Individual tree crown width models for Norway spruce and European beech in Czech Republic

A generalized nonlinear mixed-effects height to crown base model for Mongolian oak in northeast China

Crown width–diameter relationship, which is significantly influenced by various characteristics, was modelled using tree and stand measures, and plot-level random effect parameters. A proposed model precisely predicts crown width of Scots pine.
 Crown size is significantly correlated with growth and biomass of other parts of a tree, and therefore crown measures are used as predictors to develop tree growth and biomass models. We modelled crown width–diameter at breast height (DBH) allometry using data from permanent sample plots located in both monospecific and mixed species stands of Scots pine (Pinus sylvestris L.) in various parts of the Czech Republic. Among various predictors evaluated, dominant height (HDOM), height-to-DBH ratio (HDR—also known as a tree slenderness coefficient), height to live crown base (HCB), relative spacing index (RS), and basal area proportion of a species of interest (BAPOR) significantly contributed to the variations in the crown width–DBH allometry. The sample plot-level random effect parameters, which account for stand heterogeneity and randomness caused by various stochastic factors, were included through the mixed-effects modelling approach. Heteroskedasticity in the residuals was reduced through the integration of a power variance function with DBH as an independent variable. Both mixed-effects model and ordinary least square (OLS) model described more than two-thirds of the total variations in the crown width–DBH allometry with no significant trend in the residuals. The model showed that crown width increased with increasing site quality (increasing HDOM) and relative spacing index (increasing RS), and decreasing species mixture per sample plot (increasing BAPOR). However, crown width decreased with increasing tree slenderness coefficient (increasing HDR) and height to live crown base (increasing HCB). Model validation by splitting data also confirmed a high precision of the model, because it described most of the variations in the crown width–DBH allometry with no significant trend in the prediction errors. Because of more attractive fit statistics and higher prediction accuracy than that of the OLS model, the mixed-effects model with the random effect parameters estimated from crown width measurements of a sub-sample of four randomly selected Scots pine trees per sample plot is suggested for application. Application of the crown width model may have various implications that are briefly mentioned in the article.

Modelling crown width–diameter relationship for Scots pine in the central Europe

A generalized interregional nonlinear mixed-effects crown width model for Prince Rupprecht larch in northern China

Nonlinear error-in-variable models can advance the development of the systems of additive biomass equations and lead to much higher prediction accuracy of tree biomass than nonlinear seemingly unrelated regression.
 In this study, the approach of nonlinear error-in-variable models (NEIVM) was compared with nonlinear seemingly unrelated regressions (NSUR) for developing a system of nonlinear additive biomass equations using the data collected in Southern China for Pinus massoniana Lamb. Various tree variables were assessed to explore their contributions to improvement of biomass prediction using the systems of equations. It was found that diameter at breast height (D), total tree height (H) and crown width (CW) significantly contributed to the increase of prediction accuracy. The combinations of D, H, and CW led to three sets of independent variables: (1) D alone; (2) both D and H; and (3) D, H and CW together, which were used for the development of one-predictor, two-predictor and three-predictor systems of biomass equations, respectively. The results showed that both NEIVM and NSUR had high prediction accuracy of biomass for all the systems of biomass equations. For the one-predictor systems of biomass equations, both NEIVM and NSUR led to very similar predictions. However, for the two-predictor and three-predictor systems of biomass equations, the prediction accuracy of NEIVM was much higher than that of NSUR. When the two-predictor system of equations was used, in particular, NEIVM with one-step procedure, that is, by directly partitioning total tree biomass into four basic components, showed a higher accuracy of biomass prediction than NSUR for all the one-predictor, two-predictor and three-predictor systems of equations. This study implies that the NEIVM approach could provide a greater potential to develop a system of biomass equations that are dependent on the predictors with significant measurement errors.

Hua Sun

Papers

Nonlinear mixed-effects crown width models for individual trees of Chinese fir (Cunninghamia lanceolata) in south-central China