Articles containing the keyword 'growth models'

Models for individual-tree basal area growth were constructed for Scots pine (Pinus sylvestris L.), pubescent birch (Betula pubescens Ehrh.) and Norway spruce (Picea abies (L.) Karst.) growing in drained peatland stands. The data consisted of two separate sets of permanent sample plots forming a large sample of drained peatland stands in Finland. The dependent variable in all models was the 5-year basal area growth of a tree. The independent tree-level variables were tree dbh, tree basal area, and the sum of the basal area of trees larger than the target tree. Independent stand-level variables were stand basal area, the diameter of the tree of median basal area, and temperature sum. Categorical variables describing the site quality, as well as the condition and age of drainage, were used. Differences in tree growth were used as criteria in reclassifying the a priori site types into new yield classes by tree species. All models were constructed as mixed linear models with a random stand effect. The models were tested against the modelling data and against independent data sets.

• Hökkä, E-mail: hh@mm.unknown
• Alenius, E-mail: va@mm.unknown
• Penttilä, E-mail: tp@mm.unknown

This paper reports on the possibility and difficulties in building growth models from past Forest Administration records on cut and growth in the Italian Alps. As a case study, a matrix model was calibrated for uneven-aged forests in the Valsugana valley of the Trentino province. The model gave reliable predictions over 30 years, and plausible long-term forest dynamics, including steady-states that are similar to virgin forests. The results support the view that the current forests are deeply altered as to composition, relative to what would obtain from natural growth. They also support the concept of long cyclic changes in natural stands, gradually approaching a climax state. Shortcomings of the data are that they do not come from an experimental design, they are not always accurate, and they must be supplemented with other information, especially concerning mortality. Still, these cheap and available data can lead to workable models adapted to local conditions, with many management applications.

• Virgilietti, E-mail: pv@mm.unknown
• Buongiorno, E-mail: jb@mm.unknown

The effect of species mixture was studied in a mixed stand of Norway spruce (Picea abies (L.) H. Karst.) and Scots pine (Pinus sylvestris L.) by simulating around 100 different treatment schedules during the rotation in a naturally regenerated even-aged stand located on a site of medium fertility in North Karelia, Finland. Both thinning from below and thinning from above were applied. Optimum rotations were determined by maximising the net present value calculated to infinity and different treatment schedules were compared with the net present value over one rotation as per rotation applied. In the optimum treatment programme, the proportion of pines was decreased by half of the basal area in the first thinning stage and by the end of the rotation to about one third. In thinning from above, the proportion of pines can be maintained at a slightly higher level. It is economically profitable to maintain the growing stock capital at approximately the level recommended by Forest Centre Tapio, a semi-governmental forestry authority. With non-optimum species composition, the loss in net present value over one rotation can be about 10 % in thinning from below and about 20 % in thinning from above.

• Vettenranta, E-mail: jv@mm.unknown

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.

• Hynynen, E-mail: jh@mm.unknown

A spatial growth model is presented for Scots pine (Pinus sylvestris L.) on a dwarf-shrub pine mire drained 14 years earlier. The growth model accounts for the variation in tree diameter growth owing to the competition between trees, the distance between tree and ditch, and the time passed since drainage. The model was used to study the effect of tree arrangement on the post-drainage growth of a pine stand. Clustering of trees decreased the volume growth by 9–20% as compared to a regular spatial distribution. Stand volume growth, for a given number of stems, was at its maximum and variation in diameter growth at its minimum when the stand density on the ditch border was 1.5–5 higher than midway between two adjacent ditches.

• Miina, E-mail: jm@mm.unknown

Mixed linear models were constructed to describe the height development of Norway spruce (Picea abies (L.) H. Karst.) and Scots pine (Pinus sylvestris L.) advance growth after release cutting. The models related density of the overstory, time elapsed since release cutting and tree size with annual height increment. Parameters of preliminary models were estimated from a limited data set to judge the feasibility of the approach for further studies.

The PDF includes an abstract in Finnish.

• Koistinen, E-mail: ek@mm.unknown
• Valkonen, E-mail: sv@mm.unknown

Ring width at breast height is presented as a function of stem radius at breast height, the ratio between the diameter of a tree and the basal area median diameter, site index, and density of stand. By means of a conversion model ring width at stump height can be estimated as a function of ring width at breast height.

According to previous studies substantially better wood quality can be expected if mean width near the pith at stump height decreases from 3 to 2 mm. According to the present study only on the poorest sites suitable for Scots pine (Pinus sylvestris L.) planting (poor Vaccinium type) the ring width is less than 3 mm at stump height even in the thickest trees. On more fertile sites a substantial increase in the recommended planting density is required, if the mean ring width is aimed to be less than 3 mm. On the best sites it is impossible to reach mean ring width of less than 2 mm, when the density is less than 4,000 stems/ha. Only the thinnest trees on the poorest sites can have a mean ring width less than 2mm.

The PDF includes an abstract in English.

• Varmola, E-mail: mv@mm.unknown

The single tree growth models presented in this study were based on about 4,000 trees measured in 50 even-aged Scots pine (Pinus sylvestris L.) sample plots with varying density, spatial pattern of trees and stand age. Predictors that used information about tree locations decreased the relative standard error of estimate by 10 percentage points (15%), if past growth was not used as a predictor, and about 15 percentage points (30%) when past growth was one of the predictors. When ranked according to the degree of determination, the best growth models were obtained for the basal area increment, the next best for relative growth, and the poorest for diameter increment. The past growth decreased the relative standard error of estimate by 15–20 percentage points, but did not make the spatial predictors unnecessary. The degree of determination of the spatial basal area growth model was almost 80% if the past growth was unknown and almost 90% if the past growth was known. Variables that described the amount of removed competition did not improve the growth models.

The PDF includes an abstract in Finnish.

• Pukkala, E-mail: tp@mm.unknown

A theoretical framework to analyse the growth of Scots pine (Pinus sylvestris L.) is presented. Material exchange processes and internal processes that transport, transform and consume materials are identified as the components of growth. Hierarchical system is lined out. Momentary uptake of material at a single exchange site depends on the environmental condition next to the exchange site, the internal state of the biochemical system of the plant and the structure of the plant. The internal state depends on the exchange flows over period of time and the structural growth depends on the internal state. The response of these processes to the fluxes is controlled by the genetic composition of the plant.

The theoretical framework is formulated into a mathematical model. A concept of balanced internal state was applied to describe the poorly known internal processes. Internal substrate concentrations were assumed to remain constant but tissue-specific. A linear relationship between the quantity of foliage and wood cross-sectional area was assumed to describe balanced formation of structure. The exchange processes were thus described as a function of external conditions. The stand level interactions were derived from shading and effects of root density on nutrient uptake.

The approach was tested at different levels of hierarchy. Field measurements indicated that the hypothesis of the linear relationship described well the regularities between foliage and sapwood of a tree within a stand when measured at functionally corresponding height. There was considerable variation in the observed regularities in the range of geographic occurrence of Scots pine. Model simulations gave a realistic description of stand development in Southern Finland. The same model was also able to describe growth differences in Lapland after considering the effect of growing season length in the parameter values. Simulations to South Russia indicate stronger deviation from the observed patterns.

The simulations suggest interesting features of stand development. They indicate strong variability in the distribution of carbohydrates between tree parts during stand development. Internal circulation of nutrients and the reuse of the same transport structure by various needle generations had a strong influence on the simulation results.

The PDF includes a summary in Finnish.

• Nikinmaa, E-mail: en@mm.unknown

• Hökkä, Finnish Forest Research Institute, Rovaniemi Unit, Eteläranta 55, FI-96300 Rovaniemi, Finland E-mail: hannu.hokka@metla.fi
• Mäkelä, Lapland University of Applied Sciences, Jokiväylä 11 C, FI-96300 Rovaniemi, Finland E-mail: hanna.makela@edu.ramk.fi

• Sterba, BOKU – University of Natural Resources an Applied Life Sciences, Vienna, Peter Jordanstrasse 82, A-1190 Vienna, Austria E-mail: hubert.sterba@boku.ac.at

• Sironen, University of Joensuu, Faculty of Forestry, P.O. Box 111, FIN-80101 Joensuu, Finland E-mail: susanna.sironen@forest.joensuu.fi
• Kangas, Finnish Forest Research Institute, Kannus Research Station, P.O. Box 44, FIN-69101 Kannus, Finland E-mail: ak@nn.fi
• Maltamo, University of Joensuu, Faculty of Forestry, P.O. Box 111, FIN-80101 Joensuu, Finland E-mail: mm@nn.fi
• Kangas, Finnish Forest Research Institute, Kannus Research Station, P.O. Box 44, FIN-69101 Kannus, Finland E-mail: jk@nn.fi

• Minkkinen, University of Helsinki, Department of Forest Ecology, P.O. Box 27, FIN-00014 University of Helsinki, Finland E-mail: kari.minkkinen@helsinki.fi
• Laine, University of Helsinki, Department of Forest Ecology, P.O. Box 27, FIN-00014 University of Helsinki, Finland E-mail: jl@nn.fi
• Hökkä, Finnish Forest Research Institute, Rovaniemi Research Station, P.O. Box 16, FIN-96301 Rovaniemi, Finland E-mail: hh@nn.fi

• Vettenranta, Kivirinnanpolku 4, FIN-40950 Muurame, Finland E-mail: vettenr@cc.joensuu.fi