Introduction and Objectives


		Improving Biomass and Carbon Estimates for Coarse and Fine Woody Debris

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	Introduction
	Methods
	Source of Data
	Analysis
	Results
	Carbon Content
	Uncertainties of Mass Estimates
	Databases of Density Estimates
	Examples of Use
	Future Needs
	Literature Cited
	Acknowledgments
	Images of Species by Decay Class

Analysis

Woody detritus density was expressed in two ways: absolute density (mass/green volume) and relative density (decayed density/undecayed density). Relative density is alternatively called the density reduction factor in the FIA system. We used the existing data to estimate both variables for all the species inventoried by the FIA. In addition to estimating the mean values, we also estimated the uncertainty associated with these estimates of density, with the least uncertainty for species that had been sampled and the greatest for genera that had not been sampled. To estimate densities for species that had not been sampled, we examined the pattern of density reduction for related species and genera that had been sampled. In the case of CWD, we compared absolute and relative density among 5 decay classes. For FWD we were able to only use two decay classes (i.e., undecayed versus decayed), although we did this for three size classes.

Data Processing

When several sources of data for a species, genus, decay class, or size class were available we combined the values to estimate an average and standard error. When sample sizes were listed we used those to weight the average as well as the standard error of the samples. When sample sizes were not listed, we calculated a simple average and used the highest observed standard error as an estimate of uncertainty. For undecayed wood density of CWD we used estimates provided by the FIA database, which is largely derived from the Wood Handbook (US Forest Products Laboratory 1974). Although not all FWD studies reported species-specific values, we assumed that they represented the values of the dominant species in the ecosystem from which they had been sampled.

CWD Predictions

We used the available information to estimate the CWD density (absolute and relative) of each species currently encountered in the national FIA inventory. While it is important to estimate the mean density of decayed wood for all species, it is even more important to estimate the uncertainty introduced in this process. We devised a system in which the uncertainty would increase as the degree of extrapolation increased. Minimal extrapolation was involved when a species had been sampled and maximum extrapolation was involved when a genus had not been sampled. The uncertainty was expressed as the standard error of the mean. There were three levels of uncertainty:

Species that had been sampled. In this case the mean was the average of all the observed values and the uncertainty was represented by the standard error of the mean. The uncertainty in relative density was calculated as the standard error of the mean absolute density divided by the undecayed density. In this case the uncertainty term only involved sampling error.
Genera that had been sampled. If a species had not been sampled, but others in its genus had been sampled then there was some question as to where the mean would lie. The mean density was estimated by averaging the minimum and maximum relative density for the species in the genus that had been sampled. The absolute density was determined by multiplying the undecayed density of that species by the mean relative density. In this case the uncertainty involved not only sampling error, but uncertainty about the mean itself. We used the maximum difference of mean relative density observed in the genus for each decay class to provide an estimate of uncertainty associated with the genus mean. This was then increased by two standard errors of the mean of the relative density for observed species to account for sampling errors. We then assumed that 95% of the estimates of the mean would fall within that range, and divided it by 4 to rescale it to something akin to a standard error. The uncertainty of the absolute density was then calculated by multiplying the undecayed density of the species by the uncertainty in the relative density.
Species and genus not sampled. In this case the mean could lie anywhere between the minimum and maximum of the observed values. We therefore estimated the mean as the average of the minimum and maximum observed values of relative density. The absolute density was the product of the mean relative density and the undecayed density. The uncertainty was calculated as when only genera were sampled (section 2 above), however, we used the maximum difference in relative density means of all the species that had been examined.

FWD Predictions

We also estimated green and decayed density of FWD of the species encountered in the FIA inventory. For FWD undecayed density, we used actual measures or in most cases derived this from undecayed branch density to undecayed bole density ratios (branch to bole ratios). For decayed density we used either means of observed values or derived them from decayed versus undecayed FWD density ratios. As with CWD in addition to estimating the mean value we also estimated the uncertainty in FWD estimates based on the level of information available:

Species that had been sampled for FWD density. We used the mean and standard error of the observed values of undecayed and decayed density. We calculated the relative density by dividing the mean by the undecayed density. We calculated the uncertainty of the relative density by dividing the standard error of decayed density by the mean undecayed density. When the standard error had not been reported for a species, we multiplied the maximum relative variation of species where this statistic had been reported by the mean density of the species in question to provide some estimate of uncertainty.
Species lacking undecayed FWD density values. We used the mean bole density multiplied by the mean ratio of branch to bole density to estimate undecayed FWD density. The uncertainty in undecayed FWD density using this method was determined by multiplying the standard error of this ratio for all species with observations by the bole density of the species that was being estimated.
Species lacking decayed FWD density. Estimates of decayed FWD density for species that have not been sampled were computed from product of the mean ratio of decayed to green branch density for species and the green density of the species to be estimated. The uncertainty in the decayed FWD density for this set of species was estimated by:

U_{Decayed FWD}= sqrt (ID²*U_ID² +DGR²*U_DGR²)

where U_{Decayed FWD} is the uncertainty in decayed FWD density, ID is the mean initial density, U_ID is the uncertainty in initial density, DGR is the decay to undecayed ratio, and U_DGR is the uncertainty in the undecayed ratio. This formula accounts for the fact that uncertainty for decayed FWD density is a function of two uncertainties. Our formula assumed no correlation between the uncertainties.

Analysis of Uncertainty on CWD Mass Estimates

We analyzed the uncertainty of CWD mass estimates caused by using current knowledge about relative density of decay classes. This was achieved by applying various density reduction patterns that are commonly observed to the following likely decay class volume distributions:

Normal distribution. The distribution of decay classes with respect to volume depends on the time interval that the decay class represents as well as the nature of the inputs. For the five decay class system we used, the tendency is for the time interval represented to increase geometrically as decay classes advance. For example, decay class 2 lasts about twice as long as decay class 1, and decay class 3 roughly twice as long as decay class 2, etc. If the input of dead trees to the forest is uniform over time, this tends to result in a peaked volume distribution, with decay class 3 having the most volume. This is because class 3 includes a relatively long period relative to decay classes 1 and 2 and has not lost a great deal of volume to decomposition relative to decay classes 4 and 5. A steady input of CWD therefore leads to a normal distribution of decay classes in terms of volume (Harmon et al. 1986).
Exponential distributions. If there is a pulse in dead tree inputs one can also have a peak in volume which advances from decay class to decay class as the forest ages. To assess a situation in which there had been a recent pulse of input, we used a negative exponential volume distribution. To look at a pulse that occurred in the distant past we used the complement of this distribution (i.e., class 1 and 5 were switched, etc).
Uniform distribution. Although not common, we used a uniform distribution where the volume of each decay class was equal to determine an “average” uncertainty.
Observed distribution. This was based on large scale summaries from the FIA databases for the state of Maine and gives a sense of the actual operational uncertainty likely to be encountered. The data was taken from 200 plots and involved approximately 2,400 CWD pieces.

To calculate the uncertainty in CWD biomass estimates, the relative volume in each decay class was multiplied by a range of relative density reduction patterns to assess the range of mass estimates that would occur. The relative density reduction patterns that were investigated included: 1) a steady decrease from decay class to decay class, 2) an asymptotic pattern with decay classes 4 and 5 similar, 3) a mid-plateau in density decline with decay classes 2 and 3 being similar and 4) the pattern for Douglas-fir (the most commonly used pattern in previous studies). We also assessed the uncertainty for a well-sampled species (Douglas-fir) and a well-sampled genus (pines) as well as the minimum and maximum relative values observed. The latter two patterns places upper and lower uncertainty bounds on species or genera that have not been sampled. For most cases, the product of relative volume and relative density for each decay class for each relative density reduction pattern was summed and then compared to the value for Douglas-fir, which serves as a useful reference given that this pattern of density change has been used frequently. The exception was that for the overall minimum and maximum relative densities we used the mean of all species as the reference.

Analysis of Uncertainty on FWD Mass Estimates

We assessed the importance of two facets of uncertainty for estimates of FWD mass. The first aspect was the effect of having directly determined the relative density of decayed FWD; this was assessed by comparing the uncertainty in relative density of species that had actual samples versus those that did not. The second aspect involved the fact that the current system estimates an average FWD relative density, but does not account for the effect of pulses of input. Given that many sound branches and tops are left after disturbances such as harvests, pulses of FWD input are common. Immediately after a disturbance FWD density is likely to be close to the undecayed density. As the time since the disturbance increases the overall density of FWD is likely to decline at least until new material replaces it. To mimic this situation we tracked the abundance and relative density of two sources of wood: a pulse and that due to regular mortality processes. For the pulse we assumed the abundance of this FWD pool would follow a negative exponential decline. We assumed the density of the pulse would also decline, but that density would asymptote to reflect the presence of decay resistant portions of branches (i.e., knots). For the FWD generated by regular mortality processes we assumed that pool would gradually accumulate and that the density would decline to a lesser degree given that undecayed would is being added regularly. This asymptote was assumed to equal the average value we found in our analysis of the FWD dataset. We assumed the rate the pulse FWD was lost was the same as the rate the new FWD accumulated. Given that the accumulation rate is often close to the disappearance rate this assumption is reasonable (Olson 1963). We explored the effect of not knowing the decay state of FWD by varying the size of the pulse from 5, 10, and 20 times the size of the regular FWD pool. We also varied the asymptotic density of the pulse of FWD from a relative density of 0.1 to 0.4 as well as explored the effect of the decomposition rate of FWD. We then noted the difference between the minimum and the average relative density as this indicated the uncertainty that might be introduced by not noting the decay state of FWD.

Web site created by Becky Fasth and Mark Harmon

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