Accurate estimates of tree biomass are critical for forest managers to assess carbon stock. Biomass of Chinese fir (
Forest biomass comprises the arboreal fraction of all existing plant mass in the forest, including stems, branches, leaves, and roots of forest trees (
There are two methods for predicting total tree biomass with allometric equations: tree-level and component-level. The tree-level method involves a regression to predict total tree biomass. In the component-level method, prediction of total tree biomass is the sum of predictions of all tree components (leaves, branches, stem, and roots), obtained from separate regressions. There are strengths and weaknesses for each method. The tree-level biomass model predicts total tree biomass directly, but lacks detailed information on biomass of stems, branches, leaves, and roots. On the other hand, the component-level method provides more detailed information, but total tree biomass obtained by summing component predictions could often suffer from accumulation of errors and subsequently poor accuracy and precision. Moreover, in the component-level method, the sum of the biomass components can generate inconsistent results, as compared to predictions from the total biomass model (
Forecast combination, introduced by
The objective of this study was to evaluate current methods of predicting total and component biomass against the forecast combination method.
The plantations studied were at Weimin farm (Shaowu city, Fujian province) and Nianzhu farm (Fenyi city, Jiangxi province) in southern China (
Weimin farm consisted of stands of 7-, 16- and 28-year-old Chinese firs (
Tree diameter at breast height (
Standard allometric equations predict tree biomass as a power function of
where
The separate model method involves employing separate regression models to predict total tree biomass and its components: branch, leaf, root, and stem. Based on a preliminary analysis, we found that the
where all variables are as defined earlier, with added subscripts to denote component types.
The models were separate in the sense that prediction of total tree biomass from
The Additive model approach was based on the procedure developed by
where the symbol ^ on top of a variable name denotes the predicted value for that variable.
Eqn. 8 to 11 have the same forms as
Zhang et al. (
where {hat}
where (
where
The component predictions were then adjusted to add up to the combined estimator for total tree biomass. This was accomplished by multiplying the component predictions by
In this study, the two-fold leave-one-out cross validation scheme was used for model validation. First, the models were fitted using data from the Weimin farm, and then validated using data from the Nianzhu farm. Second, we treated Nianzhu data as the fit data and Weimin data the validation data. Evaluation statistics were computed based on observations pooled from the two validation data sets. The evaluation statistics of mean difference (MD), mean absolute difference (MAD), and R^{2} (
The stem biomass ranged from 14.67 to 86.67 kg, branches from 2.63 to 6.82 kg, leaves from 3.45 to 5.25 kg, and roots from 6.77 to 21.23 kg (
Parameters of the component regression models in the Additive model approach were subjected to the constraint that the sum of component predictions from the resulting models would be equal to the total biomass (
This approach involves a combined estimator, which is the weighted average of the predictions from the total biomass equation and the sum of predictions of component biomass from either (a) the separate model, or (b) the additive model.
Tree biomass additivity has long been recognized as a desirable property of biomass estimation. Several studies have successfully solved the logical inconsistency between the components and total tree predictions (
The FC1 method outperformed the Additive model method in predicting the total tree biomass, based on all three evaluation statistics. The FC1 method also produced better values of MD, MAD, and R^{2} for predicting branch, root, and stem biomass. For leaf biomass, the FC1 method resulted in better MAD, but worse MD and R^{2} values, as compared to the Additive model method (
In the Separate model method, the prediction of total tree biomass for each tree is directly derived from the total biomass regression equation. The FC1 method combined the information from this prediction and the sum of predictions from regression equations for each component biomass. The result is an improvement of two (MD and R^{2}) out of three fitting statistics for total tree biomass predictions obtained using the FC1 method, as compared with the Separate model method (
For the component biomass, predictions from the Separate model method were unadjusted predictions from the regression models. These predictions were then adjusted such that the resulting sum matched the combined estimator for total biomass in the FC1 method.
Based on all three evaluation statistics, the FC1 method showed better performances in predicting branch, root, and stem biomass as compared to the Separate model, whereas the latter method yielded more accurate predictions of leaf biomass. The opposite trend observed in leaf biomass predictions might be due to low R^{2} values of separate leaf biomass model (
The Forecast Combination method takes advantages of information from tree-level and component-level models, by providing an estimator that combines predictions from these models. To ensure additivity, component predictions from the Separate model were adjusted to match the combined estimator for total tree biomass. This approach was superior to the Additive model method in predicting total tree biomass and all of its components, except for leaf biomass.
The authors gratefully acknowledge the Fundamental Research Funds for the Central Non-profit Research Institution of CAF (CAFYBB2017ZX001-2), the National Natural Science Foundation of China (No. 31670634), and the Scientific and Technological Task in China (No. 2016YFD0600302-1).
Locations of the Chinese fir study sites in southern China.
Observed
Mean and standard deviation (SD) for tree variables and component biomass of Chinese fir by location and age. Values in parentheses are ranges.
Location | Age | n | Stats | D (cm) | H (m) | Stem (kg) | Branch (kg) | Leaf (kg) | Root (kg) |
---|---|---|---|---|---|---|---|---|---|
Weimin | 7 | 9 | Mean | 10.97 (5.7-16.3) | 7.28 (4.9-9.3) | 14.67 | 3.60 | 5.25 | 6.97 |
SD | 3.84 | 1.61 | 9.08 | 2.41 | 4.25 | 5.56 | |||
16 | 14 | Mean | 14.19 (5.6-22.5) | 11.48 (5.9-14.8) | 34.26 | 2.63 | 3.45 | 11.38 | |
SD | 5.28 | 2.70 | 22.57 | 2.50 | 3.18 | 8.90 | |||
28 | 16 | Mean | 16.86 (8.7-27.8) | 17.07 (10.3-22.7) | 71.11 | 5.72 | 4.22 | 18.41 | |
SD | 5.82 | 3.30 | 51.04 | 7.16 | 3.68 | 16.03 | |||
Nianzhu | 28 | 24 | Mean | 18.70 (7.5-30.2) | 16.89 (10.2-23.2) | 86.67 | 6.82 | 4.65 | 21.26 |
SD | 7.13 | 3.57 | 64.90 | 6.97 | 4.53 | 18.18 |
Parameter estimates and standard errors (SE) of the biomass model using Separate and Additive models in the Weimin and Nianzhu farms.
Parameter | Weimin | Nianzhu | ||
---|---|---|---|---|
Estimates | SE | Estimates | SE | |
8.2e-5 | 6.4e-5 | 8.84e-4 | 0.0013 | |
3.7571 | 0.2425 | 2.9377 | 0.4520 | |
0.0276 | 0.0215 | 0.0009 | 0.0013 | |
1.7984 | 0.2574 | 2.7953 | 0.4455 | |
0.0110 | 0.0047 | 0.0200 | 0.0103 | |
2.5401 | 0.1383 | 2.3165 | 0.2503 | |
0.0247 | 0.0053 | 0.0397 | 0.0131 | |
0.9141 | 0.0236 | 0.8647 | 0.0346 | |
0.0337 | 0.0066 | 0.0435 | 0.0156 | |
0.9211 | 0.0215 | 0.8897 | 0.0376 | |
0.0001 | 8.6e-5 | 0.0015 | 0.0021 | |
3.7089 | 0.2966 | 2.7895 | 0.4583 | |
0.0432 | 0.0396 | 0.0010 | 0.0015 | |
1.6763 | 0.3055 | 2.7802 | 0.4539 | |
0.0089 | 0.0041 | 0.0114 | 0.0058 | |
2.6206 | 0.1480 | 2.4950 | 0.2641 | |
0.0224 | 0.0049 | 0.0369 | 0.0121 | |
0.9254 | 0.0239 | 0.8726 | 0.0344 |
Evaluation statistics for total tree biomass prediction by method. (§): denotes the best method based on each fitting statistic (MD, MAD, R^{2}).
Method | MD | MAD | R^{2} |
---|---|---|---|
Separate model | 0.5761 | 8.0296^{(§)} | 0.9772 |
Additive model | -0.7199 | 8.6210 | 0.9726 |
Combined using Separate model | 0.1191^{(§)} | 8.0469 | 0.9780^{(§)} |
Combined using Additive model | 0.2020 | 8.0802 | 0.9776 |
Evaluation statistics for component biomass prediction by method. (§): denotes the best method based on each fitting statistic (MD, MAD, R^{2}).
Component | Method | MD | MAD | R^{2} |
---|---|---|---|---|
Branch | Separate model | -0.1511 | 1.9476 | 0.6601 |
Additive model | -0.487 | 2.0743 | 0.6371 | |
Combined using Separate model | -0.0853^{(§)} | 1.9307^{(§)} | 0.6786^{(§)} | |
Combined using Additive model | -0.3997 | 2.0213 | 0.6755 | |
Leaf | Separate model | 0.7034^{(§)} | 2.0181^{(§)} | 0.4952^{(§)} |
Additive model | 0.4883 | 2.0838 | 0.4424 | |
Combined using Separate model | 0.7343 | 2.0768 | 0.4332 | |
Combined using Additive model | 0.5259 | 2.1002 | 0.4311 | |
Root | Separate model | -0.2353 | 3.2619 | 0.8807 |
Additive model | -0.2625 | 3.3982 | 0.8686 | |
Combined using Separate model | -0.0046^{(§)} | 3.2564^{(§)} | 0.8905^{(§)} | |
Combined using Additive model | -0.0466 | 3.2853 | 0.8872 | |
Stem | Separate model | -0.298 | 4.7543 | 0.9832 |
Additive model | -0.4586 | 4.9985 | 0.9831 | |
Combined using Separate model | 0.1986 | 4.2931^{(§)} | 0.9865^{(§)} | |
Combined using Additive model | 0.1224^{(§)} | 4.5509 | 0.9851 |