Applied Geostatistics
http://www.acsu.buffalo.edu/~lbian/GEO497_597.html
GEO 597 Spring 2016
Instructor: Ling Bian
Office: 301A Wilkeson
T R 5:00-6:20pm, 144 Wilkeson
Office Hours: T R 6:20-7:20pm
What is it
►
The course is intended to introduce the
basic concepts and applications of applied
geostatistics, which address optimal spatial
interpolation.
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.
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.
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 associated assignments will
provide students with hands-on experience
in using the geostatistical tool.
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
Prerequisites
The course is open to graduate students
who have knowledge of univariate statistics.
► Multivariate will help but is not required.
►
Requirements
►
►
During the semester, each student should
apply the geostatistical interpolation to a
data set.
Past students’ projects
Requirements
►
A term paper






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Introduction
Literature review
Study area
Data and methods (incorporate the labs, plus…)
Results and discussion
conclusions
10-15 double-spaced pages of text, plus
tables, figures, references
Grading
Lab 1
10%
Lab 2
10%
Lab 3
10%
Project Report
70%
-------------------------------------------------------------Total
100%
Grad cut-off
A
AB+
B
BC+
C
CD+
D
F
93.33-100.0
90.00-93.32
86.67-89.99
83.33-86.66
80.00-83.32
76.67-79.99
73.33-76.66
70.00-73.32
66.67-69.99
60.00-60.66
<60
Tentative Schedule
1/26
1/28
2/02
2/04
2/09
2/11
2/16
2/18
2/23
Introduction
Spatial Description
Spatial Description
Spatial Continuity
Estimation
Random Function Models
Random Function Models
Random Function Models
Lab section 1
Tentative Schedule …
2/25
3/01
3/03
3/08
3/10
Global Estimation
Point Estimation
Ordinary Kriging
Ordinary Kriging
Block Kriging &
Search Strategy
3/14-19 Spring Break
Tentative Schedule …
3/22
Cross Validation
3/24
Modeling Sample Variogram
4/05
Modeling Sample Variogram
4/07
Lab Section 2
4/12
Lab Section 3
4/14
Co-Kriging
4/19
Co-Kriging
4/21,26,28, 5/3 Presentations
5/05
Conclusions
Software
►
ArcMap Geostatistics Analyst
►
ESRI tutorial for Geostatistical Analyst
1. Definition
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A procedure of estimating the values of
properties at un-sampled sites
►
The property may be interval/ratio values,
can be nominal and ordinal
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The rational behind is that points close
together in space are more likely to have
similar values than points far apart
2. Terminology
►
Point/line/areal interpolation
point - point, point - line, point - areal
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
2. Terminology …
►
Exact/approximate interpolation
 exact - honor the original points
 approximate - when uncertainty is
involved in the data
►
Gradual/abrupt
3. Interpolation - Linear
► Linear
interpolation
Known values
Known and predicted
values after interpolation
3. Interpolation - Linear
Assume that
changes between
two locations are
linear
3. Interpolation - Proximal
►
Thiesson polygon approach
►
Local, exact, abrupt
►
►
Perpendicular bisector of a
line connecting two points
Best for nominal data
Construction of Polygon
+ 130
+ 200
+ 150
+ 180
+ 130
Polygon of influence for x=180
Construction of Polygon..
+ 130
+ 200
+ 150
+ 180
+ 130
Draw line segments between x and other points
Construction of Polygon..
+ 130
+ 200
+ 150
+ 180
+ 130
Find the midpoint and bisect the lines.
Construction of Polygon..
+ 130
+ 200
+ 150
+ 180
+ 130
Extend the bisecting lines till adjacent ones meet.
Construction of Polygon..
+ 130
+ 200
+ 150
+ 180
+ 130
Continue this process.
3. Interpolation - Proximal
3. Interpolation – Proximal ..
►
http://gizmodo.com/5884464/
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
3. Interpolation – Trend Surface
►
►
►
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Trend surface - polynomial approach
Global, approximate, gradual
Linear (1st order): z = a0 + a1x + a2y
Quadratic (2nd order):
z = a0 + a1x + a2y + a3x2
+ a4xy + a5y2
►
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Cubic etc.
Least 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
Distance
►
Local, approximate, gradual
S wiz i
1
z = --------, wi = -----, or wi = e
S wi
d ip
-pd
i
etc.
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
►
3. Interp – Fourier Series
3. Interp – Fourier Series
►
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
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
►
3. Kriging
First rule of geography:
► Everything is related to everything
else. Closer things are more related
than distant things
► By Waldo Tobler
►
3. Interp - Kriging
►
Semivariogram
►
Sill, range, nugget
Semivariance
1 n
g(h) = ------ S (Zi - Zi+h)2
2n i=1
Sill
Range
Lag distance (h)
3. Kriging
Isotropy vs. anisotropy
4. Summary Statistics
► Parameters
(for populations) m, s2, s
► Statistics (for samples), x, S2, S
4. Basic Statistics
►
Measures of location
mean, median, mode, minimum,
maximum, lower and upper quartiles
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Measures of spread
variance, standard deviation
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Correlation
covariance, correlation coefficient