Current issue: 56(4)
Under compilation: 57(1)
For constructing growth and yield models the concept of site index as measure of productivity is crucial. Here, we use nonlinear mixed-effects models (NLME) with random individual effects and nonlinear models with dummy variables as fixed individual effects (NLFE) to fit mechanistic growth functions to stem analysis data of the economically most important tree species in Zhongtiaoshan forest region, China. The Richards and Lundqvist function are formulated into five dynamic equations (R1, R2, L1, L2 and L3) applying the generalized algebraic difference approach (GADA), which inherit polymorphism, varying asymptotes and base-age invariance. According to Akaike information criterion the R1 model as NLFE fits height growth data of Pinus tabuliformis Carrière, Pinus armandii Franch., Quercus liaotungensis Koidz., Quercus aliena Blume and Betula platyphylla Sukaczev best, while for Quercus variabilis Blume R2 as NLFE fits height growth data best. For Larix principis-rupprechtii Mayr L1 as NLME has been selected as best model, as R1 and R2 both as NLFE and NLME are not extrapolating the comparably short length of height growth data well enough. However, according to the root mean square error and bias differences between model fits of both the selected equation and the chosen model fitting approach are not so clear. Presented families of height growth curves serve as planning tools to identify site index and therefore assess productivity of forest stands in the studied region. A direct comparison of the productivity of forest stands of the same tree species is possible due to base-age invariance of the selected models.
Hybrid aspen (Populus tremula L. × P. tremuloides Michx.) is known with outstanding growth rate and some favourable wood characteristics, but models for stand management have not yet been prepared in northern Europe. This study introduces methods and models to predict tree dimensions, diameter at breast height (dbh) and tree height for a hybrid aspen plantation using data from repeatedly measured permanent sample plots established in clonal plantations in southern Finland. Dbh distributions using parameter recovery method for the Weibull function was used with Näslund’s height curve to model tree heights. According to the goodness-of-fit statistics of Kolmogorov-Smirnov and the Error Index, the arithmetic mean diameter (D) and basal area-weighted mean diameter (DG) provided more stable parameter recovery for the Weibull distribution than the median diameter (DM) and basal area-weighted median diameter (DGM), while DG showed the best overall fit. Thus, Näslund’s height curve was modelled using DG with Lorey’s height (HG), age, basal area (BA), and tree dbh (Model 1). Also, Model 2 was tested using all predictors of Model 1 with the number of trees per ha (TPH). All predictors were shown to be significant in both Models, showing slightly different behaviour. Model 1 was sensitive to the mean characteristics, DG and HG, while Model 2 was sensitive to stand density, including both BA and TPH as predictors. Model 1 was considered more reasonable to apply based on our results. Consequently, the parameter recovery method using DG and Näslund’s models were applicable for predicting tree diameter and height.
The diameter at any point on a stem and tree volume are some of the most important types of information used in forest management planning. One of the methods to predict the diameter at any point on a stem is to develop taper models. Black locust (Robinia pseudoacacia L.) occurs in almost all forests in Poland, with the largest concentration in the western part of the country. Using empirical data obtained from 13 black locust stands (48 felled trees), seven taper models with different numbers of estimated parameters were analysed for section diameters both over and under bark using fixed and mixed-effects modelling approaches. Assuming a lack of additional measurements, the best fitted taper models were used for the prediction of over bark volume using both methods. The predicted volume was compared with the results from different volume equations available for black locust. The variable-form taper model with eight estimated parameters fitted the data the best. The lowest root mean square error for volume prediction was achieved for the elaborated fixed-effects taper model (0.0476), followed by the mixed-effects taper model (0.0489). At the same time, the difference between the volume relative errors achieved based on the taper models does not differ significantly from the results obtained using the volume equations already available for black locust (two of the three analysed).
This study examines the alternatives to include crown base height (CBH) predictions in operational forest inventories based on airborne laser scanning (ALS) data. We studied 265 field sample plots in a strongly pine-dominated area in northeastern Finland. The CBH prediction alternatives used area-based metrics of sparse ALS data to produce this attribute by means of: 1) Tree-level imputation based on the k-nearest neighbor (k-nn) method and full field-measured tree lists including CBH observations as reference data; 2) Tree-level mixed-effects model (LME) prediction based on tree diameter (DBH) and height and ALS metrics as predictors of the models; 3) Plot-level prediction based on analyzing the computational geometry and topology of the ALS point clouds; and 4) Plot-level regression analysis using average CBH observations of the plots for model fitting. The results showed that all of the methods predicted CBH with an accuracy of 1–1.5 m. The plot-level regression model was the most accurate alternative, although alternatives producing tree-level information may be more interesting for inventories aiming at forest management planning. For this purpose, k-nn approach is promising and it only requires that field measurements of CBH is added to the tree lists used as reference data. Alternatively, the LME-approach produced good results especially in the case of dominant trees.