Tree Biomass Equations for the Forests of the Luquillo Mountains
Transcription
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 G. L., 1972. Use of logarithmic regression in the estimation of plant biomass. Canadian Journal of Forestry 2, BASKERVILLE, 49-53. BEARD 1. S., 1949. Natural veget ation of the Windward and Leeward Islands. Oxford Forestry Memoirs, 21, 1-1 92. B ROWN, S., G ILLESPIE, A. J. R., and L UGo , A. E. , 1989. Biomass estimation methods for tropical forests with applicatio ns to forest inventory data . Forest Science 35, 4. 881-902. B UDOWSKI, G., 1963. Fo rest succession in tropical lowlands. Turrialba 13, 42-44. CRow , T . R, 1978. Common regressions to estimate tree biomass in tropical stands. Forest Science 24, 110-114. C UNI A T., 1964. Weighted least squares method and constru ction of volume tables. Forest Science 10, 2,180-191. LrITLE, E. L, I I. and WADSWORTH, F . H ., 1964. Commo n tr ees of Puerto Ri co and the Virgin Island s. Agricultural Handbook .2 49, USD A Fore st Service, Washington, D.C. 548p. O VINGTON, J. D. and OLSON, 1. S., 1970. Biomass and chem ical content of E I Verde lower mon tane rain fore st plants. Chaper H, p. 53- 77. In H. T. Od urn and R. F. Pigeon, eds., A tropical rain forest. USAEC, TID -24270. and B OCKHEIM, J. G . 1987. Compariso n of constant and variable allometric rati os for R UARK, G . A ., MARTIN, G. L. , Tree Biomass Equations for the Forests of the Luquillo Mountains, Puerto Rico estimating Populus tremuloides biomass. Forest Science 33, 2, 294-300. SALIVIA, L. A., 1972. Historia de los temporales de Puerto Rico y las Antillas. Editorial Edil, Inc., San Juan, Puerto Rico. 385p. SCHLAEGEL, B. E., 1981. Testing, reporting and using biomass estimation models. Proceedings 1981 Southern Forest Biomass Workshop pp. 95-112. The Belle W. Baruch Forest Science Institute of Clemson University. Jane 11-12, 1981. 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 22, 1, 69-82. WmTIAKER,R. B., BORMANN, F. B., LIKENS, G. E, and SICCAMA, T. G., 1974. The Hubbard Brook ecosystems study: forest biomass and production. Ecological Monographs 44, 233-254. As the largest importer and distributor of timber and sheet materials in the UK, Meyer International is a major customer for your forest products. We have specialist companies in hardwoods, softwoods and sheet materials that sell nationally. Our network of 160 timber and builders merchants serves local markets. If you have forest products to sell, perhaps you should be talking to us. MEYER(@ MEYER INTERNATIONAL PLC Villiers House, 41-47 Strand,London WC2N 5JG Telephone: 071 8397766 Telex: 27451 Fax: 071 8395520 39 MEYER({:JJ MEYER INTERNATIONAL PLC