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Silva Fennica 1926-1997
Acta Forestalia Fennica

Articles containing the keyword 'growth models'

Category: Article

article id 5616, category Article
Hannu Hökkä, Virpi Alenius, Timo Penttilä. (1997). Individual-tree basal area growth models for Scots pine, pubescent birch and Norway spruce on drained peatlands in Finland. Silva Fennica vol. 31 no. 2 article id 5616.
Keywords: Pinus sylvestris; site quality; Picea abies; Betula pubescens; forest drainage; mixed models; peatlands; growth models
Abstract | View details | Full text in PDF | Author Info

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 (email)
  • Alenius, E-mail: va@mm.unknown
  • Penttilä, E-mail: tp@mm.unknown
article id 5607, category Article
Paola Virgilietti, Joseph Buongiorno. (1997). Modeling forest growth with management data: A matrix approach for the Italian Alps. Silva Fennica vol. 31 no. 1 article id 5607.
Keywords: forest dynamics; succession; growth models; matrix models; Italian Alps; Italy
Abstract | View details | Full text in PDF | Author Info

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 (email)
  • Buongiorno, E-mail: jb@mm.unknown
article id 5574, category Article
Jouni Vettenranta. (1996). Effect of species composition on economic return in a mixed stand of Norway spruce and Scots pine. Silva Fennica vol. 30 no. 1 article id 5574.
Keywords: Pinus sylvestris; Picea abies; net present value; mixed forests; growth models; tree species composition; forest management practices; felling methods; valuation; soil expectation value; treatment programme
Abstract | View details | Full text in PDF | Author Info

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 (email)
article id 5559, category Article
Jari Hynynen. (1995). Predicting the growth response to thinning for Scots pine stands using individual-tree growth models. Silva Fennica vol. 29 no. 3 article id 5559.
Keywords: Pinus sylvestris; thinnings; height; diameter; stem form; growth models; individual-tree; distance-dependent
Abstract | View details | Full text in PDF | Author Info

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 (email)
article id 5525, category Article
Jari Miina. (1994). Spatial growth model for Scots pine on drained peatland. Silva Fennica vol. 28 no. 1 article id 5525.
Keywords: Pinus sylvestris; drained peatlands; growth models; linear models
Abstract | View details | Full text in PDF | Author Info

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 (email)
article id 5510, category Article
Esa Koistinen, Sauli Valkonen. (1993). Models for height development of Norway spruce and Scots pine advance growth after release in southern Finland. Silva Fennica vol. 27 no. 3 article id 5510.
Keywords: Pinus sylvestris; Picea abies; Finland; growth models; advance growth; release cut
Abstract | View details | Full text in PDF | Author Info

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 (email)
  • Valkonen, E-mail: sv@mm.unknown
article id 5388, category Article
Martti Varmola. (1989). Männyn istutustaimikoiden lustonleveysmalli. Silva Fennica vol. 23 no. 4 article id 5388.
English title: A model for ring width of planted Scots pine.
Original keywords: mänty; taimikot; lustonleveys; kasvumallit; puuaineen laatu
English keywords: Pinus sylvestris; wood quality; spacing; ring width; growth models
Abstract | View details | Full text in PDF | Author Info

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 (email)
article id 5376, category Article
Timo Pukkala. (1989). Predicting diameter growth in even-aged Scots pine stands with a spatial and non-spatial model. Silva Fennica vol. 23 no. 2 article id 5376.
Keywords: Pinus sylvestris; growth prediction; spatial distribution; growth models; tree models
Abstract | View details | Full text in PDF | Author Info

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 (email)

Category: Article

article id 7681, category Article
Eero Nikinmaa. (1992). Analyses of the growth of Scots pine: matching structure with function. Silva Fennica vol. 0 no. 235 article id 7681.
Keywords: Pinus sylvestris; Scots pine; pipe model; nutrients; heartwood; growth models; carbon budget; structure; partitioning of growth; growht
Abstract | View details | Full text in PDF | Author Info

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 (email)

Category: Research article

article id 1192, category Research article
Hannu Hökkä, Hanna Mäkelä. (2015). Post-harvest height growth of Norway spruce seedlings in northern Finland peatland forest canopy gaps and comparison to partial and complete canopy removals and plantations. Silva Fennica vol. 48 no. 5 article id 1192.
Keywords: Picea abies; height growth; peatlands; growth models; advance growth; canopy gap
Highlights: Norway spruce seedlings’ height growth recovered within four years after the cutting of canopy gaps; Growth was linearly related to tree height, being highest for tallest seedlings; Seedlings in the 20 m diameter gap and in the central and northern parts in the 15 m diameter gap showed the best growth; In gaps early height growth was 60% of that in peatland spruce plantations but 2–3 times higher than in uneven-aged cut forests.
Abstract | Full text in HTML | Full text in PDF | Author Info
Recent studies have shown the establishment of Norway spruce (Picea abies (L.) Karst.) to be successful in small canopy gaps cut in drained spruce mire stands in northern Finland. The aim of this study was to quantify seedling height growth in gaps and compare it to that observed in other canopy cuttings and plantations. We sampled spruce crop seedlings (maximum density ca. 3000 ha–1) in the spring of 2013 in a field experiment in which canopy gaps of 10, 15 and 20 m in diameter had been cut in winter 2004. The total seedling height in 2013 and the length of annual shoots over the past five years (2012–2008) were recorded in the survey. Seedling height varied from 20 cm to 2.7 m, with an average of 65 cm. The average annual height growth was 7.1 cm. A mixed linear model analysis was carried out to investigate seedling height growth variation. Seedling height was linearly and positively related to growth. Height growth started to increase in the fifth growing season after cutting. Seedling height growth in the 20 m gap was slightly better than in the smaller ones. In the 15 m gap, both the centrally located seedlings and those located at the northern edge grew best. In the 20 m gap, southerly located seedlings grew more slowly than seedlings in all other locations. The average seedling height growth in this study was about 60% of that in peatland plantations, but comparable to that in mineral soil gaps, and 2–3 times higher than in uneven-age cut stands.
  • Hökkä, Finnish Forest Research Institute, Rovaniemi Unit, Eteläranta 55, FI-96300 Rovaniemi, Finland E-mail: (email)
  • Mäkelä, Lapland University of Applied Sciences, Jokiväylä 11 C, FI-96300 Rovaniemi, Finland E-mail:
article id 409, category Research article
Hubert Sterba. (2004). Equilibrium curves and growth models to deal with forests in transition to uneven-aged structure – application in two sample stands. Silva Fennica vol. 38 no. 4 article id 409.
Keywords: uneven-aged forests; growth models; stem number distribution; transformation
Abstract | View details | Full text in PDF | Author Info
Stem number distributions in uneven-aged forests are assumed to be stable, if they follow special functions, e.g. de Liocourt’s reverse J-shaped breast height diameter distribution. These distributions therefore are frequently regarded as a target in all-aged forests. Intending to convert an even-aged forest or any other forest, not yet exhibiting this sort of equilibrium, towards a steady state forest, the question rises, how to choose an appropriate equilibrium curve and how to achieve this stem number distribution by an appropriate thinning and harvesting schedule. Two stands are investigated: One dominated by Norway spruce (Picea abies), having developed from a 120 year old even-aged stand 25 years ago, after several “target diameter thinnings”. The other one is a mixed species stand of Norway spruce, white fir (Abies alba), larch (Larix europea), common beech (Fagus silvatica), and Scots pine (Pinus sylvestris), having lost its typical uneven-aged structure 20 years ago. These stands were used, together with the distance independent individual tree growth model PrognAus, to reveal that 1) there are more than only one equilibrium curve per stand, 2) not every hypothesised equilibrium can be reached with any stand, 3) an equilibrium in stem number does not necessarily mean a stable species distribution, and 4) growth models provide an excellent help to decide between several equilibrium curves and harvesting schedules to reach them.
  • Sterba, BOKU – University of Natural Resources an Applied Life Sciences, Vienna, Peter Jordanstrasse 82, A-1190 Vienna, Austria E-mail: (email)
article id 580, category Research article
Susanna Sironen, Annika Kangas, Matti Maltamo, Jyrki Kangas. (2001). Estimating individual tree growth with the k-nearest neighbour and k-Most Similar Neighbour methods. Silva Fennica vol. 35 no. 4 article id 580.
Keywords: pine; spruce; single tree growth models; non-parametric models; local estimates
Abstract | View details | Full text in PDF | Author Info
The purpose of this study was to examine the use of non-parametric methods in estimating tree level growth models. In non-parametric methods the growth of a tree is predicted as a weighted average of the values of neighbouring observations. The selection of the nearest neighbours is based on the differences between tree and stand level characteristics of the target tree and the neighbours. The data for the models were collected from the areas owned by Kuusamo Common Forest in Northeast Finland. The whole data consisted of 4051 tally trees and 1308 Scots pines (Pinus sylvestris L.) and 367 Norway spruces (Picea abies Karst.). Models for 5-year diameter growth and bark thickness at the end of the growing period were constructed with two different non-parametric methods: the k-nearest neighbour regression and k-Most Similar Neighbour method. Diameter at breast height, tree height, mean age of the stand and basal area of the trees larger than the subject tree were found to predict the diameter growth most accurately. The non-parametric methods were compared to traditional regression growth models and were found to be quite competitive and reliable growth estimators.
  • Sironen, University of Joensuu, Faculty of Forestry, P.O. Box 111, FIN-80101 Joensuu, Finland E-mail: (email)
  • Kangas, Finnish Forest Research Institute, Kannus Research Station, P.O. Box 44, FIN-69101 Kannus, Finland E-mail:
  • Maltamo, University of Joensuu, Faculty of Forestry, P.O. Box 111, FIN-80101 Joensuu, Finland E-mail:
  • Kangas, Finnish Forest Research Institute, Kannus Research Station, P.O. Box 44, FIN-69101 Kannus, Finland E-mail:
article id 603, category Research article
Kari Minkkinen, Jukka Laine, Hannu Hökkä. (2001). Tree stand development and carbon sequestration in drained peatland stands in Finland – a simulation study. Silva Fennica vol. 35 no. 1 article id 603.
Keywords: carbon; peatland; drainage; growth models
Abstract | View details | Full text in PDF | Author Info
Drained peatland forests form an important timber resource in Finland. They also form a sink for atmospheric carbon (C) because of the increased growth and C sequestration rates following drainage. These rates have, however, been poorly quantified. We simulated the tree stand dynamics for drained peatland stands with and without cuttings over two stand rotations. Simulations were done on four peatland site types and two regions in Finland with different climatic conditions, using recently published peatland tree growth models applied in a stand simulator. We then calculated the amount of C stored in the stands on the basis of previously published tree-level biomass and C content models. Finally, we developed regression models to estimate C stores in the tree stands using stand stem volume as the predictor variable. In the managed stands, the mean growth (annual volume increment) ranged from 2 to 9 m3 ha–1 a–1, depending on the rotation (first/second), site type and region. Total yield during one rotation varied from 250 to 920 m3 ha–1. The maximum stand volumes varied from 220 to 520 m3 ha–1 in the managed stands and from 360 to 770 m3 ha–1 in the unmanaged. By the end of the first post-drainage rotation the total C store in the managed stands had increased by 6–12 kg C m–2 (i.e. 45–140 g C m–2 a–1) compared to that in the undrained situation. Averaged over two rotations, the increase in the total C store was 3–6 kg C m–2. In the corresponding unmanaged stands the C stores increased by 8–15 kg m–2 over the same periods. At stand level, the C stores were almost linearly related to the stem volume and the developed regression equations could explain the variation in the simulated C stores almost entirely.
  • Minkkinen, University of Helsinki, Department of Forest Ecology, P.O. Box 27, FIN-00014 University of Helsinki, Finland E-mail: (email)
  • Laine, University of Helsinki, Department of Forest Ecology, P.O. Box 27, FIN-00014 University of Helsinki, Finland E-mail:
  • Hökkä, Finnish Forest Research Institute, Rovaniemi Research Station, P.O. Box 16, FIN-96301 Rovaniemi, Finland E-mail:
article id 670, category Research article
Jouni Vettenranta. (1999). Distance-dependent models for predicting the development of mixed coniferous forests in Finland. Silva Fennica vol. 33 no. 1 article id 670.
Keywords: Norway spruce; Scots pine; competition; growth models; Monte Carlo simulation; crown models
Abstract | View details | Full text in PDF | Author Info
Distance-dependent growth models and crown models, based on extensive material, were built for Scots pine and Norway spruce growing in a mixed forest. The crown ratio was also used as a predictor in a diameter growth model to better describe the thinning reaction. The effect of crown ratio on the growth dynamics was studied in simulation examples. Monte Carlo simulation was used to correct the bias caused by nonlinear transformations of predictors and response. After thinnings the crown ratio as a predictor was found to be a clear growth-retarding factor. The growth retarding effect was stronger among pines with thinnings from below, whereas the estimated yield of spruces over rotation was slightly greater when the crown ratio was included than without it. With each type of thinning the effect of crown ratio on pine growth was almost the same, but the growth of spruces was clearly delayed when the stand was thinned from above. Simulation examples also showed that it is profitable to raise the proportion of spruces during rotation, since spruces maintain the growth more vigorous at older ages. The total yield during 90 years rotation was about 20% higher if the stand was transformed into a pure spruce stand instead of pine.
  • Vettenranta, Kivirinnanpolku 4, FIN-40950 Muurame, Finland E-mail: (email)

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