Different approaches for estimating Caribbean subtropical wet forest stem volume from current FIA dataThomas J. Brandeis, Research Forester, USDA-FS Forest Inventory and Analysis, Southern Research Station

Introduction The Puerto Rico forest inventory resource bulletins of 1980 and 1990 reported volumes calculated following the Southern Forest Experimental Station’s methodology, which was the application of Smalian’s volume equation to different sections of each tree. Several more measurements were taken on each tree than are currently being taken under FIA national protocols to make these calculations. In the absence of these additional tree measurements, tree volume will be estimated differently for current resource reports. Different approaches to estimating tree stem volume in Puerto Rico and the US Virgin Islands are explored and compared. This study concentrates on the forests of the subtropical wet forest life zone, one of three forested life zones for which stem volumes estimates will be made in future FIA resource bulletins. Past measurements and methods During the 1980 and 1990 Puerto Rico forest inventories, the following measurements were taken on all trees with diameter at breast height (DBH) greater than 12.5 cm (see figure 1a):

DBH, outside bark double bark thickness (at DBH) stump DOB (diameter outside bark, taken at 30 cm height) total bole length (length from a 30 cm stump to a 10 cm top) pole-top DOB (if not 10 cm) total height (HT)

For trees with DBH > 27.5 cm, additional measurements were (see figure 1b):

sawlog height to DOB of 22.5 cm sawlog DOB (if not 22.5 cm)

Figure 1. Measurements taken on trees with DBH greater than 12.5 cm in the 1980 and 1990 forest inventories of Puerto Rico. Figure 1a is for pole-sized trees and figure 1b is for sawtimber-sized trees with DBH > 27.5 cm. DOB pole top

DBH

DOB stump

Pole timber (min DBH = 12.5 cm, min to DOB = 10.0 cm)

Stump height (30 cm)

DBH height (1.37 cm)

Bole length

Saw timber (min DBH = 27.5 cm, min top DOB = 22.5 cm)

DOB pole top

DOB sawlog top

DBH

DOB stump

Stump height (30 cm)

DBH height (1.37 cm)

Bole length

Sawlog length

Figure 1a. Figure 1b.

Under current inventory protocols, a volume estimate will have to be made from only a DBH (outside bark) and total height (HT) measurement. To do this, I’ve used the forest inventory data sets from 1980 and 1990 to explore three different approaches and compare the results;

1. applying a volume equation developed for the Caribbean National Forest 2. estimating stem volume from estimates of stem biomass 3. developing regression equations that model the relationship between stem volume

as calculated using Smalian’s equation in 1990, and each tree’s DBH and HT.

Methods Method 1. Applying the Wadsworth (1949) volume equation Wadsworth (1949) developed a volume equation and accompanying volume table for trees ranging in size from a DBH of 5 - 125 cm and total height from 3.0 - 36.5 m in the tabonuco (Dacryodes excelsa) forest type in the Caribbean National Forest, which falls within the subtropical wet and rain forest life zones (Ewel and Whitmore 1973).

Log10 (Volume) = 2.2020 * Log10 (DBH) + 0.4434 * Log10 (HT) – 1.8374 Method 2. Converting stem biomass to stem volume Scatena et al. (1993) estimated stem biomass for trees with diameters ranging from 2.5 – 57 cm in the subtropical wet and rain forest life zones of the Caribbean National Forest. To derive a stem volume estimate, stem biomass was converted to cubic centimeters by assuming an average specific gravity of 0.57 g/cm3 of wood.

Stem biomass = exp (0.983*{ln (DBH2 * HT)} - 3.759)

Method 3. Deriving and testing regression equations from the 1980 and 1990 forest inventory results Stem volume was calculated in 1990 by applying Smalian’s equations to different sections of the bole. Inside bark diameters and section heights were used in Smalian’s equation to calculate the wood volume of that section, where V = volume in cubic feet, HSEC = section height in feet, DIB1 = diameter inside bark at one end of section, DIB2 = diameter inside bark at other end of section, and 0.005454154 is a constant.

VSEC = [HSEC * {(DIB12) + (DIB1* DIB2) + (DIB2

2)}*0.005454154] / 3 Each section’s volume is then added together to produce a total stem volume. I used 570 pole-sized trees, 413 saw-timber trees (total 983) from the 1990 data set to develop regression equations. The square of DBH, total height and logarithmic transformation, produced the best results for estimating saw timber volume (figure 2). Pole timber was best estimated using only DBH (figure 3).

Figure 2. Relationship between sawtimber-sized stem volume as calculated using Smalian’s formula and D2H, both log transformed, for trees in the 1990 Puerto Rico forest inventory. Figure 3. Relationship between pole-sized stem volume as calculated using Smalian’s formula and diameter at breast height, both log transformed, for trees in the 1990 Puerto Rico forest inventory.

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ln(VPOLE) = -9.31599 + 1.98770[ln(DBH)]R2 = 0.9467

ln (DBH)

ln (

VPO

LE)

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2 2.5 3 3.5

ln(VPOLE) = -9.31599 + 1.98770[ln(DBH)]R2 = 0.9467

ln (DBH)

ln (

VPO

LE)

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ln(VSAW) = -8.77275 + 0.82624[ln(D2H)]R2 = 0.8127

ln (D2H)

ln (

VS

AW

)

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0

1

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8 9 10 11 12 13

ln(VSAW) = -8.77275 + 0.82624[ln(D2H)]R2 = 0.8127

ln (D2H)

ln (

VS

AW

)

Results Equation testing Stem volume was calculated using the three methods previously described for 428 pole-timber trees, and 344 saw-timber trees from the 1980 inventory data set. The calculated volume (Smalian’s), predicted volume (regression), Wadsworth (1949), and the Scatena et al. (1993) volume estimates were compared with analysis of variance (ANOVA) for all saw timber and pole-sized trees, and in 10 cm diameter classes (figure 4). ANOVA showed no significant differences between the calculated and predicted stem volumes for pole-sized trees (P-value = 0. 6791). With the exception of the 40 cm class, where the calculated volume was 11% higher than the predicted volume (P-value = 0.0303), the calculated and predicted saw-timber volumes were not significantly different at the 0.05 alpha-level. Both the calculated and predicted volumes were consistently lower than the volume estimates coming from the equations by Wadsworth (1949) and Scatena et al. (1993), which were very comparable to each other.

Conclusions Applying the regression equations developed from the 1990 forest inventory data set produces stem volume estimates comparable to direct calculation with Smalian’s formula, the method used in previous resource bulletins for Puerto Rico. However, to estimate volume growth and change over the past ten years, tree’s volume in 1990 should be re-estimated using these new regression equations rather than make the comparison using directly calculated values. These results would indicate that stem volume regression equations can also be developed for trees in the moist and dry forest life zones by taking the measurements needed for Smalian’s formula on a subset of inventoried trees. Literature Cited Scatena, F. N., W. L. Silver, T. Siccama, A. Johnson, and M. J. Sanchez. 1993. Biomass and nutrient

content of the Bisley Experimental Watershed, Luquillo experimental Forest, Puerto Rico, before and after Hurricane Hugo, 1989. Biotropica 25:15-27.

Wadsworth, F. H. 1949. The development of the forest lands resources of the Luquillo Mountains, Puerto Rico. PhD. Dissertation. University of Michigan, Ann Arbor, MI.

Figure 4. Mean stem volume estimates for 10 cm diameter (DBH) classes, with standard errors of the mean; directly calculated with Smalian’s formula (CALC), predicted from the pole and sawtimber regression models developed in this study (PRED), converted from the Scatena et al. (1993) stem biomass estimate (SCAT), and predicted from the Wadsworth (1949) volume equation (WAD).

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Photo courtesy of John Francis