Effects of Climate on Stand-Level Biomass for Larch Plantations in Heilongjiang Province, Northeast China

Abstract

Climate change affects forest resource availability, growing season length, and thus forest biomass accumulation. However, only a limited number of studies have been conducted on forest biomass management based on climate effects, particularly at the stand-level. Thus, an allometric biomass equation based on conventional and climate-based stand biomass models, was developed and compared for larch trees (Larix spp.). A total of 160 experimental plots of larch plantations have been collected in Heilongjiang Province, Northeast China. In this study, we developed four types of additive model systems for stand-level biomass: two types of the stand-level biomass basic models (M-1 and M-2) with stand variables (stand basal area (BA) and stand mean height (Hm)) as the predictors, and two types of the proposed stand-level biomass climate-based models (M-3 and M-4) with stand variables (BA and Hm) and climatic variables (mean annual temperature (MAT) and annual precipitation (AP)) as the predictors. Accordingly, this study evaluated the effects of climatic variables (MAT and AP) and stand variables (BA and Hm) on the model’s performance. Model fitting and validation results revealed that the climatic variables significantly improved the model performance of the fitted equation by increasing the coefficient of determination (R²) values and reducing the root mean square error (RMSE) values. A higher R² and a lower RMSE were consistently generated by M-2 and M-4, whereas M-1 and M-3 consistently generated a lower R² and a higher RMSE. We found that the proposed stand-level biomass climate-based model type 4 (M-4) performed better than the other models and slightly better than in previous studies of climate-sensitive models. This study provided an additional and beneficial method of analyzing climate effects on stand-level biomass estimation.

1. Introduction

Since the 1950s, global climate change has continuously affected human populations and various ecosystems on earth. While climate change is gradually impacting the world, natural disasters and extreme weather are also caused by it. The effects of these changes have been felt by wildlife and human life [1,2,3]. During the past few years, the global intergovernmental community has attempted to mitigate the effects of rising carbon emissions and limit the global temperature increase to 1.5 °C [2]. To address these environmental issues, established forest plantations through planted forests (i.e., afforestation and reforestation) have become an important tool for carbon sequestration and climate change mitigation [4,5,6,7,8]. In light of this, the United Nations Framework Convention on Climate Change (UNFCCC) has committed to reducing emissions from deforestation and forest degradation. Forest ecosystems are the major terrestrial carbon sinks, storing around 80% and 40% of terrestrial above-ground and below-ground carbon, respectively [9,10,11]. The majority of studies to date have paid more attention to estimating forest biomass rather than estimating carbon storage, due to the fact that forest carbon concentrations are estimated to be approximately constant for tree or stand components (around 50%) [12]. In addition, forest biomass estimation with high accuracy has become fundamental for sustainable forest management [12]; it also has been of interest to forest researchers throughout the world in recent decades, including American and European [13,14,15,16], Asian and Oceanian [17,18,19,20], and African [21,22,23].

A forest biomass modeling process can be conducted using a variety of procedures, and the decision to use one method over another depends on the availability of data. On a local scale, one of the most widely used approaches is that of scaling-up, which requires individual tree data sets, such as diameter at breast height (DBH), and height. It is possible to predict biomass at stand-level using the summation of individual trees’ predicted biomass model quantities. This allows forest managers and decision-makers to be more efficient in predicting biomass in terms of time and cost. Individual tree availability data, however, are rarely available on a large scale. As an alternative, it has been suggested that forest inventories be connected [24,25]. By easily measuring stand variables such as stand basal area, stand average height, and stand quadratic mean diameter at breast height, the study shows stand biomass benefits for forest biomass estimation [12,26]. According to Parresol [15], stand biomass per hectare was calculated by aggregating a number of trees. The model was then developed by predicting those variables within a stand. As an additional benefit, stand variables reduce the complexity of error propagation processes at various spatial scales [27]. Therefore, it is important to aim to predict the forest biomass at a stand-level by reducing the number of samples in forest measurement, in order to improve reliability and time-cost efficiency.

The fitting process of forest biomass parameter estimation can be estimated using linear regression or nonlinear regression, with nonlinear regression being highly effective in these estimations [28,29]. The flexibility and generality of nonlinear seemingly unrelated regression (NSUR) that was proposed by Parresol [16], make it a widely used method to estimate parameters in nonlinear stand biomass models [12]. Similar to tree biomass models, stand biomass models often encounter heteroscedasticity, and the weighting function has been used to address heteroscedasticity for each equation [12,30].

In recent years, due to the consequences of climate change, the development of biomass models has been characterized by the importance of incorporating climatic variables into the models [11,31,32]. Nonetheless, most studies on biomass modeling under climate effects focus only on individual trees in many countries and species. For example, in China, Fu et al. [33] developed an allometric equation for Masson pine (Pinus massoniana Lamb.), and Gao et al. [31] and Zeng et al. [34] developed an allometric equation for larch (Larix spp.); in South America, Laclau [13] studied biomass and carbon sequestration of ponderosa pine (Pinus ponderosa (Dougl.) Laws) and native cypress (Austrocedrus chilensis (Don) Flor. et Boutl.); in Germany, Krug [35] studied biomass and carbon dioxide sequestration of European beech (Fagus sylvatica L.); and in Europe, Forrester et al. [36] developed biomass and leaf area allometric equations for many European tree species, although only a few studies examined stand-level biomass. Moreover, it is critical to understand forest biomass’ role in carbon stocks and mitigating climate change. Unfortunately, a limited number of studies have examined the impact of climate change on stand biomass [37]. To this end, this study hypothesizes that incorporating climate variables into stand biomass models can reduce the uncertainty associated with forest biomass and carbon storage.

Larch (Larix spp.) is an important economically and ecologically valuable tree species in China, being a fast-growing coniferous tree species planted for many timber industries [34,38]. The larch tree is also highly resistant to cold conditions, making it one of the most fundamental components of the Northeast China forest ecosystem for establishing national reserve forests [38,39,40]. In China, larch plantations cover approximately 3.14 million hectares, making them the 4th most abundant tree species, which is critical in sequestering atmospheric carbon [38,41,42]. As the largest forest area in China, Heilongjiang province, with a forest coverage of 46%, has a fundamental role in China’s forest ecosystem [43]. Studies have demonstrated the importance of estimating biomass and carbon to mitigate climate change’s effects [6,44,45]. However, only a limited number of studies examine the effects of climate variables on stand-level biomass estimation [12,24,41,46,47]. Moreover, the response of larch species studies to the climate in Northeast China is still challenging [39,48,49]. Thus, this study examined the stand-level biomass model and its correlation with climate variables’ effects on larch plantations in Heilongjiang Province, Northeast China.

The objectives of this study were: (1) to develop four types of additive model systems for stand-level biomass—two basic models (M-1, M-2) and two proposed stand-level biomass climate-based models (M-3, M-4)—for larch plantations in Heilongjiang Province, Northeast China; (2) to evaluate the accuracy of model fitting and model performance on different additive methods (M-1, M-2, M-3, and M-4); and (3) to determine the effect of climatic variables on stand-level biomass estimations.

2. Materials and Methods

2.1. Study Area

This study selected larch plantation forest plots in different locations in Heilongjiang Province, Northeast China (44°04′–50°69′ N and 122°63′–132°78′ E). The province has a 454,000 km² total land area and has been designated as one of the national critical forest and grass resource distribution areas, with around 20.8 million hectares of forest (approximately 45.8% of the total land area of the province) [43,50]. The province’s elevation is approximately 36% higher than 300 m, formed by 4 major mountain ranges. This study area is located in the northern temperate continent, in a monsoon climate zone between temperate and frigid zones, and the annual average temperatures ranges from −5.0 °C to 5.0 °C, while the annual average precipitation ranges from 400 mm to 670 mm. In Heilongjiang, the forest soil type is predominantly dark brown soil. Heilongjiang province has several vegetation types, including cold temperate coniferous forests, temperate coniferous forests, and broad-leaf mixed forests [43,51,52].

The study areas were distributed north to south and west to east of Heilongjiang province. Larch trees are classified as members of the Pinaceae family and are part of the genus Larix. Typically, they are found in cold climates with plenty of moisture sites, a type of high-productivity coniferous timber production in China that is both ecologically and economically beneficial. High commercial value, better quality timber, and straight stem, are characteristics of the larch. China’s ninth National Forest Inventory reported that Larix gmelinii plantations are among the most popular larch species, and are a top ten tree species in terms of plantation area. There are 2.51 million ha of Larix gmelinii plantations in China, with a stock volume of 238 million m³ [53]. Larch is also the most important species group in the northeastern Chinese forest ecosystems, occupying approximately 25% of the forest area [39].

2.2. Data Collection

The authors identified and selected 160 experimental sampling plots of larch plantations that ranged in size from 0.09 to 0.1 ha (

Table 1. Stand and climatic variables summary of larch (Larix spp.) plantations.

Variables	Min.	Max.	Mean	SD
Bt (Mg·ha−1)	1.6596	230.1158	99.7864	62.7069
Br (Mg·ha−1)	0.2218	62.0667	23.4326	17.3993
Bs (Mg·ha−1)	0.8517	146.5333	65.2729	39.8265
Bb (Mg·ha−1)	0.2682	17.6024	8.3023	4.6180
Bn (Mg·ha−1)	0.3179	6.5581	2.7786	1.1537
BA (m2·ha−1)	0.5500	34.3008	18.8140	9.4055
Dg (cm)	6.1000	27.3000	14.5093	3.8287
Hm (m)	4.7000	21.2000	13.7085	3.4106
Age (year)	5.0000	55.0000	30.4188	10.0592
N (trees·ha−1)	80.0000	3140	1170.6480	571.0343
MAT (℃)	−1.1958	4.2875	2.0952	1.1898
AP (mm)	408.0000	629.0000	579.4375	38.0306

Abbreviations: B_t, B_r, B_s, B_b, and B_n represent stand component biomass of total, root, stem, branch, and needle (Mg·ha⁻¹), respectively. The BA, Dg, Hm, Age, and N represent the stand basal area (m²·ha⁻¹), stand quadratic mean diameter at breast height (cm), stand mean height (m), stand age (year), and stand density (trees·ha⁻¹), respectively. The terms MAT and AP represent annual temperature (°C) and annual precipitation (mm), respectively. The term Min. represents the minimum values, Max. represents the maximum values, and SD represents the standard deviation.

). We used a random sample of temporary plots in the site. The larch is the dominant tree species, and the volume of larch is ≥ 65% in each sample plot, representing a pure plantation forest by Li [49,54]. The slope of the plots ranged from 5 to 25°. The stand density was 333 to 1778 per hectare. Most plots were pure larch forest and others contained small amounts of other tree species. The biomass data was acquired from 2005 to 2019. All trees with diameters at breast height (DBH) greater than 5 cm were examined throughout the sample plot. The measurement information of individual tree variables included DBH (1.3 m above the ground), whole tree height, the first living branch height, and the position of each tree. The DBH measurement accuracy is 0.1 cm, and the other variables’ measurement accuracies are each 0.1 m. We also recorded the key stand variables of stand mean height (Hm, m) and stand age (Age, year). Other stand variables, such as stand basal area (BA, m²/ha), stand quadratic mean diameter at breast height (Dg, cm), and stand density (N, trees/ha), were also obtained. In this study, Age was the average age of the larch tree species in the sample plot, and Hm was the mean of tree height in the plot. The data regarding stand variables are shown in Table 1.

2.3. Stand Biomass Calculation

The biomass of trees was determined using species-specific biomass models, which were developed by forestry researchers [55,56] and rely on diameter at breast height. These models include total and component (root, stem, branch, and needle) biomass estimates for major tree species in Heilongjiang Province, Northeast China. Then, individual biomass components (tree root, stem, branch, and needle) and total biomass (the sum of root, stem, branch, and needle), were calculated. The procedure for obtaining plot biomass is to sum all the live biomass trees within each sample plot, and convert it into stand biomass per hectare (Equation (1)).

$${\mathrm{B}}_{\mathrm{i}}={\displaystyle \sum _{\mathrm{j}=1}^{\mathrm{n}}{\mathrm{b}}_{\mathrm{ij}}/\mathrm{A}}$$

(1)

where B_i (i = r, s, b, n, t) represents the stand root, stem, branch, needle, and total biomass (Mg·ha⁻¹); b_ij represents the biomass of the ith component of the jth tree in a sample plot (Mg); j = 1 … n represents the number of trees in each sample plot; and A represents the sample plot area (ha). The stand biomass summary statistics in this study are presented in Table 1.

2.4. Climate Data

Throughout this study, climate data were obtained from the WorldClim version 2.1 climate dataset (https://worldclim.org/, accessed on 27 September 2021); there are 19 bioclimatic variables that represent average values. The data include monthly climate data for minimum, mean, and maximum temperatures, precipitation, solar radiation, and wind speed, among other variables [32]. Following the preliminary data analysis, we selected mean annual temperature (MAT) and annual precipitation (AP) to represent annual trends in this study [57]. Moreover, the preliminary data analysis showed MAT and AP performing better in having robust relationships with stand biomass variables than did other climate variables (Figure 1). Therefore, in this study, only MAT and AP were used. The previous study in China also obtained climate data from WorldClim and used it as the study baseline data [33,41,58,59]. A statistical summary of the climatic variables in this study are presented in Table 1.

2.5. Stand Biomass Model Development

In this study, the general model system forms were developed using nonlinear seemingly unrelated regression (NSUR) proposed by Parresol [16]. NSUR is a widely used parameter estimating technique, since it may guarantee additivity by simultaneously fitting the system and considering the limitations of linear correlation between components. The flexibility and generality of NSUR allow the component models to use different independent variables and different weight functions for heteroscedasticity in the system, resulting in a low variance for the total biomass [46]. On another note, NSUR has become more flexible in adding subtotal biomass, and Parresol [16] recommends introducing one or more constraints to the concurrent systems, such as the crown or aboveground biomass. Due to its simplicity and efficiency, NSUR is used extensively in crown width models, individual tree models, and stand biomass models [8,12,49,60].

The preliminary visual has plotted the stand biomass components (i.e., root, stem, branch, and foliage) against the basal area (BA), stand mean height (Hm), mean annual temperature (MAT), and annual precipitation (AP) (Figure 1), which indicates that the relationship between the stand biomass components and the basal area is more robust than other variables. Several previous studies have also employed stand basal area to predict stand-level biomass, i.e., Castedo-Dorado et al. [27] and Bi et al. [24] demonstrated a correlation between stand biomass (component and total biomass) and the basal area (BA) [12,61]. Following the general model formed by Parresol [15] and the nonlinear model’s system of biomass additivity proposed by Parresol [16], the inventory variables were used to adjust these relations, and two forms of biomass additivity models (stand basal area and stand variable-based models with an additive error term) for larch plantations were examined on the following model form (Equations (2) and (3)).

$${\mathrm{B}}_{\mathrm{i}}{=\mathsf{\beta }}_0{\mathrm{BA}}^{{\mathsf{\beta }}_1}+\mathsf{\epsilon }$$

(2)

$${\mathrm{B}}_{\mathrm{i}}{=\mathsf{\beta }}_0{\mathrm{X}}_1{}^{{\mathsf{\beta }}_1}{\mathrm{X}}_2{}^{{\mathsf{\beta }}_2}\cdots {\mathrm{X}}_{\mathrm{n}}{}^{{\mathsf{\beta }}_{\mathrm{n}}}+\mathsf{\epsilon }$$

(3)

where B_i is the stand biomass (Mg·ha⁻¹); BA is the basal area (m²·ha⁻¹); X_n is the candidate stand variable, where BA and Hm represent the stand basal area (m²·ha⁻¹) and stand mean height (m), respectively; ${\mathsf{\beta }}_{\mathrm{i}}$ (i = 0, 1, …, n) denotes the parameters to be estimated; and $\mathsf{\epsilon }$ is the error term.

2.5.1. Basic Model

To ensure compatibility between the total biomass and the summation of each component biomass, we adopted an additive model system with five-term correlation among equations [24]. This study thus developed four types of additive model systems for stand-level biomass: two types of basic models and two types of climate-based models. The two types of basic models are: model type 1 (M-1), using simultaneous equations based on Equation (2), with the stand basal area as the only predictor (Equation (4)); and model type 2 (M-2), using simultaneous equations based on Equation (3), with the stand basal area and the stand mean height as predictors (Equation (5)).

Model type 1:

$$\{\begin{array}{l}{\mathrm{B}}_{\mathrm{r}}{=\mathrm{a}}_1{\mathrm{BA}}^{{\mathrm{b}}_1}+{\mathsf{\epsilon }}_{\mathrm{r}}\\ {\mathrm{B}}_{\mathrm{s}}{=\mathrm{a}}_2{\mathrm{BA}}^{{\mathrm{b}}_2}+{\mathsf{\epsilon }}_{\mathrm{s}}\\ {\mathrm{B}}_{\mathrm{b}}{=\mathrm{a}}_3{\mathrm{BA}}^{{\mathrm{b}}_3}+{\mathsf{\epsilon }}_{\mathrm{b}}\\ {\mathrm{B}}_{\mathrm{n}}{=\mathrm{a}}_4{\mathrm{BA}}^{{\mathrm{b}}_4}+{\mathsf{\epsilon }}_{\mathrm{n}}\\ {\mathrm{B}}_{\mathrm{t}}{=\mathrm{B}}_{\mathrm{r}}{+\mathrm{B}}_{\mathrm{s}}{+\mathrm{B}}_{\mathrm{b}}{+\mathrm{B}}_{\mathrm{n}}+{\mathsf{\epsilon }}_{\mathrm{t}}\end{array}$$

(4)

Model type 2:

$$\{\begin{array}{l}{\mathrm{B}}_{\mathrm{r}}{=\mathrm{a}}_1{\mathrm{BA}}^{{\mathrm{b}}_1}{\mathrm{Hm}}^{{\mathrm{c}}_1}+{\mathsf{\epsilon }}_{\mathrm{r}}\\ {\mathrm{B}}_{\mathrm{s}}{=\mathrm{a}}_2{\mathrm{BA}}^{{\mathrm{b}}_2}{\mathrm{Hm}}^{{\mathrm{c}}_2}+{\mathsf{\epsilon }}_{\mathrm{s}}\\ {\mathrm{B}}_{\mathrm{b}}{=\mathrm{a}}_3{\mathrm{BA}}^{{\mathrm{b}}_3}{\mathrm{Hm}}^{{\mathrm{c}}_3}+{\mathsf{\epsilon }}_{\mathrm{b}}\\ {\mathrm{B}}_{\mathrm{n}}{=\mathrm{a}}_4{\mathrm{BA}}^{{\mathrm{b}}_4}{\mathrm{Hm}}^{{\mathrm{c}}_4}+{\mathsf{\epsilon }}_{\mathrm{n}}\\ {\mathrm{B}}_{\mathrm{t}}{=\mathrm{B}}_{\mathrm{r}}{+\mathrm{B}}_{\mathrm{s}}{+\mathrm{B}}_{\mathrm{b}}{+\mathrm{B}}_{\mathrm{n}}+{\mathsf{\epsilon }}_{\mathrm{t}}\end{array}$$

(5)

where B_i (i = r, s, b, n, t) denotes the stand root, stem, branch, needle, and total biomass (t·ha⁻¹); $a_i$ $b_i$ $c_i$ $d_i$ (i = 1, 2, 3, 4) are the model parameters to be estimated in the fitting process, ${\mathsf{\epsilon }}_{\mathrm{i}}$ (i = r, s, b, n, t) denotes the stand root, stem, branch, needle, and total biomass error term; and BA and Hm are the stand basal area (m²·ha⁻¹) and stand mean height (m), respectively.

2.5.2. Stand-Level Biomass Climate-Based Model

Our study proposed the incorporation of climatic variables into a stand biomass model using the reparameterization method [62]. Based on the preliminary analysis of various stand biomass and climatic variables, it was determined that BA, Hm, MAT, and AP outperformed various statistical indicators. In order to model those two stand variables (BA and Hm) and those two climatic variables (MAT and AP), we selected them as candidate variables for the model. Further, we proposed a stand-level biomass climate-based model: model type 3 (M-3), using simultaneous equations based on Equation (4), with the stand variable (only stand basal area) and climatic variables as the predictors (Equation (6)); and model type 4 (M-4), using simultaneous equations based on Equation (5), with the multiple stand variables (stand basal area and stand mean height) and climatic variables as the predictors (Equation (7)).

Model type 3:

$$\{\begin{array}{l}{\mathrm{B}}_{\mathrm{r}}{=\mathrm{a}}_1{\mathrm{BA}}^{{(\mathrm{b}}_1{+\mathrm{c}}_1{\mathrm{MAT}+\mathrm{d}}_1\mathrm{AP}/1000)}+{\mathsf{\epsilon }}_{\mathrm{r}}\\ {\mathrm{B}}_{\mathrm{s}}{=\mathrm{a}}_2{\mathrm{BA}}^{{(\mathrm{b}}_2{+\mathrm{c}}_2\mathrm{AP}/1000)}+{\mathsf{\epsilon }}_{\mathrm{s}}\\ {\mathrm{B}}_{\mathrm{b}}{=\mathrm{a}}_3{\mathrm{BA}}^{{(\mathrm{b}}_3{+\mathrm{c}}_3{\mathrm{MAT}+\mathrm{d}}_3\mathrm{AP}/1000)}+{\mathsf{\epsilon }}_{\mathrm{b}}\\ {\mathrm{B}}_{\mathrm{n}}{=\mathrm{a}}_4{\mathrm{BA}}^{{(\mathrm{b}}_3{+\mathrm{c}}_3{\mathrm{MAT}+\mathrm{d}}_3\mathrm{AP}/1000)}+{\mathsf{\epsilon }}_{\mathrm{n}}\\ {\mathrm{B}}_{\mathrm{t}}{=\mathrm{B}}_{\mathrm{r}}{+\mathrm{B}}_{\mathrm{s}}{+\mathrm{B}}_{\mathrm{b}}{+\mathrm{B}}_{\mathrm{n}}+{\mathsf{\epsilon }}_{\mathrm{t}}\end{array}$$

(6)

Model type 4:

$$\{\begin{array}{l}{\mathrm{B}}_{\mathrm{r}}{=(\mathrm{a}}_1{+\mathrm{b}}_1{\mathrm{MAT})\mathrm{BA}}^{{(\mathrm{c}}_1{+\mathrm{d}}_1\mathrm{AP}/1000)}{\mathrm{Hm}}^{{\mathrm{f}}_1}+{\mathsf{\epsilon }}_{\mathrm{r}}\\ {\mathrm{B}}_{\mathrm{s}}{=\mathrm{a}}_2{\mathrm{BA}}^{{(\mathrm{b}}_2{+\mathrm{c}}_2\mathrm{AP}/1000)}{\mathrm{Hm}}^{{\mathrm{d}}_2}+{\mathsf{\epsilon }}_{\mathrm{s}}\\ {\mathrm{B}}_{\mathrm{b}}{=(\mathrm{a}}_3{+\mathrm{b}}_3{\mathrm{MAT})\mathrm{BA}}^{{(\mathrm{c}}_3{+\mathrm{d}}_3\mathrm{AP}/1000)}{\mathrm{Hm}}^{{\mathrm{f}}_3}+{\mathsf{\epsilon }}_{\mathrm{b}}\\ {\mathrm{B}}_{\mathrm{n}}{=(\mathrm{a}}_4{+\mathrm{b}}_4{\mathrm{MAT})\mathrm{BA}}^{{(\mathrm{c}}_4{+\mathrm{d}}_4\mathrm{AP}/1000)}{\mathrm{Hm}}^{{\mathrm{f}}_4}+{\mathsf{\epsilon }}_{\mathrm{n}}\\ {\mathrm{B}}_{\mathrm{t}}{=\mathrm{B}}_{\mathrm{r}}{+\mathrm{B}}_{\mathrm{s}}{+\mathrm{B}}_{\mathrm{b}}{+\mathrm{B}}_{\mathrm{n}}+{\mathsf{\epsilon }}_{\mathrm{t}}\end{array}$$

(7)

where B_i (i = r, s, b, n, t) denotes the stand root, stem, branch, needle, and total biomass (Mg·ha⁻¹); $a_i$ $b_i$ $c_i$ $d_i$ $f_i$ (i = 1, 2, 3, 4) are the model parameters to be estimated in the fitting process; ${\epsilon }_i$ (i = r, s, b, n, t) denotes the stand root, stem, branch, needle, and total biomass error term; BA and Hm are the stand basal area (m²·ha⁻¹) and stand mean height (m); and MAT and AP are the mean annual temperature (°C) and annual precipitation (mm), respectively.

2.6. Weighting Function to Overcome Heteroscedasticity

Forest modeling is often faced with heteroscedasticity [15,16,63,64], which is reflected by inconsistent residuals. A particular configuration is often found in the residuals of base model estimates during the stand biomass modeling process [12]. The increase or decrease in the residuals may simultaneously increase the predicted value, for instance. Therefore, in this study, we fixed the heteroscedasticity of the residuals in each stand-level biomass model and stand variable by applying the weighting function [65]. In the first step, the stand total and components models were fitted by nonlinear seemingly unrelated regression (NSUR) to obtain the residual variance with heteroscedasticity [16,66]. We modeled the residual variance using the power function and the explanatory variables [49]. Thus, we assume as follows:

$$\mathrm{E}({\mathsf{\epsilon }}_{\mathrm{i}}^2){=\mathsf{\sigma }}_{\mathrm{i}}^2{=\mathsf{\sigma }}^2({\mathrm{x}}_1^{{\mathsf{\beta }}_{\mathrm{i}1}}{\mathrm{x}}_2^{{\mathsf{\beta }}_{\mathrm{i}2}}\cdots {\mathrm{x}}_{\mathrm{n}}^{{\mathsf{\beta }}_{\mathrm{in}}})$$

(8)

where ${\mathsf{\epsilon }}_{\mathrm{i}}$ is the residuals for the i model; i is the root, stem, branch, needle, and total; ${\mathsf{\sigma }}^2$ is the variance of residuals; ${\mathsf{\beta }}_{\mathrm{i}1}$–${\mathsf{\beta }}_{\mathrm{in}}$ are parameters to be estimated; and x₁–x_n are explanatory variables.

In the second step, the unweighted residual variance with heteroscedasticity from the first step was squared while simultaneously transforming the explanatory variables by the natural logarithm (ln), and the stepwise regression was also used in the following formula:

$${\ln (\hat{\mathsf{\epsilon }}}^2{)=\ln (\mathsf{\sigma }}^2{)+\mathsf{\beta }}_{\mathrm{i}1}{(\mathrm{x}}_1{)+\mathsf{\beta }}_{\mathrm{i}2}{(\mathrm{x}}_2)+\cdots +{\mathsf{\beta }}_{\mathrm{in}}{(\mathrm{x}}_{\mathrm{n}})$$

(9)

where $\hat{\mathsf{\epsilon }}$ is the unweighted residuals; and the other symbols are as they have been previously defined in this paper.

In the third step, we estimated the Equation (9) using stepwise regression, and the weighting function for heteroscedasticity was for the ith equation. In the last step (the fourth step), fixing the weighting function, we were fitted again the equation system as in the second step, using an NSUR through SAS/ETS MODEL Procedure [67], and we added the weighting function to the procedure, thus specified as $\mathrm{resid}{.\mathrm{B}}_{\mathrm{i}}=\mathrm{resid}.{\mathrm{B}}_{\mathrm{i}}/\sqrt{({\mathrm{X}}_1^{{\hat{\mathsf{\beta }}}_{1\mathrm{i}}}{\mathrm{X}}_2^{{\hat{\mathsf{\beta }}}_{2\mathrm{i}}}\cdots {\mathrm{X}}_{\mathrm{n}}^{{\hat{\mathsf{\beta }}}_{\mathrm{ni}}})}$ (where ${\mathrm{resid}.\mathrm{B}}_{\mathrm{i}}$ is the residual of the i model) [30,68].

2.7. Statistical Analysis and Model Evaluation

We used the goodness-of-fit to measure the fitting of the basic and the proposed stand-level climate-based models by utilizing two commonly used statistical indices, the coefficient of determination (${\mathrm{R}}^2$) and the root mean square error (RMSE). In addition, the leave-one-out cross-validation method (LOOCV) was used to validate the model’s performance. The method process is as follows: First, we considered one sample from the entire data set at a time, and the other samples were elaborate in the model fitting. The validation of the one sample obtained the model parameters. Second, we repeated the first step only once each sample was taken, using all-but-one observation ($\mathrm{n}$ − 1, $\mathrm{n}$ is the number of samples) [69]. Third, after the second process, we calculated the coefficient of determination ($R^2$), the root mean square error (RMSE), the root mean square prediction error (RMSPE), the mean absolute error (MAE), the root mean square prediction error (MAPE), and the mean prediction error (MPE), to evaluate the performances of the basic and stand-level biomass climate-based models. The higher the values of $R^2$, the lesser the RMSE, RMSPE, MAE, MAPE, and MPE, indicate the accuracy of the model’s predictions. This study performed the data analyses using the SAS 9.4 version [67], and the graphical analyses using the R programming language [70]. These statistical analyses and model evaluations are as shown in Equations (10)–(15).

$${\mathrm{R}}^2=1-\frac{{\displaystyle \sum _{\mathrm{i}=1}^{\mathrm{n}}{({\mathrm{y}}_{\mathrm{i}} - {\hat{\mathrm{y}}}_{\mathrm{i}})}^2}}{{\displaystyle \sum _{\mathrm{i}=1}^{\mathrm{n}}{({\mathrm{y}}_{\mathrm{i}} - \overline{\mathrm{y}})}^2}}$$

(10)

$$\mathrm{RMSE}=\sqrt{\frac{{\displaystyle \sum _{\mathrm{i}=1}^{\mathrm{n}}{({\mathrm{y}}_{\mathrm{i}} - {\hat{\mathrm{y}}}_{\mathrm{i}})}^2}}{\mathrm{n}-1}}$$

(11)

$$\mathrm{RMSPE}=\sqrt{\frac{1}{\mathrm{n}}{\displaystyle \sum _{\mathrm{i}=1}^{\mathrm{n}}{(\frac{{\mathrm{y}}_{\mathrm{i}} - {\hat{\mathrm{y}}}_{\mathrm{i}}}{{\mathrm{y}}_{\mathrm{i}}})}^2}}$$

(12)

$$\mathrm{MAE}=\frac{{\displaystyle \sum _{\mathrm{i}=1}^{\mathrm{n}}{|(\mathrm{y}}_{\mathrm{i}} - {\hat{\mathrm{y}}}_{\mathrm{i}})|}}{\mathrm{n}}$$

(13)

$$\mathrm{MAPE}=\frac{1}{\mathrm{n}}{\displaystyle \sum _{\mathrm{i}=1}^{\mathrm{n}}\left|\frac{{\mathrm{y}}_{\mathrm{i}} - {\hat{\mathrm{y}}}_{\mathrm{i}}}{{\mathrm{y}}_{\mathrm{i}}}\right|}\times 100$$

(14)

$$\mathrm{MPE}=\frac{{\displaystyle \sum _{\mathrm{i}=1}^{\mathrm{n}}\left|{\mathrm{y}}_{\mathrm{i}} - {\hat{\mathrm{y}}}_{\mathrm{i}}\right|}}{{\displaystyle \sum _{\mathrm{i}=1}^{\mathrm{n}}{\hat{\mathrm{y}}}_{\mathrm{i}}}}\times 100$$

(15)

where ${\mathrm{y}}_{\mathrm{i}}$ is observed values, ${\widehat{\mathrm{y}}}_{\mathrm{i}}$ is estimated values, $\overline{\mathrm{y}}$ is the mean value of samples, and $n$ is the number of samples.

3. Results

3.1. Model Fitting

Parameter estimates were highly significant among the 4 types of additive model systems for stand-level biomass (M-1, M-2, M-3, and M-4) (

Table 2. Parameter estimates and standard errors (SE) of stand-level biomass models.

Model	Components	ai		bi		ci		di		fi
		Estimates	SE	Estimates	SE	Estimates	SE	Estimates	SE	Estimates	SE
M-1	Total	—	—	—	—
	Root	0.1567 **	0.0136	1.6671 **	0.0259
	Stem	1.0706 **	0.0540	1.3855 **	0.0155
	Branch	0.2874 **	0.0124	1.1467 **	0.0134
	Needle	0.3674 **	0.0133	0.7030 **	0.0116
M-2	Total	—	—	—	—	—	—
	Root	0.0795 **	0.0109	1.4521 **	0.0206	0.4964 **	0.0515
	Stem	0.5799 **	0.0289	1.1646 **	0.0110	0.4743 **	0.0222
	Branch	0.1813 **	0.0129	0.9754 **	0.0129	0.3596 **	0.0315
	Needle	0.2754 **	0.0241	0.6525 **	0.0157	0.1647 **	0.0394
M-3	Total	—	—	—	—	—	—	—	—
	Root	0.3487 **	0.0122	0.6795 **	0.0713	1.2711 **	0.1085	−0.0171 **	0.0018
	Stem	1.5837 **	0.0496	0.9862 **	0.0473	0.4471 **	0.0712
	Branch	0.4140 **	0.0126	0.6194 **	0.0532	−0.0059 **	0.0016	0.6936 **	0.0807
	Needle	0.3897 **	0.0134	0.3692 **	0.0472	0.5267 **	0.0696
M-4	Total	—	—	—	—	—	—	—	—	—	—
	Root	0.1801 **	0.0100	−0.0054 **	0.0007	0.5167 **	0.0497	1.2493 **	0.0777	0.4360 **	0.0270
	Stem	0.7178 **	0.0436	0.8753 **	0.0366	0.3854 **	0.0506	0.4649 **	0.0269
	Branch	0.2367 **	0.0174	−0.0042 **	0.0011	0.5230 **	0.0491	0.6501 **	0.0714	0.3501 **	0.0344
	Needle	0.2823 **	0.0153	−0.0049 **	0.0013	0.3153 **	0.0450	0.4960 **	0.0673	0.2172 **	0.0294

Notes: M-1 and M-2 for stand-level biomass basic model types 1 and 2, M-3 and M-4 for stand-level biomass climate-based model types 3 and 4, respectively. SE is the standard error, and a_i, b_i, c_i, d_i, and f_i are the model parameters. The asterisks (**) represent the coefficient estimates at the significance p < 0.001.

), p < 0.001; all parameters were statistically significant. Standard errors ranged from 0.0011 to 0.1085. Multicollinearity was tested using a variance inflation factor (VIF) during the modeling process, and the VIF for all models was found to be less than five. The entire dataset of larch was employed for fitting the stand total and its four component biomasses (root, stem, branch, and needle).

Furthermore, the model parameters (a_i, b_i, c_i, d_i, f_i) that determine the power of the base predictors (BA, Hm, MAT, and AP), varied from positive to negative according to the base predictor. There was a relationship between the model parameters of the predictors and the biomass components (Table 2). In the basic models (M-1 and M-2), which only employ BA and Hm as the base predictors, all power factors of BA and Hm were positive. Meanwhile, incorporating climatic variables (MAT and AP) caused several changes in the parameters of stand-level biomass climate-based models (M-3 and M-4), which showed positive and negative significant nonlinear relations between the climatic factors and the stand biomass. There were positive powers of BA in M-3, while positive powers of MAT were found in the stand root, stem, and needle biomass, but negative powers of MAT were found in the stand branch biomass. Based on these results, it was found that for the same BA, the stand root, stem, and needle biomass increased, but the stand needle biomass decreased with an increase in MAT. In addition, the powers of AP were negative in the stand root biomass, which indicates that the stand root biomass decreased as AP increased. The powers of BA, Hm, and AP in M-4 were all positive, and the powers of MAT were positive in the stand stem biomass but negative in the stand root, branch, and needle biomass. According to these results, stand stem biomass increased for the same BA, Hm, and AP, but the stand root, branch, and needle biomass decreased with increasing MAT.

The climate variables (MAT and AP) and stand variables (BA and Hm) were applied to weight function, a stepwise regression process was implemented to fulfill backward elimination and forward selection, and the results indicated that the climate variables were not significant and that the Hm was partially significant (

Table 3. The goodness-of-fit statistics and weight functions of the stand-level biomass models.

Model	Components	R2	RMSE	Weight Functions
M-1	Total	0.9636	11.9599	BA1.3139
	Root	0.9441	4.1141	BA1.0188
	Stem	0.9644	7.5111	BA1.3991
	Branch	0.9422	1.1102	BA1.5266
	Needle	0.9322	0.3004	BA0.5263
M-2	Total	0.9779	9.3159	BA1.7658Hm−0.8141
	Root	0.9503	3.8780	BA1.0090
	Stem	0.9844	4.9754	BA1.6903
	Branch	0.9542	0.9879	BA1.4848
	Needle	0.9349	0.2943	BA0.2356
M-3	Total	0.9743	10.0582	BA1.2663
	Root	0.9697	3.0309	BA2.0758
	Stem	0.9738	6.4489	BA1.6641
	Branch	0.9592	0.9330	BA1.5172
	Needle	0.9438	0.2735	BA0.9103
M-4	Total	0.9856	7.5167	BA1.6287
	Root	0.9763	2.6811	BA2.4416
	Stem	0.9874	4.4725	BA1.4808
	Branch	0.9689	0.8149	BA1.4973
	Needle	0.9479	0.2633	BA0.6226Hm1.8235

). Therefore, we used only the weight functions associated with BA. The R² for the stand-level biomass climate-based model (M-4) generally ranged from 0.9479 to 0.9874, the model with the basal area as the predictor and climatic variables as the predictor exponential function (M-3) ranged from 0.9438 to 0.9743, the model with the basal area and stand average height as the predictors (M-2) ranged from 0.9349 to 0.9844, and the model with the basal area as the only predictor (M-1) ranged between 0.9322 and 0.9644 (Table 3). In general, the goodness-of-fit analysis showed that the proposed model (M-4) performed better than the basic model (M-2), and the model using BA and Hm as predictors (M-2) performed better than the model using BA only as a predictor variable (M-1). Meanwhile, M-2 performed better than M-3 due to the Hm effects. A model with multiple variables (BA, Hm, and climatic variables) performed better than other models. However, climatic variables with BA but without Hm as variables, performed lower than climatic variables with both BA and Hm as variables. There was a consistently higher RMSE yielded by M-1 and M-3, while lower RMSE values were generated by M-2 and M-4, with M-1 yielding the highest RMSE and M-4 yielding the lowest RMSE. Additionally, the RMSE values were highest for the stand total, stem, and root biomass, and lowest for the stand branch and needle biomass.

The inclusion of MAT and AP enhanced the stand-level biomass climate-based models (M-3 and M-4), especially the stand root biomass. Overall, when M-1 and M-3 are compared using the total of all biomass components (root, stem, branch, and needle) in the stand, the R² increases from 0.97% to 2.71%, and the RMSE decreases from 8.95% to 26.32%. When M-2 and M-4 are compared using the total of all biomass components (root, stem, branch, and needle) in the stand, the R² increases from 0.30% to 2.73%, and the RMSE decreases from 10.10% to 30.86%. The model, which included climatic variables, showed significantly higher R² and significantly lower RMSE values than the model without climatic variables, indicating that the proposed stand-level climate-based model fit the biomass data better than the conventional basic models.

In this study, we also compared the influence of stand variables (BA and Hm) between the basic models (M-1 and M-2) and between the climate-sensitive climate-based models (M-3 and M-4). Model performance was improved by including BA and Hm as predictor variables (M-2), compared to using only BA as a predictor variable (M-1). Moreover, the inclusion of climatic variables (i.e., MAT, AP) and Hm into the model as the independent variables, highly improved the model performance compared to the other stand biomass models. In both the basic and proposed models, the results indicate that the stand stem biomass significantly improved with the addition of BA and Hm as predictor variables, and that Hm contributed to a significant improvement in model performance compared to BA alone as a predictor. To improve the stand biomass component model accuracy, Hm, BA, and climatic variables need to be included as independent variables.

3.2. Model Validation

Predictive performance was assessed by the leave-one-out cross-validation method (LOOCV), and the validation statistics (RMSE, RMSPE, MAE, MAPE, and MPE) were calculated (

Table 4. The validation result of the larch (Larix spp.) plantation’s stand-level biomass models.

Model	Components	RMSE	RMSPE	MAE	MAPE	MPE
M-1	Total	12.1564	0.1499	8.6032	11.2165	8.6216
	Root	4.1812	0.2305	2.8486	17.1401	12.1564
	Stem	7.5914	0.1428	5.5935	10.8353	8.5695
	Branch	1.1228	0.1422	0.8521	11.4392	10.2638
	Needle	0.3006	0.0929	0.1866	7.0029	6.7151
M-2	Total	9.4978	0.1032	6.7471	7.9600	6.7615
	Root	3.9706	0.1912	2.7974	14.8200	11.9382
	Stem	5.0620	0.0922	3.6382	6.8980	5.5738
	Branch	1.0029	0.1046	0.7004	8.3834	8.4356
	Needle	0.2981	0.0831	0.1761	6.2375	6.3369
M-3	Total	10.2127	0.1331	7.2904	9.7924	7.3060
	Root	3.0923	0.1702	2.2026	12.5073	9.3996
	Stem	6.5462	0.1344	4.6312	9.7138	7.0951
	Branch	0.9499	0.1211	0.7232	9.6681	8.7108
	Needle	0.2781	0.0841	0.1652	6.1731	5.9467
M-4	Total	7.6593	0.0958	5.5504	7.0569	5.5623
	Root	2.7315	0.1356	1.9177	10.0865	8.1837
	Stem	4.5711	0.0961	3.2952	6.7650	5.0483
	Branch	0.8335	0.0953	0.5991	7.4924	7.2163
	Needle	0.2690	0.0715	0.1498	5.1831	5.3904

Abbreviations: RMSE is the root mean square error (%), RMSPE is the root mean square prediction error (%), MAE is the mean absolute error (%), MAPE is the root mean square prediction error (%), and MPE is the mean prediction error (%).

). The validation results of the proposed models are generally better than the results of their basic models (M-4 > M-2, M-2 > M-3, and M-3 > M-1). Nevertheless, MPE varied differently from other model validations (M-4 > M-3, M-3 > M-2, and M-2 > M-1). These results suggest that both stand variables (BA, Hm) and climatic variables (MAT, AP) contribute to better model prediction precision, and that combining all four variables resulted in the best model prediction.

In general, MAPE is equivalent to MAE, but usually is used to overcome the limitations of MAE. As shown in Table 4, the MAPE values of the stand needle, stem, total, and branch biomass were lower than the stand root biomass values. Incorporating climatic variables (MAT and AP) into the models significantly reduced the MAPE values, which ranged from 10.35% to 27.02% for M-3 compared to M-1, and from 1.9% to 31.93% for M-4 compared to M-2. As one of the stand variables, Hm also played an important role in complementing the BA. By incorporating Hm into the model for M-2 compared to M-1, the MAPE has been reduced by 29%, 13.5%, 36.3%, 26.7%, and 11%, respectively, for the stand total, root, stem, branch, and needle biomasses. For M-4 compared to M-3, incorporating multiple climatic and stand variables (MAT, AP, BA, and Hm) significantly reduced the MAPE, by 28%, 19.3%, 30.3%, 22.5%, and 16%, respectively, for the stand total, root, stem, branch, and needle biomasses.

There was a significant improvement in the prediction accuracy of the stand-level biomass climate-based model (M-4) compared to other models. In addition, stem and total biomass were found to exhibit the highest accuracy compared to other biomass components. Their best fit demonstrated this to the regression line between actual and predicted values (Figure 2). Among the predictions, root biomass had the lowest accuracy. Hence, the stand-level biomass climate-based model M-4 stem biomass and total biomass estimates have the highest accuracy, and the basic model M-1 root biomass has the lowest estimation accuracy.

There were also notable differences in the performances of the proposed models (M-3 and M-4) and the basic models (M-1 and M-2) by RMSE across the various age groups (Figure 3). The groups were categorized as young forest (0–20 years), middle forest (21–30 years), near-mature forest (31–40 years), and mature forest (41–60 years) [53,71]. The four stand age groups (“Young”, “Middle”, “Near-mature”, and “Mature”) showed various results in each biomass component. The stand-level biomass climate-based model (M-4) performed the best at the needle biomass young age group (the lowest RMSE value ± 0.1%), meaning in the “Young” and “Middle” stand age groups, and consistently performed well. The M-4 RMSE values show the lowest RMSE values among all the models in almost all stand age groups; only in the needle biomass “Near-mature” and “Mature” stand age group was it found that the M-4 RMSE values were slightly larger than the M-3 RMSE values. In the stem biomass “Mature” stand age group, the M-4 RMSE values were a little bit higher than the M-2 RMSE values, while in the root biomass “Near-mature” stand age groups, the M-4 RMSE values were slightly larger than the M-3 RMSE values. In the total biomass, “Near-mature” and “Mature” stand age groups, the M-4 RMSE values were a little bit higher than the M-3 RMSE and M-2 RMSE values, respectively. Therefore, the proposed stand-level biomass climate-based model type 4 (M-4) performed better than other stand-level biomass models at different stand ages.

3.3. Comparison toward Previously Published Model

Furthermore, we compared our proposed stand-level biomass climate-based model with previously published models of climate-sensitive stand biomass, to obtain a more specific analysis. Based on our stand-level biomass climate-based model type 4 (M-4) for larch plantations in Heilongjiang province, we compared it with the climate-sensitive model type II (CSM-II) by He et al. [72] for larch plantations in northern and northeastern China. A scatterplot of the comparison can be seen in Figure 4. A three-model approach was used to fit our data.

According to a comparison (M-4) with larch plantations using the climate-sensitive equation (CSM-II), the stand biomass equation developed by He et al. [72] varied for both total and component biomass (Figure 4). As mentioned above, a total of three comparison models were examined, namely “He et al. (2021) model fitting”, “He et al. (2021)”, and “This study.” As a result, “This study” predicted values that performed well for the total biomass model as well as for all components and were able to give better predictions, outperforming the previously developed equation by He et al. (2021), in addition to which “This study” convincingly performed better on root, stem, branch, and needle. The climate-sensitive model type II by He et al. [72] overestimated the predicted value of branch, root, and needle biomass, and underestimated the value of stem and total biomass. Specifically, “He et al. (2021) model fitting” performed better than “He et al. (2021)”, suggesting that a good fitting process is necessary to achieving a better prediction of stand biomass.

4. Discussion

Among the prominent findings of forest biomass estimation is the importance of accurate field measurements [15], which are crucial in ensuring accurate forest management planning under complex climate change effects [32,73,74,75]. Stand-level biomass estimates became the foundation for forest management [14]. They had a unique characteristic: stand-level models are capable of estimating biomass for certain geographical areas and forest types, as well as estimating certain management techniques [76]. Nevertheless, few studies have examined the relationship between stand-level biomass estimation and climate variables. The primary objective of this study was to determine the influence of climate variables on the stand-level biomass estimation for larch plantations in Heilongjiang Province, Northeast China. These things considered, stand-level biomass provides significant advantages; aside from being derived from forest inventories, stand variables (stand density, stand basal area, stand volume, etc.) can be assessed without exposing the system to compound error propagation [24,27].

This study aimed to identify the gaps in information and knowledge regarding the effect of climate on stand-level biomass. A novel finding has been presented in this study that may assist in better understanding future forest management practices. The performance of the stand-level biomass models, climate effects on the stand-level biomass models, and comparison to previously developed larch species stand biomass equations, are discussed.

4.1. Performance of Basic Models and Stand-Level Biomass Climate-Based Models

This study incorporated climate data into stand-level biomass estimates for larch plantations in Heilongjiang Province, Northeast China. We obtained biomass data from forest inventory data, and climatic data from the WorldClim version 2.1 climate dataset. Four system models in two types of determination models have been figured out.

The two basic models: the model type 1 (M-1), using simultaneous equations based on Equation (2), with stand basal area as the only predictor (Equation (4)); and model type 2 (M-2), using simultaneous equations based on Equation (3), with stand basal area and stand mean height as the predictors (Equation (5)). Then, two proposed stand-level biomass climate-based models were deliberated: model type 3 (M-3), with stand basal area and climatic variables as the predictors (Equation (6)); and model type 4 (M-4), with multiple stand variables (stand basal area and stand mean height) and climatic variables as the predictors (Equation (7)).

Based on the scaling-up method, Castedo-Dorado et al. [27] noted that stand-level biomass could provide biomass estimations for local scales, while considering its efficiency at large scales is also relevant. As a result of the preliminary analyses, the basal area performed robustly and was identified as an important variable for estimating biomass at the stand-level [14,77]. Therefore, we used the basal area (BA) as the main predictor for this study’s model estimations.

Forest biomass estimation has become a critical component of global carbon balance policymaking. However, China’s management of its larch plantations, with regard to carbon sequestration and climate change mitigation, is still uncertain [38,42]. In that regard, it is important to acknowledge and take into account that the climate factors into forest biomass not only when calculating short-term simulations, but also when calculating long-term simulations. Case and Hall [78] reported that the local site biomass equations were more accurate than those applied to large areas, because the error increased when applied to different geographical scales. Thus, we focused on a specific site of larch plantations in Heilongjiang province in order to obtain a more precise assessment of the effects of climate on stand-level biomass estimation.

Since all parameter estimates for BA and Hm were positive, it was assumed that there was an increase in stand biomass as BA and Hm increased (Table 2). Following the inclusion of the climate variables, the parameter estimates were positive and negative, suggesting that a positive and a negative impact occurred on the stand biomass due to the climate effect. In addition to various statistical analyses conducted in the current study, it was also important to examine and clarify the simultaneous effects between the climatic variables and stand variables.

In this study, the goodness-of-fit showed that R² generally ranged from 0.9322 to 0.9874 (Table 3). The lower R² values found in the basic model (M-1 and M-2) ranged from 0.9322 to 0.9844, which gradually increased once the climate variables incorporated into the models as predictor variables (M-3 and M-4) ranged from 0.9438 to 0.9874. The model that included BA as the only stand variable and BA and Hm as the predictors, resulted in stable and positive parameter estimates, as evident from the results (Table 2). However, it does not reflect the response of biomass estimation under current climate change conditions, which is less reliable than recent studies conducted on climate change or forest management, in terms of changing environmental conditions [79,80]. Moreover, not only did the climatic variables contribute to improving the model performance, but also BA and Hm played a significant role in this improvement. As the RMSE decreased with a range from 3.72% to 30.64%, the biomass components of the stand-level biomass climate-based model as the multiple variable proposed model that includes BA, Hm, and climatic variables (M-4), performed better than the stand-level biomass climate-based model without Hm (M-3). In addition, when stem biomass is excluded, the RMSE decreases of M-4 compared to M-3 were more significant than those of M-2 compared to M-1. This suggests that, as a result of the model fitting, the goodness-of-fit shows that the multiple variable model (M-4) employing BA, Hm, and climate variables as the predictor variables, generally performed well compared to other models. The better performance trend of incorporating BA, Hm, and climate variables into modeling suggests more accurate estimations of stand biomass under climate change.

4.2. The Effects of Climate Variables on Stand-Level Biomass Models

Climate variables gradually improved the performance of biomass allometric models, especially the proposed stand-level biomass climate-based model (M-4). According to Wang et al. [81], the mean annual temperature of Northeast China has increased by approximately 0.35 °C per decade. This means the productivity of individual trees and stands of biomass may vary in response to increasing temperatures. In Heilongjiang province, the forest inventory data of remaining larch plantations are dominated by timber production [58], indicating that climate change could affect productivity, particularly on stem biomass productivity, as the highly precise M-4 stand stem biomass component remains accurate. This result is also related to previous studies, such as Guo et al. [79], revealing that biomass distribution within vegetation components changes due to temperature increases. Khan et al. [82] reported that stem biomass of Betula platyphylla and Larix gmelinii in Daxing’anling Mountain of Inner Mongolia was positively correlated with annual precipitation and annual maximum temperature. In addition, in this study, both needle and root biomass were also performed adequately to predict the stand biomass under the climate effects (R² > 0.99, p < 0.001), as supported by the previous study that needle biomass decreases and root biomass increases in the increasingly cold climates [83]. Despite this, Huang et al. [84] state that the aboveground biomass of boreal forests in Northeastern China is more sensitive to precipitation than temperature. The study of global forest carbon by Guo et al. [79] found that the carbon densities of boreal forests and temperate forests have similarities, and have lower biomass than subtropical and tropical forest. Although more studies have been conducted on biomass, there are still gaps in our understanding of the behavior of species-specific biomass components concerning climate change [36,85]. Hence, further study on the prediction of larch biomass, and other tree species biomass components, in terms of their rising and declining values in the past, present, and future climate change scenarios, is necessary.

4.3. Comparison with Previously Published Studies

The significant difference between this study and He et al. [72] may be influenced by the different regional scales and climate conditions. The sampling site for this study was located in Heilongjiang province, while the sampling site for He et al. [72] was spread across seven provinces in northeastern and northern China, including Heilongjiang. This recent study performed better and may be led by the model development more suitable for the regional conditions. As mentioned in previous studies, biomass modeling may vary with different forest stands and climates [86,87,88].

5. Conclusions

Two basic models (M-1 and M-2) and two proposed stand-level biomass climate-based models (M-3 and M-4) were developed using stand-level biomass data from larch plantation experimental plots in Heilongjiang Province, Northeast China. The proposed stand-level biomass climate-based model incorporating multiple variables, including MAT and AP as the climate variables and BA and Hm as the stand variables, (M-4), performed better than all of the other models. The combination of all these predictor variables allows for more precise estimations. This study also revealed that employing the stand basal area (BA) and stand mean height (Hm) as the main predictor for stand-level biomass estimation, was found to have stable performance. The M-4 was demonstrated to be a virtuous alternative and an additional method for modeling stand-level biomass under climate effects. The results of our study have implications for estimating biomass at the stand-level under climate effects and developing biomass allometric models. However, to implement these biomass models in other regions, intensive consideration must be given since climatological and environmental disparities in regions could result in different allometric relationships between predictors as well as biomass totals and components.