1. Introduction
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 [
1]. A large number of biomass data sets and allometric equations have recently been compiled to predict above ground carbon in forest trees [
2,
3,
4,
5], motivated by the need to estimate carbon stocks for national greenhouse gas balance estimates [
6]. It is important that accurate allometric equations are available to estimate carbon stocks from national plot inventory data. New Zealand has approximately 8.1 million ha of natural forest [
7]. Most natural forest types in New Zealand consist of species rich mixtures of hardwood and softwood trees and tree ferns [
8]. Allometric equations have been based on diameter at breast height (DBH), or DBH and height (H); however, DBH, H and density were included in allometric equations developed previously in New Zealand to estimate above ground biomass from plot data [
9,
10] because tree height H is not proportional to DBH [
11] and wood density differs widely among species.
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 [
12], as part of NZ’s Land Use and Carbon Analysis System (LUCAS) operated by the Ministry for the Environment. The plot size and tree measurement protocols currently being used were based on 20 × 20 m National Vegetation Survey (NVS) plots [
10,
13] to ensure consistency with site-specific surveys undertaken previously in New Zealand. Some enhancements to field protocols and calculation methods were necessary to provide improved estimates of stocks in the five IPCC terrestrial carbon pools [
14,
15,
16], and these were tested in a pilot study across a range of terrain and vegetation types in the South Island [
10]. The pilot study showed that almost 60% of the forest carbon stock consisted of live biomass with an additional 10% in the dead wood pool [
10], and it was recognized that more biomass and wood density data were needed to better represent the range of forest types and tree species [
10].
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 species-specific 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 [
17] at reduced cost relative to traditional biomass methods.
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 [
16] for natural forest:
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.
4. Discussion
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 [
21], Hall
et al. [
13], and Coomes
et al. [
10], to estimate carbon in New Zealand’s natural forest. The new biomass equations were based on approximately 140 trees and 80 tree ferns, whereas equations used previously were based on 50 trees and two tree ferns from one site in the South Island. The new equations included 12 large biomass sample trees >1 m DBH—the old equations were based on one large tree. Predictions from the old and new equations were compared using two hundred tree records selected at random from the ten most common species in the LUCAS natural forest database. Above ground carbon predictions were on average 11% higher using the new equations. Both predictions were based on a mixed-species volume equation (requiring DBH, height) and species-specific density. The comparison showed that, after almost trebling the sample size, predictions from the new volume equation (Equation 7) decreased by 2% for trees <10 cm DBH and increased by 21% for trees ≥1 m DBH compared with predictions from the old volume equation in Coomes
et al. [
10]; however, the new equation includes the volume of branches ≥10 cm in diameter. Predictions of carbon in small branches and foliage necessarily decreased using the new equations, because they apply to branches <10 cm in diameter. The density adjustment factor for hollow trunks used in the old equation was not robust, because it gave negative predictions for stem carbon in very large trees (over 5.3 m DBH). Substantially increasing the sample size would undoubtedly allow further improvement of allometric functions at considerable cost, although it seems unlikely that the predictions will change appreciably.
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 mixed-species 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 mixed-species 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 species-specific 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 mixed-species 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 mixed-species function involving DBH, H, and density was developed by Chave
et al. [
9] who considered it important to test their tropical equations using temperate forest tree biomass data. We did this by comparing above ground biomass carbon predictions from their best wet tropical forest regression model (with tree DBH, total height, and specific gravity) with our biomass data. For calculation purposes, we used the species mean breast height outerwood basic density (at 5–15 cm depth) from survey cores as the measure of specific gravity. The ratio estimator provided species-specific estimates of whole stem and large branch density for use with our natural forest above ground biomass carbon allometric Equation 8. Note that the “
b” parameter in the wet tropical forest equation applies to both the volume index (DBH
2 × H) and wood specific gravity, whereas the natural forest “
b” parameter applies only to the volume index. Model error for our natural forest allometric equation and the wet tropical forest equation averaged +3.0%
versus +2.0%, respectively for trees ≥2.5 cm DBH with complete above ground biomass data (
Figure 1). Errors tended to be larger using specific subsets of our biomass dataset, for example +8.7%
versus +6.8% for 13 beech trees, −6.6%
versus −7.1% for 29 trees of the subcanopy species
Weinmannia racemosa, +3.8%
versus +1.9% for 45 hardwood trees, +2.4%
versus +6.1% for 16 pole kauri. Model error for small trees ≥2.5 to ≤10 cm averaged −11.4% using the natural forest allometric equation and −8.3% using the wet tropical forest allometric equation; however, the impact on forest carbon stock prediction will likely be small. It is clear that both equations provided reasonable predictions of above ground biomass carbon across a range of groups of species and tree size classes.
Various other researchers have compared allometric equations they developed for estimating above-ground biomass in tropical forest [
30,
31] with the pan-tropical equations developed by Chave
et al. [
9], and concluded that general allometric equations were biased when applied at their sites. This was surprising to us, considering the results of the comparisons we made. The reported biases may be due to large differences in stem form factor among species, although biases were up to 50%. Model comparisons they made presumably involved equations based on DBH alone, DBH and density, or DBH, H, and density. If the latter type gave large differences between studies it would be useful to know if merchantable height was used instead of total height. Ignoring height assumes an invariant DBH/height relationship, which is unlikely in mixed-species forests. Furthermore, tree species composition can change both spatially and temporally, following for example the selective harvesting of desirable species. Comparisons we made, using various groupings (hardwood, podocarps, kauri, small trees), found few notable model prediction errors using either our natural forest allometric equation or the best wet tropical equation of Chave
et al. [
9].
Figure 1.
Measured
versus predicted above ground carbon for temperate hardwood/softwood trees (DBH range 2.8–142 cm) in New Zealand obtained using the natural forest equation for New Zealand and wet pan-tropical forest equation of Chave
et al. [
9]. Independent variables were breast height diameter, total height, and wood density.
Figure 1.
Measured
versus predicted above ground carbon for temperate hardwood/softwood trees (DBH range 2.8–142 cm) in New Zealand obtained using the natural forest equation for New Zealand and wet pan-tropical forest equation of Chave
et al. [
9]. Independent variables were breast height diameter, total height, and wood density.
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
et al. [
17]. Unlike outerwood basic density, the ratio estimator incorporates the effect of stem hollowing and fluting, because whole stem wood and branch density was calculated from the oven-dry mass divided by the over-bark volume of the biomass sample trees. Our results showed that the predictions of above ground biomass carbon (using Equation 8) based on ratio estimators of density, which average the density variation between trees within a species, agreed reasonably well with our above ground biomass data (
Figure 1). The scatter in
Figure 1 is hence largely due to tree-to-tree differences in density within a species and, to a lesser extent, stem form (from biomass trees). Other researchers recommended using species mean wood density in biomass regression equations [
32], which is a conclusion largely supported by our analysis of New Zealand’s national wood density database. We note that the appropriate density measure has not always been used. For example, Basuki
et al. [
30] estimated above ground biomass by multiplying the volume of stems and large branches, calculated from stem sectional measurements over bark, by the specific gravity of wood and bark disks or sector samples along the stem. Specific gravity data overestimate stem dry weight if the stem is fluted, hollow, or has butt swell. The ratio estimator we developed using biomass sample trees reduced this potential source of bias, by adjusting the basic density data from breast height core samples.
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.
4.1. Natural Forest Allometric Equations for Live Trees and Tree Ferns
Volume of the stem plus large branches ≥10 cm diameter Vstem+br≥10 (m3/tree) is estimated from DBH (cm) and total height H (m) using the mixed-species allometric equation:
Above ground biomass carbon per tree, Cagtree (kg/tree) is obtained by multiplying the estimated volume by the corresponding density assuming 50% of the mass is carbon, to which the mass of carbon in branches <10 cm in diameter over bark and foliage are added:
where dstem (kg.m−3) is the species-specific stem plus branch ≥10 cm diameter density over bark from the ratio estimator.
For tree ferns, supplementary wood density data cannot be obtained using coring methods. Tree fern above ground carbon Cagtrfn (kg/tree) is therefore estimated directly from DBH (cm) and H (m) as follows:
Below-ground biomass is estimated from above-ground biomass, using a root/shoot ratio of 25% for trees and 20% for tree ferns.
4.2. Equations for Standing Dead Stems and Logs
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 Hdead (m) in two steps using compatible volume and taper equations. Firstly, over-bark volume of an intact live stem Vstem (m3/tree) (i.e., excluding volume in large branches) with the same DBH and expected total height H as the dead stem is estimated as follows:
Secondly, the volume of a standing dead spar Vspar (m3/tree), is estimated from the estimated intact live stem volume up to the measured spar height using:
where x = (H − Hdead)/H.
The volume of dead spars is converted to carbon by multiplying by the species-specific density, assuming 50% of the mass is carbon, and a decay modifier,
m (tabulated by decay class and species in Appendix 3 and in Coomes
et al. [
10]), to allow for density reductions due to decay. Hence, carbon in dead standing spars,
Cspar is calculated as follows:
The equations for dead spars were not available when Richardson
et al. [
33] estimated dead wood in New Zealand’s natural forest. They applied the allometric volume equation developed for intact live stems to predict the volume of truncated spars from DBH and spar height, thereby significantly underestimating carbon in the dead wood pool.
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 (VCWD) from the large and small end diameters and lengths of log and branch sections, using the formula for a truncated cone, which when converted to carbon is as follows:
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 [
33]. In the future, we anticipate that the allometric equations given in this paper will be linked to decay functions described in Beets
et al. [
17], to estimate carbon stocks and changes in the dead wood pool, without requiring direct measurements of this intractable pool. This linkage is possible through their common use of ratio estimators for density. This novel approach will allow predictions of carbon stocks and changes in dead wood (pool 3) of periodically remeasured plots, provided that the date of mortality can be estimated reasonably accurately.
5. Conclusions
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) species-specific volume equations can be developed for a range of species, and (2) species-specific 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
et al. [
9] for tropical trees predicted above ground biomass carbon of our biomass trees surprisingly well in comparison with our natural forest equation. The additional tree sampling we undertook increased the sample size from 50 trees originally to 140 trees currently; however, the effect on carbon estimates was relatively small presumably because wood density, which was one of the most important variables influencing tree biomass, was well estimated using supplementary breast height outerwood density survey data.
A cost-effective 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 species-specific 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 below-ground 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
et al. [
10]. Limited root biomass data exist for New Zealand trees and tree ferns. Root data should ideally be based on country-specific data, so additional root biomass studies are warranted, especially for New Zealand tree species.