Applied GeostatisticsApplied Geostatistics http://www.geog.buffalo.edu/~lbian/GEO497_597.html

GEO 597 Spring 2012

Instructor: Ling Bian T R 11:00-12:20pm, 144 Instructor: Ling Bian T R 11:00-12:20pm, 144 WilkesonWilkeson

Office: 120 Wilkeson Office Hours: T R 11-12:20pmOffice: 120 Wilkeson Office Hours: T R 11-12:20pm

What is itWhat is it

► The course is intended to introduce The course is intended to introduce the the basic concepts and applicationsbasic concepts and applications of of applied geostatistics, which address applied geostatistics, which address optimal spatial interpolation. optimal spatial interpolation.

What is it …What is it …

► Geostatistics are considered to be one Geostatistics are considered to be one of the most sophisticated spatial of the most sophisticated spatial interpolation methods. The method is interpolation methods. The method is commonly used in many disciplines commonly used in many disciplines such as geology, engineering, such as geology, engineering, hydrology, geography, ecology, urban hydrology, geography, ecology, urban studies, and medical geography. studies, and medical geography. Geostatistics are closely related to Geostatistics are closely related to statistics and GIS. statistics and GIS.

What is it …What is it …

► Students with basic knowledge of Students with basic knowledge of statistics or GIS can take a step further statistics or GIS can take a step further to learn how to use geostatistics. The to learn how to use geostatistics. The course emphasizes the applied side of course emphasizes the applied side of geostatistics, and the method can be geostatistics, and the method can be useful in students' immediate and useful in students' immediate and future needs such as students' own future needs such as students' own theses and dissertations, or projects for theses and dissertations, or projects for their current or potential employers. their current or potential employers.

What is it …What is it …

► The course uses a well received The course uses a well received textbook for the lectures and a popular textbook for the lectures and a popular GIS software package ArcGIS for the GIS software package ArcGIS for the lab exercises. Three lab sections and lab exercises. Three lab sections and assocated assignments will provide assocated assignments will provide students with hands-on experience in students with hands-on experience in using the geostatistical tool. using the geostatistical tool.

TextText

► An Introduction to Applied An Introduction to Applied Geostatistics. Oxford University Press, Geostatistics. Oxford University Press, New York, by Isaaks, Edward.H., and New York, by Isaaks, Edward.H., and R.Mohan. Srivastava, 1989. R.Mohan. Srivastava, 1989.

►The “Ed and Mo” bookThe “Ed and Mo” book

Prerequisites Prerequisites

► The course is open to graduate The course is open to graduate students who have knowledge of students who have knowledge of univariate statistics.univariate statistics.

► Multivariate will help but is not Multivariate will help but is not required.required.

Requirements Requirements

► During the semester, each student During the semester, each student should apply the geostatistical should apply the geostatistical interpolation to a interpolation to a data setdata set. .

► Past students’ projectsPast students’ projects

Requirements Requirements

► A term paperA term paper IntroductionIntroduction Literature reviewLiterature review Study areaStudy area Data and methods (incorporate the labs, Data and methods (incorporate the labs,

plus…)plus…) Results and discussionResults and discussion conclusionsconclusions

► around 15 double-spaced pages of text, around 15 double-spaced pages of text, plus tables, figures, referencesplus tables, figures, references

GradingGrading

Lab 1 10%   Lab 2   10%   Lab 3 10% Project Report 70%  --------------------------------------------------------------   Total  100% 

Grad cut-offGrad cut-off

A 93.33-100.0 A- 90.00-93.32   B+ 86.67-89.99B 83.33-86.66B- 80.00-83.32C+ 76.67-79.99C 73.33-76.66C- 70.00-73.32D+ 66.67-69.99D 60.00-60.66F <60

Tentative ScheduleTentative Schedule

1/17        Introduction 1/17        Introduction 1/19        Spatial Description 1/19        Spatial Description 1/26        Spatial Description 1/26        Spatial Description 1/31        Spatial Continuity 1/31        Spatial Continuity 2/ 2        Spatial Continuity 2/ 2        Spatial Continuity 2/ 7        Estimation 2/ 7        Estimation 2/ 9        Random Function Models 2/ 9        Random Function Models

2/142/14 Random Function Models Random Function Models

2/162/16 Lab section 1Lab section 1

Tentative Schedule …Tentative Schedule …

2/21        Global Estimation2/21        Global Estimation2/23        Point Estimation2/23        Point Estimation2/28        Ordinary Kriging2/28        Ordinary Kriging3/ 1        Ordinary Kriging3/ 1        Ordinary Kriging3/ 6        Block Kriging 3/ 6        Block Kriging 3/ 8        Search Strategy3/ 8        Search Strategy3/12-17 Spring Break3/12-17 Spring Break

Tentative Schedule …Tentative Schedule …

3/20        Cross Validation3/20        Cross Validation3/22        Modeling the Sample Variogram3/22        Modeling the Sample Variogram3/27        3/27        Lab Section 2Lab Section 2 3/29        3/29        Lab Section 3Lab Section 3

4/ 3        Co-Kriging4/ 3        Co-Kriging 4/ 5        Co-Kriging 4/ 5        Co-Kriging 4/10, 12 Advanced Topics      4/10, 12 Advanced Topics      4/17,19,24 4/17,19,24 PresentationsPresentations 4/26        Conclusion 4/26        Conclusion

SoftwareSoftware

► ArcMap Geostatistics AnalystArcMap Geostatistics Analyst

► ESRI tutorial for Geostatistical AnalystESRI tutorial for Geostatistical Analysthttp://honeybee.helsinki.fi/GIS/y196/Ushttp://honeybee.helsinki.fi/GIS/y196/Using_ArcGIS_Geostat_Anal_Tutor.pdfing_ArcGIS_Geostat_Anal_Tutor.pdf

 

1. Definition1. Definition

► A procedure of estimating the values of A procedure of estimating the values of properties at un-sampled sites properties at un-sampled sites

►   The property may be interval/ratio The property may be interval/ratio valuesvalues

►   The rational behind is that points close The rational behind is that points close

together in space are more likely to together in space are more likely to have similar values than points far apart have similar values than points far apart

2. Terminology2. Terminology

► Point/line/areal interpolation Point/line/areal interpolation point - point,  point - line, point - point - point,  point - line, point - areal areal

2. Terminology …2. Terminology …► Global/local interpolationGlobal/local interpolation

Global - apply a single function Global - apply a single function across the entire regionacross the entire region

Local - apply an algorithm to a small Local - apply an algorithm to a small portion at a time portion at a time

2. Terminology …2. Terminology …

► Exact/approximate interpolation Exact/approximate interpolation exact - honor the original pointsexact - honor the original points approximate - when uncertainty is approximate - when uncertainty is

involved in the data involved in the data

►   Gradual/abrupt Gradual/abrupt

3. Interpolation - Linear3. Interpolation - Linear

►Linear Linear interpolationinterpolation

Known valuesKnown and predicted values after interpolation

3. Interpolation - Linear3. Interpolation - Linear

Assume that Assume that changes changes between two between two locations are locations are linearlinear

3. Interpolation - Proximal3. Interpolation - Proximal► Thiesson polygon Thiesson polygon

approach approach

► Local, exact, abrupt Local, exact, abrupt

► Perpendicular bisector Perpendicular bisector of a line connecting two of a line connecting two pointspoints

► Best for nominal data Best for nominal data

3. Interpolation - Proximal3. Interpolation - Proximal

3. Interpolation – Proximal ..3. Interpolation – Proximal ..

► http://gizmodo.com/5884464/http://gizmodo.com/5884464/

3. Interpolation – B-spline 3. Interpolation – B-spline

► Local, exact, gradualLocal, exact, gradual

► Pieces a series of Pieces a series of smooth patches into a smooth patches into a smooth surface that smooth surface that has continuous first has continuous first and second and second derivativesderivatives

► Best for very smooth Best for very smooth surfaces e.g. French surfaces e.g. French curvescurves

3. Interpolation – Trend 3. Interpolation – Trend SurfaceSurface

► Trend surface - polynomial approachTrend surface - polynomial approach► Global, approximate, gradualGlobal, approximate, gradual► Linear (1st order):Linear (1st order): z = a z = a00 + a + a11x + ax + a22yy

► Quadratic (2nd order): Quadratic (2nd order): z = az = a00 + a + a11x + ax + a22y + ay + a33xx22

+ a+ a44xy + axy + a55yy22

► Cubic etc. Cubic etc. ► Least square methodLeast square method

Trends of one, two, and three independent variables for polynomial equations of the first, second, and third orders (after Harbaugh, 1964).

3. Interpolation – Inverse 3. Interpolation – Inverse DistanceDistance

► Local, approximate, gradual Local, approximate, gradual              w wiizzii              1               1 z = --------,   wz = --------,   wii = -----,  or  w = -----,  or  wii = e = e -pd-pd

ii  etc.   etc.

             w wii               d               diipp

3. Interp – Fourier Series3. Interp – Fourier Series

► Sine and cosine approachSine and cosine approach► Global, approximate, gradual Global, approximate, gradual ► Overlay of a series of sine and cosine Overlay of a series of sine and cosine

curves curves ► Best for data showing periodicity Best for data showing periodicity

3. Interp – Fourier Series3. Interp – Fourier Series

3. Interp – Fourier Series3. Interp – Fourier Series► Fourier seriesFourier series

Single harmonic in XSingle harmonic in X11 directiondirection

Two harmonics in XTwo harmonics in X11 directiondirection

Single harmonic in both XSingle harmonic in both X1 1 and Xand X22 directions directions

Two harmonics in both Two harmonics in both directionsdirections

3. Interp - Kriging3. Interp - Kriging

► Kriging - semivariogram approach, D.G. Kriging - semivariogram approach, D.G. Krige Krige

► Local, exact, gradual Local, exact, gradual ► Spatial dependence (spatial autocorrelation)Spatial dependence (spatial autocorrelation)►   Regionalized variable theory, Regionalized variable theory,

by Georges Matheron by Georges Matheron ► A situation between truly random and A situation between truly random and

deterministic deterministic ► Stationary vs. non-stationary Stationary vs. non-stationary

3. Kriging3. Kriging

► First rule of geography:First rule of geography:► Everything is related to Everything is related to

everything else. Closer things everything else. Closer things are more related than distant are more related than distant thingsthings

► By Waldo ToblerBy Waldo Tobler

3. Interp - Kriging3. Interp - Kriging

► Semivariogram Semivariogram              1    n              1    n   (h) = ------ (h) = ------   (Z  (Zii - Z - Zi+hi+h))22                         22n  i=1 n  i=1

►   Sill, range, nuggetSill, range, nugget Sill

Range

Lag distance (h)S

emiv

aria

nce

3. Kriging3. Kriging

Isotropy vs. anisotropyIsotropy vs. anisotropy

4. Summary Statistics4. Summary Statistics

►Parameters (for populations) m, sParameters (for populations) m, s22, s, s►Statistics (for samples), x, SStatistics (for samples), x, S22, S, S

4. Basic Statistics4. Basic Statistics

► Measures of locationMeasures of location mean, median, mode, minimum, mean, median, mode, minimum, maximum, lower and upper quartilesmaximum, lower and upper quartiles

► Measures of spreadMeasures of spread variance, standard deviationvariance, standard deviation

► CorrelationCorrelation covariance, correlation coefficientcovariance, correlation coefficient