Sensitivity of Stand-Level Biomass to Climate for Three Conifer Plantations in Northeast China

: The accurate assessment of forest biomass is vital to climate change mitigation. Based on forest survey data, stand biomass models can effectively assess forest biomass carbon at large scales. However, traditional stand biomass models have ignored the potential effects of the climate on stand biomass estimation. There is still a lack of research on whether or not and in what ways the effects of the climate reduce uncertainty in biomass estimation and carbon accounting. Therefore, two types of stand biomass models, including basic stand biomass models (BBMs) and climate-sensitive stand biomass models (CBMs), were developed and tested using 311 plantation plots of Korean pine ( Pinus koraiensis Siebold & Zucc.), Korean larch ( Larix olgensisi A. Henry), and Mongolian pine ( Pinus sylvestris var. mongolica Litv.) in Northeast China. The two types of models were developed by applying simultaneous equations based on nonlinear, seemingly unrelated, regression (NSUR) to ensure additivity of the stand total and components biomass (root, stem, branch, and needle). The results of ﬁtting and leave-one-out cross-validation (LOOCV) indicated that the CBMs performed better than the corresponding BBMs. The RMSEs of the stand total biomass decreased by 3.5% to 10.6% for the three conifer species. The inﬂuence of temperature-related climate variables on the biomass of stand components was greater than that of precipitation-related climate variables. The sensitivity of the three conifer species to climate variables was ranked as Korean pine > Mongolian pine > Korean larch. This study emphasizes the importance of combining climate variables in stand biomass models to reduce the uncertainty and climate effects in forest biomass estimation, which will play a role in carbon accounting for forest ecosystems.


Introduction
Forests are suffering from rising temperatures, flooding, and increased drought [1][2][3].Climate change significantly affects the spatial distribution, species diversity, fire, and biomass of forests [4][5][6][7].Therefore, forest managers and policy-makers face new challenges, i.e., making forests mitigate or adapt to climate change, and reconsidering the balance between the benefits of wood production and forest social service [8].Regardless of how the process is implemented, accurate and defensible estimates of forest biomass and carbon stocks are always necessary [9].Large-scale or stand biomass assessment is a key component in quantifying carbon stocks and sequestration rates and in assessing the potential impacts of climate change [10].
Forest biomass is the total amount of living organic matter accumulated by the forest ecosystem in the course of long-term production [11].An accurate estimation of forest biomass is a prerequisite for forest carbon estimation, which is important for sustainable forest management and quantifying whether a forest is a carbon source or sink.A further understanding of forests' carbon stocks and fluxes will help to understand their response to changing climate conditions and the current state of the carbon cycle [12].As a result, international conventions have been jointly developed to promote the growth of carbon trading and mitigate climate warming.For example, the United Nations Framework Convention on Climate Change calls for countries to monitor forest ecosystems' carbon stocks annually.The prerequisite for forest carbon estimation is the ability to accurately estimate forest biomass.Forestry scholars and ecologists have paid close attention to individual tree biomass prediction in different regions of the world, such as South and North America [13][14][15][16], Europe [17], Asia [18][19][20], Africa [21], and Oceania [22].However, there is still a lack of research on stand biomass.
The traditional approach to implementing forest biomass estimation was to calculate the predicted values of individual tree biomass models, i.e., the scaling-up approach [23][24][25][26].The scaling-up approach requires that the information for each tree be included in the data set.However, the information may not always be available in the broader landscape [27].Large-scale forest inventories are generally aggregated into data tables that contain information on stand variables.Therefore, the traditional scaling-up approach limits the application of a stand biomass estimation.An advantageous option is to link forest biomass assessment directly to forest inventory data, providing a convenient and fast way to avoid complex error propagation procedures from the tree-level to the stand-level [28,29].Moreover, with the application of airborne and terrestrial laser scanning (ALS and TLS) in forestry, stand information has also become relatively easy to obtain [30][31][32].Consequently, stand biomass models have been developed to efficiently estimate forest biomass [33].
Global climate change has and will continue to affect forest ecosystem biomass.Exploring the influential mechanisms of climate factors on biomass is a critical issue which needs to be addressed [34].In recent years, the influence of climate on biomass has been demonstrated for various tree species and different geographical areas.Fu et al. [7] indicated that temperature-related and precipitation-related climatic variables have important effects on the aboveground biomass of trees.Bennett et al. [35] found that the mean temperature of the driest quarter was a strong predictor of forest biomass at broad spatial scales in Australia.Keith et al. [36] analyzed the combined effects of the annual mean temperature and the annual mean precipitation on the forest biomass of Eucalyptus regnans.Moreover, the mean annual temperature and the mean annual precipitation were often used in the assessment of forest biomass due to their strong association with biomass [37][38][39].To our knowledge, there has still been little exploration of how climate affects the stand total and the component's biomass.
Northeast China is suffering from unprecedented climate change [40], which will also have an impact on forest biomass.This study focused on three conifer plantation species, i.e., the Korean pine (Pinus koraiensis Siebold & Zucc.),Korean larch (Larix olgensisi A. Henry), and Mongolian pine (Pinus sylvestris var.mongolica Litv.), which were the main afforestation species in Northeast China.However, there are fewer studies on basic and climate sensitive stand biomass models [41], especially for the Korean pine and the Mongolian pine.The development of these stand biomass models provides an effective way to assess forest biomass and also supplies information on the response of stand biomass to climate change.Thus, the objectives of this study were to (1) establish basic and climate-sensitive stand biomass model systems for three conifer species; (2) evaluate the performance of climate-sensitive stand biomass model systems; and (3) assess the climate sensitivity of three coniferous species.

Study Site and Data Description
The study was conducted in Dongfeng County in the south of Jilin province, northeastern China (125 1).Dongfeng County is located in the Haddaling remnant of the Changbai Mountain branch, with a forest area of about 113,800 hectares.The main topographic feature of Dongfeng County is hilly terrain with altitudes ranging from 300 to 914 m.The climate type of Dongfeng County is a monsoonal zone with a moderate, temperate, humid climate.The average annual temperature is 4.5 • C, with a range of −37 • C to 35 • C. The average annual precipitation is 672.9 mm, with a range of 451.9 mm to 867.5 mm.Soil types are mainly dark brown soil, albic soil, meadow soil, and alluvial soil.

Study Site and Data Description
The study was conducted in Dongfeng County in the south of Jilin province, northeastern China (125°3′ E-125°5′ E, 42°18′ N-43°14′ N) (Figure 1).Dongfeng County is located in the Haddaling remnant of the Changbai Mountain branch, with a forest area of about 113,800 hectares.The main topographic feature of Dongfeng County is hilly terrain with altitudes ranging from 300 to 914 m.The climate type of Dongfeng County is a monsoonal zone with a moderate, temperate, humid climate.The average annual temperature is 4.5 °C, with a range of −37 °C to 35 °C.The average annual precipitation is 672.9 mm, with a range of 867.5 mm and 451.9 mm.Soil types are mainly dark brown soil, albic soil, meadow soil, and alluvial soil.From May to September 2021, we established 311 sample plots using stratified sampling in the main distribution areas of three conifer species, where site type was used as a categorical variable.It included 121 Korean pine plots, 90 Korean larch plots, and 100 Mongolian pine plots.Korean pine is a multi-purpose tree species with timber production and edible seeds.Therefore, combining seed and timber has become one of the primary management modes of Korean pine plantation forests.Korean larch, a cold temperate and temperate zone tree species, has cold resistance and wide adaptability.It plays a vital role in establishing fast-growing and high-yielding plantations in China because of its fast growth rate among coniferous species and its resistance to pests and diseases.The timber of the Korean larch can be used for utility poles, houses, flooring, and decoration [42].Mongolian pine is the most important tree species for water-limited regions of China due to the species' suitability for the afforestation and reforestation of semi-arid environments and sandy land areas [43].In recent decades, many Mongolian pine plantations have been developed in China's Three-North (northwest, north, and northeast) [44].It plays a major role in sand fixation, and soil and water conservation [45].From May to September 2021, we established 311 sample plots using stratified sampling in the main distribution areas of three conifer species, where site type was used as a categorical variable.It included 121 Korean pine plots, 90 Korean larch plots, and 100 Mongolian pine plots.Korean pine is a multi-purpose tree species with timber production and edible seeds.Therefore, combining seed and timber has become one of the primary management modes of Korean pine plantation forests.Korean larch, a cold temperate and temperate zone tree species, has cold resistance and wide adaptability.It plays a vital role in establishing fast-growing and high-yielding plantations in China because of its fast growth rate among coniferous species and its resistance to pests and diseases.The timber of the Korean larch can be used for utility poles, houses, flooring, and decoration [42].Mongolian pine is the most important tree species for water-limited regions of China due to the species' suitability for the afforestation and reforestation of semi-arid environments and sandy land areas [43].In recent decades, many Mongolian pine plantations have been developed in China's Three-North (northwest, north, and northeast) [44].It plays a major role in sand fixation, and soil and water conservation [45].
The sum of the individual volumes of one major tree species in each plot is 65% or more of the total volume, which meets the definition conditions of a pure plantation forest by Li [46].A few other tree species were found in the plot, including Ulmus pumila L., Betula platyphylla Sukaczev, Quercus mongolica Fisch.ex Ledeb., Fraxinus mandshurica Rupr., Picea asperata Mast., Tilia tuan Szyszyl., and Juglans mandshurica Maxim.The sample plots were distributed unevenly among the seven forest farms in Dongfeng County.The area with the most sample plots was 400-900 m 2 .The size of the sample plot depended on the stand density.In addition, 30 sample plots of 100-300 m 2 were set up due to the limitations of topography and tree species distribution conditions for the three tree species.
The tree and plot factors were measured and recorded during the sample plot survey.The tree factors are a diameter at breast height of 1.3 m (DBH, cm), total tree height, height to crown base, tree species, spatial tree location, and crown radii (east, south, west, north).The main sample plot factors are elevation, slope, geographic coordinate, canopy, and stand density.Trees with a DBH ≥5 cm, or a total tree height >1.3 m were recorded in the plots.A total of 13,140 trees were measured and recorded in all the sample plots.

Calculation of Variables and Biomass
Stand variables are important indicators of stand information, and are calculated from measured individual tree factors.The basal area (G, m 2 •ha −1 ) was calculated by the ∑ π 4 DBH 2 /A, where A is a plot area.The calculation of the stand dominant average height (Ha, m) varies depending on the plot area.If the plot area ranged from 400 to 900 m 2 , Ha was defined as the height of the 100 trees with the largest DBH per hectare.However, in small plots, using the above method cannot represent the Ha of the plots.For example, only one tree height can be selected as the dominant height in a 100 m 2 sample plot, which may lead to an overestimation of the Ha.Therefore, if the plot area was less than 400 m 2 , Ha was the height of the average of the three largest DBH trees.In this study, the stand age (Age, year) was the average age of the three coniferous species in the sample plot.The stand density (N, trees•ha −1 ) was calculated as the ratio of the total number of trees in the plot to the plot area.
The tree biomass was calculated using the species-specific biomass models published by forestry researchers [47,48], which contain total and component (root, stem, branch, and needle) biomass models for major tree species in Northeast China.Furthermore, the plot biomass was obtained by summing the biomass of individual trees in the plot.Stand biomass was the ratio of the plot biomass to the plot area.Statistical information on stand variables, the stand total biomass, and the component biomass are shown in Table 1.

Climate Data
In this study, the climate data were downloaded from (https://www.worldclim.org/, accessed on 29 October 2022), a database of high spatial resolution (1 km × 1 km) global weather and climate data.There were 19 average candidate climate variables, specifically 8 precipitation-related and 11 temperature-related variables.An additional climate variable was the annual heat moisture index (AHM = (AMT + 10)/(AP/1000)), where AMT ( • C), and AP (mm) are the annual mean temperature and annual precipitation [49].
In addition, five monthly average climate variables, including minimum temperature, maximum temperature, wind speed, solar radiation, and water vapor pressure, were downloaded and summarized as annual averages by Arcgis 10.4 software.The abbreviations and descriptions of climate variables are shown in Table 2.

Development of Stand Biomass Model
An allometric is a relationship between the growth rates of different or the same parts of an organism in different directions.The allometric growth equation has been widely used in the study of individual tree biomass models in recent decades [50].Some scholars have previously found that the equation can also be applied to the development of stand biomass models [27,51].In addition, stand variables are often involved in the development of stand biomass models, such as basal area, stand dominant height, and stand density [33,52].For this reason, the species-specific stand biomass models are based on the allometric growth equation and stand variables in the following model form: where B is component biomass; j is tree species (Korean pine, Korean larch, and Mongolian pine); β 0j -β pj are model parameters; X 1 -X p are candidate stand variables; ε j is the error terms.

Basic Model
The stand total and components biomass plotted against the basal area (G), stand dominant height (Ha), stand age (Age), and stand density (N) are shown in Figure 2. It can be seen that there was a stronger correlation between stand biomass and G than between other stand variables.Furthermore, Ha showed a significant non-linear trend with stand biomass.The modeling attempts based on different stand variables also indicated that G and Ha were better candidate stand variables than Age and N.As a result, G was the first candidate stand variable and Ha was the second candidate stand variable during the development of the stand biomass models.

Basic Model
The stand total and components biomass plotted against the basal area (G), stand dominant height (Ha), stand age (Age), and stand density (N) are shown in Figure 2. It can be seen that there was a stronger correlation between stand biomass and G than between other stand variables.Furthermore, Ha showed a significant non-linear trend with stand biomass.The modeling attempts based on different stand variables also indicated that G and Ha were better candidate stand variables than Age and N.As a result, G was the first candidate stand variable and Ha was the second candidate stand variable during the development of the stand biomass models.To satisfy the logical characteristics of additivity between stand components (roots, stems, branches, needles) and total biomass, the additivity method proposed by Parresol [16] was applied to stand biomass modeling in this study.The main structure of the method is simultaneous equations based on nonlinear, seemingly unrelated, regression To satisfy the logical characteristics of additivity between stand components (roots, stems, branches, needles) and total biomass, the additivity method proposed by Parresol [16] was applied to stand biomass modeling in this study.The main structure of the method is simultaneous equations based on nonlinear, seemingly unrelated, regression (NSUR) with cross-equation constraints and a cross-equation error correlation.In this study, basic stand biomass models (defined as BBMs) were developed for three conifer species based on the stand variables of G and Ha.The specific forms of each species are as follows: where B i is component biomass; B t is total biomass; SV is stand variables; ε i is the component model error term; ε t is the total model error term; and i is r, s, b, n, for roots, stems, branches, and needles.To explore the influence of climate variables on stand biomass prediction, we tried to introduce climate variables into the basic stand total and component biomass models (BBMs).A reparameterization approach was used in the development of the models.The approach generally has two steps; (1) building mixed-effects models with forest farm effects to determine the location of the random parameters; and (2) replacing the random parameters.The model attempts for the three species showed that 8 out of 25 climate variables had the greatest effect on biomass, including two temperature variables (AMT and TMIN), four precipitation variables (AP, PDQ, PWQ, and PDM), AHM, and ISO.The variability and information of the eight climate variables used in the region are shown in Figure 3. Subsequently, climate-sensitive stand biomass models (defined as CBMs) were developed for the three species in the following form: where CV is climate variables, the other symbols were defined as aforementioned.
( ) where Bi is component biomass; Bt is total biomass; SV is stand variables;   is the component model error term;   is the total model error term; and i is r, s, b, n, for roots, stems, branches, and needles.

Climate-Sensitive Stand Biomass Model
To explore the influence of climate variables on stand biomass prediction, we tried to introduce climate variables into the basic stand total and component biomass models (BBMs).A reparameterization approach was used in the development of the models.The approach generally has two steps; (1) building mixed-effects models with forest farm effects to determine the location of the random parameters; and (2) replacing the random parameters.The model attempts for the three species showed that 8 out of 25 climate variables had the greatest effect on biomass, including two temperature variables (AMT and TMIN), four precipitation variables (AP, PDQ, PWQ, and PDM), AHM, and ISO.The variability and information of the eight climate variables used in the region are shown in Figure 3. Subsequently, climate-sensitive stand biomass models (defined as CBMs) were developed for the three species in the following form: where CV is climate variables, the other symbols were defined as aforementioned.

Weight Function for Heteroskedasticity
The presence of heteroskedasticity would lead to an inexact standard error of the model parameter estimation [53,54].Therefore, this study applied the weight function to correct the heteroskedasticity of the residuals in each model.Several steps were required to obtain the weight function.First, NSUR was used to fit the stand total and component models, and the residuals with heteroskedasticity were obtained at this stage.The residual variance can be modeled by the power function and the explanatory variables, assuming as follows: where ε i is the residuals for the i model; i is the roots, stems, branches, needles, and total; σ 2 is the variance of residuals; β i1 -β in are parameters to be estimated; and x 1 -x n are explanatory variables.Second, the unweighted residuals with heteroskedasticity obtained in the first step were squared, then it and the explanatory variables were transformed by the natural logarithm.In addition, stepwise regression was also used in the following formula: where ε is the unweighted residuals; and the other symbols were defined as aforementioned.
Third, the parameters of the stepwise regression were retained.The weight function for the stand total and component biomass models.The models were fitted again using the NSUR in SAS/ETS MODEL Procedure [55], and weight functions were added to the procedure and specified as resid.B i = resid.B i / (x βi1 1 x βi2 2 • • • x βin n ) (where resid.B i is the residual of the i model) [56,57].

Model Evaluation
The goodness-of-fit of the basic and climate stand biomass models was evaluated by a determination coefficient (R 2 ) and a root mean square error (RMSE).This study used the leave-one-out cross-validation method (LOOCV) to validate the models.The specific implementation process of the method was as follows: one sample was taken from the entire data set at a time and the remaining samples were involved in the model fitting.The fitting parameters were obtained for the validation of one sample.Each sample was taken only once and the above steps were repeated N times (N is the number of samples).After the process, R 2 , RMSE, and the relative root mean square error (RRMSE) were calculated to evaluate the performance of the BBMs and CBMs.The mathematical expressions of the above three statistical indicators were as follows: where B i represents observed values, Bi represents predicted values, B is the average of the observed value, and n is the number of samples.

Model Development and Fitting
The full dataset of three conifer species was used for fitting stand total and component models.After model attempts, most BBMs were established using the basal area (G) and the stand dominant height (Ha).The component models using G alone were the branches of the Korean larch, and the roots and needles of the Mongolian pine.The BBMs were extended by adding one or more climate variables to the powers of G or Ha.The needle models of the Korean larch and the Mongolian pine did not introduce climate variables due to their insensitivity to climate variables or insignificant parameters.The model forms, parameter estimates, goodness-of-fit, and weight functions for three conifer species are shown in Tables 3 and 4. All parameter estimates differed significantly from zero at the p < 0.05 level.The standard error of parameters was between 0.001 and 0.582.The basic model parameters were positive, suggesting that increased stand variables G and Ha would increase stand biomass.The parameters of climate variables were positive or negative in climate-sensitive biomass models, indicating that the relationship between climate variables and stand biomass were positive or negative.Furthermore, there were also some differences in the climate variables introduced by species.Specifically, AP affected all species, while PDM affected the Korean pine and the Mongolian pine.Other climate variables affected only one of the three species.This study constructed weight functions with climate variables, G, and Ha.However, the correction of heteroskedasticity by climate variables was not significant in the stepwise regression process, and Ha was significant for the correction of heteroskedasticity in minority models.Therefore, the weight functions of most models use G alone.The BBMs and CBMs performed well and generally explained between 80% and 96% of the stand total and component biomass variability for the three conifer species (only two of all components had variability explained at less than 80%: branch for the Korean pine and needle for the Korean larch).The RMSE was generally highest for total and stem biomass and lowest for stand root, branch, and needle components.The goodness-of-fit of CBMs was better than BBMs.
The BBMs and CBMs were fitted by the simultaneous equations with NSUR in the model fitting, which considered the inherent correlation between the components.In addition, the constraint of a logical biological feature was that the total was equal to the sum of the components.Therefore, a constant 5 × 5 matrix was assumed with crosscorrelations among five equations.This study contained six constant matrices for BBMs and CBMs of Korean pine, Korean larch, and Mongolian pine.The residual correlation matrices between the stand total and components are shown in Figure 4.There were multiple close correlations between the total and the components or between the different components for the Korean pine.The correlations were closer between the total, the roots, and the stems and between the roots and the stems for the Korean larch.In comparison, the closer correlations of the Mongolian pine were shown in the total and the stems, branches, the stems and branches, the roots, and the needles.The correlations of the system of CBMs and BBMs were slightly different.Even if no climate variables were introduced in a component of the CBMs systems, the NSUR cross-equation constraints changed the correlations.The circle is smaller when the correlation coefficient is close to 0. The Bt, Ba, Br, Bs, Bb, and Bn represents stand total, belowground, stem, branch, needle biomass, respectively.

Model Evaluation
Based on the leave-one-out cross-validation (LOOCV) technique, the assessment results of three prediction statistics for BBMs and CBMs of three conifer species are listed in Table 5.The merit of this validation technique was that the systems of BBMs and CBMs could be tested and there was no loss of samples for the development models.In three conifer species, the statistical indicators of the Korean larch for the total, the roots, and the stems were significantly inferior to those of the corresponding models for the Korean pine and the Mongolian pine.While for the branch and needle biomass, the prediction accuracy of the Korean pine was lower than the other two species.The model performances improved after extending the basic stand biomass model by introducing climate variables (CBMs).The R 2 , RMSE, and RRMSE of the total and components of the Korean pine were significantly improved or decreased.For example, RMSE decreased 10.6% for the total, Figure 4.The residual correlation matrices of basic stand biomass models (BBMs) and climatesensitive stand biomass models (CBMs) for three species.The circle is larger when the correlation coefficient is near 1 and −1.The circle is smaller when the correlation coefficient is close to 0. The Bt, Ba, Br, Bs, Bb, and Bn represents stand total, belowground, stem, branch, needle biomass, respectively.

Model Evaluation
Based on the leave-one-out cross-validation (LOOCV) technique, the assessment results of three prediction statistics for BBMs and CBMs of three conifer species are listed in Table 5.The merit of this validation technique was that the systems of BBMs and CBMs could be tested and there was no loss of samples for the development models.In three conifer species, the statistical indicators of the Korean larch for the total, the roots, and the stems were significantly inferior to those of the corresponding models for the Korean pine and the Mongolian pine.While for the branch and needle biomass, the prediction accuracy of the Korean pine was lower than the other two species.The model performances improved after extending the basic stand biomass model by introducing climate variables (CBMs).The R 2 , RMSE, and RRMSE of the total and components of the Korean pine were significantly improved or decreased.For example, RMSE decreased 10.6% for the total, 11.4% for the root, 5.0% for the stem, 12.0% for the branch, and 11.4% for the needle.Moreover, the R 2 also increased for the total and the components ranging from 0.0032 to 0.0579.In contrast, the Korean larch and Mongolian pine were less sensitive to climatic variables.The CBMs performances improved for the Korean larch, RMSEs decreased by 2.7-3.5% for the total, the root, the stem, and the branch.The statistical indicator between the needle model of CBMs and that of BBMs.For CBMs of the Mongolian pine, the RMSE of the total, the stems, and the branches were decreased by 4%, 3.7%, and 5%, respectively.The statistical indicator of the root and needle model was slightly better than the corresponding models of BBMs.

Comparison of Prediction Accuracy between BBMs and CBMs
To compare the differences in the stand biomass estimates of the BBMs and CBMs and the predicted values of the stand total and the components biomass obtained by the LOOCV, this study tested the differences of three species in several age groups.The RMSE was selected to measure the difference (Figure 5).As one of the characteristics of Korean pine is that it is a slow-growing species, the age groups of its young, middle, and near-mature forests are 0-40 years, 41-60 years, and 61-80 years, respectively.The age groups of the Mongolian pine and the Korean larch are 0-20 years for the young forest, 21-30 years for the middle forest, 31-40 years for the near-mature forest, and 41-60 years for the mature forest [46].Moreover, Figure 6 shows the standardized residual against the stand total and components of BBMs and CBMs based on the data of three conifer species.Both BBMs and CBMs indicated smaller standard residuals for the roots and needles of the Mongolian pine.The standard residuals for the other components are mostly in the range of −2 to 2. For the Korean pine, the variance of the standard residuals of the components of CBMs is significantly smaller Figure 5 shows that the prediction accuracy of the stand total and component models of CBMs are better than BBMs for the Korean pine in all age groups, except for the nearmature of the root model.For the Korean larch, the trend of RMSE was similar for the total, the root, and the stem.Specifically, CBMs were inferior to BBMs in young forests and better than BBMs in mature forests; the performance of the two systems was similar in middle and near-mature forests.The branches of CBMs had higher RMSE only in young forests, while the needles of CBMs was inferior to BBMs in young and near-mature forests, which was better than BBM in middle and mature forests.For the Mongolian pine, the RMSE of the total and stems had similar trends in different age groups.CBMs were significantly better than BBMs in young and near-mature forests, and there was little difference in other age groups.The prediction of CBMs branch model was slightly inferior to BBMs in mature forests, and the branch model performed slightly better in other age groups.The RMSEs of the root of BBMs and CBMs were similar in the near-mature forest and slightly different in the other age groups.
Moreover, Figure 6 shows the standardized residual against the stand total and components of BBMs and CBMs based on the data of three conifer species.Both BBMs and CBMs indicated smaller standard residuals for the roots and needles of the Mongolian pine.The standard residuals for the other components are mostly in the range of −2 to 2. For the Korean pine, the variance of the standard residuals of the components of CBMs is significantly smaller than that of BBMs, and the median line of CBMs is closer to 0. The variance of the standard residuals of CBMs and BBMs for the other two tree species is similar.The median of CBMs of the Mongolian pine was slightly better than that of BBMs.For the Korean larch, they are similar.In short, Figure 6 indicates that the response of the climate to the stand biomass of tree species is different.Moreover, Figure 6 shows the standardized residual against the stand total and components of BBMs and CBMs based on the data of three conifer species.Both BBMs and CBMs indicated smaller standard residuals for the roots and needles of the Mongolian pine.The standard residuals for the other components are mostly in the range of −2 to 2. For the Korean pine, the variance of the standard residuals of the components of CBMs is significantly smaller than that of BBMs, and the median line of CBMs is closer to 0. The variance of the standard residuals of CBMs and BBMs for the other two tree species is similar.The median of CBMs of the Mongolian pine was slightly better than that of BBMs.For the Korean larch, they are similar.In short, Figure 6 indicates that the response of the climate to the stand biomass of tree species is different.

Simulation of Climate Effects on Stand Biomass
To further evaluate the effect of climate change on the stand biomass for three conifer species, the CBMs were used to simulate the response of the stand component biomass to climate variables (Figure 7).The positive and negative effects of climate variables on the stand components biomass were consistent with the positive and negative parameter estimates of CBMs.The stand component biomass increased with AP and PWQ, and decreased with AHM, AMT, ISO, TMIN, PDM, and PDQ.In terms of the slope of the smooth linear model, the slopes range from −4.2 to 1.5 for precipitation-related climatic variables (AP, PDM, PDQ, and PWQ) and from −11.7 to −2.3 for temperature-related climatic variables (AMT, ISO, and TMIN).Temperature-related climatic variables have a greater effect on component biomass than precipitation-related climatic variables.The combined climatic variables of temperature and precipitation (AHM) had a small effect on root biomass (slop is −0.2).Meanwhile the sensitivity of stand total biomass to two climatic gradients (minimum and maximum) were also tested, and the curves of predictive simulation were plotted (Figure 8).The total biomass increased when G and Ha increased, and decreased when climate variables increased.The rate and range of curves varied with three species.The magnitude of climate effect ranked the species Korean pine > Mongolian pine > Korean larch.
TMIN).Temperature-related climatic variables have a greater effect on component bioma than precipitation-related climatic variables.The combined climatic variables of temperatu and precipitation (AHM) had a small effect on root biomass (slop is −0.2).Meanwhile the se sitivity of stand total biomass to two climatic gradients (minimum and maximum) were al tested, and the curves of predictive simulation were plotted (Figure 8).The total biomass i creased when G and Ha increased, and decreased when climate variables increased.The ra and range of curves varied with three species.The magnitude of climate effect ranked t species Korean pine > Mongolian pine > Korean larch.

Discussion
Generally, a forest stand is a basic management unit that refers to a set of trees with common characteristics or combining some characteristics in a given space [58,59].It was also defined as a contiguous group of trees sufficiently uniform in age-class distribution, composition, and structure, whilst growing on a site of sufficiently uniform quality to be a distinguishable unit from a forestry standpoint [60,61].The assessment and management of forests require quantitative information on stands.Throughout this study, the information on stands and climate was directly used as model independent variables, which provided an effective set of model tools for stand-level biomass estimation and laid the foundation for forest carbon stock studies.

Determination of Stand Variables in the BBMs
For the development of BBMs, the basal area as an important independent variable has been confirmed by previous studies [51,52].The BBMs development in this study also used the basal area as the independent variable in all the stand component models.Furthermore, the use of stand dominant height as a second independent variable was necessary to improve the prediction precision of the total and component models due to its representation of site quality [33].Dong [28] strongly suggested that the effect of stand dominant height or stand average height on stand biomass should be considered and investigated in stand biomass models.However, the stand dominant height acquisition requires low cost and less time than the stand mean height in forest survey.Therefore, stand dominant height was used as the second variable in this study, significantly affecting most components of the three conifer species (Table 3).For forestry modeling, a simple model with a reliable prediction accuracy is more likely to be embraced by forest managers [54,62,63].Thus, the two component models (branch for Korean larch and needle for Mongolian pine) only selected the basal area for stand biomass estimation in this study (Table 3).

Discussion
Generally, a forest stand is a basic management unit that refers to a set of trees with common characteristics or combining some characteristics in a given space [58,59].It was also defined as a contiguous group of trees sufficiently uniform in age-class distribution, composition, and structure, whilst growing on a site of sufficiently uniform quality to be a distinguishable unit from a forestry standpoint [60,61].The assessment and management of forests require quantitative information on stands.Throughout this study, the information on stands and climate was directly used as model independent variables, which provided an effective set of model tools for stand-level biomass estimation and laid the foundation for forest carbon stock studies.

Determination of Stand Variables in the BBMs
For the development of BBMs, the basal area as an important independent variable has been confirmed by previous studies [51,52].The BBMs development in this study also used the basal area as the independent variable in all the stand component models.Furthermore, the use of stand dominant height as a second independent variable was necessary to improve the prediction precision of the total and component models due to its representation of site quality [33].Dong [28] strongly suggested that the effect of stand dominant height or stand average height on stand biomass should be considered and investigated in stand biomass models.However, the stand dominant height acquisition requires low cost and less time than the stand mean height in forest survey.Therefore, stand dominant height was used as the second variable in this study, significantly affecting most components of the three conifer species (Table 3).For forestry modeling, a simple model with a reliable prediction accuracy is more likely to be embraced by forest managers [54,62,63].Thus, the two component models (branch for Korean larch and needle for Mongolian pine) only selected the basal area for stand biomass estimation in this study (Table 3).

Performance of BBMs and CBMs
In this study, the BBMs and CBMs were developed for the stand biomass prediction of three conifer species.The BBMs performed well and an R 2 between 0.83 and 0.96 was produced for most of the stand total and component models for the three conifer species.
The CBMs were developed by introducing eight climatic variables (AMT, AHM, AP, ISO, PDM, PDQ, PWQ, and TMIN) into BBMs, and overall CBMs performed better than the BBMs for each species (Table 5).In addition, CBMs performed slightly better than BBMs in the standard residual plots (Figure 6).
In terms of RMSE comparison across age groups, the prediction precision of CBMs was better than BBMs on the whole (Figure 5).However, BBMs were better than CBMs in several specific age groups (e.g., the needle of the Korean larch and the stem of the Korean pine in near mature, and the Korean larch in the entire young group), which may be more tolerant to climate change or influenced by an inherent correlation of non-linear, seemingly unrelated, regression.Therefore, the BBMs can be used as an alternative for the stand biomass prediction of components in an even-aged forest.

Effect of Climate on Stand Biomass
Climate has complex influences on tree growth and thus biomass accumulation [64,65].This study found a significant effect of climate variables on stand biomass, which was mainly influenced by climate variables which were temperature-related, precipitationrelated, and drought-related for the three conifer species (Figures 7 and 8).Therefore, climate variables should be fully considered in the development of stand biomass models.
Temperature can affect forest biomass directly or indirectly through photosynthesis and ecological pathways.The temperature-related variables (AMT, TMIN and ISO) had a negative effect on the stand biomass of the Korean pine and the Korean larch.The negative effects of AMT and TMIN may be due to the discomfort of synthetic biomass in stands, because high temperatures will constrain the forest biomass due to transpiration and water availability reduction [38,66,67].Low temperatures suppress tree growth through bud damage, frost, reduced root activity, and loss of biomass [68,69].The ISO was a climatic variable because the magnitude of temperature change and its negative effect on the Korean larch biomass indicated that fluctuating temperature was important for stand biomass estimation, consistent with the negative effect of ISO on the aboveground biomass of three larch species in Gao et al. [70].In addition, this study also found a significant effect of ISO on belowground biomass.
Precipitation is an important environmental factor that can affect the moisture availability of forest ecosystems and thus affect tree growth, productivity, and biomass synthesis [71,72].The stand biomass of the three coniferous species was positively affected by AP, mainly the roots, branches, and needles.The increase in AP may facilitates the accumulation of biomass during the growing season.Stegen et al. [73] pointed out that the effect of AP on forest biomass is related to forest type, with moist and wet tropical forests not affected, while temperate forests were significantly affected.This is consistent with the temperate forests in this study being affected by AP.The increase of PWQ positively impacted the stand biomass of the Mongolian pine.The precipitation of the wettest period in northeast China occurs during the summer [74].This period is important for the growth of trees and sufficient precipitation should promote the increase of the stand biomass.Furthermore, Fu et al. [75] also found a positive effect of PWQ on the total tree biomass of the Masson pine.
The drought could limit tree growth and cause tree mortality in the stand [8,76].Our results also indicated that the stand biomass of three conifer species had significant negative correlations with PDM and PDQ, which was related to drought.Although there was a small amount of precipitation during drought periods, the effective precipitation was little due to the interception of tree canopies, understory plants, and litter [77].Drought caused a decrease in nutrient delivery and tree photosynthesis due to the water limitation of soil microorganisms and cellular processes, which ultimately led to a decrease in biomass and productivity [78,79].
The study also found that the variation in stand biomass could be explained by AHM, which was the combined climatic variables of temperature and precipitation.In reality, it indicated a co-effect of climate on tree growth and biomass accumulation.For example, the precipitation influenced the temperature in air and soil, and the temperature and evaporation influenced the effective water in the soil [80,81].
The simulated prediction curves for the two climate gradients showed different magnitudes for the three conifer species.The order of their climate sensitivity was: Korean pine > Mongolian pine > Korean larch (Figure 8).This indicated the difference in the impact of climate on tree species, and the difference was also reflected in the components (Figure 7), which aptly illustrated the complex influence of climate variables on stand biomass.

Comparison with Previous Studies
At present, few climate-sensitive stand biomass models have been reported and published for the three conifer plantation species in northeast China.He et al. [41] developed a climate-sensitive stand biomass model system for a larch plantation forest in northern and northeastern China, with RMSE of the total, the stems, the needles, and the roots reduced by 5%, 3%, 5%, and 8%, compared to the base model, and the branches were more tolerant to climate variables.However, the RMSE of the climate-sensitive stand biomass model developed for the Korean larch in this study was reduced by approximately 3% for the total, the stems, the roots, and the branches.The needle was more tolerant to climate variables.These differences may be explained by the fact that climate exhibits different sensitivities in different study areas.In addition, we also found that the climate-sensitive stand biomass model could reduce the uncertainty in stand biomass predictions for the Korean pine and the Mongolian pine.The response of the stand biomass of the Korean pine to climate variables was the strongest among the three conifer species.
Planted forests, one of the carbon pools of terrestrial ecosystems, continue to contribute social services in mitigating climate warming [82].Thus, the biomass assessment of stands in forest management was important and had a direct impact on the estimation of carbon stocks.This study found that stand biomass in coniferous plantation forests was sensitive to temperature-and precipitation-related variables.The response of each component to climatic variables was different.This provides a reference for the management of plantation forests.The modeling approach in this study could also be expected to apply to other tree species.However, this study focused on plantation forests, and climate-sensitive stand biomass models may not be suitable for biomass prediction in high tree diversity and vertically multiple forests.In addition, the effects of forest management practices such as fertilization and pruning were not considered during model development, which may lead to uncertainty in stand biomass estimation.We will explore these influences in the future.

Conclusions
In this study, a climate-sensitive stand biomass model was developed for three conifer species, namely the Korean pine, the Korean larch, and the Mongolian pine in northeast China.Eight climate variables were included in the base model to analyze the influence of climate change on stand biomass.The climate-sensitive stand biomass models performed better than their base models.The AMT, AHM, ISO, PDM, PDQ, and TMIN had negative effects and the AP and PWQ had positive effects on stand biomass.The influence of temperature-related climate variables (AMT, ISO, TMIN) on the biomass of stand components was greater than that of precipitation-related climate variables (PDM, PDQ, AP, PWQ).Furthermore, the stand biomass of the three conifer species was affected by different climatic variables, and the specific order of magnitude was as follows: Korean pine > Mongolian pine > Korean larch.This study illustrated that stand biomass estimates are significantly sensitive to climate, which will contribute to the decision-making of forest managers and understanding of forest sustainability in the context of climate change.

Figure 1 .
Figure 1.The map study area and the distribution of the spatial plots.

Figure 1 .
Figure 1.The map study area and the distribution of the spatial plots.

Figure 3 .
Figure 3.The information on climate variables in the study area.AMT, AHM, TMIN, ISO, AP, PDQ, PWQ, and PDM are annual mean temperature, annual heat moisture, minimum temperature, isothermality, annual precipitation, precipitation of driest quarter, precipitation of wettest quarter, and precipitation of driest month, respectively.

Figure 3 .
Figure 3.The information on climate variables in the study area.AMT, AHM, TMIN, ISO, AP, PDQ, PWQ, and PDM are annual mean temperature, annual heat moisture, minimum temperature, isothermality, annual precipitation, precipitation of driest quarter, precipitation of wettest quarter, and precipitation of driest month, respectively.

Figure 4 .
Figure 4.The residual correlation matrices of basic stand biomass models (BBMs) and climate-sensitive stand biomass models (CBMs) for three species.The circle is larger when the correlation coefficient is near 1 and −1.The circle is smaller when the correlation coefficient is close to 0. The Bt, Ba, Br, Bs, Bb, and Bn represents stand total, belowground, stem, branch, needle biomass, respectively.

Figure 5 .
Figure 5. Histograms of RMSE of stand total and component biomass for basic stand biomass model (BBMs) and climate-sensitive stand biomass model (CBMs) against three conifer species.

Figure 5 .
Figure 5. Histograms of RMSE of stand total and component biomass for basic stand biomass model (BBMs) and climate-sensitive stand biomass model (CBMs) against three conifer species.

Figure 5 .
Figure 5. Histograms of RMSE of stand total and component biomass for basic stand biomass model (BBMs) and climate-sensitive stand biomass model (CBMs) against three conifer species.

Figure 6 .
Figure 6.The box plot of standard residuals against the stand total and components of BBMs and CBMs for three conifer species.The boxes express the interquartile ranges.The upper and lower horizontal lines crossing the vertical bars represent the maximum and minimum standard residuals.

Figure 6 .
Figure 6.The box plot of standard residuals against the stand total and components of BBMs and CBMs for three conifer species.The boxes express the interquartile ranges.The upper and lower horizontal lines crossing the vertical bars represent the maximum and minimum standard residuals.

Figure 7 .
Figure 7. Plots of stand component biomass to climate variables for (A) Korean pine, (B) Kore larch, and (C) Mongolian pine.The red line in each plot is the estimate of the smooth function (line model) that simulate the effects of climate change on stand component biomass.

Figure 7 .
Figure 7. Plots of stand component biomass to climate variables for (A) Korean pine, (B) Korean larch, and (C) Mongolian pine.The red line in each plot is the estimate of the smooth function (linear model) that simulate the effects of climate change on stand component biomass.

Figure 8 .
Figure 8. Stand biomass prediction curves under two climate gradients by three conifer species.The curves of red and green represent the increasing climate by the gradient (minimum and maximum).

Figure 8 .
Figure 8. Stand biomass prediction curves under two climate gradients by three conifer species.The curves of red and green represent the increasing climate by the gradient (minimum and maximum).

Table 1 .
The statistical information of stand variables and biomass components.

Table 2 .
Abbreviations and descriptions of candidate climate variables.

Table 3 .
Parameters and goodness-of-fit statistics of the BBMs and weight functions for three conifer species.

Table 4 .
Parameters and goodness-of-fit statistics of the CBMs and weight functions for three conifer species.

Table 5 .
Validation of the basic stand biomass models (BBMs) and climate-sensitive biomass models (CBMs) for three conifer species.