Height-diameter models define the general relationship between the tree height and diameter at each growth stage of the forest stand. This paper presents generalized height-diameter models for mixed-species forest stands consisting of Norway spruce (Picea abies Karst.), Silver fir (Abies alba L.), and European beech (Fagus sylvatica L.) from Slovakia. The models were derived using two growth functions from the exponential family: the two-parameter Michailoff and three-parameter Korf functions. Generalized height-diameter functions must normally be constrained to pass through the mean stand diameter and height, and then the final growth model has only one or two parameters to be estimated. These "free" parameters are then expressed over the quadratic mean diameter, height and stand age and the final mathematical form of the model is obtained. The study material included 50 long-term experimental plots located in the Western Carpathians. The plots were established 40-50 years ago and have been repeatedly measured at 5 to 10-year intervals. The dataset includes 7,950 height measurements of spruce, 21,661 of fir and 5,794 of beech. As many as 9 regression models were derived for each species. Although the "goodness of fit" of all models showed that they were generally well suited for the data, the best results were obtained for silver fir. The coefficient of determination ranged from 0.946 to 0.948, RMSE (m) was in the interval 1.94-1.97 and the bias (m) was -0.031 to 0.063. Although slightly imprecise parameter estimation was established for spruce, the estimations of the regression parameters obtained for beech were quite less precise. The coefficient of determination for beech was 0.854-0.860, RMSE (m) 2.67-2.72, and the bias (m) ranged from -0.144 to -0.056. The majority of models using Korf's formula produced slightly better estimations than Michailoff's, and it proved immaterial which estimated parameter was fixed and which parameters were free.

The influence of tree species on basic density of wood, bark and small-wood was investigated here. Experimental material was obtained from 73 trees of 7 tree species, namely alder (Alnus glutinosa (L.) Gaertn.), beech (Fagus sylvatica L.), birch (Betula pendula Roth.), hornbeam (Carpinus betulus L.), Black locust (Robinia pseudoacacia L.), Sessile oak (Quercus petraea (Matt.) Liebl.) and Turkey oak (Quercus cerris L.) from the territory of Slovakia. Wood and bark samples were taken from discs cut from three trunk sections and from small-wood and branch parts coming from tree crowns. The volume of green samples was measured in graduated cylinders with a precision of 1 ml; a dry matter was measured with a precision of 0.01 g. The statistically significant effect has been shown in tree species, biomass fractions and locations on the tree. The average basic density of all species varies from 440 to 650 kg . m -3 for wood, for bark it is 380-670 kg . m -3 and for small-wood outside bark it reaches 490-650 kg . m -3 . Alder and Black locust tree species have the lowest and highest wood density, Black locust and Turkey oak of bark and alder and Turkey oak of small-wood.

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In wood production not only the quantity is important but also the quality of wood is of increasingly growing importance. Higher-quality wood has the higher utility value and price. Relatively great attention is paid to these issues in Slovakia. In the past models of tree and stand assortment tables were constructed for 8 commercially important tree species, namely for spruce, fir, pine, oak and beech (Petráš, Nociar 1990, 1991, and for larch, hornbeam and birch (Mecko et al. 1993). Together with the models of yield tables (Halaj et al. 1987; Halaj, Petráš 1998) they were also used for the construction of assortment yield tables (Petráš et al. 1996), and together with the prices of wood and costs of wood logging also for the construction of the models of value production (Halaj et al. 1990). After a short break research on the production of poplar clones Robusta and I-214 continued, Mecko (2001, 2005) elaborated the volume production of these clones in the form of models of yield tables. The research of these authors on the production quality started by the construction of tree assortment tables (Petráš et al. 2007) and continued by constructing stand assortment tables.The aim of the paper is the construction of the models of stand assortment tables for poplar clones Robusta and I-214. MATERIALS AND METHODSWe used the methodology of simulation by means of partial models, namely the following models: -Tree assortments tables, -Uniform height and volume curves, -Probability density function of diameters. Models of tree assortment tablesModels of Petráš et al. (2007) were used. They give the proportions of assortments in percent (quality and diameter classes of logs) in dependence on tree diameter d, stem quality qua and damage to stem dam according to the relation: The results obtained in research on the quality of raw timber by means of the structure of assortments for the stands of poplar clones Robusta and I-214 are presented in the paper. Models for an estimation of the structure of basic assortments of poplar stands were constructed separately for each clone in dependence on mean diameter, quality of stems, and damage to stems in the stand. The clone Robusta has higher proportions of higher-quality assortments than the clone I-214. The accuracy of models was determined on empirical material. It was confirmed by statistical tests that the models did not have a systematic error. The relative root mean-square error for main assortments of the clone I-214 is 15-27% and Robusta 13-24%.

Citation: Jamnická G, Petrášová V, Petráš R, Mecko J, Oszlányi J, 2014. Energy production in poplar clones and their energy use efficiency. iForest 7: 150-155 [online 2014-01-23] URL:Poplar clones "Robusta" and "I-214" (Populus × euramericana) are characterized by fast growth and high quality biomass production. In this investigation the calorific value of these clones was determined, and modeling of the calorific production of a whole poplar clone stands in relation to stand age and site index was performed. Eleven trees were sampled in four sites in the eastern and seven in the western part of Slovakia. Samples of bark, wood and smallwood with bark were excised from three points along the stem and from two parts of the crown. No significant differences were observed between clones with regard to either the biomass fraction or the excising location. The average calorific capacity of all biomass fractions was approximately 6.86-8.73 GJ m -3 , with the lowest bark values obtained for samples excised from the stem base. The mean annual calorific energy production for site index 20-40 was 320-380 GJ ha -1 y -1 after 17-26 years since plantation, with the clone "I-214" culminating 1-2 years earlier than "Robusta". Energy use efficiency of these clones was estimated approximately 0.4-1.6% of the incoming solar radiation.