Appendix 6. Specific examples of estimates of the mean and uncertainty for various levels in the calculation hierarchy.

These are based on five FIA sample plots located in Maine. The species was assumed to be red spruce (Picea rubens). The assumption in this set of calculations is that red spruce has had density directly measured.

Within a Decay or Size Class for a Species and Site. In plot 407074 there is a total of 18.13 m³/ha of decay class 3 CWD. The estimated mean density is 0.316 Mg/m³ and uncertainty in density is 0.112 Mg/m³. The mean mass and the uncertainty is therefore:

Mass _DC-Sp-S= 18.13m³/ha*0.316Mg/m³=5.73 Mg/ha

UncertaintyMass _DC-Sp-S= 18.13m³/ha*0.112Mg/m³=2.031 Mg/ha

Within a Species and Site. In plot 407074 there were pieces in decay classes 2-4 and none in decay classes 1 and 5. Since the density for all decay classes was measured the uncertainty is related to random sampling error. Therefore the mean and uncertainty of mass for this plot is:

Mass _Sp-S= 0 Mg/ha+0.519 Mg/ha +5.73 Mg/ha+ 1.39 Mg/ha+0 Mg/ha=7.64 Mg/ha

Uncertainty Mass _Sp-S= Square root (0.072² +2.032² + 0.312²) =2.06 Mg/ha

The relative uncertainty is therefore 27%.

Within a Species for all Sites. There are 5 plots each with its own mass and uncertainty estimate. There is no reason to believe the uncertainty in the plots is correlated. Therefore the total mass and uncertainty is:

Mass _SpSp = 7.64 Mg/ha+15.15 Mg/ha +1.34 Mg/ha+ 1.45 Mg/ha+1.42 Mg/ha=27.00 Mg/ha

Uncertainty Mass _Sp = square root (2.062² +2.892² + 0.132² +0.272² + 0.282²) =3.57 Mg/ha

The relative uncertainty is therefore 13%.

Within a Site. The uncertainty in mass for a site combines the mass of all the species at a site. There is no reason to believe that uncertainty in one species is correlated with another. Therefore the mean and uncertainty would be:

Mass_S= 7.64 Mg/ha +5.99 Mg/ha=13.64 Mg/ha

Uncertainty Mass_S= square root (2.062²+0.282²)=2.08 Mg/ha

The relative uncertainty is therefore 15%.