Estimating the most likely value of mass of FWD or CWD is straightforward. If using the relative density values, then one needs to multiply the undecayed density by the relative density for each decay or size class, and then multiply that number by the volume in each decay or size class. Summing the masses for each decay or size class gives the total mass. If using the absolute density database one multiplies the decay or size class density by the volume in each class and then sum to get the total mass.

Estimating the uncertainty in mass is complex with only an approximation of uncertainty. However, it is better to have some sense of this uncertainty than to not report it. Given that uncertainty can only be approximated, one needs to adopt several guiding principles. The first is that it is better to overestimate than to underestimate uncertainty. Therefore when there is a choice between using calculation methods that can give either higher versus lower estimates, the higher one should be selected as long as it represents a reasonable set of assumptions. Second, uncertainty estimation in a complex set of calculations can be broken down hierarchically, that is there is no reason to calculate all uncertainty terms all a once. Third, understanding the correlation between variables is important to estimating overall uncertainty because as uncertainty terms for the parts are combined the degree of correlation determines whether the uncertainty is increased or whether it is reduced. For example, if all the uncertainties for each decay class are perfectly and positively correlated, then the total uncertainly will be maximized (i.e., the masses are either all the minimums or all the maximum masses). If on the other hand, the uncertainties are perfectly and negatively correlated, then the total uncertainty will be minimized (i.e., some maximum masses are being offset by minimum masses). When there is no correlation between uncertainties in the decay classes, then the total uncertainty is intermediate. In the case of woody detritus mass estimates, the least likely case would be for all the uncertainties to be negatively correlated as there is no specific mechanism to cause this pattern.

Given the complexity of the problem there is no single formula to estimate uncertainty. One method would be to perform a Monte Carlo analysis drawing from the distributions for the decay- and size-class databases. As an alternative we combine uncertainties using calculations based on summary statistics. In the following sections we present a series of calculations to provide examples, but since each project is likely to have data structured in different ways it is best to use the examples only as guidance and not as a substitute for a project-specific analysis. To provide a hierarchical framework, we start at the finest level of detail (e.g. sampled species) and work towards more assumptions (e.f. unsampled genera). In this particular set of examples, we use subscripts to indicate the level within the hierarchy being considered (DC=decay class; Sp=species; S-site). Our example considers CWD, but a similar set of calculations could be performed for FWD if size classes were also considered. Specific examples for each level in the hierarchy are given in Appendices 5 and 6.

Within a Decay or Size Class for a Species and Site. To calculate the uncertainty for a decay class for a species at a particular site (or plot) the uncertainty can be estimated by multiplying the volume by the absolute density uncertainty values:

Uncertainty Mass _DC-Sp-S= Volume _DC-Sp-S*Uncertainty Density _DC-Sp-S

Within a Species and Site. To calculate the uncertainty for species with estimated densities at a particular site (or plot) this term can be approximated by adding uncertainty in mass for all the decay classes:

Uncertainty Mass _Sp-S= Σ Uncertainty Mass _DC-Sp-S

This assumes there is a perfect positive correlation of uncertainties for the decay classes, which reflects the fact an unsampled species is systematically under- or overestimated in terms of decay class specific densities. That is there is a consistent pattern for a species relative to the mean estimates. However, for species that have been sampled it is likely that there are few systematic differences and random relationship would be more appropriate:

Uncertainty Mass _Sp-S= sqrt Σ (Uncertainty Mass_DC-Sp-S²)

In which the uncertainty of each decay class is squared and then summed. By taking the square root of this term the total uncertainty for a species within a site can be estimated. This is based on the notion that the square of uncertainties are additive, but the uncertainties are not (i.e., variances are additive).

Within a Species for all Sites. To calculate the uncertainty for species that have not had density estimated when multiple sites (or plots) are combined, we assume the total uncertainty in mass can be estimated by adding uncertainty in mass for all the sites or plots:

Uncertainty Mass _Sp= Σ Uncertainty Mass_Sp-S

This assumes a perfect positive correlation in uncertainty, which is the most likely case for species that have not been sampled. In this case all decay classes for a species at all places was likely either under- or overestimated to the same degree. For species that have been sampled for density, it is more realistic to assume that the uncertainties are not correlated and the uncertainty represents random variation in the population:

Uncertainty Mass _Sp= sqrt Σ (Uncertainty Mass_Sp-S²)

In which the uncertainty of a species mass for each plot is squared and then summed. By taking the square root of this term the total uncertainty for the species for all sites can be estimated.

Within a Site. The uncertainty in mass for a site would combine the mass of all the species at a site. As there is no reason to believe that uncertainty in one species is correlated with another the overall uncertainty would be approximated by:

Uncertainty Mass_S= sqrt Σ (Uncertainty Mass_Sp-S²)

In which the uncertainty of each species is squared and then summed. By taking the square root of this term the total uncertainty within a site can be estimated.

All Sites. Assuming that the uncertainty in mass for each species for all sites has been estimated the uncertainty for all sites would be computed by assuming there is no correlation between sites:

Uncertainty Mass_T= sqrt Σ (Uncertainty Mass_Sp²)

In which the uncertainty of each species for all sites is squared and then summed over all species. Taking the square root of this term gives the total uncertainty at all levels.