1. Introduction
On the world’s land surface, forests cover about 4200 million hectares, and the carbon stock of forests accounts for about 45% of the world’s terrestrial carbon reserves [
1]. Aboveground biomass is an important component of forest ecosystems and accounts for a large proportion of forest carbon stock; thus, quantifying forest aboveground biomass is important for forest managers [
2].
Diameter at breast height (
DBH) and aboveground biomass (
AGB) are two important measurements of individual trees, widely used in yield estimations and forest growth [
3]. Tree
DBH is an easy measuring factor with high accuracy—all
DBH data are measured. However,
AGB is difficult to measure and has less accuracy than ground-observed
DBH—only limited tree biomass can be measured in the sample [
4]. Consequently, in the past few decades, many studies have proposed numerous equations to estimate aboveground biomass [
5,
6,
7,
8,
9,
10]. Developing an
AGB model according to ground-based
DBH has been widely applied in forest investigation and yield modeling. It is important to note that
DBH measurement in large-scale forest inventory is still time-consuming and costly.
LIDAR is a range detection system, which obtains the forest point cloud by LIDAR sensors. The LIDAR system has been used to measure the forest vegetation structure and has been applied to measure forest variables since the mid-1980s [
11]. These variables, including tree height, stem volume, crown projection area, diameter at breast height, and other variables, are significantly connected to the forest biomass [
3,
11,
12]. Using these LIDAR variables, individual tree
DBH and aboveground biomass can be estimated by developing
DBH and
AGB models, respectively [
3,
12,
13]. With some studies also using LIDAR data to predict timber volume and discern age class, LIDAR data have been widely used in forestry over the past two decades. The application of LIDAR technology has reduced the cost of forest management and provided a good opportunity for large-scale forest inventory [
11,
12].
The Bayesian method is used to integrate prior information about unknown parameters with the sample information; then, the posterior information is obtained according to the Bayes formula and the method of unknown parameters is further inferred according to the posterior information. Many studies have already used the Bayesian method to develop
DBH and
AGB models and have compared the Bayesian model with the classical model [
14,
15,
16,
17]. Zapata-Cuartas et al. [
14] presented a comparison of aboveground biomass estimation in different sample sizes using the Bayesian method and the classical method. They obtained a result that the bias in the classical method was always bigger than that in the Bayesian approach.
Although LIDAR technology and Bayesian methods are used separately in individual
DBH and
AGB modeling [
6,
13,
14,
15,
17,
18,
19,
20,
21], few studies have combined the two methods to estimate
DBH and aboveground biomass. Tenneson [
22] presented a combination of the Bayesian method and LIDAR to model LIDAR-derived forest inventory, combining the advantages of both
DBH and
AGB prediction; they used Bayesian model averaging (BMA), while we are using the hierarchical Bayesian method [
23,
24]. In this study, we used the hierarchical Bayesian method to choose the best
DBH and
AGB model to predict
DBH and aboveground biomass on the basis of LIDAR point cloud data, integrating the advantages of the Bayesian approach and LIDAR data to reduce costs compared with conventional measurements [
13,
14]. Further, compared with the classical prediction method, using the Bayesian method can improve the accuracy to a certain degree.
4. Discussion and Conclusions
In this study, an individual tree DBH and AGB model was selected from seven DBH models and five AGB models using the Bayesian method on the basis of airborne LIDAR data. When selecting a model, we ensured that all models were compared at the same level and that the random effects of the parameters were considered in the same position. The criteria of model selection were the value of DIC and the results of the parameter stationarity test. When selecting the AGB model, the independent variable DBH was the LIDAR estimated DBH, which ensured that the selected AGB model took the correlation between DBH and AGB into account.
LIDAR has the ability to measure the forest structure, and it is a useful tool for obtaining canopy information [
11]. This study used LIDAR to obtain the image data of our study area, then acquired individual tree information, including individual tree height and crown projection area, for model development. For aboveground biomass estimation, many studies have used LIDAR data. Næsset et al. [
12] used LIDAR data for estimating the timber volume of forest stands. They obtained the LIDAR canopy height and canopy cover density for timber volume estimation, and they found that LIDAR data produced equal results to aerial photointerpretation, though different sites had large differences when estimating timber volume. Holmgren et al. [
11] studied how to use LIDAR-derived data in regressive models for estimating the mean tree height and stem volume; the
R2 of mean tree height linear regression functions was between 0.89 and 0.91 and that for average stem volumes was between 0.82 and 0.9 when using the LIDAR mean tree height and LIDAR crown coverage area as variables. LIDAR is widely used in biomass prediction.
The study of forest biomass by the Bayesian method has been relatively less frequent than by the classical method. When the Bayesian method is compared to the classical method, an important difference is that the Bayesian method treats the parameters as random variables, while the classical method treats the parameters as fixed values; that is, the classical method treats the probability as the stable value of the frequency of a large number of repeated trials of events. Zapata-Cuartas et al. [
14] used the existing biomass equation reported in the literature as the prior distribution, assuming that the information can be useful to probability distributions, and validated the larger
R2 in the Bayesian method. This study used a different approach to the prior distribution—we used the parameters estimated by NLME for the prior distribution and obtained the same results.
We compared the classical method and the Bayesian method in estimating
DBH and
AGB; the results show that parameter estimation using the Bayesian method had higher stability than that using the classical method, and the
R2 of the Bayesian method was higher than that of the classical method. Zianis et al. [
17] also compared the two methods—they obtained a contrary result that the classical method was superior to the Bayesian method [
17], but they did not compare the two methods on different sample sizes. In order to show that the Bayesian method is more accurate in estimating
AGB for different sample sizes, we randomly sampled from the complete data set (
Table 6). The data showed that the Bayesian method was more efficient than the classical method for different sizes of samples, which is the same as the result for the full data set. Zapata-Cuartas et al. [
14] compared these two methods in the same way, and their results showed that for small sample sizes, the Bayesian method outperforms classical methods of least-square regression. Huang et al. [
37] used the same method and showed that when the sample size is less than 50, we should use the Bayesian method to estimate aboveground biomass. Yao et al. [
38] also presented a comparison of the Bayesian and classical methods—they found a more stable parameter value when using the Bayesian method. Thus, using the Bayesian method to estimate the aboveground biomass from small sample sizes is a good direction in biomass estimation. If classical methods are applied, especially with a small sample size, violation of statistical assumptions of error can lead to biased point estimates [
20,
39]. In addition, in this study, we have not taken into account the error propagation, thus a join model is perhaps a good method, and further studies are needed to solve the join model under the Bayesian framework for reducing the model uncertainties.
This study developed LIDAR
DBH and LIDAR
AGB models using the Bayesian method based on airborne LIDAR data. Previous studies have used the classical method to develop models and applied the classical method to airborne LIDAR data [
9,
10]. Fu et al. [
1] developed a system to predict individual tree diameter and aboveground biomass using the classical method and compared two other widely used model structures (the classical method to estimate
AGB depending on
DBH and the classical method to estimate
AGB not depending on
DBH). The current article compared the classical method to the hierarchical Bayesian method, and the results of this study showed that the Bayesian method has higher
R2 and smaller
MAD than the classical method for all sample sizes; thus, the Bayesian method was better than the classical method in estimating LIDAR
DBH and LIDAR
AGB for
Picea crassifolia Kom. in northwestern China.
Overall, this study combined the advantages of the Bayesian method and airborne LIDAR data; that is, airborne LIDAR data are easier to obtain than conventional aboveground measurements, and the Bayesian method was proven to have greater accuracy than the classical method. In addition, the present study also provides a reference for modeling with a small sample size.