Tree Biomass Equations for the Forests of the Luquillo Mountains

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Tree Biomass Equations for the Forests of the Luquillo Mountains
Commonwealth Forestry Review Volume 71(l), 1992 35
Tree Biomass Equations for the Forests of the Luquillo
Mountains, Puerto Rico*
PETER L. WEAVER and ANDREW J. R. GILLESPIE
Institute of Tropical Forestry, Southern Forest Experiment Station, USDA Forest Service, Call Box 25000, Rio Piedras,
Puerto Rico 00928
SUMMARY
Regression equations were derived to determine total above-ground biomass and above-ground woody biomass (kg per tree) as a function
of tree diameter at breast height (D, em) as the sole predictor, as well as (D 2x H (height, m) as the predictor, for the tabonuco, colorado
and dwarf forests in the Luquillo Experimental Forest of Puerto Rico.
RESUME
L'on a derive des equations de regression afin de determiner la biomasse totale au-dcssus du sol et la biomasse ligneuse au-dessus du sol
(kg par arbre) comme une fonction du diametre a hauteur d'homme (D, em) comme le seul predictor, ainsi que (D 2 X H (hauteur, m))
comme Ie predictor, pour les forets de tabonuco, colorado et nain dans la Foret experimentale de Luquillo en Porto Rico.
RESUMEN
Se derivar6n equaciones de regresion para determinar biomasa total sabre el terreno y biomasa de madera sobre el terreno (kg par arbol)
como una Iuncion del diametro al pecho (D) como el unico predictor, tanto como (D2 X H (altura)) como el predictor, para los bosques
de tabonuco, colorado y enano en el Bosque Experimental de Luquillo en Puerto Rico.
INTRODUCTION
Biomass estimates are critical for studying ecosystem structure and function (Whittakeret al., 1974). Numerous
regressions have been derived to predict tree biomass as a
function of easily measured dimensions such as diameter
and height (e.g. Crow, 1978; Brown et al., 1989). The purpose of this paper is to report various regression equations
for estimating total above-ground biomass and total aboveground woody biomass for three forest types in the Luquil10 Mountains of Puerto Rico. These equations predict
biomass on a per tree basis, independent of species, and are
expected to be useful for other mountainous Caribbean
islands with similar forest types.
THE STUDY AREA
The Luquillo Mountains rise to 1075m in elevation less
than 10km from the ocean in northeastern Puerto Rico.
Rainfall increases from 2300mm/yr at 200m to over
4500mm/yr at the summits while temperature declines from
23°C to 19°C over the same gradient. Ascending the mountains, four major forest types are encountered: tabonuco,
from the border at 150m to 600m in elevation; colorado,
from 600 to 900m; dwarf, from 900 to the 1075m summits;
and palm brake, scattered in ravines and on steep slopes
above SOOm in elevation. Comparisons of stand structure
and dynamics of these forests were summarized elsewhere
(Weaver and Murphy, 1990).
METHODS
The forests of the Luquillo Mountains were sampled for
dry weight tree biomass by different investigators during a
period of 20 years - tabonuco forest (Ovington and Olson,
1970), colorado forest (Weaver and Murphy, 1990), and
dwarf forest (Weaver, 1990). Sample trees from the tabonuco and colorado forests were cut in undisturbed stands
characterized by primary and late secondary tree species.
The dwarf forest tree samples, in contrast, were cut in a
plot that had been cleared 20 years earlier by the wreck of
an aircraft (Weaver, 1990). Three-quarters of the stems
sampled at the aeroplane wreck, however, were considered
to be primary species. The regression variables, their
ranges, and the numbers of species in each data set are
shown in Table 1. Field samples of dwarf biomass were not
partitioned into leafy and woody components.
Preliminary graphical and regression analysis indicated
that the tabonuco data, which span the range of tree diameters (D ~ tree diameter at breast height, or 104m above the
ground), would be best fit using separate regressions for
trees above and below Scm. Sampled colorado forest trees
were all >Scm in diameter. The -dwarf forest trees were
<Scm in diameter with the exception of one tree of a
species common to the colorado forest. This tree was analysed with the colorado data set.
We developed separate regressions of above-ground
woody biomass and total above-ground biomass (leafy +
woody) in kg vs. tree diameter (D) in em, and vs. D' times
tree height (H) in m (Table 2). A variety of models were
fitted to each data set to determine which model was most
* Research done in cooperation with the University of Puerto Rico, Rio
Piedras, Puerto Rico.
36 Peter L. Weaver and Andrew I. R. Gillespie
T ABLE 1.
Ranges a/ regression variables by for est typ e
8.0
•
8.0
es
••
Forest type
Variables (units)
c;
D warf
Col orado
Tabonuco
0.4 - 3.7
1.3 - 2.6
6.0 - 36.7
3.8 - 15.9
0.26 -43.91
9.30 - 882.90
9.85 - 962.81
7
0.3 -45.7
1.3 - 20.7
0.01-27.72
0.05 - 732.65
0.07 - 754.89
37
E
in
Diameter' (e m)
Height (m)
Leaf biom ass (kg)
Woody biomass (kg)
'Total biomass' (kg) 0.05 - 1.55
Tree species (#)
7
I
T ABLE 2 .
4.0
'0
,
Dwarf
C
~
2.0
0
0.0
•">
:I
]
0
-2.0
.5
-4.0
I-
D iame ter _ diamet er breast height (104m abov e ground) . 'A bove-gro und.
satisfactory. Th ese included linear weighted least squares
models (Cunia, 1964), log-log mod els corrected for bias
(e.g, Baskerville, 1972), and a modified log-log model that
allows for a variable allometric ratio (Ru ark et al., 1987).
Model selection was based on several criteria including the
coefficient of determination (r-), the fitness index
(Schlaegel, 1981), and residual analysis that focused on the
distributi on, leverage, and significance of residuals. The fitness index is computed exactly the same as r' except that it
uses residuals in original (not transformed) units, and thus
allows more appropri ate comparisons between models that
use different transfo rmations. D ifferences betwe en groups
of models were tested using a sta ndard F test in an attempt
to der ive generalized forest biomass equations. Unless otherwise stated, a pro bability level of 5% was used to determine statist ical significance. Finally, height/diam eter (HID )
ratios and the prop ort ion of leaf to tot al biomass were
graphed to explore relati onships among Irees of different
size classes and forest types.
Tabonuco
o Colorado
0
-2 .0
,
,
0.0
2.0
4.0
6.0
LnlD'H(cm'm) ]
8.0
10.0
12.0
1. Scatter of data points for total above-ground biomass
D'H in tabonuco (so lid circles), colorado (open circles) and
dw arf (triangles) forests of the L uquillo Exp erim ental Forest,
FIGURE
YS.
RES ULTS
The scatter of dat a points of In (total biomass) vs, In (D' H)
is shown in Fig. 1. The best eqnations for the colorado and
tab onuco (D ;>5cm) forests were linear mode ls that were fit
by weighted least squares regression under the assumpt ion
that the conditional variance of biomass was proportional
to D' or D'W (Table 2). The best equations for the dwarf
fore st and tabonuco forest (D < 5cm) were transformed loglog models thai were fit using unweight ed least squa res
algorithms.
There were no significanl differences be tween Ihe total
above-ground biomass regression equations of dwarf vs.
tabonuco forest (D <5cm) for eith er the equa tion based on
D alone (p = 0.063) or D'H (p = 0.72). Also, there was no
Regression equations/or bio mass by p redictor variables and fores t types in the L uquillo Experimental Forest
Bi omass
component
F.I ,
Sy.x
n
0.85
. 0.87
0.88
0.87
0.1386
0.01623
13
18
0.70
0.88
0.60
0.87
0.3788
0.01305
56
29
0.88
0.87
0.01357
17
y
~ 0.2634 D U~
Y ~ 5.7266 - 3.0469 D + 05659 IY
0.71
0.88
059
0.88
0.3926
0.01124
56
29
Y ~ 0.1338 (IYH)Y = 4.7962 + 0.0310 D' H
0.86
0.86
0.93
0.91
0.1253
0.00012
13
18
Y ~ 0.1728 (D' H)"""
Y ~ - 0.1106 + 0.02991 D'H
0.78
0.79
0.71
0.68
0.2802
0.00012
56
29
Colorado
Y ~ - 1.5556 + 0.03357 (D 'H)
0.90
0.95
0.00007
17
Tabonuco (c .Scm)
(;;,5cm)
y ~ 0.1372 (D'H )"wn
y ~ - 0.3461 + 0.02812 (D'H)
0.79
0.80
0.70
0.72
0.28255
0.00010
56
29
Forest Type
Equati on'>
D w arf
Co lorado
Y:::: 0.1817 D H 21l/i
Y = 0.1505 - 1.5305 D + 05047 D'
Tabonuco «5cm)
{a-Scm}
.y = 0.3210 D '''''
Y ~ 4.7306 - 2.8566 D + 05 832 D'
Colorad o
Y
r'
D so le predictor:
Total
Woody
Tabonuco «5cm)
(a-Scm}
~
- 3.1353 - 1.0950 D + 0.4738 D '
D 2 X H as predictor:
Tot al
D warf
Colorado
'I'abonu co (c.Scr»)
{a-Scm}
Woody
Y = Estim ated biom ass in kg, 0 :::: d.b.h . (em) . H = height (m) , r : : coe fIicienLof de terminatio n. F.I. =Fitness Index,
Sy.x e residual me an square, and n =numb er of obs ervations.
1 N ote that the exponential mod els include the correcti on term (Sy.xf2) within the intercept (Ba skervill e, 1972) .
I
Tree Biomass Equations fo r the Forests of the Luquillo Mountains, Puerto Rico
8.0
7.0
0;
"•••
.
7.0
- - Predicted
6. 0
E
5.0
Tabonuoo
0
6.0
w
4.0
",ec
3.0
0
2.0
~
1.0
lr
>
~
Dwarf
E
0
.Eo
-
0
,
0
0
,
0 '
C
:I:
o.
0.0
0. 0
1.0
3. 0
2.0
o (cm)
4. 0
5.0
5.0
4.0
.>~
~
~
•
Colora do
Dwarf
2.0
1.0
~$~~:.'
.
:i'~
0
.•
~\S c8'.~.
10
00
a
'0
30
20
D (em)
40
50
1200 .0
: 1000 .0
•
~
§
Tabonuco
0
3.0
0.0
l
~
- - Predicted
o
80 0.0
Tabonuoo
c
F IGURE 3 . Ratios of height (m) over diameter (cm) for trees
sampled in the three fo rest types of the L uquillo Experimental
Forest.
Colorado
liOO.O
'"'"
>
400.0
'"'"
c
...J
200 .0
.5
0.0 '---- -- "-"--'----'-- - - ' -10.0
20 .0
3 0.0
0.0
D (em)
-
-'--40.0
---'
50.0
significant difference between to tal above -gro und biomass
of colorado vs. tabonuco forest (D "'5cm) for equations
based on D alone (p = 0.96). For the equation based on
D'H, the equations were significantly different (p = 0.(05).
The colorado equat ion yielded estimates that were approximately 4% grea ter than the tabonuco equati on wbich,
while statistically different, may or may no t be of pra ctical
significance. Reducing tbe model to a single equation for
both forest types caused a loss of 5% in explained variation
TABLE 3 .
r-
0.4
I- •
.
.'
0
0
.(
.2
FIGURE 2. Top : Scatter of data po ints and regression line for total
abo ve-ground biomass vs. D « 5cm) in tabonuco (open circles)
and dwarf (triangles) f orests of the Luquillo Experimental Forest.
Bottom: Scatter of data points and regression line fo r total aboveground biomass vs. D ( ~5cm) in tabonuco (open circles) and
colorado (triangles) forests a/ the Lu quillo Experimental Forest.
0.5
'.
0.2 ~,.,
.. .
"
'"
'"'"
E
1Il
'0
c:
1:
Tabonuco
0.3
:
0.1 ~.;.
.~ -':.
Q.
e
Q.
•
. ... 0
.co
.:-.' ~ q
0
0
Colorado
0
0
o •
. 0
-",
D
0
10
0 0
0
20
30
D (em)
40
50
Leafy biomass/total biomass according to tree diameter
(cm) f or trees sampled in three f orests types of the Lu quiilo
Experimental Forest.
F IGURE 4 .
as reflected in the reduction of r'. When considering total
above-ground woody biomass, the re was no significant differ ence be tween colorado and tabonuco fore st (D "'5cm)
based on D (p = 0.96) or for D' H (p = 0.34). In general, the
Combined regression equations f or biomass by predictor variables and fo rest types in the L uquillo Experimental Forest
Biomass
Forest Type
component
Equatio n'>
r'
F.I.
Sy.x .
n
Colorado/Tabonuco (e-Scm)
Y = 2.6699 - 2.2332 D + 0.5491 D'
0.88
0.89
0.01335
47
Dwarfffabonuco «Scm)
Y = 0.2847 Dum
0.72
0.60
0.3573
69
Coloradoffabonuco (eScm}
Y =- 3.4548- 2.4677 D + 0.5349 D'
0.89
0.90
0.01130
46
Co lora do'Tabonuco (a-Scm )
Y = 1.3145 + 0.03023 (D'H)
0.79
0.76
0.000146
47
Dwar fffabonuco « Scm)
Y = 0.1620 (D' H )",m
0.80
0.73
0.2489
69
Colorado/T abonuco (a-Scm)
Y =- 0.9323 + 0.03062 (D'H)
0.85
0.73
0.0000909
46
D sole predictor:
Tot al
Woody
0 X H as predictor:
2
Total
W oody
I
l
37
Y = Estimated biomass in kg. D = d.b.h. (em), H = height (m), r' = coefficient of determination, F .J. = Fitness Index.
Sy.x = residua l mean squa re, and n = number of observations.
Note that the expone ntial models include the corr ection term (Sy.x/2) within the intercept {Basker ville, 1972).
38
Peter L. Weaver and Andrew J. R. Gillespie
fit was be tter for trees ;"Scm D than for trees < Scm
although the difference was gre atly reduced for models
using D and H. G ra phs of bio mass vs D, along with the
appropriate regressio n lines fro m T able 3, appear in
Figure 2. All combine d regr ession equations are reported
in T able 3.
Th e height/diameter (HID ) ratio for all trees decreases
rapidly as diameter increases from 1 thro ugh S to lOcm,
thereafter decl ining gradually (Fig. 3). Th e HID ratios for
manytabonuco forest trees < Scm in diameter are notably
greate r than for larger trees. D warf forest trees, in contras t,
have lower ratios th an tabonuco forest trees of similar
diameter indi cating th at they are shorter and/ or thic ke r.
Th e HID rati os for tabon uco and colorado trees > Scm are
.very similar. The proportion of leaf to total biomass is higher for many tab onu co trees < Scm in diamete r th an for larg er trees (Fig. 4). For tabonuco and colorado trees > Scm,
pro portions of leaf to to tal biomass are similar for trees of
co mparable size.
DI S CU SSION
Forty-five species were included in all data sets comb ined.
Three species were fo und in both th e colora do and tabonuco forests, one species was fou nd in both th e dwa rf and colora do fore sts, and on e species was common to all three
forest types. T ree height over the entire Luquill o Mountain
grad ient varies from 3m in expos ed dwarf fores t to 30m in
tabonuco for est. The normal range of canopy height varies
fro m 3 to Sm in dwarf forest, 8 to 20m in colorado forest,
and 20 to 30m in tab onuco forest (Weaver and Murphy,
1990).
Models that use D alone are local biomass equations
because they implicitly include a re lations hip between D
and H , and are most useful in the areas where the da ta
were collected. Thes e models are also useful for estimatin g
damage in hu rricane prone enviro nments such as th e
Caribbean Islan ds where height measurem en ts may be
problema tic afte r storms. Models tha t use bo th D an d H
are general biom ass eq uat ions tha t may have wider ap plication to similar fores t types.
The bre akpo int of Scm between biomass re gressions
appears due to variability in tree form and leaf load prevalent in smaller diameter classes. The HID ratios and percent of leaf to total biomass estimates show th at allometric
relationships among small trees ch ange rapidly with slight
changes in tree size. It is suggested that th e transformed
log-log model s are better suited for describing the biomass
re lation ships of sma ll trees when relation ships among
dimensions change rapidly. Alternatively, with some mor e
stable re lationships of larger trees, tradition al linear equations provide ade quate estima tes .
Other factors also influence biomass estimates . Specific
leal are as decli ne from 127cm'/g in the tabonuco fores t to
47cm' /g in th e dwarf fore st in th e Luquillo Mountains
(Weaver an d Murp hy, 1990). Mo reover, specific gravities
var y by tree species ranging from O.3g/cm 1 in Cecropia
peltata L. to 0.8g/cm' in Manilkara bidentata (A.DC.) Chev .
(Little and Wadsworth , 1964), bo th in the tabonuco forest.
Most species, however, are confined to a much narrower
ran ge betwee n 0.5 and 0.7g1cm' . Most seco ndary tree
species ten d to ha ve lighte r woods than pri mary species
(Budowski, 1963). Recurrent h urricanes in th e Caribbean
basin (Salivia, 1972) assure that secondary species, as well
as da maged prima ry species , are a regular co mpone nt of
most stands.
Specific gravities, in gen eral , appear to increase slightly
with elevat ion in the Luquillo Mo untai ns, although this
phenomenon has not be en studi ed thoroughly. The co mbined effects of leaf and stem weights may account for the
4% increase in colora do forest esti mates as compared to
those of th e tabonuco for est when usin g D'H as the total
biom ass predictor. Inclu sion of specific gravity as a predictor variable would probably increase the precision of the
regressions; however, th is would not be useful in other
moun tainous Caribbean islands where such information is
sparse or unavailable.
These equa tions may be used in a variety of ways. They
may be applied to individual trees in a sample to estimate
biomass of the sample . Alternatively, th ey may be applied
to stand averages (e.g . mean D per hal, o r a stand table
(nu mber of treeslha by D class) to estimate bioma ss per
unit area.
T he mo ntan e fores ts of Puerto Rico are similar to th ose
of ot her Carib bean island s in ter ms of tree physiognomy
an d species composition (Beard, 1949). Un til detailed
knowledge o n tree species is ava ilable for other Caribbean
islands, th e genera l equations presented here may prove
useful for estimat ing th eir total abov e-gro und biomass and
above-gro und woody bio mass.
A CKNOW LED G EMENTS
We are grateful to th e following reviewers for their helpful
comments: D r. Sa ndra Brown, Forestry Department,
University of Illinois, Urbana, IL; Dr. Th om as R. Crow,
Forestry Science Laboratory, Rh inelander, WI ; Dr. Pet er
G . Murphy , Department of Bot an y and Plant Path ology,
Michigan State U niversit y, East Lansin g, MI; and Dr. H . L.
Wright of the Oxford For estry Institute, England.
R EFERE N CES
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and B OCKHEIM, J. G . 1987.
Compariso n of constant and variable allometric rati os for
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Tree Biomass Equations for the Forests of the Luquillo Mountains, Puerto Rico
estimating Populus tremuloides biomass. Forest Science 33, 2,
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WEAVER, P. L., 1990. Succession in the elfin woodland of the
Luquillo Mountains of Puerto Rico. Biotropica 22, 1,83-89.
WEAVER, P. L.,and MURPHY, P. G., 1990. Forest structure and
productivity in Puerto Rico's Luquillo Mountains. Biotropica
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WmTIAKER,R. B., BORMANN, F. B., LIKENS, G. E, and SICCAMA,
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