TECHNICAL NOTE
Extending a Model System to Predict Biomass in Mixed-Species Southern Appalachian Hardwood Forests
ABSTRACT
Charles O. Sabatia, Thomas R. Fox, and Harold E. Burkhart Functions for estimating foliage, branches and nonmerchantable stem tops, merchantable stem, and total aboveground biomass for Appalachian hardwood trees were assembled and incorporated into an existing growth-and-yield simulator for mixed-species Appalachian hardwood forests. With these functions and user-defined stand table and stand characteristics, current estimates of biomass in the different aboveground tree components can be obtained by species and diameter class for a thinned or unthinned stand. In addition, future biomass estimates for a thinned stand can be obtained for a projection period of 1 to 10 years. These estimates can be used to assess forest ecosystem services of carbon sequestration and provide information that can be used to evaluate effects of different harvesting strategies on forest carbon and other nutrient pools. A comparison of these estimates to those obtained by the forest inventory and analysis (FIA) procedure, using data from eight FIA sample plots in the southern Appalachian region, indicated that estimating biomass directly from locally developed biomass equations may give biomass estimates for the tree bole and for tops and branches, that are different from those obtained by the FIA procedure. Keywords: biomass equations, FIA biomass estimates
S
outhern Appalachian mixed hardwood forests form a significant portion of forestland in southeastern United States. The forests occupy an area of about 30 million acres with annual timber growth and removals estimated to be 1.5 billion ft3 and 655 million ft3, respectively (Oswalt and Turner 2009). In addition to being a source of hardwood timber, the Appalachian forests play critical ecosystem service roles including carbon sequestration. A biomass prediction system for these forests is needed to compare the effects of different harvesting strategies on forest carbon and other nutrient pools. Harrison et al. (1986a, 1986b) developed a growth-and-yield system that estimates timber volume yield, by species and by diameter class, for mixed-species Appalachian hardwood forests before thinning and the projected growth and yield for a projection period of 1 to 10 years after thinning. The growth-and-yield system is called “growth and yield of Appalachian mixed hardwoods after thinning” (GHAT). Rauscher et al. (2000) found that GHAT accurately predicted growth-and-yield for mixed-species southern Appalachian hardwoods. By extending the capacity of this system, estimates of tree and tree component biomass can also be obtained in addition to the volume estimates obtained from the original GHAT model. In this project, biomass prediction functions were incorporated into GHAT to compute estimates of total aboveground, foliage, merchantable stem, and nonmerchantable tops and branches biomass by species and diameter class.
Methods The biomass functions used in this project were developed using information from the literature including biomass equations, merchantable stem biomass to total stem biomass proportion, and the proportion of total biomass in foliage for the different species. The information was assembled and converted into mathematical equations and logic-based procedures that estimate tree or tree component biomass for a single tree of a given species in a given diameter class. Total Aboveground (Stem ⴙ Branches ⴙ Foliage) and Foliage Biomass Estimating Procedures Total aboveground (TAG) biomass for each tree (excluding a 0.6-ft stump) is computed from its outside bark stem ⫹ branches (SB) biomass by adding foliage biomass as a proportional constant. This approach was adopted as there were no TAG biomass equations in the literature that could be used for the species represented in GHAT. Equations to estimate SB biomass were however available in Clark and Schroeder (1986) from where the equation SBBiomass ⫽ ␣共D2兲
(1)
was chosen. In Equation 1, SBBiomass is the outside bark dry weight in lbs for the stem and branches, D is the outside bark dbh of the tree (in.), and ␣ and  are parameters. The estimates of ␣ and  for the various species in GHAT are given in Table 1. The dbh-only biomass Equation 1 was considered sufficient for this application as
Manuscript received February 7, 2012; accepted June 29, 2012. http://dx.doi.org/10.5849/sjaf.12-005. Charles O. Sabatia (
[email protected]), Virginia Polytechnic Institute and State University, Forest Resources and Environmental Conservation, Blacksburg, VA. Thomas R. Fox (
[email protected]), Virginia Polytechnic Institute and State University. Harold E. Burkhart (
[email protected]), Virginia Polytechnic Institute and State University. This work was funded by USDA Forest Service, Coweeta Hydrologic Lab through a cooperative research agreement with Virginia Polytechnic Institute and State University. Review comments by the associate editor improved the manuscript significantly. Copyright © 2013 by the Society of American Foresters.
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Table 1. Parameter estimates used when Equation 1 is used to predict outside bark stem ⴙ branches biomass for the tree species in GHAT growth-and-yield model (assembled from Clark and Schroeder 1986).
Table 2. Parameter estimates used when Equation 1 is used to predict outside and inside bark total stem biomass for the tree species in GHAT growth-and-yield model (assembled from Clark and Schroeder 1986).
Biomass equation parameter estimates dbh ⬍ 11 in. Species a
Black cherry Northern red oak White oak Yellow-poplar Black oak Magnoliaa Black locust Basswood Birch Chestnut oak Scarlet oak Red maple Others
␣ 2.02338 3.06739 1.73738 0.87948 1.29270 0.87948 4.13741 1.94274 4.29408 0.86674 1.62952 2.02338 1.73023
Biomass equation parameter estimates
dbh ⱖ 11 in.
 1.27612 1.22338 1.33404 1.40401 1.36723 1.40401 1.08876 1.21008 1.14203 1.47585 1.34103 1.27612 1.33323
␣ 5.28790 3.28071 1.69511 1.65215 2.54650 1.65215 1.04649 1.47600 3.80734 3.40602 2.94915 5.28790 3.09465
dbh ⬍ 11 in.

Species
1.07581 1.20936 1.33917 1.27254 1.22586 1.27254 1.37539 1.26737 1.16711 1.19049 1.21733 1.07581 1.20063
a
Biomass equations for black cherry and magnolia were not available. Adopted equations for red maple and yellow-poplar respectively based on species similarity of wood properties. Parameter estimates for “Others” category are the average of parameter estimates for the species black gum, white ash, and hickory, the only species in this category for which biomass equations were available.
a
Black cherry
Northern red oak White oak Yellow-poplar Black oak Magnoliaa Black locust Basswood Birch Chestnut oak Scarlet oak
GHAT utilizes heights predicted from dbh hence a biomass equation with dbh and height as predictors would, in this application, not be different from Equation 1. The proportion of foliage biomass in a tree of a given species was used to scale up SB biomass to TAG biomass. The foliage biomass proportions in trees of the species in GHAT were computed from the SB and the TAG biomass equations of Clark et al. (1986) for species in the Piedmont region. The assumption here was that the proportion of foliage in a tree of a given size and species in the Piedmont region was the same as the proportion in a tree of the same size and species in the southern Appalachian region. White oak, yellow-poplar, chestnut oak, scarlet oak, and red maple were the only species in GHAT that had SB and TAG biomass equations available in the publication of Clark et al. (1986). For each one of these five tree species, SB and TAG biomass were estimated for each 1-in. diameter class from 1 to 30 in. The proportion of foliage biomass in a tree in a given diameter class was then computed as FPTree ⫽
TAG ⫺ SB TAG
(2)
where FPTree is the foliage proportion of total biomass. Foliage biomass proportion for a species was then computed as the average of the thirty FPTree values for the species. Tree species in GHAT, that did not have SB and TAG biomass equations in the publication of Clark et al. (1986), were assigned a foliage biomass proportion of a closely related species out of the five whose foliage biomass proportion could be computed from the Piedmont region biomass equations. By this criterion, estimates of foliage biomass proportions for the tree species in GHAT were 2.7% for white oak; 1.9% for yellow-poplar and magnolia; 3.2% for chestnut oak; 4.7% for scarlet oak, northern red oak, and black oak; 5.3% for red maple, black cherry, birch, basswood, and black locust; and 3.6% (average of the five preceding proportions) for the species in the “Others” category.
Red maple Others
dbh ⱖ 11 in.
␣

␣

2.41242 1.62534 3.11987 2.40722 1.59285 1.38070 0.76237 0.66009 1.27041 0.83649 0.76237 0.66009 4.06014 3.41664 1.74995 1.12481 3.34713 2.97489 0.89495 0.63137 0.90818 0.63385 2.41282 1.62534 1.69140 1.25573
1.17937 1.23722 1.17348 1.19591 1.31179 1.31206 1.41643 1.41104 1.34023 1.39137 1.41643 1.41104 1.05285 1.06056 1.19103 1.23786 1.17356 1.11933 1.44204 1.46903 1.41531 1.45552 1.17937 1.23722 1.30580 1.34038
3.56511 3.67497 3.82608 3.27347 3.42725 2.87565 1.76476 1.43045 5.90002 5.50646 1.76476 1.43045 0.72201 0.60942 1.49368 0.90690 3.06473 2.78946 5.38410 3.73598 4.32971 3.45720 3.56511 3.67497 2.83957 2.47923
1.09796 1.06711 1.13093 1.13186 1.15202 1.15907 1.24142 1.24978 1.02003 0.99842 1.24142 1.24978 1.41295 1.42002 1.22405 1.28276 1.14574 1.13275 1.06787 1.09831 1.08964 1.10180 1.09796 1.06711 1.18138 1.17913
a
Biomass equations for black cherry and magnolia were not available. Adopted equations for red maple and yellow-poplar, respectively based on species similarity of wood properties. Parameter estimates for “Others” category are the average of parameter estimates for the species black gum, white ash, and hickory, the only species in this category for which biomass equations were available. The parameters in bold are those for inside bark biomass.
With these proportions, TAG biomass for a single tree of a given species is computed in GHAT as TAG Biomass ⫽ ␣共D2兲共1 ⫹ k兲
(3)
where D, ␣ and  are as defined for Equation 1 and k is the foliage biomass proportion of the species (as a fraction). Foliage biomass for the tree was the positive difference between the solution of Equation 1 and that of Equation 3. Merchantable Stem and Nonmerchantable Tops and Branches Biomass Estimating Procedures Outside or inside bark merchantable stem biomass (MSB) to any specified top height or top diameter merchantability limits is computed using equations and parameter estimates from Clark and Schroeder (1986). Equation 1 is used with the parameter estimates in Table 2 to give total stem biomass (TSB). MSB is then estimated by multiplying TSB by a MSB to TSB proportion computed using the equation MSB ⫽ exp共␣d D␥兲 TSB
(4)
where d is the specified inside or outside bark top diameter merchantability limit (in.), D is the outside or inside bark dbh (in.), and ␣, , and ␥ are parameters whose estimates are given in Table 3. Where top height is the specified merchantability limit, the outside SOUTH. J. APPL. FOR. 37(2) 2013
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Table 3. Parameter estimates for Equation 4, the equation to predict the merchantable stem biomass proportion of total stem biomass, for the tree species in GHAT growth-and-yield model (assembled from Clark and Schroeder 1986). Outside bark parameter estimates
␣

␥
␣

␥
⫺1.43083 ⫺1.90345 ⫺12.00001 ⫺3.54839 ⫺4.35164 ⫺3.54839 ⫺1.27900 ⫺1.28273 ⫺0.81251 ⫺2.25664 ⫺2.65117 ⫺1.43083 ⫺2.31462
4.05497 3.95236 2.64614 3.17747 3.85984 3.17747 3.33578 3.87891 4.21844 4.00092 3.58558 4.05497 3.79800
⫺4.12303 ⫺4.27185 ⫺3.96330 ⫺3.76535 ⫺4.49173 ⫺3.76535 ⫺3.49181 ⫺3.97929 ⫺4.08482 ⫺4.35574 ⫺4.09877 ⫺4.12303 ⫺4.09313
⫺1.33864 ⫺1.76424 ⫺12.83857 ⫺3.51229 ⫺3.94567 ⫺3.51229 ⫺1.27952 ⫺1.05926 ⫺0.72051 ⫺2.22131 ⫺1.33864 ⫺1.33864 ⫺2.17120
4.16262 4.05667 2.72014 3.24724 3.93141 3.24724 3.42285 4.01311 4.31785 4.14820 4.16262 4.16262 3.90355
⫺4.20601 ⫺4.34109 ⫺4.08425 ⫺3.83278 ⫺4.53034 ⫺3.83278 ⫺3.58019 ⫺4.04160 ⫺4.13646 ⫺4.50149 ⫺4.20601 ⫺4.20601 ⫺4.16647
Species a
Black cherry Northern red oak White oak Yellow-poplar Black oak Magnoliaa Black locust Basswood Birch Chestnut oak Scarlet oak Red maple Others
Inside bark parameter estimates
a Biomass equations for black cherry and magnolia were not available. Adopted equations for red maple and yellow-poplar respectively based on species similarity of wood properties. Parameter estimates for “Others” category are the average of parameter estimates for the species black gum, white ash, and hickory, the only species in this category for which biomass equations were available.
Table 4. Parameter estimates for Equation 5, the taper equation to predict the outside bark top diameter at a specified top height, and the inside bark to outside bark diameter ratio (dratio), for the tree species in GHAT growth-and-yield model (adopted from Harrison et al. 1986b). Species
␣

dratio
Black cherry Northern red oak White oak Yellow poplar, black locust, magnolia, basswood Black oak Red maple, birch Chestnut oak Scarlet oak Others
⫺1.9213 ⫺1.7320 ⫺1.7139 ⫺1.7427
0.8750 0.7989 0.7489 0.8540
0.939 0.929 0.937 0.902
⫺1.8988 ⫺1.8285 ⫺1.6334 ⫺1.7901 ⫺1.7854
0.7965 0.8416 0.7959 0.7993 0.8304
0.925 0.934 0.909 0.939 0.927
bark value of d in Equation 4 is obtained by solving for dt in the taper equation
冉 冊 冉
dt2 h ⫽ D2 4.5
共⫺1兲
冊
H ⫺ 4.5 H⫺h
共⫹1兲
冉 冉冋 册 冋
exp ␣
h H⫺h

⫺
4.5 H ⫺ 4.5
册 冊冊 
(5) where dt is the outside bark diameter (in.) at the specified top height h (ft), D is the outside bark dbh (in.), H is the total height (ft), and ␣ and  are parameters whose estimates are given in Table 4. The inside bark option of d is obtained as the product dt ⫻ dratio where dratio is the inside bark to outside bark diameter ratio whose estimates for the tree species in GHAT are given in Table 4. A tree that does not meet the specified merchantability limits is considered to have MSB of zero. Biomass in nonmerchantable tops and branches and in trees that do not meet the specified merchantability limit is estimated as the positive difference between SB biomass and outside bark MSB. Extending the Original GHAT Model and Example Application of the Extended Model The biomass estimating procedures described in the preceding two subsections were coded into C⫹⫹ computer program functions and incorporated into the original GHAT computer program. The functions use GHAT user defined tree dbh, species, merchant124
SOUTH. J. APPL. FOR. 37(2) 2013
ability limits, and stand and site quality information to compute TAG and tree component biomass for individual Appalachian hardwood trees and sum up and convert these values to per acre biomass in tons by species and diameter class. For thinned and projected stands, the biomass functions use the dbh distribution of the residual or the projected stand to compute estimates of standing TAG or tree component biomass. The extended GHAT growth-and-yield model was used to estimate aboveground tree and tree component biomass on eight FIA plots (see Table 5) selected from the southern Appalachian region using year 2003 forest inventory data. The biomass estimates from GHAT were compared to the estimates given in the FIA database, which are computed according to the FIA procedure.
Results and Discussion The estimates of the aboveground biomass on each one of the select FIA plots in the southern Appalachian region are given in Table 5. The notable difference between GHAT and FIA estimates is that the GHAT estimates were on average 20% and 50% higher for merchantable biomass and nonmerchantable tops and branches biomass, respectively. This can be attributed to the different biomass estimation procedures in the two systems. GHAT computes the biomass using biomass equations only. On the other hand FIA estimates of bole biomass are obtained by converting the corresponding bole volume to biomass while estimates of the biomass in tops and branches are obtained through several steps that include estimating biomass in all the other aboveground tree components and subtraction from the total aboveground biomass estimate (Woudenberg et al. 2010). The aboveground tree components’ biomass estimation steps in GHAT and FIA are summarized in Figure 1. It is therefore possible that there may be significant differences in biomass estimates between a system based only on biomass equations and the FIA system. It may be necessary to evaluate the accuracy of the two approaches for certain applications, especially where local or regional biomass estimates are of interest. The modified GHAT model provides a simpler system of estimating biomass in mixed species Appalachian hardwood forests. The system estimates biomass using a smaller number of computation steps than are used in the FIA system hence could be more
Table 5.
GHAT and FIA biomass estimates for select FIA plots in the southern Appalachian region in year 2003.
Plot FIA sequence number and county location 113958263010478 Watauga, NC 114010000010478 Wilkes, NC 38247039010478 Blount, TN 38249585010478 Carter, TN 105215687010478 Dickenson, VA 105357771010478 Buchanan, VA 113909730010478 Cherokee, NC 113920774010478 Graham, NC
Biomass in bole to 4-in. top diameter (tons/ac.)
Biomass in tops and branches (tons/ac.)
Biomass in foliage (tons/ac.)
SI (ft) and SI species
Age
GHAT
FIA
GHAT
FIA
GHAT
FIA
104 yp
52
76.20
66.63
15.05
17.04
2.92
-
59 co
76
79.40
60.86
22.44
15.10
3.78
-
79 yp
29
37.99
31.04
11.11
8.70
1.95
-
59 co
82
84.41
55.38
27.64
12.15
4.29
-
81 yp
35
34.22
24.40
10.30
8.01
1.95
-
81 nro
69
30.72
36.60
10.04
8.55
1.92
-
76 yp
45
27.17
17.81
7.22
4.97
1.32
-
104 yp
49
78.42
75.39
35.91
17.54
3.52
-
co indicates chestnut oak; nro, northern red oak; yp, yellow poplar. The FIA plot locations are in southwestern Virginia (2 plots), western North Carolina (4 plots) and eastern Tennessee (2 plots). SI is site index base age 50. For GHAT application, the site index values were converted to white oak site index using the procedure of Doolittle (1958).
Figure 1.
Summary of the aboveground tree components’ biomass estimation steps in GHAT software and in the FIA database. SOUTH. J. APPL. FOR. 37(2) 2013
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accurate. In addition, GHAT is more flexible given that it can estimate merchantable biomass, and the corresponding biomass of nonmerchantable tops and branches, to any specified top diameter or top height merchantability limit. This can be useful where effects of different timber merchandizing options on forest carbon pools are to be assessed.
Conclusion We extended an existing growth-and-yield model system to provide estimates of aboveground tree and tree component biomass in even-aged mixed-species southern Appalachian hardwood stands. The extended model system computes tree and tree component biomass directly from local biomass equations. The biomass estimates obtained were generally higher than those from the FIA procedure. Biomass values for mixed species southern Appalachian hardwood stands from different estimation approaches are likely to differ significantly.
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Literature Cited CLARK, A., AND J.G. SCHROEDER. 1986. Weight, volume, and physical properties of major hardwood species in the southern Appalachian mountains. USDA For. Serv., Res. Paper No. SE-253. 63 p. CLARK, A., D.R. PHILLIPS, AND D.J. FREDERICK. 1986. Weight, volume, and physical properties of major hardwood species in the Piedmont. USDA For. Serv., Res. Paper No. SE-255. 78 p. HARRISON, W.C., T.E. BURK, AND D.E. BECK. 1986a. Individual tree basal area increment and total height equations for Appalachian mixed hardwoods after thinning. South. J. Appl. For. 10:99 –104. HARRISON, W.C., H.E. BURKHART, T.E. BURK, AND D.E. BECK. 1986b. Growth and yield of Appalachian mixed hardwoods after thinning. School of Forestry and Wildlife Resources, Virginia Tech, Blacksburg. Publication No. FWS-1-86. 48 p. OSWALT, C.M., AND J.A. TURNER. 2009. Status of hardwood forest resources in the Appalachian region including estimates of growth and removals. USDA For. Serv., Resource Bulletin No. SRS-142. 16 p. RAUSCHER, H.M., M.J. YOUNG, C.D. WEBB, AND D.J. ROBISON. 2000. Testing the accuracy of growth and yield models for southern hardwood forests. South. J. Appl. For. 24:176 –185. WOUDENBERG, S.H., B.L. CONKLING, B.M. O’CONNELL, E.B. LAPOINT, J.A. TURNER, AND W.K. L. 2010. The Forest Inventory and Analysis Database: Database description and users manual version 4.0 for phase 2. USDA For. Serv., Gen. Tech. Report No. RMRS-GTR-245. 336 p.
