1. Applied Geostatistics http://www. geog. buffalo. edu/~lbian/GEO497_597
Applied Geostatistics GEO 597 Spring 2012
Instructor: Ling Bian T R 11:00-12:20pm, 144 Wilkeson
Office: 120 Wilkeson Office Hours: T R 11-12:20pm

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

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

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

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

6. Text
An Introduction to Applied Geostatistics. Oxford University Press, New York, by Isaaks, Edward.H., and R.Mohan. Srivastava, 1989.
The “Ed and Mo” book

7. Prerequisites
The course is open to graduate students who have knowledge of univariate statistics.
Multivariate will help but is not required.

8. Requirements
During the semester, each student should apply the geostatistical interpolation to a data set.
Past students’ projects

9. Requirements A term paper
Introduction
Literature review
Study area
Data and methods (incorporate the labs, plus…)
Results and discussion
conclusions
around 15 double-spaced pages of text, plus tables, figures, references

10. Grading Lab 1 10% Lab 2 10% Lab 3 10% Project Report 70%   
Total  % 

11. Grad cut-off A 93.33-100.0 A- 90.00-93.32 B+ 86.67-89.99 B 83.33-86.66

12. Tentative Schedule
1/17        Introduction 1/19        Spatial Description 1/26        Spatial Description 1/31        Spatial Continuity 2/ 2        Spatial Continuity 2/ 7        Estimation 2/ 9        Random Function Models
2/14 Random Function Models
2/16 Lab section 1

13. Tentative Schedule …
2/21        Global Estimation 2/23        Point Estimation 2/28        Ordinary Kriging 3/ 1        Ordinary Kriging 3/ 6        Block Kriging 3/ 8        Search Strategy 3/ Spring Break

14. Tentative Schedule … 4/ 3 Co-Kriging 4/ 5 Co-Kriging
3/20        Cross Validation 3/22        Modeling the Sample Variogram 3/27        Lab Section 2 3/29        Lab Section 3
4/ 3        Co-Kriging 4/ 5        Co-Kriging
4/10, 12 Advanced Topics      4/17,19,24 Presentations
4/26        Conclusion

15. Software ArcMap Geostatistics Analyst
ESRI tutorial for Geostatistical Analyst  

16. 1. Definition
A procedure of estimating the values of properties at un-sampled sites
 The property may be interval/ratio values
 The rational behind is that points close together in space are more likely to have similar values than points far apart

18. 2. Terminology
Point/line/areal interpolation point - point,  point - line, point - areal

19. 2. Terminology … Global/local interpolation
Global - apply a single function across the entire region
Local - apply an algorithm to a small portion at a time

20. 2. Terminology … Exact/approximate interpolation
exact - honor the original points
approximate - when uncertainty is involved in the data
 Gradual/abrupt

21. 3. Interpolation - Linear
Linear interpolation
Known and predicted values after interpolation
Known values

22. 3. Interpolation - Linear
Assume that changes between two locations are linear

23. 3. Interpolation - Proximal
Thiesson polygon approach
Local, exact, abrupt
Perpendicular bisector of a line connecting two points
Best for nominal data

24. 3. Interpolation - Proximal

25. 3. Interpolation – Proximal ..

26. 3. Interpolation – B-spline
Local, exact, gradual
Pieces a series of smooth patches into a smooth surface that has continuous first and second derivatives
Best for very smooth surfaces e.g. French curves

27. 3. Interpolation – Trend Surface
Trend surface - polynomial approach
Global, approximate, gradual
Linear (1st order): z = a0 + a1x + a2y
Quadratic (2nd order):
z = a0 + a1x + a2y + a3x2
+ a4xy + a5y2
Cubic etc.
Least square method

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

29. 3. Interpolation – Inverse Distance
Local, approximate, gradual       S wizi              1 z = ,   wi = -----,  or  wi = e -pdi  etc.       S wi               dip

30. 3. Interp – Fourier Series
Sine and cosine approach
Global, approximate, gradual
Overlay of a series of sine and cosine curves
Best for data showing periodicity

31. 3. Interp – Fourier Series

32. 3. Interp – Fourier Series
Single harmonic in X1 direction
Two harmonics in X1 direction
Single harmonic in both X1 and X2 directions
Two harmonics in both directions

33. 3. Interp - Kriging Kriging - semivariogram approach, D.G. Krige
Local, exact, gradual
Spatial dependence (spatial autocorrelation)
 Regionalized variable theory,
by Georges Matheron
A situation between truly random and deterministic
Stationary vs. non-stationary

34. 3. Kriging First rule of geography:
Everything is related to everything else. Closer things are more related than distant things
By Waldo Tobler

36. 3. Interp - Kriging
Semivariogram              1    n  g(h) =  S  (Zi - Zi+h)2             2n  i=1
 Sill, range, nugget
Sill
Range
Lag distance (h)
Semivariance

37. 3. Kriging
Isotropy vs. anisotropy

38. 4. Summary Statistics Parameters (for populations) m, s2, s
Statistics (for samples), x, S2, S

39. 4. Basic Statistics Measures of location mean, median, mode, minimum,
maximum, lower and upper quartiles
Measures of spread
variance, standard deviation
Correlation
covariance, correlation coefficient