
Geostatistical Analyst An Introduction Steve Lynch and Eric Krause Redlands, CA
Presentations of interest… •
EBK – Robust kriging as a GP tool -
•
Geostatistical Simulations -
•
Thursday 9:30am – 10:00am Demo theater
Concepts and Applications of Kriging -
•
Wednesday 1:00pm – 2:00pm Demo theater
Designing and Updating a Monitoring Network -
•
Thursday 9:00am – 9:30am Demo theater
Surface Interpolation in ArcGIS -
•
Tuesday 3:30pm – 4:00pm Demo theater
Areal Interpolation – Performing polygon-to-polygon predictions -
•
Tuesday 3:00pm – 3:30pm Demo theater
Tuesday 10:15am – 11:30am 15B
Creating Surfaces -
Wednesday 8:30am – 9:45am 15A
Outline
• What is • geostatistics? • Geostatistical Analyst? • New in 10 and 10.1 • Interpolation workflow • Demonstrations • Supplementary information • Questions / Answers
What is geostatistics ?
The statistics of spatially correlated data
Semivariogram Sill
Nugget Range
Semivariogram Semivariogram(distance h) = 0.5 * average [ (valuei– valuej)2]
What is geostatistics ?
The statistics of spatially correlated data
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
Where is Geostatistical Analyst used?
Where is Geostatistical Analyst used?
Experiment conducted by the US EPA 20 years ago Isaaks & Srivastava, 1989. An Introduction to Applied Geostatistics.
•
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.
Geostatistical Analyst – Toolbar and Toolbox
Geostatistical Wizard Demonstration
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.
What’s new in 10.1 •
Areal Interpolation -
•
Empirical Bayesian Kriging (EBK) -
•
predictions can be made from one set of polygons to another set of polygons 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
Interpolation workflow •
Exploratory Spatial Data Analysis (ESDA)
•
Interpolate -
•
estimation of values at unsampled locations based on known values
Goodness of fit
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?
Exploratory Spatial Data Analysis (ESDA)
Exploratory Spatial Data Analysis (ESDA)
Kriging •
Concepts and Applications of Kriging -
Tuesday 10:15am – 11:30am 15B
Outline • Introduction to kriging • Best practices • Fitting a proper model • Variography, transformations, isotropy, stationarity • Comparing models using cross validation • Interpreting results
•
Empirical Bayesian Kriging – Robust kriging as a GP tool -
Tuesday 3:00 – 3:30pm Demo theater
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
Correlation
•
Distance
Kriging Demonstration
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
For a given distance h, the semivariogram model: γ(h)= Nugget + b|h|α
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.
Empirical Bayesian Kriging Demonstration
Goodness of fit / Model acceptance
•
Subset Features
•
Cross Validation
Cressie, 1990
•
Cross validation does not prove that the model is correct,
•
merely that it is not grossly incorrect.
Cross validation Demonstration
Geostatistical layer
•
Method and parameters
•
Pointer to the data
•
Dynamic
Output = Prediction, Prediction SE, Probability, Quantile, Condition number
Geostatistical layer Demonstration
Areal Interpolation •
reaggregation of data from one set of polygons to another set of polygons
New in ArcGIS 10.1
Areal Interpolation Demonstration
Demo theater Areal Interpolation Thursday 9:00am – 9:30am
Simple kriging
N = 500 100 8
Demo theater Geostatistical Simulations Tuesday 3:30pm – 4:00pm
Interpolation with Barriers
•
Kernel interpolation
•
Diffusion interpolation
? Cost Raster
Create Spatially Balanced Points •
Monitor road pollution
•
Convert roads to raster
•
High value = busy road
•
Low value = quite road
Sampling Network Design
Create Spatially Balanced Points (cont.)
Sampling Network Design
Densify Sampling Network •
•
Used kriging to create: -
Prediction surface
-
Standard error of prediction
Want to add 2 new sites
Sampling Network Design
Densify Sampling Network (Cont.)
Sampling Network Design
Demo theater Designing and Updating a Monitoring Network Thursday 9:30am – 10:00am
resources.arcgis.com
http://esripress.esri.com
• Thank you for attending • Have fun at UC2012 • Open for Questions • Please fill out the evaluation: www.esri.com/ucsessionsurveys First Offering ID: 637 Second Offering ID: 812
