# Allometric Equations to Estimate Aboveground Biomass in Spotted Gum (Corymbia citriodora Subspecies variegata) Plantations in Queensland

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

^{2}(Δ adj. R

^{2}from 0.099 to 0.135) but did not improve AIC, bias and MAPE. Using the single variable of CV to estimate aboveground biomass (AGB) was better than CD, with smaller AIC and MAPE less than 2.3%. We demonstrated that the allometric equations developed and validated during this study provide reasonable estimates of Corymbia citriodora subspecies variegata (spotted gum) biomass. This equation could be used to estimate AGB and carbon in similar spotted gum plantations. In the context of global forest AGB estimations and monitoring, the CV variable could allow prediction of aboveground biomass using remote sensing datasets.

## 1. Introduction

^{−1}of CO

_{2}equivalents in the main stem of the trees by age 10 [13]. The amount of CO

_{2}equivalents accumulated was up to 184 t ha

^{−1}and 159 t ha

^{−1}at an age of 10 years in the coastal Wide Bay Burnett and Central Coast—Whitsunday regions, respectively in Queensland [13]. However, the lack of allometry based on destructive sampling of trees biomass could result in inaccurate estimates of biomass and carbon accumulation for mature plantations and the estimates of Lee et al. (2011) [13] did not account for the carbon in other tree components (such as branches and leaves).

_{2}sequestration rates [14], production of biofuels, and electricity using biomass residues [12]. Several allometric models for estimating forest biomass have been established worldwide, and there are over 400 models for biomass estimation in natural forests and plantations in Australia [3,15]. The majority of these estimates were developed for natural forests such as those dominated by Eucalyptus species [3,16,17,18,19,20,21]. Biomass datasets derived through destructive sampling for spotted gum (CCV) are relatively rare and have not been published in Queensland. A study by Garcia-Florez et al. (2019) [12] sampled 16-year-old plantation grown CCV trees southwest of Lismore in north-eastern New South Wales, Australia, to estimate individual above-ground biomass components (stem, branches, bark, and crown) but not total AGB. In a native forest near Batemans Bay in southern coastal New South Wales, Ximenes et al. (2006) [22] destructively sampled 122 spotted gum (Corymbia maculata) trees to predict total AGB and commercial log biomass. However, it is difficult to ascertain whether these models could be fit in spotted gum plantations in Queensland.

## 2. Materials and Methods

#### 2.1. Study Area and Datasets

#### 2.2. Data Collection

- Prior to sampling, each sample tree was identified and provided with an ID number. Tree diameter over bark at breast height 1.3 m (D, cm) was recorded.
- Most of trees were felled using a chainsaw. However, an excavator was used to push 23 trees onto the ground as these trees were also used to determine belowground biomass [44]. After the tree was felled, total tree height (H, m) was recorded.
- Sample trees were divided into three biomass components: (1) stem; (2) large branches (>2 cm diameter); and (3) small branches (<2 cm diameter), along with foliage, buds, capsules, or flowers. These components were weighed using digital scales and fresh weight (kg) was recorded.
- For each tree, sub-samples (at least 2 kg) of these biomass components were taken to the laboratory for determining moisture content (MC%). From the base of bole to the height of the first limiting defect of each tree, a 40 mm wide disk was taken every 3.0 m for laboratory analysis.
- In the laboratory, the large branch and small branch samples were cut into small pieces and dried at 65–105 °C (as appropriate for the type of sample) until a constant weight was achieved. Stem disks were used to estimate green wood density (ρ, kg m
^{3}) prior to drying.

- 6.
- Crown diameter (CD, m) was measured before felling the trees (at step 1). The CD measurements were taken for each tree using a tape measure, averaging the measurements from along and across the planting row.
- 7.
- In the laboratory (at step 5), stem bark was removed from the disks, recording fresh weight of the bark and wood. The samples were dried, and oven-dry weight was determined. In addition, the average width of chainsaw cuts used to collect the discs was used to determine mass of sawdust based on the wood density (ρ kg m
^{−3}). The sawdust weight was added to the stem biomass. The formula for estimating stem bark and sawdust was described by Huynh et al. (2021) [45].

#### 2.3. Data Analysis

#### 2.3.1. Variable Selection and Data Preparation

^{−1}) of each tree component, such as stems, branches and foliage were described by Huynh et al. (2021) [45]. Predictor variables were the respective diameter at breast height (D), height (H), wood density (ρ), crown diameter (CD) and crown volume (CV). The CV was calculated based on crown diameter (CD, m). We presumed that the spotted gum crowns could have many different solid shapes such as a sphere, ellipsoid, cylinder, cone, and paraboloid. These shapes were calculated using different formulas in the literature as outlined by Zhu et al. (2021) [46]. We tested five formulas based on five shapes, with the sphere being selected as the most appropriate and representative shape for spotted gum.

^{3}) and CD is crown diameter (m).

#### 2.3.2. Model Fitting

^{β}+ ε was used to develop the allometric relationship between AGB (Y) and predictor variables (X). Power-law equations can be fitted as logarithmic transformations of the original data ln (Y) = ln(a) + ln(X), or as nonlinear models [47,48,49]. The application of logarithmic transformations is widely used for estimating tree biomass [3,20,39,50,51]. However, testing general AGB models for tree biomass across Australia by Paul et al. (2016) [20] recommended that weighted nonlinear modeling should be used for tree diameters over 10 cm. Huynh et al. (2021) [44] compared log-linear and nonlinear equations for predicting belowground biomass (BGB) and results showed that the overall performance of weighted nonlinear models was better than log-linear models. This result also consists of findings from Huynh et al. (2019) [49], who reported that nonlinear models produce higher reliability. In addition, we also pre-analyzed AGB equations using Furnival’s Index (FI) [50,51,52]. Preliminary results (Table S1) showed that FI values of weighted nonlinear models were lower than log-linear models. Hence in this study, we focused on weighted nonlinear regression models to develop AGB models. Weighted nonlinear models had the following general form:

^{−1}; α and β are the parameters of the model; X

_{ij}is the covariate: D (cm), H (m), ρ (kg m

^{−3}) CD (m) and CV (m

^{3}), or a combination of these variables for i

^{th}sampled tree; and ε

_{ij}is the random error related to the i

^{th}sampled tree. The variance function (ε

_{ij}) [53,54] was described in Huynh et al. (2021) [44]. In this study, the weighting variables include D, D

^{2}H, ρ, D

^{2}HCD and D

^{2}HCV.

^{β}; AGB = α × H

^{β}; AGB = α × CD

^{β}and AGB = α × CV

^{β}) were developed.

#### 2.3.3. Model Assessment and Selection

^{2}(adj. R

^{2}); (iii) average bias, (iv) root mean square error (RMSE) and (v) mean absolute percentage error (MAPE). In addition, diagnostic plots were also used to check for possible outliers and assess the goodness of fit of the models. The optimal models will have the lowest AIC, bias, RMSE and MAPE; low levels of collinearity as well as a high adj. R

^{2}. These criteria were described by Huynh et al. (2021) [44].

#### 2.3.4. Model Cross Validation

^{2}, percent bias, RMSE and MAPE [54,59,60]. Finally, a model with the fewest errors was selected as follows:

## 3. Results

#### 3.1. Basic Measurements and Tree Component Biomass

^{−3}at age of nine in trial 451D and this value increased to 736.5 kg m

^{−3}by age 20 at the same site (Table 1). There was significant variability in wood density among sites and ages (p-value = 0.007; df = 4; F-value = 3.95). The individual tree AGB among the three sites ranged from 43.9 to 1503.7 kg tree

^{−1}(Table 3).

^{−1}, whereas maximum AGB of mature trees ranged from 149.4 to 1503.7 kg tree

^{−1}. There was variation among tree components, the weight of stem was higher than other components such as large branches, small branches, and leaves (Table 3). The relative proportions of the aboveground tree biomass components are presented in Figure 1. The highest proportion of biomass was in potentially commercial logs (60.3%) while the smallest proportion was small branches and leaves.

#### 3.2. Data Exploration and Variable Selection

#### 3.3. Allometric Equations for AGB

#### 3.3.1. Including Predictor Variables Height and Wood Density

^{2}H (Equation (6)) improved adj. R

^{2}(0.975) in comparison to Equation (3) with an adj. R

^{2}= 0.963. The combination of D

^{β}× H

^{β1}(Equation (5)) and D

^{β}× ρ

^{β1}(Equation (7)) provided similar goodness of fit criteria (AIC = 546.3, adj. R

^{2}= 0.973 and MAPE = 0.0132 %). Adding three predictor variables D, H and ρ into the model (Equations (8) and (9)) reduced RMSE and MAPE, but it did not improve the AIC compared with Equation (3).

#### 3.3.2. Including CD and CV in Biomass Equations

^{2}. The adj. R

^{2}increased when adding a combination of CD-H and CD-H-ρ, with the changes in adj. R

^{2}from 0.950 (Equation (12)) to 0.967 (Equation (16)).

^{2}(0.970) relative to the combination of D and CV. Using CD (Equation (12)) and CV alone (Equation (18)) had the same value of AIC (532.6), but Equation (18) improved AGB estimates, increasing adj. R

^{2}and reducing bias, RMSE and MAPE.

#### 3.4. Cross Validation Biomass Models

#### 3.4.1. Models Using Diameter, Height and Wood Density

^{2}= 0.642) while the model using D (Equation (3)) proved to be the best (Table 5), with the lowest values of AIC = 434.4, bias = −2.2% and MAPE = 7.2% (Table 5). Adding H and ρ as a second or third variable improved the adj. R

^{2}(Δ adj. R

^{2}from 0.099 to 0.135) whereas other criteria such as AIC, bias and MAPE did not improve (Table 5).

#### 3.4.2. Models Using Crown Diameter and Crown Volume

#### 3.4.3. Cross Validation against an Independent Dataset

## 4. Discussion

#### 4.1. Equation Development and Cross Validation

^{+}cm diameter. Therefore, we suggest tree biomass equation development considers nonlinear models for large trees.

#### 4.2. Inclusion of Height and Wood Density

^{2}values while other model criteria did not improve (Table 5). Findings from van Niekerk et al. (2020) [27] also showed that adding H and ρ into allometric equations, resulted in the mean square error becoming only slightly higher than the D-based model. Our finding is also consistent with Sileshi (2014) [41] who found a small improvement in AGB prediction when H and ρ were included. The highest adj. R

^{2}(Δ adj. R

^{2}= −0.149) was found with D

^{2}H in combination (Equation (6)). However, the largest adj. R

^{2}is not the most commonly used criteria to determine the best model, as the addition of polynomial terms increases the adj. R

^{2}[20,41]. Some authors [64,65,66,67,68,69] found that D

^{2}H improved the accuracy of biomass equations. By contrast, other studies agreed that D-based allometry is a better predictor of AGB [20,27,41,70,71] based on a combination of criteria (AIC, adj. R

^{2}, bias and MAPE).

#### 4.3. Influence of Crown Diameter and Crown Volume

^{2}= 0.255 in Equation (11) while Δ AIC = −71.1 and Δ adj. R

^{2}= −0.084 in the Equation (18), and diagnostic plot (Figure S3) indicating narrow variation (Table 5 and Table S3). This finding is consistent with the results of Goodman et al. (2014) [69] and van Niekerk et al. (2020) [27] who found that using crown radius of large trees improved predicted biomass models more than height. Validation models using our data imply that using crown volume was particularly important for building confidence in estimating biomass/carbon and could potentially be applied to accurately predict AGB using remote sensing tools such as LiDAR.

#### 4.4. Evaluating Existing Applicability Models

## 5. Conclusions

^{β}, performed better than equations with other variables such as H, ρ, CD, and CV, with the lowest values of AIC, bias and MAPE. Adding more tree variables to the model led to increased adj. R

^{2}while other criteria did not improve when compared with the D-based model. A combination of D and ρ in Equation (7) had slightly improved errors compared to the equation with D and H (Equation (5)). As an alternative to the D-based equation, an equation using CV (Equation (18)) was better than applying models based on H or CD. However, additional work is needed to test the application of crown variables to predict biomass in unrepresented regions and species.

## Supplementary Materials

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

- Zolkos, S.G.; Goetz, S.J.; Dubayah, R. A meta-analysis of terrestrial aboveground biomass estimation using lidar remote sensing. Remote Sens. Environ.
**2013**, 128, 289–298. [Google Scholar] [CrossRef] - Shao, G.; Shao, G.; Gallion, J.; Saunders, M.R.; Frankenberger, J.R.; Fei, S. Improving Lidar-based aboveground biomass estimation of temperate hardwood forests with varying site productivity. Remote Sens. Environ.
**2018**, 204, 872–882. [Google Scholar] [CrossRef] - Eamus, D.; Burrows, W.; McGuinness, K. Review of Allometric Relationships for Estimating Woody Biomass for Queensland, the Northern Territory and Western Australia; Australian Greenhouse Office: Canberra, NSW, Australia, 2000.
- Canadell, J.G.; Raupach, M.R. Managing forests for climate change mitigation. Science
**2008**, 320, 1456–1457. [Google Scholar] [CrossRef] [PubMed][Green Version] - Phillips, D.L.; Brown, S.L.; Schroeder, P.E.; Birdsey, R.A. Toward error analysis of large-scale forest carbon budgets. Glob. Ecol. Biogeogr.
**2000**, 9, 305–313. [Google Scholar] [CrossRef] - IPCC. Guidelines for National Greenhouse Gas Inventories. Agriculture, Forestry and Other Land Use; IGES: Hayama, Japan, 2006; pp. 1–66.
- IPCC. 2019 Refinement to the 2006 IPCC Guidelines for National Greenhouse Gas Inventories. 2019. Available online: https://www.ipcc.ch/report/2019-refinement-to-the-2006-ipcc-guidelines-for-national-greenhouse-gas-inventories/ (accessed on 10 December 2021).
- Lee, D.J. Achievements in forest tree genetic improvement in Australia and New Zealand 2: Development of Corymbia species and hybrids for plantations in eastern Australia. Aust. For.
**2007**, 70, 11–16. [Google Scholar] [CrossRef] - Lee, D.J.; Huth, J.R.; Osborne, D.O.; Hogg, B.W. Selecting hardwood varieties for fibre production in Queensland’s subtropics. In Proceedings of the 2nd Australasian Forest Genetics Conference: Book of Abstracts; Forest Products Commission: Kalgoorlie, WA, Australia, 2009. [Google Scholar]
- Salcedo, P.G.; Maraseni, T.N.; McDougall, K. Carbon sequestration potential of spotted gum (Corymbia citriodora subspecies Variegata) in South East Queensland, Australia. Int. J. Environ. Stud.
**2012**, 69, 770–784. [Google Scholar] [CrossRef] - McMahon, L.; George, B.; Hean, R. Corymbia maculata, Corymbia citriodora subsp. variegata and Corymbia henryi; Industry and Investment, New South Wales Government: Sydney, NSW, Australia, 2010.
- Garcia Florez, L.; Vanclay, J.K.; Glencross, K.; Nichols, J.D. Developing biomass estimation models for above-ground compartments in Eucalyptus dunnii and Corymbia citriodora plantations. Biomass Bioenergy
**2019**, 130, 105353. [Google Scholar] [CrossRef] - Lee, D.J.; Brawner, J.T.; Smith, T.E.; Hogg, B.W.; Meder, R.; Osborne, D.O. Productivity of Plantation Hardwood Tree Species in North-Eastern Australia: A Report from the Forest Adaptation and Sequestration Alliance; The Australian Government Department of Agriculture, Fisheries and Forestry: Canberra, NSW, Australia, 2011.
- Chave, J.; Réjou-Méchain, M.; Búrquez, A.; Chidumayo, E.; Colgan, M.S.; Delitti, W.B.; Duque, A.; Eid, T.; Fearnside, P.M.; Goodman, R.C.; et al. Improved allometric models to estimate the aboveground biomass of tropical trees. Glob. Change Biol.
**2014**, 20, 3177–3190. [Google Scholar] [CrossRef] - Keith, H.; Barrett, D.; Keenan, R. Review of Allometric Relationships for Estimating Woody Biomass for New South Wales, the Australian Capital Territory, Victoria, Tasmania and South Australia; Australian Greenhouse Office: Canberra, NSW, Australia, 2000.
- Applegate, G.B.; Richards, B.; Charley, J.; Bevege, I. Biomass of Blackbutt (‘Eucalyptus pilularis’ Sm.) Forests on Fraser Island. Master’s Thesis, University of New England, Armidale, NSW, Australia, 1984. [Google Scholar]
- McKenzie, N.; Ryan, P.; Fogarty, P.; Wood, J. Sampling, Measurement and Analytical Protocols for Carbon Estimation in Soil, Litter and Coarse Woody Debris; Australian Greenhouse Office: Canberra, NSW, Australia, 2000.
- Williams, R.J.; Zerihun, A.; Montagu, K.D.; Hoffman, M.; Hutley, L.B.; Chen, X. Allometry for estimating aboveground tree biomass in tropical and subtropical eucalypt woodlands: Towards general predictive equations. Aust. J. Bot.
**2005**, 53, 607–619. [Google Scholar] [CrossRef] - Ximenes, F.; Bi, H.; Cameron, N.; Coburn, R.; Maclean, M.; Matthew, D.S.; Roxburgh, S.; Ryan, M.; Williams, J.; Ken, B. Carbon Stocks and Flows in Native Forests and Harvested Wood Products in SE Australia; Project No: PNC285-1112; Forest Wood Products Australia: Melbourne, VIC, Australia, 2016. [Google Scholar]
- Paul, K.I.; Roxburgh, S.H.; Chave, J.; England, J.R.; Zerihun, A.; Specht, A.; Lewis, T.; Bennett, L.T.; Baker, T.G.; Adams, M.A. Testing the generality of above-ground biomass allometry across plant functional types at the continent scale. Glob. Change Biol.
**2016**, 22, 2106–2124. [Google Scholar] [CrossRef] - Paul, K.I.; Larmour, J.; Specht, A.; Zerihun, A.; Ritson, P.; Roxburgh, S.H.; Sochacki, S.; Lewis, T.; Barton, C.V.; England, J.R.; et al. Testing the generality of below-ground biomass allometry across plant functional types. For. Ecol. Manag.
**2019**, 432, 102–114. [Google Scholar] [CrossRef] - Ximenes, F.A.; Gardner, W.D.; Richards, G.P. Total above-ground biomass and biomass in commercial logs following the harvest of spotted gum (Corymbia maculata) forests of SE NSW. Aust. For.
**2006**, 69, 213–222. [Google Scholar] [CrossRef] - Forrester, D.I.; Dumbrell, I.C.; Elms, S.R.; Paul, K.I.; Pinkard, E.A.; Roxburgh, S.H.; Baker, T.G. Can crown variables increase the generality of individual tree biomass equations? Trees
**2020**, 35, 15–26. [Google Scholar] [CrossRef] - Clark, M.L.; Roberts, D.A.; Ewel, J.J.; Clark, D.B. Estimation of tropical rain forest aboveground biomass with small-footprint lidar and hyperspectral sensors. Remote Sens. Environ.
**2011**, 115, 2931–2942. [Google Scholar] [CrossRef] - Kumar, L.; Mutanga, O. Remote Sensing of Above-Ground Biomass. Remote Sens.
**2017**, 9, 935. [Google Scholar] [CrossRef][Green Version] - Morel, A.C.; Saatchi, S.S.; Malhi, Y.; Berry, N.J.; Banin, L.; Burslem, D.; Nilus, R.; Ong, R.C. Estimating aboveground biomass in forest and oil palm plantation in Sabah, Malaysian Borneo using ALOS PALSAR data. For. Ecol. Manag.
**2011**, 262, 1786–1798. [Google Scholar] [CrossRef] - Van Niekerk, P.; Drew, D.; Dovey, S.; Du Toit, B. Allometric relationships to predict aboveground biomass of 8–10-year-old Eucalyptus grandis × E. nitens in south-eastern Mpumalanga, South Africa. South. For. J. For. Sci.
**2020**, 82, 15–23. [Google Scholar] [CrossRef] - Chave, J.; Andalo, C.; Brown, S.; Cairns, M.A.; Chambers, J.Q.; Eamus, D.; Fölster, H.; Fromard, F.; Higuchi, N.; Kira, T.; et al. Tree allometry and improved estimation of carbon stocks and balance in tropical forests. Oecologia
**2005**, 145, 87–99. [Google Scholar] [CrossRef] - Picard, N.; Rutishauser, E.; Ploton, P.; Ngomanda, A.; Henry, M. Should tree biomass allometry be restricted to power models? For. Ecol. Manag.
**2015**, 353, 156–163. [Google Scholar] [CrossRef] - Xu, Q.-S.; Liang, Y.-Z.; Du, Y.-P. Monte Carlo cross-validation for selecting a model and estimating the prediction error in multivariate calibration. J. Chemom.
**2004**, 18, 112–120. [Google Scholar] [CrossRef] - Paul, K.I.; Radtke, P.J.; Roxburgh, S.H.; Larmour, J.; Waterworth, R.; Butler, D.; Brooksbank, K.; Ximenes, F. Validation of allometric biomass models: How to have confidence in the application of existing models. For. Ecol. Manag.
**2018**, 412, 70–79. [Google Scholar] [CrossRef] - Xu, Y.; Goodacre, R. On splitting training and validation set: A comparative study of cross-validation, bootstrap and systematic sampling for estimating the generalization performance of supervised learning. J. Anal. Test.
**2018**, 2, 249–262. [Google Scholar] [CrossRef] [PubMed][Green Version] - Brown, S.; Gillespie, A.J.R.; Lugo, A.E. Biomass estimation methods for tropical forests with applications to forest inventory data. For. Sci.
**1989**, 35, 881–902. [Google Scholar] [CrossRef] - Brown, S.; Iverson, L.R. Biomass estimates for tropical forests. World Resour. Rev.
**1992**, 4, 366–384. [Google Scholar] - Brown, S. Estimating Biomass and Biomass Change of Tropical Forests: A Primer; Food & Agriculture Organization: Rome, Italy, 1997; Volume 134. [Google Scholar]
- Brown, S. Geographical Distribution of Biomass Carbon in Tropical Southeast Asian Forests: A Database; Oak Ridge National Laboratory: Oak Ridge, TN, USA, 2002. [Google Scholar]
- Burrows, W.H.; Hoffmann, M.B.; Compton, J.F.; Back, P.V.; Tait, L.J. Allometric relationships and community biomass estimates for some dominant eucalypts in Central Queensland woodlands. Aust. J. Bot.
**2000**, 48, 707–714. [Google Scholar] [CrossRef] - Ketterings, Q.M.; Coe, R.; van Noordwijk, M.; Palm, C.A. Reducing uncertainty in the use of allometric biomass equations for predicting above-ground tree biomass in mixed secondary forests. For. Ecol. Manag.
**2001**, 146, 199–209. [Google Scholar] [CrossRef] - Basuki, T.M.; van Laake, P.E.; Skidmore, A.K.; Hussin, Y.A. Allometric equations for estimating the above-ground biomass in tropical lowland Dipterocarp forests. For. Ecol. Manag.
**2009**, 257, 1684–1694. [Google Scholar] [CrossRef] - Diédhiou, I.; Diallo, D.; Mbengue, A.; Hernandez, R.; Bayala, R.; Diémé, R.; Diédhiou, P.; Sène, A. Allometric equations and carbon stocks in tree biomass of Jatropha curcas L. in Senegal’s Peanut Basin. Glob. Ecol. Conserv.
**2017**, 9, 61–69. [Google Scholar] [CrossRef] - Sileshi, G.W. A critical review of forest biomass estimation models, common mistakes and corrective measures. For. Ecol. Manag.
**2014**, 329, 237–254. [Google Scholar] [CrossRef] - Picard, R.R.; Cook, R.D. Cross-validation of regression models. J. Am. Stat. Assoc.
**1984**, 79, 575–583. [Google Scholar] [CrossRef] - Brown, S. Measuring carbon in forests: Current status and future challenges. Environ. Pollut.
**2002**, 116, 363–372. [Google Scholar] [CrossRef] - Huynh, T.; Applegate, G.; Lewis, T.; Pachas, A.N.A.; Hunt, M.A.; Bristow, M.; Lee, D.J. Species-Specific Allometric Equations for Predicting Belowground Root Biomass in Plantations: Case Study of Spotted Gums (Corymbia citriodora subspecies variegata) in Queensland. Forests
**2021**, 12, 1210. [Google Scholar] [CrossRef] - Huynh, T.; Lee, D.J.; Applegate, G.; Lewis, T. Field methods for above and belowground biomass estimation in plantation forests. MethodsX
**2021**, 8, 101192. [Google Scholar] [CrossRef] [PubMed] - Zhu, Z.; Kleinn, C.; Nölke, N. Assessing tree crown volume—A review. For. Int. J. For. Res.
**2021**, 94, 18–35. [Google Scholar] [CrossRef] - Xiao, X.; White, E.P.; Hooten, M.B.; Durham, S.L. On the use of log-transformation vs. nonlinear regression for analyzing biological power laws. Ecology
**2011**, 92, 1887–1894. [Google Scholar] [CrossRef][Green Version] - Cheng, Z.; Gamarra, J.; Birigazzi, L. Inventory of Allometric Equations for Estimation Tree Biomass—A Database for China; UNREDD Programme: Rome, Italy, 2014. [Google Scholar]
- Huy, B.; Thanh, G.T.; Poudel, K.P.; Temesgen, H. Individual Plant Allometric Equations for Estimating Aboveground Biomass and Its Components for a Common Bamboo Species (Bambusa procera A. Chev. and A. Camus) in Tropical Forests. Forests
**2019**, 10, 316. [Google Scholar] [CrossRef][Green Version] - Moore, J.R. Allometric equations to predict the total above-ground biomass of radiata pine trees. Ann. For. Sci.
**2010**, 67, 806. [Google Scholar] [CrossRef][Green Version] - Fordjour, P.; Rahmad, Z. Development of allometric equation for estimating above-ground liana biomass in tropical primary and secondary forest, Malaysia. Int. J. Ecol.
**2013**, 2013, 658140. [Google Scholar] [CrossRef][Green Version] - Furnival, G.M. An index for comparing equations used in constructing volume tables. For. Sci.
**1961**, 7, 337–341. [Google Scholar] - Picard, N.; Saint-André, L.; Henry, M. Manual for Building Tree Volume Biomapass Allometric Equations: From Field Measurement to Prediction; FAO Food Agricultural Organization of the United Nations: Rome, Italy, 2012. [Google Scholar]
- Huy, B.; Kralicek, K.; Poudel, K.P.; Phuong, V.T.; Van Khoa, P.; Hung, N.D.; Temesgen, H. Allometric equations for estimating tree aboveground biomass in evergreen broadleaf forests of Viet Nam. For. Ecol. Manag.
**2016**, 382, 193–205. [Google Scholar] [CrossRef] - Pinheiro, J.; Bates, D.; DebRoy, S.; Sarkar, D.; R.C. Team. nlme: Linear and nonlinear mixed effects models. R Package Version
**2013**, 3, 111. [Google Scholar] - Stegmann, G.; Jacobucci, R.; Harring, J.R.; Grimm, K.J. Nonlinear mixed-effects modeling programs in R. Struct. Equ. Model.
**2018**, 25, 160–165. [Google Scholar] [CrossRef] - Wickham, H.; Chang, W.; Wickham, M.H. Package ‘ggplot2’. Create Elegant Data Visualisations Using the Grammar of Graphics. R Package Version
**2016**, 2, 1–189. [Google Scholar] - Fonseca-Delgado, R.; Gómez-Gil, P. An assessment of ten-fold and Monte Carlo cross validations for time series forecasting. In Proceedings of the 10th International Conference on Electrical Engineering, Computing Science and Automatic Control (CCE), Mexico City, Mexico, 30 September–4 October 2013. [Google Scholar]
- Temesgen, H.; Zhang, C.; Zhao, X. Modelling tree height–diameter relationships in multi-species and multi-layered forests: A large observational study from Northeast China. For. Ecol. Manag.
**2014**, 316, 78–89. [Google Scholar] [CrossRef] - Huy, B.; Tinh, N.T.; Poudel, K.P.; Frank, B.M.; Temesgen, H. Taxon-specific modeling systems for improving reliability of tree aboveground biomass and its components estimates in tropical dry dipterocarp forests. For. Ecol. Manag.
**2019**, 437, 156–174. [Google Scholar] [CrossRef] - Paul, K.I.; Adams, M.; Applegate, G.; Attiwill, P.; Baker, T.; Barton, C.; Bastin, G.; Battaglia, M.; Bradford, M.; Bradstock, R.; et al. Australian Individual Tree Biomass Library, Version 2. ÆKOS Data Portal, Rights Owned by Commonwealth Scientific and Industrial Research Organisation. 2016. Available online: https://researchdata.edu.au/australian-individual-tree-biomass-library/1340678 (accessed on 7 November 2021). [CrossRef]
- Brown, S.; Sathaye, J.; Cannell, M.; Kauppi, P. Management of Forests for Mitigation of Greenhouse Gas Emissions; Cambridge University Press: Cambridge, UK, 1995. [Google Scholar]
- Montagu, K.; Düttmer, K.; Barton, C.; Cowie, A. Developing general allometric relationships for regional estimates of carbon sequestration—An example using Eucalyptus pilularis from seven contrasting sites. For. Ecol. Manag.
**2005**, 204, 115–129. [Google Scholar] [CrossRef] - Bi, H.; Turner, J.; Lambert, M.J. Additive biomass equations for native eucalypt forest trees of temperate Australia. Trees
**2004**, 18, 467–479. [Google Scholar] [CrossRef] - Ledermann, T.; Neumann, M. Biomass equations from data of old long-term experimental plots. Austrian J. For. Sci.
**2006**, 123, 47–64. [Google Scholar] - António, N.; Tomé, M.; Tomé, J.; Soares, P.; Fontes, L. Effect of tree, stand, and site variables on the allometry of Eucalyptus globulus tree biomass. Can. J. For. Res.
**2007**, 37, 895–906. [Google Scholar] [CrossRef] - Veiga, P. Allometric Biomass Equations for Plantations of Eucalyptus globulus and Eucalyptus nitens in Australia; Albert-Ludwigs University Freiburg, Faculty of Forest and Environmental Sciences: Freiburg, Switzerland, 2008. [Google Scholar]
- Xiang, W.; Liu, S.; Deng, X.; Shen, A.; Lei, X.; Tian, D.; Zhao, M.; Peng, C. General allometric equations and biomass allocation of Pinus massoniana trees on a regional scale in southern China. Ecol. Res.
**2011**, 26, 697–711. [Google Scholar] [CrossRef] - Goodman, R.C.; Phillips, O.; Baker, T.R. The importance of crown dimensions to improve tropical tree biomass estimates. Ecol. Appl.
**2014**, 24, 680–698. [Google Scholar] [CrossRef][Green Version] - Molto, Q.; Rossi, V.; Blanc, L. Error propagation in biomass estimation in tropical forests. Methods Ecol. Evol.
**2013**, 4, 175–183. [Google Scholar] [CrossRef] - Kuyah, S.; Dietz, J.; Muthuri, C.; van Noordwijk, M.; Neufeldt, H. Allometry and partitioning of above-and below-ground biomass in farmed eucalyptus species dominant in Western Kenyan agricultural landscapes. Biomass Bioenergy
**2013**, 55, 276–284. [Google Scholar] [CrossRef] - Poorter, H.; Nagel, O. The role of biomass allocation in the growth response of plants to different levels of light, CO
_{2}, nutrients and water: A quantitative review. Funct. Plant Biol.**2000**, 27, 1191. [Google Scholar] [CrossRef][Green Version] - Banin, L.; Feldpausch, T.R.; Phillips, O.; Baker, T.R.; Lloyd, J.; Affum-Baffoe, K.; Arets, E.; Berry, N.J.; Bradford, M.J.; Brienen, R.J.W.; et al. What controls tropical forest architecture? Testing environmental, structural and floristic drivers. Glob. Ecol. Biogeogr.
**2012**, 21, 1179–1190. [Google Scholar] [CrossRef] - Baker, T.R.; Phillips, O.L.; Malhi, Y.; Almeida, S.; Arroyo, L.; Di Fiore, A.; Erwin, T.; Killeen, T.J.; Laurance, S.G.; Laurance, W.F.; et al. Variation in wood density determines spatial patterns in Amazonian forest biomass. Glob. Change Biol.
**2004**, 10, 545–562. [Google Scholar] [CrossRef]

**Figure 1.**Average proportions of aboveground biomass components of plantation grown spotted gum (Corymbia citriodora subsp. variegata) trees, based on data from 52 destructively sampled trees. Please note that debark log biomass was determined from the weight of logs with their bark and the proportions of stem bark and wood estimated indirectly from stem discs from these logs [45].

**Figure 2.**Positive correlation between response variable AGB and natural logarithm of five predicted variables D, H, CD, ρ and CV with Spearman rank correlation from −1 to +1. The color intensity and the size of the circle are proportional to the correlation coefficients.

**Figure 3.**Relationship between aboveground biomass (AGB, kg tree

^{−1}and predictor variables, D (cm), H (m) and ρ (kg m

^{−3}) and weighted residuals, for the candidate Equations (3) to (9) based on data for 52 sample trees. See Table 4 for criteria associated with these regressions.

**Figure 4.**Observed and predicted plots for AGB models validated for all biomass models using MCCV method. Plots with blue border were validated for Equations (3)–(9) with compound predictor variables of D-H-ρ, cross validation procedure was used 80% data used for training, 20% data for testing, the process is repeated 100 times; Plots with green border validated and repeated 40 times for Equations (12)–(17) with compound predictor variables D-H-ρ-CD. The same process was applied for Equations (18)–(23) with compound predictor variables D-H-ρ-CV and plots with orange border. See Table S2 for criteria associated with these models.

**Figure 5.**Validation and comparison of the D-based equation of this study and published equations in different regions in Australia, with spotted gum native forests [22] and mixed hardwood forests of Eucalyptus, Corymbia and Angophora [20]. The dataset was validated by the MCCV method with 20% random splitting data and the process was repeated 100 times to average the errors.

**Table 1.**Study sites, stand age, summary of predictors of sample trees for developing allometric equations. Abbreviations as follows: n, total number of trees sampled; D, diameter at breast height (cm); H, total tree height (m); CD, crown diameter (m); and ρ, wood density (kg m

^{−3}). For each of D, H, CD and ρ, mean, minimum and maximum values are indicated.

Sites (Age) | n | Mean (min, max) | |||
---|---|---|---|---|---|

D (cm) | H (m) | CD (m) | ρ (kg m^{−3}) | ||

451G (7) | 3 | 17.8 (11.8–17.6) | 17.4 (15.3–20.4) | NA | 702.6 (646.8–752.8) |

13PHY (8) | 6 | 15.3 (12.5–18.2) | 15.4 (13.1–16.4) | NA | 676.7 (613.0–738.8) |

451D (9) | 3 | 14.4 (12.0–17.8) | 15.5 (12.6–17.5) | NA | 663.8 (631.1–713.1) |

451G (18) | 13 | 27.1 (17.6–39.9) | 27.0 (22.1–29.9) | 5.3 (3.0–7.9) | 730.8 (671.5–813.5) |

451D (20) | 27 | 28.6 (17.1–42.0) | 25.8 (20.2–32.0) | 6.1 (2.8–9.9) | 736.5 (625.7–801.0) |

Total | 52 | 25.9 (11.8–42.0) | 23.9 (12.6–32.0) | 5.9 (2.8–9.9) | 722.0 (613.0–813.5) |

**Table 2.**Type of predictor models used to develop biomass allometric equations: D is diameter at breast height (cm), H is total tree height (m), ρ is wood density (kg m

^{−3}), CD is crown diameter (m) CV is crown volume (cm

^{3}), and δ is the variance function coefficient.

Input Variable | Equation No. | Model Form | Weight Variable |
---|---|---|---|

Model set 1: Compound predictor variables including D, H and ρ, n = 52 trees | |||

D | (3) | AGB = α × D^{β} | 1/D^{δ} |

H | (4) | AGB = α × H^{β} | 1/H^{δ} |

D and H | (5) | AGB = α × D^{β} × H^{β1} | 1/D^{δ} |

(6) | AGB = α × (D^{2}H)^{β} | 1/(D^{2}H)^{δ} | |

D and ρ | (7) | AGB = α × D^{β} × ρ^{β1} | 1/D^{δ} |

D, H and ρ | (8) | AGB = α × D^{β} × H^{β1} × ρ^{β2} | 1/(D)^{δ} |

(9) | AGB = α × (D^{2}Hρ)^{β} | 1/(D^{2}Hρ)^{δ} | |

Model set 2a: Compound predictor variables including D, H, ρ and CD, n = 40 trees | |||

D | (10) | AGB = α × D^{β} | 1/D^{δ} |

H | (11) | AGB = α × H^{β} | 1/H^{δ} |

CD | (12) | AGB = α × CD^{β} | 1/CD^{δ} |

D and CD | (13) | AGB = α × D^{β} × CD^{β1} | 1/D^{δ} |

D, H and CD | (14) | AGB = α × D^{β} × H^{β1} × CD^{β2} | 1/D^{δ} |

(15) | AGB = α × (D^{2}HCD)^{β} | 1/(D^{2}HCD)^{δ} | |

D, H, ρ and CD | (16) | AGB = α × D^{β} × H^{β1} × ρ^{β2} × CD^{β3} | 1/D^{δ} |

(17) | AGB = α × (D^{2}Hρ CD)^{β} | 1/(D^{2}HρCD)^{δ} | |

Model set 2b: Compound predictor variables including D, H, ρ and CV, n = 40 trees | |||

CV | (18) | AGB = α × CV^{β} | 1/CV^{δ} |

D and CV | (19) | AGB = α × D^{β} × CV^{β1} | 1/D^{δ} |

D, H and CV | (20) | AGB = α × D^{β} × H^{β1} × CV^{β2} | 1/D^{δ} |

(21) | AGB = α × (D^{2}HCV)^{β} | 1/(D^{2}H CV)^{δ} | |

D, H, ρ and CV | (22) | AGB = α × D^{β} × H^{β1} × ρ^{β2} × CV^{β3} | 1/D^{δ} |

(23) | AGB = α × (D^{2}HρCV)^{β} | 1/(D^{2}HρCV)^{δ} |

**Table 3.**Biomass of each tree component, including stem (under bark), stem bark, large branches (≥2 cm diameter), small branches (<2 cm diameter) and leaves sampled at three sites (451D, 451G, and 13PHY). For each component mean, minimum and maximum values are presented.

Sites | n | Mean (min, max), kg | ||||
---|---|---|---|---|---|---|

Stem | Bark | Large Branches | Small Branches and Leaves | Total AGB | ||

451G (7) | 3 | 67.8 (29.0–110.0) | 16.4 (8.7–23.4) | 10.6 (5.5–16.3) | 5.3 (2.3–7.2) | 100.0 (45.5–156.8) |

13PHY (8) | 6 | 70.8 (40.1–101.9) | 12.0 (7.9–16.1) | 28.5 (8.8–44.7) | 8.9 (4.6–13.4) | 120.2 (73.3–174.1) |

451D (9) | 3 | 59.4 (26.4–98.0) | 17.0 (10.8–24.6) | 3.6 (2.1–5.4) | 4.8 (3.3–7.7) | 84.8 (43.9–135.6) |

451G (18) | 13 | 417.1 (99.0–845.9) | 55.1 (19.8–109.9) | 179.1 (21.0–666.4) | 51.1 (9.6–109.7) | 702.5 (149.4–1503.7) |

451D (20) | 27 | 329.9 (92.2–682.1) | 44.3 (18.8–75.5) | 159.1 (17.2–501.2) | 43.1 (7.2–172.5) | 576 (149.7–1431.3) |

Total | 52 | 291.1 (26.4–845.9) | 40.1 (7.9–109.9) | 131.5 (2.1–666.4) | 36.8 (2.3–172.5) | 499.4 (43.9–1503.7) |

**Table 4.**Parameter estimates and their standard errors for AGB models developed based on weighted nonlinear models: D is diameter at breast height (cm), H is total tree height (m), AIC is Akaike Information Criterion, bias is averaged bias (%), RMSE is averaged root mean square error (kg), MAPE is averaged mean absolute percent error (%). Each equation number here refers to those in Table 2.

Equation No. | Parameter Estimates | AIC | Adj. R^{2} | Bias (%) | RMSE (kg) | MAPE (%) | ||||
---|---|---|---|---|---|---|---|---|---|---|

α | β | β_{1} | β_{2} | β_{3} | ||||||

Model set 1: Compound predictor variables including D, H and ρ (n = 52 trees) | ||||||||||

(3) | 0.08220 | 2.64134 | 544.1 | 0.963 | −0.0025 | 0.0200 | 0.0085 | |||

(4) | 0.00622 | 3.49873 | 670.8 | 0.720 | 0.0001 | 0.0034 | 0.0012 | |||

(5) | 0.05251 | 2.40238 | 0.38285 | 546.3 | 0.973 | −0.0023 | 0.0316 | 0.0132 | ||

(6) | 0.02533 | 1.00656 | 554.0 | 0.975 | 0.0212 | 0.0500 | 0.0186 | |||

(7) | 0.05252 | 2.40266 | 0.38253 | 546.3 | 0.973 | −0.0023 | 0.0316 | 0.0132 | ||

(8) | 0.00233 | 2.42585 | 0.30576 | 0.49890 | 551.8 | 0.972 | 0.0001 | 0.0248 | 0.0106 | |

(9) | 0.00004 | 0.99037 | 561.6 | 0.963 | 0.0004 | 0.0004 | 0.0002 | |||

Model set 2a: Compound predictor variables including D, H, ρ and CD (n = 40 trees) | ||||||||||

(10) | 0.10606 | 2.56803 | 442.3 | 0.950 | 0.0000 | 0.0043 | 0.0009 | |||

(11) | 0.00027 | 4.45063 | 545.9 | 0.614 | 0.0000 | 0.0002 | 0.0000 | |||

(12) | 33.24309 | 1.61825 | 532.6 | 0.769 | 4.3446 | 30.0835 | 6.1784 | |||

(13) | 2.30247 | 1.07425 | 450.2 | 0.947 | −0.0003 | 0.0032 | 0.0007 | |||

(14) | 0.05153 | 2.18627 | 0.54648 | 0.11719 | 456.7 | 0.964 | 0.0007 | 0.0259 | 0.0050 | |

(15) | 0.19568 | 0.68009 | 460.3 | 0.961 | −1.0183 | 1.6823 | 0.3358 | |||

(16) | 0.00079 | 2.07194 | 0.69202 | 0.60292 | 0.18009 | 463.1 | 0.967 | 0.0031 | 0.0318 | 0.0060 |

(17) | 0.00156 | 0.69886 | 455.2 | 0.965 | 0.0347 | 0.1618 | 0.0326 | |||

Model set 2b: Compound predictor variables including D, H, ρ and CV (n = 40 trees) | ||||||||||

(18) | 15.35139 | 0.53941 | 532.6 | 0.781 | 2.7223 | 18.9797 | 3.8982 | |||

(19) | 0.09881 | 2.61161 | −0.01109 | 450.2 | 0.950 | −0.0003 | 0.0032 | 0.0007 | ||

(20) | 0.04872 | 2.18625 | 0.54650 | 0.03907 | 456.7 | 0.966 | 0.0007 | 0.0259 | 0.0050 | |

(21) | 0.95382 | 0.38323 | 496.5 | 0.908 | −0.5644 | 5.6982 | 1.1344 | |||

(22) | 0.00072 | 2.07191 | 0.69205 | 0.60293 | 0.06004 | 463.1 | 0.970 | 0.0030 | 0.0318 | 0.0060 |

(23) | 0.06581 | 0.38942 | 494.9 | 0.907 | 0.1717 | 1.2739 | 0.2542 |

**Table 5.**The comparison of cross validation results when the model based on D alone (Equations (3) and (10)) was compared with models using different predictor variables. Equation (3) was compared with Equations (4)–(9), and (10) was compared with Equations (11)–(23). A negative change in AIC, RMSE and MAPE indicates that the D-based equation is better than others. A positive change in adj. R

^{2}means the model D-based is superior. We also present the five equations here (Equations (3), (4), (10), (12) and (18)) to estimate biomass directly from D, H, CD and CV.

Equation No. | Model Form | AIC | Adj. R^{2} | Bias | RMSE | MAPE |
---|---|---|---|---|---|---|

(3) | AGB = α × D^{β} | 434.4 | 0.823 | −2.2 | 0.115 | 7.2 |

(4) | AGB = α × H^{β} | 533.1 | 0.642 | −41.7 | 0.679 | 55.3 |

(10) | AGB = α × D^{β} | 357.2 | 0.880 | −6.0 | 0.114 | 6.8 |

(12) | AGB = α × CD^{β} | 430.4 | 0.964 | −6.5 | 0.428 | 25.4 |

(18) | AGB = α × CV^{β} | 428.3 | 0.964 | −14.8 | 0.348 | 23.1 |

Δ AIC | Δ Adj. R^{2} | Δ Bias | Δ RMSE | Δ MAPE | ||

Model set 1: Compound predictor variables including D, H and ρ | ||||||

(4) | AGB = α × H^{β} | −98.7 | 0.181 | 39.4 | −0.564 | −48.1 |

(5) | AGB = α × D^{β} × H^{β1} | −6.7 | −0.099 | 1.2 | 0.016 | −0.1 |

(6) | AGB = α × (D^{2}H)^{β} | −13.2 | −0.149 | 6.2 | −0.011 | −3.4 |

(7) | AGB = α × D^{β} × ρ^{β1} | −4.0 | −0.098 | 1.1 | 0.011 | 0.8 |

(8) | AGB = α × D^{β} × H^{β1} × ρ^{β2} | −13.4 | −0.130 | 1.9 | 0.021 | 0.7 |

(9) | AGB = α × (D^{2}Hρ)^{β} | −19.8 | −0.135 | 8.6 | −0.023 | −4.2 |

Model set 2a: Compound predictor variables including D, H, ρ and CD | ||||||

(11) | AGB = α × H^{β} | −86.9 | 0.255 | 9.9 | −0.096 | −11.4 |

(12) | AGB = α × CD^{β} | −73.2 | −0.084 | 0.5 | −0.315 | −18.6 |

(13) | AGB = α × D ^{β} × CD^{β1} | −7.8 | 0.054 | 0.2 | −0.012 | −0.3 |

(14) | AGB = α × D ^{β} × H^{β1} × CD^{β2} | −19.7 | 0.003 | −1.2 | 0.021 | −0.7 |

(15) | AGB = α × (D^{2}HCD)^{β} | −16.6 | −0.084 | −2.6 | −0.010 | −0.9 |

(16) | AGB = α × D ^{β} × H^{β1} × ρ^{β2} × CD^{β3} | −24.4 | −0.047 | −1.7 | 0.017 | −1.7 |

(17) | AGB = α × (D^{2}HρCD)^{β} | −12.8 | −0.083 | −2.9 | −0.075 | −6.5 |

Model set 2b: Compound predictor variables including D, H, ρ and CV | ||||||

(18) | AGB = α × CV^{β} | −71.1 | −0.084 | 8.8 | −0.234 | −16.3 |

(19) | AGB = α × D^{β} × CV^{β1} | −9.3 | −0.046 | 0.2 | −0.026 | −4.2 |

(20) | AGB = α × D^{β} × H^{β1} × CV^{β2} | −16.2 | 0.004 | −1.2 | −0.031 | −4.5 |

(21) | AGB = α × (D^{2}HCV)^{β} | −45.7 | −0.084 | −2.2 | −0.039 | −4.2 |

(22) | AGB = α × D ^{β} × H^{β1} × ρ^{β2} × CV^{β3} | −11.8 | −0.047 | −1.7 | −0.026 | −3.9 |

(23) | AGB = α × (D^{2}HρCV)^{β} | −44.2 | −0.084 | −2.4 | −0.039 | −10.3 |

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. |

© 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Huynh, T.; Lewis, T.; Applegate, G.; Pachas, A.N.A.; Lee, D.J. Allometric Equations to Estimate Aboveground Biomass in Spotted Gum (*Corymbia citriodora* Subspecies *variegata*) Plantations in Queensland. *Forests* **2022**, *13*, 486.
https://doi.org/10.3390/f13030486

**AMA Style**

Huynh T, Lewis T, Applegate G, Pachas ANA, Lee DJ. Allometric Equations to Estimate Aboveground Biomass in Spotted Gum (*Corymbia citriodora* Subspecies *variegata*) Plantations in Queensland. *Forests*. 2022; 13(3):486.
https://doi.org/10.3390/f13030486

**Chicago/Turabian Style**

Huynh, Trinh, Tom Lewis, Grahame Applegate, Anibal Nahuel A. Pachas, and David J. Lee. 2022. "Allometric Equations to Estimate Aboveground Biomass in Spotted Gum (*Corymbia citriodora* Subspecies *variegata*) Plantations in Queensland" *Forests* 13, no. 3: 486.
https://doi.org/10.3390/f13030486