Point Estimation:

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Lecture 18 Spatial Interpolation I
Topics
Point Estimation 1. Process and Issues
References

• Chapter 8, Isaaks, E. H., and R. M. Srivastava,
  1989. Applied
• Geostatistics, Oxford University Press, New
  York
• Chapter 5, Burrough, P.A. and R.A. McDonnell,
  1998.
• Principles of Geographical Information
  Systems, Oxford
• University Press, New York, pp. 98-102.

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Outlines
1. Process and Issues 1.1 The need for spatial
interpolation (The Purpose Diagram)
1.2 The process 1.2.1 Determine the
level of details needed The
spacing of each estimation (spatial resolution)
1.2.2 Collect sample data to support the
level of details needed (the
Variable Sample Scheme Figure) 1.2.3
Examine the spatial autocorrelation from the data
set a) Degree of the spatial
autocorrelation b) Spatial extent
of the spatial autocorrelation
(The Semivariogram Approach)
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1.2 The process (continued) 1.2.4 Determine
the method to be used for interpolation
Depends on the project requirements, sample
data and the characteristics of the
methods The basic equation for
interpolation
Where Z0 is the attribute
value to be predicted at the unvisited-site
Zi is the attribute value at the i point of
the nearby locations wi is the weight
assigned to the attribute at point i, wi should
sum up to 1 (to be unbiased)
n is the total number of nearby locations
involved 1.2.5 Evaluate the interpolation
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1.3 The basic issues
1.3.1 Determine number of sample points in each
estimation 1) The requirement of the
methods 2) The density of samples and
spatial autocorrelation a) Defining
the search neighborhood (search
radius or search window) Spacing
of Sample Points a) regular
spacing (Regular Spacing Figure)
b) irregular spacing (Irregular Spacing
Figure) b) The magic number
Twice the search spacing
About 4 - 12 sample points for each estimation
without going out the range of
spatial autocorrelation
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1.3 The basic issues (continued) 1.3.1
Determine number of sample points (continued..)
c) Consequences
if too few sample points the
interpolation could be too sensitive
if too many samples too
much computation time and
too much redundancy
irrelevance in the sample data sets since sample
points too far away may be
included 1.3.2 Determine the distribution of
sample points 1) the nature of the
phenomena to be interpolated 2) the
distribution of samples (1) Two
questions a) are there
nearby samples that are redundant?
The clustering problem (The clustering
Figure)
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1.3 The basic issues (continued) 1.3.2
Determine the distribution (continued)
b) are there nearby samples relevant?
Impact of point from
different population
Relevance has to be determined by the
users understanding of the sample
data. Determination of
relevance is case dependent
and is much more important than choosing
a interpolation
techniques. (2) Search strategy
Quadrant Search (Regular
Quadrant Search, Figure 14.2)
(Revised Quadrant Search) 1.3.3 Determine the
weights The main difference among
methods is how each of them
allocate weights to sample points. 1.3.4
Uncertainty Assessment
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Questions
1. Why do we need spatial interpolation? What is
the problem of just using the samples? 2. What
are the steps involved in spatial interpolation?
What are the key issues in making an
interpolation? 3. What are the things to
consider when deciding how many sample points to
be included for an estimation at a given point?
What happens if too few or too many points are
used? 4. What the things to consider when
deciding the spatial distribution of sample
points for an estimation at a given point? Why do
people say clustering of sample points is not
desired? What is quadrant search?