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
What is different about “verification cruising”?
Conventional check cruising
“Verification cruising”
 Conducted during inventory
effort to suggest corrections
that could be made
 Conducted after inventory
effort for verification purposes
 Conducted by someone
internal to the organization,
who is checking the work of
internal cruisers or
contractors
 Conducted by outside
auditors
What is different about “verification cruising”?
Conventional check cruising
“Verification cruising”
 Lower stakes – negative
findings may result in
corrective action (if checking
employees) or docked
payment (if checking
contractors)
 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:
Error(%) 
CVerifier  CForestOwne r
CVerifier
 Can be calculated at the plot level and averaged, or calculated
across the entire sample, depending on subtle semantic differences
in the protocol used.
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)
An improvement: the paired t-test (two-sided)
 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.
An improvement: the paired t-test (two-sided)
 General formula:

Abs Bˆ  V
t
SEBˆ
Bˆ
V
SEBˆ
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).
An improvement: the paired t-test (two-sided)
 General formula:

Abs Bˆ  V
t
SEBˆ
Bˆ
V
SEBˆ
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).
An improvement: the paired t-test (two-sided)
SEBˆ 
 General formula:

SDBˆ
n
* fpc
Abs Bˆ  V
t
SEBˆ
Bˆ
V
SEBˆ
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).
An improvement: the paired t-test (two-sided)
SEBˆ 
 General formula:

SDBˆ
n
* fpc
Abs Bˆ  V
t
SEBˆ
Bˆ
V
SEBˆ
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).
A problem: sample size
n  Z / 2  Z  
2
n
Z / 2
Z
SDBˆ
MINBˆ
 SDBˆ 


 MIN ˆ 
B 

2
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
A problem: sample size
n  Z / 2  Z  
2
n
Z / 2
Z
SDBˆ
MINBˆ
 SDBˆ 


 MIN ˆ 
B 

2
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
A problem: sample size
n  Z / 2  Z  
2
n
Z / 2
Z
SDBˆ
MINBˆ
 SDBˆ 


 MIN ˆ 
B 

2
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
A problem: sample size
n  Z / 2  Z  
2
n
Z / 2
Z
SDBˆ
MINBˆ
 SDBˆ 


 MIN ˆ 
B 

2
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
A problem: sample size
n  Z / 2  Z  
2
n
Z / 2
Z
SDBˆ
MINBˆ
 SDBˆ 


 MIN ˆ 
B 

2
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
(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.
(Possible) solution: sequential sampling
 Re-measure at least two plots.
 Compute the necessary sample size:
n  Z / 2  Z  
2
 SDBˆ 


 MIN ˆ 
B 

2
(Possible) solution: sequential sampling
 If the necessary sample size has been attained, stop. Otherwise, remeasure another plot and re-evaluate.
 If stopped, compute K:
K
Z * MINBˆ
Z

 Z 
(Possible) solution: sequential sampling
 If the necessary sample size has been attained, stop. Otherwise, remeasure another plot and re-evaluate.
 If stopped, compute K:
K
Z * MINBˆ
Z

 Z 
(Possible) solution: sequential sampling
 If the necessary sample size has been attained, stop. Otherwise, remeasure another plot and re-evaluate.
 If stopped, compute K:
K
Z * MINBˆ
Z

 Z 
(Possible) solution: sequential sampling
 If the necessary sample size has been attained, stop. Otherwise, remeasure another plot and re-evaluate.
 If stopped, compute K:
K
Z * MINBˆ
Z

 Z 
(Possible) solution: sequential sampling

 If
Abs Bˆ  K
, accept null hypothesis
 If
Abs Bˆ  K

, reject null hypothesis
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*
 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:
Branches and
foliage
Bole and bark
“Belowground”
carbon
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
Ctree  f Voltree *WoodDenstree 
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, Vol 
1
* BA * HT (ft3)
3
(will not work well for hardwoods)
Appendix: How to estimate C in tree boles
 Average Volume/Basal Area Ratio (VBAR; ft3/ft2) =
1
* BA* HT
1
3
VBAR 
 * HT
BA
3
 Volume (ft3/ac) = VBAR * BA
 Mass (lbs/ac) = Vol (ft3/ac) * WoodDens (lbs/ft3)
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