# Local and General Above-Ground Biomass Functions for Pinus palustris Trees

^{1}

^{2}

^{3}

^{4}

^{5}

^{6}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Data Description

^{2}ha

^{−1}), trees per hectare (N, ha

^{−1}) and stand age (A, years). As site index (SI, m) was available for 43% of the whole dataset, that attribute was not included in the analysis. Age information for the 23 trees provided by Joseph W. Jones Ecological Research Center was not available. Due to the wide range in tree size, however, those trees were kept in the dataset and were only used for fitting local models that did not include age as covariate. Details of tree and stand characteristics of the dataset used are summarized in Table 2.

#### 2.2. Model Specification and Estimation

_{j}is tree dimension and stand variables (j = 1,…, p) such as tree DBH, total tree height (HT), Age (A), stand basal area per hectare (BA), tree number per hectare (N), and ${X}_{i}=\left({X}_{1},\dots ,{X}_{p}\right)$, and ${\mathsf{\beta}}_{1}=\left({\beta}_{l0},{\beta}_{l1},\dots ,{\beta}_{lp}\right)$ to be estimated. Each component equation can contain its own independent variables.

^{®}MODEL Procedure (SAS Institute Inc. 2011, Cary, NC, USA). In this estimation method, a constant 4 × 4 correlation matrix was assumed to describe the inherent correlations among biomass components and total biomass measured on the same tree; heteroscedasticity was addressed by having a unique weight function for each of the four equations. Briefly, in the first step of model estimation, all biomass components and total biomass for each model system were fitted separately with nonlinear ordinary least squares (OLS) and all significant variables were retained at α = 0.10. In the second step, for each model system, the equations of all tree components and total biomass with biomass component model forms selected in the first step were fitted by NSUR. In the third step, to model the heteroscedasticity for each equation in model (1), the estimated errors $({\widehat{e}}_{i})$ of the unweighted NSUR model from the second step were used as the dependent variable in the error variance model and fit to tree dimension variables as the form: $\mathrm{ln}({\widehat{e}}_{i})=\mathrm{ln}({\sigma}^{2})+{\gamma}_{i1}\mathrm{ln}({X}_{1})+\mathrm{\dots}+{\gamma}_{ip}\mathrm{ln}({X}_{p})$; the resultant significant parameter estimates ${\widehat{\gamma}}_{i1},\mathrm{\dots},{\widehat{\gamma}}_{ik}$ form the weight function $1/({X}_{1}^{{\widehat{\gamma}}_{i1}}\mathrm{\dots}{X}_{k}^{{\widehat{\gamma}}_{ik}})$ for the ith equation. In the fourth step, for each model system, the biomass components and total biomass model were refitted with NSUR after fixing the weight functions as in step 2. The resulting systems guarantee additivity in biomass equations, account for the inherent correlation among the biomass equations, and address heteroscedasticity by having a unique weighting function for each equation. Further details on the four-step NSUR fitting method can be found in Parresol [20] and Zhao et al. [21].

#### 2.3. Model Assessment and Evaluation

^{2}).

#### 2.4. Comparison Against Published Equations

## 3. Results

#### 3.1. Model Fitting

#### Model System I (Based on DBH)

#### Model System II (based on DBH and HT)

#### Model System III (based on DBH and A)

#### Model System IV (based on DBH, HT and A)

#### Model System V (based on DBH, A, N and BA)

#### Model System VI (based on DBH, HT, A, N and BA)

^{2}, and lower E, MABE and RMSE). With the inclusion of DBH and HT, including tree age information in systems IV or VI further improved the prediction of all component biomass and total biomass. There are no large differences in biomass estimation between systems IV and VI. That is, when tree DBH, HT and A information are available, system IV could be enough, and BA information is not needed for system VI. Including stand density information (BA and N), although without tree height, system V improves the prediction of branch and foliage biomass.

#### 3.2. Model Validation

#### 3.3. Comparison against Published Equations

## 4. Discussion

## 5. Conclusions

## Supplementary Materials

## Author Contributions

## Acknowledgments

## Conflicts of Interest

## References

- Madgwick, H.; Satoo, T. On estimating the aboveground weights of tree stands. Ecology
**1975**, 56, 1446–1450. [Google Scholar] [CrossRef] - Jenkins, J.C.; Chojnacky, D.C.; Heath, L.S.; Birdsey, R.A. National-scale biomass estimators for United States tree species. For. Sci.
**2003**, 49, 12–35. [Google Scholar] - Johansen, R.W.; McNab, W.H. Estimating logging residue weights from standing slash pine for prescribed burns. South. J. Appl. For.
**1977**, 1, 2–6. [Google Scholar] - Hepp, T.D.; Brister, G.H. Estimating crown biomass in loblolly pine plantations in the Carolina flatwoods. For. Sci.
**1982**, 28, 115–127. [Google Scholar] - Johnsen, K.H.; Keyser, T.; Butnor, J.R.; Gonzalez-Benecke, C.A.; Kaczmarek, D.J.; Maier, C.A.; McCarthy, H.R.; Sun, G. Forest productivity and carbon sequestration of forests in the southern United States. In Climate Change Adaptation and Mitigation Management Options: A Guide for Natural Resource Managers in Southern Forest Ecosystems; Vose, J.M., Klepzig, K.D., Eds.; CRC Press: Boca Raton, FL, USA, 2014; pp. 193–247. [Google Scholar]
- Marziliano, P.A.; Coletta, V.; Menguzzato, G.; Nicolaci, A.; Pellicone, G.; Veltri, A. Effects of planting density on the distribution of biomass in a douglas-fir plantation in southern Italy. iForest
**2015**, 8, 368–376. [Google Scholar] [CrossRef][Green Version] - Mitchell, R.J.; Kirkman, L.K.; Pecot, S.D.; Wilson, C.A.; Palik, B.J.; Boring, L.R. Patterns and controls of ecosystem function in longleaf pine–wiregrass savannas. I. Aboveground net primary productivity. Can. J. For. Res.
**1999**, 29, 743–751. [Google Scholar] [CrossRef] - Baldwin, V.C., Jr.; Saucier, J.R. Aboveground Weight and Volume of Unthinned, Planted Longleaf Pine on West Gulf Forest Sites; Research Paper SO-191; U.S. Department of Agriculture, Forest Service, Southern Forest Experiment Station: New Orleans, LA, USA, 1983; 25p.
- Samuelson, L.J.; Stokes, T.A.; Butnor, J.R.; Johnsen, K.H.; Gonzalez-Benecke, C.A.; Anderson, P.H.; Jackson, J.; Ferrari, L.; Martin, T.A.; Cropper, W.P., Jr. Ecosystem carbon stocks in Pinus palustris forests. Can. J. For. Res.
**2014**, 44, 476–486. [Google Scholar] [CrossRef] - Gonzalez-Benecke, C.A.; Gezan, S.A.; Albaugh, T.J.; Allen, H.L.; Burkhart, H.E.; Fox, T.R.; Jokela, E.J.; Maier, C.A.; Martin, T.A.; Rubilar, R.A.; et al. Local and general above-stump biomass functions for loblolly and slash pine trees. For. Ecol. Manag.
**2014**, 334, 254–276. [Google Scholar] [CrossRef] - Kralicek, K.; Huy, B.; Poudel, K.P.; Temesgen, H.; Salas, C. Simultaneous estimation of above- and below-ground biomass in tropical forests of Viet Nam. For. Ecol. Manag.
**2014**, 390, 147–156. [Google Scholar] [CrossRef] - Forrester, D.I.; Tachauer, I.H.H.; Annighoefer, P.; Barbeito, I.; Pretzsch, H.; Ruiz-Peinado, R.; Stark, H.; Cacchiano, G.; Zlatanov, T.; Chakraborty, T.; et al. Generalized biomass and leaf area allometric equations for European tree species incorporating stand structure, tree age and climate. For. Ecol. Manag.
**2017**, 396, 160–175. [Google Scholar] [CrossRef] - Frost, C.C. History and future of the longleaf pine ecosystem. In The Longleaf Pine Ecosystem—Ecology, Silviculture and Restoration; Jose, S., Jokela, E.J., Miller, D.L., Eds.; Springer: New York, NY, USA, 2006; pp. 9–48. [Google Scholar]
- Brockway, D.G.; Outcalt, K.W.; Tomczak, D.J.; Johnson, E.E. Restoration of Longleaf Pine Ecosystems; General Technical Report SRS-83; U.S. Department of Agriculture, Forest Service, Southern Research Station: Asheville, NC, USA, 2005; p. 34. [Google Scholar]
- Garbett, W.S. Aboveground Biomass and Nutrient Content of a Mixed Slash-Longleaf Pine Stand in Florida. Master’s Thesis, University of Florida, Gainesville, FL, USA, 1977. [Google Scholar]
- Taras, M.A.; Clark, A., III. Aboveground Biomass of Longleaf Pine in a Natural Sawtimber Stand in Southern Alabama; USDA Forest Service Research Paper SE 162; Department of Agriculture, Forest Service, Southeastern Forest Experiment Station: Asheville, NC, USA, 1977; p. 32.
- Gibson, M.D.; McMillin, C.W.; Shoulders, E. Above- and Below-Ground Biomass of Four Species of Southern Pine Growing on Three Sites in Louisiana; USDA Forest Service Final Report FS-SO-3201-59; USDA, Forest Service, Southern Forest Experiment Station: Pineville, LA, USA, 1985.
- Gonzalez-Benecke, C.A.; Martin, T.A.; Cropper, W.P., Jr. Whole-tree water relations of co-occurring mature Pinus palustris and Pinus elliottii. Can. J. For. Res.
**2011**, 41, 509–523. [Google Scholar] [CrossRef] - Samuelson, L.J.; Stokes, T.A.; Butnor, J.R.; Johnsen, K.H.; Gonzalez-Benecke, C.A.; Martin, T.A.; Cropper, W.P., Jr.; Anderson, P.H.; Ramirez, M.; Lewis, J. Ecosystem carbon density and allocation across a chronosequence of longleaf pine forests in the southeastern USA. Ecol. Appl.
**2017**, 27, 244–259. [Google Scholar] [CrossRef] [PubMed] - Parresol, B.R. Additivity of nonlinear biomass equations. Can. J. For. Res.
**2001**, 31, 865–878. [Google Scholar] [CrossRef] - Zhao, D.; Kane, M.; Markewitz, D.; Teskey, R.; Clutter, M. Additive tree biomass equations for midrotation loblolly pine plantations. For. Sci.
**2015**, 61, 613–623. [Google Scholar] [CrossRef] - Poudel, K.P.; Temesgen, H. Developing biomass equations for Western hemlock and red alder trees in Western Oregon forests. Forests
**2016**, 7, 88. [Google Scholar] [CrossRef] - Larson, P.R.; Kretschmann, D.E.; Clark, A., III; Isen-brands, J.G. Juvenile Wood Formation and Proper-Ties in Southern Pine; General Technical Report FPL-GTR-129; U.S. Department of Agriculture, Forest Service, Forest Products Laboratory: Madison, WI, USA, 2001. [Google Scholar]
- Gholz, H.L.; Fisher, R.F. Organic matter production and distribution in slash pine (Pinus elliottii) plantations. Ecology
**1982**, 63, 1827–1839. [Google Scholar] [CrossRef] - Gholz, H.L.; Fisher, R.F.; Pritchett, W.L. Nutrient Dynamics in Slash Pine Plantation Ecosystems. Ecology
**1985**, 66, 647–659. [Google Scholar] [CrossRef] - Waring, R.H.; Landsberg, J.J.; Williams, M. Net primary production of forests: A constant fraction of gross primary production? Tree Physiol.
**1998**, 18, 129–134. [Google Scholar] [CrossRef] [PubMed] - Vogel, J.G.; Suau, L.J.; Martin, T.A.; Jokela, E.J. Long-term effects of weed control and fertilization on the carbon and nitrogen pools of a slash and loblolly pine forest in north-central Florida. Can. J. For. Res.
**2011**, 41, 552–567. [Google Scholar] [CrossRef] - Berndes, G.; Abt, B.; Asikainen, A.; Cowie, A.; Dale, V.; Egnell, G.; Lindner, M.; Marelli, L.; Paré, D.; Pingoud, K.; et al. Forest Biomass, Carbon Neutrality and Climate Change Mitigation; From Science to Policy 3; European Forest Institute: Joensuu, Finland, 2016; p. 27. [Google Scholar]
- Landsberg, J.J.; Waring, R.H. A generalized model of forests productivity using simplified concepts of radiation-use efficiency, carbon balance and partitioning. For. Ecol. Manag.
**1997**, 95, 209–228. [Google Scholar] [CrossRef] - Gonzalez-Benecke, C.A.; Samuelson, L.J.; Martin, T.A.; Cropper, W.P., Jr.; Stokes, T.A.; Butnor, J.R.; Johnsen, K.H.; Anderson, P.H. Modeling the effects of forest management on in situ and ex situ longleaf pine forest carbon stocks. For. Ecol. Manag.
**2015**, 355, 24–36. [Google Scholar] [CrossRef][Green Version] - Gonzalez-Benecke, C.A.; Gezan, S.A.; Leduc, D.J.; Martin, T.A.; Cropper, W.P., Jr.; Samuelson, L.J. Modeling survival, yield, volume partitioning and their response to thinning for longleaf pine (Pinus palustris Mill.) plantations. Forests
**2015**, 3, 1104–1132. [Google Scholar] [CrossRef]

**Figure 1.**Location of the study sites for longleaf pine within the species natural distribution range (grey area).

**Figure 2.**Relationship between DBH and (

**a**) total tree above-stump biomass (TOTAL, kg); (

**b**) bole biomass outside bark (BOLE, kg); (

**c**) living foliage biomass (FOLIAGE, kg); and (

**d**) living branch biomass outside bark (BRANCH, kg) for longleaf pine trees used in this study.

**Figure 3.**Residual plots for each biomass component in the model system II fitted using NSUR without weight function, showing significant heteroscedasticity.

**Figure 4.**Pearson residual plots for each biomass component in the model system II fitted using NSUR method and different weight functions for each system equation with its own weight function.

Institution | n | A (years) | Stand Type | Thinning | Reference |
---|---|---|---|---|---|

Auburn University | 32 | 5–87 | Planted/Natural | Yes (if age >21 years) | Samuelson et al. (2014) |

96 | 8–188 | Planted/Natural | Yes (if age >25 years) | Samuelson et al. (2017) | |

Joseph W. Jones Ecological Research Center | 23 | 19–166 | Planted/Natural | Yes | Mitchell et al. (1999) |

University of Florida | 12 | 36–56 | Natural | Yes | Garbett (1977) |

4 | 70 | Natural | Yes | Gonzalez-Benecke et al. (2011) | |

U.S. Forest Service | 7 | 34–64 | Natural | Yes | Taras and Clark (1977) |

111 | 10–44 | Planted | No | Baldwin and Saucier (1983) | |

11 | 25 | Planted | No | Gibson et al. (1985) |

**Table 2.**Summary statistics of tree and their associated stand characteristics for the sampled longleaf pine trees.

Attribute | Unit | n | Mean | Std Dev | Minimum | Maximum |
---|---|---|---|---|---|---|

A | year | 273 | 35.4 | 25.6 | 5 | 188 |

DBH | cm | 296 | 21.4 | 13.4 | 0.8 | 54.3 |

HT | m | 296 | 15.8 | 7.4 | 1.5 | 30.4 |

N | ha^{−1} | 296 | 991 | 766 | 50 | 2750 |

BA | m^{2} ha^{−1} | 296 | 22.6 | 14.3 | 0.3 | 52.0 |

Branch | kg | 291 | 47.7 | 83.2 | 0.0 | 576.9 |

Foliage | kg | 296 | 13.6 | 15.8 | 0.0 | 99.0 |

Bole | kg | 292 | 271.2 | 344.8 | 0.3 | 1762.4 |

Total | kg | 291 | 330.4 | 431.0 | 0.6 | 2149.9 |

^{−1}); BA: stand basal area (m

^{2}ha

^{−1}); Branch: total living branch biomass (kg); Foliage: total living needles biomass (kg); Bole: above-stump stem over bark biomass (kg); Total: total above-stump biomass (kg).

**Table 3.**Parameter estimates and their asymptotic standard error and p-values for the additive biomass equation system based on diameter at breast height (DBH) only (Model System I).

Biomass Component | Variable | Parameter | Asymptotic Estimate | Standard Error | p-Value |
---|---|---|---|---|---|

Bole | ${\widehat{\beta}}_{10}$ | 0.0725 | 0.0079 | <0.0001 | |

DBH | ${\widehat{\beta}}_{11}$ | 2.5074 | 0.0317 | <0.0001 | |

Branch | ${\widehat{\beta}}_{20}$ | 0.0016 | 0.0002 | <0.0001 | |

DBH | ${\widehat{\beta}}_{21}$ | 3.0786 | 0.0387 | <0.0001 | |

Foliage | ${\widehat{\beta}}_{30}$ | 0.0214 | 0.0051 | <0.0001 | |

DBH | ${\widehat{\beta}}_{31}$ | 2.0051 | 0.0640 | <0.0001 |

**Table 4.**Parameter estimates and their asymptotic standard error and p-values for the additive biomass equation system based on diameter at breast height (DBH) and height (HT) (Model System II).

Biomass Component | Variable | Parameter | Asymptotic Estimate | Standard Error | p-Value |
---|---|---|---|---|---|

Bole | ${\widehat{\beta}}_{10}$ | 0.0273 | 0.0027 | <0.0001 | |

DBH | ${\widehat{\beta}}_{11}$ | 1.9745 | 0.0409 | <0.0001 | |

HT | ${\widehat{\beta}}_{12}$ | 0.9163 | 0.0618 | <0.0001 | |

Branch | ${\widehat{\beta}}_{20}$ | 0.0070 | 0.0021 | <0.0001 | |

DBH | ${\widehat{\beta}}_{21}$ | 3.6735 | 0.1268 | <0.0001 | |

HT | ${\widehat{\beta}}_{22}$ | −1.1735 | 0.1857 | <0.0001 | |

Foliage | ${\widehat{\beta}}_{30}$ | 0.0697 | 0.0153 | <0.0001 | |

DBH | ${\widehat{\beta}}_{31}$ | 2.1631 | 0.0908 | <0.0001 | |

HT | ${\widehat{\beta}}_{32}$ | −0.5569 | 0.1250 | <0.0001 |

**Table 5.**Parameter estimates and their asymptotic standard error and p-values for the additive biomass equation system based on diameter at breast height (DBH) and age (A) (Model System III).

Biomass Component | Variable | Parameter | Asymptotic Estimate | Standard Error | p-Value |
---|---|---|---|---|---|

Bole | ${\widehat{\beta}}_{10}$ | 0.0531 | 0.0061 | <0.0001 | |

DBH | ${\widehat{\beta}}_{11}$ | 2.1674 | 0.0398 | <0.0001 | |

A | ${\widehat{\beta}}_{13}$ | 0.4012 | 0.0338 | <0.0001 | |

Branch | ${\widehat{\beta}}_{20}$ | 0.0019 | 0.0003 | <0.0001 | |

DBH | ${\widehat{\beta}}_{21}$ | 3.0045 | 0.0395 | <0.0001 | |

Foliage | ${\widehat{\beta}}_{30}$ | 0.0259 | 0.0065 | <0.0001 | |

DBH | ${\widehat{\beta}}_{31}$ | 1.9399 | 0.0683 | <0.0001 |

**Table 6.**Parameter estimates and their asymptotic standard error and p-values for the additive biomass equation system based on diameter at breast height (DBH), height (HT) and age (A) (Model System IV).

Biomass Component | Variable | Parameter | Asymptotic Estimate | Standard Error | p-Value |
---|---|---|---|---|---|

Bole | ${\widehat{\beta}}_{10}$ | 0.0155 | 0.0013 | <0.0001 | |

DBH | ${\widehat{\beta}}_{11}$ | 1.8026 | 0.0370 | <0.0001 | |

HT | ${\widehat{\beta}}_{12}$ | 0.9220 | 0.0518 | <0.0001 | |

A | ${\widehat{\beta}}_{13}$ | 0.3068 | 0.0261 | <0.0001 | |

Branch | ${\widehat{\beta}}_{20}$ | 0.0027 | 0.0006 | <0.0001 | |

DBH | ${\widehat{\beta}}_{21}$ | 3.4396 | 0.1082 | <0.0001 | |

HT | ${\widehat{\beta}}_{22}$ | −0.9013 | 0.1549 | <0.0001 | |

A | ${\widehat{\beta}}_{23}$ | 0.2413 | 0.0796 | 0.0027 | |

Foliage | ${\widehat{\beta}}_{30}$ | 0.0504 | 0.0060 | <0.0001 | |

DBH | ${\widehat{\beta}}_{31}$ | 1.8671 | 0.0910 | <0.0001 | |

HT | ${\widehat{\beta}}_{32}$ | −0.3543 | 0.1070 | 0.0011 | |

A | ${\widehat{\beta}}_{33}$ | 0.1894 | 0.0538 | 0.0005 |

**Table 7.**Parameter estimates and their asymptotic standard error and p-values for the additive biomass equation system based on diameter at breast height (DBH), age (A), number of trees per hectare (N) and basal area (BA) (Model System V).

Biomass Component | Variable | Parameter | Asymptotic Estimate | Standard Error | p-Value |
---|---|---|---|---|---|

Bole | ${\widehat{\beta}}_{10}$ | 0.0597 | 0.0167 | 0.0004 | |

DBH | ${\widehat{\beta}}_{11}$ | 2.1131 | 0.0369 | <0.0001 | |

A | ${\widehat{\beta}}_{13}$ | 0.4143 | 0.0468 | <0.0001 | |

N | ${\widehat{\beta}}_{14}$ | −0.0672 | 0.0276 | 0.0158 | |

BA | ${\widehat{\beta}}_{15}$ | 0.1436 | 0.0326 | <0.0001 | |

Branch | ${\widehat{\beta}}_{20}$ | 0.0034 | 0.0004 | <0.0001 | |

DBH | ${\widehat{\beta}}_{21}$ | 2.9823 | 0.0454 | <0.0001 | |

BA | ${\widehat{\beta}}_{25}$ | −0.1638 | 0.0386 | <0.0001 | |

Foliage | ${\widehat{\beta}}_{30}$ | 0.0061 | 0.0039 | 0.1196 | |

DBH | ${\widehat{\beta}}_{31}$ | 1.9523 | 0.0968 | <0.0001 | |

A | ${\widehat{\beta}}_{33}$ | 0.2825 | 0.1134 | 0.0134 | |

N | ${\widehat{\beta}}_{34}$ | 0.1673 | 0.0669 | 0.0131 | |

BA | ${\widehat{\beta}}_{35}$ | −0.2193 | 0.0946 | 0.0213 |

**Table 8.**Parameter estimates and their asymptotic standard error and p-values for the additive biomass equation system based on diameter at breast height (DBH), height (HT), age (A) and basal area (BA) (Model System VI).

Biomass Component | Variable | Parameter | Asymptotic Estimate | Standard Error | p-Value |
---|---|---|---|---|---|

Bole | ${\widehat{\beta}}_{10}$ | 0.0156 | 0.0013 | <0.0001 | |

DBH | ${\widehat{\beta}}_{11}$ | 1.7983 | 0.0364 | <0.0001 | |

HT | ${\widehat{\beta}}_{12}$ | 0.9285 | 0.0509 | <0.0001 | |

A | ${\widehat{\beta}}_{13}$ | 0.3031 | 0.0249 | <0.0001 | |

Branch | ${\widehat{\beta}}_{20}$ | 0.0042 | 0.0009 | <0.0001 | |

DBH | ${\widehat{\beta}}_{21}$ | 3.4396 | 0.1122 | <0.0001 | |

HT | ${\widehat{\beta}}_{22}$ | −0.5562 | 0.1565 | 0.0005 | |

BA | ${\widehat{\beta}}_{25}$ | −0.1958 | 0.0475 | 0.0001 | |

Foliage | ${\widehat{\beta}}_{30}$ | 0.0420 | 0.0065 | <0.0001 | |

DBH | ${\widehat{\beta}}_{31}$ | 1.8393 | 0.0939 | <0.0001 | |

HT | ${\widehat{\beta}}_{32}$ | −0.2730 | 0.1129 | 0.0164 | |

A | ${\widehat{\beta}}_{33}$ | 0.1956 | 0.0549 | 0.0004 |

**Table 9.**Weight functions and fit statistics for each component in the additive biomass equation systems.

Model System | Biomass Component | Weight Function | E | MABE | RMSE | R^{2} |
---|---|---|---|---|---|---|

I | Bole | $DB{H}^{3.283}$ | −0.714 | 47.760 | 90.496 | 0.929 |

Branch | $DB{H}^{5.705}$ | −0.754 | 16.656 | 37.130 | 0.797 | |

Foliage | $DB{H}^{2.932}$ | 0.036 | 3.823 | 6.446 | 0.838 | |

Total | $DB{H}^{3.396}$ | −1.431 | 48.366 | 94.403 | 0.951 | |

II | Bole | $DB{H}^{4.716}$ | 3.281 | 34.649 | 67.064 | 0.961 |

Branch | $DB{H}^{7.197}\xb7H{T}^{-3.684}$ | 1.730 | 14.736 | 34.058 | 0.830 | |

Foliage | $DB{H}^{2.780}$ | −0.300 | 3.685 | 6.250 | 0.847 | |

Total | $DB{H}^{5.030}$ | 4.711 | 43.950 | 84.532 | 0.961 | |

III | Bole | $DB{H}^{1.908}\xb7{A}^{0.687}$ | −0.008 | 33.517 | 59.469 | 0.969 |

Branch | $DB{H}^{5.706}$ | 0.402 | 13.004 | 26.741 | 0.850 | |

Foliage | $DB{H}^{2.772}$ | 0.017 | 3.550 | 5.720 | 0.850 | |

Total | $DB{H}^{1.806}\xb7{A}^{1.102}$ | 0.412 | 33.721 | 62.646 | 0.977 | |

IV | Bole | $DB{H}^{2.073}\xb7H{T}^{1.814}\xb7{A}^{0.798}$ | −0.080 | 21.839 | 38.223 | 0.987 |

Branch | $DB{H}^{5.585}\xb7H{T}^{-1.413}$ | −0.732 | 11.252 | 24.582 | 0.873 | |

Foliage | $DB{H}^{2.067}\xb7{A}^{1.102}$ | −0.376 | 3.557 | 5.635 | 0.854 | |

Total | $DB{H}^{1.975}\xb7H{T}^{1.614}\xb7{A}^{1.163}$ | −1.189 | 28.440 | 51.307 | 0.984 | |

V | Bole | $DB{H}^{2.086}\xb7B{A}^{0.838}$ | −3.519 | 33.002 | 59.264 | 0.969 |

Branch | $DB{H}^{5.774}$ | 0.032 | 12.599 | 26.113 | 0.857 | |

Foliage | $DB{H}^{2.884}$ | 0.036 | 3.404 | 5.565 | 0.858 | |

Total | $DB{H}^{1.611}\xb7{A}^{1.239}$ | −3.452 | 33.791 | 62.196 | 0.977 | |

VI | Bole | $DB{H}^{2.068}\xb7H{T}^{1.801}\xb7{A}^{0.811}$ | 0.485 | 21.841 | 38.402 | 0.987 |

Branch | $DB{H}^{4.794}\xb7B{A}^{-0.630}$ | −0.330 | 11.306 | 24.602 | 0.873 | |

Foliage | $DB{H}^{1.990}\xb7{A}^{1.130}$ | −0.298 | 3.560 | 5.641 | 0.854 | |

Total | $DB{H}^{2.248}\xb7H{T}^{1.315}\xb7{A}^{1.104}$ | −0.143 | 28.006 | 50.856 | 0.985 |

^{2}is the coefficient of determination.

**Table 10.**Leave-one-out (LOO) cross-validation results for each biomass component in the additive biomass equation systems.

Model System | Biomass Component | E | MABE | RMSE | R^{2} |
---|---|---|---|---|---|

I | Bole | −0.85 (−0.3) | 48.42 (17.9) | 92.21 (34.0) | 0.927 |

Branch | −0.72 (−1.5) | 16.89 (35.4) | 37.97 (79.6) | 0.788 | |

Foliage | 0.04 (0.3) | 3.88 (28.5) | 6.60 (48.5) | 0.830 | |

Total | −1.52 (−0.5) | 49.05 (14.8) | 96.23 (29.1) | 0.949 | |

II | Bole | 3.38 (1.2) | 35.17 (13.0) | 68.30 (25.2) | 0.960 |

Branch | 1.79 (3.8) | 15.01 (31.5) | 34.99 (73.4) | 0.820 | |

Foliage | −0.29 (−2.1) | 3.77 (27.7) | 6.50 (47.8) | 0.835 | |

Total | 4.88 (1.5) | 44.72 (13.5) | 86.54 (26.2) | 0.959 | |

III | Bole | −0.09 (0.0) | 34.42 (12.7) | 61.54 (22.7) | 0.966 |

Branch | 0.48 (−1.0) | 13.24 (27.7) | 27.25 (57.1) | 0.844 | |

Foliage | 0.03 (0.3) | 3.62 (26.6) | 5.84 (42.9) | 0.843 | |

Total | 0.42 (0.1) | 34.55 (10.5) | 64.77 (19.6) | 0.975 | |

IV | Bole | 0.05 (0.0) | 22.46 (8.3) | 39.50 (14.6) | 0.986 |

Branch | −0.77 (−1.6) | 11.54 (24.2) | 25.29 (53.0) | 0.866 | |

Foliage | −0.36 (−2.7) | 3.65 (26.8) | 5.84 (42.9) | 0.844 | |

Total | −1.08 (−0.3) | 29.18 (8.8) | 52.94 (16.0) | 0.983 | |

V | Bole | −3.29 (−1.2) | 34.97 (12.9) | 63.97 (23.6) | 0.964 |

Branch | 0.05 (0.1) | 12.79 (26.8) | 26.66 (55.9) | 0.851 | |

Foliage | 0.04 (0.3) | 3.56 (26.2) | 5.95 (43.8) | 0.837 | |

Total | −3.19 (−1.0) | 35.79 (10.8) | 66.27 (20.1) | 0.974 | |

VI | Bole | 0.64 (0.2) | 22.48 (8.3) | 39.76 (14.7) | 0.986 |

Branch | −0.32 (−0.7) | 11.59 (24.3) | 25.29 (53.0) | 0.866 | |

Foliage | −0.28 (−2.1) | 3.66 (26.9) | 5.85 (43.0) | 0.843 | |

Total | 0.04 (0.0) | 28.72 (8.7) | 52.43 (15.9) | 0.984 |

^{2}is the coefficient of determination. Values in parenthesis corresponds to percent relative to mean observed value.

**Table 11.**Prediction statistics for each component using biomass equations developed by Baldwin and Saucier (1983) and Samuelson et al. (2017).

Model System | Component | E | MABE | RMSE | R^{2} |
---|---|---|---|---|---|

Baldwin and Saucier (1983) (BS-83) | Bole | 25.19 (9.3) | 35.96 (13.3) | 78.15 (28.8) | 0.947 |

Branch | −2.63 (−5.5) | 23.77 (49.8) | 47.01 (98.5) | 0.675 | |

Foliage | 0.99 (7.2) | 4.54 (33.3) | 7.59 (55.6) | 0.775 | |

Total | 27.85 (8.4) | 46.32 (14.0) | 99.75 (30.2) | 0.945 | |

Samuelson et al. (2017) (S-17) | Bole | −28.87 (−10.6) | 43.53 (16.1) | 85.14 (31.4) | 0.937 |

Branch | −5.22 (−10.9) | 17.96 (37.6) | 37.55 (78.7) | 0.793 | |

Foliage | −1.62 (−11.9) | 4.26 (31.3) | 6.95 (50.9) | 0.811 | |

Total | −35.71 (−10.8) | 54.08 (16.4) | 104.45 (31.6) | 0.940 |

^{2}is the coefficient of determination. Values in parenthesis corresponds to percent relative to mean observed value.

© 2018 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Gonzalez-Benecke, C.A.; Zhao, D.; Samuelson, L.J.; Martin, T.A.; Leduc, D.J.; Jack, S.B. Local and General Above-Ground Biomass Functions for *Pinus palustris* Trees. *Forests* **2018**, *9*, 310.
https://doi.org/10.3390/f9060310

**AMA Style**

Gonzalez-Benecke CA, Zhao D, Samuelson LJ, Martin TA, Leduc DJ, Jack SB. Local and General Above-Ground Biomass Functions for *Pinus palustris* Trees. *Forests*. 2018; 9(6):310.
https://doi.org/10.3390/f9060310

**Chicago/Turabian Style**

Gonzalez-Benecke, Carlos A., Dehai Zhao, Lisa J. Samuelson, Timothy A. Martin, Daniel J. Leduc, and Steven B. Jack. 2018. "Local and General Above-Ground Biomass Functions for *Pinus palustris* Trees" *Forests* 9, no. 6: 310.
https://doi.org/10.3390/f9060310