2.1. Study Area
The study area comprises approximately 7.2 million hectares of public land forests and parks tenure (hereafter, referred to as public land forests) in the state of Victoria, in southeast Australia. This area includes 4 million ha of national parks and conservation reserves, managed primarily for ecosystem and biodiversity protection, tourism, and recreation. The remaining 3.2 million ha are multiple-use state forest tenure, which include the provision of timber and non-timber forest products. Bounding extents of Victoria are north 141°47′36″ E 33°58′54″ S, east 149°58′36″ E 37°30′20″ S, south 146°17′13″ E 39°9′33″ S, and west 140°57′29″ E 34°28′23″ S.
Public land forests extend to all parts of the state and range from low multi-stemmed Mallee woodland across flat and gently undulating topography in the Northwest and Box-Ironbark forests, characterised by sparse to dense canopies of box, ironbark, and gum-barked eucalypts up to 25 m tall, on flat to undulating landscapes on rocky, auriferous soils across central Victoria. Highly variable medium and tall canopy damp sclerophyll forests are widespread across the study area, and are found on a range of loamy, clay-loam, and sandy-loam soils. Tall (up to and above 75 m) wet sclerophyll forests are found mostly in the eastern part of the study area on deep loamy soils at higher elevations. Dry sclerophyll forests are prevalent throughout the east, central, and southwest parts of the study area on clay-loam, sandy-loam, and shallow rocky soils of exposed hillsides, with canopies typically less than 25 m tall, with crooked, spreading trees [
17].
The study area is characterised by a range of different climate zones and diverse topography. The northwest region experiences semi-arid conditions, with low median annual rainfall (less than 250 mm in parts), with coastal areas experiencing a cooler temperate climate. Dry inland plains dominate much of the central and western parts of the state. The Victorian Alps—part of the Australian Great Dividing Range mountain system—extend east-west from the centre of the study area, with elevations up to 2000 m. The Victorian Alps experience the lowest average temperatures and highest precipitation (greater than 1400 mm yr−1) in the study area. This variety of climate and topography is reflected in the variation in forest types and structure across the study area.
2.3. Estimates of Carbon Stocks per Hectare
The aboveground living biomass of large trees (≥10 cm dbhob) were estimated using a generic allometric model for sclerophyll forests [
24]. The model was of the form:
where
AGB_LT_LIVEi is the aboveground biomass of live large tree
i. Although species-specific models were available for over 25 of the 132 tree species assessed, there was no significant difference between stratum means using the generic and the species specific models. For simplicity, the above single generic model was utilised.
Small trees (<10 cm dbhob) were counted but not measured, so an estimate for each of the live small trees was estimated using a generic model for small eucalypts [
24], of the form:
where
AGB_ST_LIVEi is the aboveground biomass for live small tree
i and
H is the tree height.
Estimates of standing dead wood mass for large trees were calculated by first estimating aboveground biomass as for living trees using the whole tree allometric model (Equation (1)), and then reducing the estimated biomass by the amount of biomass in leaves, twigs, and branches. The following predictive model for estimating branches, bark, and leaf biomass specifically for Victorian forests was utilised:
where
AGB_BBLBi is the mass (kg) of of branches, bark, and leaf biomass for standing dead tree
i. Therefore, estimates of standing dead wood mass for large trees were achieved as follows:
where
AGB_LT_DEADi is the mass of standing large tree dead tree
i, and
DSMi is a decay stage multiplier for tree
i. A sound decay stage (decay stage modifier of 0.8) is assumed for standing dead wood, as any further decay stage would cause collapse of the standing dead wood and addition to the fallen CWD pool.
Since we need predictions from Equations (1)–(3) in arithmetic units rather than logarithmic units, the best-fit models were back-transformed to their original form. Reverse transformation on an arithmetic scale produces a systematic underestimation of the dependent variable [
25,
26]. Several procedures for correcting bias in logarithmic regression estimates have been reported. In this study, the logarithmic bias correction term added to the intercept for these three equations before back-transformation was:
where
CF is the correction factor and
SEE2 is the standard error of the estimation [
25,
27]. Estimates of standing dead wood mass for small trees were calculated by estimating aboveground biomass as for living trees and assuming a sound decay stage (decay state modifier of 0.8) as follows:
CWD is defined as all fallen dead woody material (branches, stems, logs) that were not rooted in the soil and with minimum cross-sections of 10 cm. All CWD pieces in the large tree plot were measured for length, assigned to 10 cm diameter classes, and assigned to a decay class. Decay was classified using a three point system based on previous assessments of eucalypt CWD [
28], as outlined in
Table 1. The mass of individual CWD pieces were calculated with the following model:
where
CWDi is the mass for piece
i,
AWDi is the average wood density of tree species in Victoria (0.75 g·cm
−3, [
3]),
DSMi is decay-stage multiplier for piece
i,
AMi is the cross-sectional area of piece
i (in cm
2, the mid-range of diameter in a CWD diameter class),
Li is the length in cm, and
MSDi is the mid-section diameter class.
Mass of individual stumps was calculated as the remaining cross-sectional volume multiplied by the average wood density of trees species in Victoria (0.75 g·cm
−1) by decay classes per stand type (as above) using the following model:
where
AGB_STUMPi is the aboveground biomass for stump
i,
AWDi is the average wood density of tree species in Victoria (0.75 g cm
−3), and
DSMi is decay-stage multiplier for stump
i,
AMi is the cross-sectional area of stump
i (in cm
2),
Hi is the stump height in cm
, and
TOPDi is the top diameter of the stump
i in cm. Tree (live, dead), CWD, and stump biomass by components and size class were summed for each sample plot (i.e., using individual large tree/stump values and multiplying single small tree/stump estimates by counts), and then multiplied by 0.5 to convert mass to carbon content. These data were then converted to carbon (C) in Mg ha
−1 by dividing by the appropriate plot area, which was corrected for slope.
Litter biomass included dead plant material such as fruits, leaves, bark, and small branches (<2.5 cm). Samples were collected from 0.25 m2 frames and were sieved to remove any soil, large rocks, and CWD ≥ 2.5 cm. Samples were air-dried then oven-dried (70 °C, 24 h) to a constant recorded mass. Mass for each sample was divided by the quadrat area and averaged across the four samples to give plot-level litter mass.
Total root biomass was estimated using root:shoot ratios of 0.44, 0.28, and 0.20 for stems with aboveground biomass of <50, 50–150, and >150 Mg ha
−1, respectively. The ratios were recommended for temperate eucalypt forest based on a comprehensive review of major terrestrial biomes [
29]. Root:shoot ratios were multiplied by large and small tree stem carbon and summed to give plot-level tree root carbon.
Soil samples were air-dried at room temperature, weighed, and gently sieved to <2 mm to remove any coarse roots or rocks. A subsample was oven-dried (105 °C, 24 h) to correct for volumetric water content in the calculation of bulk density (corrected for volume of stones estimated using a specific density of 2.65 g·cm
−3; [
30]). A representative sub-sample of air-dried soil was sieved and finely ground (<0.5 mm) for analysis of total carbon by dry combustion using a LECO CHN 1000 Analyser (LECO Corp., St. Joseph, MI, USA). Sample soil carbon stocks were calculated as the product of carbon concentration, bulk density, and depth, and plot-level soil carbon stocks (Mg ha
−1) were the average of four samples per 0.1 m depth interval.
2.4. Statistical Analyses
The VFMP estimated the biomass of living trees (large and small trees), deadwood biomass (dead large trees, dead small dead trees, stumps, and CWD), litter biomass, root biomass, and soil carbon with their standard errors, at the state and stratum levels. The mean of each carbon pool (
) for the population was calculated using the following equation (see [
21], Equation (5.1) on page 91):
where
L is the number of stratum;
is the total number of units in stratum z;
is the stratum weight of stratum h;
is the sample mean of stratum h; and
The standard error of
was calculated using the following equation (see [
31], p. 30):
where
To convert from biomass (Mg ha
−1) to carbon (t ha
−1) a common proxy was utilised, based on the assumption that 50% of the biomass is carbon [
32]. However, it is acknowledged that this relationship may not hold constant over different tree species [
33,
34,
35,
36]. It was assumed that there was no error in the root-shoot models used to estimate belowground biomass. The uncertainty associated with the sum of the five estimates (aboveground living biomass, aboveground deadwood biomass, litter biomass, belowground biomass, and soil carbon) was calculated as the quadratic sum of the errors associated with the individual estimates, according to the rules for computing the propagation of uncertainties through the calculation [
37].
To analyse the variability in the C-stock in the five main C pools, across the altitude gradient, each sample plot was assigned an altitude class (seven classes, 250 m wide, starting at sea level).
The dataset was also used to investigate the relationships, at the plot level, between litter and soil C-stocks and quantitative site features, qualitative forest stand features, and quantitative tree variables. Litter and soil C-stocks were not normally distributed and data transformation did not normalise the distribution. For this reason, the correlation analysis was performed using the non-parametric Spearman correlation coefficient. The variables that were significantly correlated with litter C-stock or with soil c-stock were identified as potential explanatory variables for multivariate regression analyses. The purpose of the multivariate regressions was to test the potential to predict litter biomass and soil carbon from either commonly available VFMP inventory data, or easily collected data. Litter C-stock was added as an additional potential explanatory variable in the soil C-stock prediction because the two variables were slightly but significantly correlated. In the end, the potential quantitative explanatory variables used in the regression analysis were: for site features, elevation, aspect, slope, aboveground live biomass, and aboveground deadwood biomass (standing dead large tree, standing dead tree, stumps, slash, CWD). A stepwise multiple linear regression method was used alternatively to select the most significant variables (probability of
F-to-enter = 0.05; probability of
F-to-remove = 0.1). The conventional multivariate regression model can be expressed as follows:
where
is the dependent parameter to be predicted;
is the intercept;
i is the number of independent variables;
are the regression coefficients; and
are values of independent variables,
In this study,
refers to the litter C-stock per hectare and soil C-stock per hectare,
represent values for elevation, aspect, slope, aboveground live biomass carbon aboveground deadwood biomass carbon, and litter C-stock (in the case of the soil C-stock regression). Collinearity was diagnosed through the Variance Inflation Factor (VIF). Generally, if the VIF is less than 10, collinearity is not serious [
4,
35].