Distance-Variable Estimators for Sampling and Change Measurement

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Distance-Variable Estimators for Sampling and
Change Measurement
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Western Mensurationists June 2006
Kim Iles PhD.
Hugh Carter MSc (Candidate), RFT
hugh.carter_at_jsthrower.com
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Outline

1. Background

1. Bias (or lack of)

1. Shapes

1. Change over time

1. Compatibility

1. Simple example

1. Edge

1. Future Work

1. Summary

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Background

• A reminder of why we might want to use Variable
  Radius Plots
• (VRP) for measuring change
• - Efficiency (cost and time).
• - Remeasurement of existing plots.
• - Increase precision?

• Need a solution for applying VRP for measuring
  change over time.

• Problems encountered include
• - High variability due to on-growth.
• - Extending concepts to variables other
  than volume and BA.
• - Providing a solution that is easily
  applied and understood.

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Background Continued

• Attempts have been made to solve these
  problems, however none
• have covered them all.

• Distance-Variable estimators reduce
  variability, extend to any
• variable for any object of interest, and
  provide an easy to apply
• method.

• Distance-Variable estimators are an extension
  of the Iles method
• to any variable of interest on any sampled
  object of interest.

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Bias
Horvitz-Thompson Estimator
Potential random sample points
Object of interest
Inclusion circle
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Bias Continued
Distance-Variable Estimator
Potential random sample points
Object of interest
Inclusion circle
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Shapes
Why Use a Cone?
3x Value

• Easy to use and visualize
• - height at point is 3x value
• - height at base is 0x value

• Average at all potential sample
• points will give estimate

• Can get a simple Value Gradient

0x Value
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Shapes Continued
How do they work?
111 m2/s2/kg

• Units no longer an issue

• Average at sample points give estimate

• Sample point is ¼ of distance from edge

• Estimate ¼ 111m2/s2/kg 27.37m2/s2/kg

0 m2/s2/kg
Average of all sample points is 37 m2/s2/kg
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Change Over Time
Traditional Subtraction Method
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Change Over Time
Distance-Variable Method
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Compatibility
Both methods are compatible, however the
traditional subtraction method is more variable!
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Basal Area Example
Traditional Method (BAF 10m2/ha)
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Total
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Total
BA/ha
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On-growth
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Measurement
Distance-Variable Method (BAF 10m2/ha)
Survivor
Total
Mortality
On-Growth
On-growth
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Basal Area Example
Traditional Method (BAF 10m2/ha)
Total
Total
Survivor
Distance-Variable Method (BAF 10m2/ha)
Survivor
Total
Mortality
On-Growth
Survivor
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Basal Area Example
Traditional Method (BAF 10m2/ha)
Total
Total
Mortality
Distance-Variable Method (BAF 10m2/ha)
Survivor
Total
Mortality
On-Growth
Mortality
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Basal Area Example
Traditional Method (BAF 10m2/ha)
Total
Total
Total
Mortality Tree
Survivor Tree
On-Growth Tree
On-growth
Survivor
Mortality
Distance-Variable Method (BAF 10m2/ha)
Survivor Tree
Total
Mortality Tree
On-Growth Tree
On-growth
Survivor
Mortality
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Edge

• Existing techniques for correcting edge remain
  applicable.

- Walk-through

- Toss-back

- Mirage

• Unbiased if inclusion areas are symmetrical
  through the tree.

• If extra sample points are needed the DV
  estimator is used
• instead of the traditional estimator.

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Future Work

• Variance control through different shaped
  estimators.

• Non-stationary object sampling.

• Density surface mapping.

• Efficiency/Precision gains?

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Summary
Distance-Variable Method

• EXTENDS TO ANY VARIABLE FOR ANY OBJECT!!

• Unbiased

• Easy to apply and understand

• Smoothes change/growth curves

• Compatible

• Works with existing edge techniques

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Acknowledgements
Kim Iles Associates
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Volume Example
Traditional Method
Distance-Variable Method
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Summary

1. Background

1. Bias (or lack of)

1. Shapes

1. Change over time

1. Compatibility

1. Simple example

1. Edge

1. Future Work

1. Summary