3. Factors of soil formation (Jenny)
Spatial variability
Factors of soil formation (Jenny)
Climate
Organisms
Parent material
Topography
Time
We must live with spatial variation – it is unchangeable and irreducible
Soil carbon is complex for at least two additional reasons:
The value of soil carbon is that it is in the field. Obviously we don’t actually run a market for grain this way because the value is on removing the grain.
We have to measure the CHANGE in soil C stocks. Other commodities change from zero and the commodity is sold. With soil C we have initial, irreducible variation and more variation on top of that…
Activities designed to give credit for sequestering C in agricultural soils necessarily document the amount
1605b
Kyoto trading mechanisms (CDM, JI, national reporting)
CCX
At large scales (i.e., national inventories), coarse methods are accepted (even desired)
Voluntary programs accept rough, general estimates of C sequestered
But, when money is changing hands accuracy is important
Uncertain documentation leads to discounted payments
But soils are inherently variable and accurate measurement of changes in soil C stocks costs money.
How can uncertainty of measurements be reduced?
What are the implications for cost-effectiveness?

4. Sampling costs

5. Costs and benefits of reducing uncertainty in accounting for soil carbon credits
R. T. Conant, Colorado State University
S. Mooney, University of Wyoming
K. Gerow, University of Wyoming

6. Background: Value of C credits
Most producers will require economic incentives to change practices
Money received by producers is a function of price offered for each credit, perceived uncertainty (i.e., discounting) and transaction costs
Both uncertainty and transaction costs are related to verification and sampling
Many producers will require incentives to switch from their existing management practices to those that sequester C at a higher rate, creating C-credits. The amount of money received by the producer is a function of the price offered for each credit, the perceived certainty associated with credit creation (i.e. the seller may discount the price if they are less sure the credit really exists) and transactions costs such as those incurred measurement and monitoring credit creation, among other factors.
The costs associated with measuring soil C can vary based on the variability of soil C within the area……………….. etc

7. Methods to reduce sample variability
Increase duration between sampling
Aggregate
Alter risk acceptance
Covariance – re-sample same plots
Use spatial autocorrelation
Extrapolate using additional information
Increase # of samples analyzed
What are the costs/benefits associated w/ these?

8. 1. Increase duration between sampling
Average Cultivated soil C
(top 20cm):
14.5 Mg C ha-1
Accumulation rate
(top 20cm):
0.27 Mg C ha-1 yr-1
Soil C pool
20cm
2 years
change = 3.7%
25 years
change = 46.6%

9. 1. Increase duration between sampling
Two potential outcomes:
Decreases the number of samples required for a given precision
Can increase the precision for a given number of samples
Either way, income potential increases
Question:
Do future earnings justify reduced sampling now?
# samples
Increased duration between samples will result in a smaller number of samples taken over the project lifetime and thus lower costs of measurement.
Rich – with increased duration between samples we will also have a larger C change to detect which will also have an effect on the number of samples needed – might want to comment on this.

10. 2. Aggregation Measurement Cost per Credit ($)
Rich I anticipate my thoughts on aggregation might differ from yours in some ways – I am thinking about aggregation in terms of sampling over a larger area. For example in the Montana studies we had the areas subdivied into sub-MLRAs – when I AGGREGATED the sub-MLRAs together to form an MLRA sampling costs per credit were reduced.
Aggregating smaller areas into one large area
Decreases the cost of sampling per C-credit
I anticipate you might be thinking of aggregation in terms of aggregating individual samples to form a single composite sample…..
Anyway the following refers to aggregation of area.
This graph shows the estimated total cost of implementing a sampling scheme to measure soil C credits un a 20 year contract.
The two lines with symbols represent 2 sub-MLRAs within Montana.
The bolded continuous line is the sum of the measurement costs if each area is measured separately.
The dashed line is the total measurement cost if the areas were aggregated together initially and then measured.
The total measurement costs at the MLRA level are also 40 to 60 percent less than the total measurement costs at the sub-MLRA level. These results suggest that aggregating producers into larger contract groups can reduce total measurement costs under a per-credit contract design.
Mooney, S., J. M. Antle, S. M. Capalbo and K. Paustian Influence of Project Scale on the Costs of Measuring Soil C Sequestration. Environmental Management 33 (supplement 1): S252 - S263.

11. Reduce the standard error Results in smaller confidence interval
3. Alter risk acceptance
Reduce the standard error
Results in smaller confidence interval
Sampling is a statistically based means of estimating the number of C-credits within an area and enables the user to make probabilistic statements about the likelihood of sample estimates representing the true population. Confidence limits are generally used to describe the precision with which the true population value is captured by the sample estimates.
Credit purchasers have already shown interest in discounting their payments for credits based on the uncertainty associated with the number of credits created (the Iowa case). A large standard error will result in large confidence intervals around the mean C quantity sequestered within an area and thus a larger payment discount and a small incentive for producers to change their management practices.

12. 3. Alter risk acceptance Reducing the confidence intervals
Higher producer payments
Possible to achieve at low cost
# samples
What is the balance between risk and sampling costs?

13. 4. Covariance Diff? = f(2 (t1-t2) = 2t1 + 2t2 – 2covt1 t2)
Has management led to changes over time?
Time 1
Time 2
Diff? = f(2 (t1-t2) = 2t1 + 2t2 – 2covt1 t2)
Implication:
Large covt1 t2 small 2 (t1-t2)
Small 2 (t1-t2) likelihood of difference
covt1 t2 can be maximized by:
ensuring uniform treatments, texture, slope, aspect, etc.
re-sampling same location

14. 5. Use spatial autocorrelation
Reducing the confidence intervals
Higher producer payments
Possible to achieve at low cost
Mooney, S., K. Gerow, J. Antle, S. Capalbo and K. Paustian The Value of Incorporating Spatial Autocorrelation into a Measurement scheme to Implement Contracts for Carbon Credits. Working Paper 2005 – 101. Department of Agricultural and Applied Economics, University of Wyoming

15. 5. Use spatial autocorrelation
Payment
$10
$30
0.1R
0.15R
0.2R
Crop system change
SWF_GRA
1.93
4.96
6.57
2.69
6.83
8.93
SWF_CSW
4.19
5.44
6.41
4.14
5.22
5.81
SWF_CWW
15.21
20.10
23.30
10.78
13.95
15.62
WWF_GRA
4.89
11.84
15.50
7.93
19.06
24.71
WWF_CSW
12.50
16.86
20.66
8.21
10.72
12.08
WWF_CWW
19.01
24.89
29.15
18.43
23.54
26.27
CSW_GRA
21.62
32.08
38.84
39.59
57.31
66.67
This table shows the percentage increase in payments per C-credit as a result of using information about spatial autocorrelation to decrease the size of the confidence interval.
The figures shown are for sub-MLRA 58 high in Montana (just FYI Rich).
Using 10 percent, 15 percent and 20 percent (0.1R, 0.15R and 0.2R) of the range of spatial autocorrelation to represent the area covered by a single sample the amount producers receive is increased by between 2% to 39% at C-credit prices of $10 and between 3% to 67% at the higher price of $30/C-credit.
SWF=spring wheat fallow GRA = grass CSW= continuous spring wheat
WWF= winter wheat fallow CWW= continuous winter wheat

16. 6. Extrapolation No studies that directly examine Krieging to date
Expect that information about spatial autocorrelation will:
Decrease sample size
Decreasing measurement costs
Krieging with additional information is best method of extrapolation (Doberman et al.)
There have not been any studies that directly examine the effects of using kreiging on the costs of measuring soil C credits. However several studies have suggested that including additional information about spatial autocorrelation is likely to reduce measurement costs (Mooney et al 2004, Mooney et al 2005, Kurkalova et al 2004, Conant and Paustian 2002)

17. 7. Increase number of samples analyzed
Increase # samples analyzed
Decrease sample error
Increase confidence interval
Increase cost
If analytical costs fall dramatically (due to LIBS, NIR, EC, etc.) risk/uncertainty can be reduced and producers will be the beneficiaries.
Credit
Price
Sample Size
e=10%
95% Confid.
e=5%
99% Confid. 10
1,307
5,109
2,239 20
1,242
4,871
2,133 30
1,199
4,711
2,062 40
1,156
4,543
1,984 50
1,152
4,528
1,977
Increasing the number of samples analyzed can result in several different effects.
First, if you wish to decrease the error associated with sampling you will need a larger sample
Second if you with to increase your confidence with the sample estimate you will also need more samples
Essentially increasing the number of samples will of course increase the costs of measuring/verification – HOWEVER this may be worth it!!!
As shown on the uncertainty example previously, if C-credit prices are discounted to reflect uncertainty there is a tradeoff between having a low cost sampling scheme (that might be inaccurate) and the money that a producer receives for the contract.
The table above shows how sample size increases as you decrease error and increase confidence intervals at different credit prices.
It is important to note that each area of the country will have a slightly different response (i.e. the percentage increase in samples required will not be the same in all places).
Mooney, S., J. M. Antle, S. M. Capalbo and K. Paustian Design and Costs of a Measurement Protocol for Trades in Soil Carbon Credits. Canadian Journal of Agricultural Economics. 52(3):

18. Conclusions Soil variation is irreducible
There are several things we can do to increase statistical confidence in our measurements, thus reducing risk/uncertainty and increasing returns to producers
Improved analytical techniques could be a significant contributor in the future.