4.1. A Post-Hoc Examination of the Prediction Accuracy of AGC Stock Estimation at Stand-Level
As mentioned previously, various combinations of the LiDAR-derived tree metrics displayed mixed performance in estimating forest stand above-ground carbon. Of the 20 tree-level AGC models presented in this study, the least accurate was model V7 at the level of MAE = 200.27 ton/ha, RMSE = 209.74 ton/ha, PRMSE = 64.29%, and RMSPE = 85.59%. Assuming these values as the base values for prediction accuracy achievable via LiDAR-based AGC models, model V4M (MAE = 14.0 ton/ha, RMSE = 14.7 ton/ha, PRMSE = 6.0%, and RMSPE = 4.5%) showed an improvement of 92.99%, 93.01%, 93.01%, and 92.96%, respectively.
Table 6 displays the accuracy improvement percentage (AIP)
post hoc test using Duncan’s new multiple range test [
41,
42]. Models with the same alphabetical code were statistically insignificant at a probability level of 0.05. Obviously, a model that appropriately integrated LiDAR-derived tree metrics could improve AGC prediction accuracy. For example, models V4M, V4, V5, V8, C2, and C4 had the ability to improve AIP by at least 85% when compared to the base-level model V7. Duncan’s test suggested that the improvement in accuracy achieved by those six models was superior to the others. Model V4M achieved the best improvement with an AIP of 93% (Duncan grouping = “A”) and models V5, C4, V4, V8, and C2 were grouped as “B” indicated their AIPs were statistically equal.
4.2. Detrimental Combinations of LiDAR-Derived Tree Parameters and Increased Uncertainty in the Estimation of Stand-Level AGC
Figure 4 shows the variations between estimates of stand-level AGC stocks made as a result of ground-based inventory observations compared with estimates made by the 20 tree-level models. The tree-level models used various combinations of LiDAR-derived tree metrics. All the tree-level models were validated at the tree-level using the same assessment data as the stand-level and changes in the prediction error could be attributed to uncertainty. In this study, the prediction uncertainty of a model was measured by the difference between the model adequacy (R
2) and the overall prediction performance (OPP) (
Table 5).
Among the seven biomass-based models, models C2 and C4 revealed consistent estimation results between the measures R2 and OPP while model C6 obviously not. Although the uncertainty in models C1, C3, C5, and C7 showed a moderate consistency, the difference between these four models was that C7 achieved a high degree of model adequacy and prediction performance while C1 and C3 obtained a medium level. This is because model C6 used only the metric LH while the other models integrated additional information from the other tree metrics. In contrast to model C5 which use only the predictor LDBH, an additional metric of LH, LCR, and LCI was gradually added to model C4, C3, C2, and C1 to describe the AGC variations of individual trees. Though these models were with high level of R2, however, a significant loss of OPP in models C1 and C3 was greater than model C5. This kind of estimation inconsistency was probably induced by a poor combination of the tree metrics in models C1 and C3.
Model C1 had a variation inflation factor (VIF) of 50.2 and 39.4 for LDBH and LH and 3.6 and 4.2 for LCI and LCR. Similarly, LDBH, LH, and LCR in model C3 also has VIFs of 14.8, 12.8, and 2.3. The situations in C1 and C3 indicated a certain problem of multicollinearity which might lead to an inaccurate estimate(s) of the regression coefficients. Since the regression coefficient of LCR in models C1 and C3 was negative, which is counter to the positive linear relationship between LCR and AGC, the estimation performance should be a result of the interaction of the LDBH, LH, and LCR caused by their significant near-linear correlation in the inappropriate models. In contrast, models C2 and C4 should be free of multicollinearity because the VIFs of the models’ predictors were moderately small and each of their regression coefficients showed an identical positive sign to the relationship of the metrics. In addition, model C7 excluded LDBH and used the metrics LH, LCI, and LCR to achieve 88% of overall prediction accuracy with a VIF of 1.0–1.2 for each predictor. Comparing the difference of estimation performance between model C6 and models C2, C4, and C7 (
Table 5), it could be concluded that LCI offered additionally critical information for estimating tree individuals’ AGC and therefore able to obtain appropriate accuracy for stand-level AGC estimation.
Among the volume-based group of models, a significant uncertainty of stand-level AGC estimation was found to the models V7 and V1M. Model V7 applied only a metric lnLH while model V1M applied Type-1 LDBH and LH in the form of Schumacher-Hall formula. These two models were able to account for the variation of tree individuals’ AGC stocks in the training dataset at a level of 84%, but offered an overall prediction performance of 25%–32% to the assessment dataset. The low performance of V7 was due to the shortage of volumetric information offered by using only one metric LH as the predictor. This situation was identical to model C6. Similarly, the low performance of V1M was contributed by the Type-1 LDBH because the secondary tree metric was a derivative of LH, that is LDBH1 = exp(1.479 + 0.864lnLH). The relationship of AGC and LH went overboard by models V1 and V1M. Models V2 and V2M copied some sort of the impacts caused by the over effects of LH and LCR, this is evident due to the Type-2 diameter metric was determined as LDBH2 = exp(1.473 + 0.835lnLH + 0.003LCR2). The overall estimation performance of the models V7, V1, V1M, V2, and V2M indicated that using only LH and LCR metrics in volume-based model was not able to achieve a reliable estimation of stand-level AGC stocks.
Apparently, when the metrics LCI and LCR were banded together with LH to create the volume-based tree-level model, model V5 achieved the most consistent results at an R
2 = 0.91 and a prediction accuracy of 91% (1-RMSPE ≈ 1-PRMSE). These two quantities revealed that the model V5 was almost capable of completely maintaining the same estimation performance in the validation dataset. As the LCR was replaced by its quadratic form, it did not detrimental to the performance of model V8 because the predictors’ coefficient in explaining the variations of tree-level AGC was appropriately tuned simultaneously. Similarly, the tree metrics of height, crown radius, and competition index can be effectively integrated in the Type-4 diameter metric to create model V4M. This type of Schumacher-Hall formula was exactly able to make an estimation performance almost identical to and even better than models V5 and V8 because model V4M got extra gain of prediction accuracy for OPP = 95% greater than R-squared = 91%. However, when crown radius was removed from the derivation of Type-3 diameter metric, a prediction uncertainty was introduced to the derived model V3M and caused a value of 4% performance reduction. This is evident in the line chart of error percentage as shown in
Figure 4. On average, the models’ accuracy improvement percentage (shown in
Table 5) of V4M was significantly greater than model V4 and model V3M by 7% and 12% respectively. Thus, by combining LH, LCI, and LCR in an appropriate method, a volume-based tree-level AGC model can be a reliable method to obtain acceptable accuracy at stand-level AGC prediction as well as the biomass-based AGC model.
Finally, the performance of the biomass-based and volume-based models shown in
Table 1 and
Table 2 varied widely. In fact, these two types of AGC models are very similar because they both apply the IPCC method of using factors, e.g., carbon fraction, wood density, and biomass expansion factor to derive above-ground carbon of trees, and use LiDAR-derived metrics with regression to get to different dependent variables, namely AGC and Volume. The key difference is that the factors are gained a priori in the biomass approach but a posterior in the volume approach. It appeared that given the factors involved and the errors with their estimation, the lower R
2 and/or estimation performance for some of the AGC models was due to uncertainty caused by multicollinearity for example C1
vs. C2, and due to unexplained variances introduced by using factors obtained from the literature, for example C7
vs. V5.
4.3. Why Use Biomass-Based or Volume-Based AGC Models in Predicting Forest Carbon Stock?
As discussed in previous sections, the value of each LiDAR-derived variable in predicting carbon stock was explored. Appropriate biomass-based and volume-based models are capable of making reliable AGC estimates. In brief, three tree-level AGC models were recommended to account for the forest carbon stocks based on their superior performance in both training and validation datasets:
- (1)
biomass-based model C2: AGC = 0.000068159 × LDBH1.4299 × LH1.1708 × LCI−0.0573,
- (2)
volume-based model V4M: AGC = [0.2919(a × LDBHb × LHc)1.0026], and
- (3)
volume-based model V5: AGC = [exp(−6.2803 + 2.3774lnLH − 0.0145LCI + 0.0316LCR)] × D × BEF × CF.
The LDBH in models C2 and V4M was determined using Equation (10). The forest ecosystem is known as the largest carbon sink in the terrestrial ecosystem but it could become the largest source of carbon emissions if deforestation and forest degradation occurs continuously. From the viewpoint of national/regional/global monitoring and assessment of forest ecosystem, to regularly gathering accurate forest carbon stocks in consistent and stable ways should be quite important for local forest management organizations and global forest resources evaluation agencies. As such, using biomass-based or volume-based AGC models for continuous forest inventory (CFI) over the terrestrial ecosystem is our major concern.
In practice, species-specific wood density, biomass expansion factor, and carbon fraction must be a priori determined in the biomass approach. This prerequisite of gathering those factors would not be a problem for plantations or small-scale forest stands. However, this approach might become a limitation for large-scale national inventory, especially in a forest ecosystem with complicated species compositions over a wide range of ecological amplitudes. In contrast, the volume approach would be more convenient for three reasons. Firstly, no such a priori factor determination is required before AGC modeling can be performed. Secondly, this technique can be implemented by directly linking the LiDAR metrics to tree volume and then posteriorly, above-ground carbon. Lastly, this method can achieve a reliable accuracy and offer an approach to assess national/regional/global forest carbon stocks in an IPCC-compatible method.
4.4. Recommendations for Future Work
As Bombelli
et al. [
22] suggested, regular
in situ calculation of biomass/carbon stock via detailed forest inventory should not be postponed longer than five years. This is due to rapid changes in forest resources in some countries. High density airborne LiDAR data may be too costly for many undeveloped and developing countries to consider feasible. Further work that can effectively integrate tree-level AGC models and more stand-level metrics such as canopy cover may provide a cost-effective solution. In order to derive meaningful harmonized stand-level metrics of forest stand for such a purpose, Tomppo
et al. [
43] suggested a sample plot of 0.5 hectares would be appropriate. As a result, a terrestrial LiDAR technique [
13,
43,
44,
45,
46,
47] would be appropriate for collecting accurate ground data that minimize measurement uncertainty for stand-level AGC modeling. Additionally, it may be possible to use low resolution airborne LiDAR data or high-resolution satellite SAR images such as POLSAR [
48] and TanDEM-X [
49] to obtain parameters of forest canopy as the predictors of stand-level AGC models. This could reduce the cost of determining AGC forest stocks in the national/regional/global terrestrial ecosystems significantly.
The tree-level AGC modeling technique was developed based on airborne LiDAR-based CHM data. In general, a natural forest is generally composed of multiple canopy layers. This is particularly a common composition for broad-leaved forest. As a result, the trees grow beneath overstorey canopy will not be seen from the top and therefore could not be detected using the CHM data. In such case, high density full waveform airborne LiDAR data may help to detect tree crowns along the vertical canopy profile and the derived features would be suitable for developing a modified tree-level AGC modeling technique.