1. Introduction

2. Mixed-forests in Tasmania, Australia: A Target of Industry and then Conservation

Figure 1. Canopy stratification of mixed-forest: open Eucalyptus regnans (~72 m high) above closed myrtle and sassafras canopy. Seen from edge of logging coupe SX009C, Styx Valley, Tasmania. (a) tallest eucalypt in foreground: DBH= 4.56 m with mature myrtle hemi-epiphyte joint up to 5.4 m height on the right-hand side and sassafras joint up to 4.7 m on left hand side; (b) drone view from above closed, lower canopy (courtesy of Darren Turner), tall tree on RHS is same E. regnans tree as in (a) on LHS. (c) at ground-level: myrtle, sassafras and ferns in-between mature E. regnans.

Figure 1. Canopy stratification of mixed-forest: open Eucalyptus regnans (~72 m high) above closed myrtle and sassafras canopy. Seen from edge of logging coupe SX009C, Styx Valley, Tasmania. (a) tallest eucalypt in foreground: DBH= 4.56 m with mature myrtle hemi-epiphyte joint up to 5.4 m height on the right-hand side and sassafras joint up to 4.7 m on left hand side; (b) drone view from above closed, lower canopy (courtesy of Darren Turner), tall tree on RHS is same E. regnans tree as in (a) on LHS. (c) at ground-level: myrtle, sassafras and ferns in-between mature E. regnans.

Figure 2. Structure of lower tree trunk extending to lateral roots. (a) Urban hawthorn (Crataegus hybrid) Hobart, cut at ground level, diameter= ~0.42 m, scale bar= 0.5 m (b) Sector of cross-section of partially hollowed E. regnans or E. obliqua in logging coupe (operational logging unit) after eucalypt regeneration burn, Styx Valley, DBH 2.92 m, cut near 1.3 m (courtesy of David Green), then pinned in place, dried and sanded. Gaps between lobes due to wood shrinkage and enclosed bark that fell away. Scale bar on left= 1 m. Note wood grain pattern in the lobes such that cambium and phloem are both near the centre of the trunk and on the outside. Insets show chainsawing (top) and fresh solid surface (bottom).

Figure 2. Structure of lower tree trunk extending to lateral roots. (a) Urban hawthorn (Crataegus hybrid) Hobart, cut at ground level, diameter= ~0.42 m, scale bar= 0.5 m (b) Sector of cross-section of partially hollowed E. regnans or E. obliqua in logging coupe (operational logging unit) after eucalypt regeneration burn, Styx Valley, DBH 2.92 m, cut near 1.3 m (courtesy of David Green), then pinned in place, dried and sanded. Gaps between lobes due to wood shrinkage and enclosed bark that fell away. Scale bar on left= 1 m. Note wood grain pattern in the lobes such that cambium and phloem are both near the centre of the trunk and on the outside. Insets show chainsawing (top) and fresh solid surface (bottom).

Figure 3. Tree growth with only partial contribution to increase in the external diameter, after hollow formation. (a) Virtual slice at 1.3 m above ground of 3D model of a E. regnans (the Chapel Tree, Styx Valley) DBH 6.03 m, showing minimal buttress spurs and internal growth—the small circle near the entrance to the hollow is a young stem stalk, formed while surrounding wood was decomposing. (b) photo of the same tree showing new growth and hollow. (c) A cross-section of a E. regnans tree at 15.4 m above ground, felled during logging, coupe SX019i, showing new internal growth, including bark, but inside trunk hollow. DBH 3.84 m. Exterior of buttress did not suggest internal hollow, but at 1.3 m aboveground the tree was ~50% hollow.

Figure 3. Tree growth with only partial contribution to increase in the external diameter, after hollow formation. (a) Virtual slice at 1.3 m above ground of 3D model of a E. regnans (the Chapel Tree, Styx Valley) DBH 6.03 m, showing minimal buttress spurs and internal growth—the small circle near the entrance to the hollow is a young stem stalk, formed while surrounding wood was decomposing. (b) photo of the same tree showing new growth and hollow. (c) A cross-section of a E. regnans tree at 15.4 m above ground, felled during logging, coupe SX019i, showing new internal growth, including bark, but inside trunk hollow. DBH 3.84 m. Exterior of buttress did not suggest internal hollow, but at 1.3 m aboveground the tree was ~50% hollow.

Figure 5. Similar-sized trees with varying hollow size, relating to different carbon stocks. (a) A buttress region (‘butt’) log of DBH ~4.08 m, on permanent display in the Tyenna Valley, showing a nearly 100% solid cross section. 1 m quadrat for qualitative scale only. Photographed in 2002, logged c1965, bark has decomposed and some timber has shrunk, revealing folding of cambium layers in the buttress region. (b) 3D model of a logged and burnt E. regnans of DBH 4.18 m with ~25% of the carbon lost from the buttress region, in the Styx Valley, developed in earlier work [67,92]. The hollow had no entrance point in the buttress region (so the hollow was not indicated externally). Such 3D models allow: more accurate measurements (e.g., by burl removal); and with sufficient samples, allowed new data types and formation of new allometric equations for C accounting.

Figure 5. Similar-sized trees with varying hollow size, relating to different carbon stocks. (a) A buttress region (‘butt’) log of DBH ~4.08 m, on permanent display in the Tyenna Valley, showing a nearly 100% solid cross section. 1 m quadrat for qualitative scale only. Photographed in 2002, logged c1965, bark has decomposed and some timber has shrunk, revealing folding of cambium layers in the buttress region. (b) 3D model of a logged and burnt E. regnans of DBH 4.18 m with ~25% of the carbon lost from the buttress region, in the Styx Valley, developed in earlier work [67,92]. The hollow had no entrance point in the buttress region (so the hollow was not indicated externally). Such 3D models allow: more accurate measurements (e.g., by burl removal); and with sufficient samples, allowed new data types and formation of new allometric equations for C accounting.

Figure 6. Tree growth of a E. regnans and associated concentrated soil organic carbon. Drawing based on Figure 2.b in Dean, et al. [92], but with separated growth stages and extra detail. Aboveground shape drawn from taper formulae adjusted for ground slope [88], roots drawn from observations and literature [67,80]. For the older tree, two scenarios are portrayed: on the left the trunk remains undecomposed and on the right-hand-side the tree has hollowed out.

Figure 6. Tree growth of a E. regnans and associated concentrated soil organic carbon. Drawing based on Figure 2.b in Dean, et al. [92], but with separated growth stages and extra detail. Aboveground shape drawn from taper formulae adjusted for ground slope [88], roots drawn from observations and literature [67,80]. For the older tree, two scenarios are portrayed: on the left the trunk remains undecomposed and on the right-hand-side the tree has hollowed out.

Figure 7. Examples of stages shown in Figure 6. (a) 3D model of an ~0.6 m DBH tree trunk and parts of central tap root and lateral roots (no decomposition), (b) lower part of a 3.11m DBH tree filled with lignomor from trunk decomposition (handle of the 2 m long soil auger is visible), (c) the edge of the bowl of ligniform from a burnt and fallen tree, showing contrast with surrounding soil, (d) pushed over, burnt and wind-rowed medium-sized trunk in a plantation showing large hollow, I pushed over and burnt medium-sized trunk with small hollow, coupe SX004c (photo: Melinda Lambourne), and (f) measuring 0.9 m deep pit in bowl of lignomor under live, hollow E. regnans, l(DBH 6.08 m).

Figure 7. Examples of stages shown in Figure 6. (a) 3D model of an ~0.6 m DBH tree trunk and parts of central tap root and lateral roots (no decomposition), (b) lower part of a 3.11m DBH tree filled with lignomor from trunk decomposition (handle of the 2 m long soil auger is visible), (c) the edge of the bowl of ligniform from a burnt and fallen tree, showing contrast with surrounding soil, (d) pushed over, burnt and wind-rowed medium-sized trunk in a plantation showing large hollow, I pushed over and burnt medium-sized trunk with small hollow, coupe SX004c (photo: Melinda Lambourne), and (f) measuring 0.9 m deep pit in bowl of lignomor under live, hollow E. regnans, l(DBH 6.08 m).

3. Industry Activity, Science and Conservation in Mixed-Forest

3.4. Conservation in the Mixed-Forests

Although conserving forests from industrial activity is often dressed as a recent idea, it is centuries or millennia old. Ancient civilisations such as those of Greece, Rome, India, China and Maya also exercised forms of forest conservation, reforestation and plantations, though for more local benefit and society-oriented reasons than are the national parks of today [191–194] . These conservation initiatives were concomitant with neighbouring major forest attrition, deforestation and related land degradation issues, and consequent adjustments to societies [191,195–197] . Forest conservation was suggested in the 13^th and 14^th centuries in England, to keep forests intact for some people’s needs, in the face of flora and fauna attrition by local residents [198] . More forest conservation was later proposed in that same region, but for forest amenity’s sake, and again to counteract attrition by local residents [198] . Sourcing of forest products by local people was mainly for local usage, but also for selling further afield. In the late eighteenth and early nineteenth century, forest conservation, less damaging use of forests and even reforestation, was proposed in Brazil, due to: land becoming far less productive after slash and burn agriculture, possibly medicinally important plant species being lost, alternative uses for the timber, and important fauna species declining [199] .

As early as 1925 there was public disquiet about the misleading information in forest industry PR [200] , such as against the notion that forests cannot regrow and maintain themselves without human intervention by logging:

‘A forest may and often does maintain itself unimpaired century after century. If this were not so, why was a large part of this country covered with magnificent forest with trees several to many centuries old when the first settlers came? Can we doubt that it would still be so but for human interference?...No more nonsense can be disseminated than the idea that if we do not hurry up and cut the rest of our dwindling pernicious supply of timber the forests are going to fall down and rot like a crop of weeds. … We shall never get any real conservation in this country until people wake up to a realization of how the tentacles of commercial interests have penetrated, not only the branches of our government, but also most of the conservation organizations.’ [200]

Similar reasoning is published by advocates of corporate forestry today, when they imply that mixed-forest will turn into lower-carbon-stock rainforest and emit carbon if not logged [e.g., [201] ]. We examine the carbon balance for that process in this review.

All remnant primary forest on public land in Australia, is currently sought after by both the forest industries and those interested in conservation. National parks and other reserved forest land such as world heritage areas, have become newly contested land [202] . The goal is represented through industry mantras such as ‘a shared vision’ [203,204] . A media release by Forestry Australia (previously Institute of Foresters Australia) included:

‘The paper Reshaping forest management in Australia to provide nature-based solutions to global challenges, by Dr William Jackson and other members of the IFA/AFG, says it is time to move beyond the era of conflict and develop more holistic approaches that encompass all forest values, such as water, biodiversity, tourism and forest products, across the landscape.’ [205]

In contrast, the article they cite states:

‘To be clear, active management is not a call for commercial timber harvesting in national parks and conservation reserves.’ [206]

Overall, conservation of primary forests did not prevail in Australia because “The forest industry had the financial advantage in being able to have offices and professional lobbyists at a level the environmental movement could never match. It presented itself as the defender of employment, in ways that were as specious as the appealing pictures and that were also persuasive.” [115] . Demand grew to conserve some more forest from timber felling following intensification of logging in Australia for export pulpwood in the 1970s and 1980s, which peaked in the 90s and included further forays into national parks [207,208] . Consequently, in the 1980s some forest neighbouring pulpwood concessions in Tasmania and some national park land were assigned World Heritage status [209] . The most notable of these was an area of tall, mature mixed-forest (with 41–80 m tall eucalypts) intermingled with myrtle-dominated rainforest, bordering the northwest side of the Florentine Valley ( Figure 8 ). Without such reservation, designed by Kirkpatrick, it would have met the same fate as nearly all the mixed-forest in that valley— clearfell logging conversion to young, production forest cycles ( Figure 8 ). This century, the public’s awareness of dwindling primary forest acreage in the concessions caused further demand for World Heritage assignments, even including land that had earlier been selectively logged [210] . The extension was achieved and some its components are described below.

Figure 8. Logging extent (brown) in the Florentine Valley catchment (blue outline) as of 2012. Note the area of mature, tall mixed-forest (bright green) in the top left of the Florentine Valley that was reserved from logging and allocated into the World Heritage Area (yellow with red outline). Forest type mapping was from aerial photography interpretation by the State forestry agency, Forestry Tasmania. Projection: GDA 1994, MGA, Zone 55.

Figure 8. Logging extent (brown) in the Florentine Valley catchment (blue outline) as of 2012. Note the area of mature, tall mixed-forest (bright green) in the top left of the Florentine Valley that was reserved from logging and allocated into the World Heritage Area (yellow with red outline). Forest type mapping was from aerial photography interpretation by the State forestry agency, Forestry Tasmania. Projection: GDA 1994, MGA, Zone 55.

4. Dynamics of Soil Carbon Relevant to Measuring Forestry Effects

4.3. Linking ΔSOC to Change in Biomass, and Measuring It

Broadscale datasets where SOC can be compared against forest biomass, and where other factors are normalised, show that SOC is positively correlated with forest biomass per unit area [238,239] . Thus, where time-averaged, long-term biomass is reduced by intensive logging then it would be expected that SOC must also decrease. A long-term decline in SOC with subsequent harvest cycles over several centuries is because there’s less wood available (compared with the primary forest), both from fallen branches and trunks and from coarse roots of those trunks, to decompose into soil carbon [240–243] . That is the biological perspective, and it is mirrored in computer models, where mass is stored in matrices for live biomass carbon, dead biomass carbon, SOC pools and the atmosphere, with periodic movement of carbon between them according to half-lives of the pools.

Within the numerous findings from experiments on intensive logging and SOC that were reviewed in Dean, et al. [239] , any seeming inconsistency from the positive correlation can be explained. For example, upon examining purportedly paired sites Leuschner, et al. [244] found a long-term drop in SOC over a few centuries of logging but did not find a correlation between SOC and biomass. However, their ‘low’ biomass values were not time averaged over the logging cycle but were near the end of the cycle and on average, statistically close to the primary forest values. Assuming a Chapman-Richards type growth function, the time average biomass for the logging cycle is more likely to be ~²/₃ of the biomass at the time of logging. That lower value would have been more likely to reveal a positive correlation between biomass and SOC. Because of the laggardness of ΔSOC, average values over longer time periods are better indicators than values at a point in time. They are also more relevant to the effects of land use on climate change.

There are of course natural, long-term changes in SOC [245] that create a background against which one would observe the trend due to intensive logging. Where some of the forest biomass due to logging is moved off site, is not burnt as mill waste, and becomes a wood-product, then eventually decomposes in landfill, it can contribute to off-site SOC. For the mathematics of carbon accounting, this off-site SOC should be added to the forest’s on-site SOC.

The question arises, when will the ΔSOC due to management, become measurable by experimentation? Several cycles of reduced growth and decomposition under conditions of reduced biomass [due to logging of primary then secondary forest], are needed to change SOC sufficiently for it to show up empirically [239] . One can merge the outputs from different reports shown in Figure 2 of Dean, et al. [239] based on cycle number of the secondary-forest logging [models from: [47,241,242,246-248]]. To normalise the different data sets along the time axis, the common logging cycle duration was chosen as 80 years. The merged data provide a rough estimate of the fate of SOC for a range of species, range of soil depths and range of cycle lengths as a function of logging cycle number. This average trend can be formulated in equation form (Eq1) using Eureqa [249,250] (portrayed in Figure 9 ):

SOC% = 1,965/(14.92 + lc) + 8.944sqrt(0.0875 + lc) – 34.21

(1)

where SOC%= percentage of the original, long-term-average, primary forest SOC, lc= logging cycle [number] from 1 to 35 cycles (i.e., up to 2,800 years since first logging), R²= 0.95, Correlation coefficient= 0.97, Maximum error= 32.05, Mean squared error= 11.92, Mean absolute error= 1.475, Coefficients= 3.

Figure 9. Change in SOC, as a percent of the time-averaged-mean of the original primary forest SOC, versus cycle number of logging the secondary forest, with 0 being the logging of the primary forest. This average line was from data from the models in Figure of Dean, et al. [239] cited in the main text here; data were first converted to the relative time through each logging cycle.

Figure 9. Change in SOC, as a percent of the time-averaged-mean of the original primary forest SOC, versus cycle number of logging the secondary forest, with 0 being the logging of the primary forest. This average line was from data from the models in Figure of Dean, et al. [239] cited in the main text here; data were first converted to the relative time through each logging cycle.

The model outputs merged to create Figure 9 had cycle lengths from 50 to 100 years. For other cycle lengths the curve may extend or contract depending on the time balance between coarse root growth, and root and SOC decomposition, within each cycle. Other causes of variation in the curve will be, for example, the local environment, species, and logging procedures.

Quantitatively, Equation 1 and the curve in Figure 9 indicate that after 3 cycles of intensive logging there will be a 9% drop in SOC, 18% after 6 cycles, and 30% after 12 cycles. The trend implies that even where people are no longer logging primary forest, they will still be losing carbon if persisting with logging of the secondary forest, except after many centuries. In contrast, conversion of forest to cropland can incur a similar ΔSOC after only ~20 years [251] , making it much easier to measure, but even there, the decline continues in subsequent years before levelling off [ [230] , Figure 8 , [252–254] ]. The gradual decline in Figure 9 reveals that in order to measure ΔSOC with scientific significance, one may need to measure over several logging cycles. SOC shows a peak in the first cycle due to decomposition of the large amount of debris from primary-forest logging (unless it is mostly burnt), so it is pointless trying to detect ΔSOC that soon. This explains why many review papers indicate ambivalence about ΔSOC with logging, which is echoed in the finding of Leuschner, et al. [244] that: ‘… the long management history of nearly all Central European forests often hinders the detection of legacy effects, unless true primeval forests are used as a reference.’

A few studies have observed the cumulative effects of several logging cycles, which allows comparison with Figure 9 . Leuschner, et al. [244] , for the upper soil profile down to 0.5 m depth report a 13.5% drop in SOC after ‘several’ centuries of logging (which may correspond to three or four cycles). However, that change was averaged over three different locations then converted to a percentage, whereas if the percentages had been calculated first for each of the three locations and then those averaged, the result might differ in magnitude. For the upper soil profile down to 0.55 m Ferré, et al. [255] note a drop in SOC of ~40% over 3 or 4 logging cycles over 37 years, but that includes soil manipulation through ploughing and fertiliser addition. For the upper soil profile down to 0.6 m, Vario, et al. [256] reported a drop in SOC of up to -24% for the second logging cycle. These changes are comparable with the trends shown in Figure 9 but are higher in magnitude, considering the number of logging cycles passed.

An example of the ambivalence arising from short-term experiments is in a recent review of ΔSOC, with different anthropogenic activities [245] . Their overall finding concurred with that of Dean, et al. [239] , in that intensive logging of a primary forest followed by repeated logging cycles decreases soil carbon compared with the earlier, long-term average for the primary forest. However, they found that the change was mostly in the topsoil, whereas if allowing sufficient time for the whole soil profile to match that of the new forest cover, then that whole profile is more likely to change (as lower down changes more slowly). Conversely, another recent examination of ΔSOC with logging, though only thinning, which considered mostly short-term experiments [257] , could not find any statistically significant effects of logging. On considering the dynamics described above, short-term and surface-soil experiments cannot possibly show the long-term, whole-profile effects on SOC from logging. Thus, although Lei, et al. [257] , cited Dean, et al. [239] , they didn’t take onboard the timelines for assessing change mentioned therein.

Most chronosequence studies compare forest SOC at different ages since the first logging, against the SOC of primary forest, but only for one logging cycle [[258-260],e.g., [261,262] ]. There are few experiments on ΔSOC that span several logging cycles. They would probably use space-for-time substitution, but the non-equivalence between sites is the bane of such experiments. Often, one of the pairs has already been considered inferior for resource extraction. Undeveloped land has a long history of being less productive than developed land [50,263–266] . It will be difficult to find data in the form of equivalent paired sites, to compare with the modelling in Figure 9 . A typical example is presented here. For selective logging over about two centuries (i.e., no definitive cycles) Christophel, et al. [267] found an increase in the upper mineral soil to 0.3 m depth and a decrease in the organic layer above, and combined there is a net decrease with the logging. However, the paired sites may not have been equivalent because the mineral soil in the unmanaged forest sites had ‘larger stone contents’ [267] . Regarding that comparison of sties, the increase in stoniness % volume for the primary forests compared with the managed sites, averaged across the three locations in Christophel, et al. [267] , for the Ah, AB and BC horizons was 14%, 10% and 21%, respectively. These amounts are enough to indicate that the productivity on the sites could be different and if so, then the organic matter returns to the soil will also be different. Also, as sampling an equivalent mass of soil when making SOC comparisons is sometimes necessary [268] , the soil sampling depth would need to be between 10% and 21% deeper than -0.3 m in the stonier primary forest.

It is often inappropriate to ignore earlier land cover when portraying the carbon forecast for forestry, because of the centuries required for SOC stock to reach a new dynamic equilibrium [e.g., [230,269,270,271] ]. In ecology, where there is a major disturbance followed by a long-term change, and the flora and fauna species take time to reach a new equilibrium, that period is called ‘relaxation time’ [272,273] . That same term will be adopted here, for the forest soil organic carbon to adjust after conversion from the long-term average of a primary forest to that of the long-term secondary forest under logging cycles.

There are ~2 Mha of plantations in Australia, and ~5 Mha of mostly hardwood production forest on public land, plus between 22 and 108 Mha of privately owned or leased forest but most of which is not commercially viable [274–276] . Most of that 7 Mha of forest production land was primary forest prior to logging. And as Australia only began converting primary forests about 200 years ago, much of that area is still in the first few cycles, and consequently Australia has much more carbon to emit within the relaxation time [if it continues logging on that land].

An appropriate baseline corresponding to somewhere within the relaxation time must be included when showing a carbon forecast for a particular activity. It is often not included in bioenergy and forest carbon accounts [277] . Indeed, forest debris, waste from mills and almost any timber from forests is called ‘renewable energy’ and burning it is considered ‘carbon neutral’ by many corporate forestry proponents, because the trees can be regrown [e.g., [278] ]. But this neglects the decreasing soil carbon during the relaxation time. Time segments and baselines from within the relaxation time could be included in corporate carbon accounting. If the date of the original forest conversion to logging cycles is known, then one can estimate where in Figure 9 the current logging is acting. This would allow up-to-date life-cycle-analysis calculations for the carbon footprint of recent wood products, which could be conveyed to customers or used in national accounts.

As a corollary to the long-term emission upon conversion of primary forest to logging cycles, another perspective is offered by considering the time taken to replenish emitted carbon. Long relaxation times are also required upon soil recovery, for definitive results— to separate the signal from the background noise. Recovery requires several generations of trees to grow and decompose to sequester the carbon into the soil, as shown in the model output in Figure 10 (adapted from Dean, et al. [230] ). For diagrammatic simplicity, the SOC depletion in this example is from deforestation, rather than from logging cycles. The modelled SOC in Figure 10 starts at 0 Mg ha-1 before any vegetation contributes carbon to it, to show the spin-up time for models (mentioned above), but less time would be needed where there is nearly as much legacy carbon as in the future forest. The ripples are due to sudden death of the stand (such as from a s)and-replacing fire) but the same overall shape of the sequestration and emission occurs when modelled as annual contributions of SOC to the soil [230] .

Figure 10. Output from a simple model in Microsoft-Excel: a three-pool SOC system with half-lives of 2, 50 and 500 years where SOC was created from decomposing roots of trees that died and regrew every 200 years. Colours differentiate successive generations of trees. After ~3,000 years there was deforestation and the site left barren for 200 years (e.g., a wide forest road). Recovery of SOC took nearly 1,500 years (the ‘relaxation time’) because several generations of forest had to regrow, mature, and decompose, to supply new SOC.

Figure 10. Output from a simple model in Microsoft-Excel: a three-pool SOC system with half-lives of 2, 50 and 500 years where SOC was created from decomposing roots of trees that died and regrew every 200 years. Colours differentiate successive generations of trees. After ~3,000 years there was deforestation and the site left barren for 200 years (e.g., a wide forest road). Recovery of SOC took nearly 1,500 years (the ‘relaxation time’) because several generations of forest had to regrow, mature, and decompose, to supply new SOC.

4.4. Points of Reference for SOC Measurement

4.4.1. Difficult Locations: Under Large Trees and Deeper Down

Another reason for ambiguity over ΔSOC with logging of primary forests is that, before logging, SOC is not usually measured under large tree trunks where it is usually more concentrated and deeper in the profile than in between trees, nor is it measured under large coarse woody debris (CWD) [92,279] ( Figure 7 ). Therefore, pedogenic patches [279] of concentrated SOC could be missed before logging. During logging the large stumps and CWD are sometimes upturned, broken or bulldozed aside, such that the lignomor underneath is accessible to random soil sampling ( Figure 7 .d-e). Approximately 4% of the SOC could be missed prior to logging because of this difference in measurement before and after logging [ Figure 11 in [92] ]. This could cause inaccuracy and imprecision, or introduce bias when assessing the impact of land use on SOC.

Depth is another inadequately represented dimension when measuring SOC [224,261] . The international, minimum recommended depth for measuring SOC change is 0.3 m, principally for international comparisons [280] , with a more general recommendation of 1 m [281] . Depending on the tree species, soil profile and fragmentation of bedrock, the roots and therefore a substantial portion of the SOC from decomposition of old roots or infiltration of surface water containing tree carbon, can be below a metre depth [92,224,282–291] . The depth for SOC measurement should be guided by such factors [224,290–292] .

To measure 90% of SOC in a mixed-forest in Tasmania it was necessary to include soil down to ~1.6 m depth [92] . The depth to include at least 95% of the root biomass for Eucalyptus species is often over 2 m or deeper where the soil depth or fracturing of bedrock permits [92,282] ( Figure 11 .c). For a site in the Brazilian Amazon where SOC was measured to -10 m, only 21% of the SOC was in the top 0.3 m, ~50% to -1 m, and 16% was below -3 m [293] . Where soil or bedrock and species permit, roots of woody species extend to 10–20 m depth [294,295] , which will create pedogenic high-SOC patches after root decomposition.

The stoniness of many forest soils is often an impediment to SOC sampling. The location in Figure 11 (a) and (b) with a very thin layer (~0.2 m) of mineral soil supported forests of Eucalyptus regnans and Eucalyptus obliqua, though only to ~45 m height, rather than the 75 m typical of mixed-forests. Tree roots can occupy fissures up to several metres in bedrock and decompose there ( Figure 11 .c), creating soil and adding SOC, and contributing to translocation of water that may contain dissolved organic carbon from above [e.g., [296] ]. The inclusion of this characteristic in carbon modelling, is suggested based on experimental evidence of likely forest root decomposition in weathered and fractured bedrock plus underground transportation of some of that resultant carbon as dissolved organic carbon [289] . Organic carbon in fractures in weathered bedrock, even granitic, is linked to root distribution. The rock surface in the fractures (to < 0.02 m thickness) can contain associated soil carbon [297] . The fraction of root mass in bedrock (and hence the soil carbon derived directly from root decomposition there) naturally depends on, for example, the depth of the A and B soil horizons, tree species, climate, tree age, water distribution, and bedrock type [298–300] .

Figure 11. (a) and (b): thin soils with large boulders that would prohibit typical soil sampling to more than about 0.2 m depth. The amount of total SOC may be similar to that for other Eucalyptus regnans and E. obliqua forests of equal long-term-average biomass in that climate, and would need to be included in carbon modelling of land use. Photographed during clearfell cable logging of primary forest in coupe WE008e, near Mt. Wedge, Tasmania. (c) Roots descending over 5 m into fractured bedrock in dry schlerophyll forest, South Australia, exposed during mining. When these trees die (apart from those exposed) some of the root carbon will form local SOC.

Figure 11. (a) and (b): thin soils with large boulders that would prohibit typical soil sampling to more than about 0.2 m depth. The amount of total SOC may be similar to that for other Eucalyptus regnans and E. obliqua forests of equal long-term-average biomass in that climate, and would need to be included in carbon modelling of land use. Photographed during clearfell cable logging of primary forest in coupe WE008e, near Mt. Wedge, Tasmania. (c) Roots descending over 5 m into fractured bedrock in dry schlerophyll forest, South Australia, exposed during mining. When these trees die (apart from those exposed) some of the root carbon will form local SOC.

In a critique of a soil carbon GIS and modelling study by Dean and Wardell-Johnson [301] , McIntosh, et al. [302] referred to three reports on soil organic carbon in northern Tasmania [303–305] , as being available as points of reference for comparison for SOC down to 1 m depth, i.e., they purportedly formed benchmarks. These three reports will be examined here to portray aspects of SOC measurement appropriate for use in the calculation of land use effects on the carbon cycle and for comparison with carbon-cycle modelling.

The soil depths studied in Grant, et al. [303] , for example, are only to between 0.8 and 1.2 m depth and many have a ‘+’ sign on the last measurement. Additionally, there were some methodological issues because the experiments were not originally designed for spatial carbon assessment. They had been instigated to determine soil suitability for plantations [306] . Those methodological issues are explored here. Part of peer review is to make sure that standard scientific protocols have been followed. Science that gets published without peer review is called ‘grey literature’ and therefore using it as a basis for the next advance in science is viewed as meaning that the next step might possibly be more dubious than if using peer-reviewed science as a basis. The three 1995 Tasmanian reports [303–305] were such grey literature. Consequently, checks would have been appropriate on how applicable their data is to scientific assessment of spatial carbon accounting, under the scientific peer review process.

That ‘+’ sign indicates that the soil profile continued deeper than was sampled, therefore, it is likely that there was more carbon to be tallied than that reported. Such a comparison against modelled SOC values is often not valid because the values derived from modelling, such as in Dean and Wardell-Johnson [301] , which used CAR4D, include SOC to wherever it may have been translocated, such as down into the fractures of bedrock, or laterally offsite by groundwater or streams. Due to the limited data available, in modelling the carbon cycle in CAR4D, the entire soil profile (including fractured or semi-permeable bedrock) is treated as homogenous: undifferentiated laterally or depth-wise [301,307] . Some modelling software accounts for SOC to only 0.3 m, for highly calibrated sites or it uses very generalised profiles, or tweaks the carbon-compound half-lives or emission pathways to match SOC to 0.3 m, for example in FullCAM [ [308] ; S. H. Roxburgh, CSIRO, personal communnication, 2021].

McIntosh, et al. [302] referred to the modelled total of 685 Mg ha^-1 for the case study #1 site in Dean and Wardell-Johnson [301] , which was a E. regnans-dominated forest (introduced in [307] ) as being:

‘…more than twice the maximum measured soil C value under E. regnans available to these authors in 2010 which was 273 Mg.ha^-1 in the previously mentioned Stronach profile [21] .’

The SOC values in McIntosh, et al. [302] were only tallied to 1 m depth rather than for the full profile as in carbon modelling, which suggests that the 273 Mg ha^-1 for the Stronach site in Grant, et al. [303] (the reference ‘ [21] ’ cited in McIntosh, et al. [302] ) had also been truncated to 1 m depth from its reported 305 Mg ha^-1 to 1.2 m.

Values of SOC for the full profile can be estimated by fitting simple exponentials to reported empirical SOC data using equations of the form:

cumulative_SOC = g [1 − exp(bz)]

(2)

where z is depth in metres (negative below 0); Dean, et al. [92] . If z is lower than where SOC was measured, then the extrapolation relies on there being soil or rocks that can adsorb SOC occurring lower in the profile, or DOC or colloidal SOC being carried deeper or sideways. From soil sampling in McIntosh, et al. [302] , the site of highest SOC had 304–326 Mg ha^-1 to 1 m depth. Extrapolation using Equation 2 for this site gives ~498 Mg ha^-1. This value is closer than their declared benchmark of 273 Mg.ha^-1, to the temporal average of 685 Mg ha^-1 for site #1 modelled in Dean and Wardell-Johnson [301] , which was for the entire soil profile and any translocated SOC.

Additionally, site #1 in Dean and Wardell-Johnson [301] had above-average, long-term, live biomass, as shown later in this paper, and therefore could be expected to have above-average SOC, whereas the sites in Grant, et al. [303] are more likely to have been average. The live biomass for mature E. regnans stands can vary greatly, e.g., 262–647 → 697–1053 [57,77,92,309] , and is possibly related to the ‘site index’ (forestry terminology for potential wood volume at a particular age). If this difference persists in particular locations over successive generations of E. regnans trees, then by the positive relationship between aboveground biomass and soil carbon [mentioned above], there should be an equivalent range of SOC between those stands. On a pro-rata basis the variation in biomass found in Dean, et al. [92] for stands of approximately equal maturity, corresponds to a variation in SOC of 184-to-455 Mg ha^-1 (across the average of 330 Mg ha^-1).

Regarding suitable points of reference, there were other SOC data available back in 2010, from soil carbon accounting experiments in E. regnans-dominated forests: data from Victoria [258] had been used to calibrate the model ‘CAR4D’ [307] . For those sites, there was an estimated 1,300 to 3,000 Mg ha^-1 to 10 to 20 m depths, and a measured average of 650 Mg ha^-1 to 1 m depth [258] . The SOC in CAR4D was modelled as being less than at those Victorian sites, concomitant with the frequently shallower soils in the Styx Valley, Tasmania. Now that SOC data from experiments designed for carbon accounting are available for E. regnans-dominated forests in Tasmania [92,302,310] , CAR4D can be recalibrated.

4.4.2. Difficult Locations: Coarser Components

Not only dimensions need to be considered comprehensively but also other parts of the soil. Many, though not all, experiments involving sampling of SOC in soil have not measured the carbon in firm particles greater than 2 mm width [290,311] . The reason for this may be because: (a) they were considered chemically unable to bind to organic carbon [290,312] , (b) some researchers may do it simply to align with an established protocol, or (c) the harder fragments can be more difficult to grind in preparation for elemental analysis. But the practice can miss out on substantial portions of SOC, resulting in underestimations for some forests and possibly incorrect calibration of carbon dynamics models [290,312,313] . Significant amounts of organic carbon can be dissolved into stones or adsorbed on their weathering surfaces, with significant contribution to total SOC [314–316] .

Where there has been forest fires or post-logging burns, there may be pieces of charcoal as well as coarse mineral fragments. Without any post-logging burn, Hopmans, et al. [317] found SOC to 0.3 m depth was 209 Mg.ha^-1: with and without post-logging burns the amount of SOC in charcoal and rocks >2 mm width was 42% and 29% of the total SOC, respectively [317] . In forests with occasional fire but no post logging burns Buma, et al. [318] found that the SOC to 0.1 m depth contained ~16% charcoal in the >2 mm fraction. Holub and Hatten [213] and Harrington, et al. [319] also sampled carbon in material >2 mm width but only up to 4.75 mm width.

Charcoal is more likely to be near the surface (unless in buried sediments) and coarse stony fragments are more likely to be closer to the bedrock [313] . It is logical to include such carbon pools in forest carbon accounting related to climate change. The organic carbon associated with charcoal and mineral fragments is inherently included in earlier modelling work [47,235,269] and was measured empirically in Dean, et al. [92] . Discarding and not counting the organic carbon in the >2 mm charcoal and rock fragments in the soil, could be one of the reasons for the lower SOC benchmark suggested by McIntosh, et al. [302] .

Soil may also contain very old organic carbon that is not derived from the current or recent forest biomass, but from ‘fossil’ carbon in soil derived from sedimentary bedrock [320,321] . This could complicate modelling of forest carbon dynamics and measuring the effects of land-use-change. Organic matter found in rocks and soil during forest carbon accounting experiments originating from the forest should ideally be differentiated from that from shale, some sandstone and mudstone etc (such as the grey or black varieties). Radiocarbon dating, radiocarbon natural abundances (Δ¹⁴C), or carbon isotope ratios (δ¹³C) may allow such differentiation [322] .

4.4.3. Soil Sampling Specific for SOC Accounting

Apart from just the depth aspect, it is worth considering those 1995 Tasmanian purportedly benchmark studies more closely in different dimensions, especially as there has been further developments in science now that spatial soil carbon accounting is a common goal. When considering points of reference (benchmarks) for comparisons, one must consider possible bias and error margins. One of the aspects that has progressed considerably in the last few decades to reduce bias and error margins is elemental analysis of soils [e.g., [323,324] ]. The three 1995 Tasmania reports used a modified Walkley-Black (WB) method for carbon assay but without any mention of a correction factor:

‘These have been determined using the Walkley and Black colorimetric method (Rayment and Higginson 1992).’ [ [325] , p18], plus:

‘The procedure is that described by Rayment and Higginson (1992) using 0.5 M sodium dichromate (Na₂Cr₂O₇.2H₂O). Read absorbance using the “Cecil spectrophotometer CE 292”. Determine organic carbon values from plotted standard curve of absorbance verses organic carbon (%)’ [306]

The WB method may not measure all the organic carbon in the soil, depending on the chemical structure of the organic molecules, and on how they are bound in the soil, which in turn is dependent on for example, climate, soil type, parent rock type, tree species and land management [326–328] . And it may not measure the carbon in charcoal, as is necessary in forest carbon accounting. The WB method relies on oxidation of organic carbon, under moderate heat generated by the action of aqueous sulfuric acid, with accompanying reduction of Cr⁶⁺ to Cr³⁺, but the oxidation of carbon may be incomplete. Which is why the USA Forest Service recommends that the method should not be used [329] .The amount of oxidised carbon is determined by titration for Cr⁶⁺ or by colorimetry of the Cr³⁺, or simply by measuring the amount of CO₂ released. The recommended correction factor, which is a multiplier, is usually near 1.3 but calibration for specific environments and land use may require multipliers nearer 1.7 [330] . For some Tasmanian plantations Wang, et al. [331] found that the WB method detected 97% of the carbon found by using an Elemental Analyzer and therefore no substantial multiplier was needed, but that may have been due to the younger, loosely bound carbon [332] , and possibly as the plantations may have been sprayed with atrazine (which contains organic carbon and may not have been bound strongly to the soil). One modified-WB method uses heat to oxidise more of the carbon and thus requires a lower multiplier [327] , but the heat method was not used in the 1995 Tasmania reports, though sodium dichromate dihydrate was used instead of potassium dichromate. Meersmans, et al. [327] recommend calibrating the WB method for different soils and land use. Any use of a multiplier in the three 1995 Tasmania reports, was not reported, and the same colorimeter absorbance vs carbon curve may’ve been used for all samples, thus rendering them quite imprecise for spatial carbon accounting.

Another increase in uncertainty occurs when the soil bulk density is either not calculated or not reported, in a method appropriate for soil carbon accounting. The three 1995 Tasmania reports that McIntosh, et al. [302] suggested should be points of reference, provided the concentration of carbon in the soil as wt% from the fine, sieved soil, but the reported bulk density was the weight of the whole sample, including stones and roots, divided by the volume of the entire sample [306] . To use such data for spatial SOC calculations requires recalculating the density of the fine soil fraction using any reported stone and root volumes and weights. However, the volume of stone and roots was reported within wide ranges for the different horizons in the soil types in the area, and not precisely for the specific sample from which carbon or bulk density were measured. For soil carbon accounting it is necessary to subtract from the weight and volume of the soil core, the weight and volumes (in quantitative terms for each sample) of any material in the core that isn’t measured as part of the fine soil [333–335] . If the carbon in any of those components was derived from the forest biomass then it can be included later in the carbon accounting. Preferably, the bulk density and carbon concentration should be determined from the same sample [336] . Therefore, in those three 1995 Tasmanian reports, the volume and weight of soil within each sample volume could only be determined semi-quantitatively, and consequently with substantial error margins.

To illustrate the error margins introduced by that earlier methodology, a few examples from the three 1995 Tasmanian reports will be processed here. The amount of roots was given as, for example, ‘many medium roots’ in an A1 and a B1 horizon, ‘abundant fine roots’ in an A1 horizon and ‘common coarse roots’ in a B2t horizon. The stone content of the soil was given in more quantitative terms; for example: 2–10% granite (20-60 mm fragments) and 10–20% granite (60-200mm fragments) in a B1 horizon, 0–<2% basalt in an A1 horizon, and 20–50% sandstone in a B2 horizon. If one assumes the average densities for such rock types [337] , and assumes that the bulk density was measured with the average amount of stone volume for a particular horizon (e.g., 35% sandstone for a horizon with 20–50% sandstone by volume) then the measured bulk density can be adjusted to give an effective one. However, insufficient detail was provided for a quantitative adjustment for the root volume.

By thus accounting for stone volume, the total soil carbon for four example soil types ‘Cuckoo’, ‘Kapai’, ‘Stronach’ and ‘Maweena’ which host wet-eucalypt forests, in Grant, et al. [303] reduces from 402, 344, 305, and 331 Mg ha^-1 respectively (to the measured depths of 1.2, 1, 1.2 and 0.96 m respectively) to 180, 244, 297, and 112 Mg ha^-1 respectively. I.e., reductions of between 2 and 66 %. Due to imprecision in stone content alone, the error margin for total SOC after adjusting for stone content, is up to ~±18%. It would be higher if including error margins in the rock densities, and if the root volumes were quantified in a similar style.

4.4.4. Comparing Carbon Stocks across Climates and Time Periods

In Australian forests, and indeed globally, SOC generally increases with rainfall (assuming other factors being equal) [338–340] . The largest concentration of Tasmanian rainforests is in the west and northwest of Tasmania, which is a higher rainfall zone (on average) than where the tall-open forests in Tasmania are [301,341] . Therefore, Tasmanian rainforest could be expected, on average, to have higher SOC values than the tall-open forest. The GIS analysis in Dean and Wardell-Johnson [301] , based on national SOC and rainfall layers, and a Tasmania vegetation layer, shows this to be the case: 2218 and 1559 mm yr^-1 and 369 and 271 Mg ha^-1, respectively for rainforest and tall-open forest. Likewise, the fraction of Tasmanian rainforest in close vicinity to tall-open forest in Tasmania is expected to have lower SOC than the average rainforest. That close proximity, lower-rainfall location (average 1241 mm yr^-1) is where McIntosh, et al. [302] measured SOC in the two forest types, and found an average value of 102 Mg ha^-1 to -0.3 m depth for rainforest. When critiquing Dean and Wardell-Johnson [301] and comparing the two values for rainforest SOC, McIntosh, et al. [302] appeared to not take into account the difference in climate, and wrote:

‘…the unreferenced 369 Mg.ha^-1 of C at 0–30 cm depth quoted by Dean and Wardell-Johnson ( [27] , Table 1 ) for rainforest soils in Tasmania is over three times too high…’.

Many of the western Tasmanian rainforest soils in western Tasmania [which is where rainforests are concentrated] are organosols, with an average SOC of 450 Mg ha^-1 to 0.47 m depth [342] . Assuming equal SOC distribution over that depth gives 287 Mg ha^-1 to 0.3 m. Or alternatively, application of a simple exponential falloff with depth (Equation 2 above), gives 311 Mg ha^-1 to 0.3 m depth. If the soil profiles and bedrock allowed SOC to venture much deeper than 0.3 m, then extrapolating to the full profile gives SOC as 1200 Mg ha^-1. The value of 369 Mg ha^-1 in Dean and Wardell-Johnson [301] is 19% higher than the value of 311 Mg ha^-1 found empirically by di Folco and Kirkpatrick [342] . Such a difference is reasonable, considering that the GIS data used was a nation-wide layer.

As described above, the mixed-forest and rainforest each have their own ideal geographical ranges, with some spatial overlap if fire history permits. On pedogenesis timescales, rainforest sites in close proximity to mixed-forest sites, are possibly often occupied by mixed-forest, and vice-versa. The overlap, in the absence of logging, ebbs and flows with the vagaries of fire [119] . There was still decomposing eucalypt debris in several of the rainforest plots studied by McIntosh, et al. [302] and some contained live eucalypts:

‘While rainforest sites contained negligible quantities of live eucalypt boles (small eucalypts were encountered in just 3 rainforest sites), they contained significant quantities of eucalypt CWD ( Table 2 ). Eucalypts contributed 27% of total CWD volume and 29% of total CWD C-mass in rainforests.’ [201] ,

Thus, considering the timescales involved for change in SOC compared with those for biomass change, as described above, the experiment in McIntosh, et al. [302] was not really designed for their stated objective of differentiating between the SOC in mixed-forest and in rainforest. Moreover, these timescales may mean that such a differentiation in SOC of the ecotone region does not exist; it may only exist in the regions where rainforest and tall-open forest do not swap locations over time, and this would match with the data to-date, in the reports discussed above.

The blurred spatio-temporal boundary between mixed-forest and rainforest is in part because coarse woody debris and especially soil carbon, representative of either forest type, persists to a degree depending on its half-life. This material constitutes ‘legacy carbon’ [343,344] ( Figure 12 ). Empirical studies attempting to contrast SOC stocks in rainforest and mixed-forest in close proximity, will thus be unproductive until the transition between the two is almost complete for all forest attributes, include soil.

Figure 12. Fallen E. regnans logs spanning Cliff Creek, Styx Valley, Tasmania. The creek is centred in a 200 m wide gully mapped as API-type rainforest. The logs are remnants of previous mixed-forest. This contrast typifies the blurred spatio-temporal boundary between mixed-forest and rainforest, being in-between from a carbon dynamics perspective. The gully is not rainforest from a carbon perspective, even though living eucalyptus trees are absent.

Figure 12. Fallen E. regnans logs spanning Cliff Creek, Styx Valley, Tasmania. The creek is centred in a 200 m wide gully mapped as API-type rainforest. The logs are remnants of previous mixed-forest. This contrast typifies the blurred spatio-temporal boundary between mixed-forest and rainforest, being in-between from a carbon dynamics perspective. The gully is not rainforest from a carbon perspective, even though living eucalyptus trees are absent.

When rainforest and mixed-forest are in close proximity, and may interchange location over time, then it is appropriate to consider the effect on differences in biomass, rather than on SOC. For the purposes of carbon accounting for climate change effects, this should be considered over long time periods, to get the overall impact. A long-term, time-based average carbon stock, has equivalences to a landscape-level average at one point in time, if numerous instances of forests of different ages are present across the landscape. Here the claim by Moroni, et al. [201] that net carbon will decrease and stay that way if mixed-forest is not logged but allowed to mature and go through succession to pure rainforest is re-examined, but over a long enough time period to get representative, time-averaged carbon stock:

‘As Tasmania’s wet forests transition from mixed forest to rainforest they can be expected to lose more than half their total (live + dead, standing + downed) bole wood volume and biomass as smaller dimension rainforest trees replaced the larger eucalypts. … Certainly, setting aside Tasmanian wet eucalypt forest to store C will not deliver the usual long term C accumulation benefits common to forests elsewhere and maximizing landscape level C-stocks is likely to require periodic disturbance to maintain the C-dense eucalypts in the landscape.’ [201]

The ’periodic disturbance’ in that extract most likely implies fire and/or logging. Prior to industrialisation and without Aboriginal burning (though burning on the far east coast may have trickled effects across to the centre of the island), mixed-forests occupied large areas in Tasmania (such as in the logging concession areas) and therefore they do not need logging to exist. The Primary mixed-forest has been the foundation of export-scale commercial forestry in Tasmania for nearly a century because of its eucalypt content. Whereas extraction reconnaissance projects for rainforest areas, such as in northwest Tasmania, have found logging to be either uncommercial or to require low extraction fractions to maintain forest health [[345-347,348], p37-38]. Thus there are at least two possible reasons for the controversy over benefits of the two alternative forest types. Prior to industrialisation in the area of the logging concessions, there were sufficient periodic disturbances of perhaps once every several hundred years in the form of wildfire, e.g., 450 to 500 years [349,350] to maintain a dominance of mixed-forest. Higher-frequency disturbance at such intensity is not necessary.

More fire is inevitable in the future with anthropogenic climate change [351,352] , so the chances of succession to rainforest, or maintenance of rainforest, are less likely than normal. Rainforest attrition is forecast with climate change [353] , which will put neighbouring mixed-forests in Tasmania at risk (rather than the risk coming from replacement by rainforest). Rainforest species in mixed-forest have an intrinsic benefit in the face of climate change: they protect carbon in the wider landscape from fire [354] . CBS logging can create poor regeneration of the rainforest species and create stands more favourable to pulpwood than sawlog production (i.e., shorter wood-product half-life and therefore add to climate change) [355–357] . As the seed source for the rainforest understory becomes restricted spatially with fragmentation of mixed-forest [357] , further logging will make it more-difficult to regain primary-forest carbon levels, which will also contribute to climate change. The importance of primary forests in climate change policy has been re-iterated, with policy initiatives broached for their conservation [358] . Limiting forest fragmentation and general anthropogenic disturbance is likely to help maintain existing mesic micro-environments that protect against drying-out under climate change and thus against fire. At least 50% of rural fires in Australia are of anthropogenic origin [e.g., [359,360] ]. Eliminating that ignition source and managing combustible material near infrastructure, such as roadside grassland and farmland [361] , would help reduce forest carbon losses under climate change.

The difference in biomass accompanying the succession from mixed-forest to rainforest matches the typical case for forest succession, where the pioneer (coloniser) species is fast growing and has appreciable initial biomass [362,363] . Whereas Moroni, et al. [201] call it ‘unusual ecology’. In mixed-forest the coloniser species are eucalypts, e.g., Eucalyptus regnans. The issue of decline in biomass with forest succession was covered numerically and graphically in Dean, et al. [235] , and it was mentioned that landscape-level carbon stocks in biomass can decline if: ‘the understorey, which dominates the later stages of succession, has a lesser biomass than the maximum for the E. regnans dominated forest’.

To illustrate possible dynamics of carbon in biomass of rainforest succession and to compare it against logging, two simulations were run using CAR4D ( Figure 13 ), with two levels of understorey biomass: one very low and one higher but still only at around 20% of total stand biomass at the time of logging. Rainforest understorey can contribute 50% of total biomass prior to onset of substantial eucalypt senescence in mixed-forest [364] . Due to the low precision of understorey allometrics, no definitive quantitative result is shown in Figure 12 , but even when including wood-products, it is not necessarily the case that harvesting cycles store more carbon than long-term rainforest.

McIntosh, et al. [302] measured and compared standing biomass in the two forest types. They had a mixed-forest:rainforest biomass ratio of 1:0.45. The two scenarios in Figure 13 have ratios of 1:0.48 and 1:0.72. The first of those is close to that of McIntosh, et al. [302] . In both cases, the long-term rainforest average total carbon does not go below the long-term logging average carbon (where the carbon is summed across biomass and wood products). That is because rainforest total carbon doesn’t oscillate as much as that of a logged forest. The magnitudes in the frequent oscillations must be averaged over time, with an average that is lower than the peaks, which most likely correspond to the point at which they would be logged.

The long-term average C in biomass in rainforest can exceed the long-term eucalypt logging-cycle carbon (including wood-products) if it is a third or more of the biomass of mature wet-eucalypt primary forest ( Figure 13 .a). The C in biomass of rainforest understorey only needs to be about 15% of the C in biomass of primary mixed-forest at the time of logging, if the two forest types are to be equivalent in terms of C. However, it needs to be at least 20%, if upon succession it is to exceed the mixed-forest carbon ( Figure 13 .b). If comparing the long-term carbon stocks of pure rainforest and mixed-forest, then the long-term rainforest carbon only needs to be more than half of peak mixed-forest carbon at the time of logging of primary mixed-forest, if it is to substantially exceed long-term mixed-forest carbon ( Figure 13 .b).This is due to the more-frequent low carbon periods in mixed-forest than in rainforest. Note that this 50% requirement is very different to the 100% requirement implied in McIntosh, et al. [302] and Moroni, et al. [201] . Considering the error margins involved in modelling the carbon stocks of the two forest types and wood products, although Figure 13 .b shows rainforest carbon exceeding logged mixed-forest carbon, in the long-term, it’s likely that it is not definitive at this stage: more accurate and precise data are needed.

Rather than considering the rainforest understorey biomass within mixed-forest as a representation of what the pure rainforest will be like after succession, there’s an additional possible change upon succession that will increase rainforest biomass. Gilbert [55] noted that rainforest biomass is slightly smaller in mixed-forest than in pure rainforest but added that it was difficult to find sites of equivalent productivity, from which a significant comparison could be made. Notably though, paired mixed-forest/rainforest sites in northwest Tasmania were found to have higher rainforest wood volumes in the rainforest members [365] . Thus, some of the eucalypt biomass may be replaced by rainforest biomass upon succession, which would make rainforest have a slightly higher advantage than indicated in Figure 13 . Though another explanation for this increase in biomass for pure rainforest is that it could usually occupy higher site-index (more productive) sites than does mixed-forest.

Figure 13. Simulated aboveground carbon stocks of forest succession and logging scenarios including wood products, typical of Site-1 in Dean, et al. [47], for primary-forest and harvesting cycles (modelled using CAR4D). Important for comparisons: time-based averages of total carbon (including wood products)— dashed horizontal lines. (Solid curve=total carbon in biomass plus wood products; dashed green curve=understorey biomass; dotted red curve=E. regnans biomass, purple solid horizontal lines= total carbon stock at time of logging.) The rainforest understorey filled space between senescing eucalypts which succeeded to rainforest; afterwards intense wildfire with seeding from nearby E. regnans. New mixed-forest grows to age 320 years, then logged (parameters as in Dean, et al. [47]). Rainforest biomass was set to a maximum of ~1/3 (a) and ~1/2 (b) of peak of the mixed-forest— corresponding to 15% and 22% (respectively) of stand-level biomass at time of primary-forest logging. In (a) long-term rainforest biomass= ~half that of the time-averaged mixed-forest biomass and equal to that of the harvest cycles (including wood-products). In (b) long-term rainforest biomass= ~time-averaged mixed-forest biomass and greater than that of the harvesting cycles (including wood-products).

Figure 13. Simulated aboveground carbon stocks of forest succession and logging scenarios including wood products, typical of Site-1 in Dean, et al. [47], for primary-forest and harvesting cycles (modelled using CAR4D). Important for comparisons: time-based averages of total carbon (including wood products)— dashed horizontal lines. (Solid curve=total carbon in biomass plus wood products; dashed green curve=understorey biomass; dotted red curve=E. regnans biomass, purple solid horizontal lines= total carbon stock at time of logging.) The rainforest understorey filled space between senescing eucalypts which succeeded to rainforest; afterwards intense wildfire with seeding from nearby E. regnans. New mixed-forest grows to age 320 years, then logged (parameters as in Dean, et al. [47]). Rainforest biomass was set to a maximum of ~1/3 (a) and ~1/2 (b) of peak of the mixed-forest— corresponding to 15% and 22% (respectively) of stand-level biomass at time of primary-forest logging. In (a) long-term rainforest biomass= ~half that of the time-averaged mixed-forest biomass and equal to that of the harvest cycles (including wood-products). In (b) long-term rainforest biomass= ~time-averaged mixed-forest biomass and greater than that of the harvesting cycles (including wood-products).

5. Sustainability Interpretation for Corporate Forestry

Table 1. Ratios of areas of different species relative to those in height category E1. Based on data in ANM [52]. Each species was normalised with respect to E1 separately and for parts 1.a and 1.b separately. (a) Oldgrowth as of 1976, and (b) oldgrowth logging from 1953–1976. Comparing 1.a and 1.b shows that the taller height categories were preferentially logged.

5.1. Applying a Missing Baseline

When developing and publishing the results of carbon accounting models, the system boundaries for material flow must be acknowledged, without which unfactored emissions or double accounting may occur [4,401] . This lack of clarity may lead to knowledge gaps and publication of erroneous information [4] . A baseline (reference point, a benchmark) of 0 Mg ha^-1 for carbon stock (i.e., omitting legacy carbon such as soil carbon and logging residue— a blank slate) is often portrayed in carbon-oriented promotional material for forestry [e.g., [402] , Figure 10 ]. In Figure 14 .a promotional material from Forest & Wood Products Australia (a forestry representative body) is shown with a baseline of 0 Mg ha^-1, i.e., as though forestry management starts on a blank slate. In this review paper, the process was simulated using CAR4D. Parameters in CAR4D were generously set to a logging-cycle length of 90 years and with wood-product half-lives of 80 years for sawlog and 4 years for pulpwood. These half-lives include those of mill residues, some of which are routinely incinerated within a year of logging. Also, these longer half-lives are a proxy for some of the wood-products contributing to SOC in landfill, while noting that the methane produced there (which has a higher global warming potential than CO₂) may counterbalance the longevity of that pool [ [403,404] , p98-102]. Emissions from local and international freighting of the wood-products, and thinning between full harvests, were omitted from the simulations. The same simulation was run again but with the benchmark being the original primary forest biomass and SOC instead of starting with them at 0 Mg ha^-1 ( Figure 14 .c and Fig 14.b respectively). The largest difference in results between the two simulations is due to the neglect of the legacy SOC of the primary forest, in the corporate forestry version. The overall trend in carbon stock was down instead of up, when the legacy carbon was included. A zero or unnaturally low baseline for forest SOC is also used in some scientific calculations for assessment of forest bioenergy climate change effects, though it is often disclosed as such [e.g., [405,406] ]. Ignoring the legacy SOC would be more appropriate for plantation establishment on long-cleared land or in some of the forests in Europe considered by [407] , where logging has occurred for many centuries, but not for primary forest conversion to logging cycles. Therefore, the promotional material with a benchmark of 0 Mg ha^-1 could be an example of generic marketing.

The numerical output from CAR4D for the simulations showed that for recovery of total carbon stock to that of the time-averaged, original primary-forest, then wood-product half-lives would have to be increased to 400 and 20 years for sawlog and pulpwood respectively, including for mill residues. It would be difficult to achieve such half-lives. But if they could be achieved, then the recovery would take ~1260 years. During that time, the drop in SOC would be counterbalanced by carbon in the wood products. Meanwhile however, emissions due to the steadily decreasing SOC would contribute to climate change and consequently also to climate-change positive feedback [globally].

Similarly, life-cycle-analyses (LCA) that claim emission offsets for burning wood waste [from logging, i.e., ‘forest residue’ or ‘mill residue’] for energy require accounting of the C balance of logging, and comparison with other energy sources such as hydroelectricity, wind and solar power. Comparable system boundaries in the LCA must be used for any comparison with substitutable materials [408] . The emissions in processing and delivering the wood-product must be considered [409] , just as they are in determining the C-footprint of other industrial products. LCA will include: diesel usage during logging, in haulage [e.g., [410] ] and in international freighting; mill energy usage for virgin- and recycled-products; and NOx emissions. Such additional emissions could be high in the current market situation, as wood-product movement occurs from Tasmania to Japan, then to China and other countries, and then sometimes back to China for recycling [411] , though that latter move has been limited by some countries in recent years.

Figure 14. (a) Pamphlet advertisement by Forest & Wood Products Australia, using graph from Ximenes, et al. [[402] Figure 10] and not from DAFF & BRS as stated in the advertisement— emphasises the temporarily increasing wood-product pool— giving the illusion of increases ad infinitum. It ignores the primary forest legacy carbon. (b) and (c): output from CAR4D for Site-1 in Dean, et al. [47], drawn in ‘stacked-area’ format: (b) ignoring the primary forest carbon (i.e., zero baseline), and (c) not ignoring primary forest carbon. Style (b) would be more appropriate to use for plantations on long-cleared land or where logging has occurred for several centuries, but not for the LUC of primary forest conversion to logging cycles.

Figure 14. (a) Pamphlet advertisement by Forest & Wood Products Australia, using graph from Ximenes, et al. [[402] Figure 10] and not from DAFF & BRS as stated in the advertisement— emphasises the temporarily increasing wood-product pool— giving the illusion of increases ad infinitum. It ignores the primary forest legacy carbon. (b) and (c): output from CAR4D for Site-1 in Dean, et al. [47], drawn in ‘stacked-area’ format: (b) ignoring the primary forest carbon (i.e., zero baseline), and (c) not ignoring primary forest carbon. Style (b) would be more appropriate to use for plantations on long-cleared land or where logging has occurred for several centuries, but not for the LUC of primary forest conversion to logging cycles.

Forestry is not the only land use where legacy SOC from the previous forest makes a large difference to a carbon footprint. A major difference was found when accounting for legacy SOC when previously forested land was used for grain crops [412] . Those authors considered that inclusion to aid realism, though requiring more work and providing location-dependent outcomes for the land managers. That difference coincides with considering where along the time axis in Figure 9 , a particular logging cycle may be; giving a different future drop in SOC depending on when the accounting begins.

5.3. Terminology Hinging on Sustainability

A subtle forestry industry public relations tool is renaming activities to give the indication of more-sustainable operations, such as calling the burning of waste from timber-mills ‘re-use’ or ‘recycling’ [e.g., [415] ]. Other popular name changes are to label forests simply as biomass; the felled or still-standing timber that is not hauled out, as ‘residue’; coarse woody-debris and dead hollow trees as ‘fuel’; and the word ‘harvesting’ in place of ‘logging’ for primary forests ( Figure 15 ) [416] . The original meaning of harvest was to collect from a crop that one has sown. This renaming occurs elsewhere in society too, such as harvesting rainwater and wild seaweed, but rarely to fossil fuels. The change over time can be seen in the journal Australian Forestry, published by Taylor & Francis. Early on ‘harvesting’ was used only for plantations, which matched with its dictionary definition ( Figure 15 ). One of the first uses of it for primary forests was in the pulp and paper industry c1960, during the controversy over whether or not to leave Melbourne’s water catchment as primary forest, and the resolution was for more investment in a public relations campaign, in research, and in logging [417–419] . The number of articles in Australian Forestry including the words ‘logging’ and ‘harvesting’ has grown over time ( Figure 15 ), indicating more attention to that part of resource extraction but the growth rate for the use of the word ‘harvesting’ has nearly doubled that for ‘logging’ (0.79(0.05) and 0.34(0.06) respectively; standard errors in brackets). The two growth rates are significantly different: the probability of them being the same is P= 3.6x10^-8, in a Student’s t-test distribution. Their usage within a scientific paper is not mutually exclusive however, for example there are still logging roads and log trucks, not harvesting roads and harvest trucks, but, for example, selective-logging is now often termed selective-harvesting, in primary forests.

The terminology towards sustainability has been more embellished, where it is often claimed that wood-products sequester carbon (and therefore logging helps prevent climate change) [420–426] . Whereas as the carbon sequestration, from gas to solid, was actually performed by the trees.

Figure 8. Change in use of the words ‘logging’ and ‘harvesting’ from 1936 to 2022, in the journal Australian Forestry. Data were obtained by using the search function on the journal home page and GoogleScholar©. The word ‘harvesting’ has increased ~twice as much as the word ‘logging’, since the journal started in 1936. Initially ‘harvesting’ was exclusively for plantations, then it was increasingly for logging primary forests.

Figure 8. Change in use of the words ‘logging’ and ‘harvesting’ from 1936 to 2022, in the journal Australian Forestry. Data were obtained by using the search function on the journal home page and GoogleScholar©. The word ‘harvesting’ has increased ~twice as much as the word ‘logging’, since the journal started in 1936. Initially ‘harvesting’ was exclusively for plantations, then it was increasingly for logging primary forests.

6. Benchmarks for Conservation Directives

6.1. Measurement of Carbon Stocks by Using Proxies

Studying the sums or changes in the carbon stocks of Tasmanian forests, has only occurred during the last forty years, roughly, and sometimes as a biproduct of a different investigation [e.g., [368] ]. Therefore, actual carbon data are scarce. Different attributes of nature pique scientific interest at different times, depending on society’s needs, such as for resource extraction, atmospheric amelioration (as currently for climate change mitigation), drinking water runoff, or interest in a specific animal species. But for whatever forest attribute is in vogue, there are usually other data that can be transformed or used as a proxy. For example Johnson [530] noted that data on the change in soil carbon with forest management was often in reports that focussed on other nutrients. For carbon in trees, a long-standing proxy for carbon is merchantable timber volume, to which a ‘biomass expansion factor’ (BEF) is applied to include the carbon in the unmerchantable, aboveground parts of a tree [531] . This method misses some carbon in other parts of the forest stand however, if some species felled during logging contribute to forest biomass but are unmerchantable (such as some rainforest species amongst eucalyptus species), or if their merchantability varies with market demand. It also has a high error margin unless the BEF is tailored to each stand, which is rarely done.

In their carbon account of Tasmanian wet-sclerophyll forests, Moroni and Lewis [532] used a biomass expansion factor of 1.46, and added soil carbon values from similar soils elsewhere. That BEF value came from Snowdon, et al. [533] , where it was derived by reassessment of earlier reported data for Australian native forests in general [e.g., [534] ]. Many of the allometric ratios presented in the review by Grierson et al. [534] were based on the whole of the stem and not just on the merchantable portion, so the BEFs should be higher than theirs if based on the merchantable part only. To account for that difference, in their assessment of the C stock for the whole of State forest in Tasmania, MBAC [535] multiplied by an expansion factor of 1.25, to represent the wood in the entire stem, before applying the 1.46 expansion factor to get to the whole of the aboveground mass of the tree, and then a third expansion factor of 1.29 to account for unlogged trees in the forest stand. However, most of the data in reports such as Grierson et al. [534] , were from quite young trees, e.g., less than 100 years old and so the BEFs for mature forests should be lower [536] . This is because relatively more biomass is in the trunk for mature forest trees and therefore more of the total is merchantable (unless senescence is well established). Consequently, Snowdon et al. [533] used a lower limit of 25 years for their data collation for BEF. Possibly these two biases of whole-stem and mature-age cancel out to some degree. The average BEF given in Grierson et al. [534] for the most common eucalyptus species in the tall wet-sclerophyll forests of Tasmania, namely E. regnans, E. obliqua and E. delegatensis, was 1.32 but the average age was only 43 years. Limiting this to stands older than 24 years gives an average BEF of 1.28 (and the average age of those trees as 61 years), but that is based on entire stem volume and not just the merchantable part of the stem. This is lower than the 1.46 used in Moroni and Lewis [532] , but there’s insufficient information to give a definitive adjustment to it. For tall-open eucalyptus forests, in the Farm Forestry Toolbox, a computer program designed for tree growers and merchants in Tasmania [537] , for expanding from whole stem biomass to aboveground biomass, the default BEF is 1.313. Alternatively, based on weights from destructive sampling of small, Tasmanian E. obliqua (average DBH of 0.683 m for 44 trees) Ximenes, et al. [ [538] Table 4 & Table 10 ] reported data yielding BEFs of 1.43 and 1.58, depending on the merchantability of stem wood in the crown for pulpwood. They also showed that in that particular stand, the BEF might increase for larger trees. BEFs can range from 1.25 for a high-quality stand with sawlog and pulpwood extraction to 5.0 for a low-quality stand with sawlog usage only [ [533] , p xiv]. Therefore, the value of 1.46 might be sufficiently conservative and appropriate to use for average, larger trees. In general however, the use of BEFs will introduce large error margins for carbon accounting unless empirically derived for a particular forest stand, as in Ximenes et al. [538] . Even for different species within a stand, the BEF can vary significantly [539] .

An early eucalypt sawlog inventory (1922) for tall forests in Tasmania measures 32 transects covering 124 ha of the Florentine Valley [540] . But that dataset is difficult to compare with more-contemporary surveys as the BEFs cannot be estimated without knowing the historical merchantability criteria for eucalyptus sawlogs. The more-contemporary BEF that was applied by Moroni and Lewis [532] , caters for both sawlog and pulpwood being extracted.

After that 1920s sawlog inventory, in the pulpwood era records were kept by Australian Newsprint Mills during logging of the Styx/Florentine pulpwood concession [541] . In the midst of that activity, a detailed inventory of small plots in the Styx, Florentine and Tyenna valleys, in terms of tree species, sizes and ages, was undertaken to show related forest types on sites of different productivity and in different stages of ecological succession from mixed-forest to rainforest [55] . In that exposition there were three plots of mixed-forest and two of rainforest. Those data included girths of trees and were therefore amenable to carbon inventory, because allometric equations based on DBH can be applied, without relying on an expansion factor. The highest biomass representatives were selected from each of the two main forest types, to provide a comparison with total C found in Sanger and Ferrari [529] [where it was claimed they had the highest carbon reported in Tasmania], and to provide another datum for the mixed-forest vs. rainforest comparison (detailed above). The mixed-forest stand was 0.149 ha by Road 10 in the Florentine Valley and dominated by even-aged E. regnans, older than 300 years. The rainforest was ‘transect A’, 0.116 ha by Road 7 in the Florentine Valley and some of its trees were older than 500 years. A range of allometric equations was tested to see what difference they made to the totals ( Table 2 ). The largest rainforest trees in the two stands were assigned 25% senescence, regardless of whether or not the allometric equations already had senescence incorporated (to ensure conservative carbon stocks). To get 20% and 15% senescence in the eucalypts, the stand age in Eq. 8 of Dean, et al. [307] was set at 317.49 years and then 299.575 years, respectively. In the final comparison with Sanger and Ferrari [529] , the eucalypts were assigned 15% senescence, because although there was no crown loss, the crowns were ‘stag headed’, which indicated some demise compared with being in their prime. Although not stated in Gilbert [55] , his description suggests the API phototype for the mixed-forest plot would be E1c.M+, and that the rainforest plot was M+.

Table 2. Carbon stocks (Mg ha^-1) to 4 significant figures, of live biomass [including roots, root/shoot ratio= 0.15]. Based on data in Gilbert [55] for: (a) mixed-forest by Road 10, Florentine Valley; and (b) rainforest tree species in the same mixed-forest on the first row, and on the second row: rainforest by Road 7, Florentine Valley. Different allometric equations for understorey go from left to right across the table: ‘und’ in (a) and (b); and go from top to bottom down the table for Eucalyptus regnans: ‘Er’ in (a). Allometric equations were sought from the following publications: ‘D2020’= Dean, et al. [92] with the root C corrected as mentioned in the main text, Eq. 7; ‘D2003/2006’= Dean, et al. [307] or Dean and Roxburgh [88] which are equal to within 4 significant figures for this forest stand; ‘D2003’= Dean, et al. [307]; ‘D2011’= Dean, et al. [542] with half of the sums corresponding to incorrectly adjusted general rainforest tree equation in Keith, et al. [124] to get temperate rainforest trees (my error, not theirs); ‘D2011 corr.’= Dean, et al. [542] corrected; ‘K2000 temperate’= temperate rainforest from Keith, et al. [124]; ‘K2000 general’= general rainforest from Keith, et al. [124]; ‘new_{rainforest_C}’= new rainforest allometric equation introduced in this text (Eq. 11).

Table 2. Carbon stocks (Mg ha^-1) to 4 significant figures, of live biomass [including roots, root/shoot ratio= 0.15]. Based on data in Gilbert [55] for: (a) mixed-forest by Road 10, Florentine Valley; and (b) rainforest tree species in the same mixed-forest on the first row, and on the second row: rainforest by Road 7, Florentine Valley. Different allometric equations for understorey go from left to right across the table: ‘und’ in (a) and (b); and go from top to bottom down the table for Eucalyptus regnans: ‘Er’ in (a). Allometric equations were sought from the following publications: ‘D2020’= Dean, et al. [92] with the root C corrected as mentioned in the main text, Eq. 7; ‘D2003/2006’= Dean, et al. [307] or Dean and Roxburgh [88] which are equal to within 4 significant figures for this forest stand; ‘D2003’= Dean, et al. [307]; ‘D2011’= Dean, et al. [542] with half of the sums corresponding to incorrectly adjusted general rainforest tree equation in Keith, et al. [124] to get temperate rainforest trees (my error, not theirs); ‘D2011 corr.’= Dean, et al. [542] corrected; ‘K2000 temperate’= temperate rainforest from Keith, et al. [124]; ‘K2000 general’= general rainforest from Keith, et al. [124]; ‘new_{rainforest_C}’= new rainforest allometric equation introduced in this text (Eq. 11).

The different allometric equations used to produce Table 2 are explained in the next section. The root/shoot ratio used was 0.15, throughout, as Gilbert [55] noted that the trees were mature.

6.2. Suitable Allometric Equations for Carbon in Tree Biomass

Root mass is rarely measured directly, as it is usually more difficult for people to measure things below-ground than aboveground, similar to the difficulty with measuring higher up a tree (section 5.3). Consequently, tallying carbon often relies on assumed root:shoot ratios. For a given environment, as a tree matures, this ratio usually decreases. Throughout many carbon assessments in Tasmania a root:shoot ratio of 0.25:1 has been assumed, though the lower one of 0.15:1 was modelled for mature trees [307] , and the even lower one of 0.136:1 is the default for tall-open eucalyptus forests in the Farm Forestry Toolbox [537] . The value of 0.15:1 is an average of relevant literature values [67] . In tall-open forest, through a complex empirical and modelling process for one individual mature understorey tree a root:shoot ratio of 0.18 (±0.05):1 was found [67] . The data ranges suggest that in mixed-forests, 0.15:1 could be a suitable root:shoot ratio for both mature eucalypts and understorey rainforest trees. Therefore, it has been adopted in this report and, for the purposes of comparing carbon stocks, we convert other people’s reported values to that figure, where possible.

The allometric equations for Eucalyptus regnans, from Dean, et al. [307] and Dean and Roxburgh [88] , only produced a difference in stand-level C stocks for living biomass at the 5th significant figure, (e.g., 1201.2 and 1201.4 respectively, for the 15% eucalypt senescence scenarios with the new rainforest equation, Eq. 11) and therefore they were combined into one row in the table. The equation for Eucalyptus regnans in Dean, et al. [92] was specific to their study site in that the upper limit was in terms of the maximum live tree size observed and its degree of senescence. However, in production of that equation I had made the mistake of multiplying the root biomass twice by 0.47 instead of once, to get carbon. Therefore, the carbon stock reported in Dean, et al. [92] was a little lower than it should have been, and it requires the following multiplier before use:

(1 + 0.15) ÷ (1 + (0.47 × 0.15)) = 1.07426436

(5)

and the corrected allometric equation in full becomes:

$$Eregnan{s}_C=1.07428436\times 3.394142{DBH}^2\left\{1/\left[1+\mathrm{e}\mathrm{x}\mathrm{p}\left(5.081129DBH-27.68206\right)\right]\right\}$$

(6)

$$=3.646206{DBH}^2\left\{1/\left[1+\mathrm{e}\mathrm{x}\mathrm{p}\left(5.081129DBH-27.68206\right)\right]\right\}$$

(7)

where Eregnans__C is mass of carbon for the whole tree in Mg and DBH is in m.

The allometric equations for Eucalyptus regnans in Dean, et al. [307] and Dean and Roxburgh [88] differ only for stem volume, with more data being used to derive the equation in the newer report. The older equation [307] is:

$$V=Vol\_max\times \left(1-\left\{1/\left[1+{\left({\displaystyle \raisebox{1ex}{$DBH+0.01$}\!\left/ \!\raisebox{-1ex}{$DBH\_mid$}\right.}\right)}^k\right]\right\}\right)$$

(8)

where Vol_max= 380 m³, DBH_mid= 4.3 m, k= 2.57, V is the stem volume in m³ and DBH is in m, and the newer one [88] is :

$$V=Vol\_max\times \left(1-\left\{1/\left[1+{\left({\displaystyle \raisebox{1ex}{$DBH$}\!\left/ \!\raisebox{-1ex}{$9.2$}\right.}\right)}^2\right]\right\}\right)$$

(9)

where Vol_max= 1100 m³, V is the stem volume in m³ and DBH is in m. In both cases the equations for the other tree components and a user-adjustable senescence in the form of a two-parameter sigmoid function, are given in Dean, et al. [307] , with the influence of growth parameters for different sites explained in Dean, et al. [235] .

Figure 9. Comparison of different eucalyptus allometric equations, shown at two scales, from (a) larger to (b) smaller trees. For the equations that didn’t include root mass, it was added with a root:shoot ratio of 0.15:1. Equations’ species and references: ‘Ed 2011’= Eucalyptus delegatensis [542] but with the root portion corrected, as described in the main text; ‘Eo K2000 temperature’= E. obliqua [124]; ‘Eo W2021’= E. obliqua [543]; ‘Er D2003’= E. regnans [307], with m= 400 years and k= -6; ‘Er S2015’= E. regnans [77]; ‘Er X2018’= E. regnans [544]; ‘Er D2020’= E. regnans [92] with the root C corrected as mentioned in the main text, Eq. 7; ‘Er mid= 600, k= -6’= E. regnans [88] with an older-age but faster senescence than for Er D2003, to show flexibility of that equation.

Figure 9. Comparison of different eucalyptus allometric equations, shown at two scales, from (a) larger to (b) smaller trees. For the equations that didn’t include root mass, it was added with a root:shoot ratio of 0.15:1. Equations’ species and references: ‘Ed 2011’= Eucalyptus delegatensis [542] but with the root portion corrected, as described in the main text; ‘Eo K2000 temperature’= E. obliqua [124]; ‘Eo W2021’= E. obliqua [543]; ‘Er D2003’= E. regnans [307], with m= 400 years and k= -6; ‘Er S2015’= E. regnans [77]; ‘Er X2018’= E. regnans [544]; ‘Er D2020’= E. regnans [92] with the root C corrected as mentioned in the main text, Eq. 7; ‘Er mid= 600, k= -6’= E. regnans [88] with an older-age but faster senescence than for Er D2003, to show flexibility of that equation.

In Figure 9 it can be seen that the two allometric equations for E. obliqua diverge more sharply than do the other equations. The higher one, Eo K2000, was the average from four different environments. The highest biomass stand of those four was from an atypical poorer site [124] , but noted as having much less disturbance than the other three stands: it made the average allometric trend to higher values. The lower curve for E. obliqua in Figure 9 , [543] , was from one site with a history of relatively frequent fire [350] , being in the Huon district, in southern Tasmania, which had a longer history of agriculture, logging and urbanisation than did the Styx Valley in south-central Tasmania [545] . Indeed, the final dip in that lower-yielding equation was based on one tree alone, of DBH 2.74 m, with the next-smallest tree having a DBH of 2.02 m which is near the peak in the curve [546] . That allometric equation was therefore mostly based on the stem taper of non-senesced trees whereas the larger trees had lost their crowns and thus weren’t represented by it (Tim Wardlaw, Sustainable Timber Tasmania, pers. comm., 2024). This is an example of where equations developed from a small number of data, and therefore possibly containing a couple of extremes, may produce equations with limited applicability, and potentially low-accuracy results if applied beyond their bounds, whereas a greater range of input data is more likely to yield a more generally applicable equation.

Possible error margins from using allometric equations can be inferred from the range of trends in Figure 9 (b). For example, for a young, mature E. obliqua tree of a relatively small diameter of DBH 1.5 m, the allometric equation of Keith, et al. [124] gives the carbon mass of 10.806 Mg whereas that of Wardlaw [543] gives 7.500 Mg. If one couldn’t choose between the two equations and had to select the average, then the error margin [about the mean] is $\pm$

1.65 Mg, which is a relative error of 19%. If calculating a site’s carbon by adding up the carbon in each tree, for perhaps 20 such trees per hectare, then that relative error is transferred directly to the total carbon content. For larger trees, usually fewer data go into construction of the allometric equation and therefore its uncertainty is higher. The error margin is also higher for larger trees due to estimating the degree of senescence, or when devising the allometric equation-- how much senescence was incorporated into it for which DBH? Error margins also get added from such things as measurement errors in the plot size, land slope and DBH measurement. The discrepancy between the Er D2023 and Er D2020 allometric equations for E. regnans (in Figure 9 ) and that of Sillett, et al. [77] is nearly as great as for that between the E. obliqua equations, but that may be because Sillett, et al. [77] didn’t include internal hollows as a tree ages (for those that have them). The allometric equation from Ximenes, et al. [544] for aboveground biomass of E. regnans was based on direct weighing and therefore included carbon loss accompanying senescence, but it was only for trees with DBH ≤2 metres, and no internal hollows were noticed (F. Ximines, Dept. of Primary Industries, New South Wales, pers. comm. 2024). That equation yields carbon content close to that of Sillett, et al. [77] for young E. regnans trees, and makes the equations Er D2023 and Er D2020 look conservative.

For commercial forestry work over a larger area in Tasmania, an equation for E. obliqua stem volume (the merchantable part of the tree) was developed by State forestry, but it was based on both DBH and tree height and represented the stem taper (which was integrated to give volume) [547] . In typical commercial forestry it is important to quantify the stem, rather than the branches, because the branches are not sold. The DBH values of specimens used to calibrate that taper model ranged up to 3 m, which means it could be useful in carbon accounting. Tree height is not a reliable variable for the more-mature eucalypt trees for several reasons: (a) they may lose different amounts of the crown, from senescence, (b) short, stout trees, growing in more open conditions will have developed extra branch mass whereas trees in stands that have not thinned much will accrue greater height, (d) trees that have only recently lost their crowns have not yet invested in the extra branch mass typical of short, stout trees, (e) extra complexity will be added as a stand thins with old age, neighbouring trees may (or may not) have fallen and so the extra light reaching the tree allows a large branch mass to develop, without the tree increasing height but with increase in DBH. One outcome of the range of circumstances is that trees of larger DBH (i.e., E. regnans of 5–8 m) are often shorter [80] .

Thus, for useful allometric equations, a large range of data are needed including for the large trees experiencing a range of factors, rather than relying on extrapolation. Data on an extensive range of small, medium and large E. regnans trees in the Styx, Florentine and Arve valleys of Tasmania and in various historical records, provided the input for the carbon accounting software CAR4D, which was used for forecasting, spatial analysis, and analysis of industry and fire effects, over long time periods [88,307] .

The allometric equation for E. regnans from Sillett, et al. [77] keeps increasing for higher DBH, because it doesn’t account for eventual decline with advanced age, such as internal stem-wood decomposition (hollows) from typical senescence or fire. The allometric equation for E. delegatensis from Dean, et al. [542] initially also keeps increasing within the range of DBHs for which it was applied but it is of sigmoidal form and therefore reaches an asymptote. It was partly constructed from an allometric based on data restricted to DBH of 3.5 m from Keith, et al. [124] for E. obliqua. But other contributing parts for that equation for E. delegatensis included an allometric equation with senescence (for E. regnans), so it will be constrained. Also, senescence was subtracted on a tree-by-tree basis before tallying the stand totals in Dean, et al. [542] . Therefore, the forest carbon stocks would not have been overestimated.

An appraisal of allometric equations for the rainforest species in mixed-forest in Tasmania is necessary. Destructive sampling for specific species could give more accurate data for the rainforest understorey than volumes based on stem taper functions, and such sampling has been undertaken as part of commercial inventory. The first species-specific allometric equations for the rainforest understorey species in mixed-forest were developed by the Forestry Commission [of Tasmania] from rainforest in the South Arthur River area of northwest Tasmania [347] . Although they didn’t specify the exact range of tree sizes examined, their plots included mature rainforest across sites of different productivities. The maximum heights for myrtle trees on the more productive, well drained, sites was typically around 37 m but could be up to 45 m [347,548] . Their equations give the volume of wood in stems under the bark as a function of DBH and height, but they did not publish a formula for tree height. Such volumes were processed as part of this review to yield aboveground carbon. Height was parameterised as a function of DBH from trees on a 1 ha plot at State forestry’s research plot at Warra in southern Tasmania. The commonly used expansion factor of 1.46 [533] was used, and a basic density of 0.5 Mg m^-3 [543] . Individual tree data in that dataset from Warra were reported as part of Australia’s Terrestrial Ecosystem Research Network (TERN) project [546] , but there the allometric equation for myrtle volume used was that for a different species— New Zealand mountain beech (Nothofagus solandri var. cliffortioides) [549] , and the basic density used to convert to carbon was 0.58 Mg m^-3. The reason for choosing a different species in the TERN report was not stated and it gave stem volumes (and hence tree carbon) that were only 76.5% as high as those for Tasmanian myrtle, from Walker and Candy [347] . The TERN data from Warra were re-processed but using the allometric equation for myrtle volume from Walker and Candy [347] . The DBH range was notably restricted at the Warra site. For example, the maximum DBH and heights of myrtle were 0.448 m and 29.4 m respectively, which are smaller than for those observed in the Styx and Florentine valleys, and the earlier work in NW Tasmania. Therefore, any comparison between the relevant allometric equations for the different sites can only be done at the low end of the size spectrum. But the TERN data do offer a potentially more accurate benchmark in that range against which to compare any non-species-specific rainforest understorey allometric equations. The height as a function of DBH equation from the Warra data in Wardlaw [543] was developed from a much more restricted dataset than the Walker and Candy [347] equation for volume. Therefore, to the Warra dataset of 100 points for myrtle, a range of other DBHs and heights for myrtle were added to derive a new equation for height as a function of DBH, for myrtle trees: 2 data points from the literature [548] , 8 from my own historical data collection Tasmania-wide, and 6 from citizen science by Wilderness Society volunteers ( [92,542,550] ). These extra data had a maximum DBH of 2.39 m, and a maximum height 48 m. The new equation was constrained to match the curvature of the Wardlaw [543] equation for myrtle trees at low DBH by including in a mathematical regression, the 79 DBH-height data point pairs reported in Wardlaw [546] where the height had been calculated from their equation rather than measured in the field. The new equation, of Chapman-Richards growth-function format, was refined using Labfit [551] :

$$height=a\times e^{-\left({\displaystyle \raisebox{1ex}{$\left(2b-1.25\right)$}\!\left/ \!\raisebox{-1ex}{$DBH$}\right.}\right)}$$

(10)

where height is the tree height in m, DBH is in cm, a= 35.9377 (SD 0.8331) m, P(t)<0.001, b= 5.4261 (SD 0.2688) cm P(t)<0.001, adjR²= 0.75, Df= 117 (though less in reality due to using some calculated heights from Wardlaw [546] ), and P< 3 x 10^-8. Note that this function has essentially reached its asymptote when DBH values are as low as 1.5 m, and therefore it could reasonably be used for DBH values larger than the 2.39 m in the data set. This equation was used to get DBH-height pairs for input to the Walker and Candy [347] equation for myrtle stem volume, combined with the expansion factor 1.46 and density 580 Kg m^-3 [546] , and a root/shoot ratio of 0.15, to extend the allometric comparison process for tree carbon of rainforest understorey trees ( Figure 10 ).

Non-species specific (generic) allometric equations for the biomass of Australian rainforest trees were published in Keith, et al. [124] and given in terms of an adjustment to a global standard for rainforests for two different regions in Australia: sub-tropical and temperate. My error in Dean, et al. [542] was in subtracting the adjustment to get from global rainforest to Australian temperate rainforest, rather than adding it. The mathematical form of those equations in Keith, et al. [124] was log-log and although an upper limit on DBH wasn’t stated, the formula was only graphed for trees with DBHs between 0.1 and 1.0 m. For wider trees, the biomass would possibly have increased unrealistically due to the exponential form of the equation. Therefore, two different approaches were subsequently used. Firstly, in Dean, et al. [307] , an allometric equation was developed which gave biomasses matching those for temperate rainforest understorey from Keith, et al. [124] up to 1 m DBH ( Figure 10 (b)), but then instead of increasing exponentially for higher DBHs it was made to approach an asymptote by making it a sigmoid function ( Figure 10 (a)). Secondly, in Dean, et al. [542] , the allometric from Keith, et al. [124] was averaged with the allometric equation for rainforest trees of Dean, et al. [307] (which was halved to ensure conservative values). Although the second method still would increase exponentially, the combination gave reasonable values for DBHs up to about 3 m ( Figure 10 (a)). Note that the maximum DBH for understorey rainforest trees in the data in Gilbert [55] was about 2 m, which means that carbon stocks in Table 2 that use the Keith, et al. [124] equations are most likely too high, which leaves the new_{rainforest_C} as being more likely to be applicable.

For rainforest understorey trees there is an adjustment necessary, to a published allometric equation, due to an error I had made in the formulation of the allometric equation in Dean, et al. [542] , which was pointed out to me by Barrie May (pers. comm., CO₂ Australia Ltd., 2012) during his calculations for a report on Tasmanian carbon stocks [550] . My error was to subtract the adjustment to get from global rainforest to Australian temperate rainforest in Keith, et al. [124] , rather than add it. The effect was that the carbon stocks reported in Dean, et al. [542] were below what they should have been. I corrected that error for the comparison of different C studies here and the corresponding allometric equation is labelled ‘D2011 corr.’ in Table 2 . The error has most impact near DBH 0.5 m [and is less for other values of DBH]. If that erroneous process was applied to the stands in Gilbert [55] , it would have made an ~9.5% reduction in the stand totals for mixed-forest, and an ~24% reduction for both the rainforest understorey and the pure rainforest ( Table 2 ).

Figure 10. Comparison of different rainforest understorey allometric equations, shown at different scales, from (a) larger to, (b) medium, to (c) smaller trees. For the equations that didn’t include root mass, it was added with a root:shoot ratio of 0.15:1. ‘K2000 temperate’= temperate rainforest [124]; ‘K2000 general’= general rainforest [124]; ‘K200 temperate inc.’= incorrect adjustment to the general rainforest tree equation in Keith, et al. [124] to get rainforest trees (my error, not theirs); ‘D2003’= [307]; ‘half D2003’= D2003 divided by 2; ‘ave’= average of D2003 and K2000 temperate; ‘rain_new’= Eq. 11, new rainforest allometric equation introduced here; ‘Walker & Candy (1982)’= [347] using height derived from Eq. 10 introduced here, density of 0.58 Mg m^-3, and expansion factor of 1.46; ‘sassafras TERN’= sassafras [546].

Figure 10. Comparison of different rainforest understorey allometric equations, shown at different scales, from (a) larger to, (b) medium, to (c) smaller trees. For the equations that didn’t include root mass, it was added with a root:shoot ratio of 0.15:1. ‘K2000 temperate’= temperate rainforest [124]; ‘K2000 general’= general rainforest [124]; ‘K200 temperate inc.’= incorrect adjustment to the general rainforest tree equation in Keith, et al. [124] to get rainforest trees (my error, not theirs); ‘D2003’= [307]; ‘half D2003’= D2003 divided by 2; ‘ave’= average of D2003 and K2000 temperate; ‘rain_new’= Eq. 11, new rainforest allometric equation introduced here; ‘Walker & Candy (1982)’= [347] using height derived from Eq. 10 introduced here, density of 0.58 Mg m^-3, and expansion factor of 1.46; ‘sassafras TERN’= sassafras [546].

The Walker and Candy [347] equation is another that forecasts exponentially increasing volumes with DBH ( Figure 10 .(a)) and therefore it too cannot be used for the larger-DBH myrtle trees. The myrtles with larger DBHs that I have observed in mixed-forest in Tasmania (such as over 2 m) usually have increased hollow volume, both above and belowground, representative of senescence, and therefore their C content approaches an asymptote. To represent the additional scientific knowledge gained over the last 20 years, shown in Figure 10 , the allometric equation for C in rainforest understorey trees from Dean, et al. [307] was remodelled to give a new equation:

$$ne{w}_{rainforest\_C}=1.15\times 0.5\times 45\left(1-\left\{1/\left[1+{\left({\displaystyle \raisebox{1ex}{$\left(DBH+0.01\right)$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}\right)}^{2.5}\right]\right\}\right)$$

(11)

where new_{rainforest_C} is the carbon in the whole understorey rainforest tree in Mg and DBH is in m. The multiplier ‘1.15’ represents the root/shoot ratio, and the ‘0.5’ multiplier represents carbon being half of the biomass. This equation can be applied to all DBH ranges of rainforest trees measured in mixed-forests for typical carbon inventories in Tasmania. The carbon stock derived by this equation is much lower than that from the temperate rainforest understory allometric equation from Keith, et al. [124] , and only slightly higher than that from Walker and Candy [347] plus the expansion factor, and it is therefore conservative. It will eventually approach the same asymptote as in Dean, et al. [307] but only for higher DBH values than observed. At low DBH (< 0.5 m) it gives less carbon than does the Walker and Candy [347] process but more carbon than does the equation for sassafras from Wardlaw [546] . But that latter equation assumes a cone above 1.3 m and it is therefore quite approximate, and sassafras is relatively shade tolerant so has a high branch volume and therefore its corresponding expansion factor is probably higher than the 1.46 used in that work.

As with the graphs of the allometric equations for eucalypts ( Figure 9 ) it is worth gauging the precision (or error margins) of allometric equations for the understorey species from Figure 10 . For example, for a tree of DBH 0.5 m: there’s a variation between the equations of ~33%. The difference between curves gives an indication of the possible error margins that can be assigned to the total rainforest understorey carbon in a mixed-forest or rainforest study site. The wide error margin is another reason why the new_{rainforest_C} allometric equation was chosen for use rather than that of Keith, et al. [124] in tallying carbon stocks for the comparison process. In this way, the total, even if still with a high error margin, could not be viewed as excessive, and indeed for trees of DBH 1 m, it is in the lower half of the spread of carbon values.

6.3. Inventories of Carbon at the Landscape Scale

A major, publicly available inventory of the primary tall-eucalypt forests in Tasmania was by ANM [52] , to describe the forests in terms of merchandise, namely the pulpwood and possibly sawlog merchantable volumes in the Styx/Tyenna/Florentine pulpwood concession area. Some details from this assessment were given in Section 2 above. As pulpwood uses more of the stem of a mature eucalypt tree than does sawlog alone, then a BEF can be applied to process the merchantable volume data of ANM [52] into carbon in live biomass of the forest stand. Appendix 4 in ANM [52] gives yields [of pulpwood plus sawlogs] in terms of Mg per hectare for oldgrowth forests in the concession, based on ‘recent production records’ from ‘various contractors’ over the period 1976 to 1977.

The yields were grouped under the API types (see section 2), grouped by eucalypt height and canopy coverage. The yields reported were for greenwood as delivered to the pulp mill and were not for dry biomass. This is confirmed by the density they found when comparing volumes with weights at the mill: 1.057 Mg m^-3, which they used for calculating spatial yield tables and annual extraction rates [52 p10 & 21]. Therefore, to get those yields of greenwood mass to dry biomass (before dividing by 2 to get carbon) they must be multiplied by the basic density of E. regnans (which was the main timber logged from which the yields were obtained) and divided by 1.057. The basic density of 0.5124 Mg m^-3 [307] was used here, being for E. regnans, as it was the main timber logged from which the yields were obtained [52] . The usual expansion factor of 1.46 was applied, to get whole aboveground mass and a factor 1.15 to include roots. The product was then multiplied by 1.29 to include the trees in the coupe that were not logged, such as those considered unmerchantable, or on stream banks, or killed in escaped regeneration burns [535] (to give column 5 in Table 3 ). This may account to some degree for rainforest trees which not taken off-site but just felled or burnt (not all species were pulped). The values thus derived are in Table 3 , where the phototypes were also grouped to match the grouping used in a Tasmania-wide forest C assessment by Moroni, et al. [552] : column 5 in Table 3 .

If the reported yields in ANM [52] are processed differently, there is a strong similarity in C stocks for some API-types with those reported by Moroni, et al. [552] . If it is assumed that ANM’s reported yields were for dry timber (not green timber), and the carbon in roots is not added, and no 1.29 non-merchantable-tree-factor is applied, then one obtains the values in column 6 of Table 3 . Numeric values from Moroni, et al. [552] were not available directly but were read off their graphs, with an error of about ⁺/-10 Mg ha^-1 [553] and are given in column 7 in Table 3 . By comparing columns 6 and 7 it appears that values of C stock in live biomass for E1a and b, E1c and d, and E2c and d in Moroni, et al. [552] , are identical [within error margins] to the C in aboveground live biomass derived from the reported yields in ANM [52] but assuming they were for dry biomass and not adding root mass. However, Moroni, et al. [552] describe their method as:

‘Total standing tree volume (standing gross bole volume) was estimated from sample plot data collated in 2007 from >3500 permanent and temporary inventory plots. … Standing-tree bole volumes are converted to forest C mass as described below. Bole volumes of all standing living and dead trees of all species were multiplied by a basic density of 500 kg m⁻³ [31] allowing biomass to be estimated. Total above-ground live-tree biomass (bole, branches and foliage) was estimated from live bole biomass by multiplying by an expansion factor of 1.46 [32] . Root biomass was included by multiplying total above-ground biomass by 1.25.’

It is not possible to tell if the similarity for those three averaged API types (columns 6 and 7 in Table 3 ) is coincidence or not. But if they were calculated from the same data set then the carbon values in Moroni, et al. [552] are missing the carbon in roots and are thus too low. Similarly, the carbon values may also be too low because it’s likely that some rainforest species such as myrtle and sassafras, or some portion of them, may not have been tallied in the ANM inventories, as only eucalypts and Acacia dealbata (silver wattle) were pulped in that era [52] . But, conversely, if the carbon values in Moroni, et al. [552] were calculated from that ANM [52] data set then they will be too high as the original data were for green wood (including moisture). Regardless, the values for the different API types in Table 3 are averages over hundreds of hectares and thus unlikely to represent local peaks such as in Sanger and Ferrari [529] .

Table 3. Oldgrowth merchantable timber yields (pulpwood + sawlog) from the Styx/Florentine concession [52], converted to spatial C density, and compared with Tasmanian forest carbon stocks from Moroni, et al. [552]. AG= aboveground, PA= API type averaged. Units Mg ha^-1 = tonnes per hectare.

Table 3. Oldgrowth merchantable timber yields (pulpwood + sawlog) from the Styx/Florentine concession [52], converted to spatial C density, and compared with Tasmanian forest carbon stocks from Moroni, et al. [552]. AG= aboveground, PA= API type averaged. Units Mg ha^-1 = tonnes per hectare.

API type	ANM [52] green yield (Mg ha-1)	yield x 1.46 x 0.5 = AG C (Mg ha-1)	PA	ANM [52] yield, expanded C with roots (Mg ha-1)	PA AG C assumingdry yield(Mg ha-1)	Moroni, et al. [552 Figure 3] C in biomass (Mg ha-1)
E1a	718	524.1	E1a, E1b	340	473	470
E1b	578	421.9
E1c	699	510.2	E1c, E1d	232	322	319
E1d	183	133.7
E2a	514	394.8	E2a, E2b	310	432	285
E2b	641	467.95
E2c	361	263.5	E2c, E2d	175	244	244
E2d	307	224.1

Forest stands with peaks in carbon content may not be reported as high volumes in logging records as the trees may not be merchantable, e.g., due to strong senescence when pulpwood is not marketable. In the pulpwood era one of the highest merchantable volumes reported was 150,000 super feet [hoppus] per acre [96,541] . This was converted to C in Mg ha^-1, using a value for logs of 0.0030045 to convert super feet to m³ [554] , converting to per hectare, and using the same multiplication factors as for column 5 in Table 3 , giving: 618 Mg ha^-1 of carbon in live biomass (including roots). Two example stands with this C stock had areas of 0.81 ha and 11 ha, of predominantly 100 to 150–160 year old E. regnans mixed-forest with API-type E1a* (i.e., eucalypts over 76 m high and 70–100% eucalyptus crown cover— high stand density), on steep slopes, in coupe L.38 in Lords block, Florentine valley [541] . They were clearfell logged then burnt (CBS), from 1959 to 1962, so will not reach the same carbon content until the year ~2120, and only if unlogged and if climate change allows a similarly productive and fire-free climate there until then. The stands were considered ‘young’ mixed-forest as the rainforest understorey, although up to ~30–37 m high, was not well developed, but would have developed broader, denser crowns, as the eucalypts underwent self-thinning [and if they had not been logged] [555] . This carbon stock is nearly double the average for the E1a API-type and the logging record refers to the site as ‘extremely productive’. It demonstrates that the broader forest averages, even within one API-type, cannot compete with smaller sites for high carbon stocks.

Now that some of the variety in allometric equations and expansion factors has been shown, it is an appropriate point to describe what must be compared when gauging contenders for the status of highest carbon stocks in Tasmania, as claimed by Sanger and Ferrari [529] for their study plot. The C stock in live biomass (above and below ground) from their Table 2 is 916 Mg ha^-1. The error margin on that value can be partly gleaned from the standard deviation between the data on their 4 transects in their Table B2: ~50% of the mean. No error margin is mentioned for the C in their individual trees with DBH >2.5 m, so it would have to be estimated from the imprecision in allometric equations, such as +/- 20%, from the derivation of the equations shown above in this section. There is also an accrued error from imprecision in each measurement made in the forest (section 2). Overall, as a rough guide, one could reasonably assume +/- 25% error, (229 Mg ha^-1), which makes the reported C in live biomass including roots, in Sanger and Ferrari [529] between 687 and 1145 Mg ha^-1. Therefore, as a rough guide for comparison with other reports, one must check if the C in live plant biomass in that other data is at least: (a) 687 Mg ha^-1 if the root:shoot ratio used is 0.25:1; or (b) 632 Mg ha^-1 if the root:shoot ratio used is 0.15:1; or (c) 549 Mg ha^-1 if only aboveground C in live plant biomass is reported. Where possible, the root:shoot ratio in other data were converted to 0.15:1, to put all data sets on the same footing. There will also be error margins on the other data, so any overlap could be from two directions. If there is overlap then the two data points are indistinguishable. In reports where dead biomass and soil carbon are also reported, they can provide more detail and possibly more certainty in the comparison. One must also consider the area of forest measured, as it is easier to get a high carbon value in a small, non-randomly located plot (e.g., a 0.05 ha study plot centred around a non-senesced tree of DBH 5 m), than in a larger area such as 5,000 ha, which by its nature, must be more medium. In this, comparing size of study areas could however lead to an unintentional bias, because Sanger and Ferrari [529] stated that their study area was not randomly located but selected because ‘it had the highest density of large trees that were safe for climbing’.

6.8. Placing the Pro-Conservation Report on a Level Playing Field

Where possible, for the purpose of comparing carbon stocks, the root:shoot ratio of 0.15:1 has been applied to other data collections mentioned in this section. Consequently, that must also be done to the data reported in Sanger and Ferrari [529]. Also for making an equitable comparison, some of the other factors used in that report must be adjusted: (a) account for ground slope, (b) use the new rainforest allometric equation, and (c) use species specific wood densities and allometric equations for the eucalyptus trees where possible.

There are firstly some possibly larger matters to address though in Sanger and Ferrari [529] regarding what appears to be their particular adoption of standard scientific processes, for example (a) citing of earlier work, (b) error margins; (c) accounting for senescence in the larger trees, especially trunk hollows; (d) some missing information; and I comparing results with those in earlier work. Those will be addressed these here. The issue of incorrect citing of earlier literature was discussed above and will only be mentioned again with respect to tree hollows etc.

When citing the equations used from Dean, et al. [542], except in one instance, Sanger and Ferrari [529] transcribed them verbatim, even copying errors in the original work (some of which had been corrected in a corrigendum). For example, Eq3 in Dean, et al. [542] for the temperate rainforest understorey aboveground biomass:

was copied as:

“U_AGB = 0.001exp x (2.5667 ln (DBH) + 8.9133)”, Sanger and Ferrari [529],

where the multiplication sign, ‘X’, after ‘exp’ is incorrect mathematical syntax. And the ‘0.01’ in Eq. 2 in Dean, et al. [542] was transcribed verbatim but had been corrected to 0.1 in the corrigendum [568]. The corrigendum was uncited so it may have been inadvertently missed. The exception to their verbatim transcriptions was the allometric equation for E. delegatensis, namely Eq. 2 in Dean, et al. [542]:

which was transcribed as:

‘E_AGB = 1612.4 x (1- (1/ 1 + ((DBH + 0.01)/12.714)^2.2283)’, [529].

The ‘del’ is missing in the transcription. Notably Sanger and Ferrari [529] describe it as being an ‘averaging allometric equation’ for ‘eucalypt trees’, whereas in Dean, et al. [542] it is specifically described as being designed for the aboveground biomass of E. delegatensis trees. An allometric equation developed for one species has been erroneously stated as generic for all eucalyptus species. That would mislead readers about the earlier publication and might result in other people copying that error for their own calculations further afield, while citing the original publication (the amplification effect). A possible reason for the error is that Sanger and Ferrari [529] wanted an equation that would suit any eucalypt species in their study plot. Such a generic equation was already available, at least for trees of DBH ≤ 1 m [124], and it could have been adopted and modified for senescence in trees with larger DBH values, following for example Dean, et al. [92], possibly using individual tree data [124,543,544].

Some information missing from Sanger and Ferrari [529] is the species names for the trees measured and modelled. This is important in deciding parameters for carbon accounting. Only the eucalypt species present in the larger 98 ha surrounding their ~2 ha study plot are mentioned. One could assume the species in the study plot are the same as in the larger 98 ha, but in Sanger and Ferrari [529] their choice of allometric equations suggests a subset. In the surrounding 98 ha of forest there were E. regnans, E. obliqua and E. globulus, with no mention of E. delegatensis being present (though they used an allometric equation developed for that species), whereas in the public media, the first author, Sanger, stated:

‘What makes it really special ... is that there are giant trees from four different species of eucalypt tree,…’ [569]

There are strong links between the publication, Sanger and Ferrari [529], an internet Facebook page and a commercial internet site run by a company called the ‘The Tree Projects’ [570,571]. On that commercial site E. delegatensis is mentioned as being in the larger forest stand, and only E. obliqua , E. regnans and E. globulus are featured on their Facebook site [571]. This is helpful but some uncertainty remains as to the species present in their study plot.

There could be a difference in species between their plot and the surrounds because: (a) they only measured 2% (by area) of the ‘Grove of Giants’ (their name for the 100 ha total), and (b) the average height of the trees with DBH over 2.5 m that they measured was 56 m (maximum height 72 m, and maximum DBH 5.12 m) whereas the surrounds have some trees near 80 m tall and a maximum DBH > 6 m. Thus, maybe a higher proportion of the trees in their plot were E. obliqua or their plot was more senesced than the surrounds. But this cannot be determined, especially as it can’t be determined whether the latitude and longitude provided for their plot refers to the centre, or a corner, or just somewhere in the larger 100 ha expanse. The URL web data link for ‘the data that support the findings’ provided in Sanger and Ferrari [529] does not lead to a web page, and when contacted, the journal’s administration didn’t provide an alternative URL.

Typically in scientific papers on forest carbon, the tree species are mentioned in the Introduction or Methods sections. An even more useful place to mention them in this case [529], would have had been in their Table B1, where the individual DBHs were listed for trees with DBH >2.5 m. As the species in the understorey were not mentioned, they cannot provide a clue about the fire history and thus the likely eucalypt assemblage. However, the company’s website provides geographic coordinates for the walking trail in the ‘Grove of Giants’ and overlaying that with the State forest agency’s API-type map of 1984, gives the API types as E1b.S.ER and E1c.S. The ‘S’ indicates scrub (understorey < 15 m) and the ‘ER’ indicates young (regenerated) eucalypts present with the oldgrowth trees. Photos of trees being measured on the company’s Facebook page supports these API types, and a range of eucalyptus and understorey species [571]. In a traverse along the recommended walking trail in the ‘Grove of Giants’ by J. Kirkpatrick (University of Tasmania, pers. Comm., 2024) myrtle, sassafras, celery-top pine and Tasmanian Laurel (Anopterus glandulosus) were seen in the understorey, making it young rainforest understorey, rather than scrub. It had possibly begun to mature, since the State forestry’s aerial photography. In summary, the relative concentration of different eucalypt species in the study plot of Sanger and Ferrari [529] cannot be determined from any of the information publicly available. Therefore, the error margin on the study plot’s carbon content could be increased further.

Their choice of mixing different allometric equations for different parts of their data processing of the eucalyptus trees in Sanger and Ferrari [529], namely for E. regnans from Sillett, et al. [572] and E. delegatensis from Dean, et al. [542], seems unnecessary, and could possibly lead to some bias, causing inaccuracy in the carbon stocks. For small eucalyptus trees in southern Tasmania (where the ‘Grove of Giants’ is) Bowling [573] found that for small regrowth eucalyptus trees (mostly with DBH < 0.64 m) the volume (for a given DBH and height) does not vary much between species, though some trends in deviation from the norm were noticed. With more data for each species, some definitive trends appear. For example, even for trees of the same DBH (1 m) and height (58 m), the wood volume in the stem, from integrating under their taper equation curves (Figure 11), for E. obliqua [574], E. delegatensis [574], and E. regnans [88], is 13.3, 12.5 and 12.0 m³ respectively— a spread of about 10%. The taper equation for E. obliqua mentioned above by Goodwin [547], gave a volume of 12.8 m³, and could have been graphed in Figure 11 but was not because in the mid-section it was too close to the curve for E. delegatensis. (For people who might use these equations, I just mention here that there’s a typographical erro) in Goodwin [547] which could cause confusion: the equations for α₂ and α₃ in the parabolic part of the ta)er, are actually for α₃ and α₂, respectively.)

Furthermore, Ilic [575] gave the basic densities of E. obliqua, E. delegatensis and E. regnans as 580, 524 and 485 Kg m^-3, respectively. This reinforces the sequence of decreasing mass that was indicated by the taper equations for equal-dimensioned trees in that species sequence. When normalised to the mass for E. obliqua, the mass ratios for that sequence are: 1: 0.850: 0.756. This gives a value to the imprecision (error margin) associated with not identifying the species— possibly up to about ±12 %. Wood density is an important contributor to carbon calculations when applying an allometric equation that is otherwise intended to be generic across species [576].

Additionally, E. regnans are commonly known to be, on average, the more-buttressed of the ash-type eucalypts, which could induce a potential extra error margin if mixing allometric equations between species. There is minimal information available for allometric equations of non-plantation E. globulus, (which are likely to be in the study plot of Sanger and Ferrari [529]) and it is considered an area of necessary research, but young specimens have an average basic density near 600 Kg m^-3 [577].

Figure 11. Different stem shapes of some eucalyptus species with the same DBH (1 m) and height (58 m), based on taper equations, showing difference in underbark wood volume, which yield a volume range of ~10%. The roughness for E. regnans near the top of the buttress region is because its taper equation was for over-bark shape, and the bark becomes thinner there.

Figure 11. Different stem shapes of some eucalyptus species with the same DBH (1 m) and height (58 m), based on taper equations, showing difference in underbark wood volume, which yield a volume range of ~10%. The roughness for E. regnans near the top of the buttress region is because its taper equation was for over-bark shape, and the bark becomes thinner there.

The benefit for Sanger and Ferrari [529] from choosing an allometric equation for E. delegatensis for their smaller trees is that it gives a medium volume. But if their trees were mostly E. obliqua or E. globulus, then they may have underestimated the volumes, or overestimated them if they were E. regnans.

Accounting for senescence in older trees is important when determining carbon stocks [307,309,578]. Sanger and Ferrari [529] state that they used an equation for E. regnans, from Sillett, et al. [572] to calculate missing carbon due to hollows etc.:

‘Internal decay was factored by equations to predict occurrence and volume of decay related to tree size was also derived from Sillett et al. (2010).’

However, in ‘Sillett et al. (2010)’ it is explicitly mentioned that internal decay was not accounted for, which was confirmed with its lead author: ‘Our published numbers for EURE do not account for hollows or decay’ (Steve Sillett, Cal. Poly. Humboldt, pers. Com. 2023). Consequently, to put carbon stocks on a level playing field for comparison purposes, some carbon must be subtracted from that apportioned to the larger trees in Sanger and Ferrari [529]. There is no reason to believe that the eucalypts in the plot of Sanger and Ferrari [529] had less hollows than those with which they are being compared here, such as in the Styx and Florentine Valleys. Both senescence and fire, and their combination, will increase the likelihood of lost carbon from the tree trunks. Therefore, it is shown here, how at least as much fire has occurred in the locality of the ‘Grove of Giants’, as in the Styx and Florentine Valleys.

Fire can increase hollows beyond that from normal senescence, especially in the buttress region or an existing hollow, because of turbulent flow. Turbulent flow, will in places, increase the speed of passing air and therefore delivers more oxygen, which pushes the exothermic reaction forward, creating a hotter, larger and longer burn. For a tree trunk this increases loss of carbon compared with wood decomposition alone. Such a fire is shown in Figure 12 after a light, prescribed burn of surrounding buffel grass in central Australia.

Figure 12. Intense fire due to turbulent flow in tree hollow River Red gum (Eucalyptus camaldulensis), following a light, prescribed burn of feral agricultural grass (Cenchrus ciliaris) in Todd River, central Australia. Carbon was still being emitted the following day after the grass had long-since self-extinguished. Similar release of carbon and hollow enlargement could occur for ground-level forest fires.

Figure 12. Intense fire due to turbulent flow in tree hollow River Red gum (Eucalyptus camaldulensis), following a light, prescribed burn of feral agricultural grass (Cenchrus ciliaris) in Todd River, central Australia. Carbon was still being emitted the following day after the grass had long-since self-extinguished. Similar release of carbon and hollow enlargement could occur for ground-level forest fires.

Strong evidence of fire in the region of the ‘Grove of Giants’ is that there are young eucalypts in the stand (the ‘ER’ in the API type) and that the understorey is not mature. Additionally, in the nearby Warra ecological research site, which also has a history of recent fire, the mature eucalypts were noted to be ‘almost invariably hollow, or at least heavily decayed at their centre’ [350]. Comparing maps for the ‘Grove of Giants’ region and the Styx Valley show that the creek lines have quite different vegetation: no rainforest gullies surrounding the ‘Grove of Giants’ whereas they prevail in the Styx Valley. In the former the gullies contain eucalypts <110 years old and mature eucalypts, possibly constituting wet-eucalypt forest rather than rainforest (Figure 13).

Figure 13. Indicators from vegetation of more frequent fire near the study area of (a) Sanger and Ferrari [529] with mature and young eucalypts in the creek lines (black square= study plot), compared with (b) the central Styx Valley with rainforest in the creek lines. Hence probably more hollow development in the mature eucalypts in (a). Blue lines= creeks and rivers. Vegetation categories based on API types from State forest agency maps.

Figure 13. Indicators from vegetation of more frequent fire near the study area of (a) Sanger and Ferrari [529] with mature and young eucalypts in the creek lines (black square= study plot), compared with (b) the central Styx Valley with rainforest in the creek lines. Hence probably more hollow development in the mature eucalypts in (a). Blue lines= creeks and rivers. Vegetation categories based on API types from State forest agency maps.

Several of the trees in the photos of the ‘Grove of Giants’ showed indicators for deep basal cavities [570,571]. In three dimensions they are clearer. For example, a 3D model based on aerial LiDAR of one of the largest E. globulus trees in the larger 100 ha surrounding their study plot, shows two deep basal fissures and higher up a deep stem indentation, which could lead to an internal basal hollow [579].

One of the largest E. regnans trees measured in Tasmania in the last 20 years, the ‘El Grande’ tree (which I measured to have a DBH of 6.19 m), had a stem volume of 406 m³ but had internal stem hollows, which may have reduced that wood volume by up to 40%, down to 244 m³ [77]. The measured volume for the E. globulus tree [mentioned in the last paragraph], when not accounting for stem hollows was 325 m³ [569]. But this could be much lower if the internal losses are similar to that in the El Grande tree. In Sanger and Ferrari [529] crown loss is already taken into account for the trees with DBH >2.5 m as the calculations include tree height. Dean, et al. [542] subtracted 25% from the eucalypt mass to account for internal hollows. Combining the two influences, it is reasonable to subtract 15% from the values in Sanger and Ferrari [529] from the trees with DBH >2.5 m, to place their plot’s total carbon on a level playing field for comparison purposes. Although this may sound like maligning of the larger trees, it is only to prevent overestimation of their carbon stock, and it does not detract from their numerous other values such as wind attenuation, carbon storage and cycling, local climate moderation and unique ecological contributions.

The variation in hollow occurrence described in section 2 suggests that in the absence of definitive detail, one must allow for a balanced and adjustable degree of hollowing. Other than assuming an average internal decomposition which can be adjusted for location [307], other methods are destructive sampling [124] [but then the tree dies] and coring. The latter method was used by Sillett, et al. [580] for individual Coast redwood (Sequoia sempervirens) and for stand-level carbon accounting they modelled the shape of trunk internal decay for trees with DBH > 2 m, through reductions in wood density..

Ground slope was not mentioned in Sanger and Ferrari [529]. Slope doesn’t usually make much difference to soil organic carbon calculation [other than depth calculation on steep slopes] because the cores or pits are dug vertically, and the extrapolation to a hectare is done assuming the surface of the collected sample is horizontal. On very steep slopes however, one may not be digging only downwards but, from the soil’s perspective, sideways too, and therefore measuring more of the topsoil, giving higher carbon stocks than due. Sloping ground makes a difference to the biomass calculation, as the projected plot area is reduced, which increases the calculated carbon in biomass per hectare, by the secant of the cosine of the slope. Using GoogleEarth Pro©, the typical slope in the ‘Grove of Giants’ was found to be about 20% or 11°, which increases carbon in biomass by about 2%, from the values reported in Sanger and Ferrari [529]. The projected plot area becomes 1.914 ha rather than the original 1.95 ha. The ground slope from a cross-section of the 3D model from LiDAR data of the large E. Globulus [581] was 9(±1)°,which would increase carbon in biomass by 1.2%. In Sanger and Ferrari [529], there was initially some uncertainty about the plot that they had laid out, because it was twice described as 100 x 130 m, once as 150 x 130, twice as 19,500 m³, and once as 2 ha. On balance that is 4:2 in favour of 150 x 130 m, which was used in the recalculations here, before adjusting for slope.

In each measurement of trunk diameter there is an error margin when reading a distance off the tape. This type of error margin is usually taken as ± two tenths of the minimum graduation mark on the measuring device, but it also depends on a user’s experience level. People who routinely measure tree diameters have acquired habits that reduce error in placement of the tape before any reading is taken, such as sliding the tape to-and-fro a few times to make sure it has achieved the minimum local girth. Other basics include making sure the tape is perpendicular to the axis of the trunk or branch, and that it is not over any local swelling such as from a burl or branch development, but rather below or above it (or both, and then the average taken). Such information was passed on to the citizen science crew for the group measurements made in some earlier work [e.g., 92,542]. From photographs in public media on the internet however, it appears to have not been passed on to the arborists deployed for data collection in Sanger and Ferrari [529]. There were instances of tapes over substantial amounts of shed bark from higher up the tree, tapes not level for trunk and DBH measurements, tape over part of a burl, and a tape over a large branch-collar [569,571]. These all add apparent wood volume, rather than simply increasing the error margins. Measurements were taken off some photos in the public media that showed incorrect measurement technique in citizen science data collection in the ‘Grove of Giants’ [569,571 19-December-2022, 19-January-2023, 23-February-2023]. The angle from perpendicular [to the trunk axis] on diameter measurements was between 5 and 9°, giving an extra trunk volume (locally) of ~0.4 and 1.6% respectively. The extra diameter over the bark strands from higher up the trunk was ~5%, which translates directly to the same percentage of extra volume. The placing of the tape over the branch collar gave an extra volume (locally) of ~21%. It cannot be established if the examples provided in public media were exceptions or the typical procedure adopted. A rough estimate from the non-perpendicular diameter tapes may be, overall, conservatively in the order of 1%, which is insubstantial. If it was as high as 5% on average then that would be a significant factor when comparing carbon stocks. Most humans are outside of their normal 2D oecumene (as discussed in section 3) when climbing tall trees and this makes measurement more difficult, but practice of standard measurement techniques can help overcome difficulties and ensure less error in measurement. Regardless of the errors in measurement, due to the uniqueness of tree climbing, allowing public access to the data (by activating the mentioned data repository link in their paper) would have enefitted science by allowing improvement to existing allometric equations.

Having described several studies and summarised their data in the tables above, they can now be compared with the carbon stocks derived by Sanger and Ferrari [529], but only after adjustment of the latter for common allometric equations, wood density, senescence; and ground slope.

To summarise the differences between the reassessed and original calculations in Sanger and Ferrari [529], the multiplication factors are explained here. To convert from my earlier erroneous understorey allometric that they used, to the newly developed one here, without knowledge of their individual DBH measurements, I applied the ratio from Table 2(b) for the mixed-forest site assessment of Gilbert [55]: 158.9/162.5 = 0.97785 (which decreases biomass). The root:shoot ratio of 0.15 was used rather than the 0.25 in Sanger and Ferrari [529] (which decreases biomass). A wood density of 512.4 Kg m^-3 was used rather than their 520 Kg m^-3. I applied an 11° ground slope to the wood measurements (which increases live and dead biomass). And I applied a 15% senescence to eucalyptus trees with DBH > 2.5 m if their height was less than the typical 75 m (assuming, in the absence of other information, that the trees are E. regnans) and some senescence had already been deducted by measurement of reduced height (another reduction of live plant biomass). The results are shown in Table 9.

It is worth noting the effect of different amounts of senescence in the large trees. Assuming no senescence in the larger trees, other than that originally measured (by reduced crown mass), increases the C in study-wide live biomass by 9.9 % from 742.2 to 815.5 Mg ha^-1, whereas assuming 20% senescence in the larger trees decreases C in study-wide live biomass by only 3.3%, to 717.8 Mg ha^-1. This gives another indication of likely error margins.

The error margins for the biomass values from Sanger and Ferrari [529] were earlier described as ±25%, and the corresponding absolute values for the adjusted data are shown in Table 9. The error margins assigned to their values for CWD and soil organic carbon to 0.3 m depth [in that table] were the standard error (standard deviation divided by square root of sample size (namely 4)) found experimentally. Those standard deviations could be reduced by collecting more data. But to decrease the error margins in the biomass carbon values, more intensive experimental procedures would be needed, and if still using allometric equations, then more experiments to get relevant ones, such as for mature E. globulus (if present).

6.9. Comparison of the Carbon Stocks from Different Reports

In Figure 14, the first comparison of the carbon stocks in the study plot of Sanger and Ferrari [529] with other studies, is of living plant biomass, then studies that included other pools too are shown, such as dead plant biomass and SOC. For the graphs, the tally from Sanger and Ferrari [529] was set as the benchmark to compare others against, as they claimed to have the most carbon reported in Tasmania. For ease of visualisation in the graphs error margins have only been applied to that tally from Sanger and Ferrari [529], but further on the influence of equivalent error margins on all the data being compared, is examined. There are of course error margins associated with the other reports, some of which may be as high or higher than those in Sanger and Ferrari [529]. The graphs are simpler this first way though, when there are many data points, and therefore they are easier to interpret.

The data points from reports that are centred below the lower error margin of Sanger and Ferrari [529]) are not shown in the graphs and in the table, in order to be conservative with showing possible competitors. This is also partly because, with science at its current level of development and field sampling so limited, forest-based carbon data for the tall eucalypt forests are generally too imprecise to warrant closer interrogation.

Although it is generally not permitted in scientific journal publications to show both graphs and tables of the same data, it is done so here because they provide different information. The graphs provide a useful visualisation of the distribution of values whereas Table 10 is useful for providing data for further work, such as in future comparisons. Often when retrieving data for this paper (and earlier ones) it has been necessary to use the software Datagrabber [582] to extract information from graphs, a process which adds its own error margins, in addition to those in the original data. Thus, in the interests of science both types are provided here, and it is suggested that it be considered as a scientific standard.

Figure 14. Comparison of carbon stocks in different pools, from Sanger and Ferrari [529] with those from other studies. The horizontal dashed lines are the error margins for Sanger and Ferrari [529], from Table 9. The code name is shown in column 4 of Table 10. In (c) the points that didn’t have SOC measurements adding to their total C, but still got within the error margins of Sanger and Ferrari [529] with all its pools, are shown as grey squares. Point G59 did not have debris or SOC measured, but still was within the margins in all figures.

Figure 14. Comparison of carbon stocks in different pools, from Sanger and Ferrari [529] with those from other studies. The horizontal dashed lines are the error margins for Sanger and Ferrari [529], from Table 9. The code name is shown in column 4 of Table 10. In (c) the points that didn’t have SOC measurements adding to their total C, but still got within the error margins of Sanger and Ferrari [529] with all its pools, are shown as grey squares. Point G59 did not have debris or SOC measured, but still was within the margins in all figures.

Table 10. Summary of carbon stocks, to 3 significant figures, for different pools that are within the error margins of those in Sanger and Ferrari [529] and therefore indistinguishable from them; plus projected area and aerial photo interpretation (API) type. Note that the area may not necessarily be the maximum area, merely a sample, except for Dean, et al. [307] where the 20 ha is mostly modelled but with an empirical base for the whole stand.

Table 10. Summary of carbon stocks, to 3 significant figures, for different pools that are within the error margins of those in Sanger and Ferrari [529] and therefore indistinguishable from them; plus projected area and aerial photo interpretation (API) type. Note that the area may not necessarily be the maximum area, merely a sample, except for Dean, et al. [307] where the 20 ha is mostly modelled but with an empirical base for the whole stand.

In Figure 14 the error margins are allocated only to the benchmark datum, namely the tally in Sanger and Ferrari [529]. The error margin for the biomass pool (alive and dead) was set at ±25%. If the same error had been set for the total carbon at their site then the contenders would only have to reach [100% minus 25% which is] 75% of the total, to be indistinguishable from it. If the benchmark and all the contenders have the same error margins as each other, then what percentage of the benchmark do the contenders have to reach to be indistinguishable from that benchmark? The answer, which is the error margins on the benchmark and on the test reports, is not 12.5% (25 divided by 2). It is given by the following equation:

$$em\_perc=100\left\{{\displaystyle \raisebox{1ex}{$\left(100-test\_perc\right)$}\!\left/ \!\raisebox{-1ex}{$\left(100+test\_perc\right)$}\right.}\right\}$$

(12)

where em_perc is the error margin on both the benchmark and the test report (the contender) as a percentage (equal on both) and test_perc is what percentage of the benchmark datum, the test report datum has to reach to be indistinguishable from the benchmark. If the report datum plus the em_perc error margin surpasses the benchmark datum minus the em_perc error margin, then the benchmark and test are indistinguishable. Also, if one subtracts em_perc from the benchmark datum and adds it to the test report datum, and if the two results are equal then the two datums are indistinguishable.

From Equation 12, the value equivalent to ±25% error on the benchmark Sanger and Ferrari [529] but none on the test reports, is 2500/175= ±14.28571% error margin on the benchmark and on the test reports. All the reports mentioned in this section were tested, by assigning that error margin to both them and to the benchmark, and the result was the same as in Table 10 and Figure 14. As people are used to the base 10 system and multiples of it, for the sake of making visualisation easier, the ±14.28571% can be approximated to ±15%. It then should become obvious to people who routinely work in forest carbon accounting, that this error margin (15% on all reports, or ±25% on only the benchmark) is conservative. For example, consider the errors, starting with running a tape measure through a forest on a hillside, placing a tape at 1.3 m aboveground around the buttress of mature trees, reading the tape, and the errors in allometric equations (such as can be inferred from Figure 9 and Figure 10) and errors in estimating the degree of senescence, in trees that are afflicted.

If one knows the error margin on both the test report and benchmark and wants to know what fraction of the benchmark a test report has to reach to be comparable with it, then that is given by:

$$test\_perc={\displaystyle \raisebox{1ex}{$\left(100-em\_perc\right)$}\!\left/ \!\raisebox{-1ex}{$\left\{1+\raisebox{1ex}{$em\_perc$}\!\left/ \!\raisebox{-1ex}{$100$}\right.\right\}$}\right.}$$

(13)

where em_perc and test_perc are as in Eq. 12. For example, if the error margin on both reports is 20% then the test report datum only has to be 80/1.2 = 66.666 (reoccurring) % of the benchmark datum to be indistinguishable from it. The two latter equations incidentally represent an arc of a circle of radius √(150²+150²) and the various possibilities are best shown in Figure 15.

Figure 15. Relationship between the fraction of the benchmark report datum that a test report has to reach (%), and the error margins on both reports (%) for the two reports, for them to be indistinguishable. This simplifies comparisons of various reports if one can assume equal error margins for them. The curve is given mathematically in Equations 12 and 13.

Figure 15. Relationship between the fraction of the benchmark report datum that a test report has to reach (%), and the error margins on both reports (%) for the two reports, for them to be indistinguishable. This simplifies comparisons of various reports if one can assume equal error margins for them. The curve is given mathematically in Equations 12 and 13.

The error margins for these data types, as mentioned in section 2, are partly genuine error margins, in the physics sense, and partly indicative of natural variation in biology. Most often in biology the former type are not shown, only the latter, which accrues as a range of values due to un-measured influences. Other places that genuine measurement errors are not mentioned are, for example, in financial matters, such as a domestic electricity bill, because then one could apply an equivalent margin when paying it. In biology the natural variation is usually assumed to be much larger than the measurement error and it is the only one cited, usually in the form of a standard deviation or standard error, as in the soil carbon value in Sanger and Ferrari [529]. That method assumes that sufficient samples have been acquired to include all relevant effects, and that similar effects operate elsewhere. However, when making comparisons, such as of carbon stocks, then stating an indicative error margin is much more important, the measurement error should be included too. Therefore, the overall ~±15% error margin that is used here (or the ±25% on only the benchmark) is conservative.

The SOC in different studies was measured to different depths. To provide a comparison it was therefore necessary to trim the depth of soil being considered to the minimum, which was -0.3 m in Sanger and Ferrari [529] and possibly also in Moroni and Lewis [532]. Although Sanger and Ferrari [529] claimed to be the most comprehensive carbon study of Tasmanian forests they did not measure as deeply as did some others, didn’t include SOC in moist stones and only had four sample points, but they did understand that latter shortcoming. Their soil carbon section was better than some of the earlier reports in that it used elemental analysis for carbon rather than the Walkley-Black method and it did include carbon in large charcoal particles. In future work, if for different locations it becomes routine to examine SOC further down or laterally, and significantly different amounts of SOC are there or have been translocated by water, then the competition would have to be rerun and it may provide better discrimination.

Regarding the competition declared by Sanger and Ferrari [529] of the highest carbon stocks in Tasmania— Figure 14 shows that they are no longer the clear winners, but approximately equal with several other sites. Additionally, if SOC and CWD had been measured for the site in Gilbert [55], then it may have the most carbon. The large error margins and natural variability in the current state of carbon accounting science for mature forests mean that many different sites are indistinguishable (Figure 14), a situation that was also noted in forest carbon comparisons nearly 20 years ago [88], though detail has improved since then.

One must also consider the size of the area sampled and its randomness of selection. The 20 ha for the site in Dean, et al. [307] is the largest in Table 9, but that was mostly a simulation study, so it can be disregarded. Several carbon studies didn’t reach the contenders table, perhaps because of their larger size. That leaves, from Table 9, the area of 5.59 ha for the Styx Valley part of Study 3 in May, et al. [550] as the only study site larger than the 1.914 ha of Sanger and Ferrari [529]. But the allometric equations used in the former study may not be comparable, e.g., the high-yielding temperate rainforest equation of Keith, et al. [124] may have been used. Notably, some of the same raw data were used in both May, et al. [550] and Dean, et al. [92], but the tally was lower in the latter study, which also included a larger area.

The 0.149 ha site in the Florentine Valley of Gilbert [55], measured before almost the entire valley was logged, has arguably the highest carbon stock to date for a Tasmania forest, but a relatively small area. However, it was possibly selected because, rather than being an extreme case, it was representative of high biomass forests that existed prior to logging. Logging records or the Styx and Florentine Valleys show that typical forest stands of specific height cohort and with a high wood volume were typically each from 1 to 15 ha in size [541]. The average size of the stands of the same forest type, E1c.M+ as measured in Gilbert [55], from the aerial phototype mapping of Forestry Tasmania, was ~21 ha (standard deviation 29 ha). These figures give a likely indication for the extent of the stand in Gilbert [55]. Nevertheless, neither that study nor Sanger and Ferrari [529] had selected their study plots totally at random within a forest type. Random site selection is partly interchangeable with studying a larger area, and so the Study 3 in May, et al. [550] with its larger area comes into consideration again, but it still raises scepticism for the reasons mentioned earlier. Overall then, the benchmark and contenders in Table 9 and Figure 14 remain indiscernible, except possibly for the larger area in Sanger and Ferrari [529], i.e., unless the size of their plot was also non-random, not just its location. If the size was not random, then for a more level comparison the area limits of forest stands sampled in the other studies in Table 9 would need to be determined. On balance, questions that consequently arise are: how much of the ‘Grove of Giants’ is represented by the ~1.9% of it sampled; is the majority of it much lower C, equivalent or higher? and similarly for the surrounds of other sites in Table 9.

A pertinent question from a carbon conservation perspective is: where else in Tasmania are there high carbon forests? Table 10 indicates that it’s likely to be in forests with either E1 or E2 phototype and with at least a 20% crown cover of eucalypts. For example, there is an area of forest similar in size and appearance, as seen from GoogleEarth ©, similar to the ‘Grove of Giants’, ~3.2 km to the north. Further afield, using an API-type map of 2012 from the Tasmanian State forestry agency, there was ~42,400 ha of either mature E1 or E2 with eucalypt crown coverage of at least 50%, left standing within Tasmania’s original southern central pulpwood concession boundaries. After the logging and the WHA extension of the late 1980s there was ~32,700 ha left in State forest and after further logging and the 2013 WHA extension there was ~13,300 ha left in State forest to be logged. From GIS analysis of the 2012 data, logging appears to have been concentrated in the Florentine, Tyenna and Styx Valleys and the largest contiguous stands of primary, mature E1 and E2 forest that now remain, are in at the northern and southern extremities of the original pulpwood concession, such as near the ‘Grove of Giants’, a little to north in the Russell River area, further south in the Kermandie catchment and north of the main Florentine catchment near Wayatinah. As the conservation activities for the ‘Grove of Giants’ stand show, conservation effort appears to have switched from the centre of the Florentine and Styx pulpwood concession since some of that central part of it formed part of the WHA extension of 2013. Its focus has recently intensified on the large individual trees, perhaps because both the general public and the State forest agency have revealed a sensitivity on that topic, and because the large trees are probably emblems of contrast with current human civilisation. They are current levers to gain conservation areas— but smaller and smaller examples become icons as the larger ones fall to various effects of the inexorable human consumption of nature. How then to most expediently identify the prominent stands? Apart from simply walking through Tasmania’s forests, LIDAR is currently a common remote sensing method for determining tree height and this could be combined with stand density (the forestry term for the number of trees per hectare) to find likely stands of high carbon stock, but it would need ground-truthing to determine the degree of hollow formation in the trees. Height alone may not be sufficient though for high carbon mass and biodiversity. Stand density will play a part in carbon accumulation but may detract from biodiversity. For example the highest concentration of the tallest trees was in the Andromeda block in the Styx Valley Kostoglou [87], but their diameters were below average, which indicated a high stand density even when mature— they may have germinated from an atypically intense burn which limited early regeneration of the rainforest understorey and later growth of large hemi-epiphytes. When viewing sites with potentially high carbon mass, there will be a trade-off between stand density (including old and recent fire effects), senescence (which may be accompanied by regeneration to for mixed-aged stands and more carbon, as in Keith, et al. [309]) and basal diameter (which can allow dominance of the carbon tally from a few individuals), and it’s likely that site contention can only be solved through thorough measurement.

7. Conclusions

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