Articles by Timo Pukkala

The study proposes a technique which enables the computation of user-defined indices for species diversity. These indices are derived from characteristics, called diversity indicators, of inventory plots, stand compartments, and the whole forest holding. The study discusses the modifications required to be made to typical forest planning systems due to this kind of biodiversity computation. A case study illustrating the use of the indices and a modified forest planning system is provided. In the case study, forest-level species diversity index was computed from the volume of dead wood, volume of broadleaved trees, area of old forest, and between-stand variety.

At the stand level, the area of old forest was replaced by stand age, and variety was described by within-stand variety. All but one of the indicators were further partitioned into two to four sub-indicators. For example, the volume of broadleaved trees was divided into volumes of birch, aspen, willow, and other tree species. The partial contribution of an indicator to the diversity index was obtained from a sub-priority function, determined separately for each indicator. The diversity index was obtained when the partial contributions were multiplied by the weights of the corresponding indicators and then were summed. The production frontiers computed for the harvested volume and diversity indices were concave, especially for the forest-level diversity index, indicating that diversity can be maintained at satisfactory level with medium harvest levels.

• Pukkala, E-mail: tp@mm.unknown
• Kangas, E-mail: jk@mm.unknown
• Kniivilä, E-mail: mk@mm.unknown
• Tiainen, E-mail: at@mm.unknown

In the method presented in this study, a group of experts evaluate, in a pairwise manner, a set of forest areas with respect to the game species considered. On the basis of these comparisons, relative priorities of forest areas are estimated using the eigenvalue technique. Using regression analysis, a habitat suitability function is estimated in which the priority is predicted by measures already familiar in forest planning. As a case study, a habitat suitability function was estimated for black grouse (Tetrao tetrix, Lururus tetrix L.). The function is applicable in forestry planning carried out using modern planning techniques.

The PDF includes an abstract in Finnish.

• Kangas, E-mail: jk@mm.unknown
• Karsikko, E-mail: jk@mm.unknown
• Laasonen, E-mail: ll@mm.unknown
• Pukkala, E-mail: tp@mm.unknown

Yield of Cupressus lusitanica Mill. was modelled by predicting the diameter distribution of trees at given stand ages. The beta distribution was used as a theoretical distribution. The models used for the calculation of diameter distribution were based on 66 temporal sample plots with varying age, site and stand density. The growing sites of Cupressus lusitanica were divided into four classes on the basis of age and dominant height. Using the stand models developed in the study, the yield and profitability of different thinning schedules was evaluated by a simulation technique. In the simulated treatment regimes, the mean annual increment varied from 6.6 m³/ha in the poorest site class to 16.6 m³/ha in the best class with rotation lengths ranging from 25 years (best sites) to 34 years (poorest sites). With typical planting densities (1,600 trees/ha), thinnings increase the total harvest by a few percentage points and improved the profitability of plantation forestry.
The PDF includes an abstract in Finnish.

• Pohjonen, E-mail: vp@mm.unknown
• Pukkala, E-mail: tp@mm.unknown

Ten trails, one kilometre each, were evaluated by 15 persons for scenic beauty, recreational value and variety. All trails passed through commercially managed forests dominated by conifers. The trails were first evaluated by viewing computer simulations based on a series of graphical illustrations of forest landscapes, then from a slide show, and finally in the field. In the computer simulation and slide show, landscape pictures along the trail at an interval of 35–40 m were presented for 3–4 seconds. The ranks between slide show and field were slightly more similar than those between simulation and field. The mean correlation of 12 persons between the field ranking and assessment of either computer simulations or slide shows or graphics than scenic beauty or recreational value. Spearman’s rank correlations computed from median scores of a group of 12 peers were clearly better than the average of individual persons varying from 0.6 to 0.9.

The PDF includes an abstract in Finnish

• Nousiainen, E-mail: in@mm.unknown
• Pukkala, E-mail: tp@mm.unknown

The model predicts the base diameter of the thickest living branch of a tree growing in a planted or naturally regenerated even-aged stand. A mixed model type was used in which the residual variation was divided into within-stand and between-stand components. The study material consisted of 779 trees measured in 12 plots located in 20 to 35 years old Scots pine (Pinus sylvestris L.) stands (breast height age 10 to 20 years). Branch diameter was closely connected to the breast height diameter of the stem. In a stand of a certain age, competition by close neighbours slightly decreased branch diameter in a given diameter class. According to the model, the greatest difference is between trees subjected to very little competition and those subjected to normal competition. The model was used in simulated stands with varying age, density, and tree arrangement. The simulations showed that trees with rapid diameter growth at young age had thicker branches at a given breast height diameter than trees with slower diameter growth. However, a very slow growth rate did not produce trees with branches thinner than those possessing a medium growth rate.
The PDF includes an abstract in Finnish.

• Pukkala, E-mail: tp@mm.unknown
• Karsikko, E-mail: jk@mm.unknown
• Kolström, E-mail: tk@mm.unknown

An alternative approach to formulating a forestry goal programming problem is presented. First, single objective optima levels are solved. The Analytical Hierarchy Process is applied in the estimation of a priori weights of deviations from the goal target levels. The ratios of the weights can be interpreted as relative importance of the goals, respectively. The sum of the weighted deviations from all single optima levels associated with the management goals is minimized. Instead of absolute deviations, relative ones are used. A case study problem of forest management planning with several objectives, measured in different units, is analysed.

The PDF includes an abstract in Finnish.

• Kangas, E-mail: jk@mm.unknown
• Pukkala, E-mail: tp@mm.unknown

The simulation model consists of a method to generate theoretical Norway spruce (Picea abies (L.) H. Karst.) stands, and a spatial growth model to predict the growth of these stands. The stand generation procedure first predicts the tree diameters from a few stand characteristics and from tree locations. Tree age and height are predicted using spatial models. Spatial growth models were made for both diameter growth and basal area growth. Past growth was used as a predictor in one pair of models and omitted in another pair. The stand generation method and the growth models were utilized in studying the effect of tree arrangement and thinning method on the growth of a Norway spruce stand.

The PDF includes an abstract in Finnish.

• Pukkala, E-mail: tp@mm.unknown
• Kolström, E-mail: tk@mm.unknown

Linear programming was used to analyse the land use alternatives in the Debre Birhan Fuelwood Plantation area, in the central highlands of Ethiopia. The region represents a rural, high-altitude area, where the main land uses are grazing and cultivation of barley, wheat and pulses. To alleviate fuelwood shortage, large plantations of Eucalyptus globulus Labill. have been established. Livestock has traditionally used the major part of the production capacity of the sites. A decrease in the number of cattle would facilitate a considerable increase in the production of cereals, pulses, fuelwood and construction timber. The optimal share of the land for arable crops, grazing and tree plantations would be about 40, 45 and 15% respectively.

The PDF includes an abstract in Finnish.

• Pukkala, E-mail: tp@mm.unknown
• Pohjonen, E-mail: vp@mm.unknown

The paper presents a simple model of long-term forest management planning in tree plantations. The model is particularly suitable for developing countries where the research resources are limited. The management plan is prepared in two steps. First, one or several treatment schedules are simulated for each calculation unit (age class, compartment, etc.) over the selected planning period. Second, an optimal combination treatment schedules according to the selected objectives and constraints is searched by mathematical programming. The simulation of growth is based on the prediction of the diameter distribution at the desired time point. All stand characteristics are derived from this distribution. The models needed in the yield simulation can be estimated from temporary sample plots. A case study management plan for 13,000 ha of Pinus kesiya (Royle ex Gordon) plantations in Zambia is presented to demonstrate the system.

The PDF includes an abstract in Finnish.

• Pukkala, E-mail: tp@mm.unknown
• Mubita, E-mail: om@mm.unknown
• Saramäki, E-mail: js@mm.unknown

The study uses the methodology of ecological field theory to model the effect of Scots pine (Pinus sylvestris L.) seed trees on the density of tree seedlings and other plants in the field layer. The seed trees had a clear effect on the expected value of the amount and distribution of the ground vegetation. The vicinity of seed trees had an adverse effect on the growth of grasses, herbs and seedlings, while mosses were most abundant near the trees. Models based on the ecological field approach were derived to describe the effect of seed trees on the ground vegetation.

The PDF includes an abstract in Finnish.

• Kuuluvainen, E-mail: tk@mm.unknown
• Pukkala, E-mail: tp@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 study presents two methods of predicting tree dimensions in a Scots pine (Pinus sylvestris L.) stand if only the location of trees is known. The first method predicts the tree diameter from the spatial location of neighbours. In the second method the diameter distribution of a subarea is estimated from the local stand density. This distribution is then sampled to obtain diameters. In both methods the tree height is predicted with a spatial model on the basis of diameters and locations of trees. The main purpose of the presented models is to generate realistic stands for simulation studies.

The PDF includes an abstract in Finnish.

• Pukkala, E-mail: tp@mm.unknown

The economic analysis is based on computer simulations which covered a seedling rotation and three successive coppice rotations. Calculations were carried out for the four site productivity classes in Eucalyptus globulus plantations. The rotation length that maximized the land expectation value is 12–20 years for seedling rotation and 8–16 years for coppice rotations with discounting rates 2–8%. The mean wood production is over 40 m³/ha/a in the best site class and about 10 m³/ha/a in the poorest class with rotation lengths ranging from 10 to over 20 years. Thinnings increase the wood production and land expectation value by a few percentage points. In areas suitable to Eucalyptus globulus growth, the land expectation value is considerably higher in forestry than in agriculture, except in very poor areas or with very high rate of interest.

The PDF includes an abstract in Finnish.

• Pohjonen, E-mail: vp@mm.unknown
• Pukkala, E-mail: tp@mm.unknown

The study presents methods that incorporate the amenity of a forest area into the management planning. The management plan is based on treatment schedules simulated for each compartment over the 20-year planning period. The best combination of treatment schedules is selected by multi-objective optimization. The amenity is divided into two parts: (1) within-stand amenity and (2) the amenity of landscape when viewed afar (distant scene). The within-stand amenity is expressed in terms of adjective sum which is estimated from stand characteristics. The adjective sum of the whole area in a selected year can be taken as an objective or constraining variable of optimization. The assessment of the distant scene is based on computer illustrations which show the predicted temporal change of landscape according to a particular management plan.

The PDF includes a summary 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

The utilization of direct radiation was studied in five model stands of Poisson-type tree distribution and cone-shaped crowns. The radiation extinction depended on the self-shading of the crown and the shading caused by other trees. The results indicate that at low sun elevation a stand populated by very narrow-crowned trees is most effective in light interception and photosynthesis. At high sun elevation a broad-crowned canopy is best illuminated and most favourable for photosynthesis. A stand with a two-storey canopy is effective in all latitudes when the crowns are moderately narrow. In two-storey canopies the foliage of the lower storey can be better illuminated than in the lower parts of the upper storey, because of the smaller self-shading in the small crowns of the lower storey. A canopy where the crown volume is concentrated on few big crowns is less effective than a canopy consisting of many small crowns.

The PDF includes an abstract in Finnish.

• Pukkala, E-mail: tp@mm.unknown
• Kuuluvainen, E-mail: tk@mm.unknown

The study material consisted of 13 rather old Norway spruce (Picea abies (L.) H. Karst.) and 17 Scots pine (Pinus sylvestris L.) stands located in different parts of Finland. In each stand the seed crops, radial growth and amount of latewood were measured during a period of about ten years. Seed production reduces the radial growth of spruce and pine in the year of seed maturing. In Southern and Central Finland also the proportion of latewood is reduced. Seed production accounts for about 14% of the variation in radial growth of a spruce stand growing in Lapland, and 27% in other parts of Finland. In pine stands the seed crop explains 19% of the variation in radial growth in Lapland, and only 7% in the rest of Finland. In spruce stands an average seed crop reduces radial growth by 14% in Lapland and 5% in the rest of the country. An abundant seed production causes a reduction of about 20%. In southern parts of Finland, the proportion of latewood is reduced by 5% in an average seed year and by 24% in a good seed year. In pine stands an average seed crop decreases the width of annual ring by 5%, and a good seed crop by 15%. Outside Lapland, also the proportion of latewood is reduced: in an average seed year by 5%, and in a good seed year by 16%. The reduction in volume growth of spruce stands due to an average seed crop was estimated to be about 10% in Lapland, and 6% in other parts of Finland. A prolific seed production causes a reduction of 20%. In old pine stands the reduction is 5% in an average seed year, and 15% in a good seed year.

The PDF includes an abstract in English.

• Pukkala, E-mail: tp@mm.unknown

The seed crop of Norway spruce (Picea abies (L.) H. Karst.) and Scots pine (Pinus sylvestris L.) is predicted with the help of mean monthly temperatures during May–August one and two years before the flowering year. The prediction models were made separately for Lapland and for the rest of Finland. The models are based on 10-year periods of seed crop measurements and climatic data. The total number of time series was 59.

In Lapland, Norway spruce flowered abundantly and produced an abundant seed crop after warm July–August and two years after cool July–August. In other parts of Finland, warm June and July produced a good flowering year, especially if these months were cool two years before the flowering year.

In Lapland, Scots pine flowered abundantly if the whole previous growing season was warm. Elsewhere in Finland, a cool June preceded prolific flowering in the coming year if the rest of the growing season was considerably warmer than the average.

The prediction models explained 37–49 % of the variation in the size of the seed crop. The occurrence of good and poor seed years was usually predicted correctly. Using the presented models, the prediction of the seed crop is obtainable 1.5 year for Norway spruce and 2.5 year for Scots pine before the year of seed fall.

The PDF includes an abstract in English.

• Pukkala, E-mail: tp@mm.unknown

The effect of competition on the radial growth of Scots pine (Pinus sylvestris L.) was studied in three naturally regenerated stands located in North Karelia, Finland. The competition situation of an individual tree was described with various competition indices which depended on the sizes and distances from the neighbouring trees. One competition index explained about 50% of the variation in 5-year radial growth in one stand. If all stands were combined, one index explained 43.5%, two indices 48.9% and three indices 51.2% of the variation. In one stand, the best competition indices accounted for about 20% of that variation which could not be explained by tree diameter. If all three stands were combined, the best index explained 11% of the residual variation. About 40% of the variation in 5-year radial growth could not be explained by the diameter and competition indices.
The PDF includes an abstract in Finnish.

• Pukkala, E-mail: tp@mm.unknown
• Kolström, E-mail: tk@mm.unknown

In the model the regeneration process is derived into three subprocesses: birth, growth and mortality of seedlings. The main emphasis is on the birth process where the following phases are simulated: seed crop, quality of seeds, maturity of seeds, predation of seeds and germination. The parameters are based on data published in Finland. Part of the parameters are obtained directly from the investigations and part is proposed by the author. The model can be calibrated by changing parameter values. The simulation is made with the help of random numbers which have the same means as the estimates and the same distributions as the residuals of the equations used in simulation. The time step of the model is one year. The number of emerged seedlings in one year is obtained by multiplying the seed crop with the probabilities that the seed passes different phases of the birth process. Because of stochasticity the regeneration period is simulated several times. From the results it is possible to evaluate the risk and succeeding probability of the regeneration. The main drawbacks of the simulation method are the lack of empirical parameters and the difficulty of testing. The model could be further developed by including spatiality into the model.

The PDF includes an abstract in Finnish.

• Pukkala, E-mail: tp@mm.unknown

The effect of the size of seed crop, dispersal of seeds and the early development of seedlings on the density and spatial distribution of young Scots pine (Pinus sylvestris L.) stands are evaluated on the basis of theoretical models. The models include (i) number and spatial distribution of parent trees on the regeneration area, (ii) size of annual seed crop, (iii) seed dispersal from a particular parent tree, (iv) germination of the seeds (germination percentage), (v) death of ageing seedlings after the establishment process, and (vi) height growth of the seedlings.

As expected, stand density and spatial distribution varied within a large range in relation to the density of the parent trees and the distance from them. The simulations also showed that natural seedling stands can be expected to be heterogenous due to the geometry of seed dispersal, emphasizing the frequency of young and small trees. The properties of the seedling stands were, however, greatly dependent on the density of the parent trees and the length of the regeneration period.

The PDF includes an abstract in Finnish.

• Kellomäki, E-mail: sk@mm.unknown
• Hänninen, E-mail: hh@mm.unknown
• Kolström, E-mail: tk@mm.unknown
• Kotisaari, E-mail: ak@mm.unknown
• Pukkala, E-mail: tp@mm.unknown

The paper examines the needs, premises and criteria for effective public participation in tactical forest planning. A method for participatory forest planning utilizing the techniques of preference analysis, professional expertise and heuristic optimization is introduced. The techniques do not cover the whole process of participatory planning, but are applied as a tool constituting the numerical core for decision support. The complexity of multi-resource management is addressed by hierarchical decision analysis which assesses the public values, preferences and decision criteria toward the planning situation. An optimal management plan is sought using heuristic optimization. The plan can further be improved through mutual negotiations, if necessary. The use of the approach is demonstrated with an illustrative example. Its merits and challenges for participatory forest planning and decision making are discussed and a model for applying it in general forest planning context is depicted. By using the approach, valuable information can be obtained about public preferences and the effects of taking them into consideration on the choice of the combination of standwise treatment proposals for a forest area. Participatory forest planning calculations, carried out by the approach presented in the paper, can be utilized in conflict management and in developing compromises between competing interests.

• Kangas, E-mail: jk@mm.unknown
• Loikkanen, E-mail: tl@mm.unknown
• Pukkala, E-mail: tp@mm.unknown
• Pykäläinen, E-mail: jp@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

Ingrowth is an important element of stand dynamics in several silvicultural systems, especially in continuous cover forestry. Earlier predictive models for ingrowth in Finnish forests are few and not based on up-to-date statistical methods. Ingrowth is here defined as the number of trees over 1.3 m entering a plot. This study developed new ingrowth models for Scots pine (Pinus sylvestris L.), Norway spruce (Picea abies (L.) H. Karst.) and birch (Betula pendula Roth and B. pubescens Ehrh.) using data from the permanent sample plots of the Finnish national forest inventory. The data were over-dispersed compared to a Poisson process and had many zeros. Therefore, a zero-inflated negative binomial model was used. The total and species-specific stand basal areas, temperature sum and fertility class were used as predictors in the ingrowth models. Both fixed-effects and mixed-effects models were fitted. The mixed-effects model versions included random plot effects. The mixed-effects models had larger likelihoods but provided biased predictions. Also censored prediction was considered where only a certain maximum number of ingrowth trees were accepted for a plot. The models predicted most pine ingrowth in pine-dominated stands on sub-xeric and xeric sites where stand basal area was low. The predicted amount of spruce ingrowth was maximized when the basal area of spruce was 13 m² ha^–1. Increasing temperature sum increased spruce ingrowth. Predicted birch ingrowth decreased with increasing stand basal area and towards low fertility classes. An admixture of pine increased the predicted amount of spruce ingrowth.

• Lappi, University of Eastern Finland, P.O. Box 111, FI-80101 Joensuu, Finland E-mail: juha.lappi.sjk@gmail.com
• Pukkala, University of Eastern Finland, P.O. Box 111, FI-80101 Joensuu, Finland E-mail: timo.pukkala@uef.fi

Korean pine (Pinus koraiensis Siebold & Zucc.) is economically the most important tree species in northeast China. Korean pine plantations are established and managed for the production of timber and seeds. Despite the importance of the species, few models have been developed for the comparison of alternative management schedules. Model development is affected by the fact that permanent sample plots and thinning experiments have not been designed and managed for modeling purposes. The permanent sample plots include few non-thinned plots, and weak trees are removed in thinning treatments, leading to low mortality rate. Moreover, the measurement interval is irregular. This study used optimization-based modeling approach in tree-level diameter increment and survival modeling to deal with the above problems. Models for self-thinning limit were developed to alleviate the problem of underestimated mortality arising from the features of the data. In addition, improved site index and individual-tree height models were developed. The model of Lundqvist and Korf was used as the site index model and the model proposed by Schumacher as the height model. Quantile regression was used to model the maximum stand basal area and maximum number of trees as a function of mean tree diameter and site index. Tree diameter, stand basal area, basal area in larger trees and site index were used as the predictors of diameter increment and tree survival. The models developed in this study constitute a model set that is suitable for simulation and optimization studies. The models produced simulation results that correspond to measured stand development.

• Jin, Key Laboratory of Sustainable Forest Ecosystem Management - Ministry of Education, School of Forestry, Northeast Forestry University, Harbin 150040, Heilongjiang, People’s Republic of China http://orcid.org/0000-0003-2971-2709 E-mail: xingji_jin@163.com
• Pukkala, Key Laboratory of Sustainable Forest Ecosystem Management - Ministry of Education, School of Forestry, Northeast Forestry University, Harbin 150040, Heilongjiang, People’s Republic of China; University of Eastern Finland, P.O. Box 111, FI-80101 Joensuu, Finland E-mail: timo.pukkala@uef.fi
• Li, Key Laboratory of Sustainable Forest Ecosystem Management - Ministry of Education, School of Forestry, Northeast Forestry University, Harbin 150040, Heilongjiang, People’s Republic of China http://orcid.org/0000-0002-4058-769X E-mail: fengrili@126.com
• Dong, Key Laboratory of Sustainable Forest Ecosystem Management - Ministry of Education, School of Forestry, Northeast Forestry University, Harbin 150040, Heilongjiang, People’s Republic of China http://orcid.org/0000-0002-3985-9475 E-mail: ldonglihu2006@163.com

Based on data from long-term experimental fields with Norway spruce (Picea abies (L.) H. Karst.), we developed new stem taper and bark functions for Norway. Data was collected from 477 trees in stands across Norway. Three candidate functions which have shown good performance in previous studies (Kozak 02, Kozak 97 and Bi) were fitted to the data as fixed-effects models. The function with the smallest Akaike Information Criterion (AIC) was then chosen for additional analyses, fitting 1) site index-dependent and 2) age-dependent versions of the model, and 3) fitting a mixed-effects model with tree-specific random parameters. Kozak 97 was found to be the function with the smallest AIC, but all three tested taper functions resulted in fairly similar predictions of stem taper. The site index-dependent function reduced AIC and residual standard error and showed that the effect of site index on stem taper is different in small and large trees. The predictions of the age-independent and age-dependent models were very close to each other. Adding tree-specific random parameters to the model clearly reduced AIC and residual variation. However, the results suggest that the mixed-effects model should be used only when it is possible to calibrate it for each tree, otherwise the fixed-effects Kozak 97 model should be used. A model for double bark thickness was also fitted as fixed-effects Kozak 97 model. The model behaved logically, predicting larger relative but smaller absolute bark thickness for small trees.

• Pukkala, University of Eastern Finland, P.O. Box 111, FI-80101 Joensuu, Finland https://orcid.org/0000-0003-2853-9510 E-mail: timo.pukkala@uef.fi
• Holt Hanssen, Norwegian Institute of Bioeconomy Research, P.O. Box 115, NO-1431 Ås, Norway https://orcid.org/0000-0002-1715-3092 E-mail: kjersti.hanssen@nibio.no
• Andreassen, Norwegian Institute of Bioeconomy Research, P.O. Box 115, NO-1431 Ås, Norway https://orcid.org/0000-0003-4272-3744 E-mail: kjell.andreassen@nibio.no

• Pukkala, University of Eastern Finland, School of Forest Sciences, P.O. Box 111, FI-80101 Joensuu, Finland E-mail: timo.pukkala@uef.fi
• Hokkanen, Finnish Forest Research Institute, P.O. Box 18, FI-01301 Vantaa, Finland E-mail: th@nn.fi
• Nikkanen, Finnish Forest Research Institute, Finlandiantie 18, FI-58450 Punkaharju, Finland E-mail: tn@nn.fi

• Pasalodos-Tato, INIA, Instituto Nacional de Investigación y Tecnología Agraria y Alimentaria. Madrid, Spain E-mail: pasalodos.maria@inia.es
• Pukkala, University of East Finland, Joensuu, Finland E-mail: tp@nn.fi
• Rigueiro-Rodríguez, University of Santiago de Compostela, Lugo, Spain E-mail: arr@nn.es
• Fernández-Nunez, University of Santiago de Compostela, Lugo, Spain E-mail: efn@nn.es
• Mosquera-Losada, University of Santiago de Compostela, Lugo, Spain E-mail: mrml@nn.es

• Pukkala, University of Joensuu, Faculty of Forest Sciences, P.O. Box 111, FI-80101 Joensuu, Finland E-mail: timo.pukkala@joensuu.fi

• Zeng, University of Joensuu, Faculty of Forest Sciences, P. O. Box 111, FI-80101 Joensuu, Finland E-mail: hongcheng.zeng@joensuu.fi
• Pukkala, University of Joensuu, Faculty of Forest Sciences, P. O. Box 111, FI-80101 Joensuu, Finland E-mail: tp@nn.fi
• Peltola, University of Joensuu, Faculty of Forest Sciences, P. O. Box 111, FI-80101 Joensuu, Finland E-mail: hp@nn.fi
• Kellomäki, University of Joensuu, Faculty of Forest Sciences, P. O. Box 111, FI-80101 Joensuu, Finland E-mail: sk@nn.fi

• Heinonen, University of Joensuu, Faculty of Forestry, P.O. Box 111, FI-80101 Joensuu, Finland E-mail: tero.heinonen@joensuu.fi
• Kurttila, Finnish Forest Research Institute, Joensuu Research Unit, P.O. Box 68, FI-80101 Joensuu, Finland E-mail: mk@nn.fi
• Pukkala, University of Joensuu, Faculty of Forestry, P.O. Box 111, FI-80101 Joensuu, Finland E-mail: tp@nn.fi

• Palahí, Centre Tecnológic Forestal de Catalunya. Passeig Lluis Companys, 23, 08010, Barcelona, Spain E-mail: marc.palahi@ctfc.es
• Pukkala, University of Joensuu, Faculty of Forestry, P.O. Box 111, 80101 Joensuu, Finland E-mail: tp@nn.fi
• Trasobares, Foreco Technologies, Av. Diagonal 416, Estudio 2, Barcelona 08037, Spain E-mail: at@nn.es

• Pukkala, University of Joensuu, Faculty of Forestry, P.O. Box 111, FI-80101 Joensuu, Finland E-mail: timo.pukkala@joensuu.fi
• Miina, Finnish Forest Research Institute, Joensuu Research Unit, P.O. Box 68, FI-80101 Joensuu, Finland E-mail: jm@nn.fi

• Pukkala, University of Joensuu, Faculty of Forestry, P.O. BOX 111, FI-80101 Joensuu, Finland E-mail: timo.pukkala@forest.joensuu.fi
• Kurttila, Finnish Forest Research Institute, Joensuu Research Centre, P.O. Box 68, FI-80101 Joensuu, Finland E-mail: mk@nn.fi

• Heinonen, University of Joensuu, Faculty of Forestry, P.O. Box 111, FI-80101 Joensuu, Finland E-mail: th@nn.fi
• Pukkala, University of Joensuu, Faculty of Forestry, P.O. Box 111, FI-80101 Joensuu, Finland E-mail: timo.pukkala@joensuu.fi

• Ihalainen, University of Joensuu, P.O. Box 111, FIN-80101 Joensuu, Finland E-mail: marjut.ihalainen@joensuu.fi
• Salo, The Finnish Forest Research Institute, Joensuu Research Centre, P.O. Box 68, FIN-80101 Joensuu, Finland E-mail: ks@nn.fi
• Pukkala, University of Joensuu, P.O. Box 111, FIN-80101 Joensuu, Finland E-mail: tp@nn.fi

• 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

• Ihalainen, University of Joensuu, Faculty of Forestry, P.O. Box 111, FIN-80101 Joensuu, Finland E-mail: marjut.ihalainen@forest.joensuu.fi
• Pukkala, University of Joensuu, Faculty of Forestry, P.O. Box 111, FIN-80101 Joensuu, Finland E-mail: tp@nn.fi

• Kangas, Finnish Forest Research Institute, Kannus Research Station, P.O. Box 44, FIN-69101 Kannus, Finland E-mail: jyrki.kangas@metla.fi
• Leskinen, Finnish Forest Research Institute, Kannus Research Station, P.O. Box 44, FIN-69101 Kannus, Finland E-mail: pl@nn.fi
• Pukkala, University of Joensuu, Faculty of Forestry, P.O. Box 111, FIN-80101 Joensuu, Finland E-mail: tp@nn.fi

• Tahvanainen, Finnish Forest Research Institute, P.O. Box 68, FI-80101 Joensuu, Finland E-mail: timo.tahvanainen@metla.fi
• Kaartinen, University of Joensuu, Faculty of Forestry, P.O. Box 111, FI-80101 Joensuun yliopisto, Finland E-mail: kk@nn.fi
• Pukkala, University of Joensuu, Faculty of Forestry, P.O. Box 111, FI-80101 Joensuun yliopisto, Finland E-mail: tp@nn.fi
• Maltamo, University of Joensuu, Faculty of Forestry, P.O. Box 111, FI-80101 Joensuun yliopisto, Finland E-mail: mm@nn.fi