Current issue: 53(4)
Individual tree-growth models for diameter and height, and a model for the cylindrical stem form factor are presented. The aims of the study were to examine modelling methods in predicting growth response to thinning, and to develop individual-tree, distance-independent growth models for predicting the development of thinned and unthinned stands of Scots pine (Pinus sylvestris L.). The models were constructed to be applicable in simulation systems used in practical forest management planning. The models were based on data obtained from eleven permanent thinning experiments located in even-aged Scots pine stands in Southern and Central Finland.
Two alternative models were developed to predict tree diameter growth in thinned and unthinned stands. In the first model, the effect of stand density was described using stand basal area. In the alternative model, an explicit variable was incorporated referring to the relative growth response due to thinning. The magnitude of the growth response was expressed as a function of thinning intensity. The Weibull function was employed to describe the temporal distribution of the thinning response. Both models resulted in unbiased predictions in unthinned and in moderately thinned stands. An explicit thinning variable was needed for unbiased growth prediction in heavily thinned stands, and in order to correctly predict the dynamics of the growth response.
In the height growth model, no explicit thinnning variable referring thinning was necessary for growth prediction in thinned stands. The stem form factor was predicted using the model that included tree diameter and tree height as regressor variables. According to the results obtained, the information on the changes in the diameter/height ratio following the thinning is sufficient to predict the change in stem form.
A nonlinear programming algorithm was combined with two individual-tree growth simulators consisting of distance-independent diameter and height growth models and mortality models. Management questions that can be addressed by the optimization model include the timing, intensity and type of thinning, rotation age, and initial density. The results were calculated for Norway spruce (Picea abies (L.) H. Karst.) stands on Oxalis-Myrtillus site in Southern Finland, where the stand density after clearing of a seedling stand is about 2,000 trees/ha.
The optimum thinning programs were characterized by late first thinnings (at dominant height of 15–17 m) and relatively high growing stock levels. It was optimal to thin from above, unless mean annual increment was maximized instead of an economic objective. In most cases, the optimum number of thinnings was two or three. Compared to a no-thinning alternative, thinnings increased revenues by 15 –45% depending on the objective of stand management. Optimum rotation was strongly dependent on the interest rate.
Hooke and Jeeves’ direct search method was used for determining optimum solutions. The performance of the optimization algorithm was examined in terms of the number of functional evaluations and the equivalence of the objective function values of repeated optimizations.
The PDF includes a summary in Finnish.