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Speciesspecific and mixedspecies volume and above ground biomass allometric equations were developed for 15 indigenous tree species and four tree fern species in New Zealand. A mixedspecies tree equation based on breast height diameter (DBH) and tree height (H) provided acceptable estimates of stem plus branch (>10 cm in diameter over bark) volume, which was multiplied by live tree density to estimate dry matter. For dead standing spars, DBH, estimated original height, actual spar height and compatible volume/taper functions provided estimates of dead stem volume, which was multiplied by live tree density and a density modifier based on log decay class from field assessments to estimate dry matter. Live tree density was estimated using ratio estimators. Ratio estimators were based on biomass sample trees, and utilized density data from outerwood basic density surveys which were available for 35 tree species sampled throughout New Zealand. Foliage and branch (<10 cm in diameter over bark) dry matter were estimated directly from tree DBH. Tree fern above ground dry matter was estimated using allometric equations based on DBH and H. Due to insufficient data, below ground carbon for trees was estimated using the default IPCC root/shoot ratio of 25%, but for tree ferns it was estimated using measured root/shoot ratios which averaged 20%.
Mankind has the potential to greatly influence atmospheric CO_{2} concentrations through the effects of land use change and forest management activities on the terrestrial biomass carbon pool [
New Zealand’s natural forest carbon balance is estimated using a national network of inventory plots installed on an 8 km grid, with plots first measured between 2002 and 2007 [
A systematic biomass sampling programme across the whole of New Zealand’s natural forest area was not possible because tree felling was not permitted in the conservation estate. New biomass data were therefore collected from sites where recent tree falls had occurred following cyclonic storms and from plantations where felling was permitted. Biomass data collection procedures were designed to allow the development of speciesspecific allometric equations for estimating dry matter directly from DBH and H. In addition, indirect calculation methods that utilized supplementary density data from national breast height outerwood density surveys were included, because these allowed improved estimates of whole stem plus branch wood density by species using ratio estimators [
This paper documents the forest biomass study sites and sampling procedures that allowed the development of allometric equations for calculating tree and tree fern carbon stocks in pools 1–3 below, consistent with New Zealand’s definitions of carbon pools [
1. Above ground biomass (AGB) for stems ≥2.5 cm DBH;
2. Below ground biomass in live roots (BGB);
3. Dead wood (includes standing dead trees, spars, and dead roots, and coarse woody debris ≥10 cm in diameter on the forest floor);
4. Litter (includes dead leaves, reproductive parts, and woody debris <10 cm in diameter), and fermenting (F) and humus (H) material on the forest floor, and
5. Mineral soil organic carbon to 30 cm depth.
The litter and soil pools are directly assessed in LUCAS natural forest plots. Carbon stock calculation methods for pools 4 and 5 and for regenerating natural forest are described elsewhere.
Biomass measurements were made at six sites in the North Island and one site in the South Island of New Zealand.
Biomass sampling of podocarp forest occurred at a 40 ha trial established in 1979 at Okurapoto (latitude 38°39' S and longitude 176°42' E) in Whirinaki Forest. Altitude averaged 460 m [
This study site is situated in southern beech forest at Clements Mill Road in Kaimanawa Forest (latitude 38°57' S and longitude 176°13' E). Altitude averaged 750 m, precipitation averaged ca. 1700 mm per year, and MAT averaged 9.5 °C. The terrain was undulating, and as at Okurapoto, the soil parent material was derived from ejecta from the Taupo volcanic centre, the last major episode being the Taupo eruption (ca. 1800 years BP). The forest canopy ranged 25–35 m in height, and was dominated by red beech (
Trees were felled during construction of a predatorproof fence at Mount Maungatautari (797 m altitude, latitude 38°01' S and longitude 175°34' E), in the Waikato District. Altitude of biomass tree locations ranged 300–400 m. Annual rainfall at Maungatautari averaged 1374 mm and annual daily temperature at Cambridge, 18 km to the northwest averaged 13.3 °C. The forest canopy ranged 20–30 m in height, and was dominated by tawa, mangeao (
Kauri (
A naturally regenerated kauri stand at Mangatangi in the Hunua ranges (latitude 37°07' S and longitude 175°13' E) was being thinned in February 1980 and biomass trees were selected as part of the thinning operation. Mean annual precipitation and temperature at Hunua were 1411 mm and 14.1 °C, respectively. Tree height at three plots installed in the vicinity of the kauri biomass study averaged 10.5 m and contained 1440 stems/ha with a basal area of 29.1 m^{2}/ha. Ring counts indicated a stand age of approximately 130 years. Over 90% of the stems and 93% of the basal area comprised kauri, the remaining trees being tanekaha (
Stem and crown biomass of canopy and understorey species were measured in mature beech/podocarp forest at Tawhai State Forest, Maimai (latitude 42°05' S and longitude 171°48' E) [
Above and below ground biomass of tree ferns was measured at Whakarewarewa Forest, Rotorua (latitude 38°11' S and longitude 176°18' E). Altitude ranged 465–505 m, annual rainfall averaged 1500 mm, and temperature averaged 12.7 °C. The terrain was undulating and the soil type was Whakarewarewa hill soil [
Tree biomass measurement protocols largely follow those described in Beets
For biomass trees, breast height basic density or specific gravity (ovendry mass at 105 °C/green saturated volume from water displacement) was measured at 0–5 and 5–15 cm depths under bark on two opposing parallel sided radial strips cut from breast height disks, to allow the development of ratio estimators (described in
Height of the caudex was measured from ground level to the top of the solid woody part of the caudex, caudex diameter was measured at the base (0.15 m), breast height (1.4 m) and at 1m intervals along the caudex, and volume calculated using the using the formula for truncated cones. Live and dead fronds were removed and weighed. The caudex was weighed fresh and 50 mm thick disk (except the basal disk which was 25 mm thick) samples were cut at 1m intervals along the caudex and weighed. The oven dry weight of caudices, live fronds, and dead fronds were calculated by applying the respective fresh weight sampling fractions to the sample data. Samples were ovendried at 70 °C.
Tree fern root systems were extracted by manual digging, cut into manageable sections, and the entire root system processed in the laboratory. Cutting roots into sections revealed substantial amounts of mineral soil trapped within the fibrous root matrix. Root sections were therefore washed over a 3 mm screen with a moderate pressure water hose to remove mineral soil visible on the surface, ovendried at 70 °C and weighed. Mineral soil imbedded inside the fibrous root matrix was removed after the sections were pulverized in a chipper. The pulverized material was thoroughly mixed and a sample (approximately 10% by weight of the entire root system) immediately weighed to determine the sampling fraction by weight. Mineral soil in the sample was separated from the root material using a combination of flotation and manual sorting. Carbon was assumed to comprise 50% of the root oven dry mass.
Breast height outerwood basic density measurements acquired throughout New Zealand were compiled in a Wood Density database, together with information on species, region, tree age, and number of trees sampled per survey. When calculating carbon in stems and branches from volume and density, the national carbon stock estimate can be improved by combining the wood density survey data with data from the biomass sample trees. The ratio estimator [
where
The wood density database contained various measures of wood density, including merchantable log basic density, breast height outerwood (0–5 cm depth or in some cases the outer 5 rings) basic density, and breast height (5–15 cm depth) basic density. To make use of all the data the various density measures were converted as follows:
1. If breast height basic density at 5–15 cm depth was measured, the ratio estimator was applied (following Beets
2. If merchantable log basic density was measured, the ratio estimator was multiplied by 1.03 (1.03 was derived from the wood density database and converts breast height basic density at 0–5 cm depth to breast height basic density at 5–15 cm depth. It should be noted that merchantable log basic density and breast height basic density at 0–5 cm depth have a 1:1 conversion, based on the database).
3. If breast height outerwood (0–5 cm) basic density was measured, the ratio estimator was multiplied by 1.03.
The components available for analysis included volume and carbon in the stem plus large branch ≥10 cm diameter over bark, carbon in branch <10 cm diameter, and carbon in foliage. Allometric equations were developed to estimate carbon in stem plus branch ≥10 cm diameter directly from DBH and H. In addition, indirect estimates of carbon in stem plus branch ≥10 cm diameter were obtained by multiplying volume (from the allometric equation based on DBH and H) by the corresponding density. Carbon in branches <10 cm and foliage were estimated directly from DBH and the components were summed to give above ground live tree carbon. Tree components were estimated separately and summed because all components were not measured on every tree. The tree and tree fern biomass data are given in
The following allometric regression equation was used:
where
Equation 2 was fitted using a generalized linear regression model with gamma error distribution and log link function [
The volume of standing dead stems, which often occur as truncated spars, was calculated using the following compatible volume (Equation 3) and taper (Equation 4) functions [
where
A list of tree species, the number of biomass trees with crown and stem data used to develop allometric equations, and their mean dimensions are given by site in
Tree and tree fern species sampled at biomass study sites throughout New Zealand, sample size (n for stem, crown, root), and mean diameter at breast height (DBH) and height (H).
Site  Species  Sample size  

Means  



DBH (cm)  H (m)  
Whirinaki 

10  0  36.9  26.5  

18  0  95.8  50.1  

2  0  140.0  52.0  

12  0  75.3  38.8  

1  0  107.6  46.7  

7  0  49.2  34.3  
Kaimanawa 

16  0  39.5  24.1  

12  1  59.3  27.2  
Hunua 

6  6  19.4  14.6  
Taranaki 

20  10  33.2  23.1  
Maimai 

2  2  89.0  32.2  

11  11  41.8  20.9  

1  1  32.0  23.9  

36  36  8.6  7.8  
Maungatautari/Manawahe 

7  1  40.1  20.7  

2  2  30.0  14.3  

6  0  40.0  18.0  

4  0  35.5  19.5  

15  0  36.5  19.3  

1  0  20.4  8.2  

1  0  33.0    
Maimai 

2  2  19.4  7.7  
Maungatautari 

1  1  28.5  8.2  
Whakarewarewa 

20  20  4  27.3  2.7 

20  20  5  21.6  4.6  

20  20  5  14.3  2.9  

20  20  4  15.9  3.2 
Mixedspecies allometric equations are given in
Mixedspecies allometric equations for estimating stem and large branch volume and component carbon for natural forest trees, sample size (

Stem & Branch (≥10 cm) Volume_{ob} (m^{3}/tree)  Stem & Branch (≥10 cm) Carbon (kg/tree)  Branch (<10 cm) Carbon (kg/tree)  Foliage Carbon (kg/tree) 


DBH^{2}·H (cm^{2}·m)  DBH^{2}·H (cm^{2}·m)  DBH (cm)  DBH (cm) 

4.83 × 10^{−}^{5}  1.62 × 10^{−2}  1.75 × 10^{−2}  1.71 × 10^{−2} 

0.978  0.943  2.20  1.75 
Deviance explained %  98.9  98.8  96.7  85.2 
Sample size

141  127  70  70 
Tests of species differences in these allometric equations were highly significant (
Allometric equations for estimating stem and large branch volume and component carbon for natural forest trees with species specific parameters. Values in a column followed by the same letter do not differ significantly (least significant difference test with

Stem & Brch (≥10 cm) Volume_{ob} (m^{3}/tree)  Stem & Brch (≥10 cm) Carbon (kg/tree)  Branch (<10 cm) Carbon (kg/tree)  Foliage Carbon (kg/tree)  


DBH^{2}·H (cm^{2}·m)  DBH^{2}·H (cm^{2}·m)  DBH (cm)  DBH (cm)  

0.968  0.936  0.936  1.595  

5.39  bc  0.0157  de  0.0156  0.0541  a 

5.46  ab  0.0190  bc  

5.46  b  0.0182  bcd  

4.90  bc  0.0105  f  

4.65  bc  0.0141  def  0.0274  0.0045  d 

4.67  bc  0.0170  bcde  

4.33  ac  0.0135  ef  0.0147  0.0071  cd 

4.84  bc  0.0116  f  

5.47  b  0.0189  abcd  0.0147  0.0090  cd 

6.18  a  0.0256  a  0.0220  0.0474  a 

5.14  bc  0.0196  ab  0.0219  0.0167  bc 

5.53  ab  0.0208  ab  0.0138  0.0132  bc 

5.58  ab  0.0222  ab  

5.45  abc  0.0129  cdef  

5.15  bc  0.0168  cde  0.0172  0.0186  b 
Deviance explained %  99.1  99.3  99.3  95.0  
Sample size n  141  127  70  70  
Test for species differences 
The number of biomass trees with sectional measurements for developing compatible volume and taper functions and their mean dimensions are given in
Sample size (
Minimum  Mean  Maximum  Standard Deviation  

DBH  115  5.3  52.9  142.0  34.7 
H  115  7.7  27.9  59.2  12.7 
Stem volume_{ob}  115  0.011  5.46  32.1  7.91 
Form factor  115  0.254  0.485  0.691  0.078 
Based on these trees, the overbark volume
And the following equation for estimating the volume of a dead stem or spar with measured height H_{dead} was obtained by integrating the fitted Equation 4 along the stem length up to the measured height:
where
To estimate the volume of standing dead stems (or spars) using Equations 5 and 6 the height H of a live stem with the same DBH as the dead stem must be estimated using the live stem height/diameter function for the species and plot where the dead stem occurs. If H is less than H_{dead},
Allometric equations for estimating the volume of the caudex and above ground carbon of tree ferns at Whakarewarewa are given in
Mixedspecies allometric equations for estimating caudex volume and component carbon for tree ferns, sample size (

Caudex Volume (m^{3}/tree)  Caudex & Frond Carbon (kg/tree)  Caudex Carbon (kg/tree)  Root Carbon (kg/tree) 


DBH^{2}·H (cm^{2}·m)  DBH^{2}·H (cm^{2}·m)  DBH^{2}·H (cm^{2}·m)  DBH^{2}·H (cm^{2}·m) 

1.34 × 10^{−5}  2.70 × 10^{−3}  1.10 × 10^{−3}  6.99 × 10^{−4} 

1.22  1.19  1.25  1.14 
Deviance explained %  93.1  91.6  91.9  81.0 

80  80  80  18 
The fibrous nature of tree fern caudices precludes density determination from breast height cores, and above ground biomass carbon (caudex and fronds) of tree ferns therefore needs to be estimated using the generic allometric equation in
Allometric equations for estimating caudex volume and component carbon for tree ferns with species specific parameters. Values in a column followed by the same letter do not differ significantly (least significant difference test with

Caudex Volume (m^{3}/tree)  Caudex & Frond Carbon (kg/tree)  Caudex Carbon (kg/tree)  Root Carbon (kg/tree) 


DBH^{2}·H (cm^{2}·m)  DBH^{2}·H (cm^{2}·m)  DBH^{2}·H (cm^{2}·m)  DBH^{2}·H (cm^{2}·m) 

1.26  1.06  1.23  1.20 

1.06 × 10^{−5} a  8.45 × 10^{−3} a  1.32 × 10^{−3} ab  4.05 × 10^{−4} b 

8.15 × 10^{−6} b  7.59 × 10^{−3} a  1.36 × 10^{−3} ab  4.37 × 10^{−4} b 

1.01 × 10^{−5} a  5.31 × 10^{−3} c  1.13 × 10^{−3} b  3.38 × 10^{−4} b 

1.03 × 10^{−5} a  6.33 × 10^{−3} b  1.48 × 10^{−3} a  7.90 × 10^{−4} a 
Deviance explained %  94.1  93.6  92.7  90.4 
Sample size

80  80  80  18 
Test for species differences 
A small number of root biomass studies have been made in New Zealand, and more studies of tree root biomass should be undertaken. While the few studies in natural forest were comprehensive, sampling variation was large and encompassed IPCC defaults for root/shoot ratios in temperate broadleaf forest [
Ratios of whole stem and branch ≥10 cm density to breast height outerwood basic density and the number of biomass sample trees on which the ratios were based are given in
Number of biomass trees with the requisite data (
Species 

Ratio of whole stem to 0–5 cm BH basic density  Ratio of whole stem to 5–15 cm BH basic density  

Mean  s.e.  Mean  s.e.  

20  0.969  cde  0.017  0.938  a  0.015 

5  0.891  def  0.035  0.898  ac  0.029 

10  1.083  ab  0.024  0.933  ab  0.021 

2  0.909  cdef  0.055  0.807  ac  0.047 

2  0.831  ef  0.055  0.785  ac  0.047 

2  0.976  bcde  0.055  0.993  a  0.047 

7  0.846  f  0.029  0.844  c  0.025 

5  0.940  cde  0.035  0.913  a  0.029 

2  0.869  def  0.055  0.879  ac  0.047 

2  1.010  bcd  0.055  0.886  abc  0.047 

6  1.018  bc  0.032  0.904  ab  0.027 

4  0.999  bcd  0.039  0.891  ab  0.033 

1  1.234  a  0.077  0.806  b  0.066 
All species  68  0.968  0.013  0.905  0.009  
Test for species differences 
National estimates of whole stem and branch ≥10 cm density were obtained by applying the ratio estimator for all species to the breast height outerwood basic density means of the 35 tree species in national wood density surveys (
Carbon stocks/ha can be estimated by applying allometric equations to independent variables such as the DBH and height measured in inventory plots. The new allometric equations for live and dead trees and tree ferns reported in this paper are intended to replace methods used previously by Beets [
Our tree biomass procedures combined the stem with the large branches because they were often difficult to distinguish, particularly in hardwood species. In addition, because sampling of windfall trees was necessary, biomass measurement focused on the stem and large branches ≥10 cm diameter owing to the loss of foliage and small branches. Biomass of small branches, twigs, and foliage of recent windblown trees with green foliage present, and of felled trees, were measured. After allowing for the effects of stem diameter, biomass of branches <10 cm in diameter over bark did not differ significantly among species; however for foliage the parameter for kauri exceeded that in other species. This may reflect the comparatively young age of the kauri stands. The foliage parameter for silver beech also appeared to be higher than in other species, although uncertainty was large because only three silver beech crowns were measured. Nevertheless, the overall impact of using mixedspecies equations to estimate branches <10 cm in diameter and foliage carbon can be expected to be small, because 85% of the above ground biomass carbon was contained in stems and large limbs, while only 13% was in branches <10 cm diameter, and 1.7% in foliage.
Species differences in stem form were statistically significant but small when examined by species group–for example, the model error for volume of stems plus branches ≥10 cm diameter averaged +0.3% for podocarps, −0.3% for Kauri, −2.9% for hardwoods and −0.5% overall, which justifies the use of a mixedspecies allometric model to estimate volume. Model error for trees ≥5.0 to ≤10 cm diameter averaged −5.7%, which indicates that volume of small trees was slightly underestimated. The model error was +0.4% for planted kauri and −1.2% for kauri in naturally regenerating natural forest, which indicates that plantation grown kauri is similar in stem form to naturally regenerated kauri.
The speciesspecific allometric equations for estimating above ground dry matter directly from DBH and H demonstrated the importance of including density as an independent variable when using mixedspecies allometric equations. With only a limited amount of tree biomass data, we think it is important to utilize the supplementary breast height outerwood density survey data when estimating carbon stocks in New Zealand’s natural forest. It was assumed that carbon comprised 50% of the dry matter. This assumption is expected to be reasonable when applied over a wide range of tree species and components; however, this assumption should ideally be tested.
A mixedspecies function involving DBH, H, and density was developed by Chave
Various other researchers have compared allometric equations they developed for estimating aboveground biomass in tropical forest [
Measured
Our analysis showed that regional variation in mean breast height outerwood basic density was not statistically significant in all but a few species, so national estimates of whole stem and branch ≥10 cm density over bark were obtained by species using a ratio estimator, following methods in Beets
We expect the tree fern equations to be reasonably robust, given the comparatively large sample size (80 tree ferns). Tree ferns at Maimai and Maungatautari sites were within the range found at Whakarewarewa; however, sampling would need to be extend to a broader range of sites to demonstrate how broadly applicable they are in New Zealand. Our tree fern root biomass study gave an overall average root/shoot ratio of 20%. We recommend that this ratio be applied to all tree fern species, because root biomass measurements were restricted to only four or five individuals per species and some species were not sampled at all.
The following sections provide a summary of the calculations steps needed to estimate the carbon stock in live biomass and dead wood pools.
Volume of the stem plus large branches ≥10 cm diameter
Above ground biomass carbon per tree,
where
For tree ferns, supplementary wood density data cannot be obtained using coring methods. Tree fern above ground carbon C
Belowground biomass is estimated from aboveground biomass, using a root/shoot ratio of 25% for trees and 20% for tree ferns.
The volume of dead stems and truncated spars is estimated from DBH (cm), the expected total height when live H (m), and the measured spar height H_{dead} (m) in two steps using compatible volume and taper equations. Firstly, overbark volume of an intact live stem
Secondly, the volume of a standing dead spar
where
The volume of dead spars is converted to carbon by multiplying by the speciesspecific density, assuming 50% of the mass is carbon, and a decay modifier,
The equations for dead spars were not available when Richardson
A similar approach can be used to estimate carbon in logs lying on the forest floor (coarse woody debris from fallen and snapped stems and limbs), by firstly calculating log volume (
The measurement of dead wood volume on the forest floor can be onerous and difficult owing to fragmentation, and furthermore allocating decay classes is fraught with difficulties. Methods involving the use of structural equations also appear to be inadequate for estimating dead wood pools [
The tree and tree fern biomass data described in this paper enabled the development of new allometric functions for predicting the above ground biomass carbon in natural forest in New Zealand from diameter and height measurements in plots. These equations can likely be further improved by measuring more biomass trees so that (1) speciesspecific volume equations can be developed for a range of species, and (2) speciesspecific ratio estimators for density can be developed. In addition, national wood density surveys could be extended to cover a wider range of species. Nevertheless, the new allometric equations for estimating above ground tree carbon from volume and density appear to provide reliable estimates for NZ’s natural forest even with relatively limited biomass data.
In comparison, above ground biomass measurements of an astoundingly large number of topical trees have been acquired in the past (approximately 2500 trees). It was clear from comparisons we made that the best allometric equation of Chave
A costeffective approach for countries with limited biomass data for developing allometric equations may be to measure volume and the corresponding stem (and large branch) density, above ground biomass, and breast height outerwood density of approximately 200 sample trees selected across a range of species. The biomass data would need to be supplemented with national breast height outerwood basic density survey data across a range of important species. In addition site and speciesspecific DBH/Height relations will need to be developed from plot inventory data as inputs to general allometric equations that estimate above ground biomass carbon from volume (from DBH and H) and wood density. Finally, consideration should be given on how best to estimate dead wood.
Above and belowground biomass data for tree ferns showed that root/shoot ratios were on average approximately 20%, which is slightly lower than the default value of 25% used previously for natural forest by Coomes
Diameter, height, volume, whole stem and branch wood plus bark density, basic density at breast height (BH), and biomass carbon data for live hardwood and softwood trees and tree ferns sampled from forest throughout New Zealand.
Ratio estimators of species mean whole stem and branch >10 cm density (dstem) over bark derived from national wood density surveys. The number of trees sampled, and the
The Ministry for the Environment provided funding to compile biomass datasets and develop new allometric equations for LUCAS. Tree biomass studies were funded by the Ministry of Science and Technology, and the tree fern biomass study was funded by the Ministry of Primary Industries. We thank Scion staff who provided assistance with tree and tree fern biomass measurements over a number of years. The compatible volume and taper functions for estimating the truncated volume of dead standing trees were developed by Mina van der Colff, Scion.
The authors declare no conflict of interest.