v 1.0 carbon on the stump: how forest carbon inventories are verified and why it is important...

Carbon on the stump:how forest carbon inventories are verified and

why it is important

Western Mensurationists’ Meeting, June 2011

Banff, Alberta, Canada

Zane Haxton

Verification Forester

Scientific Certification Systems

The agenda

What is different about “verification cruising”?

How do we verify inventories?

Some metrics and statistical techniques for inventory verification


Conventional check cruising

Conducted during inventory effort to suggest corrections that could be made

Conducted by someone internal to the organization, who is checking the work of internal cruisers or contractors

“Verification cruising”

Conducted after inventory effort for verification purposes

Conducted by outside auditors


Conventional check cruising

Lower stakes – negative findings may result in corrective action (if checking employees) or docked payment (if checking contractors)

“Verification cruising”

Higher stakes – negative findings may result in a repeat of the entire inventory

Forest inventory verification

A sample-based process

Select random plots of plots to re-measure

Re-measure the plots using the same sampling protocol and type of equipment used by the forest owner

In the beginning: percent error

General formula:

Can be calculated at the plot level and averaged, or calculated across the entire sample, depending on subtle semantic differences in the protocol used.

Verifier

rForestOwneVerifier(%)C

CCError

An improvement: the paired t-test (two-sided)

One method is to conduct a statistically valid sample of original measurement plots… you can then employ a Paired t-Test to compare the check volumes against the original. Using a t-test makes it clear that:

You have a sample; and that

The confidence of your conclusions depends on sample size among other things.

(Paraphrased from John Bell & Associates Inventory & Cruising Newsletter, “Check cruising”, January 1999, available at

http://www.proaxis.com/~johnbell/regular/regular45a.htm)


Null hypothesis: there is no (really important) difference between verifier and forest owner measurements.

Alternative hypothesis: there is a (really important) difference between verifier and forest owner measurements.


General formula:

Estimated bias of the forest owner’s inventory, as determined by comparison with verifier measurements (in units).

Maximum allowable inventory bias (in same units)

Standard error of the estimated bias (in same units).

B

SE

VBAbst

ˆ

ˆ

B̂

V

BSE ˆ


General formula:

Estimated bias of the forest owner’s inventory, as determined by comparison with verifier measurements (in units).

Maximum allowable inventory bias (in same units)

Standard error of the estimated bias (in same units).

B

SE

VBAbst

ˆ

ˆ

B̂

V

BSE ˆ

fpcn

SDSE B

B*ˆˆ

A problem: sample size

The sample size needed

The Z-value for the given value of α.

The Z-value for the given value of β

The expected standard deviation of the bias estimate

The smallest degree of bias we want to be able to detect

2

ˆ

ˆ22/

B

B

MIN

SDZZn

BSD ˆ

BMIN ˆ

2/ZZ

n

(Possible) solution: sequential sampling

Null hypothesis: there is no difference between verifier and forest owner measurements.

Alternative hypothesis: there is a difference between verifier and forest owner measurements.


Re-measure at least two plots.

Compute the necessary sample size:

2

ˆ

ˆ22/

B

B

MIN

SDZZn


If the necessary sample size has been attained, stop. Otherwise, re-measure another plot and re-evaluate.

If stopped, compute K:

ZZ

MINZK B

ˆ*


If , accept null hypothesis

If , reject null hypothesis

KBAbs ˆ

KBAbs ˆ

Possible refinements:

Sample in batches of plots

Sample normally for some minimum sample size, then adopt sequential sampling

Require the null hypothesis to be accepted across a minimum number of samples before verifying the inventory

Conclusions:

This is an exciting time to be doing forest inventory work!

Advances in forest inventory verification may also be applicable to check cruising.

We’ll let you know!

Special thanks to:

Tim Robards, Spatial Informatics Group John Nickerson, Climate Action Reserve Ryan Anderson, Scientific Certification Systems

Another idea: equivalence testing*

In t-testing, the null hypothesis is one of no difference, so an inventory is accepted unless statistically significant evidence indicates that the forest owner’s measurements are defective.

Equivalence testing, originally developed for model validation, puts the burden of proof on the forest owner by reversing the null hypothesis.

*See Robinson and Froese, 2004, “Model validation using equivalence tests”, Ecological Modelling 176:349-358

Another idea: equivalence testing

Procedure:

Beforehand, construct a “region of indifference” (e.g. ±15% of the forest owner’s estimated carbon stocks) and select an α-level.

Calculate a “special confidence interval”, equal to two one-sided confidence intervals of size α, around the bias estimate.

If the special confidence interval falls outside the region of indifference, the null hypothesis is not rejected. Otherwise, it is rejected.

Another idea: equivalence testing

0

Picture credit: Robinson and Froese 2004

Appendix

Carbon exists in:

“Belowground” carbon

Branches and foliage

Bole and bark

How is carbon quantified?

Carbon is quantified in terms of mass – most commonly Mg/ac or Mg/ha

1 Mg = 1 metric tonne

1 Mg = 1,000 kg = 2,204.6 lbs

1 Mg CO2e (or CO2-e) = (44/12) Mg C ≈ 3.67 Mg C

treetreetree WoodDensVolfC *

How to estimate C in tree boles*

* This exercise was inspired by page 40 of K. Iles, 2009, “The Compassman, The Nun, and the Steakhouse Statistician”

Using your thumb as an angle gauge, estimate the basal area (BA; ft2/ac).

Estimate average tree height (HT; ft)

Assuming conical tree form, (ft3)

(will not work well for hardwoods)

HTBAVol **3

1

Appendix: How to estimate C in tree boles

Average Volume/Basal Area Ratio (VBAR; ft3/ft2) =

Volume (ft3/ac) = VBAR * BA

Mass (lbs/ac) = Vol (ft3/ac) * WoodDens (lbs/ft3)

HTBA

HTBAVBAR *

3

1**31

Appendix: How to estimate C in tree boles

Biomass (Mg/ac) = Mass (lbs/ac) / 2,204.6

C mass (Mg/ac) = Mass (Mg/ac) * 0.5

CO2-e mass (Mg/ac) = C * (44/12)

… and there you go!

An example from the California redwoods

BA = 240 ft2/ac HT = 120 ft VBAR = (1/3) * 120 = 40 ft3/ft2

Vol/ac = 240 * 40 = 9,600 ft3/ac Biomass = 9,600 * 21.22 = 203,712 lbs/ac = 92.4 Mg/ac C mass = 92.4 * 0.5 = 46.2 Mg/ac CO2-e mass = 46.2 * (44/12) = 169.4 Mg/ac

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