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.

[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.

[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.

[Additive aboveground biomass equations based on different predictors for natural Tilia Linn]. / åŸºäºŽä¸åŒé¢„æµ‹å˜é‡çš„å¤©ç„¶æ¤´æ ‘å¯åŠ æ€§åœ°ä¸Šç”Ÿç‰©é‡æ¨¡åž‹æž„å»º.

Biomass is a basic quantitative character of forest ecosystem. Biomass data are foundation of researching many forestry and ecology problems. Accurate quantification of tree biomass is critical and essential for calculating carbon storage, as well as for studying climate change, forest health, forest productivity, nutrient cycling, etc. Constructing biomass models is considered a good approach to estimate forest biomass. Based on biomass data of 97 sampling trees of natural Tilia Linn. in Xiaoxing'an Mountains and Zhangguangcai ranges, three additive systems of individual tree biomass equations were developed: based on tree diameter at breast height (D) only, based on tree diameter at breast height and height (H), and based on the best models. The nonlinear seemly unrelated regression was used to estimate the parameters in the additive system of biomass equations. The heteroscedasticity in model residuals was addressed by applying a unique weight function to each equation. The individual tree biomass model validation was accomplished by Jackknifing technique. The results showed that three additive systems of individual tree biomass equations could fit and predict the biomass of Tilia Linn. well (adjusted coefficient of determination Ra2>0.84, mean predicted error percentage MPE<8.5%, mean absolute error MAE<16.3 kg,mean standard error percentage MPSE<28.5%). The biomass equations of stem and aboveground were better than biomass equations of branch, foliage and crown. Adding total tree height and crown factor in the additive systems of biomass equations could significantly improve model fitting performance and predicting precision (Ra2 improved from 0.01 to 0.04, MAE decreased from 0.01 to 4.55 kg), narrow the confidence interval of the predicted value and the biomass of stem, foliage and aboveground were increased more than the biomass of branch and crown. In general, the equations of the additive system based on the best models produced the best model fitting, followed by that of the additive system based on D and H, and that based on D. It was essential to develop biomass model by adding total tree height and crown factor.

[Stand-level biomass estimation models for the tree layer of main forest types in East Daxing'an Mountains, China.] / å¤§å ´å®‰å²­ä¸œéƒ¨ä¸»è¦æž—åˆ†ç±»åž‹ä¹”æœ¨å±‚ç”Ÿç‰©é‡ä¼°ç®—æ¨¡åž‹.

Forest biomass estimation methods of regional scale attract most attention of the resear-chers, with developing stand-level biomass model being a research trend. Based on the biomass data from fix forest types, two additive systems of biomass equations based one- and two-variable were developed. The model error structure (additive vs. multiplicative) of the allometric equation was evaluated using the likelihood analysis. The nonlinear seemingly unrelated regression (NSUR) was used to estimate the parameters in the additive system of stand-level biomass equations. The results showed that the assumption of multiplicative error structure was strongly supported for the stand-level biomass equations of total and components for those forest types. Thus, the additive system of log-transformed biomass equations was developed. The adjusted coefficient of determination of the additive system of biomass equations was 0.78-0.99, the mean relative error was between -2.3%-6.9%, and the mean absolute relative error was between 6.3%-43.3%. Adding mean tree height in the additive systems of biomass equations could significantly improve the model fitting performance and predicting precision for most of the models. The biomass equations of total, aboveground and stem were better than biomass equations of root, branch, foliage and crown. In order to estimate model parameters more effectively, the additivity property of estimating tree total, sub-totals, and component biomass should be taken into account. Overall, the stand-level biomass models established in this study would be suitable for predicting stand-level biomass of six forest types in Daxing'an mountains.

[Predicting models of leaf area for trees in Larix olgensis plantation.] / 人工长白落叶松立木叶面积预估模型.

Leaf area influences dry matter production of trees, as well as the growth of trees and forest stands. The accurate estimation of leaf area plays an important role in analyzing the growth of trees and forest stands. Based on data of 76 Larix olgensis trees in a plantation of Heilongjiang Province, predicting models of branch leaf area (BLA) and crown leaf area (CLA) were constructed, respectively. The results showed that a form of lnBLA=ß1+(ß2+b2)lnBD+(ß3+b3)lnRDINC+ß4lnDBH+ß5lnHT/DBH+(ß6+b6)lnCR was selected as the optimal BLA mixed-effect model with the considera-tion of tree-level random effects, composed of three random-effect on lnBD, lnRDINC and lnCR (ßi represented model fixed parameters, bi represented model random-effect parameters, BD was branch diameter, RDINC was the relative depth into crown from tree apex, DBH was tree diameter at breast height, HT/DBH represented the ratio of tree height to DBH, and CR represented the ratio of crown length to tree height). The adjusted coefficient of determination (Ra2), residual mean squares error (RMSE), mean error (ME), mean absolute error (MAE) and precision estimation (P) of the optimal BLA mixed model were 0.90, 0.5477, -0.03, 0.24 and 91%, respectively, indicating the model had a good performance in predicting. The CLA was calculated by predicted values of all branches based on developed BLA model and the final form of CLA model was as follows: lnCLA=γ0+γ1lnDBH+γ2CR (γi, model parameters). Results of likelihood ratio test (P>0.05) showed that plot-level random effect had no influence on the model performance, which can be ignored. The CLA model got a good-fitting effect with R2 and RMSE being 0.87 and 0.3847, respectively. The CLA predicting model developed in this study could provide a good prediction of CLA for L. olgensis trees and provided a theoretical basis for the research on distribution of leaf area and photosynthesis.

[Individual tree diameter increment model for natural Betula platyphylla forests based on meteorological factors]. / åŸºäºŽæ°”è±¡å› å­çš„ç™½æ¡¦å¤©ç„¶æž—å•æœ¨ç›´å¾„ç”Ÿé•¿æ¨¡åž‹.

Based on the 212 re-measured permanent plots for natural Betula platyphylla fore-sts in Daxing'an Mountains and Xiaoxing'an Mountains and 30 meteorological stations data, an individual tree growth model based on meteorological factors was constructed. The differences of stand and meteorological factors between Daxing'an Mountains and Xiaoxing'an Mountains were analyzed and the diameter increment model including the regional effects was developed by dummy variable approach. The results showed that the minimum temperature (Tg min) and mean precipitation (Pg m) in growing season were the main meteorological factors which affected the diameter increment in the two study areas. Tg min and Pg m were positively correlated with the diameter increment, but the influence strength of Tg min was obviously different between the two research areas. The adjusted coefficient of determination (Ra2) of the diameter increment model with meteorological factors was 0.56 and had an 11% increase compared to the one without meteorological factors. It was concluded that meteorological factors could well explain the diameter increment of B. platyphylla. Ra2 of the model with regional effects was 0.59, and increased by 18% compared to the one without regional effects, and effectively solved the incompatible problem of parameters between the two research areas. The validation results showed that the individual tree diameter growth model with regional effect had the best prediction accuracy in estimating the diameter increment of B. platyphylla. The mean error, mean absolute error, mean error percent and mean prediction error percent were 0.0086, 0.4476, 5.8% and 20.0%, respectively. Overall, dummy variable model of individual tree diameter increment based on meteorological factors could well describe the diameter increment process of natural B. platyphylla in Daxing'an Mountains and Xiaoxing'an Mountains.

[Maximum density-size line for Larix olgensis plantations based on quantile regression.] / 基于分位数回归的长白落叶松人工林最大密度线.

Based on 378 permanent and 415 temporary plots from Northeast China, the relationship of maximum stand density and quadratic mean diameter at breast height of treesfor Larix olgensis plantation was developed. Linear quantile regression model with different quantiles (τ=0.90, 0.95, 0.99) was used and the optimal model for the maximum density-size line model was selected. The ordinary least square (OLS) and maximum likelihood (ML) regression were also employed to develop the maximum density-size line by using the arbitrary selected data. Generalized Pareto model of extreme value theory was used to calculate the number of limited maximum trees based on the current stands so that the limited density-size line was developed. The linear quantile regression model was compared with the other methods. The results showed that selecting 5 points within the whole diameter class for the maximum density-size line model development would get the satisfying prediction model. The fitting line would deviate from the maximum density-size line with the increasing points selected. The method of ML was superior to OLS in parameter estimation. The linear quantile regression model with the quantile of 0.99 achieved similar fitting results compared with ML regression and the estimation results was much stable. Traditional approach that selecting fittng data was considered arbitrary so that linear quantile regression with quantile of 0.99 was selected as the best model to construct the maximum density-size line with the estimates for the parameters as k=11.790 and ß=-1.586, and k=11.820 and ß=-1.594 for the limited density-size line model. The determined limited density-size line was above the maximum density-size line but the difference was not pronounced. The validation results by using the data of permanent sample plots showed the models were suitable to predict the maximum and limited density line of the current forest stands, which would provide basis for the sustainable management of L. olgensis plantation.

[Carbon storage of forest vegetation and allocation for main forest types in the east of Da-xing'an Mountains based on additive biomass model]. / åŸºäºŽå¯åŠ æ€§ç”Ÿç‰©é‡æ¨¡åž‹çš„å¤§å ´å®‰å²­ä¸œéƒ¨ä¸»è¦æž—åž‹æ£®æž—æ¤è¢«ç¢³å‚¨é‡åŠå ¶åˆ†é .

Based on the biomass investigation data of main forest types in the east of Daxing'an Mountains, the additive biomass models of 3 main tree species were developed and the changes of carbon storage and allocation of forest community of tree layer, shrub layer, herb layer and litter layer from different forest types were discussed. The results showed that the carbon storage of tree layer, shrub layer, herb layer and litter layer for Rhododendron dauricum-Larix gmelinii forest was 71.00, 0.34, 0.05 and 11.97 t·hm-2, respectively. Similarly, the carbon storage of the four layers of Ledum palustre-L. gmelinii forest was 47.82, 0.88, 0, 5.04 t·hm-2, 56.56, 0.44, 0.04, 8.72 t·hm-2 for R. dauricum-mixed forest of L. gmelinii-Betula platyphylla, 46.21, 0.66, 0.07, 6.16 t·hm-2 for L. palustre-mixed forest of L. gmelinii-B. platyphylla, 40.90, 1.37, 0.04, 3.67 t·hm-2 for R. dauricum-B. platyphylla forest, 36.28, 1.12, 0.18, 4.35 t·hm-2 for L. palustre-B. platyphylla forest. The carbon storage of forest community for the understory vegetation of R. dauricum was higher than that of the forest with L. palustre. In the condition of similar circumstances for the understory, the order of carbon storage for forest community was L. gmelinii forest > the mixed forest of L. gmelinii-B. platyphylla > B. platyphylla forest. The carbon storage of different forest types was different with the order of R. dauricum-L. gmelinii forest (83.36 t·hm-2)> R. dauricum-mixed forest of L. gmelinii-B. platyphylla (65.76 t·hm-2) > L. palustre-L. gmelinii forest (53.74 t·hm-2)> L. palustre-mixed forest of L. gmelinii-B. platyphylla (53.10 t·hm-2)> R. dauricum-B. platyphylla forest (45.98 t·hm-2) > L. palustre-B. platyphylla forest (41.93 t·hm-2). The order of carbon storage for the vertical distribution in forest communities with diffe-rent forest types was the tree layer (85.2%-89.0%) > litter layer (8.0%-14.4%) > shrub layer (0.4%-2.7%) > herb layer (0-0.4%).

[Comparison of three stand-level biomass estimation methods]. / 三种林分生物量估算方法的比较.

At present, the forest biomass methods of regional scale attract most of attention of the researchers, and developing the stand-level biomass model is popular. Based on the forestry inventory data of larch plantation (Larix olgensis) in Jilin Province, we used non-linear seemly unrelated regression (NSUR) to estimate the parameters in two additive system of stand-level biomass equations, i.e., stand-level biomass equations including the stand variables and stand biomass equations including the biomass expansion factor (i.e., Model system 1 and Model system 2), listed the constant biomass expansion factor for larch plantation and compared the prediction accuracy of three stand-level biomass estimation methods. The results indicated that for two additive system of biomass equations, the adjusted coefficient of determination (Ra2) of the total and stem equations was more than 0.95, the root mean squared error (RMSE), the mean prediction error (MPE) and the mean absolute error (MAE) were smaller. The branch and foliage biomass equations were worse than total and stem biomass equations, and the adjusted coefficient of determination (Ra2) was less than 0.95. The prediction accuracy of a constant biomass expansion factor was relatively lower than the prediction accuracy of Model system 1 and Model system 2. Overall, although stand-level biomass equation including the biomass expansion factor belonged to the volume-derived biomass estimation method, and was different from the stand biomass equations including stand variables in essence, but the obtained prediction accuracy of the two methods was similar. The constant biomass expansion factor had the lower prediction accuracy, and was inappropriate. In addition, in order to make the model parameter estimation more effective, the established stand-level biomass equations should consider the additivity in a system of all tree component biomass and total biomass equations.

[Spatial heterogeneity of canopy photosynthesis for Larix olgensis.] / é•¿ç™½è½å¶æ¾å† å±‚å ‰åˆä½œç”¨çš„ç©ºé—´å¼‚è´¨æ€§.

Based on a 14-year-old planted Larix olgensis in the Maoershan Forest Farm, Heilongjiang Province in 2014, the spatial heterogeneity of photosynthetic indicators, environmental factors and photosynthetic physiological parameters were analyzed, meanwhile the relationship between net photosynthetic rate (Pn) and other indicators were studied. Results showed that in the vertical direction, Pn, stomatal conductance (gs) and transpiration rate (Tr) were higher in upper than middle and lower canopy significantly, intercellular CO2 concentration (Ci) increased in the sequence of upper < middle < lower canopy. Photosynthetic active radiation (PAR) decreased from outside of upper to inside of lower canopy significantly, vapor pressure deficit (VPD) and needle leaf temperature (Tl) in upper canopy were respectively higher than in middle and lower canopy significantly, while relative humidity (RH) showed no significant difference with spatial location. The mean value of maximum Pn(Pn max), dark respiration rate (Rd), light compensation point (LCP) and light sa-turation point (LSP) followed the pattern of upper > middle > lower canopy and decreased by 32.7%, 55.8%, 80.2% and 51.6% from upper to lower canopy respectively. Apparent quantum yield (AQY) in lower canopy was 1.2 and 1.3 times as much as that of middle and upper canopy, respectively. In the horizontal direction, Pn, gs, Tr, PAR and VPD were significantly higher from outside to inside in the upper crown, but Ci and RH showed no significant diffe-rence. The mean value of Pn max, Rd, LCP and LSP declined by 0.4%, 37.7%, 42.0% and 16.4% from outside to inside, on the contrary, AQY was 0.7% higher from inside to outside. Ci was the main physiological impact factor for Pn, and PAR was an important environmental factor that had the most obvious influence on Pn, especially in weak light region. Therefore, spatial heterogeneity should be considered necessarily when simulating and/or predicting the tree canopy photosynthesis.

[Branch quantity distribution simulation for Pinus koraiensis plantation in Heilongjiang Pro-vince, China.] / 黑龙江省红松人工林枝条分布数量模拟.

Based on the measurement of 955 branch samples of 65 Korean pine (Pinus koraiensis) trees in 12 plots from Mengjiagang forest farm, Heilongjiang Province, and by using Poisson model and negative binomial model, the second-order branch count models for Korean pine were developed in this paper. AIC, Pseudo-R2, RMSE and Vuong test were selected to compare the goodness-of-fit statistics of the models. The results indicated that the first-order branch count in a whorl was 3 to 5, with mean value of 4, and the first-order branch count in a whorl for Korean pine plantation associated with its own characteristics. The second-order branch count of the first-order standard branch had a large discrete degree. All subset regression techniques were used to develop the second-order branch count model. The negative binomial regression model E(Y)=exp(ß0+ß1lnRDINC+ß2RDINC2+ß3HT/DBH+ß4CL+ß5DBH) was selected as the optimal second-order branch count model (ß represented the parameter, RDINC represented the relative depth into crown from tree apex, HT represented the total tree height, DBH represented the tree diameter at breast height, CL represented the crown length). Pseudo-R2 of the optimal model was 0.79, the mean error was close to 0 and the mean absolute error was less than 7. For the developed model, the parameter values of lnRDINC, CL and DBH were negative, and the parameter values of RDINC2 and HT/DBH were positive. With the increase of RDINC, the number of second-order branch had a peak value in the tree crown. On the whole, the precision of the second-order branch count model for Korean pine plantation was 96.4%, which would be suitable for predicting the second-order branch count for the study area and provide a theoretic basis for branch photosynthesis and biomass research.

[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.