ArcGIS®
9Using ArcGIS® Geostatistical Analyst
Copyright © 2001, 2003 ESRIAll Rights Reserved.Printed in the United States of America.
The information contained in this document is the exclusive property of ESRI. This work is protected under United States copyright law and the copyrightlaws of the given countries of origin and applicable international laws, treaties, and/or conventions. No part of this work may be reproduced or transmittedin any form or by any means, electronic or mechanical, including photocopying or recording, or by any information storage or retrieval system, except asexpressly permitted in writing by ESRI. All requests should be sent to Attention: Contracts Manager, ESRI, 380 New York Street, Redlands, CA 92373-8100, USA.
The information contained in this document is subject to change without notice.
DATA CREDITSCarpathian Mountains data supplied by USDA Forest Service, Riverside, California, and is used here with permission.
Radioceasium data supplied by International Sakharov Environmental University, Minsk, Belarus, and is used here with permission. Copyright © 1996.
Air quality data for California supplied by California Environmental Protection Agency, Air Resource Board, and is used here with permission.Copyright © 1997.
Radioceasium contamination in forest berries data supplied by the Institute of Radiation Safety “BELRAD”, Minsk, Belarus, and is used here withpermission. Copyright © 1996.
CONTRIBUTING WRITERSKevin Johnston, Jay M. Ver Hoef, Konstantin Krivoruchko, and Neil Lucas
DATA DISCLAIMER
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Attribution.pmd 11/25/2003, 4:46 PM1
iii
Contents 1 Welcome to ArcGIS Geostatistical Analyst 1 !"#
2 Quick-start tutorial 11$ %%&' %& %(&)&' #&**) (&+
3 The principles of geostatistical analysis 49, -, .*/* ( %0 " !" #
4 Exploratory Spatial Data Analysis 81.1"2#1"#1"# * (
TOC.p65 03/07/2001, 4:00 PM3
iv USING ARCGIS GEOSTATISTICAL ANALYST
12 * (#3* (($ * %-%3* %-3* %- %- %-#, %-(, %%%
5 Deterministic methods for spatial interpolation 11345$1. 5%%'$1.%%#45*5%-'*%455%'%45 *5%'6/7%(
6 Creating a surface with geostatistical techniques 131.82%, %, %' %, % , %#' %(, %'%, %-
TOC.p65 03/07/2001, 4:00 PM4
CONTENTS v
'%%, %, %' %, **%'**% , 9%(' 9%-, %'%
7 Using analytical tools when generating surfaces 167$&%# % 1* )%#%1* )%#+: %#(+: %(" %(' 5%( ' 5%(( * --,;</='< >-,-'* *-'* *-($ 9%%1 9%6 %6* & %#
TOC.p65 03/07/2001, 4:00 PM5
vi USING ARCGIS GEOSTATISTICAL ANALYST
8 Displaying and managing geostatistical layers 219.2-" .5?5"'6 '*(1-' 55* +
9 Additional geostatistical analysis tools 239'& -+ %+ *
Appendix A 247
Appendix B 275
Glossary 279
References 285
Index 287
TOC.p65 03/07/2001, 4:00 PM6
IN THIS CHAPTER
1
Welcome to ArcGIS Geostatistical Analyst 1• Exploratory spatial data analysis
• Semivariogram modeling
• Surface prediction and errormodeling
• Threshold mapping
• Model validation and diagnostics
• Surface prediction using cokriging
• Tips on learning GeostatisticalAnalyst
Welcome to the ESRI® ArcGIS® Geostatistical Analyst extension foradvanced surface modeling using deterministic and geostatistical methods.Geostatistical Analyst extends ArcMap™ by adding an advanced toolbarcontaining tools for exploratory spatial data analysis and a geostatisticalwizard to lead you through the process of creating a statistically validsurface. New surfaces generated with Geostatistical Analyst cansubsequently be used in geographic information system (GIS) models and invisualization using ArcGIS extensions such as ArcGIS Spatial Analyst andArcGIS 3D Analyst™.
Geostatistical Analyst is revolutionary because it bridges the gap betweengeostatistics and GIS. For some time, geostatistical tools have beenavailable, but never integrated tightly within GIS modeling environments.Integration is important because, for the first time, GIS professionals canbegin to quantify the quality of their surface models by measuring thestatistical error of predicted surfaces.
Surface fitting using Geostatistical Analyst involves three key steps(demonstrated on the following pages):
• Exploratory spatial data analysis
• Structural analysis (calculation and modeling of the surface properties ofnearby locations)
• Surface prediction and assessment of results
The software contains a series of easy-to-use tools and wizards that guideyou through each of these steps. It also includes a number of unique toolsfor statistical spatial data analysis.
ch01_Welcome.pmd 11/25/2003, 2:54 PM1
2 USING ARCGIS GEOSTATISTICAL ANALYST
Exploratory spatial data analysis, <!" 5@ 5!" *< < * @
A number of exploratory spatial data analysis tools are used to investigate the properties of ozone measurements takenat monitoring stations in the Carpathian Mountains.
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WELCOME TO ARCGIS GEOSTATISTICAL ANALYST 3
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The two phases of geostatistical analysis of data are illustrated above. First, the semivariogram/covariance wizard was used tofit a model to winter temperature data for the USA. This model was then used to create the temperature distribution map.
Welcome.p65 03/05/2001, 2:27 PM3
4 USING ARCGIS GEOSTATISTICAL ANALYST
Surface prediction and error modeling
Here, Geostatistical Analyst has been used to produce a prediction map of radioceasium soil contamination levels in the country ofBelarus after the Chernobyl nuclear power plant accident.
Welcome.p65 3/21/01, 7:58 AM4
WELCOME TO ARCGIS GEOSTATISTICAL ANALYST 5
Threshold mapping+*** 5 @
Locations shown in dark orange and red indicate a probability greater than 62.5% that radioceasium contamination exceeds the upperpermissible level (critical threshold) in forest berries.
Welcome.p65 03/05/2001, 2:27 PM5
6 USING ARCGIS GEOSTATISTICAL ANALYST
Model validation and diagnostics$ *5*@** * @ 55? @
The validation wizard is used to assess a model developed to predict organic matter for a farm in Illinois.
Welcome.p65 03/05/2001, 2:27 PM6
WELCOME TO ARCGIS GEOSTATISTICAL ANALYST 7
Surface prediction using cokriging
In this example, exploratory spatial data analysis tools are used to explore spatial correlation betweenozone (primary variable) and nitrogen dioxide (secondary variable) in California. Because the variables arespatially correlated, cokriging can use the nitrogen dioxide data to improve predictions when mappingozone.
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8 USING ARCGIS GEOSTATISTICAL ANALYST
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WELCOME TO ARCGIS GEOSTATISTICAL ANALYST 9
Contacting ESRI
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Welcome.p65 03/05/2001, 2:27 PM10
IN THIS CHAPTER
11
With Geostatistical Analyst, you can easily create a continuous surface,or map, from measured sample points stored in a point-feature layer, rasterlayer, or by using polygon centroids. The sample points may be measurementssuch as elevation, depth to the water table, or levels of pollution, as is the casein this tutorial. When used in conjunction with ArcMap, Geostatistical Analystprovides a comprehensive set of tools for creating surfaces that can be usedto visualize, analyze, and understand spatial phenomena.
Tutorial scenario
The U.S. Environmental Protection Agency is responsible for monitoringatmospheric ozone concentration in California. Ozone concentration is mea-
sured at monitoring stations throughout the state.The locations of the stations are shown here. Theconcentration levels of ozone are known forall of the stations, but we are also interested inknowing the level for every location in California.However, due to cost and practicality, monitoringstations cannot be everywhere. GeostatisticalAnalyst provides tools that make the best predic-tions possible by examining the relationshipsbetween all of the sample points and producing acontinuous surface of ozone concentration,standard errors (uncertainty) of predictions, andprobabilities that critical values are exceeded.
Quick-start tutorial 2• Exercise 1: Creating a surface
using default parameters
• Exercise 2: Exploring your data
• Exercise 3: Mapping ozone con-centration
• Exercise 4: Comparing models
• Exercise 5: Mapping the probabil-ity of ozone exceeding a criticalthreshold
• Exercise 6: Producing the finalmap
ch02_Tutorial.pmd 11/25/2003, 4:33 PM11
12 USING ARCGIS GEOSTATISTICAL ANALYST
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Semivariogram/Covariance modeling
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30 USING ARCGIS GEOSTATISTICAL ANALYST
Directional semivariograms
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34 USING ARCGIS GEOSTATISTICAL ANALYST
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IN THIS CHAPTER
49
The principles of geostatistical analysis 3• Understanding deterministic
methods
• Understanding geostatisticalmethods
• Working through a problem
• Basic principles behindgeostatistical methods
• Modeling a semivariogram
• Predicting unknown values withkriging
• The Geostatistical Analystextension
Geostatistical Analyst uses sample points taken at different locations in alandscape and creates (interpolates) a continuous surface. The samplepoints are measurements of some phenomenon such as radiation leakingfrom a nuclear power plant, an oil spill, or elevation heights. GeostatisticalAnalyst derives a surface using the values from the measured locations topredict values for each location in the landscape.
Geostatistical Analyst provides two groups of interpolation techniques:deterministic and geostatistical. All methods rely on the similarity of nearbysample points to create the surface. Deterministic techniques usemathematical functions for interpolation. Geostatistics relies on bothstatistical and mathematical methods, which can be used to create surfacesand assess the uncertainty of the predictions.
Geostatistical Analyst, in addition to providing various interpolationtechniques, also provides many supporting tools. These tools allow you toexplore and gain a better understanding of the data so that you create thebest surfaces based on the available information.
This chapter will provide an overview of the theory behind deterministic andgeostatistical interpolation techniques. The first part of the chapter willintroduce you to the deterministic interpolation methods. You will then beexposed to geostatistical methods through an example, and then you willread about the principles, concepts, and assumptions that provide thefoundation for geostatistics.
ch03_BasicConcepts.pmd 11/25/2003, 2:58 PM49
50 USING ARCGIS GEOSTATISTICAL ANALYST
Understanding deterministic methods
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THE PRINCIPLES OF GEOSTATISTICAL ANALYSIS 51
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Visualizing local polynomial interpolation
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THE PRINCIPLES OF GEOSTATISTICAL ANALYSIS 53
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BasicConcepts.p65 3/21/01, 8:05 AM54
THE PRINCIPLES OF GEOSTATISTICAL ANALYSIS 55
=
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Locations Distance Cal. Distances Difference2 Semivariance(1,5),(3,4) sqrt[(1-3)2 + (5-4)2] 2.236 25 12.5
(1,5),(1,3) sqrt[02 + 22] 2 25 12.5
(1,5),(4,5) sqrt[32 + 02] 3 0 0(1,5),(5,1) sqrt[42 + 42] 5.657 225 112.5
(3,4),(1,3) sqrt[22 + 12] 2.236 0 0
(3,4),(4,5) sqrt[12 + 12] 1.414 25 12.5
(3,4),(5,1) sqrt[22 + 32] 3.606 100 50
(1,3),(4,5) sqrt[32 + 22] 3.606 25 12.5(1,3),(5,1) sqrt[42 + 22] 4.472 100 50
(4,5),(5,1) sqrt[12 + 42] 4.123 225 112.5
22 )()( jijiij yyxxd −+−=
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BasicConcepts.p65 03/06/2001, 11:58 AM55
56 USING ARCGIS GEOSTATISTICAL ANALYST
Binning the Empirical SemivariogramLag Distance Pairs Distance Av. Distance Semivariance Average
1+-2 1.414, 2 1.707 12.5, 12.5 12.52+-3 2.236, 2.236, 3 2.491 12.5, 0, 0 4.1673+-4 3.606, 3.606 3.606 50, 12.5 31.254+-5 4.472, 4.123 4.298 50, 112.5 81.25
5+ 5.657 5.657 112.5 112.5
(1, 5) (3, 4) (1, 3) (4, 5) (5, 1) Γ Matrix (Gamma)
(1, 5) 0 30.19 27.0 40.5 76.37 1 (3, 4) 30.19 0 30.19 19.09 48.67 1 (1, 3) 27.0 30.19 0 48.67 60.37 1 (4, 5) 40.5 19.09 48.67 0 55.66 1 (5, 1) 76.37 48.67 60.37 55.66 0 1
1 1 1 1 1 0
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BasicConcepts.p65 03/06/2001, 11:58 AM56
THE PRINCIPLES OF GEOSTATISTICAL ANALYSIS 57
Inverse of Γ Matrix (Gamma) -0.02575 0.00704 0.0151 0.00664 -0.00303 0.3424 0.00704 -0.04584 0.01085 0.02275 0.0052 -0.22768 0.0151 0.01085 -0.02646 -0.00471 0.00522 0.17869 0.00664 0.02275 -0.00471 -0.02902 0.00433 0.28471 -0.00303 0.0052 0.00522 0.00433 -0.01173 0.42189 0.3424 -0.22768 0.17869 0.28471 0.42189 -41.701
Point Distance g Vector for (1,4) (1,5) 1 13.5 (3,4) 2 27.0 (1,3) 1 13.5 (4,5) 3.162 42.69 (5,1) 5 67.5
1
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BasicConcepts.p65 03/06/2001, 11:58 AM57
58 USING ARCGIS GEOSTATISTICAL ANALYST
G Vector Weights (λ) g Vector Times Weights13.5 0.46757 6.312195 27.0 0.09834 2.65518 13.5 0.46982 6.34257 42.69 -0.02113 -0.90204 67.5 -0.0146 -0.9855
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Kriging Variance 13.2396 Kriging Std Error 3.6386
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BasicConcepts.p65 03/06/2001, 11:58 AM58
THE PRINCIPLES OF GEOSTATISTICAL ANALYSIS 59
Random processes with dependence
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BasicConcepts.p65 03/06/2001, 11:58 AM59
60 USING ARCGIS GEOSTATISTICAL ANALYST
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BasicConcepts.p65 03/06/2001, 11:58 AM60
THE PRINCIPLES OF GEOSTATISTICAL ANALYSIS 61
Modeling a semivariogram
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BasicConcepts.p65 3/21/01, 8:06 AM61
62 USING ARCGIS GEOSTATISTICAL ANALYST
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THE PRINCIPLES OF GEOSTATISTICAL ANALYSIS 63
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BasicConcepts.p65 03/06/2001, 11:58 AM63
64 USING ARCGIS GEOSTATISTICAL ANALYST
Center of semivariogram surface
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BasicConcepts.p65 03/06/2001, 11:58 AM64
THE PRINCIPLES OF GEOSTATISTICAL ANALYSIS 65
21
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BasicConcepts.p65 03/06/2001, 11:58 AM65
66 USING ARCGIS GEOSTATISTICAL ANALYST
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BasicConcepts.p65 03/06/2001, 11:58 AM66
THE PRINCIPLES OF GEOSTATISTICAL ANALYSIS 67
Fitting a model to the empirical semivariogram
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BasicConcepts.p65 03/06/2001, 11:58 AM67
68 USING ARCGIS GEOSTATISTICAL ANALYST
Sill
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Understanding a semivariogram—the range, sill,and nugget
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BasicConcepts.p65 03/06/2001, 11:58 AM68
THE PRINCIPLES OF GEOSTATISTICAL ANALYSIS 69
Accounting for directional influences—trend andanisotropy
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70 USING ARCGIS GEOSTATISTICAL ANALYST
Variable A
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BasicConcepts.p65 03/06/2001, 11:58 AM70
THE PRINCIPLES OF GEOSTATISTICAL ANALYSIS 71
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BasicConcepts.p65 03/06/2001, 11:58 AM71
72 USING ARCGIS GEOSTATISTICAL ANALYST
Point Number
X-Coordinate Y-Coordinate Value
1 1 3 105 2 1 5 100 3 1 6 95 4 3 4 105 5 3 6 105 6 4 5 100 7 5 1 115 8 6 3 120 9 6 6 110 10 7 1 120
Using the Geostatistical Analyst to fit a model to asemivariogram
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THE PRINCIPLES OF GEOSTATISTICAL ANALYSIS 73
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BasicConcepts.p65 03/06/2001, 11:58 AM73
74 USING ARCGIS GEOSTATISTICAL ANALYST
Kriging
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BasicConcepts.p65 03/06/2001, 11:58 AM74
THE PRINCIPLES OF GEOSTATISTICAL ANALYSIS 75
Neighborhood Point Number
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x-coordinate y-coordinate Value
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BasicConcepts.p65 03/06/2001, 11:58 AM75
76 USING ARCGIS GEOSTATISTICAL ANALYST
i 1 2 3 4 5 6 1 0.000 36.091 40.065 60.920 71.564 1.000 2 36.091 0.000 40.065 52.221 81.855 1.000 3 40.065 40.065 0.0000 25.881 60.920 1.000 4 60.920 52.221 25.881 0.000 67.559 1.000 5 71.564 81.855 60.920 67.559 0.000 1.000 6 1.000 1.000 1.000 1.000 1.000 0.000
i 1 2 3 4 5 6 1 -0.0191 0.01005 0.00776 -0.0021 0.00336 0.2114 2 0.01005 -0.0187 0.00472 0.00402 -0.0001 0.24891 3 0.00776 0.00472 -0.0317 0.01619 0.00304 -0.1038 4 -0.0021 0.00402 0.01619 -0.0214 0.00324 0.27739 5 0.00336 -0.0001 0.00304 0.00324 -0.0095 0.36607 6 0.2114 0.24891 -0.1038 0.27739 0.36607 -47.922
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BasicConcepts.p65 03/06/2001, 11:58 AM76
THE PRINCIPLES OF GEOSTATISTICAL ANALYSIS 77
i λi Valuei
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BasicConcepts.p65 03/06/2001, 11:58 AM77
78 USING ARCGIS GEOSTATISTICAL ANALYST
A guide to the Geostatistical Analyst extension
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BasicConcepts.p65 03/06/2001, 11:58 AM78
THE PRINCIPLES OF GEOSTATISTICAL ANALYSIS 79
Explore the data
Fit am odel
Performdiagnostics
Comparethe m odels
Representthe data
Add layers and display in ArcMap.
Investigate the statistical and spatial properties ofyour data.
Choose a model to create a surface. TheGeostatistical Wizard is used in the definition andrefinement of an appropriate model.
Assess the quality of the output surface usingCross-Validation and Validation tools. This will helpyou understand how well the model predicts thevalues at unmeasured locations.
More than one surface can be produced. Thesurface can be compared using cross-validationstatistics.
Create subsets
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BasicConcepts.p65 03/06/2001, 11:58 AM79
BasicConcepts.p65 03/06/2001, 11:58 AM80
IN THIS CHAPTER
81
4• What is Exploratory Spatial Data
Analysis?
• The Exploratory Spatial DataAnalysis tools
• Examining the distribution of thedata
• Looking for global and localoutliers
• Looking for global trends
• Examining spatial autocorrelationand directional variation
• Understanding covariation amongmultiple datasets
Exploratory Spatial Data Analysis allows you to examine your data indifferent ways. Before creating a surface, ESDA enables you to gain adeeper understanding of the phenomena you are investigating so that youcan make better decisions on issues relating to your data. The ESDAenvironment is composed of a series of tools, each allowing a view into thedata. Each view can be manipulated and explored, allowing differentinsights about the data. Each view is interconnected with all other views aswell as with ArcMap. That is, if a bar is selected in the histogram, thepoints comprising the bar are also selected on the QQPlot (if opened), onany other open ESDA view, and on the ArcMap map.
The ESDA environment is designed to explore, as its name implies.However, there are certain tasks that are useful in most explorations.Exploring the distribution of the data, looking for global and local outliers,looking for global trends, examining spatial autocorrelation, andunderstanding the covariation among multiple datasets are all useful tasks toperform on your data. The ESDA tools can assist you with these tasks aswell as many others.
Exploratory Spatial Data Analysis
ch04_ESDA.pmd 11/25/2003, 3:02 PM81
82 USING ARCGIS GEOSTATISTICAL ANALYST
What is Exploratory Spatial Data Analysis?
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ESDA.p65 3/21/01, 8:08 AM82
EXPLORATORY SPATIAL DATA ANALYSIS 83
Exploratory Spatial Data Analysis
Selection of Data Points
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Select by location Select using ESDA tool
Histogram tool
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Voronoi mapping tool Voronoi mapping tool
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ESDA.p65 3/21/01, 8:08 AM83
84 USING ARCGIS GEOSTATISTICAL ANALYST
Exploratory Spatial Data Analysis tools
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ESDA.p65 03/07/2001, 12:44 PM84
EXPLORATORY SPATIAL DATA ANALYSIS 85
Value
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ESDA.p65 03/07/2001, 12:44 PM85
86 USING ARCGIS GEOSTATISTICAL ANALYST
Tools (pan,zoom, etc.) Voronoi map Cell values
Selecteddataset
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ESDA.p65 03/07/2001, 12:44 PM86
EXPLORATORY SPATIAL DATA ANALYSIS 87
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ESDA.p65 03/07/2001, 12:44 PM87
88 USING ARCGIS GEOSTATISTICAL ANALYST
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ESDA.p65 03/07/2001, 12:44 PM88
EXPLORATORY SPATIAL DATA ANALYSIS 89
General QQPlotNormal QQPlot
Plot of the quantiles of the inputdataset versus quantiles of thestandard normal distribution
Input dataset Attribute to use
Transformationto apply
Plot of the quantiles oftwo datasets
Attributes to useInput datasets
ESDA.p65 03/07/2001, 12:44 PM89
90 USING ARCGIS GEOSTATISTICAL ANALYST
Trend analysis
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East–Westtrend line
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Vertical control
Horizontal control
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Each line representsthe location andvalue (height) ofeach data point.
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EXPLORATORY SPATIAL DATA ANALYSIS 91
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sample locations
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Semivariogram/Covariance cloud
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ESDA.p65 03/07/2001, 12:44 PM91
92 USING ARCGIS GEOSTATISTICAL ANALYST
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ESDA.p65 03/07/2001, 12:44 PM92
EXPLORATORY SPATIAL DATA ANALYSIS 93
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Selectedattributes
The crosscovariance cloud
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94 USING ARCGIS GEOSTATISTICAL ANALYST
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ESDA.p65 03/07/2001, 12:45 PM94
EXPLORATORY SPATIAL DATA ANALYSIS 95
Examining the distribution of the data
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ESDA.p65 03/07/2001, 12:45 PM95
96 USING ARCGIS GEOSTATISTICAL ANALYST
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Using the Histogram tool to examine distributions
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ESDA.p65 03/07/2001, 12:45 PM96
EXPLORATORY SPATIAL DATA ANALYSIS 97
Understanding distributions with the QQPlot
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98 USING ARCGIS GEOSTATISTICAL ANALYST
Examining thedistribution ofyour data
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Examining thedistribution with theHistogram tool
1. Click on the point featurelayer in the ArcMap table ofcontents that you wish toexplore.
2. Click on the GeostatisticalAnalyst toolbar, click ExploreData, then click Histogram.
Tip
The QQPlot
Exploring the distributionthrough the QQPlot
1. Click on the point featurelayer in the ArcMap table ofcontents that you wish toexplore.
2. Click on the GeostatisticalAnalyst toolbar, click ExploreData, then click NormalQQPlot.
ESDA.p65 03/07/2001, 12:45 PM98
EXPLORATORY SPATIAL DATA ANALYSIS 99
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100 USING ARCGIS GEOSTATISTICAL ANALYST
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ESDA.p65 03/07/2001, 12:45 PM100
EXPLORING SPATIAL DATA ANALYSIS 101
Identifying globaland local outliers
Identifying global outliersusing the Histogram tool
1. Click on the point or polygonfeature layer in the ArcMaptable of contents that youwish to explore.
2. Click on the GeostatisticalAnalyst toolbar, click ExploreData, then click Histogram.
See Also
Looking for globaloutliers through theSemivariogram/Covariance Cloud
1. Click on the point or polygonfeature layer in the ArcMaptable of contents that youwish to explore.
2. Click on the GeostatisticalAnalyst toolbar, click ExploreData, then click Semivari-ogram/Covariance Cloud.
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102 USING ARCGIS GEOSTATISTICAL ANALYST
Finding local outliersusing Voronoi map
1. Click on the point or polygonfeature layer in the ArcMaptable of contents that youwish to explore.
2. Click on the GeostatisticalAnalyst toolbar, click ExploreData, then click Voronoi Map.
ESDA.p65 03/07/2001, 12:45 PM102
EXPLORATORY SPATIAL DATA ANALYSIS 103
Looking for global trends
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ESDA.p65 03/07/2001, 12:45 PM103
104 USING ARCGIS GEOSTATISTICAL ANALYST
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ESDA.p65 3/21/01, 8:09 AM104
EXPLORING SPATIAL DATA ANALYSIS 105
Looking forglobal trends # )
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Identifying global trendswith the Trend Analysistool
1. Click on the point or polygonfeature layer in the ArcMaptable of contents that youwish to explore.
2. Click on the GeostatisticalAnalyst toolbar, click ExploreData, then click TrendAnalysis.
See Also
!
ESDA.p65 03/07/2001, 12:45 PM105
106 USING ARCGIS GEOSTATISTICAL ANALYST
Examining spatial autocorrelation and directional variation
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ESDA.p65 03/07/2001, 12:45 PM106
EXPLORATORY SPATIAL DATA ANALYSIS 107
Looking for directional influences with theSemivariogram/Covariance Cloud tool
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ESDA.p65 03/07/2001, 12:45 PM107
108 USING ARCGIS GEOSTATISTICAL ANALYST
Examiningspatial structureand directionalvariation
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Understanding spatialstructure
1. Click on the point or polygonfeature layer in the ArcMaptable of contents that youwish to explore.
2. Click on the GeostatisticalAnalyst toolbar, click ExploreData, then click Semivari-ogram/Covariance Cloud.
See Also
ESDA.p65 3/21/01, 8:10 AM108
EXPLORATORY SPATIAL DATA ANALYSIS 109
Exploring covariation among multiple datasets
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ESDA.p65 03/07/2001, 12:45 PM109
110 USING ARCGIS GEOSTATISTICAL ANALYST
Exploring the correlation between two datasets
Data pairing for the Los Angeles area with high cross-correlation between ozone and nitrogen dioxide
ESDA.p65 03/07/2001, 12:45 PM110
EXPLORING SPATIAL DATA ANALYSIS 111
Understandingspatialcovariationamong multipledatasets
Understanding spatialcovariation using theCrosscovariance Cloud
1. Right-click on the pointfeature layer in the ArcMaptable of contents identifyingthe first layer in thecrosscovariance analysisand click Properties.
2. Click on Selection.
3. Click on the symbol radiobutton.
4. Click on the symbol.
5. Choose a color and size forthe selection.
Repeat steps 1–5 for thesecond layer to be used inthe crosscovariance analysis,but choose different selectionsizes and colors.
6. Highlight the layers in theArcMap table of contents byholding down the Ctrl keywhile left-clicking on the twolayers.
7. Click on GeostatisticalAnalyst, click Explore Data,and click CrosscovarianceCloud.
ESDA.p65 3/21/01, 8:15 AM111
112 USING ARCGIS GEOSTATISTICAL ANALYST
8. Click on the appropriateattribute for each layer in theAttribute dropdown list.
9. Input the Lag Size andNumber of Lags.
10. Check Search Direction.
11. Click on the center blue linein the Covariance Surfaceand spin the search directionuntil it points to the anglewhere you believe there is ashift; in this example it is270 degress (given in theangle direction box).
12. Brush some points in thecovariance cloud by holdingdown the left mouse buttonand dragging it over some ofthe points. Examine where,on the ArcMap map, thepairs of points are that werebrushed.
ESDA.p65 3/21/01, 8:15 AM112
IN THIS CHAPTER
113
Deterministic methods for spatial interpolation 5• How Inverse Distance Weighted
interpolation works
• Creating a surface using InverseDistance Weighted interpolation
• How global polynomialinterpolation works
• Creating a map using globalpolynomial interpolation
• How local polynomialinterpolation works
• Creating a surface using localpolynomial interpolation
• How radial basis functionsinterpolation works
• Creating a surface using radialbasis functions interpolation
There are two main groupings of interpolation techniques: deterministic andgeostatistical. Deterministic interpolation techniques create surfaces frommeasured points, based on either the extent of similarity (e.g., InverseDistance Weighted) or the degree of smoothing (e.g., radial basis functions).Geostatistical interpolation techniques (e.g., kriging) utilize the statisticalproperties of the measured points. The geostatistical techniques quantify thespatial autocorrelation among measured points and account for the spatialconfiguration of the sample points around the prediction location.Geostatistical techniques will be discussed in Chapter 6, ‘Creating a surfacewith geostatistical techniques’.
Deterministic interpolation techniques can be divided into two groups: globaland local. Global techniques calculate predictions using the entire dataset.Local techniques calculate predictions from the measured points withinneighborhoods, which are smaller spatial areas within the larger study area.Geostatistical Analyst provides the global polynomial as a global interpolatorand the Inverse Distance Weighted, local polynomial, and radial basisfunctions as local interpolators.
A deterministic interpolation can either force the resulting surface to passthrough the data values or not. An interpolation technique that predicts avalue identical to the measured value at a sampled location is known as anexact interpolator. An inexact interpolator predicts a value that is differentfrom the measured value. The latter can be used to avoid sharp peaks ortroughs in the output surface. Inverse Distance Weighted and radial basisfunctions are exact interpolators, while global and local polynomial areinexact.
ch05_Deterministic.pmd 11/25/2003, 3:02 PM113
114 USING ARCGIS GEOSTATISTICAL ANALYST
How Inverse Distance Weighted interpolation works
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Deterministic.p65 03/07/2001, 12:50 PM114
DETERMINISTIC METHODS FOR SPATIAL INTERPOLATION 115
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Deterministic.p65 03/07/2001, 12:51 PM115
116 USING ARCGIS GEOSTATISTICAL ANALYST
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DETERMINISTIC METHODS FOR SPATIAL INTERPOLATION 117
The samplepoints
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Deterministic.p65 03/07/2001, 12:51 PM117
118 USING ARCGIS GEOSTATISTICAL ANALYST
Creating a mapusing IDW'+ '" # " ,-# ( &# , -!
Creating a predictionmap
1. Click on the point layer onwhich to perform IDW in theArcMap table of contents.
2. Start the GeostatisticalAnalyst.
3. Click the Attribute dropdownmenu and click the attributeon which to perform IDW inthe Choose Input Data andMethod dialog box.
4. Click the Inverse DistanceWeighting method.
5. Click Next.
6. Specify the desired param-eters in the IDW Set Param-eters dialog box and clickNext.
7. Examine the results on theCross Validation dialog boxand click Finish.
8. Click on the Output LayerInformation dialog box andclick OK.
See Also
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Tip
Using a database fileinstead of a point layer' '( )* + ,( $
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Deterministic.p65 03/07/2001, 12:51 PM118
DETERMINISTICAL METHODS OF SPATIAL DATA INTERPOLATION 119
Creating a predictionmap using validation
1. Click on the point layer onwhich to perform IDW in theArcMap table of contents.
2. Start the GeostatisticalAnalyst.
3. Click the Attribute dropdownmenu and specify the field onwhich to perfom IDW in theChoose Input Data andMethod dialog box.
4. Check Validation.
5. Pick a point layer file in theInput Data dropdown menuor browse for the desiredlayer.
6. Click the Attribute dropdownmenu and specify the field onwhich to validate the IDWinterpolation within theChoose Input Data andMethod dialog box.
7. Click the Inverse DistanceWeighting method.
8. Click Next.
9. Specify the desired param-eters in the IDW Set Param-eters dialog box and clickNext.
10. Examine the results on theCross Validation andValidation dialog boxes andclick Finish.
11. Click on the Output LayerInformation dialog box andclick OK.
Tip
Creating training and testdatasets-+. +/%0+ 1
See Also
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Using validation(), +)
Deterministic.p65 03/07/2001, 12:51 PM119
120 USING ARCGIS GEOSTATISTICAL ANALYST
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DETERMINISTIC METHODS FOR SPATIAL INTERPOLATION 121
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Deterministic.p65 03/07/2001, 12:51 PM121
122 USING ARCGIS GEOSTATISTICAL ANALYST
Creating a mapusing globalpolynomial inter-polation. " ' " " # "
Creating a predictionmap
1. Click on the point layer onwhich to perform GlobalPolynomial Interpolation inthe ArcMap table of contents.
2. Start the GeostatisticalAnalyst.
3. Click the Attribute dropdownmenu and click the attributeon which to perform GlobalPolynomial Interpolation inthe Choose Input Data andMethod dialog box.
4. Click the Global PolynomialInterpolation method andclick Next.
5. Specify the desired order ofpolynomial in the GlobalPolynomial Interpolation SetParameters dialog box andclick Next.
6. Examine the results on theCross Validation dialog boxand click Finish.
7. On the Output Layer Informa-tion dialog box click OK.
Deterministic.p65 03/07/2001, 12:51 PM122
DETERMINISTIC METHODS FOR SPATIAL INTERPOLATION 123
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124 USING ARCGIS GEOSTATISTICAL ANALYST
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DETERMINISTICAL METHODS OF SPATIAL DATA INTERPOLATION 125
Creating a mapusing localpolynomialinterpolation/ '" '
Creating a predictionmap
1. Click on the point layer onwhich to perform LocalPolynomial Interpolation inthe ArcMap table of contents.
2. Start the GeostatisticalAnalyst.
3. Click the Attribute dropdownmenu and click the attributeon which to perform LocalPolynomial Interpolation inthe Choose Input Data andMethod dialog box.
4. Click the Local PolynomialInterpolation method.
5. Click Next.
6. Specify the desired param-eters in the LP InterpolationSet Parameters dialog boxand click Next.
7. Examine the results on theCross Validation dialog boxand click Finish.
8. On the Output Layer Informa-tion dialog box, click OK.
See Also
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Deterministic.p65 03/07/2001, 12:51 PM125
126 USING ARCGIS GEOSTATISTICAL ANALYST
How radial basis functions work
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Deterministic.p65 03/07/2001, 12:51 PM126
DETERMINISTIC METHODS FOR SPATIAL INTERPOLATION 127
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DETERMINISTICAL METHODS OF SPATIAL DATA INTERPOLATION 129
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Creating a predictionmap using RBFs
1. Click on the point layer onwhich to perform RadialBasis Functions in theArcMap table of contents.
2. Start the GeostatisticalAnalyst.
3. Click the Attribute dropdownmenu and click the attributeon which to perfom RadialBasis Functions in theChoose Input Data andMethod dialog box.
4. Click the Radial BasisFunctions method.
5. Click Next.
6. Click on the Kernel Functionsdropdown menu and click thedesired Radial BasisFunction in the RBF Interpo-lation Set Parameters dialogbox.
7. Specify the desired param-eters in the RBF Set Param-eters dialog box and clickNext.
8. Examine the results on theCross Validation dialog boxand click Finish.
9. On the Output Layer Informa-tion dialog box, click OK.
See Also
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Deterministic.p65 03/07/2001, 12:51 PM129
Deterministic.p65 03/07/2001, 12:51 PM130
131
IN THIS CHAPTER
Creating a surface with geostatistical techniques 6• What are geostatistical interpola-
tion techniques?
• Understanding kriging models
• Understanding output surfaces
• Creating a map using defaults
• Understanding transformationsand trends
• Understanding and mapping with:
• Ordinary kriging
• Simple kriging
• Universal kriging
• Indicator kriging
• Probability kriging
• Disjunctive kriging
• Cokriging
In the previous chapter, you learned about deterministic techniques forinterpolation. Deterministic techniques used the existing configuration of thesample points to create a surface (Inverse Distance Weighted) or fit amathematical function to the measured points (global and local polynomialand radial basis functions). In this chapter, you will get an overview of thedifferent geostatistical interpolation techniques. As their name implies,geostatistical techniques create surfaces incorporating the statisticalproperties of the measured data. Because geostatistics is based on statistics,these techniques produce not only prediction surfaces but also error oruncertainty surfaces, giving you an indication of how good the predictionsare.
Many methods are associated with geostatistics, but they are all in the krigingfamily. Ordinary, simple, universal, probability, indicator, and disjunctivekriging along with their counterparts in cokriging are available inGeostatistical Analyst. Not only do these kriging methods create predictionand error surfaces, but they can also produce probability and quantile outputmaps depending on your needs.
Kriging is divided into two distinct tasks: quantifying the spatial structure ofthe data and producing a prediction. Quantifying the structure, known asvariography, is where you fit a spatial-dependence model to your data. Tomake a prediction for an unknown value for a specific location, kriging willuse the fitted model from variography, the spatial data configuration, and thevalues of the measured sample points around the prediction location.Geostatistical Analyst provides many tools to help you determine whichparameters to use, but it also provides reliable defaults that you can use tomake a surface quickly.
ch06_GeoStatistics.pmd 11/25/2003, 3:03 PM131
132 USING ARCGIS GEOSTATISTICAL ANALYST
What are geostatistical interpolation techniques?
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CREATING A SURFACE WITH GEOSTATISTICAL TECHNIQUES 133
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GeoStatistics.p65 03/07/2001, 2:46 PM134
CREATING A SURFACE WITH GEOSTATISTICAL TECHNIQUES 135
Understanding output surface types
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GeoStatistics.p65 03/07/2001, 2:46 PM135
136 USING ARCGIS GEOSTATISTICAL ANALYST
Creating akriging map usingdefaults "
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Using the defaults
1. Click the point layer on whichyou wish to perform kriging inthe ArcMap table of contents.
2. Start the GeostatisticalWizard.
3. Click the Attribute dropdownmenu, and click the attributeon which you wish to performkriging.
4. Click the Kriging method.
5. Click Next.
6. On all subsequent dialogboxes, click Next.
7. On the Cross Validationdialog box, click Finish.
8. On the Output Layer Informa-tion dialog box, click OK.
Tip
Using the Finish button7+ $)"
GeoStatistics.p65 03/07/2001, 2:46 PM136
CREATING A SURFACE WITH GEOSTATISTICAL TECHNIQUES 137
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GeoStatistics.p65 03/07/2001, 2:46 PM137
138 USING ARCGIS GEOSTATISTICAL ANALYST
Understanding ordinary kriging
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GeoStatistics.p65 03/07/2001, 2:46 PM138
CREATING A SURFACE WITH GEOSTATISTICAL TECHNIQUES 139
Creating a mapusing ordinarykriging. # 4# # '" "
Creating a predictionmap
1. Click the point layer on whichyou wish to perform OrdinaryKriging in the ArcMap table ofcontents.
2. Start the GeostatisticalAnalyst.
3. Click the Attribute dropdownlist, and click the attribute onwhich you wish to performordinary kriging.
4. Click the Kriging method.
5. Click Next.
6. Click Prediction underOrdinary Kriging.
7. Click Next.
8. Specify the desired param-eters in the Semivariogram/Covariance Modeling dialogbox and click Next.
9. Specify the desired param-eters in the SearchingNeighborhood dialog box andclick Next.
10. Examine the results on theCross Validation dialog boxand click Finish.
11. On the Output Layer Infor-mation dialog box, click OK.
Tip
Using a database fileinstead of a point layer7,( $ '( )* +
See Also
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Tip
Important parameters' +8+
GeoStatistics.p65 03/07/2001, 2:46 PM139
140 USING ARCGIS GEOSTATISTICAL ANALYST
Creating a predictionstandard error map
1. Right-click on the predictionsurface in the ArcMap table ofcontents that was createdusing Ordinary Kriging andclick Create PredictionStandard Error Map.
Creating a prediction mapusing validation
1. Click the point layer on whichyou wish to perform ordinarykriging in the ArcMap table ofcontents.
2. Start Geostatistical Analyst.
3. Click the Attribute dropdownlist and specify the field onwhich you wish to performordinary kriging.
4. Click the Kriging method.
5. Check Validation and specifythe validation dataset andattribute.
6. Click Next.
7. Follow steps 6 through 10 in‘Creating a prediction map’ onthe previous page andexamine the results on theValidation dialog box andthen click Finish.
Tip
Creating training and testdatasets !"#$
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Using validation%&!' &
GeoStatistics.p65 3/21/01, 8:12 AM140
CREATING A SURFACE WITH GEOSTATISTICAL TECHNIQUES 141
Creating a predictionmap while applying atransformation
1. Click the point layer on whichyou wish to perform ordinarykriging in the ArcMap table ofcontents.
2. Start the GeostatisticalAnalyst.
3. Click the Attribute field onwhich you wish to performordinary kriging.
4. Click the Kriging method.
5. Click Next.
6. Expand the list underOrdinary Kriging and clickPrediction.
7. Click the desired transforma-tion from the Transformationdropdown menu.
8. Click Next.
9. Follow steps 9 through 12 in‘Creating a prediction mapusing detrending’ on thefollowing page.
Tip
Utilizing ESDA fordetermining modelparameters!$) ++8++9+
See Also
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GeoStatistics.p65 03/07/2001, 2:46 PM141
142 USING ARCGIS GEOSTATISTICAL ANALYST
Creating a predictionmap using detrending
1. Click the point layer on whichyou wish to perform ordinarykriging in the ArcMap table ofcontents.
2. Start Geostatistical Analyst.
3. Click the Attribute dropdownlist and select the attribute onwhich you wish to performordinary kriging.
4. Click the Kriging method.
5. Click Next.
6. Click Prediction underOrdinary Kriging.
7. Click the Order of TrendRemoval dropdown menu andchoose an option.
8. Click Next.
9. Specify the desired param-eters in the Detrending dialogbox and click Next.
10. Specify the desired param-eters in the Semivariogram/Covariance Modeling dialogbox and click Next.
11. Specify the desired param-eters in the SearchingNeighborhood dialog boxand click Next.
12. Examine the results on theCross Validation dialog boxand click Finish.
13. On the Output Layer Informa-tion dialog box, click OK.
Tip
Detrending7+)
See Also
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GeoStatistics.p65 03/07/2001, 2:46 PM142
CREATING A SURFACE WITH GEOSTATISTICAL TECHNIQUES 143
Understanding simple kriging
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GeoStatistics.p65 03/07/2001, 2:47 PM143
144 USING ARCGIS GEOSTATISTICAL ANALYST
Creating a predictionmap
1. Click the point layer on whichyou wish to perform simplekriging in the ArcMap table ofcontents.
2. Start the GeostatisticalAnalyst.
3. Click the Attribute field onwhich you wish to performsimple kriging.
4. Click the Kriging method.
5. Click Next.
6. Expand the list under SimpleKriging and click Prediction.
7. Specify the Mean Value.
8. Click Next.
9. Specify the desired param-eters in the Semivariogram/Covariance Modeling dialogbox and click Next.
10. Specify the desired param-eters in the SearchingNeighborhood dialog boxand click Next.
11. Examine the results on theCross Validation dialog boxand click Finish.
12. On the Output Layer Informa-tion dialog box, click OK.
Creating a mapusing simplekriging. #4# # 5"
See Also
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GeoStatistics.p65 03/07/2001, 2:47 PM144
CREATING A SURFACE WITH GEOSTATISTICAL TECHNIQUES 145
Creating a quantile map
1. Follow the steps in ‘Creatinga prediction map’ on theprevious page, except clickQuantile Map in step 6,rather than Prediction.
2. Click the Quantile up anddown arrow buttons tospecify the quantile level.
3. Follow steps 7 through 12 in‘Creating a prediction map’on the previous page.
See Also
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Creating a probabilitymap
1. Follow the steps in ‘Creatinga prediction map’ on theprevious page, except clickProbability Map in step 6,rather than Prediction.
2. Type a value in the Thresholdinput or click the Set... buttonand set the threshold on thePrimary Threshold selectiondialog box.
3. Click either the Exceed orNOT Exceed radio buttons.
4. Click Next.
5. Follow steps 7 through 12 in‘Creating a prediction map’on the previous page.
GeoStatistics.p65 3/21/01, 8:16 AM145
146 USING ARCGIS GEOSTATISTICAL ANALYST
Tip
Using validation(), +)
Creating a predictionstandard error map
1. Right-click on the predictionsurface in the ArcMap tableof contents that was createdusing simple kriging andclick Create PredictionStandard Error Map.
Tip
Creating training and testdatasets-+. +/%09+ &1
GeoStatistics.p65 03/07/2001, 2:47 PM146
CREATING A SURFACE WITH GEOSTATISTICAL TECHNIQUES 147
Creating a predictionmap while applying atransformation
1. Click the point layer on whichyou wish to perform simplekriging in the ArcMap table ofcontents.
2. Start the GeostatisticalAnalyst.
3. Click the Attribute field onwhich you wish to performsimple kriging.
4. Click the Kriging method.
5. Click Next.
6. Expand the list under simplekriging and click Prediction.
7. Click the desired transforma-tion from the Transformationdropdown menu.
8. Click Next.
9. Follow steps 9 through 12 in‘Creating a prediction map’,earlier in the chapter.
Tip
Exploratory Spatial DataAnalysis tools!$) ++98++9+
See Also
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GeoStatistics.p65 03/07/2001, 2:47 PM147
148 USING ARCGIS GEOSTATISTICAL ANALYST
Creating a predictionmap while applying atransformation withdeclustering
1. Click the point layer on whichyou wish to perform simplekriging in the ArcMap table ofcontents.
2. Start the GeostatisticalAnalyst.
3. Click the Attribute field onwhich you wish to performsimple kriging.
4. Click the Kriging method.
5. Click Next.
6. Expand the list under SimpleKriging and click Prediction.
7. Click Normal Score under theTransformation dropdownmenu.
8. Check Declustering beforeTransform.
9. Click Next.
10. Specify the desired param-eters in the Declusteringdialog box and click Next.
11. Specify the desired param-eters in the Normal ScoreTransformation dialog boxand click Next.
12. Follow steps 9 through 12 in‘Creating a prediction map’,earlier in the chapter.
See Also
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Tip
Using declustering, !
GeoStatistics.p65 03/07/2001, 2:47 PM148
CREATING A SURFACE WITH GEOSTATISTICAL TECHNIQUES 149
Examining the bivariatedistribution whencreating a prediction map
1. Click the point layer on whichyou wish to perform simplekriging in the ArcMap table ofcontents.
2. Start Geostatistical Analyst.
3. Click the Attribute field onwhich you wish to performsimple kriging.
4. Click the Kriging method.
5. Click Next.
6. Expand the list under SimpleKriging and click Prediction.
7. Check Examine BivariateDistribution.
8. Specify Mean Value and thenumber of Quantiles tocheck.
9. Click Next.
10. Specify the desired param-eters in the Semivariogram/Covariance Modeling dialogbox and click Next.
11. Explore the Semivariogram/Covariance Modeling(Examine Bivariate Distribu-tion) dialog box and clickNext.
12. Follow steps 10 through 12in ‘Creating a predictionmap’, earlier in the chapter.
Tip
Bivariate distribution
See Also
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GeoStatistics.p65 3/21/01, 8:16 AM149
150 USING ARCGIS GEOSTATISTICAL ANALYST
Understanding universal kriging
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GeoStatistics.p65 3/21/01, 8:16 AM150
CREATING A SURFACE WITH GEOSTATISTICAL TECHNIQUES 151
Creating a mapusing universalkriging. # 4# # '"
Creating a predictionmap
1. Click the point layer on whichyou wish to perform universalkriging in the ArcMap table ofcontents.
2. Start Geostatistical Analyst.
3. Click the Attribute field onwhich you wish to performuniversal kriging.
4. Click the Kriging method andclick Next.
5. Under Universal Kriging,expand the list and clickPrediction.
6. Click the Order of Trenddropdown menu and click thedesired order.
7. Click Next.
8. Specify the desired param-eters in the Detrendingdialog box and click Next.
9. Specify the desired param-eters in the Semivariogram/Covariance Modeling dialogbox and click Next.
10. Specify the desired param-eters in the SearchingNeighborhood dialog boxand click Next.
11. Examine the results on theCross Validation dialog boxand click Finish.
12. On the Output Layer Infor-mation dialog box, click OK.
See Also
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GeoStatistics.p65 03/07/2001, 2:47 PM151
152 USING ARCGIS GEOSTATISTICAL ANALYST
Creating a predictionstandard error map
1. Right-click on the predictionsurface in the ArcMap table ofcontents that was createdusing universal kriging andclick Create PredictionStandard Error Map.
Tip
Utilizing ESDA fordeterminingtransformations!:$') ++8++9+
GeoStatistics.p65 03/07/2001, 2:47 PM152
CREATING A SURFACE WITH GEOSTATISTICAL TECHNIQUES 153
Understanding thresholds
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GeoStatistics.p65 03/07/2001, 2:47 PM153
154 USING ARCGIS GEOSTATISTICAL ANALYST
Understanding indicator kriging
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GeoStatistics.p65 03/07/2001, 2:47 PM154
CREATING A SURFACE WITH GEOSTATISTICAL TECHNIQUES 155
Creating a mapusing indicatorkriging. '"
Creating a probabilitymap
1. Click the point layer on whichyou wish to perform indicatorkriging in the ArcMap table ofcontents. Start the Geostatis-tical Analyst.
2. Click the Attribute field onwhich you wish to performindicator kriging.
3. Click the Kriging method.
4. Click Next.
5. Expand the list underIndicator Kriging and clickProbability Map.
6. Type the Threshold value orclick the Set... button and setthe threshold on the PrimaryThreshold selection dialogbox.
7. Click either the Exceed orNOT Exceed radio buttons.
8. Click Next.
9. Set additional cutoffs on theAdditional Cutoffs selectiondialog box.
10. Specify the desired param-eters in the Semivariogram/Covariance Modeling andSearching Neighborhooddialog boxes and click Nextin each dialog box.
11. Examine the results on theCross Validation dialog boxand click Finish.
12. On the Output Layer Infor-mation dialog box, click OK.
Tip
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GeoStatistics.p65 03/07/2001, 2:47 PM155
156 USING ARCGIS GEOSTATISTICAL ANALYST
Understanding probability kriging
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GeoStatistics.p65 03/07/2001, 2:47 PM156
CREATING A SURFACE WITH GEOSTATISTICAL TECHNIQUES 157
Creating a mapusing probabilitykriging.
Creating a probabilitymap
1. Click the point layer on whichyou wish to perform probabil-ity kriging in the ArcMaptable of contents.
2. Start the GeostatisticalAnalyst.
3. Click the Attribute field onwhich you wish to performprobability kriging.
4. Click the Kriging method.
5. Click Next.
6. Expand the list underProbability Kriging and clickProbability Map.
7. Type in the Threshold valueor click the Set... button andset the threshold on thePrimary Threshold selectiondialog box.
8. Click either the Exceed orNOT Exceed radio buttons.
9. Click Next.
10. Specify the desired param-eters in the Semivariogram/Covariance Modeling andSearching Neighborhooddialog boxes and click Nextin each dialog box.
Tip
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GeoStatistics.p65 03/07/2001, 2:47 PM157
158 USING ARCGIS GEOSTATISTICAL ANALYST
12. Examine the results on theCross Validation dialog boxand click Finish.
13. On the Output Layer Infor-mation dialog box, click OK.
GeoStatistics.p65 03/07/2001, 2:47 PM158
CREATING A SURFACE WITH GEOSTATISTICAL TECHNIQUES 159
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GeoStatistics.p65 03/07/2001, 2:47 PM159
160 USING ARCGIS GEOSTATISTICAL ANALYST
Creating a mapusing disjunctivekriging
Creating a predictionmap
1. Click the point layer on whichyou wish to perform disjunc-tive kriging in the ArcMaptable of contents.
2. Start the GeostatisticalAnalyst.
3. Click the Attribute field onwhich you wish to performdisjunctive kriging.
4. Click the Kriging method.
5. Click Next.
6. Expand the list underDisjunctive Kriging and clickPrediction. Specify MeanValue. Optionally, specifyNormal Score Transformation(NST) and click Next.
7. If an NST was indicated,specify the desired param-eters in the NST dialog boxand click Next.
8. Specify the desired param-eters in the Semivariogram/Covariance Modeling dialogbox and click Next.
9. Specify the desired param-eters in the SearchingNeighborhood dialog box andclick Next.
10. Examine the results on theCross Validation dialog boxand click Finish.
11. On the Output Layer Infor-mation dialog box, click OK.
Tip
Using a database fileinstead of a point layer
Tip
Important parameters!"!#!!
See Also
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GeoStatistics.p65 3/21/01, 8:17 AM160
CREATING A SURFACE WITH GEOSTATISTICAL TECHNIQUES 161
Creating a probabilitymap
1. Follow the steps in ‘Creatinga prediction map’ on theprevious page, except clickon Probability Map in step 6rather than Prediction.
2. Type in the Threshold valueor click the Set... button andset the threshold on thePrimary Threshold selectiondialog box.
3. Click either the Exceed orNOT Exceed radio buttons.
4. Specify Mean Value andNormal Score Transformation.Click Next.
5. Follow steps 7 through 11 in‘Creating a prediction map’earlier in the chapter.
See Also
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Creating a predictionstandard error map
1. Right-click on the predictionsurface in the ArcMap table ofcontents that was createdusing disjunctive kriging andclick Create PredictionStandard Error Map.
Tip
A prediction standard errormap!, !!!-.!/0!
GeoStatistics.p65 3/21/01, 8:17 AM161
162 USING ARCGIS GEOSTATISTICAL ANALYST
Creating a standard errorof indicators map
1. Follow the steps for ‘Creatinga probability map’ previouslyin this chapter, except clickStandard Error of Indicatorsin step 6 rather than Predic-tion.
GeoStatistics.p65 03/07/2001, 2:47 PM162
CREATING A SURFACE WITH GEOSTATISTICAL TECHNIQUES 163
Creating a predictionmap with declustering
1. Click the point layer on whichyou wish to perform disjunc-tive kriging in the ArcMaptable of contents.
2. Start the GeostatisticalAnalyst.
3. Click the Attribute field onwhich you wish to performdisjunctive kriging.
4. Click the Kriging method.
5. Click Next.
6. Expand the list underDisjunctive Kriging and clickPrediction.
7. Click Normal Score under theTransformation dropdownmenu.
8. Check Declustering beforeTransform.
9. Click Next.
10. Specify the desired param-eters in the Declusteringdialog box and click Next.
11. Specify the desired param-eters in the Normal ScoreTransformation dialog boxand click Next.
12. Follow steps 8 through 11 in‘Creating a prediction map’,previously in this chapter.
Tip
Using declustering
GeoStatistics.p65 3/21/01, 8:17 AM163
164 USING ARCGIS GEOSTATISTICAL ANALYST
Examining the bivariatedistribution whencreating a prediction map
1. Click the point layer on whichyou wish to perform disjunc-tive kriging in the ArcMaptable of contents.
2. Click the GeostatisticalAnalyst toolbar and clickGeostatistical Wizard.
3. Click the Attribute field onwhich you wish to performdisjunctive kriging.
4. Click the Kriging method.Click Next.
5. Expand the list underDisjunctive Kriging and clickPrediction.
6. Check Examine BivariateDistribution and specifyMean Value or NST.
7. Specify the desired param-eters in the Semivariogram/Covariance Modeling dialogbox and click Next.
8. Explore the Semivariogram/Covariance Modeling dialogbox (Examine BivariateDistribution) and click Next.
9. Follow steps 9 through 11 in‘Creating a prediction map’,previously in this chapter.
See Also
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GeoStatistics.p65 3/21/01, 8:17 AM164
CREATING A SURFACE WITH GEOSTATISTICAL TECHNIQUES 165
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GeoStatistics.p65 03/07/2001, 2:47 PM165
166 USING ARCGIS GEOSTATISTICAL ANALYST
Creating a mapusing cokriging
Creating a predictionmap
1. Click the point layers onwhich you wish to performcokriging in the ArcMap tableof contents.
2. Click the GeostatisticalAnalyst toolbar and clickGeostatistical Wizard.
3. Click the CoKriging method.
4. Click the Attribute field onwhich you wish to performcokriging for all datasets(switch between dataset tabsto specify the parameters).
5. Click Next.
6. Click the desired cokrigingmethod and output layer typein the Geostatistical Methodslist. Click Next.
7. Specify the parameters in theDetrending dialog box if theOrder of Trend Removal wasspecified for all datasets.Click Next.
8. Specify the parameters in theSemivariogram/CovarianceModeling dialog box for alldatasets. Click Next.
9. Specify the desired param-eters in the SearchingNeighborhood dialog box forall datasests and click Next.
10. Examine the results on theCross Validation dialog boxand click Finish.
11. On the Output Layer Informa-tion dialog box, click OK.
See Also
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GeoStatistics.p65 3/21/01, 8:17 AM166
IN THIS CHAPTER
167
Using analytical tools when generating surfaces 7• Investigating spatial structure:
variography
• Determining the neighborhoodsearch size
• Performing cross-validation toassess parameter selections
• Assessing decision protocol usingvalidation
• Comparing one model withanother
• Modeling distributions and deter-mining transformations
• Checking for the bivariate normaldistribution
• Implementing declustering toadjust for preferential sampling
• Removing trends from the data
There are many steps that you go through when creating a surface. In eachof these steps, you specify a number of parameters. Geostatistical Analystprovides a series of dialog boxes containing analytical tools to assist you indetermining the values for the parameters. Some of these dialog boxes andtools are applicable to almost all interpolation methods such as specifyingthe search neighborhood, cross-validation, and validation. Others arespecific to the geostatistical methods (kriging and cokriging), such asmodeling semivariograms, transformations, detrending, declustering, andchecking for bivariate normal distributions.
Within each dialog box, there are a series of tasks that can be accomplishedusing the tools. In this chapter, the concepts for the most frequentlyperformed tasks are discussed and the steps identified. Depending on yourdata, none, some, or all of the tasks and their parameters might be explored.As with all parameters, Geostatistical Analyst provides reliable defaults,some of which have been calculated specifically for your data. However,you may have additional insight into your data from prior knowledge of thephenomena under study or that you gained through the exploratory toolsprovided with Geostatistical Analyst, which you can use to refine theparameters to create an even more accurate surface.
ch07_AnalyticalTools.pmd 11/25/2003, 3:04 PM167
168 USING ARCGIS GEOSTATISTICAL ANALYST
Investigating spatial structure: variography
Semivariograms and covariance functions
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USING ANALYTICAL TOOLS WHEN GENERATING SURFACES 169
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AnalyticalTools.p65 03/07/2001, 2:49 PM169
170 USING ARCGIS GEOSTATISTICAL ANALYST
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Range
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AnalyticalTools.p65 03/07/2001, 2:49 PM170
USING ANALYTICAL TOOLS WHEN GENERATING SURFACES 171
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172 USING ARCGIS GEOSTATISTICAL ANALYST
Theoretical model
Empirical values
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Using the empirical data to estimate theoreticalmodels
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AnalyticalTools.p65 03/07/2001, 2:49 PM172
USING ANALYTICAL TOOLS WHEN GENERATING SURFACES 173
Empirical values
Theoretical model
Highest cross-covariance is shifted to the west.
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AnalyticalTools.p65 03/07/2001, 2:49 PM173
174 USING ARCGIS GEOSTATISTICAL ANALYST
The Semivariogram/Covariance Modeling dialog box
Empiricalsemivariogram
surface
Semivariogramvalue
Omnidirectionalmodel
Availablesemivariogram
models
Associatedparametervalues
Semivariogramcloud
Lag distance
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USING ANALYTICAL TOOLS WHEN GENERATING SURFACES 175
Modelingsemivariogramsand covariancefunctions6 "! "
## ' #
Selecting a model
1. On the Semivariogram/Covariance Modeling dialogbox, click on the desiredsemivariogram model.
You will notice that the yellowline modeling in theSemivariogram dialog boxwill change to reflect themodel that is selected.
See Also
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Tip
Selecting the model+))+!+9+
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176 USING ARCGIS GEOSTATISTICAL ANALYST
Exploring for directionalautocorrelation
1. Check Show Search Direc-tion.
2. Click the up or down arrowsof the Angle Direction toexplore for the desireddirectional angle.
Alternatively, in thesemivariogram map, clickand hold the middle blue lineand drag to the desireddirection.
3. Click the up or down arrowsof the Angle Tolerance toadjust the angle of tolerance.
Alternatively, in the semivari-ogram map, click and holdeither of the red directionalindicator lines and drag tothe desired angle.
4. Click the up or down arrowsof the Bandwidth.
Alternatively, in thesemivariogram map, clickand hold either of the purplelines located on the bound-ing square. Drag to thedesired width.
Tip
Autocorrelation in yourdata
Tip
This is a graphicalexploration only ! "#
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USING ANALYTICAL TOOLS WHEN GENERATING SURFACES 177
Modeling anisotropy
1. Check Anisotropy on theSemivariogram/CovarianceModeling dialog box.
Notice the single yellow linebecomes many lines whenanisotropy is checked.
Tip
Calculating the optimalparameters +A $+*)+
Altering the anisotropyparameters
1. Check Anisotropy on theSemivariogram/CovarianceModeling dialog box.
Note: The Minor Range andDirection check boxesbecome active.
2. To change the major range,click the pencil icon abovethe Major Range input(which makes the input boxactive) and type in thedesired range.
3. To change the minor range,click the pencil icon abovethe Minor Range input(which makes the input boxactive) and type in thedesired range.
Tip
Checking thesemivariogram afteranisotropy is checked))',++
Tip
Checking the anisotropycheck box# )+34; =++B'3(AC(C'4
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178 USING ARCGIS GEOSTATISTICAL ANALYST
4. To change the angle direc-tion, click the pencil iconabove the Direction input(which makes the input boxactive) and type in thedesired angle.
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USING ANALYTICAL TOOLS WHEN GENERATING SURFACES 179
Changing the lag sizeand number of lags
1. On the Semivariogram/Covariance Modeling dialogbox, type the desired LagSize.
2. Click the up or down arrowsor type in the desired valuein order to change theNumber of Lags.
Tip
Choosing a lag size' > 9
Tip
Calculating the optimalparameters + $+*)+
Changing the partial silland nugget
1. On the Semivariogram/Covariance Modeling dialogbox, click on the pencilabove the Partial Sill input(which makes the input boxactive) and type in thedesired value.
2. Check the Nugget check box,click on the pencil iconabove the Nugget input(which makes the input boxactive), and type in thedesired value.
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180 USING ARCGIS GEOSTATISTICAL ANALYST
Handling measurementerror
1. Check the Error Modelingcheck box.
2. Move the scroll bar todetermine the percentages ofMicroStructure and Measure-ment Error for the nugget.
Alternatively, type thepercentages or values intothe input boxes.
Tip
Zero measurement error,>;$=)
Tip
Instrument error()@
Tip
Multiple measurements,+B' )(: $):
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USING ANALYTICAL TOOLS WHEN GENERATING SURFACES 181
Determining the neighborhood search size
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Semivariogramenvelope
Check Anisotropy to showsemivariogram envelope
(i.e., semivariogram curvesfor all directions).
Use the Search Direction tool todetermine the location of the
range in a particular direction.
AnalyticalTools.p65 3/21/01, 8:20 AM181
182 USING ARCGIS GEOSTATISTICAL ANALYST
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Ellipse with four sectors
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USING ANALYTICAL TOOLS WHEN GENERATING SURFACES 183
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If not enough points areavailable within the searchneighborhood, the softwareselects the nearest availablepoints (this yellow pointbelongs to the upper-rightsector).
Only two points are availablein this sector.
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184 USING ARCGIS GEOSTATISTICAL ANALYST
The Searching Neighborhood dialog box
Click to previewthe surface.
Number of points usedto predict a value at a
test location.
The minimum number of pointsto be used (they may lie outside
the search ellipse).
Geometry andnumber of sectorsused in the search.
Crosshairsdefine the test
location.
Points used andassociated
weights.
Prediction fortest location.
AnalyticalTools.p65 3/21/01, 8:20 AM184
USING ANALYTICAL TOOLS WHEN GENERATING SURFACES 185
Determining theneighborhoodsearch size $ " "
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Changing the number ofpoints to include in aneighborhood
1. On the Searching Neighbor-hood dialog box, click theNeighbors to Include up anddown arrows.
Alternatively, type in thedesired value.
2. To set a minimum of points toinclude in the neighborhood,check the Include at Leastcheck box and click the upand down arrows until thedesired value is reached.
Alternatively, type the valuein the input field.
Tip
Assessing a neighborhood 9 9+++ B9',
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186 USING ARCGIS GEOSTATISTICAL ANALYST
Altering the shape of theneighborhood
1. On the Searching Neighbor-hood dialog box, click thedesired ellipse icon tochange the default neighbor-hood shape type.
2. Check the Shape check box.
The controls in the shapeframe will become active.
3. Click the Angle up or downarrows or type in the desiredangle to alter the angle of theellipse.
4. Type the desired value in theMajor and Minor Semiaxisinput fields to alter the shapeof the ellipse.
In the display window of thedialog box, the ellipse willreflect the changes.
Tip
Weight values- +9DD;=
Tip
, ($+ (A$
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USING ANALYTICAL TOOLS WHEN GENERATING SURFACES 187
Determining theprediction for a specificlocation
1. The number of neighborsused for prediction and theprediction are displayedbelow the input fields (in thebottom right of the dialogbox). To initiate a newprediction location, click thedesired location in thedisplay area of the dialogbox.
2. Alternatively, enter thelocation in the X and Y inputfields.
The prediction and number ofneighbors are updatedimmediately with the newlocation.
Tip
The predicted value7# $EF+G&@34
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188 USING ARCGIS GEOSTATISTICAL ANALYST
Altering the map view
1. On the Searching Neighbor-hood dialog box, to zoom inon the map display, click theZoom In button, then drag abox around the area of themap on which the zoom willoccur.
2. To zoom out on the mapdisplay, click the Zoom Outbutton.
3. To pan around in the mapdisplay, click the Pan buttonand move the mouse into themap display, hold down theleft mouse button, and movethe cursor.
The map will move incoordination with the cursor.
4. To display the map using thefull extent, click the FullExtent button.
5. To preview the outputsurface, click the Previewtype dropdown menu andclick Surface. To return to theprevious view, click Neigh-bors.
AnalyticalTools.p65 03/07/2001, 2:49 PM188
USING ANALYTICAL TOOLS WHEN GENERATING SURFACES 189
Performing cross-validation and validation
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AnalyticalTools.p65 03/07/2001, 2:49 PM189
190 USING ARCGIS GEOSTATISTICAL ANALYST
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USING ANALYTICAL TOOLS WHEN GENERATING SURFACES 191
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AnalyticalTools.p65 03/07/2001, 2:49 PM191
192 USING ARCGIS GEOSTATISTICAL ANALYST
The Cross Validation and Validation dialog box
Line of best fit 1:1 Line
Results fromcross-validationor validation
Summarystatistics
Cross-validationscatter plot
Save to a file
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USING ANALYTICAL TOOLS WHEN GENERATING SURFACES 193
Performing cross-validation to as-sess parameterselections( " 7" 8 $ 9#4 # 4 # $4 :
/
Examining the predictedfit
1. On the Cross Validationdialog box, select either thePredicted, Error, Standard-ized Error, or QQPlot tabaccording to the desiredmethod in which you want toview the results.
Selecting a particularpoint
1. On the Cross Validationdialog box, in the table at thebottom right, click on the rowrepresenting the point ofinterest.
When a row is selected, thepoint is highlighted in thechart above.
Tip
Selecting points- +)
Tip
Viewing all rows andcolumns! +
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194 USING ARCGIS GEOSTATISTICAL ANALYST
Saving the cross-validation statistics to afile
1. Click Save Cross Validation.
2. Navigate to the location tosave the dataset.
3. Type the name of the dataset.
4. Click the type of dataset.
5. Click Save.
Tip
Viewing a saved table++ )' + 9) C9)'( )7
AnalyticalTools.p65 03/07/2001, 2:49 PM194
USING ANALYTICAL TOOLS WHEN GENERATING SURFACES 195
Assessingdecision protocolusing validation;"
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Creating the subsets touse for validation
1. Add the dataset that you wishto subset to ArcMap.
2. Click Create Subsets.
3. Click the dropdown arrowand click on the dataset thatyou wish to subset.
4. Click Next.
5. Optionally, change thelocation and/or name for theoutput geodatabase file.
6. Optionally, change thedefault subset names.
7. Click and drag the slider tothe required position.
8. Click Finish.
Tip
Dividing the training andtest dataH
See Also
09++3)49++
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196 USING ARCGIS GEOSTATISTICAL ANALYST
Performing validation
1. Click the Add Data buttonand navigate to the test andtraining datasets (createdfollowing the steps on theprevious page). Click Add.
2. Start the GeostatisticalAnalyst Wizard.
3. Click the Input Datadropdown arrow and clickthe training layer (created bysubsetting the originaldataset on the previouspage).
4. Click the Attribute dropdownarrow and click the attributeyou want to use in theinterpolation.
5. Check the Validation checkbox.
6. Click the Input Datadropdown arrow and clickthe test dataset (created bysubsetting the originaldataset on the previouspage).
7. Click the Attribute dropdownarrow and click the sameattribute you chose for thetraining dataset.
8. Click the Method you wish touse.
9. Click Next on this and allsubsequent dialog boxesuntil you reach the Validationdialog box.
10. Optionally, click to save thevalidation table to a data-base.
Tip
Opening a saved table++ )' '(+ 9) C9)'( )7
Tip
Highlighting values- +)
Viewing all rows andcolumns! +
Tip
AnalyticalTools.p65 03/07/2001, 2:49 PM196
USING ANALYTICAL TOOLS WHEN GENERATING SURFACES 197
Comparing one model with another
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AnalyticalTools.p65 03/07/2001, 2:49 PM197
198 USING ARCGIS GEOSTATISTICAL ANALYST
The Cross Validation Comparison dialog box
Fitted linefor layer 1
Summarystatistics for
layer 1
Cross-validation
scatter plot forlayer 1
Summarystatistics forlayer 2
Fitted linefor layer 2
Cross-validationscatter plot for
layer 2
1:1 line forlayer 1
1:1 line forlayer 2
AnalyticalTools.p65 03/07/2001, 2:49 PM198
USING ANALYTICAL TOOLS WHEN GENERATING SURFACES 199
Comparingone model withanother. 5 ) )<::8 < ::8 < : ) ::8 @
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Performing comparison
1. Right-click one of the layersin the ArcMap table ofcontents you wish to com-pare and click on Compare.
2. Click the second layer in thecomparison in the Todropdown menu.
3. Click the various tabs to seethe different results of thecomparison.
4. Click Close to close theCross Validation Comparisondialog box.
See Also
09++3)49++
AnalyticalTools.p65 03/07/2001, 2:49 PM199
200 USING ARCGIS GEOSTATISTICAL ANALYST
Modeling distributions and determining transformations
Box–Cox, arcsine, and log transformations
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AnalyticalTools.p65 03/07/2001, 2:49 PM200
USING ANALYTICAL TOOLS WHEN GENERATING SURFACES 201
Normal score transformation
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AnalyticalTools.p65 03/07/2001, 2:49 PM201
202 USING ARCGIS GEOSTATISTICAL ANALYST
The Normal Score Transformation distribution dialog box
Choose number ofGaussian kernels
EmpiricalCumulativeDistributionfunction
FittedCumulativeDistributionfunction(red line)
Number ofhistogram bars
Approximation method:Direct (default), linear,Gaussian kernels
Fitted probability density(for Gaussian kernels only)
Histogram of datarepresenting probabilitydensity
Dataset
AnalyticalTools.p65 03/07/2001, 2:50 PM202
USING ANALYTICAL TOOLS WHEN GENERATING SURFACES 203
Comparing normal score transformation to othertransformations
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AnalyticalTools.p65 03/07/2001, 2:50 PM203
204 USING ARCGIS GEOSTATISTICAL ANALYST
Usingtransformations(log, Box–Cox,and arcsine).
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Using transformations
1. On the Geostatistical MethodSelection dialog box, clickthe desired transformation inthe Transformation dropdownmenu.
2. Click Next.
3. Follow the dialog boxes tocreate a surface.
Tip
When you can transform )),( $
AnalyticalTools.p65 03/07/2001, 2:50 PM204
USING ANALYTICAL TOOLS WHEN GENERATING SURFACES 205
Using the normalscoretransformation " )
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Modeling distributions
1. Click the Simple or Disjunc-tive Kriging interpolationmethod to use for thedistribution.
2. On the Geostatistical MethodSelection dialog box, clickNormal Score in the Transfor-mation dropdown list.
3. Click Next.
4. Alternatively, click Cumula-tive Distribution to switch thedisplay of the graph.
5. Alternatively, type the numberof bars you wish to display inthe chart.
6. Click the Dataset Selectiondropdown arrow to switchbetween datasets (only forcokriging where you havetwo or more datasets).
AnalyticalTools.p65 03/07/2001, 2:50 PM205
206 USING ARCGIS GEOSTATISTICAL ANALYST
Checking for the bivariate normal distribution
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AnalyticalTools.p65 03/07/2001, 2:50 PM206
USING ANALYTICAL TOOLS WHEN GENERATING SURFACES 207
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AnalyticalTools.p65 03/07/2001, 2:50 PM207
208 USING ARCGIS GEOSTATISTICAL ANALYST
The Examine Bivariate Distribution dialog box
Fitted covariancefunction toempirical
covariance onindicators (yellow
line)
Empiricalcovariance on
indicators
Theoreticalcurve of
indicatorcovariance,
assuming datacomes from
bivariate normaldistribution(green line)
AnalyticalTools.p65 03/07/2001, 2:50 PM208
USING ANALYTICAL TOOLS WHEN GENERATING SURFACES 209
Checking forbivariatedistribution
Checking for bivariatedistribution
1. Click the Add Data button onthe ArcMap toolbar and addthe layer you wish to checkfor bivariate distribution.
2. Start the GeostatisticalWizard.
3. Click either Kriging orCokriging.
4. Click Next on the ChooseInput Data and Methoddialog box.
5. Click the Simple or Disjunc-tive Kriging/Cokrigingmethod to use.
6. Check Examine BivariateDistribution and selectNormal Score Transformation.
7. Choose the Dataset combi-nation you wish to use(cokriging only).
8. Type the number of quantilesto check.
9. Click Next.
10. Click the ApproximationMethod in the dropdownmenu, set the parameters,and click either ProbabilityDensity or CumulativeDistribution radio buttons onthe Normal Score Transfor-
Tip
Methods that enable thebivariate distribution to bechecked
AnalyticalTools.p65 3/21/01, 8:20 AM209
210 USING ARCGIS GEOSTATISTICAL ANALYST
11. Specify the desired param-eters in the Semivariogram/Covariance Modeling dialogbox and click Next.
12. Explore the bivariatedistribution on the ExamineBivariate Distribution dialogbox. Click Next.
AnalyticalTools.p65 03/07/2001, 2:50 PM210
USING ANALYTICAL TOOLS WHEN GENERATING SURFACES 211
Implementing declustering to adjust for preferential sampling
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AnalyticalTools.p65 03/07/2001, 2:50 PM211
212 USING ARCGIS GEOSTATISTICAL ANALYST
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AnalyticalTools.p65 03/07/2001, 2:50 PM212
USING ANALYTICAL TOOLS WHEN GENERATING SURFACES 213
The Declustering dialog box
Griddisplayingcell size
Ratio of cell“height” to
“width”
Set cellsize
Color legend correspondingto the size of the polygons
Plot of weightedmean versus
grid size
Orientation of the grid
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214 USING ARCGIS GEOSTATISTICAL ANALYST
Declustering toadjust forpreferentialsampling
Performing celldeclustering
1. Click Kriging or Cokriging onthe Choose Input Data andMethod dialog box.
2. Click either Probability,Disjunctive, or SimpleKriging or Cokriging meth-ods.
3. Click the Normal Scoretransformation in the Trans-formation dropdown menu.
4. Check Declustering beforeTransform.
5. Click Next.
6. Click the Dataset Selectiondropdown arrow and clickthe dataset you wish todisplay (cokriging only).
7. Specify the desired param-eters.
8. Click the tabs to switchbetween the Cell Size,Anisotropy, and Angle charts.
9. Change cell size, anisotropy,shift, and angle to find theextremum in the graph.
10. Alternatively, click theDeclustering Methoddropdown arrow and clickPolgonal to switch to apolygon declusteringdisplay.
11. Click Next.
Tip
Using declustering
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USING ANALYTICAL TOOLS WHEN GENERATING SURFACES 215
12. Click the ApproximationMethod in the dropdownmenu, set the parameters,and click either ProbabilityDensity or Cumulativedistribution radio buttons onthe Normal Score Transfor-mation dialog box. ClickNext.
13. Specify the desired param-eters in the Semivariogram/Covariance Modeling dialogbox and click Next.
14. Specify the desired param-eters in the SearchingNeighborhood dialog boxand click Next.
15. Examine the results on theCross Validation dialog boxand click Finish.
16. On the Output Layer Informa-tion dialog box, click OK.
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216 USING ARCGIS GEOSTATISTICAL ANALYST
Removing trends from the data
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USING ANALYTICAL TOOLS WHEN GENERATING SURFACES 217
The Detrending dialog box (Standard option)
The datasetbeing detrended
Controls for thetrend display
The neighborhoodsearch size
The power ofthe polynomial
Map legend
SearchingNeighborhood
settings
The estimatedtrend display
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218 USING ARCGIS GEOSTATISTICAL ANALYST
Removing globaland local trendsfrom the data:detrending. ( @#, -!
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Using the slider toestimate the trend
1. On the Geostatistical MethodSelection dialog box, clickeither Ordinary Kriging,Universal Kriging, or Disjunc-tive Kriging and the desiredoutput surface type in theGeostatistical Method treeview.
2. Click the dropdown arrow onthe Order of Trend Removaland click the order for thetrend.
3. Click Next.
Note: If the order of trend isanything but None, then theDetrending dialog box willfollow when clicking Next.
4. On the Detrending dialogbox, by moving the sliderbetween the two extremes,you define the window sizefor fitting the polynomial fromGlobal to Local.
Alternatively, to set theneighborhood parametersclick Advanced Options>>.
5. Click Next.
Tip
The order of your trendsH9 +
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IN THIS CHAPTER
219
Displaying and managing geostatistical layers 8• What is a geostatistical layer?
• Adding layers
• Working with layers in a map
• Managing layers
• Viewing geostatistical layers inArcCatalog
• Representing a geostatistical layer
• Changing the symbology of ageostatistical layer
• Data classification
• Setting the scales at which ageostatistical layer will bedisplayed
• Predicting values for locationsoutside the area of interest
• Saving and exporting geostatisti-cal layers
ArcMap and Geostatistical Analyst provide a wide variety of tools withwhich to display and manage your data. With the display tools, you cancreate fine cartographic output and explore or analyze your data to gaingreater insights in order to make more effective decisions. Exploration isparticularly important when using Geostatistical Analyst because throughthese insights you are able to build better models and create more accuratesurfaces.
Even though the management tools may not directly aid in the creation ofsurfaces with Geostatistical Analyst, these tools are indispensable fororganizing and ordering the map session as well as your own thinking.
Many of the display and management tools that are applicable to anyArcMap layer are also applicable to a geostatistical layer. In this chapter, wewill only discuss the general layer tools that are most often used whenworking with Geostatistical Analyst and the tools that are specific to ageostatistical layer. Please refer to Using ArcMap for additional tools thatcan be applied to all layer types, including geostatistical layers.
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220 USING ARCGIS GEOSTATISTICAL ANALYST
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What is a geostatistical layer?
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DISPLAYING AND MANAGING GEOSTATISTICAL LAYERS 221
Contours
Grid
Hillshade
Combination of contours, filled contours, and hillshade
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222 USING ARCGIS GEOSTATISTICAL ANALYST
Adding layers'6 # # B # #
#"# B B ## 6 #
Adding layers
1. Click the Add Data button onthe ArcMap Standard toolbar.
2. Click the Look in dropdownarrow and navigate to thefolder that contains the layer.
3. Click the layer.
4. Click Add.
Adding a group layer
1. Right-click on Layers in theArcMap table of contents andclick New Group Layer.
2. Right-click the resulting NewGroup Layer in the table ofcontents and click Properties.
3. Click the General tab.
4. Optionally, name the grouplayer.
5. Optionally, check the Visiblecheck box to make the GroupLayer visible.
6. Optionally, set the ScaleRange.
7. Click the Group tab.
8. Click Add and navigate to adataset you wish to add.
9. Click Add.
10. Continue adding the desireddatasets to the group byrepeating steps 8 and 9.
11. Click OK.
Tip
Revealing hidden layersE ;=+9))2E
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DISPLAYING AND MANAGING GEOSTATISTICAL LAYERS 223
Working withlayers in a map
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Turning the display of alayer on or off
1. Check the check box to theleft of the layer name to turnthe layer on or off.
Zooming and panning alayer
1. Click View in the ArcMapmenu bar, click Toolbars, andcheck Tools.
2. Various tools, accessedthrough icons on the Toolstoolbar, can be used toexplore the map.
Moving a layer to changeits drawing order
1. In the table of contents, clickand drag the layer up ordown to the desired position.
A black line indicates wherethe layer will be placed.
2. Release the mouse pointer todrop the layer into the newposition.
See Also
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224 USING ARCGIS GEOSTATISTICAL ANALYST
Managing layers6 # B ## #
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Changing the name of alayer
1. Click the layer in the table ofcontents to select it.
2. Click again on the name.
This will highlight the nameand enable it to be changed.
3. Type the new name.
Copying a layer
1. Right-click the layer you wantto copy and click Copy.
2. Right-click the Layers dataframe.
3. Click Paste Layer(s).
Removing a layer
1. Right-click the layer you wantto remove and click Remove.
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DISPLAYING AND MANAGING GEOSTATISTICAL LAYERS 225
Viewinggeostatisticallayers inArcCatalogB ""((""4"
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Starting ArcCatalog andenabling GeostatisticalAnalyst
1. Click the Start button on theWindows taskbar.
2. Point to Programs.
3. Point to ArcGIS.
4. Point to ArcCatalog.
The ArcCatalog windowappears. Now, click the Toolsmenu, click Extensions, andcheck Geostatistical Analyst.Click Close.
Tip
Metadata'+))
Tip
Accessing ArcCatalog' '( )'
Previewing data
1. Start ArcCatalog.
2. Navigate to the desiredgeostatistical layer in thetable of contents.
3. Click the Preview tab.
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226 USING ARCGIS GEOSTATISTICAL ANALYST
Viewing layer metadata
1. Start ArcCatalog.
2. Navigate to the desiredgeostatistical layer in thetable of contents.
3. Click the Metadata tab.
4. Click the Description tab toretrieve a general descriptionof the layer.
5. Click the Spatial tab toexplore the spatial character-istics of the layer such as itsbounding coordinates.
6. Click the Attributes tab toexamine other informationabout the layer.
7. Input or change any meta-data information.
See Also
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DISPLAYING AND MANAGING GEOSTATISTICAL LAYERS 227
Representing ageostatisticallayer "
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Displaying ageostatistical layer asfilled contours
1. Right-click the desiredgeostatistical layer in theArcMap table of contents andclick Properties.
2. Click the Symbology tab.
3. Click Filled Contours in theShow list and check theaccompanying check box.
4. Set the desired parameters.
5. Click OK.
Displaying ageostatistical layer as agrid
1. Right-click the desiredgeostatistical layer in theArcMap table of contents andclick Properties.
2. Click the Symbology tab.
3. Click Grid in the Show listand check the accompanyingcheck box.
4. Set the desired parameters.
5. Click OK.
Tip
Viewing multiple datasets++
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228 USING ARCGIS GEOSTATISTICAL ANALYST
Displaying thegeostatistical layer as ahillshade
1. Click the desired geostatisti-cal layer in the ArcMap tableof contents and click Proper-ties.
2. Click the Symbology tab.
3. Click Hillshade in the Showlist and check the accompa-nying check box.
4. Set the desired parameters.
5. Click OK.
Tip
Shortcut to the layerproperties 9) '()E0 $
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Displaying thegeostatistical layer ascontours
1. Click the desired geostatisti-cal layer in the ArcMap tableof contents and click Proper-ties.
2. Click the Symbology tab.
3. Click Contours in the Showlist and check the accompa-nying check box.
4. Set the desired parameters.
5. Click OK.
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DISPLAYING AND MANAGING GEOSTATISTICAL LAYERS 229
Changing thesymbology of ageostatisticallayer6 . # #" $" "
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Changing the colorscheme
1. Right-click the geostatisticallayer and click Properties.
2. Click the Symbology tab.
3. Click on either Contours,Grid, or Filled Contours forthe layer from the Show list.
4. Click the Color Rampdropdown arrow and click acolor scheme.
5. Click OK.
Tip
Zooming'> >, C9))C
Changing the colorinteractively
1. Right-click a symbol from thelegend of a geostatisticallayer.
2. Click a color for the symbol.
All values in the displayrepresented with this symbolwill be displayed in thechosen color.
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230 USING ARCGIS GEOSTATISTICAL ANALYST
Data classification
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Display.p65 03/07/2001, 3:41 PM230
DISPLAYING AND MANAGING GEOSTATISTICAL LAYERS 231
Equal interval
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232 USING ARCGIS GEOSTATISTICAL ANALYST
Smart quantiles
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DISPLAYING AND MANAGING GEOSTATISTICAL LAYERS 233
Classifying data+#
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Setting a predefinedclassification method
1. In the table of contents, right-click the geostatistical layeryou want to classify and clickProperties.
2. Click the Symbology tab.
3. Click Classify.
4. Click the Method dropdownarrow and click a classifica-tion method.
5. Click the up/down arrows onthe Classes input box to setthe desired number ofclasses.
6. Click OK on the Classificationdialog box.
7. Click OK on the LayerProperties dialog box.
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234 USING ARCGIS GEOSTATISTICAL ANALYST
Manually altering theclass breaks
1. In the table of contents, right-click the geostatistical layeryou want to classify manuallyand click Properties.
2. Click the Symbology tab.
3. Click Classify.
4. Click the Method dropdownarrow and click Manual.
5. Click the up/down arrow ofthe Classes input box untilthe desired number ofclasses is reached.
6. Click and drag the classbreaks to the desired posi-tion.
7. Alternatively, type in specificclass breaks.
8. Alternatively, check theCustom Min & Max checkbox, then type specificminimum and maximumvalues to include in theclassification.
9. Click OK on the Classificationdialog box.
10. Click OK on the Symbologytab.
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DISPLAYING AND MANAGING GEOSTATISTICAL LAYERS 235
Setting the scalesat which ageostatisticallayer will bedisplayed6 " $3# !
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Setting the scale range
1. Right-click the geostatisticallayer and click Properties.
2. Click the General tab.
3. Click Don’t show layer whenzoomed.
4. Set the scale range byinputting the out beyond andin beyond entries.
5. Click OK.
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236 USING ARCGIS GEOSTATISTICAL ANALYST
Predicting valuesfor locationsoutside the areaof interest1#B " E" # "
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Extrapolating values
1. Right-click the geostatisticallayer that you want toextrapolate values for in theArcMap table of contents andclick Properties.
2. Click the Extent tab.
3. Click a custom extent enteredbelow in the Set the extent todropdown list.
4. Type the new values into theVisible Extent.
Alternatively, use the extentof any other available layer.
5. Click OK.
Tip
$+ $):$
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DISPLAYING AND MANAGING GEOSTATISTICAL LAYERS 237
Saving andexportinggeostatisticallayers
! " #
Saving a mapcomposition
1. Click the File menu and clickSave As.
2. Navigate to the directory inwhich you want to save themap.
3. Change the map name ifdesired.
4. Click Save.
Tip
Distributing ageostatistical layer
Saving individual layers
1. Right-click the geostatisticallayer you wish to save in theArcMap table of contents andclick Save As Layer File.
2. Navigate to the directory inwhich you want to save thelayer.
3. Change the layer name ifdesired.
4. Click Save.
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238 USING ARCGIS GEOSTATISTICAL ANALYST
Exporting a geostatisticallayer to a raster
1. Right-click the geostatisticallayer in the ArcMap table ofcontents, click Data, and clickExport to Raster.
2. Set the desired properties forthe resulting raster such asthe number of rows andcolumns, cell size, number ofpredictions in each cell(Block Interpolations), andthe name and location for theraster.
3. Click OK.
Exporting a geostatisticallayer to a vector format
1. Right-click the geostatisticallayer in the ArcMap table ofcontents, click Data, and clickExport to Vector.
2. Specify the output format(e.g., shapefile, personalgeodatabase, or SDEdatabase).
3. Select Contours or FilledContours from the Exportdropdown menu.
4. Click OK.
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IN THIS CHAPTER
239
Additional geostatistical analysis tools 9• Changing the parameters of a
geostatistical layer: methodproperties
• Predicting values for specifiedlocations
• Performing validation on ageostatistical layer created from asubset
• Stratifying your data for betterpredictions
There are many supporting tools in ArcMap and Geostatistical Analyst toassist in geostatistical analysis. You can change the parameters in a model,retrieve predictions for specific locations, perform validation from subsets,spatially divide your data, interpolate each division, and then combine theresults. This chapter is not an exhaustive list of tools that will help withgeostatistical analysis. Instead, it discusses some of the more commonlyused tools that will aid in your analysis. But you should be aware thatbecause Geostatistical Analyst is integrated into ArcMap, there arecountless functions that you can and will use in your analysis. The morefamiliar you become with ArcMap and the supporting Geostatistical Analystextensions, the more tools you will find that meet your specific need tocreate even more accurate surfaces.
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240 USING ARCGIS GEOSTATISTICAL ANALYST
Changing theparameters of ageostatisticallayer: methodproperties " B# "6 1 # " " " 0 " # " # "$ "
Using method properties
1. Right-click the geostatisticallayer in the ArcMap table ofcontents and click MethodProperties.
The options availabledepend on the techniqueused to create the originalsurface. Follow these stepswhen the prediction surfaceis created by a krigingmethod.
2. Click on the desired krigingmethod.
3. Click Next on the Geostatisti-cal Method Selection dialogbox.
4. Optionally, change any of themodel parameters and clickNext on the Semivariance/Covariance Modeling dialogbox.
5. Optionally, define a newsearch neighborhood andclick Next on the SearchingNeighborhood dialog.
6. Assess the cross-validationresults. Has the outputimproved? If not, repeat steps2 to 5. If yes, Click Finish onthe Cross Validation dialogbox.
7. Click OK on the Output LayerInformation dialog box.
Tip
Understanding methodproperties(0 $ 9++
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ADDITIONAL GEOSTATISTICAL ANALYSIS TOOLS 241
Predicting valuesfor specifiedlocations 2 # "
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Using map tips
1. Create a geostatistical layerusing any of the methodsdiscussed in Chapters 5 or 6.
2. Right-click the geostatisticallayer and click Properties.
3. Click the Display tab.
4. Check Show MapTips.
5. Click OK.
6. Place the cursor over a pointof interest on the layer.
The value at that location isdisplayed.
Tip
Selecting points using theattribute table, 39))7' 4
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242 USING ARCGIS GEOSTATISTICAL ANALYST
Predicting at specificlocations from a pointlayer
1. Right-click in the ArcMaptable of contents thegeostatistical layer that wascreated using observed dataand click Prediction.
2. Click the Input Datadropdown arrow and clickthe layer containing thelocations for which you wantto obtain predictions.
3. Identify the directory to storethe output dataset in byclicking the browse buttonnext to Specify outputshapefile or feature class.
4. Browse or type the directoryand name for the output file.
5. Click Save and OK.
6. Add the prediction file to theArcMap table of contentswhen prompted.
7. Right-click the predictionlayer and click Open AttributeTable to display the results.
The predicted values at thespecified locations will bedisplayed in the table.
Tip
Other ways to view theresults
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ADDITIONAL GEOSTATISTICAL ANALYSIS TOOLS 243
Performingvalidation on ageostatisticallayer createdfrom a subset " 4 " 2##!# A " A # # # #
Creating subsets
1. Click the GeostatisticalAnalyst toolbar and clickCreate Subsets.
2. Click the Input Layerdropdown arrow and clickthe layer to be divided.
3. Click Next.
4. Click and drag the slider barto an appropriate location toselect the relative percent-ages of training and testdata.
By default, the output datasetis named according to thefollowing convention: “inputfiledataset”+“_sets.mdb”, forexample,inputpoints_sets.mdb, whereinputpoints is the name of theinput dataset containing thepoints.
5. Click Finish.
The training and testdatasets form two tables inthe personal geodatabase.
Tip
Dividing the dataset+ + + @)+9 +
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244 USING ARCGIS GEOSTATISTICAL ANALYST
Performing validationusing subsets
1. Click the Add Data icon onthe Standard toolbar inArcMap. Navigate to thefolder in which the subsetdata was saved (if it is not inthe ArcMap table of con-tents).
2. Click both the training andtest layers (click one layer,then hold down the Shift keyand click the other).
3. Click Add.
4. Click the GeostatisticalAnalyst toolbar and clickGeostatistical Wizard.
5. Click the Input Datadropdown menu and click thetraining dataset.
6. Click an appropriate method.
7. Click Next and follow thedialog boxes to create asurface.
8. Right-click the newly createdgeostatistical layer and clickValidation....
9. Click the test dataset in theInput Data dropdown menu.
10. Click the same attribute inthe Attribute dropdown menuthat the surface was createdin.
11. Type a name and locationfor saving the output(validation) dataset.
12. Click OK.
Tip
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ADDITIONAL GEOSTATISTICAL ANALYSIS TOOLS 245
13. When queried, add thevalidation layer to theArcMap table of contents.
14. Right-click the new layerand click Open AttributeTable.
The results of the validationare displayed for assess-ment.
Tip
The resulting output files+.+ ++ $9+3& !4
AdditionalTools.p65 03/08/2001, 3:49 PM245
AdditionalTools.p65 03/08/2001, 3:49 PM246
IN THIS APPENDIX
247
Appendix A• Deterministic methods
• Inverse distance weightedinterpolation
• Global polynomial interpolation
• Local polynomial interpolation
• Radial basis function interpola-tion
• Geostatistical methods
• Declustering dialog box
• Distribution modeling dialog box
• Semivariogram/Covariancedialog box
• Bivariate distribution dialog box
• Kriging formulas
• Cross Validation dialog box
There are many formulas and unique implementation concepts underlyingGeostatistical Analyst. The formulas and technical concepts are presentedhere in this appendix. It is assumed that you have some training inmathematics or geostatistics before reading this appendix.
Following the appendix are references from commonly used textbooks andjournal articles for the mathematical details of the methods used inGeostatistical Analyst. In some cases, when the details are not easily foundin textbooks, we give greater detail.
AppendixA.pmd 11/25/2003, 3:17 PM247
248 USING ARCGIS GEOSTATISTICAL ANALYST
Deterministic methods
Inverse distance weighted interpolation
Global polynomial interpolation
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APPENDIX A 249
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AppendixA.p65 3/21/01, 8:25 AM249
250 USING ARCGIS GEOSTATISTICAL ANALYST
Geometric anisotropy
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AppendixA.p65 03/08/2001, 2:38 PM250
APPENDIX A 251
Declustering dialog box
Cell declustering
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AppendixA.p65 03/08/2001, 2:38 PM251
252 USING ARCGIS GEOSTATISTICAL ANALYST
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AppendixA.p65 03/08/2001, 2:38 PM252
APPENDIX A 253
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AppendixA.p65 03/08/2001, 2:38 PM253
254 USING ARCGIS GEOSTATISTICAL ANALYST
h y-direction
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AppendixA.p65 03/08/2001, 2:38 PM254
APPENDIX A 255
4<5 5**5 @*<5@ *@
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AppendixA.p65 03/08/2001, 2:38 PM255
256 USING ARCGIS GEOSTATISTICAL ANALYST
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AppendixA.p65 03/08/2001, 2:38 PM256
APPENDIX A 257
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AppendixA.p65 03/08/2001, 2:38 PM257
258 USING ARCGIS GEOSTATISTICAL ANALYST
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AppendixA.p65 03/08/2001, 2:38 PM258
APPENDIX A 259
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AppendixA.p65 3/21/01, 8:25 AM259
260 USING ARCGIS GEOSTATISTICAL ANALYST
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AppendixA.p65 3/21/01, 8:25 AM260
APPENDIX A 261
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AppendixA.p65 3/21/01, 8:25 AM261
262 USING ARCGIS GEOSTATISTICAL ANALYST
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APPENDIX A 263
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AppendixA.p65 03/08/2001, 2:39 PM263
264 USING ARCGIS GEOSTATISTICAL ANALYST
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AppendixA.p65 03/08/2001, 2:39 PM264
APPENDIX A 265
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AppendixA.p65 05/11/2001, 12:55 PM265
266 USING ARCGIS GEOSTATISTICAL ANALYST
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AppendixA.p65 03/08/2001, 2:39 PM266
APPENDIX A 267
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AppendixA.p65 03/08/2001, 2:40 PM267
268 USING ARCGIS GEOSTATISTICAL ANALYST
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AppendixA.p65 03/08/2001, 2:40 PM268
APPENDIX A 269
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AppendixA.p65 03/08/2001, 2:49 PM269
270 USING ARCGIS GEOSTATISTICAL ANALYST
Probability kriging
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AppendixA.p65 3/21/01, 8:23 AM270
APPENDIX A 271
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AppendixA.p65 3/21/01, 8:23 AM271
272 USING ARCGIS GEOSTATISTICAL ANALYST
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AppendixA.p65 3/21/01, 8:24 AM272
APPENDIX A 273
Cross-validation summaries
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AppendixA.p65 03/08/2001, 2:41 PM273
AppendixA.p65 03/08/2001, 2:41 PM274
IN THIS APPENDIX
275
Appendix BThis appendix provides an overview of the methods that are available withthe Geostatistical Analyst. The following chart describes thecharacteristics of each method, summarizes its advandages anddisadvantages, and shows the type of output it creates. By comparing thedifferences between these methods you can determine which ones youshould use in your application.
• A comparison of the GeostatisticalAnalyst methods
AppendixB.pmd 11/25/2003, 4:38 PM275
276 USING ARCGIS GEOSTATISTICAL ANALYST
Method Deterministic/ Output Computing Exact Advantages Disadvantages Assumptions2
Stochastic Surface Time/ InterpolatorTypes Modeling
Time1
Inverse Deterministic Prediction Fast/Fast Yes Few parameter No assessment ofDistance decisions prediction errors;Weighted produces “bulls eyes”
around data locations None
Globalpolynomial Deterministic Prediction Fast/Fast No Few parameter No assessment of
decisions prediction errors;may be too smooth;edge points have largeinfluence None
Local Deterministic Prediction Moderatelypolynomial Fast/Moderate No More parameter No assessment of
decisions prediction errors;may be too automatic None
Radial Deterministic Prediction Moderately Yes Flexible and No assessment of Nonebasis Fast/Moderate automatic with prediction errors;functions some parameter may be too automatic
decisions
Kriging Stochastic Prediction; Moderately Yes without Very flexible; Need to make Data comes from aPrediction Fast/Slower measurement allows assessment many decisions on stationary stochasticStandard error; of spatial transformations, process, and someErrors; No with autocorrelation; trends, models, methods require thatProbability; measurement can obtain parameters, and the data comes from aQuantile error prediction standard neighborhoods normal distribution
errors; manyparameter decisions
Cokriging Stochastic Prediction; Moderate/ Yes without Very flexible; Need to make Data comes from aPrediction Slowest measurement can use information many decisions on stationary stochasticStandard error; in multiple datasets; transformations, process, and someErrors; No with allows assessment trends, models, methods require thatProbability; measurement of spatial cross- parameters, and the data comes fromQuantile error correlation; neighborhoods a normal distribution
many parameterdecisions
1. Computing time is computer-processing time to create a surface. Modeling time includes user-processing time to make decisions on model parameters and search neighborhoods.2. We assume that all methods are predicting a smooth surface from noisy data.
A comparison of the Geostatistical Analyst methods
AppendixB.p65 03/08/2001, 10:51 AM276
APPENDIX B 277
Descriptions
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AppendixB.p65 03/08/2001, 10:51 AM277
AppendixB.p65 03/08/2001, 10:51 AM278
279
12Glossary anisotropy ( )
autocorrelation O ;
bandwidth O ()
bin #
cokriging ( ) ( ) ( );! !
correlation; 0< <
covariance ?
Glossary.p65 03/08/2001, 11:28 AM279
280 USING ARCGIS GEOSTATISTICAL ANALYST
crosscorrelation
crosscovariance
cross-validation
crossvariogram !
deterministic "# #$"%&'( %')* &
%##&%&%#&
detrending %"&
directional influences+
dissimilarity,# #
empirical ! "$"
estimation
first-order polynomial%&-'
Glossary.p65 3/21/01, 8:26 AM280
GLOSSARY 281
"""./-%
.
".
&
geostatistics(0'( 01"
global polynomial interpolation2(
histogram
interpolate 3 "
intrinsic stationarity
inverse distance weighted interpolation2(
isotropy %& %&
kriging % &%&4#
lag%& %&%&
least-squares fit %& 5!
linear model of coregionalization # #
Glossary.p65 3/21/01, 8:26 AM281
282 USING ARCGIS GEOSTATISTICAL ANALYST
local polynomial interpolation2( $
long-range variation6 7#
mean stationarity
nugget
ordinary kriging%&2## #
partial sill '
polynomial '"" #-""""
.
".
.8'
"
prediction
prediction standard error! ! 9: #;<
probability map % &
QQPlot !
quantile! =- !
Glossary.p65 3/21/01, 8:26 AM282
GLOSSARY 283
radial basis functions2(
regression %& " !
residuals6 %"&
range
searching neighborhood 2
second-order polynomial%"& '"""./<%
.
".
.
".
.
"&
second-order stationarity
semicrossvariogram
semivariogram
semivariogram values
short-range variation6
sill ! (
spatial dependence
Glossary.p65 3/21/01, 8:26 AM283
284 USING ARCGIS GEOSTATISTICAL ANALYST
spherical model
spline interpolation2( $
stationarity
surface
trend ""
unimodal ""
univariate distribution #
validation
variogram !
variography' "
Glossary.p65 3/21/01, 8:26 AM284
285
References !
< % <BG'4! $ =*P!
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C#;<BB' 1?1FLE
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<'/<BGE# %&'()(>95CGB7C+'
<G/ ?<BB+01H ?*P!FLC
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<L!24 "<BLB((##1H ?*P!'G<
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References.p65 03/08/2001, 11:30 AM285
286 USING THE GEOSTATISTICAL ANALYST
! "#" $"""% &' ()* + ,! +-
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References.p65 3/21/01, 8:26 AM286
287
12Index A
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index2.p65 03/09/2001, 11:13 AM287
288 USING ARCGIS GEOSTATISTICAL ANALYST
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index2.p65 03/09/2001, 11:13 AM288
INDEX 289
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index2.p65 03/09/2001, 11:13 AM289
290 USING ARCGIS GEOSTATISTICAL ANALYST
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INDEX 291
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index2.p65 03/09/2001, 11:13 AM291
292 USING ARCGIS GEOSTATISTICAL ANALYST
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INDEX 293
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INDEX 295
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296 USING ARCGIS GEOSTATISTICAL ANALYST
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INDEX 297
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298 USING ARCGIS GEOSTATISTICAL ANALYST
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index2.p65 03/09/2001, 11:13 AM298
INDEX 299
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index2.p65 03/09/2001, 11:13 AM299
300 USING ARCGIS GEOSTATISTICAL ANALYST
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index2.p65 03/09/2001, 11:13 AM300