Stem moisture content prediction model for Larix olgensis based on beta regression.

To investigate the longitudinal variation patterns of sapwood, heartwood, bark and stem moisture content along the trunk of artificial Larix olgensis, we constructed mixed effect models of moisture content based on beta regression by combining the effects of sampling plot and sample trees. We used two sampling schemes to calibrate the model, without limiting the relative height (Scheme Ⅰ) and with a limiting height of less than 2 m (Scheme II). The results showed that sapwood and stem moisture content increased gradually along the trunk, heartwood moisture content decreased slightly and then increased along the trunk, and bark moisture content increased along the trunk and then levelled off before increasing. Relative height, height to crown base, stand area at breast height per hectare, age, and stand dominant height were main factors driving moisture content of L. olgensis. Scheme Ⅰ showed the stable prediction accuracy when randomly sampling moisture content measurements from 2-3 discs to calibrate the model, with the mean absolute percentage error (MAPE) of up to 7.2% for stem moisture content (randomly selected 2 discs), and the MAPE of up to 7.4%, 10.5% and 10.5% for sapwood, heartwood and bark moisture content (randomly selected 3 discs), respectively. Scheme Ⅱ was appropriate when sampling moisture content measurements from discs of 1.3 and 2 m height and the MAPE of sapwood, heartwood, bark and stem moisture content reached 7.8%, 11.0%, 10.4% and 7.1%, respectively. The prediction accuracies of all mixed effect beta regression models were better than the base model. The two-level mixed effect beta regression models, considering both plot effect and tree effect, would be suitable for predicting moisture content of each part of L. olgensis well.

Height-diameter model of broad-leaved mixed forest based on species classification in Maoershan, Northeast China.

The complex stand structure and high species diversity of natural forests pose great challenges for analyzing stand growth and formulating reasonable plans for forest management. The height-diameter relationship is of great significance for predicting stand growth and formulating forest management measures. Based on survey data of 48 broad-leaved mixed forest plots in Maoershan, we classified 23 tree species into four groups based on species structure, growth characteristics and bionomics. We established a generalized model including stand, tree competition, species mixing and species diversity variables by reparameterization method, and a two-level mixed effect model of plot and tree species group. We tested the prediction ability of the model by leave-one-out cross-validation method. The results showed that the Ratkowsky (1990) model was the optimal basic model. The introduction of dominant height, basal area of trees larger than the object tree, basal area proportion of each species, and Shannon index could better explain the height-diameter relationship of broad-leaved mixed forest in Maoershan. The introduction of the mixed effect model of plot and tree species group could significantly improve the prediction accuracy of the model, with a Ra2 of 0.83. Under the same gradient of environmental factors, intolerant tree species exhibited higher tree heights than shade-tolerant tree species. In this study, we used the constructed tree height-diameter model to analyze the effects of species mixing and tree functional traits on tree height, which provided a theoretical basis for accurately predicting height of different tree species and analyzing the growth relationships in broadleaved mixed forests.

Model construction for height to crown base of Larix olgensis based on mixed-effects model and quantile regression.

Height to crown base is an important index reflecting the characteristics of tree crown. It is of great significance to accurately quantify height to crown base for forest management and increasing stand production. We used nonlinear regression to construct the height to crown base generalized basic model, and further extended that to the mixed-effects model and quantile regression model. The prediction ability of the models was evaluated and compared by the 'leave-one-out' cross-validate. Four sampling designs and different sampling sizes were used to calibrate the height to crown base model, and the best model calibration scheme was selected. The results showed that based on the height to crown base generalized model including tree height, diameter at breast height, basal area of the stand and average dominant height, the prediction accuracy of the expanded mixed-effects model and the combined three-quartile regression model were obviously improved. The mixed-effects model was slightly better than the combined three-quartile regression model, and the optimal sampling calibration scheme was to select five average trees. The mixed-effects model with five average trees was recommended to predict the height to crown base in practice.

[Construction and precision analysis of individual tree biomass model of Larix olgensis considering random effects]. / 考虑随机效应的长白落叶松立木生物量模型构建及精度分析.

Accurate estimation of forest biomass in China is crucial for the study of carbon cycle and mechanisms underlying carbon storage in global terrestrial ecosystems. Based on the biomass data of 376 individuals of Larix olgensis in Heilongjiang Province, we used seemingly unrelated regression (SUR) method to build a univariate biomass SUR model with diameter at breast height as the independent variable and considering the random effect at the sampling site level. Then, a seemingly unrelated mixed effect (SURM) model was constructed. As the calculation of random effects of SURM model did not require the empirically measured values of all dependent variables, we analyzed the deviations from the following four types in detail: 1) SURM1, the random effect was calculated according to the measured biomass of stem, branch and foliage; 2) SURM2, the random effect was calculated according to the measured value of tree height (H); 3) SURM3, the random effect was calculated according to the measured crown length (CL); 4) SURM4, the random effect was calculated according to the measured values of H and CL. The results showed that the fitting effect of branch and foliage biomass models was improved significantly after considering the horizontal random effect of the sampling plot, with R2 being increased by more than 20%. The fitting effect of stem and root biomass models were improved slightly, with R2 being increased by 4.8% and 1.7%, respectively. When using five randomly selected trees to calculate the horizontal random effect of the sampling plot, the prediction performance of SURM model was better than that of SUR model and SURM model considering only fixed effects, especially SURM1 model (MAPE% of stem, branch, foliage and root was 10.4%, 29.7%, 32.1% and 19.5%, respectively). Except for SURM1 model, the deviation of SURM4 in predicting stem, branch, foliage and root biomass was smaller than that of SURM2 and SURM3 models. In actual prediction, although the prediction accuracy of SURM1 model was the highest, it needed to measure aboveground biomass of several trees, and the use cost was relatively high. Therefore, the SURM4 modelled on measured H and CL was recommended to predict the standing tree biomass of L. olgensis.

[Constructing biomass models for natural Quercus mongolica based on Bayesian seemingly unrelated regression]. / åŸºäºŽè´å¶æ–¯ä¼¼ä¹Žä¸ç›¸å ³å›žå½’æ–¹æ³•çš„å¤©ç„¶è’™å¤æ Žç”Ÿç‰©é‡æ¨¡åž‹æž„å»º.

In this study, the biomass models for natural Quercus mongolica in Heilongjiang Province were constructed based on the predictors of diameter at breast height (D) and tree height (H) by several methods including multivariate likelihood analysis and seemingly unrelated regression. The results showed that the H could significantly improve the stem biomass model, with the coefficient of determination (R2) being increased from 0.953 to 0.988 and the root mean square error (RMSE) being reduced by 14 kg, but it had no significant improvement for the biomass model of branch, foliage, and root. The error structures of both biomass model systems (only D and D-H) were multiplicative, indicating that the linear models after logarithmic transformation were more appropriate. The R2 for the biomass models of stem, branch, foliage and root were 0.953-0.988, 0.982-0.983, 0.916-0.917, and 0.951-0.952, while the RMSE were 13.42-27.03, 6.84-7.00, 1.95-1.97 and 9.71-9.84 kg. Compared with the feasible generalized least squares (FGLS) approach, Bayesian estimation had similar fitting performance and provided parameter estimates with different variations. The standard errors of parameters for FGLS were 0.054-0.211. There were similar variations (standard deviations of 0.055-0.221) for the two Bayesian estimation with no prior information (DMC and Gibbs1). The Gibbs sampler with a multivariate normal distribution with a mean vector of 0, variances of 1000 and covariances of 0 (Gibbs2) or the prior information from the historical researches summary for Quercus trees biomass models (Gibbs3) produced greater variation than those of FGLS, DMC, and Gibbs1 (stan-dard deviations were 0.080-0.278), while Gibbs sampler with the prior information obtained from own data (Gibbs4) provided the lower variations than others (standard deviations were 0.004-0.013). The Gibbs4 approach provided the narrowest 95% prediction interval and produced the smaller prediction biases, with the average absolute error percentage (MAPE) for stem, branch, foliage, root and total of the only-D biomass model being 19.8%, 24.7%, 24.6%, 29.0% and 13.1%, while MAPE for the corresponding components of D-H biomass model kept same except for stem and total decreased to 10.5% and 9.8%, which indicated that Gibbs4 could provide more accurate biomass predictions. Compared with classical statistics, accurate prior information made Bayesian seemingly unrelated regression an advantage in estimation stability and uncertainty reduction.

[Analysis of carbon concentration and allometric growth model of carbon content for Larix olgensis]. / 长白落叶松含碳率分析及含碳量异速生长模型.

Forest carbon storage accounts for about 45% of terrestrial carbon storage. Accurate assessment of forest carbon storage is of great significance to the scientific management and planning of forests. Based on the data of 77 sampling Larix olgensis trees from Mengjiagang, Shangzhi Maoershan, Xiaojiu Forest Farm and Dongjing, Lin-kou Forestry Bureaus of Jiamusi, Heilongjiang Province from 2015 to 2018, we analyzed the partition of carbon content and variation of carbon concentration for five tree components (i.e., wood, bark, branch, leaf, and root). The mono-element and dual-element additive models of carbon content for each component of L. olgensis were deve-loped. The nonlinear seemly unrelated regression was used to estimate the parameters in the additive models, while the jackknife resampling technique was used to verify and evaluate the developed models. The results showed that the weighted mean carbon concentration of each component differed significantly, branches (49.3%) > bark (48.7%) > foliage (48.5%) > wood (48.2%) > root (47.1%). The aboveground and belowground carbon content accounted for about 80% and 20% of the total carbon content, respectively. The adjusted coefficient of determination (Ra2) of additive models of carbon content was greater than 0.89, the mean absolute error was less than 4.1 kg, and the mean absolute error percentage for most models was less than 30%. Adding tree height in the additive models of carbon content could significantly improve model fitting performance and predicting precision. The additive models of carbon content of total, aboveground, wood and bark were better than that of carbon content of branch, foliage, root and crown.

[Effects of mixing proportions on carbon storage and allocation in mixed plantation of Larix olgensis and Fraxinus mandshurica]. / æ··äº¤æ¯”ä¾‹å¯¹é•¿ç™½è½å¶æ¾å’Œæ°´æ›²æŸ³æ··äº¤æž—ç¢³å‚¨é‡åŠå ¶åˆ†é æ ¼å±€çš„å½±å“.

In this study, four types of mixed Larix olgensis and Fraxinus mandshurica plantations were selected according to the rows-mixing proportions (type Ⅰ: 5:3, type Ⅱ: 6:4, type Ⅲ: 5:5, type Ⅳ: 1:1). The see-mingly unrelated biomass models of L. olgensis and F. mandshurica were developed for obtaining biomass values, and the difference and composition of carbon storage in each forest layer and ecosystem were analyzed. The results showed that carbon storage of arbor layer in different stand types was 39.86-50.12 t·hm-2, the carbon storage of arbor layer inⅠ, Ⅱ and Ⅳ was significantly higher than that in type Ⅲ. The carbon storage of understory was 0.10-0.30 t·hm-2, with that in type Ⅱ being significantly higher than other types. Carbon storage of litter layer was 4.43-6.96 t·hm-2, with type Ⅱ and Ⅲ being significantly higher than those of the other types. In the soil layer, carbon storage was 34.97-54.66 t·hm-2. The carbon storage of soil layer in type Ⅱ was significantly greater than those in the other types. At the whole ecosystem level, carbon storage of type Ⅰ-Ⅳ was 90.43, 108.27, 85.83 and 89.92 t·hm-2, respectively. Type Ⅱ had significantly greater carbon storage than the other types. The arbor layer and soil layer were the major carbon pools in the ecosystem, which accounted for 43.3%-55.7% and 38.7%-50.5% of the total, respectively. Our results suggested that mixing by six rows of L. olgensis and four rows of F. mandshurica was better for future planting.

Biomass Functions and Carbon Content Variabilities of Natural and Planted Pinus koraiensis in Northeast China.

The population of natural Korean pine (Pinus koraiensis) in northeast China has sharply declined due to massive utilization for its high-quality timber, while this is vice versa for Korean pine plantations after various intensive afforestation schemes applied by China's central authority. Hence, more comprehensive models are needed to appropriately understand the allometric relationship variations between the two origins. In this study, we destructively sampled Pinus koraiensis from several natural and plantation sites in northeast China to investigate the origin's effect on biomass equations. Nonlinear seemingly unrelated regression with weighted functions was used to present the additivity property and homogenize the model residuals in our two newly developed origin-free (population average) and origin-based (dummy variable) biomass functions. Variations in biomass allocations, carbon content, and root-to-shoot ratio between the samples obtained from plantations and natural stands were also investigated. The results showed that (1) involving the origin's effect in dummy variable models brought significant improvement in model performances compared to the population average models; (2) incorporating tree total height (H) as an additional predictor to diameter at breast height (D) consistently increase the models' accuracy compared to using D only as of the sole predictors for both model systems; (3) stems accounted for the highest partitioning proportions and foliage had the highest carbon content among all biomass components; (4) the root-to-shoot ratio ranged from 0.18-0.35, with plantations (0.28 ± 0.04) had slightly higher average value (±SD) compared to natural forests (0.25 ± 0.03). Our origin-based models can deliver more accurate individual tree biomass estimations for Pinus koraiensis, particularly for the National Forest Inventory of China.

Characteristics and emergency mitigation of the 2018 Laochang landslide in Tianquan County, Sichuan Province, China.

This paper describes a recent landslide event, which occurred at Liucheng village in Tianquan County, Sichuan Province, China, on July 15, 2018. The Laochang landslide described in this research is an outstanding and valuable reference for understanding the characteristics of such kind of landslides that are geologically similar to the landslide. The deformation characteristics of the landslide are investigated based on field investigations, drilled boreholes, and exploratory trenches. The 225 residents of 64 households living on the flat platform were threatened by the landslide. Therefore, to guarantee the safety of human life and property becomes the primary emergency task. The anti-sliding piles were taken to stabilize the landslide and mitigate impacts caused by the landslide. Based on the analysis of the monitoring data, the effectiveness of anti-sliding piles is evaluated. The results indicate that the anti-sliding piles are effective in increasing the stability of the landslide, and this work can provide a reference for similar slope engineering projects.

[Prediction models of sapwood density, heartwood density, and bark density in Larix olgensis plantation]. / äººå·¥é•¿ç™½è½å¶æ¾æ ‘å¹²è¾¹æã€å¿ƒæå’Œæ ‘çš®å¯†åº¦é¢„æµ‹æ¨¡åž‹.

In this study, the Beta regression models of sapwood, heartwood, and bark density of Larix olgensis were constructed. A total of 35 trees were destructively sampled from plantations in three different sites, Linkou Forestry Bureau of Heilongjiang Province, Dongjingcheng Forestry Bureau, and Maoershan Experimental Forest Farm of Northeast Forestry University. AIC, R2, BIAS, RMSE and LRT were used as the goodness-of-fit statistics to compare and select the most optimal models for sapwood, heartwood, and bark density. The jackknife resampling technique was used to verify and evaluate the developed models. The results showed that the independent variables of the optimal sapwood, heartwood, and bark density model were not identical. Sapwood density had a good relationship with tree age, tree height, relative height, and the square of relative height. The independent variables of the optimal heartwood density model were annual growth, relative height, and the square of relative height. The independent variables of the optimal bark density model were tree age, annual growth, relative height, and the square of relative height. The analysis of the optimal model showed that from the base to the tip of the trunk, sapwood density decreased gradually, heartwood density initially decreased and then increased regularly, bark density initially increased and then decreased gradually. The established Beta regression models could predict sapwood, heartwood, and bark density of L. olgensis at any position in the research area and be an essential basis for the study of trunk average density and biomass.

[Ground diameter-height models of naturally regenerated seedlings and saplings under broad-leaved mixed forest in Maoershan Mountains.] / å¸½å„¿å±±é˜”å¶æ··äº¤æž—å¤©ç„¶æ›´æ–°å¹¼è‹—å¹¼æ ‘åœ°å¾„-æ ‘é«˜æ¨¡åž‹.

Based on the investigation data of seedlings and saplings from 48 plots in natural broad-leaved forest of Maoershan Experimental Forest Farm of Northeast Forestry University in Heilongjiang Province, the optimum model of ground diameter (D0) - height (H) was selected from eight alternative models as the basic model for the main regeneration tree species, and then the stand factors were parameterized, and the mixed effect model of sampling plot level was developed. The basic model and the mixed effect model were tested by independent samples. The results showed that there was a significant positive correlation between ground diameter and tree height of seedlings and saplings and that power function or model containing power function could better fit the relationship. The introduction of stand factors [dominant height of forest (HT), average diameter at breast height (Dg), basal area of forest (BA)] could improve the fitting effect of the model, with the residual root mean square error (RMSE) of each tree species decreasing by 1.3%-7.4% (average 3.8%), adjusted coefficient of determination (Ra2) only increasing by 0.1%-1.1% (average 0.6%) and Akaike info criterion (AIC) decreasing by 3.2%-35.2% (average 11.4%). Mixed effect models were developed for 10 tree species, such as Ulmus propinqua, Tilia and Fraxinus mandshurica. The Ra2 of mixed effect models was larger than that of the basic model, with an enhancement of 0.5%-3.5% (average 2.2%). RMSE and AIC decreased by 3.9%-20.3% (ave-rage 13.9%) and 4.0%-44.4% (average 22.3%) than that of the basic model. Model test results showed that, compared with the basic model, the average absolute error (MAE) of mixed effect model was reduced by 0.0001-0.46 m, with an average reduction of 0.08 m, and the average prediction error percentage (MPSE) decreased by 0.1%-6.2%, with an average reduction of 2.0%. The mixed effect model could improve the fitting effect and prediction ability of the model. The ground diameter-height model of seedlings and samplings of main regeneration species in broad-leaved mixed forest was developed in this study, which provides a reference for structure analysis and stand growth prediction of natural broad-leaved forest.

Evaluation of Four Methods for Predicting Carbon Stocks of Korean Pine Plantations in Heilongjiang Province, China.

A total of 89 trees of Korean pine (Pinus koraiensis) were destructively sampled from the plantations in Heilongjiang Province, P.R. China. The sample trees were measured and calculated for the biomass and carbon stocks of tree components (i.e., stem, branch, foliage and root). Both compatible biomass and carbon stock models were developed with the total biomass and total carbon stocks as the constraints, respectively. Four methods were used to evaluate the carbon stocks of tree components. The first method predicted carbon stocks directly by the compatible carbon stocks models (Method 1). The other three methods indirectly predicted the carbon stocks in two steps: (1) estimating the biomass by the compatible biomass models, and (2) multiplying the estimated biomass by three different carbon conversion factors (i.e., carbon conversion factor 0.5 (Method 2), average carbon concentration of the sample trees (Method 3), and average carbon concentration of each tree component (Method 4)). The prediction errors of estimating the carbon stocks were compared and tested for the differences between the four methods. The results showed that the compatible biomass and carbon models with tree diameter (D) as the sole independent variable performed well so that Method 1 was the best method for predicting the carbon stocks of tree components and total. There were significant differences among the four methods for the carbon stock of stem. Method 2 produced the largest error, especially for stem and total. Methods 3 and Method 4 were slightly worse than Method 1, but the differences were not statistically significant. In practice, the indirect method using the mean carbon concentration of individual trees was sufficient to obtain accurate carbon stocks estimation if carbon stocks models are not available.

[Branch growth of Korean pine plantation based on nonlinear mixed model].

Based on the branch analysis data from 36 sample trees in a Korean pine plantation in Mengjiagang Forest Farm of Heilongjiang Province, Northeast China, and by using Mitcherlich and Richards equations as the models of branch diameter and branch length growth, respectively, the effects of sampling plot and sample tree were investigated, and the nonlinear mixed models of branch diameter and branch length growth were established by the PROC NLMIXED procedure of SAS software. The evaluation statistics such as Akaike information criterion (AIC), Bayesian information criterion (BIC), -2Log likelihood, and likelihood ratio test (LRT) were used to compare the prediction precisions of the models. When considering plot effect, and taking alpha1 and alpha3 and beta1 and beta3 as the random parameters, respectively, the models of branch diameter and branch length growth had the best performance. When considering tree effect, and taking alpha2 and alpha3 and beta2 and beta3 as the random parameters, respectively, the models of branch diameter and branch length growth had the best performance. The nonlinear mixed model could not only reflect the mean variation of branch growth, but also show the differences among the individual trees. No matter considering plot effect or tree effect, the fitting precision of the nonlinear mixed model was better than that of the ordinary regression analysis model. Moreover, the fitting precision of the nonlinear mixed model was better when considering tree effect than considering plot effect.

[Linear mixed modeling of branch biomass for Korean pine plantation].

Based on the measurement of 3643 branch biomass samples of 60 Korean pine (Pinus koraiensis) trees from Mengjiagang Forest Farm, Heilongjiang Province, all subset regressions techniques were used to develop the branch biomass model (branch, foliage, and total biomass models). The optimal base model of branch biomass was developed as lnw = k1 + k2 lnL(b) + k3 lnD(b). Then, linear mixed models were developed based on PROC MIXED of SAS 9.3 software, and evaluated with AIC, BIC, Log Likelihood and Likelihood ratio tests. The results showed that the foliage and total biomass models with parameters k1, k2 and k3 as mixed effects showed the best performance. The branch biomass model with parameters k5 and k2 as mixed effects showed the best performance. Finally, we evaluated the optimal base model and the mixed model of branch biomass. Model validation confirmed that the mixed model was better than the optimal base model. The mixed model with random parameters could not only provide more accurate and precise prediction, but also showed the individual difference based on variance-covariance structure.

[Compatible biomass models for main tree species with measurement error in Heilongjiang Province of Northeast China].

Based on the biomass data of 516 sampling trees, and by using non-linear error-in-variable modeling approach, the compatible models for the total biomass and the biomass of six components including aboveground part, underground part, stem, crown, branch, and foliage of 15 major tree species (or groups) in Heilongjiang Province were established, and the best models for the total biomass and components biomass were selected. The compatible models based on total biomass were developed by adopting the method of joint control different level ratio function. The heteroscedasticity of the models for total biomass was eliminated with log transformation, and the weighted regression was applied to the models for each individual component. Among the compatible biomass models established for the 15 major species (or groups) , the model for total biomass had the highest prediction precision (90% or more), followed by the models for aboveground part and stem biomass, with a precision of 87.5% or more. The prediction precision of the biomass models for other components was relatively low, but it was still greater than 80% for most test tree species. The modeling efficiency (EF) values of the total, aboveground part, and stem biomass models for all the tree species (or groups) were over 0.9, and the EF values of the underground part, crown, branch, and foliage biomass models were over 0.8.