# 3. METHODS FOR ESTIMATING BIOMASS DENSITY FROM EXISTING DATA

This primer discusses two approaches for estimating the biomass density of woody formations based on existing forest inventory data. The first approach is based on the use of existing measured volume estimates (VOB per ha) converted to biomass density (t/ha) using a variety of "tools" (Brown et al. 1989, Brown and Iverson 1992, Brown and Lugo 1992, Gillespie et al. 1992). The second approach directly estimates biomass density using biomass regression equations. These regression equations are mathematical functions that relate oven-dry biomass per tree as a function of a single or a combination of tree dimensions. They are applied to stand tables or measurements of individual trees in stands or in lines (e.g., windbreaks, live fence posts, home gardens). The advantage of this second method is that it produces biomass estimates without having to make volume estimates, followed by application of expansion factors to account for non-inventoried tree components. The disadvantage is that a smaller number of inventories report stand tables to small diameter classes for all species. Thus, not all countries in the tropics are covered by these estimates. To use either of these methods, the inventory must include all tree species. There is no way to extrapolate from inventories that do not measure all species.

Use of forest inventory data overcomes many of the problems present in ecological studies. Data from forest inventories are generally more abundant and are collected from large sample areas (subnational to national level) using a planned sampling method designed to represent the population of interest. However, inventories are not without their problems. Typical problems include:

· Inventories tend to be conducted in forests that are viewed as having commercial value, i.e., closed forests, with little regard to the open, drier forests or woodlands upon which so many people depend for non-industrial timber.

· The minimum diameter of trees included in inventories is often greater than 10 cm and sometimes as large as 50 cm; this excludes smaller trees which can account for more than 30% of the biomass.

· The maximum diameter class in stand tables is generally open-ended with trees greater than 80 cm in diameter often lumped into one class. The actual diameter distribution of these large trees significantly affects aboveground biomass density.

· Not all tree species are included, only those perceived to have commercial value at the time of the inventory.

· Inventory reports often leave out critical data, and in most cases, field measurements are not archived and are therefore lost.

· The definition of inventoried volume is not always consistent.

· Very little descriptive information is given about the actual condition of the forests, they are often described as primary, but diameter distributions and volumes suggest otherwise (e.g., Brown et al. 1991, 1994).

· Many of the inventories are old, 1970s or earlier, and the forests may have disappeared or changed.

Despite the above problems, many inventories are very useful for estimating biomass density of forests. In the next two sections, details of the methods for using existing forest inventory data for biomass density estimation are presented.

## 3.1 APPROACH 1: BIOMASS DENSITY BASED ON EXISTING VOLUME DATA

The method presented here is based on existing volume per ha data and is best used for secondary to mature closed forests only, growing in moist to dry climates. It should be used for closed forest only because the original data base used for developing this approach was based on closed forests. The primary data needed for this approach is VOB/ha, that is inventoried volume over bark of free bole, i.e. from stump or buttress to crown point or first main branch. Inventoried volume must include all trees, whether presently commercial or not, with a minimum diameter of 10 cm at breast height or above buttress if this is higher. If the minimum diameter is somewhat larger, the VOB/ha information can be used with some adjustments as shown below. However, such adjustments to the primary data introduce larger errors in the estimate.

### 3.1.1 GENERAL EQUATION

Biomass density can be calculated from VOB/ha by first estimating the biomass of the inventoried volume and then "expanding" this value to take into account the biomass of the other aboveground components as follows (Brown and Lugo 1992):

 (Eq. 3.1.1) Aboveground biomass density (t/ha) = VOB * WD * BEF where: WD = volume-weighted average wood density (1 of oven-dry biomass per m3 green volume) BEF = biomass expansion factor (ratio of aboveground oven-dry biomass of trees to oven-dry biomass of inventoried volume)

### 3.1.2 VOLUME-WEIGHTED AVERAGE WOOD DENSITY (WD)

Wood density here is defined as the oven-dry mass per unit of green volume (either tons/m3 or grams/cm3). Wood densities for trees of tropical American forests tend to be reported in these units. In contrast, few data on wood density for trees in tropical Africa and Asia are expressed in these units (Reyes et al. 1992). Rather, wood density is expressed in units of mass of wood at 12% moisture content per unit of volume at 12% moisture content. A regression equation was developed by Reyes et al. (1992) to convert wood density based on 12% moisture content to wood density based on oven-dry mass and green volume (Eq. 3.1.2).

 (Eq. 3.1.2) Y = 0.0134 + 0.800 X (r2= 0.99; number of data points n = 379) where: Y = wood density based on oven-dry mass/green volume X = wood density based on 12% moisture content

Ideally, a weighted average (based on dominance of each species as measured by volume) wood density value is best used here, calculated as follows.

 (Eq. 3.1.3) WD = {(V1/Vt *WD1 + (V2/Vt) *WD2 +........... (Vn/Vt)* Wdn where: V1, V2,.... Vn = volume of species 1, 2,.. to the nth species Vt = total volume WD1 WD2,..... Wdn = wood density of species 1, 2,...... to the nth species

However, sufficient wood density data of forest species to do such calculations are not always available. In these situations it is best to estimate a weighted mean wood density based on known species, using an arithmetic mean from the table below for unknown species. Wood density data for 1180 tropical tree species are given in Appendix 1.

The arithmetic mean and most common wood density values (t/m3 or g/cm3) for tropical tree species by region

 Tropical region No. of species Mean Common range Africa 282 0.58 0.50-0.79 America 470 0.60 0.50-0.69 Asia 428 0.57 0.40-0.69

(from Reyes et al. 1992)

### 3.1.3 BIOMASS EXPANSION FACTOR (BEF)

Broadleaf forests: Biomass expansion factor is defined as: the ratio of total aboveground oven-dry biomass density of trees with a minimum dbh of 10 cm or more to the oven-dry biomass density of the inventoried volume. Such ratios have been calculated from inventory sources for many broadleaf forest types (young secondary to mature) growing in moist to seasonally dry climates throughout the tropics. Sufficient data were included in these inventory sources to independently calculate aboveground biomass density and biomass of the inventoried volume (Brown et al. 1989). The reported inventoried volume in the studies was based on the definition given above. Analysis of these data show that BEFs are significantly related to the corresponding biomass of the inventoried volume according to the following equations (Brown and Lugo 1992):

 (Eq. 3.1.4) BEF = Exp{3.213 - 0.506*Ln(BV)} for BV < 190 t/ha 1.74 for BV>=190t/ha (sample size = 56, adjusted r2 = 0.76) where: BV = biomass of inventoried volume in t/ha, calculated as the product of VOB/ha (m3/ha) and wood density (t/m3)

Conifer forests: No model for calculating biomass expansion factors for native conifer forests is available at present because of the general lack of sufficient data for the type of analysis performed for the broadleaf forests. However, one would expect that BEFs for tropical pine forests would vary less than for broadleaf forests because of the generally similar branching pattern exhibited by different species of pine trees. Biomass expansion factors have been calculated based on a limited data base of 12 stands of Pinus oocarpa growing in Guatemala (Peters 1977) and the methodology given in Brown et al. (1989). The inventoried volume in this case was defined as volume over bark/ha from the stump to the tip of the tree; i.e. main stem based on total height. Volumes of these stands ranged from 64 to 331 m3/ha. The BEFs based on biomass of the main stem ranged from 1.05 to 1.58, with a mean of 1.3 (standard error of 0.06). No significant relationship between BEF and main stem biomass was obtained. Until additional data become available, a BEF of 1.3 can be used, with caution, for biomass estimation of pine forests.

### 3.1.4 EXAMPLES OF CALCULATIONS OF BIOMASS DENSITY

To demonstrate the application of this methodology, aboveground biomass density is calculated for the following examples:

Example 1.

Broadleaf forest with a VOB = 300 m3/ha and weighted average wood density; WD = 0.65 t/m3

Step 1 Calculate biomass of VOB: = 300 m3/ha x 0.65 t/m3 = 194 t/ha

Step 2 Calculate the BEF (Eq. 3.1.4): BV > 190 t/ha, therefore BEF = 1.74

Step 3 Calculate aboveground biomass density (Eq. 3.1.1): = 1.74 x 300 x 0.65

= 338 t/ha

Example 2.

Broadleaf forest with a VOB = 150 m3/ha and weighted average wood density, WD = 0.55 t/m3

Step 1 Calculate biomass of VOB: = 150 m3/ha x 0.55 t/m3 = 82.5 t/ha

Step 2 Calculate the BEF (Eq. 3.1.4): BV < 190 t/ha, therefore BEF = 2.66

Step 3 Calculate aboveground biomass density (Eq. 3.1.1): = 2.66 x 150 x 0.55

= 220 t/ha

As can be seen from these two examples, although there is a two-fold difference in VOB/ha, there is only a 1.5-fold difference in aboveground biomass density.

### 3.1.5 ADJUSTMENTS TO APPROACH USING VOLUME EXPANSION FACTORS (VEF)

Forest inventories often report volumes to different standards, e.g., to minimum diameters greater than 10 cm. These inventories maybe the only ones available, and thus it is important that a means to unify the volume data to some kind of standard be developed so that these inventories can be used to estimate biomass density.

In an attempt to unify data on inventoried volume measured to a minimum diameter greater than 10 cm, volume expansion factors (VEF) were developed (Brown 1990). After 10 cm, a common minimum diameter for inventoried volumes ranges between 25-30 cm. Data from inventories that reported volumes to minimum diameters in this range were combined into one data set to obtain sufficient number of studies for analysis. The VEF is defined here as the ratio of inventoried volume for all trees with a minimum diameter of 10 cm and above (VOB10) to inventoried volume for all trees with a minimum diameter of 25-30 cm and above (VOB30). The uncertainty in extrapolating inventoried volume based on a minimum diameter of larger than 30 cm to inventoried volume to a minimum diameter of 10 cm is likely to be large and is not suggested. Estimates of the VEFs were based on a few inventories from tropical Asia and America which provided sufficient detail for this analysis (see Brown 1990). Volume expansion factors based on these inventories ranged from about 1.1 to 2.5, and they were related to the VOB30 as follows:

 (Eq. 3.1.5), VEF = Exp{1.300 - 0.209*Ln(VOB30)} for VOB30 < 250 m3/ha = 1.13 for VOB30 > 250 m3/ha (sample size = 66, adjusted r2 = 0.65)

To demonstrate the use of this correction factor to estimating biomass density, consider the following example:

Broadleaf forest with a VOB30 = 100 m3/ha and weighted average wood density; WD = 0.60 t/m3

Step 1 Calculate the VEF from Eq. 3.1.5: = 1.40

Step 2 Calculate VOB10: = 100 m3/ha x 1.40 = 140 m3/ha

Step 3 Calculate biomass of VOB10: = 140 m3/ha x 0.60 t/m3 = 84 t/ha

Step 4 Calculate the BEF from Eq. 3.1.4: BV < 190 t/ha, therefore BEF = 2.64

Step 5 Calculate aboveground biomass density (Eq. 3.1.1): = 2.64 x 140 x 0.60

= 222 t/ha

### 3.1.6 USE OF INVENTORIES OF OPEN FORESTS AND WOODLANDS

No general approach for estimating aboveground biomass density of open forests and woodlands based on inventoried volume has been developed because of the general lack of suitable data. The method described above for closed forests is not generally applicable because trees have different branching patterns (often multi-stemmed) and inventoried volume of open forests and woodlands is usually measured to different standards than for closed forests. For example, inventories done in open forests and woodlands generally report inventoried volume per ha to minimum diameters less than 10 cm, and also often include branch volume. Earlier work suggested that total aboveground biomass density of open forests could be up to three times the inventoried volume (Brown and Lugo 1984), however further field testing would be needed to confirm this. It is recommended that the approach described in section 3.2 (next) for estimating aboveground biomass density be used for open forests and woodlands.

## 3.2 APPROACH 2: BIOMASS DENSITY BASED ON STAND TABLES

Another estimate of biomass density is derived from the application of biomass regression equations to stand tables. The method basically involves estimating the biomass per average tree of each diameter (diameter at breast height, dbh) class of the stand table, multiplying by the number of trees in the class, and summing across all classes. A key issue is the choice of the average diameter to represent the dbh class. For small dbh classes (10 cm or less), the mid-point of the class has been used (e.g., Brown et al. 1989). The quadratic-mean-diameter of a dbh class would be a better choice, particularly for wider diameter classes. If basal area for each dbh class is known, the quadratic-mean-diameter (QSD) of trees in the class, or the dbh of a tree of average basal area in the class, should be used instead. To calculate the QSD, first divide the basal area of the diameter class by the number of trees in the class to find the basal area of the average tree. Then the dbh = 2 x {square root (basal area/3.142)}. For example, the dbh of a tree of basal area of 707 cm2 = 2 x {square root (707/3.142)} = 30 cm.

### 3.2.1 BIOMASS REGRESSION EQUATIONS

The biomass regression equations for broadleaf forests were developed from a data base that includes trees of many species harvested from forests from all three tropical regions (a total of 371 trees with a dbh ranging from 5 to 148 cm from ten different sources; see Appendix 2; equation 3.2.2 in the table below was developed by Martinez-Yrizar et al. (1992)). The biomass regression equations can provide estimates of biomass per tree. The data base was stratified into three main climatic zones, regardless of species: dry or where rainfall is considerably less than potential evapotranspiration (e.g. <1500 mm rain/year and a dry season of several months), moist or where rainfall approximately balances potential evapotranspiration (e.g. 1500-4000 mm rain/year and a short dry season to no dry season), and wet or where rainfall is in excess of potential evapotranspiration (e.g. >4000 mm rain/year and no dry season). These rainfall regimes are just guides, and generally apply to lowland conditions only. As elevation increases, as in mountainous areas, temperature decreases as does potential evapotranspiration and the climate zone becomes wetter at a given rainfall. For instance, an annual rainfall of 1200 mm in the lowlands would be the dry zone, but at about 2500 m it would be the wet zone. Therefore, judgement should be used in selecting the appropriate equation.

Figure 1 - Relationship between oven-dry biomass of tropical trees and dbh for (a) biomass regression equations by all climatic zones and trees with dbh between 5 to 40 cm, and (b) equations for moist and wet zones for trees in the full range of dbh. The equations are given in Section 3.2.1.

(a) All zones (b) Moist and wet zones Biomass regression equations for estimating biomass of tropical trees. Y= biomass per tree in kg, D = dbh in cm, and BA = basal area in cm2

 Equation Number Climatic zone Equation Range in dbh (cm) Number of trees Adjusted r2 3.2.1 DRY a Y = exp{-1.996+2.32*ln(D)} 5-40 28 0.89 3.2.2 Y =10^{-0.535+log10 (BA)} 3-30 191 0.94 3.2.3 MOIST b Y = 42.69-12.800(D)+1.242(D2) 5-148 170 0,84 3.2.4 Y = exp{-2.134+2.530*ln(D)} 0.97 3.2.5 WET c Y = 21.297-6.953(D)+0.740(D2) 4-112 169 0.92

None of the regression equations should be used for estimating the biomass of trees whose diameter greatly exceeds the range of the original data.

a Eq. 3.2.1 revised from Brown et al. (1989) for dry forest in India, and Eq. 3.2.2 from Martinez-Yrizar et al. 1992 for dry forest in Mexico (original equation based on BA). For dry zones with rainfall less than 900 mm/year use equation 3.2.2 and for dry zones with rainfall > 900 mm/year use equation 3.2.1. "exp" means "e to the power of".

b Both equations are based on the same data base; A. J. R. Gillespie, pers. comm. based on a revision of equation in Brown et al. (1989).

c From Brown and Iverson (1992)

Analysis of the data bases implied that the trees within the dry and wet zones could be grouped together within a zone (Brown et al. 1989). Within the moist zone, the analysis indicated that different data bases were not statistically homogeneous and theoretically could not be grouped. For practical purposes, however, the moist zone was considered to be the population of interest and the different data bases were considered to be subsamples from this population. Thus a combined regression for the pooled data sets was developed (Brown et al. 1989).

Biomass regression equations for several species of pines combined into one data base was also developed. A simple method for estimating the biomass of palms was also developed (Frangi and Lugo 1985).

Broadleaf forests: Details of the: (1) evaluation of several linear, nonlinear, and transformed nonlinear regression equations, (2) the testing of the behavior of the equations, and (3) selection of the final equations are given in Brown et al. (1989). A listing of the original data are given in Appendix 2.

The behaviour of all these regression equations as a function of dbh is illustrated in Figure 1. Application of all five regression equations for smaller diameter classes shows that for a given dbh biomass is highest for trees in the moist zone (Fig. 1a; Eq. 3.2.3 and 3.2.4), followed by trees in the wet zone (Eq. 3.2.5), and trees in the dry zone (Eq. 3.2.1 and 3.2.2).

The regression equation for dry zone trees given by Eq. 3.2.1 gives higher biomass per tree for a given diameter than the regression developed for the Mexican dry zone (Eq. 3.2.2; see Fig. la). As tree diameters increase, the difference becomes larger so that by diameter 40 cm (the upper limit for the data bases) the biomass per tree based on Eq. 3.2.1 is about 1.7 times higher than that based on Eq. 3.2.2. The main reason for this trend is that the trees used for developing Eq. 3.2.1 grow in a dry deciduous forest zone of India that receives about 1200 mm/year of rainfall in contrast to the dry deciduous forests in Mexico where rainfall averaged about 700 mm/year. The result of this difference in rainfall regime is that the Mexican trees are shorter than those in India, and thus biomass for a given diameter is less. For example, height for the Mexican trees commonly ranged between 4 to 9 m, with an average height of about 7 m (Martinez-Yrizar et al. 1994), whereas those in India had heights up to about 15m (Bandhu 1973).

The tropical dry forest zone describes areas where rainfall is less than 1500 mm/year or so. For a dry zone where rainfall is similar to that for the dry deciduous zone of Mexico (about 700 to 900 mm/year or less), Eq. 3.2.2 could be used. For dry zone 'forests at the wetter end of the zone, i.e., rainfall greater than 900 mm/year, Eq. 3.2.1 should be used. However, because of the high variability of tree biomass with rainfall in the dry zone, it is recommended that local biomass regression equations be developed, or at least a few trees harvested to test how well the two equations presented here fit the local conditions.

The moist zone equations (Eq. 3.2.3 and 3.2.4) give essentially the same biomass estimates for trees with dbhs up to about 80 cm (Fig. 1b). After this diameter limit, estimates of the biomass per tree diverge markedly. However, the estimates from Eq. 3.2.4 are closer to the original data (cf. Appendix 2) and the r2 of the regression equation is higher than for Eq. 3.2.3 (0.97 versus 0.84). It is not recommended that any of the regression equations be used for estimating the biomass of trees whose dbh greatly exceeds the range of the original data. However, if trees with dbh greater than 160 cm or so are encountered in an inventory, it is recommended that Eq. 3.2.3 be used for these trees as the function behaves better in these larger classes. Equation 3.2.4 is an exponential function and biomass per tree increases rapidly at large diameters. In the ideal situation where many trees with dbhs larger than 150 cm are encountered, some new field measurement of their biomass should be made (see section 4.).

It is important that the biomass of trees with large dbh be estimated as accurately as possible because their contribution to the biomass of a forest stand is much more than their number suggests. For example, in mature moist tropical forests, the biomass in trees of dbh greater than 70 cm can account for as much as 40% of the stand's biomass density, although the number of these trees corresponds to less than 5% of all trees (Brown and Lugo 1992, Brown 1996).

The regression equation for trees in the wet zone (Eq. 3.2.5) matches the original data well and behaves well at larger diameters. As with the moist equation however, caution should be taken in using the equation much beyond the original data.

Palm trees: In many tropical moist and wet forests, palms are sometimes common. Estimating their biomass is difficult as few studies have been made on this topic. Furthermore, many different species exist with different forms, different proportions of their mass in leaves, and different stem densities. To estimate the biomass of palms, height measurements as well as diameter measurements will be needed. A simple way to estimate their biomass is to compute the volume of the stem as a cylinder (basal area x stem height) and then multiply this by an estimate of the density. Wood density of palms varies considerably by species and within the stem of the same species, and it can range from about 0.25 to almost 1.0 t/m3 (Rich 1987). The biomass of the leaves also has to be added, which in total may range from 10 to 65% of the stem biomass (Frangi and Lugo 1985, Rich 1986). An alternative approach is to use a regression equation developed for the palm Prestoea montana, a common species in the moist forests of Puerto Rico. Two regression equations were developed, based on either total height or stem height as follows (from Frangi and Lugo 1985):

 (Eq. 3.1.6) Y (biomass, kg) = 10.0 + 6.4 * total height (m); n=25, r2=0.96

 (Eq. 3.1.7) Y (biomass, kg) = 4.5 + 7.7 * stem height (m); n=25, r2=0.90

An example is given here to demonstrate the variation in the estimates from the three different methods. For a palm of 15 cm diameter, 15 m total height, and 12 m stem height, the biomass estimates are:

 Method 1 Based on volume: stem volume = 0.21 m3, wood density = 0.25 t/m3; stem mass = 53.0 kg; assume leaves are 65% of stem, total biomass = 87 kg Method 2 Based on Eq. 3.2.6: total biomass = 86 kg Method 3 Based on Eq. 3.2.7: total biomass = 97 kg

The three methods give similar values. Unless the forest is composed mostly of palms, any of these methods would be suitable for estimating biomass of palms scattered throughout moist or wet forests. However, the variation in wood density by species must be taken into consideration; higher wood density estimates need to be used for denser species. In the case of forest stands where palms are dominant, local biomass regression equations would need to be developed, or at least measurements of wood density of dominant palm species would need to be measured (see section 4.).

Conifer forests: Few data on the biomass of conifer trees for tropical zones exist. To develop a preliminary biomass regression equation, data on the biomass of harvested pine trees from eight literature sources, including pine forests from the southeastern USA, India, and Puerto Rico were compiled. Several species of pine included in these sources were combined into one data base and analyzed as was done for the broadleaf forests. The resulting equation is:

 (Eq. 3.1.8) Y(kg) = exp{-1.170+2.119*ln(D)} D = dbh, cm; range in dbh = 2-52 cm; number of trees =63; adjusted r2=0.98

For most situations where an estimate of the biomass density of pine forests is needed, Eq. 3.2.8 can be used. However, if time and resources are available, a local biomass regression equation should be developed.

Below is an example of how to use the biomass regression equations with stand tables. The stand table example is for a moist forest in Ghana. Biomass density of this forest was estimated using the moist equation, Eq. 3.2.3. Maximum diameters are at about the upper limit for this equation (about 150 cm).

Use if the biomass regression equation, an example

 Diameter class (cm) 5-20 20-40 40-60 60-90 90-120 120-150 >150 1. Number trees/ha 794 161 25.2 12.3 3.3 1.05 0.23 2. Mid-point of class, cm a 12.5 30 50 75 105 135 155 b 3. Biomass of tree at mid-point of class using Eq. 3.2.3; kg 70.5 646 2353 6563 15375 29038 41 187 4. Biomass of all trees, t/ha = (product of rows 1 and 3)/1000° 56 104 59.3 80.7 50.8 30.5 9.5 Total aboveground biomass = sum of row 4 = 391 t/ha

a As no additional information was available the mid-point of the diameter class was assumed to represent the class; as the classes are wide this could overestimate the biomass density estimate.

b Assumed to be diameter of largest class; choice of this upper limit when no additional data are present is problematic (see section 3.2.4).

c To convert kg to t

Although the approach presented here has emphasized the use of regression equations with stand tables, the regression equations can also be used with individual tree measurements from stands. Using individual tree measurements overcomes the problem of choosing the diameter of the class.

### 3.2.3 PROBLEMS WITH REGRESSION APPROACH

Several problems exist with this method, namely: (1) the small number of large diameter trees used in the regression equations (e.g., for the moist equation, the largest dbh was 148 cm, with only five trees >100 cm diameter), (2) the open-ended nature of the large diameter classes of the stand tables, (3) wide and often uneven-width diameter classes, (4) selection of the appropriate average diameter to represent a diameter class, and (5) missing smaller diameter classes (i.e., incomplete stand tables to minimum diameter of 10 cm). To overcome the potential problem of the lack of large trees (problem 1), equations were selected that were expected to behave reasonably up to 150 cm or so or upon extrapolation somewhat beyond this limit (Brown et al. 1989). Rarely are stand tables encountered that contain trees much larger than the maximum dbh used in the regression.

The problem with open-ended large diameter classes is knowing what diameter to assign to that class. Sometimes additional information is included that educated estimates can be made, but this is often not the case. Clearly, further improvements in reporting the distribution of the largest diameter trees in stand tables would improve the reliability of the biomass density estimates as it is often these large trees that account for significant proportions of the total biomass density (Brown and Lugo 1992, Brown 1995). In the above example, the approximately 1.3 trees greater than 120 cm constitute about 70% of the biomass represented by the 794 trees in the smallest class.

Many inventories often report stand tables with wide and/or uneven-width classes. The most unbiased biomass density estimate is obtained when diameter classes are small, about 10 cm wide or smaller, and are even-width for the whole stand table. This problem is illustrated by the following example for a moist forest where in Example A the classes are 10 cm wide and in Example B two classes are combined to make them 20 cm wide.

Example A

 Diameter class (cm) 10-19 20-29 30-39 40-49 50-59 60-69 70-79 80-89 90-99 100-109 110-119 >120 Number of stems/ha 183 80 35.1 11.8 4.7 2.3 1.5 0.9 0.5 0.4 0.2 0.5 Biomass/tree (kg) at mid-point of class(Eq. 3.2.3) 112 407 954 1 802 2995 4570 6563 9008 11936 15375 19354 23900 Biomass of trees (product of rows 1 and 2), t/ha 20.5 32.6 33.5 21.3 14.1 10.5 9.8 8.1 6.0 6.2 3.9 12.0 Total biomass density =178 t/ha

Example B

 Diameter class (cm) 10-29 30-49 50-69 70-89 90-109 >110 1. Number of stems/ha 263 46.9 7.0 2.4 0.9 0.7 2. Biomass/tree (kg) at mid-point of class(Eq. 3.2.3) 232 1 338 3732 7727 13590 21 555 3. Biomass of trees (product of rows 1 and 2), t/ha 60.9 62.7 26.1 18.5 12.2 15.1 Total biomass density =196 t/ha

The biomass density in Example B, based on the 20 cm wide classes, is about 10% higher than that in Example A, based on the 10 cm wide class. In general, wider classes will overestimate the biomass density. However, regular estimation of biomass density as part of inventory analysis or accessibility to the field data should not encounter these problems because original inventory data generally includes details down to individual trees. Estimating the biomass of individual trees in inventory plots directly would overcome problems (2) to (4) given above. Foresters have wide experience in these type of calculations as they are basically no different from estimating volumes from volume equations.

To overcome the problem of incomplete stand tables, an approach has been developed for estimating the number of trees in smaller diameter classes based on number of trees in larger classes (Gillespie et al. 1992). It is recommended that the method described here be used for estimating the number of trees in one to two small classes only to complete a stand table to a minimum diameter of 10 cm. It is also emphasized that this method should only be used when no other data for biomass estimation are available.

The method is based on the concept that uneven-aged forest stands have a characteristic exponential or "inverse J-shaped" diameter distribution. These distribution have a large number of trees in the small classes and gradually decreasing numbers in medium to large classes. Pull details of the theory behind the approach and of the different methods tested are given in Gillespie et al. (1992). The best method was the one that estimated the number of trees in the missing smallest class as the ratio of the number of trees in dbh class 1 (the smallest reported class) to the number in dbh class 2 (the next smallest class) times the number in dbh class 1. This method is demonstrated in the following example:

1 Assume that: the minimum diameter class is 20-30 cm and we wish to estimate the number of trees in the 10-20 cm class.

2 The number of trees in the 20-30 cm class equals 80, and the number in the 30-40 cm class equals 35.

3 The estimated number of trees in the 10-20 cm class is the number in the 20-30 cm class x (number in 20-30/number in 30-40); this equals 80 x (80/35) =183.

To use this approach, diameter classes must be of uniform width, preferably no wider than 10-15 cm, and should not be used for estimating numbers of trees in more than two "missing' classes.

## 3.3 BIOMASS ESTIMATES OF INDIVIDUAL

The regression equations reported above can be applied to inventories of individual trees planted in lines, as living fence posts, for dune stabilization, for fuelwood, etc. Biomass estimates for individual trees are particularly useful in drier regions where the trees are grown for all the aforementioned products and services. However, as discussed above, the regression equations for dry zone trees are based on a small data base. Furthermore, trees grown in lines or in more open conditions generally display different branching patterns and are likely to have more biomass for a given diameter than a similar diameter tree grown in a stand. Although the above regression equations could be used where no other data exist for rough approximations, new regression equations need to be developed for trees growing in open conditions.

## 3.4 BIOMASS ESTIMATES FOR PLANTATIONS

Estimating the biomass density of plantations can be done using techniques similar to those for native forests as described above. Inventoried volume can be converted to aboveground biomass density using Eq. 3.1.1 outlined in Section 3.1. However, the equation for BEFs (Eq. 3.1.4) would not necessarily work in the case of plantations of broadleaf species because tree form is likely to be different in managed forests and definitions of inventoried volumes are also likely to be different. It is recommended that BEFs be locally derived. The biomass regression equations for broadleaf species (Eq. 3.2.1-3.2.5) could also be used for plantations, but once again caution should be taken with their use. Direct biomass measurements of representative plantation trees should be made to check the validity of the regression equations, or even better local biomass regression equations should be developed. See Section 4 for further details on methods.

For plantations of conifer species, the average BEF of 1.3 given for pine forests in Section 3.1.3 could be used if measured volume was based on the total stem. In the case where diameters of individual plantation trees or diameter distributions are given, Eq. 3.2.8 could be used, taking the same precautions as for broadleaf species. Kadeba (1989) developed biomass regression equations for plantations of Pinus caribaea trees growing in the savanna zone of Nigeria with annual rainfall ranging from 1250 to 1800 mm/year. However, the data base spanned a small diameter range, about 15-25 cm, and each equation was based on 12 trees only. For situations that mimic the conditions of Kadeba's study, the reader is referred to his work.

In situations where lack of resources prevent the development of local biomass regression equations for plantations, use of any or the above approaches would give a reasonably good estimate of the aboveground biomass density.

## 3.5 BIOMASS OF OTHER FOREST COMPONENTS

This primer does not include methods or approaches for making biomass density estimates for (1) understorey (including e.g., bamboo or rattan), (2) belowground woody biomass such as fine and coarse roots, (3) forest floor fine litter (e.g., dead leaves, twigs, fruits, etc.), nor (4) lying and standing dead wood. Most efforts on biomass estimation to date have generally focused on the aboveground tree component because it accounts for the greatest fraction of total biomass density and the methods are straightforward and generally do not pose too many logistical problems. Commonly reported ranges of biomass density estimates for these other components are given below, although they must be used with caution as the data base on which they are built is limited.

Summary of estimates of biomass density of other forest components, expressed as a percent of aboveground biomass in trees

 Component Percent of aboveground! biomass of mature forest! Understorey £ 3 Belowground (roots) 4-230 Fine litter (dead plant material) £ 5 Dead wood 5-40

(sources of these data are given in the text)

The amount of biomass in understorey shrubs, vines, and herbaceous plants can be variable but is generally about 3 percent or less of the aboveground biomass of more mature forests (Jordan and Uhl 1978, Tanner 1980, Hegarty 1989, Lugo 1992). However, in secondary forests or disturbed forest, this fraction could be higher (e.g., up to 30%; Brown and Lugo 1990, Lugo 1992) depending on age of the secondary forest and openness of canopy. Palms are common in many tropical moist forests and they are also often ignored in forest inventories. Their contribution to total biomass density can be very variable, from nearly 100 percent to less than a few percent (see section 3.2.1 above for more details on estimating the biomass of this component).

The biomass of roots varies considerably among tropical forests depending mainly upon climate and soil characteristics (Brown and Lugo 1982, Sanford and Cuevas 1996). Root biomass is often expressed in relation to aboveground biomass, such as a root-to-shoot ratio (R/S ratio). A recent review of the literature gives the R/S ratios (from Sanford and Cuevas 1996) shown in the table on the next page.

These estimates of R/S are based on only a few studies (about 30) and not all of them are consistent with respect to depth of sampling and nor whether coarse roots were included. It seems clear from this discussion that more studies of root biomass and their relationship with other factors such as aboveground biomass, climate and soil, are needed.

The amount of dead plant material in a forest, or detritus, is composed of fine litter on the forest floor, (leaves, fruits, flowers, twigs, bark fragments, branches less than 10 cm diameter, etc.), standing dead trees and snags, and lying dead wood greater than 10 cm diameter. The biomass density of fine litter ranges from about 2 to 16 t/ha (average of 6 t/ha or less than 5% of aboveground biomass), with higher values generally in moist environments although no clear trend is apparent in the data base (Brown and Lugo 1982). The amount of fine litter on the forest floor represents the balance between inputs from litterfall and outputs from decomposition, both of which vary widely across the tropics.

The amount of dead wood in tropical forests is poorly quantified but extremely variable. It is potentially a large pool of organic matter, perhaps accounting for an amount equivalent to less than 10 percent to more than 40 percent of the aboveground biomass of a forest depending upon forest age and climatic regime (Saldarriaga et al. 1986, Uhl et al. 1988, Uhl and Kauffman 1990; Delaney et al. 1997). Lack of data on this significant forest component obviously can lead to underestimates of the total amount of biomass in a forest.

It is clear from the above discussion that ignoring these other forest components can seriously underestimate the total biomass of a forest by an amount equivalent to about 50 percent or more of aboveground biomass. Although beyond the scope of this primer, it is apparent that logistically and economically feasible methods and approaches must be developed to estimate this significant quantity of biomass and its range of uncertainty, especially for improving estimates of terrestrial sources and sinks of carbon and biogeochemical cycles of other elements.

 Forest type Range of R/S Average R/S Moist forest growing on spodosols 0.7 - 2.3 1.5 Lowland moist forest 0.04 - 0.33 0.12 Montane moist forests 0.11 - 0.33 0.22 Deciduous forests (e.g., tropical dry and seasonal forests) 0.23 - 0.85 0.47