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Articles containing the keyword 'taper curve'

Category: Article

article id 5496, category Article
Aatos Lahtinen. (1993). On the construction of shape preserving taper curves. Silva Fennica vol. 27 no. 1 article id 5496. https://doi.org/10.14214/sf.a15657
Keywords: interpolation; monotony; shape preserving; quadratic spline; taper algorithm; taper curves
Abstract | View details | Full text in PDF | Author Info

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 (email)
article id 5187, category Article
Fuhe Luo. (1983). Determination of stem value. Silva Fennica vol. 17 no. 3 article id 5187. https://doi.org/10.14214/sf.a15170
Keywords: Pinus sylvestris; Scots pine; modelling; pulpwood; saw log; stem value; taper curve model; bark model; cubic spline interpolation
Abstract | View details | Full text in PDF | Author Info

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 (email)
article id 5047, category Article
Pekka Kilkki, Martti Varmola. (1979). A nonlinear simultaneous equation model to determine taper curve. Silva Fennica vol. 13 no. 4 article id 5047. https://doi.org/10.14214/sf.a14904
Keywords: Pinus sylvestris; diameter; mathematical models; taper curve
Abstract | View details | Full text in PDF | Author Info

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 (email)
  • Varmola, E-mail: mv@mm.unknown
article id 4995, category Article
Pekka Kilkki, Matti Saramäki, Martti Varmola. (1978). A simultaneous equation model to determine taper curve. Silva Fennica vol. 12 no. 2 article id 4995. https://doi.org/10.14214/sf.a14849
Keywords: Pinus sylvestris; Scots pine; diameter; mathematical models; taper curve
Abstract | View details | Full text in PDF | Author Info

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 (email)
  • Saramäki, E-mail: ms@mm.unknown
  • Varmola, E-mail: mv@mm.unknown

Category: Article

article id 7332, category Article
M. Lappi-Seppälä. (1936). Tutkimuksia männyn ja koivun runkomuodosta. Silva Fennica vol. 44 no. 4 article id 7332. https://doi.org/10.14214/aff.7332
English title: Studies on stem forms of Scots pine and Betula sp.
Original keywords: runkomuoto; runkokäyrä; Scots pine; tyvilaajenema
English keywords: taper curve; stem curve; butt swelling
Abstract | View details | Full text in PDF | Author Info

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 (D0,25h: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 (email)
article id 7650, category Article
Aatos Lahtinen. (1988). On the construction of monotony preserving taper curves. Silva Fennica vol. 0 no. 203 article id 7650. https://doi.org/10.14214/aff.7650
Keywords: taper curve; quadratic spline
Abstract | View details | Full text in PDF | Author Info

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 (email)
article id 7621, category Article
Pekka Kilkki, Martti Varmola. (1981). Taper curve models for Scots pine and their applications. Silva Fennica vol. 0 no. 174 article id 7621. https://doi.org/10.14214/aff.7621
Keywords: Scots pine; taper curve; methods; taper curve model
Abstract | View details | Full text in PDF | Author Info

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 (email)
  • Varmola, E-mail: mv@mm.unknown

Category: Research article

article id 10309, category Research article
Petteri Seppänen, Antti Mäkinen. (2020). Comprehensive yield model for plantation teak in Panama. Silva Fennica vol. 54 no. 5 article id 10309. https://doi.org/10.14214/sf.10309
Keywords: simulation; teak; decision support system; Tectona grandis; Panama; taper curve; volume equation; yield model
Highlights: Tree level teak stem volume models, taper model and three sets of stand level yield models were developed using large empirical datasets; 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 timber product outputs were found like actual harvests with an exception that the models marginally underestimate the share of logs in very large diameter classes.
Abstract | Full text in HTML | Full text in PDF | Author Info

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 (email)
  • Mäkinen,  Simosol Oy. Hämeenkatu 10, FI-11100 Riihimäki, Finland E-mail: antti.makinen@simosol.fi

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