## Biomass Equations

Biomass equations can be used to estimate the weight of the tree based on the measured DBH or DBH and height of each tree in the sample plots. Using biomass equations is a common and cost-effective method to estimate biomass of tree species present in a forest or plantation, and has been explained in detail in Chapter 15.

This section illustrates how the equations are developed and applied in estimating the weight of individual trees as well as biomass per hectare of forests and plantations.

Developing a biomass equation Biomass equations are available only for some dominant commercial tree species. A few generic equations for broad forest types are also available. However, the equations are often specific to not only species, but also locations. Further, biomass equations developed using mature trees cannot be used for younger trees, and vice versa. Biomass equations are not available for most local or native forest tree species, which makes it desirable to develop biomass equations wherever possible to suit the local tree species and age of the stand. The process involves the following steps:

Step 1: Select the forest or plantation strata, select the sample plots, identify the dominant tree species and measure the DBH and height of all the trees in the sample plots (Chapter 10) Step 2: Select a few dominant tree species from the forest or plantation Step 3: For the identified tree species, randomly select at least 30 trees to represent different girth sizes present in the forest or plantation Step 4: Measure DBH and height of each tree of the selected species Step 5: Cut the selected trees to the ground and separate each felled tree into the trunk, twigs and branches

Step 6: Cut the tree into pieces of an appropriate size to weigh them directly with a field balance and determine dry weight

° If cutting a large tree trunk into smaller pieces is not feasible, estimate the volume (pr2H) of a large piece of the tree trunk by measuring its diameter and height; r = (diameter/2) and H = height

Step 7: Estimate the weight of each tree by weighing the whole tree; for large trees, calculate the weight by multiplying the volume with wood density Step 8: Plot the weight of the tree (y-axis) against the DBH (y-axis) to obtain the best fit between the variables; the curve could be linear or non-linear Step 9 Develop the biomass equation linking tree weight to DBH alone or to DBH and height using any of the software packages available, such as Microsoft Excel or SPSS (statistical package for social scientists)

° Methods for developing linear and non-linear biomass equations using data on DBH, height and weight of trees are given in most textbooks on statistics and forest mensuration. Further discussion on developing and using biomass equations can be found in Brown (1997) and Parresol (1999) ° Estimate the constant (a) and regression coefficient (b) for the biomass equation along with the coefficient of determination (r2), which explains the proportion or percent variation in biomass (dependent variable) as a function of DBH (independent variable)

One of the limitations of biomass equations is that harvesting about 30 or more trees of a given tree species may not be feasible or permitted, except for plantation species. Further, the harvesting process is also expensive. Therefore, biomass equations are developed only for the dominant tree species; for the rest, generic equations can be used. Application of biomass equation Most projects of climate change mitigation and roundwood production and greenhouse gas inventories require estimation of above-ground biomass, and it can be estimated as follows:

Step 1: Select the biomass equation for the dominant species present in the forest or plantation

° The equation may have been developed for the specific project or for another project in the region with similar vegetation, soil and other features ° If locally developed biomass equation is not available, search for one in the literature or in databases developed for a species with similar tree structure

° If species-specific biomass equations are not available, use generic equations

Step 2: Enter the DBH and height data of measured trees in the sample plots separately for each tree species into a database Step 3: Enter the equation into Excel or any other appropriate software and link the database to the equations Step 4: Use DBH and height data along with species-specific biomass equation to estimate the weight of individual trees using a software package

The weight of the tree can be estimated even using a simple calculator by substituting the DBH (and height) into the equation, especially if the number of observations is small

Step 5: Aggregate the biomass of all trees in the sample plots for each species for which biomass equation is developed or available Step 6: Extrapolate the biomass values (tonnes) from sample plots to per hectare biomass value (tonnes dry biomass per hectare) Step 7: If biomass equation is not available for some minor tree species, use the biomass equation of a tree species closest to it in terms of tree form, height and crown spread

Biomass conversion and expansion factor In using biomass equations developed using only the merchantable volume, it is necessary to convert the value to whole-tree biomass (which includes stems, twigs and branches) using Biomass Conversion and Expansion Factors (Table 17.3). These factors can be generated in the field or obtained from literature (for details, refer to Section 17.1.6). Biomass equations based on DBH and/or height Biomass equations can be linear, quadratic, cubic, logarithmic and exponential. Often generic biomass equations are used for estimating the above-ground biomass (Table 17.4). In addition to biomass equations for individual trees, they are also available for estimating biomass at per hectare scale.

Usually only the volume of a tree is measured since measuring the weight, particularly of large trees, is difficult in the field. Many biomass equations are indeed biomass volume equations. Tree volume is related to parameters such as DBH and height. The volume (m3) estimated using the equations needs to be converted to biomass in tonnes per tree or per hectare using the density of the species. The following steps could be adopted for estimating the volume as well as the biomass of the trees:

Step 1: Select the forest or plantation strata, select sample plots, identify the dominant tree species and measure the DBH and height of all the trees in the sample plots

Step 2: Select the biomass volume estimation equation for the dominant tree species or for all the species for which species-specific equations are available (Table 17.5)

Table 17.3 Default biomass conversion and expansion factors (BCEF) (tonnes of biomass per cubic metre of wood volume) for humid tropical zone. (From IPCC 2006.)

Growing stock level (m3)

Table 17.3 Default biomass conversion and expansion factors (BCEF) (tonnes of biomass per cubic metre of wood volume) for humid tropical zone. (From IPCC 2006.)

Growing stock level (m3)

 <10 11-20 21-40 41-60 61-80 80-120 120-200 >200 Conifers 4 1.75 1.25 1 0.8 0.76 0.7 0.7 (3-6) (1.4-2.4) (1-1.5) (0.8-1.2) (0.7-1.2) (0.6-1) (0.6-0.9) (0.6-0.9) Natural forest 9 4 2.8 2.05 1.7 1.5 1.3 0.95 (4-12) (2.5-4.5) (1.4-3.4) (1.2-2.5) (1.2-2.2) (1-18) (0.9-1.6) (0.7-1.1)
 R2/sample DBH range Forest typea Equation size (cm) Tropical moist hardwoods' Y= EXP[-2.289 + 2.694LN(DBH) 0.98/226 -0.021(LN(DBH) )] 5-148 Tropical wet hardwoodsb Y = 21.297-6.953(DBH) + 0.92/176 0.740(DBH) 4-112 Temperate/tropical pines Y = 0.887 + [(10,486(DBH)284/ 0.98/137 (DBH2.84) + 376,907] 0.6-56 Temperate US eastern hardwoods Y = 0.5 + [(25,000(DBH)25)/ 0.99/454 ( (DBH25) + 246,872 1.3-83.2

aUpdated from Brown (1997), Brown and Schroeder (1999) and Schroeder et al. (1997); Y= dry biomass in kg/tree, DBH = diameter at breast height, LN = natural log; EXP = "e raised to the power of'

bDelaney et al. (1999); Y= biomass in kg/tree, HT = height of trunk (m), LN = natural log aUpdated from Brown (1997), Brown and Schroeder (1999) and Schroeder et al. (1997); Y= dry biomass in kg/tree, DBH = diameter at breast height, LN = natural log; EXP = "e raised to the power of'

bDelaney et al. (1999); Y= biomass in kg/tree, HT = height of trunk (m), LN = natural log

 Species Model a b R2 SE Bauhinia racemosa Y = a + b'X (X = GBH2*height) 0.0431 0.0025 0.97 3.17 Zizphus xylopyra log10 Y = a + b*logX (X = GBH) -3.20 2.87 0.94 0.12 Tectona grandis Log Y = a + b*logX (X = GBH) -2.85 2.655 0.98 0.075 Lannea coromandelica Y = a + b*X (X = GBH2*height) -1.84 0.002 0.98 14.49 Miliusa tomentosa Y = a + b'X (X = GBH2*height) -0.68 0.0024 0.99 1.33

° If no species-specific equations are available, use generic equations or those specific to a given forest or plantation type

Step 3: Enter the DBH, height and the biomass volume equation into a software package such as Excel

Step 4: Calculate the volume of each tree based on the DBH or DBH and height using the software

Step 5: Aggregate the volume of all the sample trees by species if species-specific equations are used to obtain the total volume of the trees (m3)

Step 6: Convert the volume of the trees in the sample plots to biomass in tonnes using density of biomass for the selected species

° If species-specific density values are not available or cannot be derived for all the species, use the density of the dominant species for converting the whole forest or plantation volume to biomass

° If the equation provides only the merchantable volume, use biomass conversion and expansion factor to obtain total biomass in kilograms per hectare or tonnes per hectare

Step 7: Extrapolate the biomass from the sample plot area to tonnes of biomass per hectare.

Basal area based biomass equations Basal area of all the trees of a given species or of all trees in the sample plots can be estimated using the DBH values.

Evergreen forest: biomass (t/ha) = -2.81 + 6.78 (BA), r2= 0.53 (Murali et al. 2005)

Deciduous forest: biomass (t/ha) = 11.27 + 6.03 (BA) + 1.83 (height), r2 = 0.94

(Murali et al. 2005)

Eucalyptus hybrid volume (V in m3/ha) = - 2.4992 + 0.287 (BA) + height

(from field measurements)

where:

BA = basal area in square metre per hectare. 