Using Simulation to Assess the Accuracy of a Forest ...€¦ · Using Simulation to Assess the...

Using Simulation to Assess the Accuracy of a Forest Inventory System

Steve Fairweather, Ph.D., ACFFairweather Biometrics, LLCPO Box 1023Welches, Oregon 97067

[email protected]

© 2019 Fairweather Biometrics, LLC Western Forest Economists, 6/4/2019



I. The Nature of a Stand-Based Inventory

II. The Problem

III. Why We’re Interested

IV. Basic Steps

V. Example Simulations for a Single Stand

VI. Example for a Small Group of Stands

VII. Example for a Stand Over Time

VIII.Large Ownership Example

© 2019 Fairweather Biometrics, LLC

I. The Nature of a Stand-Based

Inventory…

Inherited summary

data in 2004;

“updated” to 2019

Cruised 2010;

grown to 2019

Cruised Jan. 2019

Never cruised; stratum

average from 2015,

grown to 2019

The estimate of

the total inventory

is the sum of the

individual stand

estimates.


Western Forest Economists, 6/4/2019


II. The Problem ….If all the stand estimates are based on new

cruises, we can assess the reliability of the

total inventory estimate using conventional

stratified sampling formulas; we can

construct a confidence interval for the total

inventory estimate.

But not when the individual stand

estimates are from a mix of sources.




III. Why We’re

Interested… • 2001 -------------------------


• 2002 – Sarbanes-Oxley Act

• 2004 – How does a forest products

company CEO sign off on the annual

report stating the total forest

inventory?



III. Why We’re

Interested…


• In timberland acquisition due diligence,

inventory verification is usually a key component.

• Field-based checking is expensive and

has to be done in a short amount of time.

• An office audit of inventory practices is cheaper

and quicker, but not particularly convincing.


• Accuracy assessment by simulation provides a

quick, low cost, and understandable alternative.


III. Why We’re

Interested…



• Accuracy Assessment by

Simulation – given the

characteristics of the ownership, and

given the inventory practices and

protocols in place, state the

probability of the inventory estimate

being within a specified error

tolerance; both for the total inventory,

and for individual stands.

Generate

a Model

Forest

Describe the

inventory

system/protocols

being used

In many

replications, apply

the protocols to

the model forest

and note how the

protocols perform

in each replication

Use the

distribution of

replication results

to assess the

average

(expected)

accuracy of the

inventory system.

IV. Basic Steps …





V. Example Simulations for a Single Stand…

Stand No. 102 –

• “Perfect Knowledge”

• 31 acres, age 28

• 12,877 bf/a

• mixed conifer

Cruise –

• n = 21 plots

• CV = 70%





Stand No. 102 –

• “Perfect Knowledge”

• 31 acres, age 28

• 12,877 bf/a

• mixed conifer

Every time we cruise

this stand, we can get

a different estimate of

the volume per acre

Cruise –

• n = 21 plots

• CV = 70%





101 cruises (25%)

were within +/- 5%

of true volume/a





194 cruises (48%)

were within +/- 10%

of true volume/a




VI. Example for a Small Group of Stands…

Suppose we have a small ownership of 3 stands. We can simulate cruising in each stand and combine the results for the total ownership.





Suppose we have a small ownership of 3 stands. We can simulate cruising in each stand and combine the results for the total ownership.

How reliable will our estimate of the total inventory be?

Could a low cruise in one stand offset a high cruise in another stand?





This sounds like a

confidence interval, but it

is not. It is a new metric

for describing accuracy.




VII. Example for a Stand Over Time…

Most of our current stand-based inventory estimates are the result of annual updates that try to account for growth and removals.





Most of our current stand-based inventory estimates are the result of annual updates that try to account for growth and removals.

Therefore our simulation has to account for past cruise estimates, growth, and the use of a growth model, with its own inherent error.





Specifying the possible error for predicted volume by the growth model …





Specifying the possible error for predicted volume by the growth model …

Could a bad initial cruise be offset by a bad growth prediction?



Generate

a Model

Forest

Describe the

inventory

system/protocols

being used

In many

replications, apply

the protocols to

the model forest

and note how the

protocols perform

in each replication

Use the

distribution of

replication results

to assess the

average

(expected)

accuracy of the

inventory system.



VIII. Large Ownership Example…


Generate a

Model Forest

that (1) resembles

the forest of

interest, and (2)

about which we

have perfect

knowledge.





Generate a Model Forest





Describe the

inventory

system/protocols

being used

For example -

• Cruise stands on a 10-year cycle

• Usually, n=14 plots in a cruised stand

• Do cruise new residual stands

• Don’t cruise new clearcuts

• Don’t cruise stands less than 10 acres

• Assign stratum average to uncruised

stands in first year of simulation

• Grow initial stand estimates forward until

the stand is cruised or cut





Describe the

inventory

system/protocols

being used

Assumptions (and Sources of Error) -

• Stands to be cruised each year are selected

randomly

• Underlying CV = 70% for volume

• Zero bias in our cruise procedure

• Observed capability of our growth model

over a 10-year period ranges from 75% to

130% of the true volume

• All stand acreage figures are correct

• All stands were assigned to the correct

stratum at the start





Generate

a Model

Forest

Describe the

inventory

system/protocols

being used

In many

replications, apply

the protocols to

the model forest

and note how the

protocols perform

in each replication

Use the

distribution of

replication results

to assess the

average

(expected)

accuracy of the

inventory system.





Estimating the

total inventory

(i.e., sum of all

the stand

estimates).






Steve Fairweather, Ph.D., ACFFairweather Biometrics, LLCPO Box 1023Welches, Oregon 97067

[email protected]


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