The two main approaches for deriving tree biomass (or carbon) allometrics are destructive sampling (including weighing and carbon assay) and taper formulas. Information was combined from published reports that had used both of these methods. A commonly used approximation where carbon assay is not performed, such as part of destructive sampling, is to assume that C is 50 wt% of dry matter (biomass or necromass). The measured fraction can vary from 42% to 61%, depending on species, plant component and environment (Thomas and Martin, 2012) but 50% is a commonly used proportion (Gifford, 2001), and is a compromise
67 between the IPCC’s 47% (Aalde et al., 2006) and the effect of the likely contribution from volatile compounds lost during typical assay (Thomas and Martin, 2012). For wet-sclerophyll E. obliqua in Tasmania, Ximenes et al. (2008a) found the fraction in
stem cross sections to be 0.497(0.004), being close to 0.5— which was used throughout in the present work.
3.3.3.1
Eucalyptus delegatensis allometric
Allometrics for mainland populations of E. delegatensis ssp. delegatensis are not
differentiated here from those for the Tasmanian endemic subspecies E. delegatensis
ssp. tasmaniensis Boland, due to similarity in growth habit.
The available biomass allometric for the dominant canopy species (E. delegatensis)
covered the DBH range 0.119–0.832 m (Raison et al. unpublished, in Keith et al., 2000), which was too limited, as the mature trees in the Florentine reached over 4.5 m. Merchantable volume allometrics covered the DBH range 0.616–1.656 m (Wang and Hamilton, 2003). However, biomass allometrics for the related ash species, E. obliqua and E. regnans, covered the DBH ranges 0.262–2.84 m (Keith et al., 2000)
and 0.01–6.45 m (Dean et al., 2003; Dean and Roxburgh, 2006) respectively.
The relationships between biomass and stem volume, for these three eucalypts, are known within limited ranges of DBH (mentioned in Chapter 1). Their stem volumes can be calculated using the Farm Forestry Toolbox (FFT) (Warner, 2007), which requires input of DBH and tree height. Within the FFT the majority of stem taper formulas and their accommodated range of DBH, for species encountered in this study, were commercial-in-confidence and consequently they could not be deployed in this project. Only one of the formulas was publically available— for E. obliqua
(Goodwin, 1992), which accommodated DBH 0.1–2.8 m. Nevertheless, one useful observation from using the FFT, was that for a given DBH and height, stem volume was in the order wet E. obliqua > E. delegatensis > E. regnans. Biomass allometrics
68 the DBH range 0.1–1.0 m: the same sequence applies to biomass, as noted for stem volume from the FFT. Thus the sequence represents common trends in both taper and basic density. Thus combining E. obliqua and E. regnans allometrics would have
provided a reliable approximation for E. delegatensis.
The allometric for merchantable volume could not be directly converted to one for biomass owing to the location-specific criteria for merchantability and the absence of an accompanying allometric for entire stem volume. However in the same report there was a merchantable volume allometric for E. regnans over a comparable DBH
range (Wang and Hamilton, 2003). A new allometric equation was derived using the approximation that merchantable volume was an equal fraction of the whole stem volume for both species. When combined with the allometric for E. regnans stem
volume from Dean and Roxburgh (2006) the ratio of merchantable volumes for the two species yielded the stem volume of E. delegatensis, for a given DBH. The stem
volume was converted to dry biomass using the basic density of 524 kg m-3 for E. delegatensis (Ilic 1997) and combined with other aboveground components (e.g.
branches and leaves) as for E. regnans from Dean et al. (2003), to provide an
allometric for aboveground biomass for E. delegatensis. The corresponding
allometric was called Edel_by_ratio.
Thus there were three possible biomass allometrics for E. delegatensis: E. obliqua, E. regnans, and Edel_by_ratio. As none of the three was overwhelmingly more suited
to E. delegatensis over the sampled range of DBH, the average of the three, forming
a new allometric equation, was used. That average was fitted by [non-linear] regression in Minitab 17 statistical software to a logistic form. Settings in Minitab were left at defaults (apart from the choice of equation) and the refinement algorithm used was Gauss-Newton. A range of equation types was examined using the computer program Eureqa which performs [automated] symbolic regression (Schmidt and Lipson, 2009), but the fit was only improved on the logistic form when using an order five polynomial (i.e. six parameters instead of the three for the logistic function). The logistic function was therefore retained, and it had the additional benefits of being better defined than the polynomial for high DBH (similarly when
69 compared with log/log allometrics, which can increase exponentially) and providing reasonable biomass for DBH below 0.1 m. Adoption of the logistic form had also been found suitable for juvenile to advanced-mature E. regnans allometry (e.g. Dean
et al., 2003; Dean and Roxburgh, 2006).
3.3.3.2
Rainforest understorey allometric
For the rainforest understorey species, no species-specific biomass allometrics were available. For only one of the observed species (Acacia dealbata), stem volume
could be calculated using the FFT, however the formulae were not available, the applicable DBH range in the FFT was unknown, and tree heights had not been measured. Species-specific allometrics are unavailable for many of the understorey species, including that with most likely the highest biomass, myrtle (personal communication, Forestry Tasmania, 2009). Two generic biomass allometrics for rainforest species were: (i) for temperate rainforest species (Keith et al., 2000) and (ii) wet-sclerophyll and mixed-forest species (Dean et al., 2003). The Keith et al. (2000) allometric was comprised of two parts: generic rainforest, and a correction for temperate rainforest (in the form of graphed data points), both covering the DBH range 0.1–1.0 m. A single allometric for temperate rainforest was derived from those two components4. The temperate rainforest allometric gave an aboveground biomass
for a rainforest tree of DBH 2 m that was 131% of that for an E. delegatensis tree of
the same DBH (using the average allometric for E. delegatensis derived in this
work— Eq3-2 below). This was considered unreasonable because of the height difference between the two species, namely canopy versus understorey, and because a myrtle of that size in the mixed-forests of the Styx and Florentine Valleys would most likely have a substantial portion of senescence. The allometric was adjusted for
4 That derivation as shown in the original publication of this work— Dean et al. (2012)
doi:10.1080/11263504.2011.638332, was found to be incorrect (Barrie May, CO2 Australia, personal
70 senescence by subtracting 33.33% for trees with DBH≥ 1.5 m and using Eureqa (Schmidt and Lipson, 2009) to form a new, single allometric for the DBH range 0.1– 3.0 m. The 33.33% corresponds to the second of three decomposition stages used for coarse woody debris (1, 0.3333 and 0.6666 of original mass present).
The allometric given in Dean et al. (2003), was intended for use within the spatio- temporal carbon modelling software, CAR4D. In applications of CAR4D however the formula was rarely used in its raw form, but adjusted to suit environmental conditions through scaling the biomass magnitude and growth rate (Dean et al., 2004). The most common adjustment for mixed-forest was to scale the understorey magnitude by 0.5 (e.g. Dean et al., 2004; Dean and Roxburgh, 2006) (‘Dean et al. 2003/4’ hereafter). That adjustment was applied here. Thus there were two allometrics available for the rainforest species: (i) temperate rainforest extrapolated and adjusted for senescence, and (ii) Dean et al. 2003/2004.
As neither of the Keith et al. (2000) temperate-rainforest-corrected-for-senescence allometric, nor the Dean et al. 2003/4 allometric were overwhelmingly more suited to the understorey in E. delegatensis mixed-forest over the sampled range of DBH, the
average of the two was used (which provided an additional gauge to uncertainty in understorey biomass). That average was formulated as a quadratic-logistic function, fitted by symbolic regression in Eureqa. As for E. delegatensis, symbolic regression
revealed that the fit could only be improved using a polynomial of order 5, and therefore the logistic function was retained.
DBH size distributions of species (per hectare) for the plots were tallied across the study area, corrected for plot size (in projection), allocated to DBH classes and graphed as histograms. DBH class width was varied between species to provide maximum clarity in the histograms, (e.g. class width for E. delegatensis was 0.2 m).
The aboveground biomass allometrics were applied to the categories, rather than to the trees separately prior to tallying. The C in aboveground biomass per unit area for
E. delegatensis, in the sample plots, was calculated using the three allometrics, and
71 biomass for E. delegatensis was multiplied by 0.7, 0.75, 0.8 and 1 to test the effect of
accommodating senescence on stand-level carbon stocks (i.e. the sensitivity of the allometrics to senescence). Similarly to E. delegatensis, the C in aboveground
understorey biomass was calculated for both contributing allometrics and their average, for comparison purposes.
The allometric used for determining the carbon in snags was the average of the three eucalypt allometrics described above for aboveground biomass, i.e. the penultimate allometrics for E. delegatensis. Apart from height loss, to accommodate general loss
of branches, bark, and unrecorded internal voids, the calculated aboveground mass was multiplied by 0.6666, in addition to the recorded decay class factor. For example, a snag of decay class S (i.e. 0.33333) had the necromass of an equivalent- sized living tree, multiplied by 0.2222. Loss of height was interpreted by multiplying the necromass from the allometric by the proportion of the original height remaining. That, in effect, assumed a cylindrical stem and was therefore more conservative than volume based on stem taper, when more of the upper stem had decomposed. The original height was estimated from the height-DBH relationship for E. regnans
(Dean et al., 2003) but with an adjustment to accommodate E. delegatensis possibly
being of shorter stature, and to blend with the measured DBH-height pairs; i.e. a new allometric was derived. Parameters in that height allometric were varied to gauge its impact on calculated necromass. The volume of hollows, fallen logs and branches was calculated as a frustum of a cone. For snags and stumps the volume was converted to mass using the basic density of 524 kg m-3 for E. delegatensis (Ilic,
1997) and applying the same decay factors as for the solid section (i.e. all necromass was calculated as if it were E. delegatensis.) For fallen logs and branches the volume
was converted to mass using a conservative basic density of 400 kg m-3, and the recorded decay class. Necromass was pooled and calculated on a per plot basis, then averaged over the study area.
72