Geostatistics in Practice: Interpolation Through Examples...Geostatistical Interpolation Assumptions...
Transcript of Geostatistics in Practice: Interpolation Through Examples...Geostatistical Interpolation Assumptions...
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Geostatistics in Practice: Interpolation
Through Examples Prahlad Jat
Eric Krause
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Sessions of note…Tuesday
• Interpolating Surfaces in ArcGIS (1:00-2:00 SDCC Rm33C)
• Kriging: An Introduction to Concepts and Applications (2:30-3:30 SDCC Rm33C)
• Geostatistical Analyst: An Introduction (4:00-5:00 SDCC Rm30C)
Wednesday
Thursday
• Surface Interpolation in ArcGIS (11:15-12:00 SDCC Demo Theater 10)
• Empirical Bayesian Kriging and EBK Regression Prediction in ArcGIS (2:30-3:15 SDCC Demo Theater 10)
• Geostatistics in Practice: Learning Interpolation Through Examples (8:30-9:30 SDCC Rm30A)
• Polygon-to-Polygon Predictions Using Areal Interpolation (11:15-12:00 SDCC Demo Theater 10)
• Geostatistical Analyst: An Introduction (1:00-2:00 SDCC Rm30A)
• Using Living Atlas Data and ArcGIS Pro for 3D Interpolation (2:30-3:30 SDCC Rm 30C)
• Interpolating Surfaces in ArcGIS (4:00-5:00 SDCC Rm15A)
• Kriging: An Introduction to Concepts and Applications (4:00-5:00 SDCC Rm15B)
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Geostatistical Analyst Resourceshttp://esriurl.com/GeostatGetStarted
• GeoNet – community.esri.com
- Blogs
- Free textbook and datasets
- Spatial Statistical Analysis For GIS Users
- Lots of discussions and Q&A
• Learn GIS – learn.arcgis.com
- Model Water Quality Using Interpolation
- Analyze Urban Heat Using Kriging
- Interpolate 3D Oxygen Measurements in Monterey Bay
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Outline
• Interpolation
• Demo: interpolation with barriers
• Geostatistical interpolation
• Steps in geostatistical interpolation
• Demo: geostatistical interpolation (impact of mean trend)
• Advanced geostatistical Interpolation (EBK, Regression EBK)
• Demo: EBK, Regression EBK
• From 2D to 3D
• Demo: 3D
• Questions
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What is interpolation?
• Predict values at unknown locations using values at measured locations
• Why: Cost prohibitive & impractical to measure values everywhere
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Interpolation methods
Deterministic method:
- Solely based on mathematical functions (not based on statistical theory)
- IDW (Inverse Distance Weighted), Spline interpolation
- Not able to estimate prediction error
Geostatistical method:
- Based on both mathematical functions and statistical models (spatial autocorrelation)
- Can account for direction dependent weighting
- Kriging
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Demo
Interpolation with
Barriers
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Why Geostatistical Methods for Interpolation?
✓ Theory based advanced interpolation methods
✓ Quantify the spatial autocorrelation
✓ Account for the spatial configuration of measured sample values (directionality in data)
✓ Unlike deterministic methods, they also provide the uncertainty of predictions
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Geostatistical Interpolation Assumptions
✓ Data is normally distributed
✓ Data has spatial autocorrelation
✓ Data has no local trend
✓ Data exhibits stationarity
✓ Mean stationarity: mean is constant between samples & is independent of location
✓ Intrinsic stationarity: the variance of the difference is the same between any two points
that are at the same distance and direction apart no matter which two points you choose.
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Steps in Geostatistical Interpolation
❑ Exploratory spatial data analysis (ESDA)
❑ Mean trend analysis
❑ Modeling autocorrelation (semivariogram)
❑ Search neighborhood and performing interpolation
❑ Cross validation
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Steps in Geostatistical Interpolation
❑ Exploratory spatial data analysis (ESDA)
Purpose: to maximize insight into the data
- To detect outliers
- To explore the distribution of data (determine: data transformation)
Techniques:
- Data visualization
- Charting/plotting (histogram, QQ plot)
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Steps in Geostatistical Interpolation
❑ Mean trend analysis
Mean trend: Systematic and gradual changes across study domain
Z(s) = µ(s) + ε(s)
trend random errorWhy: Identifying and removing mean trend may improve interpolation accuracy
Challenge: No magical way to decompose data uniquely into trend & random error
Risk: Overfitting
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Steps in Geostatistical Interpolation
❑ Modeling semivariogram (autocorrelation)
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Steps in Geostatistical Interpolation
❑ Search neighborhood and perform interpolation
Neighborhood Prediction Prediction error
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Steps in Geostatistical Interpolation
❑ Cross validation
Cross validation: Technique to evaluate the reliability of the model
Why: Predictions of every interpolation method are different
Method: leave-one-out cross validation (LOOC)
- Iteratively discard each sample
- Use remaining points to estimate value at measured location
- Compare predicted versus measured value
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Steps in Geostatistical Interpolation
❑ Cross validation
Cross validation statistics:
Error = (predicted value - true value )
- Root-Mean-Square (RMS): root of average squared errors
- Root-mean-square standardized (RMSS): standardized RMSE
- Mean error: average of the errors
- Mean standardized error: standardized mean errors
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Demo
Geostatistical
Interpolation
Impact of mean trend on
- variogram modeling
- cross validation
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Advanced geostatistical Interpolation
Limitations with traditional geostatistical methods:
✓ Modeled semivariogram perfectly captures spatial autocorrelation
✓ A single semivariogram can truly represent autocorrelation
in the entire study area
(spatial dependency is equally distributed over the whole study area)
Solution: EBK (Empirical Bayesian Kriging) , Regression EBK
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EBK (Empirical Bayesian Kriging), Regression EBK
EBK
✓ Easier to run: requires minimal interaction
✓ Better handles small and nonstationary datasets
✓ Doesn’t assume one semivariogram model fits the entire data
Regression EBK
✓ Use explanatory variable to improve predictions
✓ Handles multicollinearity using PCA (principle component analysis)
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Demo
Geostatistical
InterpolationEBK/Regression EBK
- stationarity
- regression
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From 2D to 3D
More and more 3D data are collected
Datasets in geosciences have samples in 3D space
Example: Oceanographic data
EBK in 3D (new in Pro2.3): Empirical Bayesian Kriging in 3D space)
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Demo
Geostatistical
Interpolation
EBK3D
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