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Silva Fennica 1926-1997
Acta Forestalia Fennica

Articles by Martti Varmola

Category: Research article

article id 436, category Research article
Martti Varmola, Hannu Salminen, Mauri Timonen. (2004). Thinning response and growth trends of seeded Scots pine stands at the arctic timberline. Silva Fennica vol. 38 no. 1 article id 436.
Growth patterns and reactions of Scots pine (Pinus sylvestris L.) to thinning in extremely harsh climatic conditions were studied in two seeded Scots pine stands located on the arctic timberline. Coniferous trees usually do not form closed stands at the timberline, but occur only in scattered tree groups. The trial was established in two stands in 1985–1986 when the trees were at an age of 47 and 56 years and an average dominant height of 6.0–6.9 m. The trial was remeasured in 1998. The thinning treatments reduced the stem number for five different levels; final density of 300, 550, 800, 1050, and 1300 stems ha–1 and unthinned. The experiment had a randomised block design with four replications in each stand. The increased growing space provided by thinning accelerated diameter growth after a delay of 2–3 years. The differences between the radial growth of the thinning treatments were very clear during the whole 13- to 14-year observation period. Annual increment of the mean diameter was regularly the higher, the larger the spacing. Dominant diameter was less influenced by treatments. There were no significant differences in dominant height between any of the treatments. Both basal area and volume were regularly the greater the higher the stem number was. Even a relatively light thinning had a distinct positive effect on tree growth, i.e. not carrying out thinning resulted in a production loss of merchantable wood. According to the results, seeded stands on the arctic timberline can grow surprisingly well in favourable conditions and reach a dominant height of 12–14 m in 100 years and a mean annual increment of 1.0–1.5 m3 ha–1 y–1 over a rotation period of 130–160 years. Based on increment figures and thinning reactions, a spacing of ca. 1000 stems ha–1 can be recommended.
  • Varmola, The Finnish Forest Research Institute, Rovaniemi Research Station, P.O.Box 16, FIN-96301 Rovaniemi, Finland ORCID ID:E-mail: (email)
  • Salminen, The Finnish Forest Research Institute, Rovaniemi Research Station, P.O.Box 16, FIN-96301 Rovaniemi, Finland ORCID ID:E-mail:
  • Timonen, The Finnish Forest Research Institute, Rovaniemi Research Station, P.O.Box 16, FIN-96301 Rovaniemi, Finland ORCID ID:E-mail:

Category: Article

article id 5635, category Article
Tommi Ruha, Martti Varmola. (1997). Precommercial thinning in naturally regenerated Scots pine stands in northern Finland. Silva Fennica vol. 31 no. 4 article id 5635.

The effects of precommercial thinning on the quantity and external quality of young Scots pine (Pinus sylvestris L.) stands were examined over two 10-year periods in an experiment comprising five stands growing on sub-dry sites in Finnish Lapland, northern Finland. The thinning treatments applied resulted in stand densities of 625, 1111, 1600, 2500 and 4444 stems ha-1 and a no-treatment, unthinned plot with a randomised block lay-out of two or three replications in each stand. The dominant height of the stands varied between 4 and 8 m at the time of thinning.

The trees reacted only slightly to the increase in growing space during the first ten years following precommercial thinning. During the second 10-year period, increased growing space was reflected more clearly in diameter and volume increment. These reactions were more evident in stands thinned at an early stage. The increment of the thinnest 100–200 trees ha-1 in each treatment was poor. The results showed that when the main principle in precommercial thinning is to achieve even spacing, the remaining smallest trees fail to react positively to the increase in growing space. In other words, the target of precommercial thinning should be to concentrate the increment on the tallest trees, even though they are located in groups. The external quality of the trees in stands where precommercial thinning was carried out at a later stage was high, and the diameter of the thickest branch along the butt log remained under 20 mm. Branch diameter was greater in stands thinned at an early stage. The effect of precommercial thinning on branch diameter when comparing the extreme treatments averaged 5 mm. When the aim of stand management is to combine high quality and good yield in naturally regenerated Scots pine stands in northern Finland, precommercial thinning should not be carried out before the dominant height of 7–8 m. The intensity of precommercial thinning depends on the yield targets of the first commercial thinning. A spacing of 2,500 stems ha-1 satisfies the requirements of both high quality and adequate yield.

  • Ruha, ORCID ID:E-mail:
  • Varmola, ORCID ID:E-mail:
article id 5495, category Article
Hannu Salminen, Martti Varmola. (1993). Influence of initial spacing and planting design on the development of young Scots pine (Pinus sylvestris L.) stands. Silva Fennica vol. 27 no. 1 article id 5495.

Three Scots pine (Pinus sylvestris L.) plantations carrying 35 plots with initial spacings from 800 to 5,000 plants/ha were studied. Planting designs varied from a square to a rectangle with 5-metre row distance, the plant-to-plant distance being 0.8 metres. At current dominant height of 6 m, rectangularity had no effect on height, diameter, or volume growth of trees. Slight ovality of stems was observed in rectangular plots but the differences in the cross-wise mean diameters were very small, not over 1.1 mm in terms of plot-wise means. The diameter of the thickest living branch of a tree was linearly dependent of the dbh. The branches were clearly thicker between the planting rows at under 1,600 stems/ha stand density. A non-square planting pattern is a conceivable alternative when the line corridors suitable for mechanized silvicultural operations are preferred.
The PDF includes an abstract in Finnish.

  • Salminen, ORCID ID:E-mail:
  • Varmola, ORCID ID:E-mail:
article id 5388, category Article
Martti Varmola. (1989). Männyn istutustaimikoiden lustonleveysmalli. Silva Fennica vol. 23 no. 4 article id 5388.
English title: A model for ring width of planted Scots pine.

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, ORCID ID:E-mail:
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.

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, ORCID ID:E-mail:
  • Varmola, ORCID ID:E-mail:
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.

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, ORCID ID:E-mail:
  • Saramäki, ORCID ID:E-mail:
  • Varmola, ORCID ID:E-mail:
article id 7621, category Article
Pekka Kilkki, Martti Varmola. (1981). Taper curve models for Scots pine and their applications. Acta Forestalia Fennica no. 174 article id 7621.

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, ORCID ID:E-mail:
  • Varmola, ORCID ID:E-mail:

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