Modeling extreme values for height distributions in Pinus pinaster, Pinus radiata and Eucalyptus globulus stands in northwestern Spain

doi:10.3832/ifor1447-008

Modeling extreme values for height distributions in Pinus pinaster, Pinus radiata and Eucalyptus globulus stands in northwestern Spain

J Javier Gorgoso-Varela⁽¹⁾ , J Daniel García-Villabrille⁽²⁾, Alberto Rojo-Alboreca⁽²⁾

iForest - Biogeosciences and Forestry, Volume 9, Issue 1, Pages 23-29 (2015)
doi: https://doi.org/10.3832/ifor1447-008
Published: Jul 25, 2015 - Copyright © 2015 SISEF

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Methods of estimating extreme height values can be used in forest modeling to improve fits to the marginal distribution of heights in the following bivariate diameter-height models: the S_BB Johnson’s distribution, the bivariate beta (GDB-2) distribution, the bivariate Logit-Logistic (LL-2) distribution and the power-normal (PN) distribution. Some applications to LiDAR derived data are also possible, e.g., for error calibration. Practical applications in forest management may also be considered, e.g., for pruning. In probability theory and statistics, the generalized extreme value (GEV) distribution, also known as the Fisher-Tippett distribution, is a family of continuous probability distributions that combine the Gumbel, Fréchet and Weibull distributions. This study compared the three distributions for fitting extreme values of tree heights (maximum and minimum heights), which were measured in 185 permanent research plots in Pinus pinaster Ait. stands, 97 research plots in Pinus radiata D. Don stands, and 128 research plots in Eucalyptus globulus Labill. Most of the eucalyptus stands were measured three times giving a total of 304 measurements. All plots are located in northwestern Spain. The Bias, Mean Absolute Error (MAE) and Mean Square Error (MSE) of the mean relative frequency of trees were used to evaluate the goodness-of-fit of the different functions, as well as the Kolmogorov-Smirnov statistic D_n. The Gumbel and the Weibull cumulative distribution functions (CDFs) proved suitable for describing extreme values of height distributions of the above-mentioned tree species in northwestern Spain. The Fréchet distribution was only used to model maximum values and yielded the poorest results in all cases.

Keywords

Gumbel, Fréchet, Weibull, Minimum Height, Maximum Height

Authors’ address

(1)

Departamento de Biología de Organismos y Sistemas, Universidad de Oviedo, Escuela Politécnica de Mieres, c/ Gonzalo Gutiérrez Quirós s/n, E-33600 Mieres, Asturias (Spain)

(2)

Unidade de Xestión Forestal Sostible (UXFS), Departamento de Enxeñaría Agroforestal, Universidade de Santiago de Compostela, Escola Politécnica Superior, Campus Universitario s/n, E-27002 Lugo, Galicia (Spain)

Corresponding author

J Javier Gorgoso-Varela
gorgoso@uniovi.es

Citation

Gorgoso-Varela JJ, García-Villabrille JD, Rojo-Alboreca A (2015). Modeling extreme values for height distributions in Pinus pinaster, Pinus radiata and Eucalyptus globulus stands in northwestern Spain. iForest 9: 23-29. - doi: 10.3832/ifor1447-008

Academic Editor

Emanuele Lingua

Paper history

Received: Sep 18, 2014
Accepted: Mar 21, 2015

First online: Jul 25, 2015
Publication Date: Feb 21, 2016
Publication Time: 4.20 months

Open Access

This article is distributed under the terms of the Creative Commons Attribution-Non Commercial 4.0 International (https://creativecommons.org/licenses/by-nc/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

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