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

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

Category : Article

article id 7650, category Article

Aatos Lahtinen. (1988). On the construction of monotony preserving taper curves. Acta Forestalia Fennica 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

Category : Research article

article id 344, category Research article

Juha Lappi. (2006). Smooth height/age curves from stem analysis with linear programming. Silva Fennica vol. 40 no. 2 article id 344. https://doi.org/10.14214/sf.344

Keywords: height growth; spline; ring counts; second order difference; Issa

Abstract | View details | Full text in PDF | Author Info

Stem analysis data defines a range of possible heights for each age. A smooth stem/age curve is obtained with linear programming (LP) when the sum of the absolute second differences of heights is minimized subject to constraints obtained from the stem analysis. The method is analogous to cubic splines. A LP problem can include additional constraints that are based on the assumption that the crosscut is randomly located within the annual height increment. The method produces smoother height curves than Issa method which is utilizing second order differences of ring counts. It was found using simulated data that the method provides better results than earlier methods for short bolts if height growth is sufficiently regular.

Lappi, Finnish Forest Research Institute, Suonenjoki Research Unit, Juntintie 154, FI-77600 Suonenjoki, Finland E-mail: juha.lappi@metla.fi

article id 619, category Research article

Annika Kangas, Matti Maltamo. (2000). Percentile based basal area diameter distribution models for Scots pine, Norway spruce and birch species. Silva Fennica vol. 34 no. 4 article id 619. https://doi.org/10.14214/sf.619

Keywords: stand structure; diameter distribution prediction; distribution-free method; rational spline

Abstract | View details | Full text in PDF | Author Info

Information about diameter distribution is used for predicting stand total volume, timber volume and stand growth for forest management planning. Often, the diameter distribution is obtained by predicting the parameters of some probability density function, using means and sums of tree characters as predictors. However, the results have not always been satisfactory: the predicted distributions practically always have a similar shape. Also, multimodal distributions cannot be obtained. However, diameter distribution can also be predicted using distribution-free methods. In the percentile method, the diameters at certain percentiles of the distribution are predicted with models. The empirical diameter distribution function is then obtained by interpolating between the predicted diameters. In this paper, models for diameters at 12 percentiles of stand basal area are presented for Scots pine, Norway spruce and birch species. Two sets of models are estimated: a set with and one without number of stems as a predictor. Including the number of stems as a predictor improved the volume and saw timber volume estimates for all species, but the improvements were especially high for number of stems estimates obtained from the predicted distribution. The use of number of stems as predictor in models is based on the possibility of including this characteristic to measured stand variables.

Kangas, Finnish Forest Research Institute, Kannus Research Station, P.O. Box 44, FIN-69101 Kannus, Finland E-mail: annika.kangas@metla.fi
Maltamo, Finnish Forest Research Institute, Joensuu Research Station, P.O. Box 68, FIN-80101 Joensuu, Finland E-mail: mm@nn.fi

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