# Estimation of Aboveground Oil Palm Biomass in a Mature Plantation in the Congo Basin

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

^{2}× stem height, weighted by tissue infra-density. For leaf biomass (fruits + leaflets + petioles + rachises), the equation was of a similar form, but included the leaf number instead of infra-density. The allometric model combining the stem and leaf biomass yielded the best estimates of the total aboveground oil palm biomass (coefficient of determination (r

^{2}) = 0.972, p < 0.0001, relative root mean square error (RMSE) = 5%). Yet, the model was difficult to implement in practice, given the limited availability of variables such as the leaf number. The total aboveground biomass could be estimated with comparable results using DBH

^{2}× stem height, weighted by the infra-density (r

^{2}= 0.961, p < 0.0001, relative RMSE (%RMSE) = 5.7%). A simpler model excluding infra-density did not severely compromise results (R

^{2}= 0.939, p < 0.0003, %RMSE = 8.2%). We also examined existing allometric models, established elsewhere in the world, for estimating aboveground oil palm biomass in our study area. These models exhibited performances inferior to the best local allometric equations that were developed.

## 1. Introduction

^{−1}during the period 2010–2015, from the estimated 9.5 Mha year

^{−1}during the 1990s [2].

^{2}× stem height was used by Hughes et al. [25] in southern Mexico to estimate biomass for wild palms (Astrocaryum mexicanum Liebm. ex Mart.) with DBHs < 10 cm. Cole and Ewel [26] also considered the same variable combination for four economically valuable forest species, but also included the leaf count in the estimation of the aboveground biomass in açai palm (Euterpe oleracea Mart.) plantations (DBH < 20 cm) in the Atlantic Lowlands of Costa Rica. Goodman et al. [27] studied the allometric relationships of nine species in the Arecaceae, including Attalea phalerata Mart. ex Sprung, which is a source of vegetable oil [28]. These authors substituted the dry-matter fraction for the leaf count in palm plantations covering all the stages of development (DBH between 4 and 50 cm) in Amazonian Peru, while Da Silva et al. [22] considered the stem infra-density in the case of young (DBH 3–13 cm) forest açai or açaí-solitário (Euterpe precatoria Mart.) in Amazonian Brazil.

## 2. Materials and Methods

#### 2.1. Study Area

#### 2.2. Data Collection

#### 2.2.1. Field Data Measurement

_{T}) and total height (H

_{TOT}), were recorded using a standard measuring tape (DBH in cm and heights in m). The stem height was measured from the stump to the first branch, while the total height was taken from the stump to the top of the crown. The total number of leaves (N

_{F}) on each palm was also counted. Following these measurements, the palm stem was sectioned into logs at fixed 0.5 m increments. The diameters and heights of the palm trees in the flood prone and neighboring areas were smaller (less than 52 cm for DBH and less than 16.4 m for H

_{TOT}) than those located on the dryland (more than or equal to 52 cm for DBH and 15.1 m for H

_{TOT}). The basic statistics of the measurements that were taken in the field are summarized in Table 1.

#### 2.2.2. Laboratory Measurements

#### 2.3. Establishment and Validation Allometric Models

_{e}-transformed form of the equation is used to linearize the expression, while at the same time homogenizing the variance, which increases the validity of statistical tests that are being used [34,35,36]. The equation can be rewritten as

_{T}, H

_{TOT}, ρ and N

_{F}. To obtain unbiased estimations with log-transformed models, the bias caused by the conversion of ln (y) to the original non-transformed scale y, should be corrected. The correction factor (CF) was used to make this correction [26,27,30], such as CF = exp(root mean square error (RMSE)

^{2}/2), where RMSE is the mean square error of the regression equation. The original untransformed scale of y could be obtained by y = (CF × a)X

^{b}[30]. To develop the equations, 60% of the oil palms were randomly selected and used (i.e., 11 of 18 palms). The remaining 40% (7 oil palms) were set aside for the independent validation of the results. Both the data for development and validation were randomly located over drylands and flood prone areas.

^{2}), the residual standard error (σ), the Akaike information criterion (AIC), the relative error (ER), the relative percentage error (%ER), and the root mean square error (RMSE) and its percentage (%RMSE). Similar metrics have been used in previous studies [30,37,38]. The expressions for calculating ER and RMSE are as follows:

_{i}is the observed value for palm i, and y

_{i}is its predicted value. The relative RMSE (%RMSE) was calculated as a percentage by dividing the RMSE by the observed mean [38]. The relative percent error (%ER) was obtained by multiplying ER by 100. The interpretation of the metrics differed when attempting to characterize the best performance. The higher the r

^{2}, the more robust the equation was considered. In contrast, the lower the AIC value, the better the model fit. In all cases, the errors (ER, %ER, σ, RMSE, %RMSE) should be as small as possible. However, Kuyah et al. [39] and Yang et al. [30] have recommended giving more weight to the bias and RMSE rather than to an adjusted r

^{2}or AIC in deciding the final optimal model [30].

#### 2.4. Comparisons with Existing Biomass Allometric Models

## 3. Results

#### 3.1. Distribution of Biomass Proportions

^{2}= 0.999, p < 0.0001).

#### 3.2. Relationships between Variables

_{TOT}, H

_{T}and N

_{F}could be explained by the diameter (DBH). As shown in Table 4 and Figure 3, the respective allometric relationships were significant (p < 0.05) between the dependent variables ρ, H

_{TOT}, H

_{T}and N

_{F}, vs. the independent variable DBH, with a moderate to strong r

^{2}(0.538 to 0.806). The %RMSE was < 3% (Table 4). On the one hand, the strongest relationship was obtained between the stem height and the DBH (r

^{2}= 0.806; p = 0.0001). On the other hand, the weakest relationship (albeit, statistically significant) with the DBH was obtained with the total tree height (r

^{2}= 0.538; p = 0.010).

#### 3.3. Allometric Biomass Models That Were Developed

^{2}≥ 0.564, p < 0.05; %ER < 1.3%). Model 6, which was based upon DBH, yielded the highest r

^{2}= 0.959 (p < 0.0001) and the lowest errors (%RMSE = 0.54%, %ER = 0.003%) compared to all the other local models (7 and 8) using individual explanatory variables (ρ, H

_{T}and H

_{TOT}) (Table 5).

^{2}> 0.8; p ≤ 0.0001; AIC < −55.4) were more efficient than those designed using the total heights (%RMSE < 1.8; r

^{2}> 0.5; p ≤ 0.008; AIC < −45.4). The allometric models of the aboveground biomass using composite variables (DBH

^{2}H

_{T}or DBH

^{2}H

_{T}ρ) performed in a manner that was relatively similar to those solely based upon DBH (Table 5).

^{2}values of 0.930 and 0.679, respectively. The errors associated with these relationships were relatively small (%RMSE = 0.76%; RMSE = 0.04 kg for stems, %RMSE = 0.10%; RMSE = 2.19 kg for leaves) (Table 5). All of the allometric models estimating stem and leaf biomasses (13 and 14), with the exception of Model 15, exhibited evaluation performances that were close to those of Model 12 (Table 5). Errors for Model 15 in predicting stem and leaf biomass were lower (RMSE < 0.094 kg; %RMSE < 1.96%) than those for Models 12, 13 and 14 (RMSE < 0.14 kg; %RMSE < 3.28%). In summary, according to the results that we obtained, the total aboveground biomass of oil palm was best correlated with the DBH compared to the stem or leaf biomass (Figure 4).

#### 3.4. Validation of Local Allometric Models

_{TOT}, H

_{T}and N

_{F}) and the DBH, together with the allometric relationships that were obtained with log sections. Validation results are reported in Table 6. All the variables that were considered were significantly related to DBH (r

^{2}≥ 0.66; p ≤ 0.026), with relatively small errors (%RMSE ≤ 9.6%; %ER ≤ 7.5%). The relationships that were obtained for the total height (Model 4) and infra-density (Model 1) appeared to be the most robust following validation (Table 6).

^{2}H

_{T}) contributed to the improvement of all the validation criteria of these allometric models. As an example, the root mean square error decreased from 8.2% to 5.7% when moving from Model 9 (excluding infra-density) to Model 11 (including infra-density). In the same vein, taking into account the leaf number (N

_{F}) in allometric models using DBH

^{2}H

_{T}improved the estimates of leaf biomass and by extension, the entire palm tree. The results of Allometric Models 14 and 15 clearly showed these improvements compared to models in which the leaves were not considered.

^{2}(0.939, p < 0.0001), the smallest AIC (45.3) and the lowest %RMSE (8.2%) among all the allometric models using structural parameters that were measured directly on oil palm (DBH and H

_{T}) (Table 7). With the addition of a variable that is not directly measurable, such as infra-density (ρ), Allometric Model 11 slightly improves upon Allometric Model 9. Allometric Model 15 includes both infra-density and leaf number (a parameter usually not available). This model exhibited the best performance in this study, with a relative RMSE of 5% (Table 7). By combining the aboveground biomass of the stems (DBH

^{2}H

_{T}ρ) and leaves (DBH

^{2}H

_{T}N

_{F}), Model 15 stands out as the best of the local biomass allometric models that were developed in the study (Table 7). The expressions of these three (3) models are described below:

#### 3.5. Validation of Existing Allometric Biomass Models

_{T}, and ρ and N

_{F}as composite explanatory variables, the two existing models produced errors of less than 24% (Table 8). The allometric equation DaSilva2015b from Da Silva et al. [22] provided an %RMSE of 10.9%. However, this error was almost double that produced by Allometric Model 15 in this study. Figure 5b illustrates the results of the five existing models that produced the lowest errors in our study area. The results of the three best local allometric models that were proposed in this study are also shown for comparison purposes. Dispersion is greater in the estimated biomasses for larger diameters (>52 cm). The allometric equations ColEwe2006 [26] and Thenk2004b [20] systematically underestimated the biomass in the area. The associated errors were generally > 20%. Other existing allometric models in Figure 5b produced relative errors < 15%, although they were not developed specifically for the region. Of course, local models were more efficient with relative errors that were generally < 10%.

## 4. Discussion

#### 4.1. Interpretation of Biomass Distribution

#### 4.2. Evaluation of Local Allometric Biomass Equations

^{2}H

_{T}(Model 9) is effective in estimating palm biomass on the study site, as has been the case in other tropical areas [18,25,36]. The cylindrical shape of the oil palm stem, geometrically characterized by the combination DBH

^{2}H

_{T}, could explain the strong relationship with biomass. Indeed, the latter is essentially concentrated in the stem (Figure 2). Estimating biomass using DBH

^{2}H

_{T}is an alternative, non-destructive method in different tropical oil palm-producing regions.

^{−3}. The estimate was within the range from 0.21 to 0.41 g·cm

^{−3}that was defined by Supriadi et al. [40] for Elais guineensis-type palms. The relationship between biomass and infra-density appears to be very significant (see Allometric Model 5, Table 7). Thus, the weighting of the composite variable DBH

^{2}H

_{T}with infra-density resulted in considerable improvement in palm biomass prediction, as demonstrated by the very small error (%RMSE = 5.8%) that was obtained with Allometric Model 11 (Table 7). The combination of the three variables (DBH, H

_{T}, ρ) has also provided significant results in previous work [21,22].

^{2}H

_{T}ρ (Model 11) or DBH

^{2}H

_{T}(Allometric Model 9). Despite incurring larger errors, Allometric Model 9 remains an interesting alternative to Models 11 and 15 in the absence of infra-density or leaf number data.

#### 4.3. Comparison of Local Models to Existing Allometric Biomass Models

_{T}= 8.8 m; ρ = 0.3306 g·cm

^{−3}). This could be the cause of their strong performance, especially in class 1 DBH. The DBHs (3.9 and 12.7 cm) that were used to establish the allometric models of Da Silva et al. [22] could have caused the slightly larger errors that were observed in class 2.

## 5. Conclusions

^{2}H

_{T}) emerged as the most interesting and perhaps useful explanatory variable for estimating oil palm biomass in the current study. It was the basis of the three best models that were obtained. The best of the three (Allometric Model 15) integrates the contributions of leaves and is characterized by a low error (%RMSE about 5%). The second high-performance allometric model, which weights DBH

^{2}H

_{T}by infra-density, also produces a low error of about 6%. The third allometric model (Model 9), which was based solely upon DBH

^{2}H

_{T}, was the most practical alternative, given its relatively small error (about 8%) and the fact that information on infra-density and palm leaf number is not always available. The study shows that some allometric equations developed in other regions could have been used to estimate the palm biomass in the site that we selected in the Congo Basin, but with slightly larger errors than those of the three proposed allometric models. However, several existing models were not applicable because of the large errors they produced in the site, due to differences in palm oil species, age or site conditions.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Appendix A

**Table A1.**Field and laboratory data that were used to develop aboveground biomass models for oil palm.

Plot Number | B_{F} (Total Fresh Aboveground Biomass of Oil Palm) (kg) | DBH (Diameter at Breast Height, 1.3 m) (cm) | H_{TOT} (Total Height) (m) | H_{T} (Stem Height) (m) | N_{F} (Number of Leaves Per Palm) | DMF (Dry Mass Fraction) Stem Mean | Dmf (Mean Dry Mass Fraction) Of Oil Palm | ρ (Mean Infra-Density of Oil Palm Stem) (g·cm ^{−3}) | B_{Rachis} (Dry Rachis Biomass) (kg) | B_{FSR} (Dry leaf Biomass without Rachis) (kg) | B_{Leaf} (Dry Leaf Biomass of Oil Palm: Petioles, Fruits, Rachises and Leaflets) (kg) | B_{Stem} (Dry Stem Biomass of Oil Palm) (kg) | B (Total Dry Aboveground Biomass (kg) |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|

1 | 1336.80 | 50.9 | 16.3 | 8.0 | 32 | 0.2914 | 0.2857 | 0.2819 | 59.8752 | 52.9108 | 112.786 | 269.1137 | 381.8997 |

2 | 1643.30 | 53.6 | 16.7 | 9.1 | 36 | 0.3085 | 0.2818 | 0.2921 | 63.0907 | 70.4268 | 133.5175 | 329.4937 | 463.0112 |

3 | 1950.20 | 57.6 | 16.4 | 10.0 | 38 | 0.3081 | 0.2853 | 0.3279 | 66.9161 | 70.0291 | 136.9452 | 419.4599 | 556.4051 |

4 | 1176.95 | 49.2 | 15.0 | 7.4 | 30 | 0.3105 | 0.2836 | 0.2587 | 50.7830 | 53.1305 | 103.9135 | 229.9270 | 333.8405 |

5 | 1259.35 | 49.6 | 15.3 | 7.8 | 30 | 0.3314 | 0.2832 | 0.2872 | 43.1878 | 59.7505 | 102.9383 | 253.6564 | 356.5947 |

6 | 1227.44 | 50.4 | 15.3 | 7.5 | 29 | 0.3008 | 0.2902 | 0.2993 | 42.3007 | 36.6779 | 78.9786 | 277.2167 | 356.1953 |

7 | 1462.40 | 53.7 | 16.5 | 8.8 | 37 | 0.3365 | 0.2846 | 0.2917 | 55.4954 | 63.7667 | 119.2621 | 296.9790 | 416.2411 |

8 | 1623.30 | 55.3 | 16.2 | 8.5 | 34 | 0.3343 | 0.2855 | 0.2972 | 69.4109 | 67.4892 | 136.9001 | 326.5954 | 463.4955 |

9 | 1710.05 | 54.9 | 16.1 | 8.5 | 39 | 0.3471 | 0.2843 | 0.3077 | 74.2342 | 74.5585 | 148.7927 | 337.3431 | 486.1358 |

10 | 1294.15 | 51.3 | 15.5 | 8.5 | 31 | 0.2972 | 0.2901 | 0.2927 | 55.4954 | 46.9775 | 102.4729 | 272.9780 | 375.4509 |

11 | 1763,1 | 55.9 | 18.2 | 9.5 | 38 | 0.3115 | 0.2869 | 0.3180 | 83.1600 | 63.0959 | 146.2559 | 359.6233 | 505.8792 |

12 | 1803.75 | 57.9 | 16.6 | 9.8 | 38 | 0.3099 | 0.2862 | 0.3030 | 45.6964 | 68.9378 | 114,6342 | 401,5572 | 516.1914 |

13 | 1156.25 | 50.7 | 15.3 | 8.1 | 27 | 0.2987 | 0.2852 | 0.2749 | 29.3832 | 47.7701 | 77.1533 | 252,6299 | 329.7832 |

14 | 1672.25 | 57.4 | 17.0 | 8.5 | 37 | 0.2857 | 0.2814 | 0.3260 | 62.5918 | 74.5959 | 137.1877 | 333.4184 | 470.6061 |

15 | 1543.70 | 55.4 | 16.6 | 9.5 | 32 | 0.2536 | 0.2889 | 0.2935 | 65.1420 | 52.9177 | 118.0597 | 327.9238 | 445.9835 |

16 | 1216.85 | 51.1 | 15.0 | 7.4 | 28 | 0.2650 | 0.2822 | 0.2776 | 41.2474 | 51.4161 | 92.6635 | 250.6978 | 343.3613 |

17 | 1021.80 | 48.8 | 14.5 | 6.65 | 30 | 0.2706 | 0.2826 | 0.2500 | 40.8038 | 48.7180 | 89.5218 | 199.1936 | 288.7154 |

18 | 1493.20 | 52.0 | 15.1 | 8.8 | 33 | 0.2727 | 0.2871 | 0.2950 | 68.2466 | 48.4361 | 116.6827 | 311.9835 | 428.6662 |

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**Figure 3.**Allometric relationships between the variables and the DBH of the 11 oil palms used in this study to develop local biomass models: (

**a**) relationship between total height vs. DBH; (

**b**) relationship between stem height vs. DBH; (

**c**) relationship between infra-density vs. DBH; and (

**d**) relationship between number of leaves vs. DBH.

**Figure 4.**Allometric relationships between the biomass components of 11 oil palms and their corresponding DBH.

**Figure 5.**Comparison of the selected existing allometric models with the best allometric models that were proposed in this study: (

**a**) biomass variation according to DBH; (

**b**) relative error variation according to DBH.

**Figure 6.**Errors in the allometric models when considering the two DBH classes (48–52 cm, 52–58 cm).

**Table 1.**Summary of the field measurements for 18 felled oil palms: n is the number of oil palms; DBH, H

_{T}, H

_{TOT}and N

_{F}are respectively the diameter at breast height (cm, measured 1.3 m above the ground surface), the stem height (m), the total height (m) and the leaf number per tree.

Parameter | Minimum | Maximum | Mean | SE | %SE |
---|---|---|---|---|---|

DBH | 48.8 | 57.9 | 53.1 | 0.71 | 1.34 |

H_{T} | 6.65 | 10.0 | 8.46 | 0.22 | 2.60 |

H_{TOT} | 14.5 | 18.2 | 15.97 | 0.22 | 1.38 |

N_{F} | 27 | 39 | 33.27 | 0.92 | 2.77 |

**Table 2.**Summary of the infra-density, dry mass fractions and the average total dry mass of the palm components for 18 individuals that were felled in Makouké, central Gabon.

Components | Minimum | Maximum | Mean | SE | % SE |
---|---|---|---|---|---|

Descriptive Statistical Parameters for Dry Mass Fractions (DMF) | |||||

Stem | 0.253 | 0.347 | 0.301 | 0.006 | 2.020 |

Petiole | 0.134 | 0.245 | 0.194 | 0.007 | 3.805 |

Fruit | 0.156 | 0.221 | 0.190 | 0.009 | 5.059 |

Rachis | 0.233 | 0.335 | 0.277 | 0.006 | 2.386 |

Leaflet | 0.198 | 0.386 | 0.322 | 0.010 | 3.215 |

Whole oil palm | 0.281 | 0.290 | 0.285 | 6.10^{−4} | 0.220 |

Descriptive Statistical Parameters for Infra-Density (g·cm^{−3}) | |||||

Stem | 0.25 | 0.3279 | 0.2930 | 0.0048 | 1.639 |

Descriptive Statistical Parameters for Total Dry Mass of Oil Palm Compartments (kg) | |||||

Stem | 199.19 | 419.46 | 302.77 | 13.66 | 4.51 |

Petiole | 20.89 | 46.31 | 33.28 | 1.64 | 4.92 |

Fruit | 14 | 82.5 | 58.57 | 10.54 | 17,99 |

Rachis | 29.38 | 83.16 | 56.50 | 3.31 | 5.86 |

Leaflet | 13.29 | 29.57 | 21.42 | 1.03 | 4.83 |

Leaf (Petioles, Fruit, Rachis + Leaflets) | 77.15 | 148.79 | 114.93 | 5.19 | 4.52 |

Stem + Leaf | 288.72 | 556.41 | 417.69 | 17.78 | 4.26 |

**Table 3.**Existing biomass models that were considered. B = total aboveground biomass (kg); B

_{F}= total aboveground fresh biomass of an oil palm (kg); B

_{Stem}= stem biomass (kg); N

_{F}= number of leaves; B

_{FSR}= leaf biomass without rachis (kg); B

_{Rachis}= rachis biomass (kg); DBH = diameter at breast height (in cm, measured 1.3 m above ground surface); H

_{Tcm}= stem height of a palm (cm); CF = correction factor; n = number of palms that were sampled.

**r**= coefficient of determination. The other variables have been previously defined in the text.

^{2}Source | Geographic Region | Palm Species | Existing Biomass Model (kg tree^{−1}) | CF | r^{2} | n |
---|---|---|---|---|---|---|

Khalid et al. [4] | Malaysia | Elaeis guineensis | B_{F} = 725 + 197 × H_{TOT} | 0.96 | 7 | |

Thenkabail et al. [20] | Benin | Elaeis guineensis | B_{F} = 1.5729 × H_{Tcm} – 8.2835 | 0,97 | 7 | |

B = 0.3747 × H_{Tcm} + 3.6334 | 0.98 | 7 | ||||

Hughes et al. [25] | Mexico | Astrocaryum mexicanum | B = exp(3.6272 + 0.5768 × ln(DBH^{2}H_{T})) CF/10^{6} | 1.02 | 0.73 | 15 |

Saldarriaga et al. [18] | Colombia and Venezuela | Common | B = exp(−6.3789 – 0.877 × ln(1/DBH^{2}) + 2.151 × ln(H_{T})) | 0.89 | 19 | |

Goodman et al. [27] | Amazonia (Peru) | Common | B = 0.0950 × (DMF × DBH^{2}H_{T}) | 0.99 | 106 | |

Da Silva et al. [22] | Brazil | Euterpe precatoria | B = 0.167 × (DBH^{2}H_{T}ρ) ^{0.883} | 0.98 ^{1} | 20 | |

B_{Stem} = exp(0.1212 + 0.90 × ln(DBH^{2}H_{T}ρ)) | 0.98 ^{1} | 20 | ||||

B_{Leaf} = exp(0.0065 + 0.69 × ln(DBH^{2}H_{T}N_{F})) | 0.94 ^{1} | 20 | ||||

Cole and Ewel [26] | Tropical zone (Costa Rica) | Euterpe oleraceae | B_{Stem} = 0.0314 × (DBH^{2}H_{T})^{0.917} × CF | 1.04 | 0.95 | 156 |

B_{FSR} = 0.0237 × (DBH^{2}H_{T}N_{F})^{0.512} × CF | 1.036 | 0.94 | 182 | |||

B_{Rachis} = 0.0458 × (DBH^{2}H_{T}N_{F})^{0.388} × CF | 1.036 | 0.90 | 187 |

^{1}Da Silva [22] used adjusted values of the coefficient of determination (R

_{adj}

^{2}) rather than r

^{2}.

**Table 4.**Criteria for evaluating the allometric relationships between the DBH and the dependent variables using data from 11 oil palms in Makouké, central Gabon. Values of the coefficients a and b of the models are given; σ is the residual standard error (in kg); p is the p-value of the model. CF is the correction factor for the log-transformed equation. Residual standard errors (σ, in kg), Akaike Information Criterion (AIC), relative error (ER), relative percentage error (%ER), root-mean-square error (RMSE, in kg) and its percentage (%RMSE) are shown for each equation.

Model | a | b | r^{2} | σ | AIC | CF | p | ER | %ER | RMSE | %RMSE |
---|---|---|---|---|---|---|---|---|---|---|---|

Model 1: ln(ρ) = a + b × ln(DBH) | −5.057 | 0.967 | 0.674 | 0.037 | −73.343 | 1.0006 | 0.002 | 75 × 10^{−5} | 0.075 | 0.034 | 2.793 |

Model 2: ln(N_{F}) = a + b × ln(DBH) | −3.892 | 1.868 | 0.804 | 0.051 | −63.390 | 1.0011 | 0.0001 | 17.5 × 10^{−5} | 0.017 | 0.046 | 1.327 |

Model 3: ln(H_{T}) = a + b × ln(DBH) | −4.342 | 1.608 | 0.806 | 0.044 | −66.843 | 1.0008 | 0.0001 | 34.6 × 10^{−5} | 0.034 | 0.039 | 1.869 |

Model 4: ln(H_{TOT}) = a + b × ln(DBH) | −0.179 | 0.746 | 0.538 | 0.038 | −69.769 | 1.0006 | 0.010 | 15.4 × 10^{−5} | 0.015 | 0.034 | 1.258 |

**Table 5.**Local allometric biomass models that were developed in this study. B is the total dry aboveground oil palm biomass. B

_{Stem}, B

_{Leaf}, B

_{FSR}and B

_{Rachis}are respectively stem, leaf (including petioles, rachis and leaflets), rachis-free leaf and rachis biomasses. P is the p-value of the model. Residual standard error (σ, in kg), the correction factor (CF), the ER and the RMSE are shown for each equation.

Model | a | b | r^{2} | σ | AIC | P | CF | ER | %ER | RMSE | %RMSE | |
---|---|---|---|---|---|---|---|---|---|---|---|---|

Allometric Equations Using Infra-Density (ρ) or DBH as the Predictor | ||||||||||||

Model 5 | ln(B) = a + bln(ρ) | 8.755 | 2.223 | 0.685 | 0.099 | −48.985 | 0.002 | 1.0041 | 22.1 × 10^{−5} | 0.022 | 0.089 | 1.488 |

Model 6 | ln(B) = a + bln(DBH) | −6.256 | 3.100 | 0.959 | 0.035 | −71.480 | <0.0001 | 1.0005 | 2.8 × 10^{−5} | 0.002 | 0.032 | 0.535 |

Equations using height as the predictor | ||||||||||||

Model 7 | ln(B) = a + bln(H_{T}) | 2.616 | 1.604 | 0.824 | 0.074 | −55.383 | 0.0001 | 1.0022 | 12.3 × 10^{−5} | 0.012 | 0.067 | 1.112 |

Model 8 | ln(B) = a + bln(H_{TOT}) | −0.443 | 2.333 | 0.562 | 0.117 | −45.350 | 0.008 | 1.0056 | 30.4 × 10^{−5} | 0.030 | 0.106 | 1.755 |

Allometric Equations Using DBH and Height as Composite Predictors | ||||||||||||

Model 9 | ln(B) = a + bln(DBH^{2}H_{T}) | −2.335 | 0.832 | 0.942 | 0.042 | −67.606 | <0.0001 | 1.0007 | 4 × 10^{−5} | 0.004 | 0.038 | 0.638 |

Allometric Equations Using DBH, Height and Infra-Density as Composite Predictors | ||||||||||||

Model 10 | ln(B) = bln(DBH^{2}H_{T} ρ) | 0.683 | 0.999 | 0.0439 | −68.560 | 0.0001 | 1.0008 | −2.1 × 10^{−5} | −0.002 | 0.040 | 0.669 | |

Model 11 | ln(B) = a + bln(DBH^{2}H_{T} ρ) | 0.277 | 0.651 | 0.938 | 0.043 | −66.938 | <0.0001 | 1.0008 | 4.3 × 10^{−5} | 0.004 | 0.039 | 0.658 |

Allometric Equations Using DBH, H_{T}, ρ or N_{F} as Composite Variables to Estimate Aboveground Biomass from Its Components (Stems, Rachises, Leaves with/without Rachises) | ||||||||||||

Model 12 | ln(B_{Stem}) = a + bln(DBH) | −6.776 | 3.147 | 0.930 | 0.048 | −64,933 | <0.0001 | 1.0010 | 5.6 × 10^{−5} | 0.005 | 0.043 | 0.762 |

ln(B_{Leaf}) = a + b(DBH) | −7.188 | 3.014 | 0.679 | 0.115 | −45,605 | 0.002 | 1.0055 | 51.4 × 10^{−5} | 0.051 | 0.104 | 2.197 | |

Model 13 | ln(B_{Stem}) = a + bln(DBH^{2}H_{T}) | −2.831 | 0.848 | 0.921 | 0.051 | −63,594 | <0.0001 | 1.0010 | 6.4 × 10^{−5} | 0.006 | 0.046 | 0.810 |

ln(B_{FSR}) = a + bln(DBH^{2}H_{T}N_{F}) | −3.124 | 0.530 | 0.564 | 0.146 | −40,430 | 0.008 | 1.0088 | 115.1 × 10^{−5} | 0.115 | 0.132 | 3.257 | |

ln(B_{Rachis}) = a + bln(DBH^{2}H_{T}N_{F}) | −4.041 | 0.597 | 0.702 | 0.122 | −44,332 | 0.001 | 1.0062 | 74.9 × 10^{−5} | 0.074 | 0.111 | 2.724 | |

Model 14 | ln(B_{Stem}) = bln(DBH^{2}H_{T} ρ) | 0.645 | 0.999 | 0.037 | −71.844 | <0.0001 | 1.0006 | 11 × 10^{−5} | 0.011 | 0.034 | 0.610 | |

ln(B_{Leaf}) = bln(DBH^{2}H_{T}N_{F}) | 0.351 | 0.999 | 0.103 | −46.406 | <0.0001 | 1.0061 | 109.6 × 10^{−5} | 0.109 | 0.110 | 2.320 | ||

Model 15 | ln(B_{Stem}) = a + bln(DBH^{2}H_{T} ρ) | −0.295 | 0.678 | 0.958 | 0.037 | −70.429 | <0.0001 | 1.0006 | 3.4 × 10^{−5} | 0.003 | 0.033 | 0.594 |

ln(B_{Leaf}) = a + bln(DBH^{2}H_{T}N_{F}) | −2.852 | 0.561 | 0.747 | 0.103 | −48.205 | 0.001 | 1.0043 | 40.4 × 10^{−5} | 0.040 | 0.093 | 1.952 |

**Table 6.**Validation of the allometric relationships between the individual explanatory variables (ρ, H

_{TOT}, H

_{T}and N

_{F}) and the DBH (for estimates of a and b, see Table 4).

Model | r^{2} | AIC | p | ER | %ER | RMSE | %RMSE |
---|---|---|---|---|---|---|---|

Model 1: ln(ρ) = a + b × ln(DBH) | 0.787 | −60.077 | 0.008 | 0.034 | 3.407 | 0.014 | 4.845 |

Model 2: ln(N _{F}) = a + b × ln(DBH) | 0.750 | 13.371 | 0.012 | 0.075 | 7.552 | 3.098 | 9.638 |

Model 3: ln(H _{T}) = a + b × ln(DBH) | 0.660 | −3.111 | 0.026 | 0.0006 | 0.068 | 0.645 | 7.697 |

Model 4: ln(H _{TOT}) = a + b × ln(DBH) | 0.927 | −15.660 | 0.001 | 0.001 | 0.136 | 0.583 | 3.712 |

**Table 7.**Validation of the local allometric models of oil palm biomass; estimates for a and b are available in Table 5.

Model | r^{2} | AIC | P | ER | %ER | RMSE | %RMSE |
---|---|---|---|---|---|---|---|

Allometric Equations Using a Single Explanatory Variable, i.e., Infra-Density or DBH | |||||||

Model 6: ln(B) = a + bln(DBH) | 0.887 | 49.601 | 0.002 | 0.091 | 9.109 | 45.386 | 11.253 |

Model 5: ln(B) = a +bln(ρ) | 0.757 | 54.962 | 0.011 | 0.010 | 1.079 | 38.143 | 9.457 |

Allometric Equations Using Height as an Explanatory Variable | |||||||

Model 8: ln(B) = a +bln(H_{TOT}) | 0.730 | 55.712 | 0.014 | 0.012 | 1.242 | 41.954 | 10.402 |

Model 7: ln(B) = a + bln(H_{T}) | 0.810 | 53.234 | 0.006 | 0.042 | 4.157 | 38.854 | 9.633 |

Allometric Equations Using DBH and Height as Compound Explanatory Variables | |||||||

Model 9: ln(B) = a + bln(DBH^{2}H_{T}) | 0.939 | 45.305 | 0.0003 | 0.065 | 6.501 | 33.027 | 8.188 |

Allometric Equations Using DBH, Height, and ρ as Compound Explanatory Variables | |||||||

Model 10: ln(B) = bln(DBH^{2}H_{T} ρ) | 0.961 | 42.153 | 0.0001 | 0.048 | 4.815 | 26.786 | 6.641 |

Model 11: ln(B) = a + bln(DBH^{2}H_{T} ρ) | 0.961 | 42.206 | 0.0001 | 0.042 | 4.247 | 23.339 | 5.786 |

Allometric Equations Using Biomass Components (Stems, Rachises, Leaves with/without Rachis) | |||||||

Model 12: ln(B) = [ln(B_{Stem}) + ln(B_{Leaf})] = [a_{1}+b_{1}ln(DBH) + a_{2}+b_{2}ln(DBH)] | 0.887 | 49.605 | 0.002 | 0.089 | 8,916 | 44.856 | 11.121 |

Model 13: ln(B) = [ln(B_{Stem}) + ln(B_{FSR}) + ln(B_{Rachis})] = [a_{1}+b_{1}ln(DBH^{2}H_{T}) + a_{2}+b_{2}ln(DBH^{2}H_{T}N_{F}) + a_{3}+b_{3}ln(DBH^{2}H_{T}N_{F})] | 0.956 | 42.950 | 0.0001 | 0.052 | 5.268 | 27.325 | 6.774 |

Model 14: ln(B) = [ln(B_{Stem}) + ln(B_{Leaf})] = [b_{1}ln(DBH^{2}H_{T}ρ) + b_{2}ln(DBH^{2}H_{T}N_{F})] | 0.969 | 40.519 | < 0.0001 | 0.044 | 4.420 | 21.352 | 5.294 |

Model 15: [B_{Stem} + B_{Leaf}] = [a_{1} + b_{1}ln(DBH^{2}H_{T}ρ) + a_{2} + b_{2}ln(DBH^{2}H_{T}N_{F})] | 0.972 | 39.922 | < 0.0001 | 0.036 | 3.684 | 20.692 | 5.130 |

**Table 8.**Comparison of the existing allometric biomass models to the corresponding local models that were developed in this study.

Reference | Name | ER | %ER | RMSE | %RMSE |
---|---|---|---|---|---|

Allometric Equations Using Height as an Explanatory Variable | |||||

Khalid et al. [4] | Khal1999 | 1.725 | 172.583 | 669.968 | 166.109 |

Thenkabail et al. [20] (Dry biomass model) | Thenk2004b | −0.198 | −19.838 | 96.752 | 23.988 |

Thenkabail et al. [20] (Fresh biomass model) | Thenk2004a | −0.077 | −7.752 | 55.317 | 13.715 |

This study | Model 7 | 0.042 | 4.157 | 38.854 | 9.633 |

Allometric Equations Using DBH and Height as Compound Explanatory Variables | |||||

Saldarriaga et al. [18] | Sald1988 | −0.999 | −99.999 | 410.677 | 101.821 |

Hughes et al. [25] | Flyn1999 | −0.999 | −99.996 | 410.664 | 101.818 |

This study | Model 9 | 0.065 | 6.501 | 33.027 | 8.188 |

Allometric Equations Using DBH, Height and Infra-Density or Dry Mass Fraction as Composite Explanatory Variables | |||||

Goodman et al. [27] | Good2013 | −0.994 | −99.408 | 408.402 | 101.257 |

Da Silva et al. [22] (Not compartmentalized allometric biomass model) | DaSil2015a | 0.024 | 2.413 | 37.699 | 9.347 |

This study | Model 11 | 0.042 | 4.247 | 23.339 | 5.786 |

Allometric Equations Estimating Aboveground Biomass (B) from Biomass Components (Stems, Leaves or Rachis) Using DBH, H_{T} and ρ or N_{F} | |||||

Cole and Ewel [26] | ColEwe2006 | −0.211 | −21.122 | 92.841 | 23.018 |

Da Silva et al. [22] (Compartmentalized allometric biomass model) | DaSil2015b | 0.050 | 5.007 | 44.157 | 10.948 |

This study | Model 15 | 0.036 | 3.684 | 20.692 | 5.130 |

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## Share and Cite

**MDPI and ACS Style**

Migolet, P.; Goïta, K.; Ngomanda, A.; Mekui Biyogo, A.P.
Estimation of Aboveground Oil Palm Biomass in a Mature Plantation in the Congo Basin. *Forests* **2020**, *11*, 544.
https://doi.org/10.3390/f11050544

**AMA Style**

Migolet P, Goïta K, Ngomanda A, Mekui Biyogo AP.
Estimation of Aboveground Oil Palm Biomass in a Mature Plantation in the Congo Basin. *Forests*. 2020; 11(5):544.
https://doi.org/10.3390/f11050544

**Chicago/Turabian Style**

Migolet, Pierre, Kalifa Goïta, Alfred Ngomanda, and Andréana Paola Mekui Biyogo.
2020. "Estimation of Aboveground Oil Palm Biomass in a Mature Plantation in the Congo Basin" *Forests* 11, no. 5: 544.
https://doi.org/10.3390/f11050544