A Comparison of Aboveground Biomass Estimates from Different Allometric Formulas using Vegetation Sampling

Protocol in Rouge National Urban Park

by

Rebecca Maria Barakat

A thesis submitted in conformity with the requirements for the degree of Master of Forest Conservation

Faculty of Forestry University of Toronto

© Copyright by Rebecca Maria Barakat 2017

A Comparison of Aboveground Biomass Estimates from Different

Allometric Formulas using Vegetation Sampling Protocol in Rouge

National Urban Park

Rebecca Maria Barakat

Faculty of Forestry

University of Toronto

2017

Abstract Forests are an important part of the global carbon cycle and their ability to mitigate atmospheric

carbon dioxide levels is increasingly being recognized. The sale of carbon credits represents a significant

emerging opportunity for realizing additional revenue from forested land while promoting carbon

storage and sequestration, biodiversity conservation, sustainable forest management, and strategic

landscape planning (IPCC 2007). When considering the potential application for a forest carbon offset

project within a multifunctional landscape such as southern Ontario it is critical to build upon available

and proven tools that accurately estimate biomass and carbon stocks (Puric-Mladenovic et al. 2016). The

Vegetation Sampling Protocol (VSP) (Puric-Mladenovic et al. 2009), an inventory and monitoring

protocol, can be used to quantify baselines and support subsequent monitoring for forest carbon offset

projects. However, to estimate carbon offsets from the forest agreeing on a set of tree allometric

equations that accurately and consistently predict biomass is a priority. This study contributes to the

understanding of forest carbon quantification in southern Ontario by comparing live aboveground

biomass estimates (AGB) derived from three commonly used allometric formulas (Lambert et al. 2005,

Jenkins et al. 2003 and Ter-Mikaelian and Korzukhin 1997) using VSP DBH data from plots situated

within Rouge National Urban Park (RNUP). In order to determine whether there are any statistical

differences between the three allometric formulas, sets of test-statistics were used on all species

considering all sampled plots, all species and the most common tree species by DBH class and

component biomass where applicable. Results from this study show that the formulas generate

significantly different estimates of biomass, more noticeably for the smaller sized DBH classes. The set of

formuals by Jenkins et al. (2003) consistently overestimated AGB more than the other two formulas

especially for the softwood species. Component biomass was significantly different for foliage but not

for stem biomass. Until a set of standardized formulas specific for southern Ontario are created, the

results of this study suggest that RNUP uses the average of the three formulas for total AGB estimation

since the value was not significantly different from two of the three sets of generalized formulas.

Accurate local (RNUP) and regional (southern Ontario) carbon storage estimates could be used to

improve long-term landscape and land-use planning, enhance forest management and forest

conservation measures and support the province’s plans for creating carbon offset projects from the

forest sector.

Acknowledgements

I would like to thank Dr. Danijela Puric-Mladenovic, Dr. Sean Thomas, Rouge National Urban

Park (RNUP) - Parks Canada, Leonardo Cabrera, Cassandra Stabler, Wasyl Bakowsky, David J. Bradley, the

Vegetation Sampling Protocol crew at RNUP and the OMNRF, and the 2015 Master of Forest

Conservation class at the University of Toronto for their contribution and continuous support.

Table of Contents

i. Abstract

ii. Acknowledgements

1. Introduction

1.1 Biomass

1.2 Rouge National Urban Park - Study Area

2. Objectives and Hypotheses

3. Methods and Statistical Analysis

Figure 1 – VSP

4. Results

Figure 2 – Mean total aboveground biomass, all plots, all species

Figure 3 – Mean foliage and stem biomass

Figure 4 – Mean foliage biomass by species

Figure 5 – Mean stem biomass by species

Figure 6 – Mean total aboveground biomass, all plots, all species by DBH class

Figure 7 – Mean total aboveground biomass, all plots, Sugar Maple by DBH class

Figure 8 – Mean total aboveground biomass, all plots, Eastern Hemlock by DBH class

Figure 9 – Mean total aboveground biomass, all plots, Eastern White Cedar by DBH class

Figure 10 – Mean total aboveground biomass, all plots, Red Oak by DBH class

5. Discussion and Recommendations

6. Conclusions

7. Literature Cited

8. Appendix A

1. Introduction Ontario is currently one of the largest per capita greenhouse gas emitters in the world (MOECC

2015). In order to reduce greenhouse gas emission levels and transition to a low-carbon economy the provincial government announced its intention, in April 2015, to join the cap and trade system under the Western Climate Initiative and make carbon pricing a basis in Ontario's fight against climate change. Ontario’s Five Year Climate Change Action Plan 2016 – 2020 outlines seven key action areas that define how the cap and trade auction proceeds will be spent one of which is the transition towards sustainable agricultural lands and forests (MOECC 2016). To meet provincial goals of cutting greenhouse gas pollution to 15 per cent below 1990 levels by 2020, 37 per cent by 2030 and 80 per cent by 2050, Ontario is developing a regulatory proposal to allow the creation of emissions offsets in uncapped sectors such as agriculture and forestry, to ensure that they are used in ways that are sustainable and enhance the removal of carbon from the atmosphere (MOECC 2016). As outlined in the plan the province will develop a Land Use Carbon Inventory and a Forest Carbon Policy Framework to assess the potential of forests and other land uses to emit, remove and store carbon (MOECC 2016). To enhance carbon storage the province will take actions to protect natural areas and promote conservation efforts such as increasing tree planting or expanding protected areas (MOECC 2016).

Terrestrial carbon sequestration is recognized as one of the measures to mitigate the impacts of climate change, and forests, because of their high carbon density, play an important role as changes in the carbon stock of trees determine whether a forest acts as a source or sink of atmospheric carbon (Kurz et al. 2002). Studies show that southern Ontario forests have reduced carbon stocks and thus the potential to act as larger carbon sinks (Puric-Mladenovic et al. 2016). In southern Ontario, 80-90% of forests and woodlots are privately owned and sprawled among many fragments. Though they may not seem to have a significant impact on Ontario’s carbon storage and sequestration, cumulatively they can be a significant carbon sink (Puric-Mladenovic et al. 2016). It is therefore necessary to have diverse mechanisms, tools and incentives to encourage landowners, conservation groups and protected area managers to manage their forest for carbon storage and sequestration.

Forest carbon offset projects generate carbon credits through the application of conservation measures that increase the amount of carbon stored in a forest ecosystem including innovative forest management practices, restoration of degraded land, afforestation, reforestation and avoided deforestation (IPCC 2007). The carbon offset market is an anticipated area of interest to landowners and conservation groups in southern Ontario (MOECC 2016). It may serve as a source of revenue and an incentive for private landowners to manage their forests for both carbon and biodiversity conservation (Miller et al. 2012) and for protected area managers to support projects that protect standing forests, restore degraded forests as well as measure and verify the amount of carbon stored over time (NCC 2016). But developing forest management or conservation projects that produce carbon offset credits is a complex process. The prerequisite to actual implementation depends on accurate biomass and carbon density estimates which depend on forest type, tree species, species size/diameter (Jenkins et al. 2003) stand age, topography, site productivity, historical forest use, and existing management (Puric-Mladenovic et al. 2016). However, one of the most fundamental requirements for a forest carbon offset project is estimating the amount of carbon stored in forests at a project’s outset and monitoring it over time (Puric-Mladenovic et al., 2015).

Forest inventory is the first step towards estimating the amount of carbon stores and defining the baseline condition against which carbon changes can be quantified and compared over time (Olander and Ebeling 2010). To estimate carbon stored, it is necessary to have a suitable and standardized inventory protocol/sampling design that is comprehensive, user friendly, rigorous and can be applied to both local and regional level carbon estimates (Puric-Mladenovic et al. 2009). The protocol

also needs to support subsequent carbon offset monitoring (Puric-Mladenovic et al. 2016). The Vegetation Sampling Protocol (VSP) (Puric-Mladenovic et al. 2009), an inventory and monitoring protocol, has been used in southern Ontario more intensively since 2005 as it is detailed, applicable to the local scale and standard across spatial and temporal scales (Day and Puric-Mladenovic 2012). VSP is a modular sampling approach that involves the use of fixed-area plots (as determined by a randomly stratified VSP grid) to sample different vegetative strata and as a result can be adapted to support the diverse information needs for forest management, conservation and land use planning (Puric-Mladenovic et al. 2016). VSP collects data on tree species and sizes using diameter at breast height (DBH), plant abundance and environmental disturbance information within fixed-area (400 m2) forest plots (Puric-Mladenovic et al. 2016) and can therefore be used to estimate plot level aboveground tree biomass. Thus, it can be used as a carbon inventory protocol to calculate the amount of stored carbon, develop baseline conditions for forest carbon offset projects, project changes in carbon stock under current management practices and quantify and compare changes through time (Puric-Mladenovic et al. 2016). The protocol can be adjusted to collect data for a variety of inventory needs, including urban, peri-urban and rural landscapes and is therefore ideal for inventory use in settled southern Ontario landscapes. It can also be used within protected areas that are comprised of different ecosystems and landscape types.

In addition to the use of a standard inventory protocol, accurate carbon estimates depend on species-specific allometric equations for generating estimates of biomass in standing live trees (Lambert et al. 2005 and Jenkins et al. 2003). When forest inventory plot data (DBH or height) are used for estimating biomass density (organic dry mass per unit area), tree biomass equations that can be consistently and accurately applied on a regional or local scale are essential in accounting for carbon budgets (Lambert et al. 2005). Research should be carried out to develop or identify the most appropriate allometric equations for biomass estimation since different equations can yield different results (Puric-Mladenovic et al. 2016). Accurate regional carbon storage estimates could be integrated into land-use and conservation planning and could support the development of forest carbon offset projects (Puric-Mladenovic et al. 2016). For the province to create carbon credits from uncapped sectors such as forestry agreeing on a set of allometric formulas for use in Southern Ontario becomes a priority.

1.1 Biomass

Allometry describes the growth of trees and is based on the principle that proportions between height and diameter, between crown height and diameter, between biomass and diameter follow rules that are the same for all trees, big or small, as long as they are growing under the same conditions. This relationship can be used to predict a tree variable (typically its biomass) from another dimension (e.g. its diameter) (Breu et al. 2012); an allometric equation is a formula that quantitatively formalizes this relationship.

Aboveground biomass (ABG) in standing live trees is commonly derived based on tree DBH (diameter at breast height 1.3m) measure or DBH/height of trees in a fixed area plot. The biomass estimates for every tree are then derived from tree measurements and species-specific allometric equations that describe the relationship between the measured variable and individual-tree biomass (Devine et al. 2013). By summing the estimated biomass values for the individual trees on a plot and standardizing for land area covered by that plot one can estimate plot-level biomass in Mg/ha or kg/m2 which can then be aggregated to provide estimates for the stand and forest (Jenkins et al. 2013). This relationship between measured variable and biomass is possible due to the existence of species and site-specific equations/regression functions developed based on destructively sampling, oven drying and weighing representative trees across a range of sizes (Devine et al. 2013). The allometric formulas developed for a specific tree species on a specific site can be generalized and become a useful and

practical tool for biomass estimation since they provide an alternative to the destructive sampling of trees and can be used on large spatial scales and on different sites (Ter-Mikaelian and Korzukhin 1997). None have been created specifically for use in Southern Ontario although three are most commonly used or favoured.

Ter-Mikaelian and Korzukhin (1997) developed a comprehensive review of biomass equations for 65 North American tree species (Ter-Mikaelian and Korzukhin 1997). The review included equations and parameters for aboveground biomass for six tree components including stem wood, stem bark, stem total (wood and bark) and foliage. The review employed biomass data using various published equations and fit a new equation to the generated data (Pastor et al. 1984). This method calculates individual tree biomass using the simple allometric formula:

M=aDb

where: M is the oven-dry weight of the biomass component of a tree (kg); D is DBH (cm); and a and b are parameters. The review included and appendix with the DBH and parameter range over which the parameters were calibrated (Ter-Mikaelian and Korzukhin 1997). This same formula is also used calculate component biomass, simply by changing the parameters (Puric-Mladenovic and Morrison 2009).

Since the comprehensive review there had been an increasing need for generalized and consistent biomass equations. With an objective of creating a method to estimate forest biomass across regional boundaries at regional and national scales, Jenkins et al. (2003) compiled all available published biomass equations for U.S. tree species, including all applicable information from studies conducted in Canada, and adopted a “modified meta-analysis” based on Pastor et al. (1984) generalized regression method (Jenkins et al. 2003). This method divides tree species into ten species groups in order to compute aboveground biomass and two general groups for calculating component ratios (hardwood and softwood):

bm=Exp (β0 + β1 ln dbh) where: bm is total aboveground biomass (kg dry weight) for trees 2.5 cm DBH and larger and β0, β1 are species based model parameters (Jenkins et al. 2003). This estimate can then be used to calculate a specific tree component using the following ratio:

ratio = Exp (β0 + β1/dbh)

where: ratio is the ratio of the component to total aboveground biomass (dry weight) for trees 2.5 cm DBH and larger and β0 and β1 are component and species class (hard vs. softwood) based model parameters (Jenkins et al. 2003). Equations for predicting biomass of tree components were developed as proportions of total aboveground biomass for hardwood and softwood groups for five component parts including total aboveground (above the root collar), foliage, merchantable stem wood, merchantable stem bark, and coarse roots (Jenkins et al. 2003). The ratio result is then multiplied by the total aboveground biomass to determine the component weight. A different set of diameter-based allometric formulas used to derive dry biomass from tree measurements in southern Ontario were developed by Lambert et al. (2005) from archival biomass data, collected at the beginning of the 1980s through the ENergy from the FORest research program (ENFOR) of the Canadian Forest Service (Lambert et al. 2005). The formulas support calculations of dry biomass of four tree components including wood, bark, branches, and foliage. The following biomass equation incorporates the measured DBH and a set of species-specific coefficients for each compartment:

biomasscomponent= βcomponent1×Dβcomponent2+ecomponent

where: biomasscomponent is biomass measured in dry kilograms; D is tree diameter at breast height (cm); βcomponent(n) P are model parameters, and ecomponent are error terms (Lambert et al. 2005). The two features that characterized their equations include (1) the estimated biomass of the compartments (foliage, branch, wood, and bark) constrained to equal the total biomass, and (2) dependence among compartment error terms of the same tree accounted for both the model parameters, and the variance prediction (Lambert et al. 2005). The national biomass equations were produced with emphasis on estimating their bias and error (Lambert et al. 2005).

While both Jenkins et al. (2003) and Ter-Mikaelian and Korzukhin (1997) excluded biomass equations that required tree height (the second most common independent variable used to predict biomass), Lambert et al. (2005) produced a separate set of equations based on tree height and DBH. Height is often excluded from biomass equations because it is more difficult, time consuming and costly for larger number of plots. Furthermore, inventory data and databases with include height measurements are often inconsistent and incomplete and can increase error when creating generalized allometric formuals based on height and DBH (Jenkins et al. 2003). Other site level measurements such as site index, wood density or soil texture were also excluded from all the formulas.

1.2 Rouge National Urban Park- Study Area

Rouge National Urban Park is one of the largest nature reserves in Southern Ontario (79.5km2), surrounding three major watersheds (Rouge, Duffins Creek and Petticoat) and overlapping the cities of Toronto, Markham and Pickering (Parks Canada 2015). It is part of the Carolinian (7E Ecoregion) and Great-Lakes St. Lawrence (6E Ecoregion) Ecoregions (Parks Canada 2015). RNUP’s position in the Greater Toronto Area (GTA) makes it nationally significant ecologically because it provides a contiguous natural corridor from the Oak Ridges Moraine to the shores of Lake Ontario (Wilson 2012). RNUP’s has three primary types of land cover: Agricultural lands (57 %); urban spaces and roads (24 %); Natural ecosystems: forests (12 %) and wetlands (6 %). Within the forested areas of RNUP, carbon storage is an ecosystem service that contributes highly to the natural capital assets of the park (Wilson 2012). Understanding of such ecosystem services is important in policy making particularly with respect to resource conservation, and allocation of financial resources in RNUP.

The park can serve a model for Southern Ontario considering the ecological, geographic, and ownership fragmentation of forested land of the region and the land cover types in RNUP. Accurate carbon estimates on a local scale (RNUP) are necessary for the future development of forest carbon offset projects on a regional scale (Southern Ontario).

2. Objectives and Hypotheses

VSP tree DBH data from plots situated within Rouge National Urban Park were applied to three allometric formulas (Jenkins et al. 2003, Lambert et al. 2005, and Ter-Mikaelian and Korzukhin 1997) with the objective of demonstrating a difference in live aboveground biomass estimates between formulas. These allometric formuals are most commonly used and have been identified as the best candidates for biomass estimation in Southern Ontario (Puric-Mladenovic and Morrison 2009). A statistically significant difference between formulas for (1) all species considering all sampled plots (2) all species and the most common tree species by DBH class and (3) component biomass where applicable will stress the importance of agreeing on a set of allometric formulas for biomass and carbon density

estimation. Accurate local (RNUP) and regional (southern Ontario) carbon storage estimates could be used to improve long-term landscape and land-use planning, enhance forest management and forest conservation measures, support future carbon offset projects from the forest sector and are necessary for the transition towards sustainable lands and forests.

3. Methods and Statistical Analysis

A total of 50 VSP plots were sampled in 2015 in several forest types including Eastern Hemlock, Eastern White Cedar, Eastern White Pine, mixed deciduous, Sugar Maple and Oak. Plot locations were extracted from a VSP regional systematic grid overlaid with a map of the park boundaries. Precise GPS coordinates marked the centres of all plots. All plots had a fixed area of 400m2 and were circular with a set radius of 11.28m. Ropes (11.28m) were extended from the centre of the plot in the main cardinal directions and the coordinates of the centre point of each plot were recorded using an SXBlue high precision GPS unit. Within each plot five additional 1m2 subplots were established, one at the centre and four along the 5.64m mark halfway along the radius of the rope (Fig. 1).

Fig 1. - Circular VSP plots have a fixed area of 400m2

and a radius of 11.28m. There are five 1m2

subplots (red

squares) within each plot.

The procedure enabled the collection of information on vegetation, tree height and diameter, soil, topography, as well as some habitat and hydrological indicators. All live trees and standing dead trees (snags) with more than 5cm of diameter at breast height within the plot were identified and their diameters were measured using a diameter tape. In addition, heights of the three most representative trees inside each plot were also measured using a Suunto clinometer. The extent of similar canopy and species conditions outside of the plot (vegetation homogeneity) was also assessed.

The VSP tree data were used to estimate live aboveground biomass using DBH based allometric formulas as per Lambert et al. 2005, Jenkins et al. 2003 and Ter-Mikaelian and Korzukhin 1997. Biomass was also estimated based on Ter-Mikaelian’s other allometric formulas (See appendix A) and an average was generated for comparison. The biomass calculation from every tree component (foliage, stem, crown etc.) was summed to give the total biomass of a tree in a plot. The residuals were plotted to test whether the assumptions of homoscedasticity, homogeneity and normality were met. To determine whether there are any statistical differences between the three allometric formulas, sets of test-statistics (two-tail) were used on (1) the means of the total AGB and their average for all plots using all sampled species (2) the DBH classes for all the sampled species and the most common tree species for all 50 plots combined and (3) the mean foliage and mean stem biomass where applicable. The species

with the highest number of occurrences across plots were Sugar Maple (n=398), Eastern Hemlock (n=251), Eastern White Cedar (n=200) and Red Oak (n=94). The DBH classes were divided into 12 classes split by 5cm increments beginning from a DBH of 5 cm until 60cm+. The largest available DBH was 78 cm for a red oak. Finally, a Chi- square test was used to test for significant differences by DBH class (for the four species) due to the three different allometric formulas. Not all component biomass estimates were comparable since the studies defined the compartments differently but stem and foliage biomass according to Jenkins et al. (2003) and Lambert et al. (2005) were defined in the same manner so another set of test-statistics (two-tail) were run on all the species together and the hardwood and softwood species separately for all plots.

4. Results

Fig. 2 - Mean (± SE) total aboveground biomass (kg) and their average for all 50 plots calculated using the three different allometric formuals (a- Lambert et al. 2005), (b-Jenkins et al. 2003), (c - Ter-Mikaelian and Korzukhin 1997), (d-the average of the three) and (e- Ter-Mikaelian et. al averages). Letters on figure indicate significant differences (p>0.05) of the T-test: a,b= 0.02974; b,c= 2.95E-09; a,c= 4.8E-06; b,d= 0.00266; c,d= 6.9E-05; c,e= 4.74E-06. There was no significant difference between a,d= 0.369468; a,e= 0.685172; b,e= 0.097187.

The plot of the mean total AGB for the species for all 50 plots shows significant differences between all allometric formulas (Fig. 2). The original formula by Ter-Mikaelian and Korzukhin (1997) produced the lowest mean AGB whereas the equations by Jenkins et al. (2003) produced the highest AGB estimate, and while both estimates were significantly different from the average of the three formulas the estimated AGB by Lambert et al. (2005) was not. The mean AGB produced from the average of the various Ter-Mikaelian formulas was not significantly different from Lambert et al. (2005) or Jenkins et al. (2003).

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Fig 3. - Mean component biomass (± SE) A- foliage (kg) and B- stem for all 50 plots, for all sampled species, calculated using the two different allometric formuals (Lambert et al. 2005 and Jenkins et al. 2003). There was a significant difference (p>0.05) for foliage biomass (p=1.78E-06) but no significant difference for stem biomass (p=0.880259).

Component biomass for all the species for all 50 plots was significantly different for foliage biomass (p=1.78E-06) but was not significantly different for stem biomass (p=0.880259) (Figs. 2 and 3). The equations according to Lambert et al. (2005) overestimated foliage biomass more than Jenkins et al. (2003). This effect was evident for both softwood species where large significant differences existed (eastern white cedar (p=6.86E-23), eastern hemlock (p=1.62E-21)) and red oak (p=0.043461) but not for sugar maple (p= 0.494082) (Fig. 4). The significant differences between the estimates of the two formulas for stem biomass were only evident for eastern white cedar (p= 0.001609) but not for any of the other species (sugar maple (p= 0.297276), eastern hemlock (p= 0.88637) or red oak (p= 0.142445)) (Fig 5).

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Fig 4. - Mean (± SE) foliage biomass (kg) for all 50 plots, for all sugar maple, eastern white cedar, eastern hemlock and red oak calculated using the two different allometric formuals (Lambert et al. 2005 and Jenkins et al. 2003). There was a significant difference (p>0.05) for eastern white cedar (p=6.86E-23), eastern hemlock (p=1.62E-21) and red oak (p=0.043461) but no significant difference for sugar maple (p= 0.494082).

Fig 5. - Mean (± SE) stem biomass (kg) for all 50 plots, for all sugar maple, eastern white cedar, eastern hemlock

and red oak calculated using the two different allometric formuals (Lambert et al. 2005 and Jenkins et al. 2003).

There was a significant difference (p>0.05) for eastern white cedar (p= 0.001609) but no significant difference for

sugar maple (p= 0.297276), eastern hemlock (p= 0.88637) or red oak (p= 0.142445).

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Fig. 6 - Mean (± SE) total aboveground biomass (kg) for all 50 plots, for all sampled species, divided by DBH class, and calculated using the three different allometric formuals (a- Lambert et al. 2005), (b-Jenkins et al. 2003)), (c – Average of Ter-Mikaelian formulas). Letters on figure indicate significant differences (p>0.05) from the T-test.

For all sampled species, divided by DBH class, Lambert et al. (2005) and the average Ter-Mikaelian and Korzukhin formulas produced more similar results than that of Jenkins et al. (2003) which tended to estimate a higher mean AGB than the other two allometric equations. This may be because their formulas are based on species sampled from sites/soils that are more productive but also since the authors provide specific DBH limits based on species, for example the minimum DBH for sugar maple is different from that of red oak for the same allometric equation. Lambert et al. (2005) and Jenkins et al. (2003) estimates were significantly different in ten out of the twelve DBH classes (Fig 6). With higher samples sizes (all species, all plots) there was more of a significant difference in AGB estimates for the smaller size DBH classes than for the higher DBH classes. For the higher DBH classes (60+) Lambert et al. (2005) and Terk et al. average formulas showed less significantly different AGB estimates than Jenkins et al. (2003).

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Fig 7. - Mean (± SE) total aboveground biomass (kg) for all 50 plots, for sugar maple (Acer saccharum; n=398), divided by DBH class, and calculated using the three different allometric formuals (a- Lambert et al. 2005), (b-Jenkins et al. 2003)), (c – Average of Ter-Mikaelian formulas). Letters on figure indicate significant differences (p>0.05) from the T-test.

Fig 8. - Mean (± SE) total aboveground biomass (kg) for all 50 plots, for eastern hemlock (Tsuga canadensis; n=251), divided by DBH class, and calculated using the three different allometric formuals (a- Lambert et al. 2005), (b-Jenkins et al. 2003)), (c – Average of Ter-Mikaelian formulas). Letters on figure indicate significant differences (p>0.05) from the T-test.

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Fig 9. - Mean (± SE) total aboveground biomass (kg) for all 50 plots, for eastern white cedar (Thuja occidentalis; n=200), divided by DBH class, and calculated using the three different allometric formuals (a- Lambert et al. 2005), (b-Jenkins et al. 2003)), (c – Average of Ter-Mikaelian formulas). Letters on figure indicate significant differences (p>0.05) from the T-test.

Fig 10. - Mean (± SE) total aboveground biomass (kg) for all 50 plots, for red oak (Quercus rubra; n=94), divided by DBH class, and calculated using the three different allometric formuals (a- Lambert et al. 2005), (b-Jenkins et al. 2003)), (c – Average of Ter-Mikaelian formulas). Letters on figure indicate significant differences (p>0.05) from the T-test.

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5-10 10-15 15-20 20-25 25-30 30-35 35-40 40-45 45-50 50-55 55+

Me

an A

bo

vegr

ou

nd

Bio

mas

s (k

g)

DBH (cm)

Quercus rubra

Lamb

Jen

TerK

a,b a,c

a,b a,c

a,b a,c

a,b a,c

a,b a,c

The results of the Chi-squared test for the four species split by DBH class indicated a significant difference (p=0.004212) in biomass estimation between the formulas (Fig. 7-10). There was a general trend of consistent significant differences from 35cm – 55 cm when assessed individually (may be due to the availability and accuracy of growth curves at these DBH classes). Jenkins et al. (2003) produced higher estimates than the other two formulas for both the softwood species (eastern hemlock and eastern white cedar) and lower estimates than the Terk et al. average formulas for both the hardwood species (sugar maple and red oak). Compared with Terk et al. average formulas, Lambert et al. (2005) produced higher estimates for the softwoods and lower estimates for the hardwoods.

5. Discussion and Recommendations

Providing accurate measurements of forest carbon is difficult without precise measurements of biomass. Biomass estimates are largely dependent on the inventory protocol and tree allometric formulas used. Moreover, the accuracy of a tree biomass estimate depends on how well the allometric equation represents the trees to which it is applied (Devine et al. 2013). Sources of error when using previously constructed biomass equations/regression functions come from the assumption that the tree population for which the regression function was calculated and the tree population being inventoried are very similar, however, it is generally true that the regression functions may vary considerably from one forest area to the next (Wharton and Cunia 1986). Allometric relationships are species-specific and may be influenced by numerous factors including site quality, associated overstory and understory vegetation and tree genetics (Devine et al. 2013).

Potential errors in estimating forest biomass using species and site-specific allometric equations applied to different sites/regions include, the application of coefficients developed for one site or species that may not apply to the site or species of interest; the use of sample trees that may not be representative of the target population because of factors such as size range and stand conditions and; the use of generalized equations that may inherit shortcomings of published equations, including statistical error, inconsistent standards, inconsistent tree component definitions and inconsistent methodologies (Lambert et al. 2005, Jenkins et al. 2013). Moreover, the use of generalized equations may be biased in favor of species for which published equations exist and may create forced estimates when published equations do not exist. The formulas developed by Lambert et al. (2005), Jenkins et al. (2003) and Ter-Mikaelian and Korzukhin (1997) may also differ due to the availability, type and quality of archived biomass data sets, sampled species, site location, site quality, inventory method (the absence of a standard sampling plan and the absence of a standard tree harvesting protocol to collect the biomass), and the statistical method used (Jenkins et al. 2003).

Errors in estimates of biomass stocks are also believed to result from the absence of allometric equations for the higher diameter classes in general and for the smaller diameter classes in particular (below 10 cm) (Singh et al. 2011). Limited numbers of studies have attempted to develop such equations. Allometric equations focus on estimating biomass for timber and industrial purposes and thus there is an absence of reliable equations for smaller diameter class trees. Existing equations for higher diameter classes tend to overestimate the biomass (Singh et al. 2011). A study by Chakraborty et al. (2016) comparing DBH based biomass equations (from their study) with published equations for European beech trees reported that with an increase in DBH, the overestimation by previously published equations became higher. The ability to report compatible estimates of aboveground biomass is hampered by a large variety of minimum DBH thresholds, ranging from 0 cm to 12 cm (Tompoo et al. 2010). Estimates of AGB based on the 0cm threshold for example are not compatible with those based on a 5cm threshold (Tompoo et al. 2010). In this study, for all sampled species (Fig. 3) there was more of a significant difference in aboveground biomass estimates for the smaller size DBH classes (5-10cm,10-

15cm) than for the higher DBH classes (50-55cm, 55-60cm and 60-65+cm). There was also the trend of larger relative increases in mean biomass after the 55cm DBH threshold for all the formulas. Errors due to diameter extremes could be encountered when using the equations developed by Lambert et al. (2005) since the authors did not include diameter limits from the plot sources where the trees were measured, leaving users to apply any sized tree to the formula (Puric-Mladenovic 2009). However, for the higher DBH classes (60+) Lambert et al. (2005) and Terk et al. average formulas showed less significantly different AGB estimates than Jenkins et al. 2003 (Fig 2). The allometric equations used may produce inconsistent estimates due to the absence of larger trees within our forests.

The California Cap-and-Trade Program has a set of approved allometric equations to estimate biomass and carbon stocks with DBH ranges for trees (sampled to develop the equations) that warn against applying the equations to trees with a DBH outside of the given range as it may increase the error in estimates (CEPA 2010). It is therefore recommended that authors of studies that develop generalized allometric equations such as those of Lambert, Jenkins and Ter-Mikaelian to define the DBH thresholds associated with their equations. Establishing DBH thresholds becomes especially important when calculating biomass for Southern Ontario or RNUP because forest stands even within a single property vary greatly in density and stand development, and thus have different ranges of carbon stocks. This is in part due to the age, heterogeneity, fragmentation, urban stresses and past management regimes associated with the forest stands (Puric-Mladenovic et al. 2015, de-Miguel et al. 2015). Furthermore, while focus should be directed towards developing allometric equations that more accurately estimate AGB for trees with larger diameters, more dependable estimation of biomass and carbon sequestration in the forest would also require development of allometric equations for the smaller diameter classes of all tree species (Singh et al. 2011).

From a hardwood/Softwood species perspective, Aguaron and Mcpherson (2012) found that for open-grown trees, at sizes larger than 35 cm DBH, the above-ground biomass (from generalized equations) was about 25% less than predicted for hardwoods and about 10% less for softwoods. The results of the generalized singletree equations that underestimated AGB more for hardwoods and less for softwoods are like those of Lambert et al. (2005) in this study which produced higher estimates for the softwoods and lower estimates for the hardwoods. The estimates by Jenkins et al. (2003) also mirrored this pattern, but with considerably higher mean values for the softwoods at larger DBH classes (>35cm). Aguaron and Mcpherson (2012) also found that the differences in estimates for hardwoods and softwoods were less noticeable for smaller sized trees, which was in accordance with this study’s findings. To explain causes for different estimates it is useful to examine differences among species that are most important by virtue of their relative abundance and size. For example, red oak is not the most abundant species, but had the highest estimated biomass according to all three sets of equations. Larger trees such as red oak bare the biomass and are the largest carbon pool within plot. Uncertainty, in biomass and carbon stocks largely results due to lack of species-specific allometric equations for each species (Chakraborty et al. 2016) but the development of such equations is very expensive, time consuming and invasive. The reliability of the AGB estimates can be improved using genus-specific equations over generic mixed-species equations (Huy et al. 2016). Huy et al. (2016) found no substantial differences in accuracy among the developed equations for the same genus in different regions or countries, which signals the need for the development of such equations. Development of genus-specific equations can address errors associated lumping too many species into a one or two parameter groups or the limits of not providing parameters for all species as can be encountered with the formulas developed by Jenkins et al. (2003) or Ter-Mikaelian and Korzukhin (1997)(Puric-Mladenovic 2009).

Carbon partitioning for a typical forest tree is reported to be about 17% in roots, 50% in trunk, 30% in branches and stems, and 3% in foliage (Aguaron and Mcpherson 2012). The density of a site influences tree biomass partitioning (allocation of biomass due to genetics) and carbon storage

(Aguaron and Mcpherson 2012, de-Miguel et al. 2014) and differences in estimates of biomass components are highly related to differences in stand development (St. Clair 1993). Trees partition more biomass to the stem and less to the crown with increasing stand age and increasing influence of competition (St. Clair 1993); and trees in open-grown conditions do not compete as directly with other trees, and are allowed to branch into spreading crowns that support ample foliage (Aguaron and Mcpherson 2012). In 2014, a study by De-Miguel et al. (2014) assessed intraspecific differences in aboveground biomass of Pinus brutia sampled throughout different stands of the natural distribution area of the species. They found that trees had higher stem biomass and lower crown biomass in dense even-aged stands than in more uneven-aged and sparse stands. Their results also suggest that forest management-induced stand structure may have a significant influence on the way biomass and carbon are distributed within the tree, since depending on the resulting stand structure, trees adopt different ways to allocate biomass and carbon (de-Miguel et al. 2015). Their study highlights the importance of considering forest stand structure and past forest management practices when aiming at predicting biomass and carbon stock in different components, especially when DBH is used as the only predictor of tree biomass (de-Miguel et al. 2014). The estimates from Lambert et al. (2005) from this study generated significantly different results for foliage biomass likely due to sampling on less dense/younger stands concentrated in southern Ontario. In contemporary multi-objective forest management and planning where predictions of biomass and carbon in separate components are required, sets of allometric equations such as those of Jenkins et al. (2003) may present an issue since they cluster more than 200 species into hardwoods/softwoods for component calculation (Puric-Mladenovic et al. 2016). Moreover, Differences in component biomass allocation at tree level can be propagated to stand/forest levels. For example, De- Miguel et al. (2012) showed that “uneven-aged equations” in an even-aged stand of 25-m2 ha−1 in basal area produced overestimation of 104.6 % in crown biomass and underestimation of 25.3%in stem biomass when compared to the prediction based on the allometric equation fitted for even-aged stands. Therefore, when calculating the biomass of a specific component, especially when using DBH only, it is important to consider stand structure and past forest management practices then fit localized formulas (De- Miguel et al. 2012). Providing stand structure-sensitive models has much to do with increasing the degree of localization when fitting localized allometric equations and yielding predictions (Ishihara et al. 2015). Local allometric models most likely provide accurate aboveground biomass estimates, and if based on large enough and balanced samples, they may contribute to decrease the level of uncertainty in biomass and carbon prediction at forest and landscape levels (van Breugel et al. 2011).

Studies that developed species-specific equations and compared biomass estimates with those of generalised allometric equations often found that the equations predicted the biomass of certain compartments with more certainty. For example, St. Clair (1993) found that published equations more accurately predicted stem biomass than crown biomass of Douglas fir trees in his study. St. Clair attributed the higher certainty of predicting stem biomass to the DBH measurements given that both are directly related and measure stem size. The author attributed the higher uncertainty in predicting crown biomass to family differences in partitioning and competition. If a researcher is trying to accurately estimate biomass of a certain compartment, the addition of variables such as height can significantly improve estimates. For example, the study by Chakraborty et al. (2016) found that, for stem biomass, the equations from past studies overestimated the biomass as DBH increased and although the inclusion of height did not influence the predictions for overall above-ground biomass, it did improve the estimation of stem biomass. Ishihara et al. (2015) also found that inclusion of tree height in addition to stem diameter improved the performance of the generic equation only for stem biomass and had no apparent effect on aboveground, branch, leaf, and root biomass at the site level. This outcome is reasonable for stem biomass because tree height and stem taper are correlated and might be influenced by stand density, species composition, tree social class and site quality (Chakraborty et al. 2016). In the

equations of António et al. (2007), the use of tree height as the second predictor decreased residual variation by 72 % for stem wood biomass, 8 % for stem bark, 12 % for foliage, and 10 % for branches. Chave et al. (2005) reduced the standard error of biomass estimates from 19.5 to 12.5% when tree height was included as a predictor. The use of predictors accounting for the vertical tree and stand structure can improve the quality of the models and their potential applicability to different sites. Stand variables that can be affected by forest management operations as predictors in biomass models result in instant changes in predicted biomasses. Therefore, it has been recommended to use tree-level predictors (i.e., DBH, tree height, crown dimensions) only.

On an individual species level, several studies indicated that site quality affects AGB estimation more than distance/country/forest type. More than one study using different species and their associated species ranges did not find significant differences in between-country total AGB (De-Miguel et al. 2014). The effect of site quality on biomass estimation even within a single species has been reported multiple times in the literature, for example, all of the published equations used for the total AGB calculation in St. Clair’s 1993 study significantly overestimated the biomass for Douglas-Fir trees when applied to dry sites. De-Miguel et al. (2015) found that total AGB differences between stands in different countries and regions were not large although there were significant intra-specific differences in biomass and carbon allocation in individual Pinus brutia trees and stands that differ in development or management. Moreover, Ishihara et al. (2015) reported that local/site-specific equations generate significant differences even in same forest type (boreal, temperate, subtopical). They found that generalized allometric equations provided more accurate estimates for aboveground biomass and for all component biomass compared with localized equations for sites different from one of interest even if it was in the same forest type i.e. in boreal, temperate, and subtropical natural forests (Ishihara et al. 2015). Furthermore, the authors found that the best generic equations included explanatory variables that represent interspecific differences in allometry as they reduced error by 4–12% compared to the generic equations that did not include the interspecific difference. For aboveground and stem biomass, the best generic equations had species-specific wood specific gravity as an explanatory variable and for branch, leaf, and root biomass, the best equations had functional types (deciduous angiosperm, evergreen angiosperm, and evergreen gymnosperm) instead of functional traits (wood specific gravity or leaf mass per area). Furthermore, a recent study by Huy et al. (2016) found that DBH, height and wood density affected aboveground biomass and increasing the number of input variables from one to three reduced the uncertainty of the estimates. Compared with Lambert et al. (2005) whose equations are based on tree species sampled exclusively from Canada, Jenkins et al. (2003) sampled trees from both Canada and Eastern US, thus, further exploration into the landscape level differences between these two methods may reveal that they are interchangeable (Puric-Mladenovic 2009).

Finally, this study recommends that Rouge National Urban Park uses the average of the three formulas for total AGB estimation. The mean value of the average of three formulas in this study was not significantly different from Lambert et al. (2005) whose formulas were developed based on samples collected from Canada with a large number of plots from southern Ontario, however, it is advised that the estimates be used with discretion since the study did not provide any DBH thresholds. Moreover, the mean value of the average of three formulas was also not significantly different from Ter-Mikaelian et al. average formulas. Southern Ontario should use DBH based formulas since measuring height for carbon offsets is too expensive and prone to error. However, for specific component biomass calculation, such as stem biomass (which makes up the majority of the live AGB estimation), it is recommended that height or species-specific wood specific gravity be factored into the equations since the measures have been shown to significantly improve estimates.

6. Conclusions

The EcoFiscal Commission, a group of Canadian economists who study carbon-pricing, estimate that Ontario's plan will have an equivalent price of $19.40 per tonne by 2020. Depending on the allometric formula used to estimate biomass from field data, the amount of carbon stored across the landscape differs and so will the approximate dollar price per metric ton (tonne) of CO2. A study by Puric-Mladenovic et al. (2016) which calculated total carbon and CO2 contained in Eco district 6E14 based on the three formulas as per SOLRIS woodland mapping reported the following results: Metric tons of Carbon Metric tons of CO2 Metric tons

CO2/ha $/Eco district

Lambert et al. (2005) 3,083,387.5 11,316,032 228.0 219531

Jenkins et al. (2003) 3,348,656.1 12,289,568 247.0 238418

Ter-Mikaelian & Korzukhin (1997)

2,962,000.4 10,870,541 219.0 210888

Average 3,131,348 11,492,047 231.6 222946

The monetary difference in estimates between Jenkins et al. (2003) (the formula that produced

the highest estimates) and Ter-Mikaelian & Korzukhin (1997) (the formula that produced the lowest estimates) is 27,530$ which is quite significant. Moreover, if a woodland owner with a 100 ha parcel of land were to generate revenue from avoided deforestation, based on the average metric tons of CO2 per ha (231.6) could generate about 4,493$ per decade.

Despite the issues that exist with generalized allometric formulas, they remain the only efficient, non-destructive and more practical tools for biomass estimation. It is therefore necessary to either develop a set of standard formulas for use in southern Ontario or refine the ones that are most commonly used so that they generate consistent and accurate estimates of biomass. Accurate estimates will provide project developers with the ability to better measure carbon within forests, and as such lead to greater economic opportunities, improved forest conservation, and increased mitigation of the effects of climate change. Future studies should aim to compare forest carbon estimates derived from a ground-based technique with forest carbon estimates derived from the three allometric formulas (Lambert et al. 2005, Jenkins et al. 2003 and Ter-Mikaelian and Korzukhin 1997).

7. Literature Cited

Aguaron, E., & Mcpherson, E. G. (2012). Comparision of Methods for Estimating Carbon Dioxide Storage by Sacramento´s Urban Forest. Carbon sequestration in urban ecosystems (pp. 43-71). Retrieved from http://www.springerlink.com/index/10.1007/978-94-007-2366-5 António N, Tomé M, Tomé J, Soares P, Fontes L (2007) Effect of tree, stand and site variables on the allometry of Eucalyptus globulus tree biomass. Can J For Res 37:895–906 Breu, F., Guggenbichler, S., & Wollmann, J. (2012). Manual for building tree volume and biomass allometric equations: from field measurement to prediction. Vasa (p. 215). Retrieved from http://medcontent.metapress.com/index/A65RM03P4874243N.pdf California Environmental Protection Agency, Air Resources Board. Proposed Regulation to Implement the California Cap-and-Trade Program PART II. Rep. no. 95814. Sacramento: California Air Resources Board, Office of Climate Change, 2010. Print. Air Resources Board Compliance Offset Urban Forest Project Protocol. Canada. Ministry of the Environment and Climate Change. Ontario's Climate Change Discussion Paper 2015. Queen's Printer for Ontario, 2015.

Canada. Ministry of the Environment and Climate Change. Ontario's Five Year Climate Change Action Plan 2016-2020. Queen's Printer for Ontario, 2016.

Chakraborty, T., Saha, S., & Reif, a. (2016). Biomass equations for European beech growing on dry sites. iForest - Biogeosciences and Forestry, 009, e1-e7. Retrieved from http://www.sisef.it/iforest/?doi=ifor1881-009 Chave J, Andalo C, Brown S, Cairns MA, Chambers JQ, Eamus D, Fölster H, Fromard F, Higuchi N, Kira T, Lescure JP, Nelson BW, Ogawa H, Puig H, Riéra B, Yamakura T (2005) Tree allometry and improved estimation of carbon stocks and balance in tropical forests. Oecologia 145:87–99

Day, A.N. and Puric-Mladenovic. (2012). Forest inventory and monitoring information to support diverse management needs in the Lake Simcoe watershed. The Forestry Chronicle, 88(2) 140-146. De-Miguel, S., Pukkala, T., Assaf, N., & Shater, Z. (2014). Intra-specific differences in allometric equations for aboveground biomass of eastern Mediterranean Pinus brutia. Annals of Forest Science, 71(1), 101-112. Devine, Warren D.; Footen, Paul W.; Harrison, Robert B.; Terry, Thomas A.; Harrington, Constance A.; Holub, Scott M.; Gould, Peter J. 2013. Estimating tree biomass, carbon, and nitrogen in two vegetation control treatments in an 11-year-old Douglas-fir plantation on a highly productive site. Res. Pap. PNW-RP-591. Portland, OR: U.S. Department of Agriculture, Forest Service, Pacific Northwest Research Station. 29 p.

Duke, Rick, Sasha Lyuste, and Jake Schmidt. "Reducing Pollution Outside of the Carbon Cap: The Role of Offsets and Complementary Policies." Natural Resources Defense Council Policy Brief 2.0nd ser. CAP (2009): © Natural Resources Defense Council, May 2009. Web. 4 Nov. 2016.

Huy, B., Poudel, K.P., Kralicek, K., Dinh Hung, N., Van Khoa, P., Tan Phìng, V., & Temesgen, H. (2016). Allometric equations for estimating tree aboveground biomass in tropical dipterocarp forests of Vietnam. Forests, 180 (7). doi:10.3390/f7080180 www.mdpi.com/journal/forests IPCC, 2007. Contribution of Working Group III to the Fourth Assessment Report of the Intergovernmental Panel on Climate Change. Edited by Metz, B., Davidson, O.R., Bosch, P.R., Dave, R., Meyers, L.A. Cambridge University Press, Cambridge, United Kingdom and New York, New York, USA.

IPCC (2014). Climate Change 2014 Mitigation of Climate change, Chapter 5: Drivers, Trends and Mitigation, Intergovernmental Panel on Climate Change IPCC. Ishihara, M. I., Utsugi, H., Tanouchi, H., Aiba, M., Kurokawa, H., Onoda, Y., Nagano, M., et al. (2015). Efficacy of generic allometric equations for estimating biomass: A test in Japanese natural forests. Ecological Applications, 25(5), 1433-1446. Ecological Society of America.

Jenkins, J. C., Chojnacky, D. C., Heath, L. S., & Birdsey, R. A. (2003). National-scale biomass estimators for

United States tree species. Forest Science, 49(1), 12-35.

Kurz, W. A., Apps, M., Banfield, E., & Stinson, G. (2002). Forest carbon accounting at the operational scale. Forestry Chronicle. Lambert, M.-C., Ung, C.-H., & Raulier, F. (2005). Canadian national tree aboveground biomass equations.

Canadian Journal of Forest Research, 35(8), 1996-2018.

Miller, Kristell A., Stephanie A. Snyder, and Michael A. Kilgore. “An assessment of forest landowner interest in selling forest carbon credits in the Lake States, USA.” Forest Policy and Economics 25 (2012): 113-122. Print. Nature Conservancy of Canada. "Carbon: Frequently Asked Questions." NCC: Carbon: Frequently Asked Questions. Nature Conservancy of Canada, 2016. Web. 15 Nov. 2016. Olander, J.T. and Ebling, J. 2010. Building Forest Carbon Projects: A Step-by-step Guide. Forest Trends. Accessed March 23, 2016 https://books.google.ca/books?id=bYW4ZwEACAAJ

Pastor J., J.D. Aber and J.M. Melillo. 1984. Biomass prediction using generalized allometric regressions for some northeast tree species. For. Ecol. Manage. 7:265-274. Puric-Mladenovic, D. and H. Morrison. (2009). Allometric Formulas and methods for Biomass Estimates using Vegetation Sampling Protocol Data. Faculty of Forestry ,University of Toronto and Ontario Ministry of Natural Resources. Puric-Mladenovic, D. and Clark. G. 2010. Predictive modeling and mapping of biomass and carbon for Eco-district 6e14. Faculty of Forestry, University of Toronto. http://www.forestry.utoronto.ca/SettledLandscapes/BruceBiomassExplorer/

Puric-Mladenovic, D., Gleeson, J. and Nielson, G. (2016). Estimating Carbon Storage in Southern Ontario Forests at Regional and Stand Levels. Science and Research Branch, Ministry of Natural Resources and Forestry, Climate Change Research Note No. 12. 22 p. Singh, V., Tewari, A., Kushwaha, S. P. S., & Dadhwal, V. K. (2011). Formulating allometric equations for estimating biomass and carbon stock in small diameter trees. Forest Ecology and Management, 261(11), 1945-1949. St. Clair, J.B. (1993). Family differences in equations for predicting biomass and leaf area in Douglas fir (pseudotsuga menziesii var menziesii). Forest Science, 39 (4),743-755. Ter-Mikaelian, M. T., & Korzukhin, M. D. (1997). Biomass equations for sixty-five North American tree

species. Forest Ecology and Management, 97(1), 1-24.

Tomppo, E., Gschwantner, T., Lawrence, M., & McRoberts, R. E. (2010). National Forest Inventories Pathways for Common Reporting. (E. Tomppo, T. Gschwantner, M. Lawrence, & R. E. McRoberts, Eds.)Media (p. 612). Springer Heidelberg Dordrecht London New York. van Breugel M, Ransijn J, Craven D, Bongers F, Hall JS (2011). Estimating carbon stock in secondary forests: decisions and uncertainties associated with allometric biomass models. For Ecol Manage 262:1648–1657 Wharton, E. H., & Cunia, T. (1987). Estimating tree biomass regressions and their error, proceedings of the workshop on tree biomass regression functions and their contribution to the error. General Technical Reports, GTR-NE-117, 303. Welham, Clive. "Forest Carbon Projects." Forest Carbon Projects. 3GreenTree Ecosystem Services Ltd., 2012. Web. 04 Nov. 2016. Wilson, Sara. (2012). Canada’s wealth of Natural Capital: Rouge National Park. David Suzuki Foundation. 60 p. Zhao, F., Guo, Q., & Kelly, M. (2012). Allometric equation choice impacts lidar-based forest biomass estimates: A case study from the Sierra National Forest, CA. Agricultural and Forest Meteorology, 165, 64-72.

8. Appendix A - Other Ter-Mikaelian formulas

Region Authors and Year

Upper Great Lakes Perala and Alban, 1994

West Viginia

Brenneman, B.B., Frederick, D.J., Gardner, WE., Schoenhofen, L.H. and Marsh, P.L., 1978.