Articles containing the keyword 'growth model'

A process-oriented tree and stand growth model is extended to be applicable to the analysis of timber quality, and how it is influenced by silvicultural treatments. The tree-level model is based on the carbon balance and it incorporates the dynamics of five biomass variables as well as tree height, crown base, and breast height diameter. Allocation of carbon is based on the conservation of structural relationships, in particular, the pipe model. The pipe-model relationships are extended to the whorl level, but in order to avoid a 3-dimensional model of entire crown structure, the branch module is largely stochastic and aggregated. In model construction, a top-down hierarchy is used where at each step down, the upper level sets constraints for the lower level. Some advantages of this approach are model consistency and efficiency of calculations, but probably at the cost of reduced flexibility. The detailed structure related with the branching module is preliminary and will be improved when more data becomes available. Model parameters are identified for Scots pine (Pinus sylvestris L.) in Southern Finland, and example simulations are carried out to compare the development of quality characteristics in different stocking densities.

• Mäkelä, E-mail: am@mm.unknown
• Ikonen, E-mail: vi@mm.unknown
• Vanninen, E-mail: pv@mm.unknown

The effects of two alternative formulations of sapwood senescence on the behaviour of model LIGNUM (with parameter values adjusted for Scots pine (Pinus sylvestris L.) growing southern Finland) were studied. The two alternatives were autonomous sapwood senescence assuming a maximum age for the tree ring, and sapwood senescence that is controlled by the mortality of foliage. For the latter alternative two hypothetical further mechanisms were stipulated. All the formulations were implemented in LIGNUM. Simulations were made with all model variants for fertile and poor soil conditions using high, normal and low rates of foliage mortality. The simulation results were compared against of a data set consisting of 11 open grown Scots pine trees from southern Finland. Observations of heartwood proportion were used in this study. They show that heartwood starts to increase in trees from age of approximately 20 years onwards. The simulation results showed no differences between fertile and poor soil conditions as regards heartwood formation. Of the variants of foliage-controlled sapwood senescence the one where death of sapwood in a tree segment induces sapwood senescence in the tree parts below only slightly was the best. This and the autonomous sapwood senescence corresponded equally well to the observations. In order to make more refined conclusions additional data and simulations are necessary.

• Sievänen, E-mail: rs@mm.unknown
• Nikinmaa, E-mail: en@mm.unknown
• Perttunen, E-mail: jp@mm.unknown

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

The effect of grouping on 5-year old volume increment was studied by a simulation technique using spatial growth models estimated in Scots pine (Pinus sylvestris L.) stands in the phase of the first commercial thinning. A total of 24 model stands were regenerated by applying 12 spatial processes for two different diameter distributions. In addition to model stands, 6 different thinnings were simulated in two real stands. The clustering of trees was described with Fisher’s grouping index and by estimating the relative interception of diffuse radiation. In model stands with constant diameter distribution the correlation between the grouping index and volume increment ranged from -0.81 to -0.91. The correlation between volume increment and interception was 0.81–0.83 with one diameter distribution and 0.70 if both distributions were combined. In one thinned stand the correlation between the growth estimate and grouping index varied between -0.33 and 0.76. The correlation between interception and growth was about 0.30 in one stand and 0.72 if both stands were combined. Small irregularities do not decrease the volume production of a young Scots pine stand, but if the clustering is considerable or there are reasonably wide harvest strips, growth will be reduced by 10–20%.

The PDF includes a summary in Finnish.

• Pukkala, E-mail: tp@mm.unknown

A sensitive framework has been developed for modelling young radiata pine (Pinus radiata D. Don) survival, its growth and size class distribution, from time of planting to age 5 or 6 years. The data and analysis refer to the Central North Island region of New Zealand. The survival function is derived from a Weibull probability density function, to reflect diminishing mortality with the passage of time in young stands. An anamorphic family of trends was used, as very little between-tree competition can be expected in young stands. An exponential height function was found to fit best the lower portion of its sigmoid form. The most appropriate basal area/ha exponential function included an allometric adjustment which resulted in compatible mean height and basal area/ha models. Each of these equations successfully represented the effects of several establishment practices by making coefficients linear functions of site factors, management activities and their interactions. Height and diameter distribution modelling techniques that ensured compatibility with stand values were employed to represent the effects of management practices on crop variation. Model parameters for this research were estimated using data from site preparation experiments in the region and were tested with some independent data sets.

• Mason, E-mail: em@mm.unknown
• Whyte, E-mail: aw@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

Norway’s most common tree species, Picea abies (L.) Karst. (Norway spruce), is often infected with Heterobasidion parviporum Niemelä & Korhonen and Heterobasidion annosum (Fr.) Bref.. Because Pinus sylvestris L. (Scots pine) is less susceptible to rot, it is worth considering if converting rot-infested spruce stands to pine improves economic performance. We examined the economically optimal choice between planting Norway spruce and Scots pine for previously spruce-dominated clear-cut sites of different site indexes with initial rot levels varying from 0% to 100% of stumps on the site. While it is optimal to continue to plant Norway spruce in regions with low rot levels, shifting to Scots pine pays off when rot levels get higher. The threshold rot level for changing from Norway spruce to Scots pine increases with the site index. We present a case study demonstrating a practical method (“Precision forestry”) for determining the tree species in a stand at the pixel level when the stand is heterogeneous both in site indexes and rot levels. This method is consistent with the concept of Precision forestry, which aims to plan and execute site-specific forest management activities to improve the quality of wood products while minimising waste, increasing profits, and maintaining environmental quality. The material for the study includes data on rot levels and site indexes in 71 clear-cut stands. Compared to planting the entire stand with a single species, pixel-level optimised species selection increases the net present value in almost every stand, with average increase of approximately 6%.

• Aza, Norwegian University of Life Sciences, Department of Ecology and Natural Resource Management, PO Box 5003, NO-1432, Ås, Norway https://orcid.org/0000-0002-6416-6697 E-mail: anfe@nmbu.no
• Kallio, Norwegian University of Life Sciences, Department of Ecology and Natural Resource Management, PO Box 5003, NO-1432, Ås, Norway E-mail: maarit.kallio@nmbu.no
• Pukkala, University of Eastern Finland, P.O. Box 111, FI-80101 Joensuu, Finland E-mail: timo.pukkala@uef.fi
• Hietala, Norwegian Institute of Bioeconomy Research, PO Box 115, NO-1431 Ås, Norway E-mail: ari.hietala@nibio.no
• Gobakken, Norwegian University of Life Sciences, Department of Ecology and Natural Resource Management, PO Box 5003, NO-1432, Ås, Norway E-mail: terje.gobakken@nmbu.no
• Astrup, Norwegian Institute of Bioeconomy Research, PO Box 115, NO-1431 Ås, Norway E-mail: rasmus.astrup@nibio.no

The aim of this study was to develop individual-tree diameter and height growth models for Scots pine, Norway spruce, and pubescent birch growing in drained peatlands in Finland. Trees growing in peatland sites have growth patterns that deviate from that of trees growing in mineral soil sites. Five-year growth was explained by tree diameter, different tree and stand level competition measures, management operations and site characteristics. The drainage status of the site was influencing growth directly or in interaction with other variables. Site quality had a direct impact but was also commonly related to current site drainage status (need for ditch maintenance). Recent thinning increased growth of all species and former PK fertilization increased growth of pine and birch. Temperature sum was a significant predictor in all models and altitude for spruce and birch. The data were a subsample of the 7th National Forest Inventory (NFI) sample plots representing northern and southern Finland and followed by repeated measurements for 15–20 yrs. Growth levels predicted by the models were calibrated using NFI11 data to remove bias originating from the sample of the modelling data. The mixed linear models technique was used in model estimation. The models will be incorporated into the MOTTI stand simulator to replace the current peatlands growth models.

• Repola, Natural Resources Institute Finland (Luke), Natural resources, Eteläranta 55, FI-96300 Rovaniemi, Finland E-mail: jaakko.repola@luke.fi
• Hökkä, Natural Resources Institute Finland (Luke), Natural resources, Paavo Havaksen tie 3, FI-90014 University OF Oulu, Finland E-mail: hannu.hokka@luke.fi
• Salminen, Natural Resources Institute Finland (Luke), Natural resources, Eteläranta 55, FI-96300 Rovaniemi, Finland E-mail: hannu.salminen@luke.fi

Genetically improved Norway spruce (Picea abies (L.) Karst.) and Scots pine (Pinus sylvestris L.) are used extensively in operational Swedish forestry plantations to increase production. Depending on the genetic status of the plant material, the current estimated genetic gain in growth is in the range 10–20% for these species and this is expected to increase further in the near future. However, growth models derived solely from data relating to genetically improved material in Sweden are still lacking. In this study we investigated whether an individual tree growth model based on data from unimproved material could be used to predict the height increment in young trials of genetically improved Norway spruce and Scots pine. Data from 11 genetic experiments with large genetic variation, ranging from offspring of plus-trees selected in the late 1940s to highly improved clonal materials selected from well performing provenances were used. The data set included initial heights at the age of 7–15 years and 5-year increments for almost 2000 genetic entries and more than 20 000 trees. The evaluation indicated that the model based on unimproved trees predicted height development relatively well for genetically improved Norway spruce and there was no need to incorporate a genetic component. However, for Scots pine, the model needed to be modified. A genetic component was developed based on the genetic difference recorded within each trial, using mixed linear models and methods from quantitative genetics. By incorporating the genetic component, the prediction errors were significantly reduced for Scots pine. This study provides the first step to incorporate genetic gains into Swedish growth models and forest management planning systems.

• Egbäck, Swedish University of Agricultural Sciences, Southern Swedish Forest Research Centre, P.O. Box 49, 230 53 Alnarp, Sweden E-mail: samuel.egback@slu.se
• Nilsson, Swedish University of Agricultural Sciences, Southern Swedish Forest Research Centre, P.O. Box 49, 230 53 Alnarp, Sweden E-mail: urban.nilsson@slu.se
• Nyström, Swedish University of Agricultural Sciences, Department of Forest Resource Management, Skogsmarksgränd, 901 83 Umeå, Sweden E-mail: kenneth.nystrom@slu.se
• Högberg, Skogforsk, Ekebo, 268 90 Svalöv, Sweden E-mail: karl-anders.hogberg@skogforsk.se
• Fahlvik, Swedish University of Agricultural Sciences, Southern Swedish Forest Research Centre, P.O. Box 49, 230 53 Alnarp, Sweden E-mail: nils.fahlvik@slu.se

• 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

• Henke, Department Ecoinformatics, Biometrics & Forest Growth, University of Göttingen, 37077 Göttingen, Germany E-mail: mhenke@uni-goettingen.de
• Huckemann, Institute of Mathematical Stochastics, University of Göttingen, 37077 Göttingen, Germany E-mail: huckeman@math.uni-goettingen.de
• Kurth, Department Ecoinformatics, Biometrics & Forest Growth, University of Göttingen, 37077 Göttingen, Germany E-mail: wk@informatik.uni-goettingen.de
• Sloboda, Department Ecoinformatics, Biometrics & Forest Growth, University of Göttingen, 37077 Göttingen, Germany E-mail: bslobod@web.de

• Fox, School of Forest and Ecosystem Science, University of Melbourne, Burnley Campus, 500 Yarra Blvd, Richmond, Victoria 3121 Australia E-mail: jcfox@unimelb.edu.au
• Bi, Forest Resources Research, New South Wales Department of Primary Industries, PO Box 100, Beecroft, NSW 2119 Australia E-mail: hb@nn.au
• Ades, School of Forest and Ecosystem Science, University of Melbourne, Burnley Campus, 500 Yarra Blvd, Richmond, Victoria 3121 Australia E-mail: pka@nn.au

• Huuskonen, University of Helsinki, Dept. of Forest Ecology, P.O. Box 27, FI-00014 University of Helsinki, Finland E-mail: sh@nn.fi
• Hynynen, The Finnish Forest Research Institute, Vantaa Research Unit, P.O. Box 18, FI-01301 Vantaa, Finland E-mail: jh@nn.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

• Pukkala, University of Joensuu, Faculty of Forestry, P.O. Box 111, FIN-80101 Joensuu, Finland E-mail: timo.pukkala@joensuu.fi
• Miina, Finnish Forest Research Institute, Joensuu Research Centre, P.O. Box 68, FIN-80101 Joensuu, Finland E-mail: jm@nn.fi
• Palahí, European Forest Institute, Torikatu 34, FIN-80100 Joensuu, Finland E-mail: mp@nn.fi

• 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

• Nyström, SLU, Department of Forest Resource Management and Geomatics, SE-901 83 Umeå, Sweden E-mail: kenneth.nystrom@resgeom.slu.se
• Ståhl, SLU, Department of Forest Resource Management and Geomatics, SE-901 83 Umeå, Sweden E-mail: gs@nn.se

• 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