<abstract xmlns="http://www.w3.org/1999/xhtml"><p> 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</p></abstract>

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

Height-Diameter Models for Mixed-Species Forests Consisting of Spruce, Fir, and Beech

National Forest Centre, Forest Research Institute Zvolen, T.G. Masaryka 22, 960 92 Zvolen, Slovakia

Slovak Academy of Sciences, Institute of Landscape Ecology, Štefánikova 3, 814 99 Bratislava, Slovakia

Forest Research and Management Institute, Forest Research Station for Norway Spruce Silviculture, Calea Bucovinei 73 bis, 725100 Campulung Moldovenesc, Romania

Folia Forestalia Polonica

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Height-diameter models define the general relationship between the tree height and diameter at each growth stage of the forest stand. This paper presents...

Height-Diameter Models for Mixed-Species Forests Consisting of Spruce, Fir, and Beech

Published Online: Sep 25, 2014

Page range: 93 - 104

Received: Nov 11, 2013

Accepted: Mar 11, 2014

DOI: https://doi.org/10.2478/ffp-2014-0009

Keywords
height-diameter models, mixed-species forests, Abies alba, Picea abies, Fagus sylvatica

© 2014

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Height-Diameter Models for Mixed-Species Forests Consisting of Spruce, Fir, and Beech

Published Online: Sep 25, 2014

Page range: 93 - 104

Received: Nov 11, 2013

Accepted: Mar 11, 2014

DOI: https://doi.org/10.2478/ffp-2014-0009

Keywordsheight-diameter models, mixed-species forests, Abies alba, Picea abies, Fagus sylvatica

© 2014

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Keywords
height-diameter models, mixed-species forests, Abies alba, Picea abies, Fagus sylvatica