# Contributions of height allometry and within-species trait variation to uncertainty in estimates of tropical forest carbon stocks

Hannah Carle, Teresa Neeman, Helen Murphy, David Bauman, Oliver Binks, Ingrid Coughlin, Andrew Ford, Adrienne Nicotra, Patrick Meir

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## To cite this version:

Hannah Carle, Teresa Neeman, Helen Murphy, David Bauman, Oliver Binks, et al.. Contributions of height allometry and within-species trait variation to uncertainty in estimates of tropical forest carbon stocks. Forestry, 2025, 10.1093/forestry/cpaf084. hal-05441947

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# Contributions of height allometry and within-species trait variation to uncertainty in estimates of tropical forest carbon stocks

Hannah Carle ID<fnref n="1" />,*, Teresa Neeman<fnref n="2" />, Helen Murphy<fnref n="3" />, David Bauman ID<fnref n="4" />,<fnref n="5" />,<fnref n="6" />, Oliver Binks ID<fnref n="7" />, Ingrid Coughlin<fnref n="8" />, Andrew Ford<fnref n="3" />, Adrienne Nicotra<fnref n="2" />, Patrick Meir<fnref n="9" />

## Abstract

Tropical forests host globally significant carbon stocks, which are relied on to help mitigate the effects of human-induced climate change. Characterizing the uncertainty around carbon stock estimates is thus essential to inform the carbon budgets needed to safely limit global warming, with implications for policy and decision-making worldwide. We used a large forest inventory dataset from the Australian tropical rainforest (7208 stems) to evaluate height:diameter (H:DBH) allometric variation and quantified within-species variation in wood density (WD) and woody tissue carbon ([C]) content (98 trees). Together, H:DBH, wood density, and woody tissue C were used to estimate forest carbon stocks (i.e. the carbon content of woody biomass: CAGB). Using simulations, we then provide estimates and recommendations on the uncertainty around CAGB. H measurement errors contributed more random error (4.5%) to CAGB than the best performing (site-level) H:DBH allometric models (±2.4%) and led to under-estimation of CAGB by roughly 15%. Comparison of H:DBH allometric models that were developed at different biogeographic scales shows that widely used pantropical models substantially over-estimated tree H, and thus tropical forest CAGB, at some Australian sites by close to 100%. By contrast, wood trait variation generated just 3% uncertainty in CAGB, which is reassuring since global wood trait datasets often contain a single record or a few records for tropical species. Our findings reinforce the promise of laser scanning technologies to improve biomass estimation via more accurate measurements of canopy height and nondestructive development of local-to-regional allometric models, which provide clear advantage over pantropical equations.

**Keywords:** height allometry; intraspecific variation; carbon stock; uncertainty; natural assets; LTER

## Introduction

Accurately quantifying forest carbon underpins our capacity to make and enforce accurate carbon budgets and to ensure cost-effective and trustworthy investments in natural capital. Tropical forests have the potential to deliver substantial climate change mitigation (Griscom et al. 2017, Walker et al. 2022); they have absorbed large quantities of human carbon dioxide emissions to date and represent vast carbon stocks (Pan et al. 2011, Phillips et al. 2017, Pan et al. 2024). However, the total magnitude of carbon stocks and fluxes for tropical forests remains highly uncertain (Pan et al. 2024), which limits the capacity of governments, industries, and ecology practitioners to assess or manage climate change (Brienen et al. 2015, Hubau et al. 2020, Bauman et al. 2022) and land use threats (Malhi and Phillips 2004,

Murphy and Romanuk 2014), or to fully leverage opportunities via natural capital. Largely, these uncertainties arise from the current methodologies used to estimate carbon.

Aboveground woody biomass (AGB, Mg) is generally estimated using allometric equations that are empirically derived from tree harvest data, collated at broad geographic scales (Chave et al. 2005, Feldpausch et al. 2012, Chave et al. 2014). These allometric equations rely on some or all of the following variables: tree height (H, m) (Feldpausch et al. 2012), tree diameter—most often diameter at breast height (DBH, cm)—and wood density (WD, g cm⁻<fnref n="3" />). The initial calculation of tree volume is a function of DBH and H, where height is sometimes measured but often estimated from DBH in one of several ways. AGB is a function of tree volume multiplied by WD [Equation (1), Chave et al. (2014)], which is then multiplied by the percentage carbon content in woody tissue ([C])

<footnote n="1">¹Hawkesbury Institute for the Environment, Western Sydney University, Bourke Street, Richmond NSW 2753, Australia</footnote>

<footnote n="2">²Research School of Biology, Australian National University, 134 Linnaeus Way, Acton ACT 2601, Australia</footnote>

<footnote n="3">³Commonwealth Scientific and Industrial Research Organisation (CSIRO), TBuilding 145, James Cook University, James Cook Drive, Townsville, QLD 4811, Australia</footnote>

<footnote n="4">⁴AMAP, University Montpellier, CIRAD, CNRS, INRAE, IRD, Montpellier, 2196 Bd de la Lironde, 34980 Montferrier-sur-Lez, France</footnote>

<footnote n="5">⁵Environmental Change Institute, School of Geography and the Environment, University of Oxford, S Parks Rd, Oxford OX1 3QY, UK</footnote>

<footnote n="6">⁶Laboratoire d'écologie Végétale et Biogéochimie, Université Libre de Bruxelles, Campus Plaine, Bâtiment BC (5th Floor, Wing C), Boulevard du Triomphe, CP 244, 1050 Brussels, Belgium</footnote>

<footnote n="7">⁷CREAF (Centro de Investigación Ecológica y Aplicaciones Forestales), Campus UAB, Edifici C, 08193 Bellaterra (Cerdanyola del Vallès), Barcelona, Spain</footnote>

<footnote n="8">⁸Australian Plant Phenomics Network, School of Agriculture, Food and Wine, University of Adelaide, Building WT81, Hartley Grove, Urrbrae SA 5064, Australia</footnote>

<footnote n="9">⁹School of Geosciences, University of Edinburgh, Crew Building, King's Buildings West Mains Road, EH9 3JW Edinburgh, United Kingdom</footnote>

<footnote>*Corresponding author. Hawkesbury Institute for the Environment, Western Sydney University, Richmond, NSW, Australia. E-mail: H.Carle@westernsydney.edu.au</footnote>
(Thomas and Martin 2012, Martin et al. 2018) to give an estimate of carbon in AGB ($C_{AGB}$).

Biases arising from AGB allometric equations, including in relation to tree-size and sample-size error-dependency, have been dealt with elsewhere (Chave et al. 2004, Hunter et al. 2013, Molto et al. 2013, Ledo et al. 2016). Here, we focus on biases associated with the constituent components of AGB models, which vary across landscapes (Chave et al. 2004, Roxburgh et al. 2015) and with ontogeny (Falster et al. 2018, Rodriguez-Zaccaro et al. 2019). Of these AGB components, DBH is usually measured for all trees, $H$ is sometimes measured for a subset of trees, and WD is usually sourced from databases of species-, family-, or genus-level values compiled from the literature. Sometimes, one or more of these variables is not measured or is unavailable due to limited budgetary resources or other logistic constraints. When these variables are not measured, they must be somehow approximated (based on equations or known or expected distributions), and these approximations can generate systematic and random errors in forest carbon estimates. The uncertainties associated with such approximations should thus be carefully considered and reported, based on knowledge of the magnitude and drivers of variation in each parameter.

Tree $H$ is particularly difficult to measure due to canopy density and complexity in tropical forests (Larjavaara et al. 2013) and is often estimated from DBH, based on the allometric relationship between $H$ and DBH ($H:DBH$). The form of $H:DBH$ is a nondecreasing curve that may or may not be asymptotically bounded (Ledo et al. 2016). Missing $H$ values can be estimated using published allometric models or models derived from $H$ and DBH measurements at a given study site (or collection of sites), and choice of the $H:DBH$ equation is integral to the accuracy and precision of biomass estimates (Chave et al. 2005, Feldpausch et al. 2012, Molto et al. 2013). $H:DBH$ allometry varies across scales, however, due to environmental, ecological, and phylogenetic factors (Feldpausch et al. 2011, Banin et al. 2012, Ibanez et al. 2018, Jucker et al. 2022). Trees in drier climates or in stands with higher basal area, for example, tend to be shorter at a given DBH (Feldpausch et al. 2011, Binks et al. 2023). While it might be expected that $H:DBH$ models defined at smaller spatial scales—continent, region, or stand—would consistently outperform more widely applicable pantropical models, the evidence for this is mixed (Banin et al. 2012, Feldpausch et al. 2012, Ledo et al. 2016). Particularly in forest types with high species diversity, and in situations where the scale and extent of $H:DBH$ variation is not well characterized, the potential benefits of using smaller-scale allometric equations may be counteracted by sample size and representativity issues, resulting in poor out-of-sample predictions (Chave et al. 2004, Hunter et al. 2013).

There is additional uncertainty in $C_{AGB}$ because of measurement errors in DBH and $H$. DBH measurement errors ($\epsilon_{DBH}$) are generally small in magnitude and have been well characterized by repeat measurements (Condit et al. 2004); nonetheless, these errors do scale to $C_{AGB}$. Conversely, $H$ measurement errors ($\epsilon_{Hmeas}$) tend to be highly variable and biased (whether from laser rangefinder or clinometer and tape measure methods) (Hunter et al. 2013, Larjavaara et al. 2013). Use of Light Detection And Ranging (LiDAR) laser scanning (LS) methods to measure tree $H$ and AGB is expanding. This method estimates the geometry of target objects by emitting laser pulses from a scanner and recording the response time of reflections from the target. Expanding use of LS methods will undoubtedly improve measurement-related uncertainties in $C_{AGB}$—particularly for large trees, since $H$ measurement error and allometric error

typically increase with tree size (Calders et al. 2014, Disney 2019, Burt et al. 2020, Terryn et al. 2024). A recent pantropical evaluation of the $H$ measurement bias associated with traditional inventory methods [cross-validated using terrestrial laser scanning (TLS)] suggests it is -5.3% to -25.4% (for 30 m trees), ranging up to -41.3% for very tall tropical trees (77 m dipterocarps) (Terryn et al. 2024). Despite increasing performance advantages to LS over traditional allometric approaches (e.g. Terryn et al. 2024), the advantages are likely dependent on forest type, and LS remains challenging to deploy in remote locations and is technically demanding in terms of postprocessing (Lines et al. 2022). Thus, many contend that traditional inventory methods are likely to continue in broad use for years to come—all at a time when carbon markets are developing at an unprecedented pace, and the need for accurate accounting of ecosystem carbon is greater than ever.

The next component of $C_{AGB}$ estimation is WD. Inclusion of WD in AGB allometric models is thought to reduce uncertainty in estimates of AGB even more than inclusion of tree $H$ (Chave et al. 2005). WD varies among species and species turnover substantially influences stand-level biomass (Baker et al. 2004, Phillips et al. 2019). Genus-level data are commonly used if species-level data are unavailable. WD also varies within species—across environmental gradients (Patiño et al. 2009) and with tree size (Phillips et al. 2019). The magnitude of within-species WD variation is not well characterized, although one assessment of 50 Neotropical tree species, which had more than six measurements available (Chave et al. 2004), suggested a within-species standard deviation (SD) of 10%. Using a pantropical mean for WD in place of species-specific WD values results in a 15% over-estimate of global carbon stocks in tropical forests (Baker et al. 2004, Phillips et al. 2019). Not accounting for within-species WD variation can bias estimates of AGB (Molto et al. 2013). There is hence a clear need to better evaluate WD variation and the extent to which it scales to estimates of $C_{AGB}$.

The influence of [C] variation on $C_{AGB}$ estimation has received comparatively little attention. [C] in trees increases with WD and generally increases with tree diameter (Ma et al. 2020) but may also vary across landscapes via environmental influences on growth and WD (Elias and Potvin 2003, Martin et al. 2018, Ma et al. 2020). While the magnitude of [C] differences is typically small (between 0.40 and 0.50 for tropical angiosperm species) (Thomas and Martin 2012, Martin et al. 2018), the effect of [C] on $C_{AGB}$ is multiplicative, so small inaccuracies may scale to large differences in $C_{AGB}$ (Elias and Potvin 2003, Martin et al. 2018). An important first step has been to develop robust estimates of mean [C] for different biomes (Thomas and Martin 2012, Martin et al. 2018). Assuming that 50% of AGB was [C] (instead of using a tropical mean derived from data) led to over-estimates of global tropical forest carbon stocks by 20.1 Pg C or 8.9% (Martin et al. 2018).

Here, we assess uncertainties around $C_{AGB}$ for Australian moist tropical forests that arise from site-to-site variation in $H:DBH$ and within-species variation in WD and [C]. We compare the magnitude of these uncertainties with those arising from $H$ and DBH measurement errors and $H:DBH$ allometric model choice (comparing models derived at different biogeographic scales). To do this, we used extensive forest inventory records ($H$ and DBH measurements) from 20 sites in the Queensland Permanent Rainforest Plots—Commonwealth Scientific and Industrial Research Organisation (QPRP-CSIRO) network and measured WD and [C] for 255 wood cores from seven common species. These data are used to simulate $C_{AGB}$ and quantify the uncertainties associated
<figure><img src="image_3.png" /><figcaption>**Figure 1.** (a) Site locations of the 20 plots in Queensland, Australia, and (b) an example of height-diameter (H:DBH) allometry in two plots. (a) ‘×’ indicates locations where wood cores were sampled. (b) Weibull functions fit to H and DBH measurements from different sites illustrate divergent allometries; EP37 Eungella (orange, upper line) and EP29 Mount Fisher (green, low line) differ in elevation (920 and 1200 m, respectively), stem density (246 and 438 stems at last census: Table S1) and maximum stem diameter (156.6 and 93.4 cm).</figcaption></figure>

with each variable. Based on these analyses, we make recommendations about measurement, sampling, and allometric model practices relevant to forest carbon practitioners globally.

# Materials and methods

## Site data

The QPRP network includes 20 0.5 ha (100 × 50 m) plots that were established by the CSIRO between 1971 and 1982 (Bradford et al. 2014) (now QPRP-CSIROplots). The plots capture much of the biogeographical diversity of Australian tropical forests (Fig. 1), with mean annual rainfall ranges from 1200 to 7000 mm and mean annual temperature ranges from 16°C to 26°C (see Table S1 for details).

In these plots, stems ≥10 cm DBH were resurveyed every 2–15 years (mean 3.17 ± 1.73 years, median 2.12), and mortality or physical damage was recorded. Tree height was measured at the time when plots were established and again in 1998. When each plot was established, researchers estimated tree heights, validated against canopy measurements using the triangulation method with a clinometer and measuring tapes (Graham et al. 2006). In 1998, tree *H* was measured using either the triangulation method or a laser rangefinder (Bushnell, Kansas, US) (Graham et al. 2006). All stems have been identified to the species level. The resulting dataset includes records for 10 701 trees over the 49-year observation window.

## Variation in wood density and carbon content

We collected 255 wood microcores (Trophor Microcorer, CMC, Italy) from 98 trees belonging to seven common species across the plot network (Table 1). Focal species were selected on the basis of abundance (minimum two individuals at three plots per species) across plots with contrasting altitude and/or latitude. We attempted to sample trees that represented a wide range of DBH size classes for each species at each site. The microcore samples were collected opportunistically during a field campaign in June 2022 and so are geographically restricted to plots within 200 km of the towns of Cairns and Atherton.

For each tree, we cut bark windows roughly 15 cm below DBH at three points around the circumference of the tree, and sampled microcores (2 × 15 mm) from each window, resulting in 255 samples from 98 stems. Wood cores were stored in small

humidified Eppendorfs and processed within 24 h. We estimated the dimensional volume of the fresh wood cores (Chave 2005), using length measured to the closest 0.5 mm and the internal diameter of the Trophor microcore. We stored the cores in vials with silicon beads and dried them for 3 days in a 70°C oven before measuring their dry mass. We estimated WD by dividing dry mass by volume (g cm⁻³).

To assess [C] and WD, wood cores were prepared for mass spectrometry by grinding the entire core to homogenize across growth rings. Approximately 1 mg of ground material was analysed for carbon bulk content using an Elementar Isoprime CF-IRMS (Continuous-flow Isotope Ratio Mass Spectrometer). Carbon measurements were calibrated against standards of C₃ Beet sucrose (Beet87) and a C₄ cane (ANU) sucrose and are reported as percentage mass.

We estimated within-species variation in WD and [C] using the coefficient of variation (CV = standard deviation divided by the mean). We evaluated the sources of variation in stem-level WD and [C] using simple (linear) regression models parameterized by tree DBH, species, and site, with two-way interactions to enable species wood traits to vary differently across sites and tree sizes (i.e. WD ~ DBH × species + site × species). We partitioned variance from these linear models to each fixed effect by estimating the R² of each factor or interaction (sum of squares for each factor divided by the total sum of squares for all model factors). We further tested for an expected positive association between [C] and WD (Martin et al. 2018) at the interspecies level ([C] ~ WD) and within species ([C] ~ WD + (1|species): package ‘lmerTest’ (Kuznetsova et al. 2017)). These models and all following analyses were done in R version 4.5.0 (R Core Team 2025).

## Estimating tree height

Tree heights are commonly estimated from DBH data by fitting a function to available height and diameter measurements of a species or forest stand. We created a randomized 50–50 (training-test) split of the available height data, stratified by measurement year and tree size. We derived site-level (20 sites, models fit to each site) and regional (all 20 sites together) H:DBH allometric models from the training dataset using function ‘nls’ in package ‘car’ (Fox and Weisberg 2019) to fit Weibull three-parameter functions (Ledo et al. 2016) and extracted the coefficients *a*, *b*, and *k* of these
<table><caption>**Table 1.** Wood core sampling for seven common species in the QPRP network. Sampling of wood microcores was done during a 2022 field campaign, for a minimum of three sites per species (n<sub>site</sub>) and minimum of nine samples per species (n<sub>stem</sub>). We attempted to capture a representative range of DBH for each species at each site (min and max DBH).</caption><thead><tr><th>Species</th><th>Code</th><th>n<sub>site</sub></th><th>n<sub>stem</sub></th><th>Mean n<sub>stem</sub>/site</th><th>Min. DBH (cm)</th><th>Max. DBH (cm)</th></tr></thead><tbody><tr><td>Aleurites rockinghamensis</td><td>Ar</td><td>3</td><td>13</td><td>4</td><td>14.6</td><td>91.0</td></tr><tr><td>Antirhea tenuiflora</td><td>At</td><td>3</td><td>11</td><td>4</td><td>11.1</td><td>25.4</td></tr><tr><td>Endiandra monothyra subsp. monothyra</td><td>Emm</td><td>4</td><td>10</td><td>2</td><td>10.7</td><td>31.1</td></tr><tr><td>Flindersia brayleyana</td><td>Fb</td><td>3</td><td>13</td><td>4</td><td>14.1</td><td>124.3</td></tr><tr><td>Franciscodendron laurifolium</td><td>Fl</td><td>3</td><td>28</td><td>9</td><td>10.1</td><td>72.7</td></tr><tr><td>Litsea leefeana</td><td>Ll</td><td>3</td><td>14</td><td>5</td><td>15.4</td><td>57.0</td></tr><tr><td>Xanthophyllum octandrum</td><td>Xo</td><td>3</td><td>9</td><td>3</td><td>13.0</td><td>50.7</td></tr></tbody></table>

models:

$$H = a \times (1 - \exp(-b \times (\text{DBH}^k))) \quad (1)$$

We then evaluated the performance of these H:DBH allometric models alongside three widely used H:DBH models from the literature (also Weibull three-parameter functions) using the test dataset. These additional models included one Australian and two pantropical functions (Feldpausch et al. 2012), with one of the pantropical functions additionally parameterized by environmental stress (E) (Chave et al. 2014). This parameter E combines temperature seasonality (TS), precipitation seasonality (PS), and maximum climatological water deficit (MCWD) to approximate major biogeographic differences across latitudes and elevations (Chave et al. 2014). To calculate E, monthly climate data were extracted from ANUClimate v.2.0 (0.01° grid) (Hutchinson et al. 2022). TS and PS were calculated as the standard deviation of monthly mean temperature (°C) and monthly rainfall (mm), expressed as a percentage of the mean (multiplied by 100). Monthly maximum climatological water deficit (MCWD) was calculated by identifying the most extreme monthly CWD in the previous 12-month period, where CWD is a measure of cumulative water deficit based on rainfall and actual evapotranspiration (Aragão et al. 2007, Malhi et al. 2009). MCWD was reset to zero at the wettest month of the year, based on 30-year (1981–2010) mean monthly precipitation values and given an upper bound of 1000 mm deficit. We calculated E for each plot at each census using the 6 months of data before and after each census date (n = 256). These census-level values for E were then averaged (across censuses) for each plot.

## Estimating aboveground biomass

Aboveground biomass (AGB) was modelled using the Chave et al. (2005) moist forest equation. We preferred this equation over more recently published equations in Chave et al. (2014) because their performance is comparable and we preferred an equation defined using moist forest data only over the alternative, which used moist, dry, and wet forest data.

Tree H for calculation of AGB was taken from five different H:DBH allometric models: one site-level model, one regional model, and three models from the literature. WD (g cm⁻³) data collated from literature and field collections (Bradford and Murphy 2019) was used to calculate the mean WD for each species (note that this database does not indicate whether the same or multiple methods were used to derive WD, which may introduce additional variation).

We used heartwood measurements where available (426 species) or otherwise combined heartwood and crosswood measurements (36 species). Where species-level values were not available, we averaged available heartwood data at the genus level (12 species) or for all available heartwood samples (3 species). We note that the median number of samples per species is n = 1. The biomass of strangler figs (n = 59) was calculated based on measurements or estimates of DBH of all stem segments combined. Palms, cycads, and lianas were excluded from all analyses.

## Assessing height:diameter model choice

We first evaluated whether H:DBH allometric variation results in distinct allometries among sites. We fit two H:DBH allometric models to data for trees with DBH within a size range common to all plots (10.0–58.3 cm DBH)—one with unique parameter estimates for each plot and one without. These were fit using the ‘nls’ function in the R package ‘car’ and were compared using analysis of variance and AIC.

We then assessed the relative performance of a suite of five H:DBH allometric model sets (one set of 20 site-level models, 1 regional model, and 3 models from the literature) in reference to measurements of H (H<sub>meas</sub>). To do this, we quantified tree-level H<sub>mod</sub> error by calculating mean error (ME, metres) as the sum of individual errors (H<sub>mod</sub> – H<sub>meas</sub>) divided by the number of trees, symmetric signed percentage bias (SSPB, %), and median symmetric accuracy (MSA, %) (Morley et al. 2018). We also compared percentage bias and uncertainty for AGB estimates (as derived from H<sub>mod</sub> versus H<sub>meas</sub>) aggregated at the plot level, using ME and root mean squared error (RMSE), normalized to AGB. We also quantified errors in each 10 cm diameter size class (trees >100 cm DBH were grouped together due to lower numbers of individuals) using ME of AGB for trees in each 10 cm DBH size class in each plot, normalized to AGB in that sample.

## Simulations of uncertainty in AGB

We simulated uncertainty in AGB estimates given five scenarios: (i) no information about uncertainty; (ii) information on measurement precision and bias for H and DBH; (iii) within-species variation in WD and/or [C]; (iv) H:DBH allometric model uncertainty; and (v) information for (ii–iv) together. Given each information scenario, we ran 1000 simulations based on all trees alive at the last census (7208 stems). For each tree, DBH measurements, database WD values, and modelled heights were used as the basis
<figure><img src="image_4.png" /><figcaption>**Figure 2.** Overview of data sources, workflow, and how parameters (red text) were derived and utilized in subsequent models and simulations. Climate data included temperature (temp.), precipitation (precip.), and climatological water deficit (CWD) (see Methods for details).</figcaption></figure>

for a simulated tree, for which simulated values of each variable were randomly sampled from normal distributions adjusted for bias and uncertainty (as standard deviations). These simulated tree measurements were then used to calculate plot-level (0.5 ha) C<sub>AGB</sub>, resulting in 1000 C<sub>AGB</sub> estimates per plot. These were multiplied by two to convert to per-hectare estimates. Means and standard deviations (SD) of simulated C<sub>AGB</sub> estimates were used to summarize within-site uncertainty, while means and standard errors (se) were used to summarize among-plot variability. Below, we detail how information on precision and bias was incorporated in these simulations.

Characterising H<sub>meas</sub> errors at our remote field sites would require resource-intensive canopy access and was beyond the

scope of the present study. Instead, we approximated H<sub>meas</sub> error distributions (ε<sub>Hmeas</sub>) based on two prior studies (Hunter et al. 2013, Larjavaara et al. 2013) and simulated height measurement errors using ε<sub>Hmeas</sub> ~ N(H<sub>meas</sub> - 2.1, 6.8 m). DBH measurement errors were approximated with distribution ε<sub>DBHmeas</sub> ~ N(DBH<sub>meas</sub>, 0.25 cm) based on experience of repeat measurements by our team.

For WD, we simulated from normal distribution ε<sub>WD</sub> ~ N(μ<sub>WD</sub>, σ<sub>WD</sub>), where μ<sub>WD</sub> was species mean WD and σ<sub>WD</sub> was the average standard deviation for species WD, as calculated from the database described above (Bradford and Murphy 2019). For [C], we simulated from distribution ε<sub>[C]</sub> ~ N(0.465, σ<sub>[C]</sub>), where 0.465 is the current best estimate of [C] for tropical angiosperms
<figure><img src="image_5.png" /><figcaption>**Figure 3.** Sources of variation in wood density (WD) and woody tissue carbon content ([C]) for seven species at five sites. Variance was partitioned from linear models with fixed effects for species, tree diameter (DBH), site, and select interactions. The 'species:site' interaction accounts for intraspecific variability among sites, the 'site' fixed effect is the average site effect across species present at each site and reflects differing species assemblages. Model residuals are shaded grey.</figcaption></figure>

(Martin et al. 2018) and σ$_{[C]}$ was the average standard deviation for species-level [C].

H:DBH model errors were simulated using a truncated normal distribution: ε$_{est}$ ~ N(H$_{mod}$ + model bias, RMSE), where plot-level RMSE was used to approximate a standard deviation. Tree height simulations were truncated such that H was between 5 m and the maximum measured H in the forest + 5 m. For simulation scenario (5), which combined H$_{meas}$ and height allometric model uncertainties, we added normally distributed errors from H$_{meas}$ and H$_{mod}$ before applying the truncation.

# Results

## Variation in wood density and carbon content

Roughly half of stem-level variation in WD and [C] was captured by species differences (Fig. 3). Beyond species, both traits varied significantly in relation to DBH, and wood trait variation with DBH and among sites was dependent on species (Table S2). The dependency of [C] on WD showed that [C] correlated with WD at the interspecies level (ANOVA: F = 8.55(1,252), P = .004, model R² = 0.292) but not for individuals within a species (i.e. a linear mixed effects model with species as a random effect: P = .747, model R² = 0.033).

The coefficient of variation (CV) for WD ranged between 5% and 14% within species (7 species, n = 9–28 stems per species: Table 1) and between 5% and 9% within sites (across up to five focal species within each site) (Fig. 2). The magnitude of WD variation was similar when calculated from average species wood density values (i.e. species WD means only, SD = 0.09, n = 7) versus from all intraspecific wood density values pooled together (i.e. including intraspecific variation, SD = 0.11, n = 255). The coefficient of variation (CV) for [C] ranged between 21% and 62% within species and 16% and 57% within sites (across species within each site). Mean [C] (46.1 ± 1.6%; SD) calculated from all 254 wood samples was comparable to the pantropical mean for angiosperms (Fig. 2b; 45.6 ± 0.2%: Martin et al. (2018)), however, estimates of [C] from WD using the best available equation (Martin et al. 2018) tended to over-estimate [C] by 0.8% mass (–0.6% to 2.5%) at species level and by –8.3% to 12.4% in individual samples.

## Assessing height:diameter model choice

The 20 QPRP-CSIRO plots differed substantially in H:DBH allometry based on H$_{meas}$ and DBH$_{meas}$ errors (Table S3). The

H:DBH allometric model stratified by site was significantly better than the unstratified, regional model (ANOVA: F = 19.018(57, 18425), P < .001). Site-level empirical H:DBH models minimized both random error and systematic bias in H$_{mod}$, while our regional empirical model generated slightly more uncertainty (Table 2, Fig. 5). Models derived at larger biogeographic scales consistently resulted in over-estimates of plot-level AGB. The Australia-region H:DBH model (Feldpausch et al. 2012) demonstrated a mean individual H$_{mod}$ bias of 12.5% (+1.5 m), which scaled to a mean plot-level AGB bias of 7.7%. One pantropical H:DBH model (Feldpausch et al. 2012) generated a mean individual H$_{mod}$ bias of 17.2% (+2.3 m) and a mean plot-level AGB bias of 16.9%; the second pantropical H:DBH model (Chave et al. 2014) generated a mean individual H$_{mod}$ bias of 71.0% (10.5 m) and a mean plot-level AGB bias of 66.6% respectively (Table 2), with mean plot-level AGB bias ranging from 25.8 to 101.1% among plots. Precision in plot-level AGB (percentage errors) generally declined for larger size classes (Fig. 5).

## Simulations of uncertainty in forest carbon

The magnitude of mean uncertainty around per-hectare C$_{AGB}$ (standard deviation of plot-level C$_{AGB}$ normalised to regional mean C$_{AGB}$) ranged from 1.9% to 5%, depending on the choice of the H:DBH allometric model (Table S4). Biases in C$_{AGB}$ increased with the scale at which the H:DBH model was defined (Fig. 5a, Table 2, Table S4), being greatest for the Chave et al. (2014) pantropical H:DBH model (mean plot-level bias 34.1%) (Table S4).

The magnitude of mean uncertainty around per-hectare C$_{AGB}$ arising from measurement errors was as follows: ±0.2% from DBH$_{meas}$ (0.3 Mg C ha⁻¹); ±4.8% from H$_{meas}$ (11.1 Mg C ha⁻¹); and 4.4% from DBH$_{meas}$ and H$_{meas}$ errors combined (10.3 Mg C ha⁻¹). The magnitude of uncertainty around per-hectare C$_{AGB}$ arising from within-species variation in WD and [C] was small: ±3.2% (6.8 Mg C ha⁻¹) and ±0.7% (1.5 Mg C ha⁻¹), respectively (Fig. 5b, Table S4).

Given information on H$_{meas}$, DBH$_{meas}$, WD, and [C] variation, as well as uncertainty associated with the best-performing (site-level) H:DBH model, resulting uncertainty around per-hectare C$_{AGB}$ was ±4.5% or 10.4 Mg C ha⁻¹ (Fig. 5b: Table S4). Under any of the information scenarios, C$_{AGB}$ varied by 26%–32% among plots (Table S4).

# Discussion

We assessed the uncertainty around mean per-hectare C$_{AGB}$ given allometric and within-species wood trait variation for 20 floristically and structurally diverse plots in Australian moist tropical rainforest (Fig. 1a). The choice of the H:DBH allometric model generated the largest uncertainty around forest carbon estimates, with site-level models performing notably better than pantropical ones. Height measurement errors contributed most uncertainty to per-hectare C$_{AGB}$ (4.9% within-plot SD: Table S4), whereas diameter measurement error had a negligible effect (0.1%). Within-species variation in wood density contributed substantially more uncertainty (1.7%) to C$_{AGB}$ than within-species variation in [C] (0.7%). Given information on all these sources of uncertainty together, and assuming the use of site-level H:DBH models, the average random error on per-hectare C$_{AGB}$ was 6.4% while the mean bias across plots was 9.8% (Table S4).

Allometric and within-species trait variation thus appear to contribute considerably less uncertainty to C$_{AGB}$ than that associated with either AGB allometric models (10%–20%: Keller et al. 2001, Chave et al. 2004, Molto et al. 2013) or sampling issues
<figure><img src="image_6.png" /><figcaption>**Figure 4.** Wood density (LHS) and woody tissue carbon content (RHS) across species (top panels, in dark grey: n = 255 wood cores, 98 stems, 5 sites) and within-species (see Table 1 for species names, codes, sample sizes). Species are represented by the same colours for wood density and carbon content. LHS: dashed blue line indicates median wood density for all tree species in the QPRP-CSIRO plot network (unpublished data, CSIRO, n = 770 samples, 460 tree species). RHS: dashed red line indicates the current best estimate of mean [C] for tropical angiosperms (Martin et al. 2018). RHS: light-grey density distribution (dotted line marked at median for visual aid) depicts estimates of [C] derived from our WD measurements using a global regression equation (Martin et al. 2018).</figcaption></figure>

<figure><img src="image_7.png" /><figcaption>**Figure 5.** Size dependency of errors for aboveground biomass (AGB) derived from five H:DBH allometric model sets. Mean error (ME, sum of individual errors) was calculated for each 10 cm DBH size class in each plot and normalized to AGB in that sample. Points represent average ME across plots, with confidence intervals at two standard errors. Errors are shown for five model sets: site-level models derived from training data at each site (i.e. 20 models), a regional model derived from training data at all sites combined (one model, n = 20 sites), an Australian-region model from the literature and two pantropical models (Feldpausch et al. 2012, Chave et al. 2014). Total sample sizes for each size class were: 10–19.9 cm = 4553, 20–29.9 cm = 1325, 30–39.9 cm = 651, 40–49.9 cm = 380, 50–59.9 cm = 197, 60–69.9 cm = 105, 70–79.9 cm = 68, 80–89.9 cm = 43, 90–99.9 cm = 27, >100 cm = 35.</figcaption></figure>

related to the size and representativeness of the plot (roughly 10% for a total sample size of 5 ha: (Clark and Clark 2000, Chave et al. 2004). Note that the impact of sampling uncertainties is sensitive to the number and size of plots sampled. An additional 16% random error is associated with weight measurements of AGB to construct AGB allometric equations according to traditional methodologies (Chave et al. 2004). We did not assess uncertainty

caused by partial sampling of a heterogeneous landscape or uncertainties in the biomass of other life forms (Chave et al. 2004, Malhi et al. 2006), which we have not estimated here. Below, we provide further discussion of uncertainties arising from within-species wood trait variation, H:DBH allometric variation, and measurement errors and provide recommendations to help guide data collection under realistic scenarios.
<table><caption>**Table 2.** Accuracy (bias) and precision (variation) of five *H:DBH* allometric models derived at different biogeographic scales. Errors were calculated by comparing measured tree heights (*H*<sub>meas</sub>) with modelled tree heights (*H*<sub>mod</sub>). Plot-level accuracy and bias measures were based on aboveground biomass (AGB) estimates derived from *H*<sub>meas</sub> versus *H*<sub>mod</sub>. Accuracy measures are mean error (ME) and symmetric signed percentage bias (SSPB). Precision measures are median symmetric accuracy (MSA) and root mean squared error (RMSE). AGB error measures were normalised to plot-level AGB. Minimum and maximum errors for plots are given in square brackets.</caption><thead><tr><th rowspan="2">H:DBH allometric model</th><th colspan="3">Tree H</th><th colspan="2">Plot-level AGB</th><th rowspan="2">Reference</th></tr><tr><th>ME (m)</th><th>SSPB (%)</th><th>MSA (%)</th><th>ME (%)</th><th>RMSE (%)</th></tr></thead><tbody><tr><td>Site level</td><td>-0.1</td><td>0.2</td><td>16.7</td><td>-1.2 [-10.4, 2.5]</td><td>2.6</td><td>This study</td></tr><tr><td>Regional</td><td>0.0</td><td>1.9</td><td>17.2</td><td>1.4 [-11.6, 21.0]</td><td>7.8</td><td>This study</td></tr><tr><td>Feldpausch Aus</td><td>1.5</td><td>12.5</td><td>19.4</td><td>7.7 [-7.6, 32.5]</td><td>9.6</td><td>(Feldpausch et al. 2012)</td></tr><tr><td>Feldpausch panrop.</td><td>2.3</td><td>17.2</td><td>21.5</td><td>16.9 [1.8, 39.7]</td><td>16.3</td><td>(Feldpausch et al. 2012)</td></tr><tr><td>Chave panrop. (E)</td><td>10.5</td><td>71.0</td><td>71.1</td><td>66.6 [-25.8, 101.1]</td><td>68.3</td><td>(Chave et al. 2014)</td></tr></tbody></table>

<figure><img src="image_8.png" /><figcaption>**Figure 6.** Carbon concentration in aboveground biomass (C<sub>AGB</sub>) estimated from simulations of tree height (H), diameter (DBH), wood density (WD), and woody tissue carbon content [C]. Simulations were based on data for living trees in the QPRP-CSIRO network (20 sites, 7210 stems). Simulations approximate mean uncertainty in C<sub>AGB</sub> arising from: (LHS) choice of *H:DBH* allometric models derived at different biogeographic scales; (RHS) other sources, including *H* measurement errors (*H*<sub>meas</sub>), DBH measurement errors (DBH<sub>meas</sub>), and within-species variation in WD and/or [C]. Plotted is mean plot-level C<sub>AGB</sub> ± 2 SD (20 sites, each site first summarized as the mean of 1000 simulations), where SD is the mean of within-site standard deviations (also based on 1000 repeat simulations for each site). C<sub>AGB</sub> estimated using site-level *H:DBH* models is plotted on both panels (with a triangle) ± 2 SD (shaded grey), to aid visual comparisons.</figcaption></figure>

## Variation in wood density and woody tissue carbon content

Though limited by sample size, our analysis indicates that species differ in their patterns of WD variation among sites and in relation to tree size. This is consistent with our expectations that species phenotypic plasticity differs and could be driven by a myriad of climate, ecological, or site characteristics in addition to phylogenetic differences (Patiño et al. 2009, Richardson et al. 2013, Martin

et al. 2018). Our measured within-species WD variation (<15%, 7 species, n per species >9) was of similar magnitude to one prior estimate (10%, 42 species, n per species >6) (Chave et al. 2004) and consistent with suggestions that among-site WD variation accounts for no >20% of observed WD variation (Sungpalee et al. 2009, Siefert et al. 2015). Certain aspects of our wood sampling approach may variously lead to under- or over-estimation of WD variation. We did not sample across the full biogeographic extent of each species, for example, and we sampled the most abundant species, which may have more variable wood traits than less common, more ecologically restricted species.

Given the small uncertainty in C<sub>AGB</sub> originating from within-species WD variation (1.7%), WD databases should continue to prioritise greater species-level representation, which will help reduce total error in forest carbon estimates (Phillips et al. 2019). Nonetheless, greater characterisation of within-species WD variation would be useful in advancing our capacity to predict biogeographic and age- and size-related variations in WD that influence C<sub>AGB</sub>. The nature of size-related WD variation is still not well characterized, despite suggestions that the magnitude of this variation could be similar to species differences (Fortunel et al. 2020) and larger than site differences (Sungpalee et al. 2009, Siefert et al. 2015). We found that WD is lower in smaller DBH stems, consistent with some prior studies (Elias and Potvin 2003, Sungpalee et al. 2009), though Ma et al. (2020) reported WD increased with DBH. WD has also been shown to change radially through the stem and with height in the stem, in a nonsystematic manner (Plourde et al. 2014, Burt et al. 2020). In addition to mediating forest biomass at scale (Baker et al. 2004), WD variation is important to understand because it appears to be a main trait indicating drought mortality risk (O'Brien et al. 2017). More dense wood also likely has higher [C] (Elias and Potvin 2003), likely due to changes in cell wall thickness (Thomas et al. 2007, Buttò et al. 2021).

Although within-species [C] variation was greater than for WD, variation in [C] contributed less to C<sub>AGB</sub> uncertainty because of the small value of the [C] coefficient. In fact, our simulations indicate a more minor influence of [C] on C<sub>AGB</sub> than prior work, which suggested that better consideration of species differences in [C] could reduce the random error around C sequestration estimates by up to 10% (Elias and Potvin 2003), and could correct systematic errors by 1.6%-5.8% (Thomas and Martin 2012). Our simulations of within-species [C] variation suggest that species-level information is likely to provide sufficient accuracy and precision for forest carbon estimates.

The collation of a Global Woody Tissue Carbon Concentration Database (GLOWCAD) is already underway, with 3676 records
available for 864 species (Doraisami et al. 2022). Although this
 extends the database assembled by Martin et al. (2018) (n = 2228,
 636 species), both data collections still pale in comparison to the
 species richness of tropical forests globally and are far from being
 representative. Roughly one third of these data are from tropical
 forests, but there are no records from Australian tropical forest
 species and almost none from the Asian tropics. Our analysis
 appears to corroborate this under-sampling issue in two ways.
 First, despite similar mean [C] from our data as for tropical
 angiosperms globally (Martin et al. 2018), when we attempted to
 predict [C] from WD using the global regression equation in Martin
 et al. (2018), we systematically over-estimated [C], suggesting the
 equation itself is not representative of species at Australian sites.
 Second, the positive correlation between [C] and WD that we
 found at the interspecies level (R² = 0.292) was lost when species
 differences were accounted for using random effects. As such,
 we caution that equations to estimate [C] should be applied with
 care. We suggest that researchers prioritize the collection of new
 [C] data and further explore the factors that drive variation in
 [C] within and between species, including climate and ontogeny.
 Continued efforts to extend GLOW-CAD and similar databases
 will enable further understanding of [C] and WD variation and
 their effects on forest carbon uncertainties.

Height:diameter allometric model choice

Our simulations showed that overestimation of *H* by pantropical *H*:DBH models (by 17%–71%) compounded to over-estimation of mean *C*<sub>AGB</sub> by 34.5%. Total error and bias associated with the choice of *H*:DBH allometric model increased from site- to regional- to pantropical models, consistent with other work (Feldpausch et al. 2012, Ledo et al. 2016, Sullivan et al. 2018, Terryn et al. 2024) and the expectation that local models better account for environmental conditions, disturbance history, and forest structure. That *H* and AGB bias differed substantially among plots (Table 2) further implicates the importance of allometric variation within regions, due to differences in vegetation structure, history, and climate (Table S1). We thus strongly favour development of (at least) regional-scale—rather than pantropical—allometric equations for the major continental groupings of forests in each biome.

Our findings clearly indicate that direct measures of *H* should
be made at as many sites with appropriate stem counts as possi-
ble, either to enable the derivation of site-level *H*:DBH allometries
or to at least ensure that diverse site-specific *H*:DBH relationships
are represented in regional models. This might be achieved with
small samples of trees (as little as 20–50, or 8% of trees in a
1 ha plots), particularly when including the largest trees, and
can reduce hectare-scale uncertainty around AGB (Hunter et al.
2013, Sullivan et al. 2018). Acknowledging that resources are often
limited, it may be preferable to prioritise *H* measurements in sites
that are particularly impacted by disturbance or environmental
stress. At such sites, where shorter trees are likely to dominate at
a given DBH, using local *H*:DBH models should go a long way to
reducing overestimation of regional or pantropical forest carbon
(Brown et al. 1989, Chave et al. 2005).

Bias resulting from the use of pantropical *H*:DBH models was
large and probably arises due to insufficient representation of
Australian moist tropical forest in the data used to construct
the models. Australian tropical forests are somewhat structurally
distinct from other continents, among the most short-statured
at a given DBH (Feldpausch et al. 2011) and have among the
highest basal area per hectare of any tropical forests globally
(Feldpausch et al. 2012, Bradford and Murphy 2019). There are,

however, general inconsistencies in the biases resulting from use
of pantropical models in different systems. Feldpausch et al.
(2012) reported similar AGB uncertainties resulting from use of
their *H*:DBH models as found in our study; however, Chave et al.
(2014) reported much greater bias when using the Feldpausch
et al. (2012) *H*:DBH model. In contrast, Chave et al. (2014) reported
a mean AGB bias of 5.31% for their pantropical model, but the
same model generated a mean plot-level AGB bias of 66.6% at
QPRP-CSIRO sites. These inconsistencies might indicate differ-
ent suitability of allometric equations among contexts (even for
models derived from global datasets) or, to some extent, because
of differences between how errors are calculated among stud-
ies. Practitioners may wish to evaluate the appropriateness of
pantropical and regional *H*:DBH allometric equations for a given
application by quantifying model errors in relation to a subset of
tree *H* measurements for their study area.

We also note some inconsistencies in the size-dependence of
errors among *H*:DBH models, which mirror observations that, for
different forest types, *H*<sub>meas</sub> bias can increase or decrease with *H*
(Terryn et al. 2024). Chiefly, the regional Feldpausch et al. (2012)
model tended to over-estimate *H* (and therefore AGB) of small
trees (Fig. 5), which could result in overestimation of forest carbon
at sites with more small stems. Large bias across size classes
resulting from use of the Chave et al. (2014) pantropical *H*:DBH
model is of particular concern. They may reflect prior suggestions
that inclusion of climate parameters in allometric models is not
universally advantageous (Hunter et al. 2013) or may reflect the
shortcomings of using gridded climate data products in topo-
graphically complex regions like tropical Queensland. Biases, in
particular in large size classes, can substantially shift per-hectare
AGB estimates (Molto et al. 2013), since large trees contribute
disproportionately to plot-level biomass (Bradford and Murphy
2019). Future work might emphasize site-level measurements
of climate to better explain site-level vegetation structure and
allometry. In any case, we recommend that practitioners avoid
use of generic allometric equations and instead derive site-level
or regional models wherever feasible.

Deployment of TLS has led to recent publication of the first
pantropical H:DBH allometric equations based on TLS-derived H
measurements rather than traditional inventory measurements.
This work suggests that H:DBH models derived from traditional
inventory methods tend to underestimate H across the range of
H (Terryn et al. 2024), consistent with prior characterizations of
the error distributions associated with traditional measurement
techniques (Hunter et al. 2013, Larjavaara et al. 2013), which were
used to account for H measurement error in our simulations
here. This TLS-derived pantropical model is associated with mean
uncertainty of 19.1% and mean bias of -4.8% (Terryn et al. 2024)—
uncertainties of a similar magnitude to the pantropical models
evaluated here. TLS clearly offers promise for rapid development
of H measurement databases, which should be used to derive
local-scale H:DBH allometries; however, the use of TLS-derived
H measurements as inputs to AGB models derived from under-
estimates of H (using traditional inventory methods) may lead
to over-estimation of AGB (Terryn et al. 2024). Of course, if the
goal is to convert from tree volumes to biomass and carbon, LS
methods also rely on prior inventory measurements and botanical
identification in order to match stems with appropriate wood
density values.

Height measurement error

The approximated -2.1 m downward bias for *H*<sub>meas</sub> (Hunter
et al. 2013, Larjavaara et al. 2013) scaled to an average 8.1%
under-estimation of per-hectare C<sub>AGB</sub> (Table SIV). This estimate is very similar to a prior scaling of clinometer measurement errors, which resulted in an average uncertainty of 6% in plot-level biomass (Hunter et al. 2013). The real magnitude of AGB underestimation from H<sub>meas</sub> bias is not well defined in our study, however, as it depends strongly on description of the H measurement error distribution. Clinometer measurements (tangent method) have variously been shown to overestimate H of tall trees, and the precision of this method is probably size-dependent, between 3% and 20% of total H (Williams et al. 1994, Hunter et al. 2013). Some authors have approximated this imprecision as 10% of total H (Chave et al. 2004), but laser rangefinder measurements (sine method) can be biased by >100% (Larjavaara et al. 2013). By way of comparison to allometric approaches, the RMSE of AGB estimates made from high-resolution, space-borne LS by Global Ecosystem Dynamics Investigation (GEDI) is 30%-40% (Dubayah et al. 2020).

Laser scanning methods provide a new scope to reduce the error associated with *H* measurement and AGB estimation (de Tanago et al. 2017). One group reported a 15-fold improvement in accuracy from TLS over allometric estimation of AGB (Burt et al. 2021). In addition, some work suggests that, while allometric uncertainty can increase exponentially with tree size, TLS uncertainty does not (Calders et al. 2015). Given these advantages, TLS combined with UAV-LS will very likely provide more accurate and scalable measurements of *H* and AGB in the coming decades (Brede et al. 2022, Terryn et al. 2022). The application of these sensor methods to AGB estimation remains limited at present, due to the still high cost of the technology and limited global availability. This need will likely be addressed in the coming years with additional support from the GEO-TREES initiative and the European Space Agency's Radar-based BIOMASS Mission (launched in 2025). Canopy climbing approaches could provide more accurate *H* measurements than traditional methods and help bridge the 'accuracy gap' until broader rollout of LS methods is achieved; however, the intensive resourcing required to support such an approach is widely prohibitive.

There is also scope to use statistical methods which include measurement error on the component variables of C<sub>AGB</sub> to fit allometric models that better reflect these inherent uncertainties. Given the extent to which H<sub>meas</sub> errors scale to C<sub>AGB</sub>, it may be preferable to establish baselines of H error distributions at each study site, via repeat measurements of H by different field technicians, to enable accounting for the influence of H<sub>meas</sub> errors on estimates of AGB and continued use of traditional allometric approaches. Doing so would supplement the use of LS technologies where location or resourcing do not currently support their use and support further development of LS technologies by improving the association between traditional inventory measurements and those from LS.

## Conclusion

H:DBH models from the literature tended to over-estimate *H* and lead to highly variable C<sub>AGB</sub> uncertainty among plots, whereas site-level H:DBH models minimized total error and bias for estimates of *H*, AGB, and C<sub>AGB</sub>. Height measurement error introduced roughly 5% uncertainty to per-hectare estimates of forest carbon, which is appreciable but relatively small in comparison to the uncertainties associated with pantropical H:DBH and AGB allometric models. Within-species WD variation and [C] variation contributed <3% uncertainty to C<sub>AGB</sub>; thus, efforts to database WD and [C] values should remain directed towards species-level

(rather than within-species) records. Current pan-biome equations to estimate [C] from WD exhibit inconsistencies that require further development and should be applied with caution.

All existing and planned remote sensing datasets rely on field data and allometric estimates for calibration (Dubayah et al. 2020, Brede et al. 2022). While increasing use of TLS will likely reduce *H* and AGB measurement error, current limitations of these methods necessitate the continued development of robust allometric approaches that rely on inventory data. The pursuit to constrain uncertainties around forest carbon estimates has direct implications for detection of forest changes through time and should underpin ongoing assessments of the carbon budgets needed to limit global warming below 2°C.

## Acknowledgements

We acknowledge the work of Dr Geoff Stocker to establish the QPRP plots used in this study, as well as the funding and administration support of CSIRO. We also acknowledge the CSIRO staff and many fieldwork volunteers who have maintained and censused the plots since 1971, and the many traditional owner groups who are custodians of these lands.

## Author contributions

Hannah Jayne Carle (Conceptualization, Data curation, Formal analysis, Funding acquisition, Investigation, Methodology, Resources, Validation, Visualization, Writing—original draft, Writing—review & editing), Teresa Neeman (Conceptualization, Methodology, Writing—review & editing), Helen Murphy (Conceptualization, Data curation, Funding acquisition, Investigation, Resources, Writing—review & editing), David Bauman (Conceptualization, Data curation, Writing—original draft, Writing—review & editing), Oliver Binks (Investigation, Writing—review & editing), Ingrid Coughlin (Conceptualization, Investigation, Methodology, Writing—review & editing), Andrew Ford (Investigation, Resources, Writing—review & editing), Adrienne Nicotra (Funding acquisition, Investigation, Project administration, Supervision, Writing—original draft, Writing—review & editing), and Patrick Meir (Conceptualization, Investigation, Project administration, Supervision, Writing—original draft, Writing—review & editing)

## Supplementary data

Supplementary data are available at *Forestry Journal* online.
*Conflict of interest*: None declared.

## Funding

This work was supported by a seed grant funding from the Research School of Biology, The Australian National University to H.C., Australian Government Research and Training Partnership scholarship to H.C., European Union's Horizon 2020 research and innovation program under the Marie Skłodowska-Curie grant agreement no. 895799 to DB, and Catalan Science and Technology grant, Beatriu de Pinós, BP2021 00224 to OB.

## Data availability

Data supporting these results can be found as cited in-text or can be released on request from Helen Murphy, CSIRO.
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