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Many studies have quantified uncertainty in forest carbon (C) storage estimation, but there is little work examining the degree of uncertainty in shrubland C storage estimates. We used field data to simulate uncertainty in carbon storage estimates from three error sources: (1) allometric biomass equations; (2) measurement errors of shrubs harvested for the allometry; and (3) measurement errors of shrubs in survey plots. We also assessed uncertainty for all possible combinations of these error sources. Allometric uncertainty had the greatest independent effect on C storage estimates for individual plots. The largest error arose when all three error sources were included in simulations (where the 95% confidence interval spanned a range equivalent to 40% of mean C storage). Mean C sequestration (1.73 Mg C ha^{–1} year^{–1}) exceeded the margin of error produced by the simulated sources of uncertainty. This demonstrates that, even when the major sources of uncertainty were accounted for, we were able to detect relatively modest gains in shrubland C storage.

Shrublands are one of the most widely distributed biomes globally [

Individual-level allometric approaches for shrublands are required for building mechanistic models of C sequestration (e.g., [

There are numerous studies presenting individual-level allometric equations for estimating the biomass of shrubs and trees in regenerating shrublands (e.g., [

Many studies have quantified the amount and sources of uncertainty involved in using individual-level allometric approaches to estimate forest C storage (e.g., [

Within-model uncertainty depends not only on the ability of individual tree or shrub dimensions to predict biomass for harvested individuals, but also on how well the harvested individuals sample the population of interest. Often, many small and very few large individuals are harvested, due to logistical constraints (e.g., [

Further, it is often assumed, without justification, that measurement error for the dimensions of harvested individuals is negligible. We are unaware of any work estimating how measurement errors for the dimensions of harvested individuals might influence the uncertainty of plot-level C estimates. This could potentially be a large effect since any source of uncertainty in fitting allometric models affects biomass estimates for all individuals sampled in plots. The final obvious source of uncertainty is errors in the measurement of individual dimensions (usually trunk diameter and height) on plots. Available evidence suggests this should not be a major source of uncertainty at the plot level, since measurement errors should balance out, as long as there is no bias in the error distribution (e.g., [

We aim to assess uncertainty in C storage estimates from three error sources: (1) uncertainty in the shrub biomass predictions provided by the allometric equations, (2) uncertainty in the allometric equations due to errors in the measurement of harvested shrub dimensions, and (3) errors in the measurement of the dimensions of shrubs in survey plots (these error sources are defined in more detail in

Our study was conducted at two sites: Oxford in the eastern South Island of New Zealand (43°10'34" S 172°06'48" E), and d’Urville Island, off the northern coast of the South Island (40°49'21" S 173°50'22" E). Shrublands eligible for carbon credits cover 461 ha at the Oxford site and 179 ha at the d’Urville site. The major shrubland species at the Oxford site were the invasive shrubs

A total of 27 plots (17 plots at Oxford and 10 plots at d’Urville) were located randomly within shrubland areas and surveyed in 2008. A stratified random sampling design was employed where plots were randomly located within vegetation types and the sampling intensity was proportional to the area covered by each of the major vegetation types. Of this full set of plots, a representative subset of 18 plots (8 plots at Oxford and 10 plots at d’Urville) were re-measured in 2012. Within each 20 × 20 m plot, a 5 × 5 m sub-plot was selected for shrub basal diameter and height measurements. Each shrub was allocated a unique shrub number. If a shrub forked below 10 cm, each stem (with diameter > 0.5 cm and height > 30 cm) was assigned a unique tag ID. Basal diameter (and stem status: live or dead) of all tagged stems and height of the tallest stem were re-measured. For shrubs with basal or breast height diameter < 2.5 cm, callipers were used to measure two orthogonal diameters to record the maximum width and the diameter at right angles to this. For diameters > 2.5 cm a tape was used for measurement of both biomass and shrub dimensions. To compare with diameter measured with a tape, orthogonal diameters (d1 and d2) were converted to an average (dav) from the formula dav = sqrt(d1 × d2). For calculation purposes, the basal areas of stems from the same shrub were summed for each shrub, and the measured height assigned to the shrub. Shrubs that were dead at time of first measurement and shrubs that had died over the period between 2008 and 2012 were considered to be “litter”, because diameters were less than 10 cm, and, hence, not big enough to be “coarse woody debris” according to standard New Zealand forest mensuration protocols [

Shrubs and small trees outside the plot boundary were harvested in order to construct allometric relationships. Harvests were conducted for both survey dates. Selected individuals were representative of the plot as a whole in terms of species composition, weighted by contribution to biomass. Therefore, average- to large-sized shrubs were selected. A total of four shrubs were harvested per plot and weighed. Overall, 162 shrubs were harvested. Large shrubs that had woody stems and branches were subdivided into foliage and stem before weighing as separate categories. Sub-samples of shrubs were transported to the laboratory in order to derive fresh weight:dry weight comparisons. Biomass samples were oven-dried at 65 °C to a constant mass (

Plot inventory data in 2008 and 2012 were converted to oven-dry weight per hectare using an allometric equation developed from biomass data collected in both years (2008 and 2012), across both sites and across all species present in the plots. To estimate C stocks per plant, allometric models of the following general form were derived from the biomass data:
^{2}), Height is maximum shrub height (m), and

Our approach differed from GLM in that the coefficients (

To apply the allometric function to plot measurement data, summed basal areas were obtained for each shrub and multiplied by maximum plant height. For a small number of shrubs (<0.2% of all shrubs surveyed) height was not measured and these missing heights were estimated from species-specific height/diameter functions. The allometric function was then applied to each plant to estimate its dry weight, and these were summed to provide per-hectare values for each plot. For re-measured plots, stock changes were obtained by subtracting the 2008 stock estimate from the 2012 stock.

We used bootstrapping to assess the uncertainty in the coefficient estimates for the allometric equations and for the fitted shrub-dry-weight estimates. To perform bootstrapping we randomly selected 70% of the harvested shrub dataset (without replacement) on which the allometric equations were fitted. We then used the remaining 30% of the dataset to assess goodness of fit of the allometric equations. This process was repeated for 10^{4} permutations to generate a bootstrapped mean and 95% confidence interval (CI) for regression coefficients and predicted-dry-weight values. We stored the coefficient values for each permutation to estimate the effect of allometric uncertainty on C storage estimate error (see

We based our simulations of measurement errors on the data quality limits (DQLs) stipulated for estimation of shrubland C storage in New Zealand. These limits require 95% of basal diameters to be with 1 cm of the “true” measurement and shrub-canopy-height measurements to be within 10 cm of the “true” measurement. We used these DQLs to define Gaussian measurement error distributions for basal diameter and height measurements, with a 95% probability of measurement error occurring within ±2 DQL units. To simulate measurement errors for harvested shrubs and shrubs occurring in survey plots we randomly selected error values from these distributions for each measurement.

Harvest shrub measurement errors and bootstrapping introduced uncertainty into C storage estimates by causing variation in values for the linear coefficient and intercept in the allometric equation. Measurement errors for shrubs in plots introduced uncertainty by causing variation in C estimates for individual shrubs.

We simulated C measurement uncertainty for all possible combinations of the uncertainty sources we studied. This gave seven types of simulation in total: (1) harvest shrub measurement error, (2) plot shrub measurement error, (3) bootstrapped allometric uncertainty, (4) harvest and plot shrub measurement error, (5) harvest measurement error and bootstrapped allometric uncertainty, (6) plot measurement and allometric uncertainty, and (7) harvest and plot measurement error and allometric uncertainty. For simulations incorporating only a single source of uncertainty (simulation types 1–3), all data, except those involved in the source of uncertainty being simulated, were identical to the original dataset (see

Schematic diagram for simulation of independent effects of the three sources of uncertainty studied—harvest and plot measurement error and bootstrapped allometry uncertainty—on carbon (C) storage estimate errors.

^{6} simulations in total). When combining harvest measurement error and bootstrapped allometric uncertainty (simulation type 5) for each harvest error simulation we generated 1000 bootstrapped values for the linear coefficient and intercept, and then combined these coefficient values with the observed measurements for shrubs in plots to estimate C storage (again giving 10^{6} simulations in total). When combining bootstrapped allometric uncertainty and plot measurement errors (simulation type 6) for each bootstrapped estimate of allometric coefficients we ran 1000 plot measurement error simulations. When combining all three sources of uncertainty (simulation type 7), we used 1000 harvest measurement error simulations. For each harvest error simulation, we generated 1000 bootstrapped values for the allometric coefficients and then ran 1000 plot measurement error simulations (giving 10^{9} simulations in total).

Schematic diagram for simulation of interactive effects between the three sources of uncertainty studied—harvest and plot measurement error and bootstrapped allometry uncertainty—on carbon (C) storage estimate errors.

For each simulation, we recorded the estimated C storage of individual plots, as well as the mean C storage across plots. For each type of simulation we used these results to estimate the mean and 95% CI bounds (

The basal area × height allometric equation accurately (

Allometric relationship between harvested shrub dry weight and shrub total basal area multiplied by shrub height (

Bootstrapped allometric uncertainty had the greatest independent effect on C storage estimates for individual plots (^{–1} or 42% of observed C storage). However, in all simulations the degree of uncertainty varied considerably amongst individual plots (^{–1} or 28% of observed mean C.

Mean (SimMeanC) and lower and upper 95% confidence interval limits (SimHighBound and SimLowBound) for carbon (C) estimate uncertainty simulations using the basal area approach. Simulated sources of uncertainty were diameter and height measurement errors for harvested shrubs (

Mean 95% confidence interval breadth (

Mean (SimMeanC) and lower and upper 95% confidence interval limits (SimHighBound and SimLowBound) for the effect of interactions between different sources of error on carbon (C) estimate uncertainty simulations using the basal area approach. Simulated sources of uncertainty were diameter and height measurement errors for harvested shrubs (

95% confidence interval (CI) breadth for simulated C storage estimates of individual plots expressed in absolute terms (

Mean and 95% confidence interval breadth (

In all of the re-measured plots, C storage in 2012 was greater than for 2008 (

Mean simulated carbon (C) storage estimates for individual plots in the 2012 measurement

Across all plots and for both of the study sites considered separately, C sequestration was significantly greater than zero (

Our results show that the allometric equation used to estimate the biomass of individual shrubs is likely to be the greatest source of uncertainty in shrubland C storage estimates. This concurs with existing studies of uncertainty in forest C storage, where allometries for estimating tree biomass are generally the greatest source of uncertainty (e.g., [^{–1} year^{–1}). Considerable time and effort may be required for basal diameter measurements when stem densities are high. However, this might be offset by the requirement of fewer plots relative to more rapid, but less precise methods (e.g., [

We can scale up our plot level results for either site to assess the potential economic viability of the approach used in our study. Post-cultural shrublands at the two study sites combined cover a total area of 640 ha. Using our estimated mean sequestration rate for each site, post-cultural shrublands across the combined areas will have sequestered around 3680 Mg C, or 13,520 Mg CO_{2}e (± s.e. 2907) between 2008 and 2012. Obviously, the economic viability of our survey method would depend heavily on carbon prices. With a unit price of US $20 per Mg CO_{2}e our method could be applied for less than 10% of the money gained from carbon credits. Further, it may be possible that a reduction in sampling intensity would still allow us to detect changes in C storage with reasonable accuracy. Indeed, the sampling intensity we have used to estimate C sequestration (one plot per 37 ha) is much greater than that used in New Zealand’s national carbon monitoring system (one plot per 6400 ha).

In New Zealand, methods for estimating C storage in shrublands differ greatly from those used in forests [

This difference in allometric approaches could potentially cause biases in documenting C stock changes during succession from shrubland to forest. This is because stand- and individual-level approaches are unlikely to scale in exactly the same way as shrubs and saplings are replaced by trees, potentially leading to under- or over-estimation of C gains during the transition from shrubland to forest. Use of the individual-based allometric approach we have presented here through all stages of shrubland succession would provide much better continuity in C storage estimates during succession. This is especially true since, like tree allometries, the individual shrub allometry uses stem diameter and plant height to estimate biomass.

The individual-based allometric approach we have presented here, if applied to large-scale carbon monitoring programs, could greatly increase our power to model C sequestration during early woody succession. This is because it would permit application of individual-based forest dynamics models such as the perfect plasticity approximation (PPA) of Purves

It is possible that we have underestimated the true uncertainty in our shrubland C storage estimates. The errors we have included are only a small subset of the potential causes of uncertainty in plot-based C mensuration methods. Some of these additional uncertainty sources are errors in plot layout and horizontal area estimation, missed or double-counted stems, and data-entry errors. Holdaway

This study shows that individual-level allometries provide considerable power to detect C sequestration in post-cultural shrublands. The allometric approach that we have used should be considered in designing large-scale C monitoring programmes for shrublands since it provides a high degree of accuracy and would also facilitate estimation of C storage changes in transitions from shrubland to forest. Further, our approach could be very beneficial in developing general models tracking C gain during succession from shrubland to forest.

This project was supported by Ministry for Primary Industries’ Sustainable Land Management and Climate Change (SLMACC) funding (contract C04X1102 to New Zealand Forest Research Institute). These Carbon Neutral Public Service (CNPS) plot data were made available by New Zealand’s Ministry for the Environment. We thank Wildlands, who installed and measured the CNPS plots in 2008 using carbon assessment procedures developed for the CNPS by Peter N. Beets. We also thank Graeme Oliver and Stephen Pearce for assistance with plot re-measurement and shrub biomass sampling and processing in 2012.

The authors declare no conflict of interest.