Articles containing the keyword 'taper'

Process-based tree growth models are recognized to be flexible tools which are valuable for investigating tree growth in relation to changing environment or silvicultural treatments. In the context of forestry, we address two key modelling problems: allocation of growth which determines total wood production, and distribution of wood along the stem which determines stem form and wood quality. Growth allocation and distribution are the outcome of carbon translocation, which may be described by the Munch theory. We propose a simpler gradient process to describe the carbon distribution in the phloem of conifers. This model is a reformulation of a carbon diffusion-like process proposed by Thornley in 1972. By taking into account the continuity of the cambium along the stem, we obtain a one-dimensional reaction-diffusion model which describes both growth allocation between foliage, stem and roots, and growth distribution along the stem. Distribution of wood along the stem is then regarded as an allocation process at a smaller scale. A preliminary sensitivity analysis is presented. The model predicts a strong relationship between morphology and foliage-root allocation. It also suggests how empirical data, such as stem analysis, could be used to calibrate and validate allocation rules in process-based growth models.

• Deleuze, E-mail: cd@mm.unknown
• Houllier, E-mail: fh@mm.unknown

There exists an algorithm for construction interpolating quadratic splines which preserves the monotony of the data. The taper curves formed with this algorithm, QO-splines, have many good qualities when a sufficient number of measured diameters of a tree is available. In fact, they may even be superior to certain shape preserving taper curves, MR-splines. This algorithm can be modified to preserve also the shape of the data. In the present paper, the quality of taper curves constructed by a new shape preserving from of the algorithm is examined. For this purpose, taper curves are formed for different sets of measurements and their properties are compared with the ones of QO-splines and MR-splines. The results indicate that these new shape-preserving taper curves are in general better than QO-splines and MR-splines even if the differences may be small in many cases. The superiority is the clearer the less measurements are available.

The PDF includes an abstract in Finnish.

• Lahtinen, E-mail: al@mm.unknown

A dynamic programming approach toward stem value estimation for standing Scots pine (Pinus sylvestris L.) trees was developed. The determination of the saw log value was based on the sawing pattern and on the final products composition. The combination of taper curve models and bark models providing taper curves both over bark and under bark, which constituted the basis of the optimum stem scaling. A computer program was developed to determine the optimum log sequence of the stem aiming at maximizing the value of the final products. To examine the reliability of the computation system, 445 Scots pine sample trees from 29 stands were used as a test material. The stem values of sample trees were calculated in two ways: 1) with 12 measured diameters, and 2) with 12 estimated diameters derived from measured tree characteristics. In both cases the values of the intermediate diameters were calculated via cubic spline interpolation.

The PDF includes a summary in Finnish.

• Luo, E-mail: fl@mm.unknown

In the original set of equations derived by regression analysis, relative-height diameters (endogenous variables) are presented as nonlinear functions of the other relative-height diameters and of the height of the tree (an exogenous variable). Any of the original equations can be replaced by an interpolation formula which links a measured diameter to the four closest relative-height diameters. The solution of the simultaneous equation model yields 10 relative-height diameters. Intermediate values are obtained to avoid biases due to the nonlinearity of the simultaneous model equations.

The PDF includes a summary in Finnish.

• Kilkki, E-mail: pk@mm.unknown
• Varmola, E-mail: mv@mm.unknown

A simultaneous equation model to determine taper curve for Scots pine is presented. The diameters at relative heights are endogenous variables and height an exogenous variable. Any equations may be substituted by the measured value of diameter. Solution of the system of equations yields 11 diameters at relative heights. Intermediate values are obtained by interpolation. Interpolation allows the use of diameters measured at absolute heights, too.

The PDF includes a summary in Finnish.

• Kilkki, E-mail: pk@mm.unknown
• Saramäki, E-mail: ms@mm.unknown
• Varmola, E-mail: mv@mm.unknown

In this paper the use of butt and top diameters of pulpwood bolts for volume determination is analysed. The study is based on the taper data of Scots pine (Pinus sylvestris L.) stems. According to the results, the use of the mean of butt and top diameters in the volume determination under Finnish condition causes a positive error in small stems. If the stems are so big that the butt portions of the stems can be used as saw logs, the remaining top bolts, used as pulpwood, are estimated to be smaller than they are in reality. Accordingly, there is a negative error.

The PDF includes a summary in English.

• Kärkkäinen, E-mail: mk@mm.unknown

The stem form influences the value and volume of the stem. Sample trees in homogenous mixed stand of Scots pine (Pinus sylvestris L.) and Betula sp. were measured to define the stem form of the trees, and to develop research methods. The height of butt swelling and the turning point of taper curve varies greatly. In Scots pine and Betula sp. it was typically between the 2/10 and 3/10 height of the tree. Consequently, the theoretical normal curves describing stem form, where the turning point of taper curve is situated under the breast height diameter, are not entirely generally applicable. There was a correlation between the base curve and the form of actual taper curve of the stem. The form of the top of the stem depends on the structure and dimensions of the crown. The most reliable measuring point to define taper curve would be a diameter that is above butt swelling, near the turning point of the taper curve. Length of the crown can be used to deduce the form of the top of the stem. According to the study, the volume tables could be based on diameter on breast height, slenderness of the stem (D_0,25h:h) and length of the crown. Age of the tree and position in the stand influence stem form, but the forest site type seemed not to have clear effect on the stem form.

The PDF includes a summary in German.

• Lappi-Seppälä, E-mail: ml@mm.unknown

A monotony preserving taper curve can be constructed by using a quadratic spline. An algorithm is presented which is suitable for this purpose. It is used to the construction of a taper curve when several measured diameters of a tree are available. These taper curves are formed for different sets of measurements and their properties are evaluated. It appears that the monotony preserving quadratic spline can give a better taper curve than the usual cubic spline.

The PDF includes a summary in Finnish.

• Lahtinen, E-mail: al@mm.unknown

Taper curve models based on simultaneous equations were derived. The data consisted of 492 Scots pines (Pinus sylvestris L.) from Southern Finland. Two systems of simultaneous equations were constructed, one without the crown ratio and the other with the crown ratio as an exogenous variable. The endogenous variables consisted of 24 relative-height diameters and the height of the tree. The parameters of the model were derived by the ordinary least squares method.

In most applications, the height of the tree was exogenised. The logarithmically linear relationships between the relative-height diameters were utilized in the solution algorithm. The algorithm included both standard matrix operations and an iterative part in which the taper curve was fitted to any measured diameters by the natural cubic spline interpolation formula.

The models were applied to the derivation of taper curves, stem volumes, timber assortment percentages, and stem values. An experiment was also made to derive diameter and height increments from the taper curve model.

The reliability of the models was tested on the original data.

The PDF includes a summary in Finnish.

• Kilkki, E-mail: pk@mm.unknown
• Varmola, E-mail: mv@mm.unknown

The diameter at any point on a stem and tree volume are some of the most important types of information used in forest management planning. One of the methods to predict the diameter at any point on a stem is to develop taper models. Black locust (Robinia pseudoacacia L.) occurs in almost all forests in Poland, with the largest concentration in the western part of the country. Using empirical data obtained from 13 black locust stands (48 felled trees), seven taper models with different numbers of estimated parameters were analysed for section diameters both over and under bark using fixed and mixed-effects modelling approaches. Assuming a lack of additional measurements, the best fitted taper models were used for the prediction of over bark volume using both methods. The predicted volume was compared with the results from different volume equations available for black locust. The variable-form taper model with eight estimated parameters fitted the data the best. The lowest root mean square error for volume prediction was achieved for the elaborated fixed-effects taper model (0.0476), followed by the mixed-effects taper model (0.0489). At the same time, the difference between the volume relative errors achieved based on the taper models does not differ significantly from the results obtained using the volume equations already available for black locust (two of the three analysed).

• Bronisz, Institute of Forest Sciences, Warsaw University of Life Sciences-SGGW, Nowoursynowska 159, PL 02-776 Warsaw, Poland E-mail: karol.bronisz@wl.sggw.pl
• Zasada, Institute of Forest Sciences, Warsaw University of Life Sciences-SGGW, Nowoursynowska 159, PL 02-776 Warsaw, Poland https://orcid.org/0000-0002-4881-296X E-mail: Michal.Zasada@wl.sggw.pl

The purpose of this study was to prepare a comprehensive, computerized teak (Tectona grandis L.f) plantation yield model system that can be used to describe the forest dynamics, predict growth and yield and support forest planning and decision-making. Extensive individual tree and permanent sample plot data were used to develop tree-level volume models, taper curve models and stand-level yield models for teak plantations in Panama. Tree volume models were satisfactorily validated against independent measurement data and other published models. Tree height as input parameter improved the stem volume model marginally. Stand level yield models produced comparable harvest volumes with models published in the literature. Stand level volume product outputs were found like actual harvests with an exception that the models marginally underestimate the share of logs in very large diameter classes. The kind of comprehensive model developed in this study and implemented in an easy to use software package provides a very powerful decision support tool. Optimal forest management regimes can be found by simulating different planting densities, thinning regimes and final harvest ages. Forest practitioners can apply growth and yield models in the appropriate stand level inventory data and perform long term harvest scheduling at property level or even at an entire timberland portfolio level. Harvest schedules can be optimized using the applicable financial parameters (silviculture costs, harvesting costs, wood prices and discount rates) and constraints (market size and operational capacity).

• Seppänen, Verdas Oy, Kihlinkuja 7, FI-50600 Mikkeli, Finland E-mail: petteri@verdas.fi
• Mäkinen,  Simosol Oy. Hämeenkatu 10, FI-11100 Riihimäki, Finland E-mail: antti.makinen@simosol.fi

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

• Pérez, Ambiente Tierra S.A., Apartado 733-2250, Tres Ríos, Cartago, Costa Rica E-mail: diegoperez@costarricense.cr
• Kanninen, Center for International Forestry Research (CIFOR), Bogor, Indonesia E-mail: mk@nn.id

• Dean, CRC for Greenhouse Accounting, The Australian National University, GPO Box 475, Canberra, ACT 2601, Australia E-mail: cdean@rsbs.anu.edu.au