*
 

iForest - Biogeosciences and Forestry

*

Height-diameter models for maritime pine in Portugal: a comparison of basic, generalized and mixed-effects models

Esteban Gómez-García (1-2)   , Teresa F Fonseca (2), Felipe Crecente-Campo (1), Luís R Almeida (2), Ulises Diéguez-Aranda (1), Shongming Huang (3), Carlos P Marques (2)

iForest - Biogeosciences and Forestry, Volume 9, Issue 1, Pages 72-78 (2015)
doi: https://doi.org/10.3832/ifor1520-008
Published: Jun 11, 2015 - Copyright © 2015 SISEF

Research Articles


Tree height is a key variable in forest monitoring studies and for forest management. However, tree height measurement is time consuming, and the recommended procedure is to use estimates from height-diameter models. Here, we compare height-diameter model forms and approaches for predicting tree height (h) as a function of tree diameter at breast height (d) and additional stand level covariates. Four model forms were evaluated: (i) basic models (which only used d as predictor variable); (ii) generalized models (which used d and stand-level predictor variables); (iii) a mixed-effects model based on the best basic model; and (iv) a mixed-effects model based on the best generalized model. Several alternatives aimed at minimizing height measurement effort were tested in terms of accuracy and applicability. From a practical point of view, the selected generalized model is recommended for estimating the height of maritime pine in Portugal. The results also show that a calibrated basic mixed model provides more accurate results than a basic model locally fitted when the number of h-d observations is limited.

  Keywords


Pinus pinaster Ait., Sampling Design, Local Model, Stand Variables, Generalized h-d Relationship, Calibration

Authors’ address

(1)
Esteban Gómez-García
Felipe Crecente-Campo
Ulises Diéguez-Aranda
Departamento de Ingeniería Agroforestal, Universidade de Santiago de Compostela, Escuela Politécnica Superior, R/ Benigno Ledo, Campus universitario, E-27002 Lugo (Spain)
(2)
Esteban Gómez-García
Teresa F Fonseca
Luís R Almeida
Carlos P Marques
Department of Forest Sciences and Landscape Architecture, University of Trás-os-Montes e Alto Douro, Apartado 1013, 5001-801 Vila Real (Portugal)
(3)
Shongming Huang
Forest Management Branch, Alberta Ministry of Sustainable Resource Development, 8th Floor, 9920-108 Street, Edmonton, Alberta T5K 2M4 (Canada)

Corresponding author

 
Esteban Gómez-García
esteban.gomez@usc.es

Citation

Gómez-García E, Fonseca TF, Crecente-Campo F, Almeida LR, Diéguez-Aranda U, Huang S, Marques CP (2015). Height-diameter models for maritime pine in Portugal: a comparison of basic, generalized and mixed-effects models. iForest 9: 72-78. - doi: 10.3832/ifor1520-008

Academic Editor

Vicente Rozas

Paper history

Received: Dec 02, 2014
Accepted: Mar 04, 2015

First online: Jun 11, 2015
Publication Date: Feb 21, 2016
Publication Time: 3.30 months

Breakdown by View Type

(Waiting for server response...)

Article Usage

Total Article Views: 41532
(from publication date up to now)

Breakdown by View Type
HTML Page Views: 34635
Abstract Page Views: 2146
PDF Downloads: 3709
Citation/Reference Downloads: 35
XML Downloads: 1007

Web Metrics
Days since publication: 3236
Overall contacts: 41532
Avg. contacts per week: 89.84

Article Citations

Article citations are based on data periodically collected from the Clarivate Web of Science web site
(last update: Feb 2023)

Total number of cites (since 2016): 20
Average cites per year: 2.50

 

Publication Metrics

by Dimensions ©

Articles citing this article

List of the papers citing this article based on CrossRef Cited-by.

 
(1)
AFN (2010)
5° Inventário Florestal Nacional. Apresentação do Relatório Final [5th National Forest Inventory. Presentation of the Final Report]. National Forestry Authority, National Coordination of Forest Management, Lisbon, Portugal, pp. 14. [in Portuguese]
Online | Gscholar
(2)
Almeida LFR (1999)
Comparação de metodologias para estimação de altura e volume em povoamentos de pinheiro bravo no Vale do T’mega [Assessment of maritime pine forest stands height and volume estimation methodologies in T’mega valley]. Graduate thesis, UTAD, Vila Real, Portugal, pp. 109. [in Portuguese]
Gscholar
(3)
Burkhart HE, Strub MR (1974)
A model for simulation of planted loblolly pine stands. In: “Growth models for tree and stand simulation” (Fries J ed). Royal College of Forestry, Stockholm, Sweden, pp. 128-135.
Gscholar
(4)
Calama R, Montero G (2004)
Interregional nonlinear height-diameter model with random coefficients for stone pine in Spain. Canadian Journal of Forest Research 34: 150-163.
CrossRef | Gscholar
(5)
Castedo Dorado F, Diéguez-Aranda U, Barrio Anta M, Sanchez Rodríguez M, Von Gadow K (2006)
A generalized height-diameter model including random components for radiata pine plantations in northwestern Spain. Forest Ecology and Management 229: 202-213.
CrossRef | Gscholar
(6)
Castedo Dorado F, Diéguez-Aranda U, Álvarez González JG (2007)
A growth model for Pinus radiata D. Don stands in north-western Spain. Annals of Forest Science 64: 453-465.
CrossRef | Gscholar
(7)
Crecente-Campo F, Tomé M, Soares P, Diéguez-Aranda U (2010)
A generalized nonlinear mixed effects height-diameter model for Eucalyptus globulus L. in northwestern Spain. Forest Ecology and Management 259: 943-952.
CrossRef | Gscholar
(8)
Curtis RO (1967)
Height-diameter and height-diameter-age equations for second-growth Douglas-fir. Forest Science 13: 365-375.
Online | Gscholar
(9)
Davidian M, Giltinan D (1995)
Nonlinear models for repeated measurement data. Chapman and Hall, New York, USA, pp. 360.
Online | Gscholar
(10)
De-Miguel S, Mehtälo L, Shater Z, Kraid B, Pukkala T (2012)
Evaluating marginal and conditional predictions of taper models in the absence of calibration data. Canadian Journal of Forest Research 42: 1383-394.
CrossRef | Gscholar
(11)
Diéguez-Aranda U, Castedo-Dorado F, Álvarez-González JG, Rodríguez-Soalleiro R (2006)
Dynamic growth model for Scots pine (Pinus sylvestris L.) plantations in Galicia (north-western Spain). Ecological Modelling 191: 225-242.
CrossRef | Gscholar
(12)
Fang Z, Bailey RL (2001)
Nonlinear mixed effects modeling for slash pine dominant height growth following intensive silvicultural treatments. Forest Science 47: 287-300.
Online | Gscholar
(13)
Fonseca TF (2004)
Modelação do crescimento, mortalidade e distribuição diamétrica, do pinhal bravo no Vale do T’mega [Modelling of growth, mortality and diameter distribution of maritime pine in the Valley of T’mega]. PhD thesis, UTAD, Vila Real, Portugal, pp. 248. [in Portuguese]
Gscholar
(14)
Fonseca TF, Parresol B, Marques C, De Coligny F (2012)
Models to implement a sustainable forest management - an overview of the ModisPinaster model. In: “Sustainable Forest Management - Current Research” (Garcia JM, Díez Casero JJ eds). InTech, Rijeka, Croatia, pp. 321-338.
CrossRef | Gscholar
(15)
García O (1994)
The state-space approach in growth modelling. Canadian Journal of Forest Research 24: 1894-1903.
CrossRef | Gscholar
(16)
Gregoire TG, Schabenberger O, Barret J (1995)
Linear modelling of irregularly spaced, unbalanced, longitudinal data from permanent-plot measurements. Canadian Journal of Forest Research 25: 137-156.
CrossRef | Gscholar
(17)
Huang S, Titus SJ, Wiens DP (1992)
Comparison of nonlinear height-diameter functions for major Alberta tree species. Canadian Journal of Forest Research 22: 1297-1304.
CrossRef | Gscholar
(18)
Huang S, Price D, Titus SJ (2000)
Development of ecoregion-based height-diameter models for white spruce in boreal forests. Forest Ecology and Management 129: 125-141.
CrossRef | Gscholar
(19)
Huang S, Meng SX, Yang Y (2009)
Prediction implications of nonlinear mixed-effects forest biometric models estimated with a generalized error structure. In: Proceedings of the “Joint Statistical Meetings, Section on Statistics and the Environment”. Washington (DC, USA), 1-6 Aug 2009. American Statistical Association, Alexandria, Virginia, USA, pp. 1174-1188.
Gscholar
(20)
Hynynen J, Ojansuu R, Hökkä H, Siipilehto J, Salminen H, Haapala P (2002)
Models for predicting stand development in MELA system. Finnish Forest Research Institute, Research Paper 835, Helsinki, Finland, pp. 116.
Gscholar
(21)
Krumland BE, Wensel LC (1988)
A generalized height-diameter equation for coastal California species. Western Journal of Applied Forestry 3: 113-115.
Online | Gscholar
(22)
Lappi J (1997)
A longitudinal analysis of height/diameter curves. Forest Science 43: 555-570.
Online | Gscholar
(23)
Lindstrom MJ, Bates DM (1990)
Nonlinear mixed-effects models for repeated measures data. Biometrics 46: 673-687.
CrossRef | Gscholar
(24)
Littell RC, Milliken GA, Stroup WW, Wolfinger RD, Schabenberger O (2006)
SAS® for mixed models (2nd edn). SAS Institute Inc., Cary, NC, USA, pp. 840.
Gscholar
(25)
Loetsch F, Zöhrer F, Haller KE (1973)
Forest Inventory (vol II). BLV Verlagsgesellschaft, München, Germany, pp. 469.
Gscholar
(26)
López Sánchez CA, Gorgoso JJ, Castedo Dorado F, Rojo A, Rodríguez R, Álvarez González JG, Sánchez F (2003)
A height-diameter model for Pinus radiata D. Don in Galicia (northwest Spain). Annals of Forest Science 60: 237-245.
CrossRef | Gscholar
(27)
Marques CP (1991)
Evaluating site quality of even-aged maritime pine stands in northern Portugal using direct and indirect methods. Forest Ecology and Management 41: 193-204.
CrossRef | Gscholar
(28)
Meng SX, Huang S, Lieffers VJ, Nunifu T, Yang Y (2008)
Wind speed and crown class influence the height-diameter relationship of lodgepole pine: nonlinear mixed effects modeling. Forest Ecology and Management 256: 570-577.
CrossRef | Gscholar
(29)
Parresol BR, Fonseca TF, Marques CP (2010)
Numerical details and SAS programs for parameter recovery of the SB distribution. Gen. Tech. Rep. SRS-122, Southern Research Station, USDA Forest Service, Asheville, NC, USA, pp. 27.
Gscholar
(30)
Peng C (2001)
Developing and validating nonlinear height-diameter models for major tree species of Ontario’s boreal forest. Northern Journal of Applied Forestry 18: 87-94.
Online | Gscholar
(31)
Pinheiro JC, Bates DM (1998)
Model building for nonlinear mixed effects model. Department of Statistics, University of Wisconsin, Madison, WI, USA, pp. 11.
Gscholar
(32)
Pretzsch H (2010)
Forest dynamics, growth and yield. Springer-Verlag, Berlin, Germany, pp. 664.
Gscholar
(33)
Russell MB, Amateis RL, Burkhart HE (2010)
Implementing regional locale and thinning response in the loblolly pine height-diameter relationship. Southern Journal of Applied Forestry 34: 21-27.
Online | Gscholar
(34)
SAS Institute Inc (2009)
SAS/STAT® 9.2 User’s Guide (2nd edn). SAS Institute Inc., Cary, NC, USA, pp. 7869.
Gscholar
(35)
Schmidt M, Kiviste A, Gadow Kv (2011)
A spatially explicit height-diameter model for Scots pine in Estonia. European Journal of Forest Research 130: 303-315.
CrossRef | Gscholar
(36)
Schwarz G (1978)
Estimating the dimension of a model. Annals of Statistics 6 (2): 461-464.
CrossRef | Gscholar
(37)
Searle SR, Cassela G, McCulloch CE (1992)
Variance components. Wiley, New York, USA, pp. 501.
Gscholar
(38)
Sharma M, Parton J (2007)
Height-diameter equations for boreal tree species in Ontario using a mixed-effects modeling approach. Forest Ecology and Management 249: 187-198.
CrossRef | Gscholar
(39)
Sharma M, Zhang SY (2004)
Height-diameter models using stand characteristics for Pinus banksiana and Picea mariana. Scandinavian Journal of Forest Research 19: 442-451.
CrossRef | Gscholar
(40)
Soares P, Tomé M (2002)
Height-diameter equation for first rotation eucalypt plantations in Portugal. Forest Ecology and Management 166: 99-109.
CrossRef | Gscholar
(41)
Temesgen H, Hann DW, Monleon VJ (2007)
Regional height-diameter equations for major tree species of southwest Oregon. Western Journal of Applied Forestry 22: 213-219.
Online | Gscholar
(42)
Tomé M (1988)
Modelação do crescimento da árvore individual em povoamentos de Eucalyptus globulus Labill. (1ª rotação) na região centro de Portugal [Modelling of the individual tree growth in Eucalyptus globulus Labill. (1st rotation) in the central region of Portugal]. PhD thesis, Instituto Superior de Agronomía, Universidade Técnica de Lisboa, Lisbon, Portugal, pp. 256. [in Portuguese]
Gscholar
(43)
Trincado G, Curtis LV, Burkhart HE (2007)
Regional mixed-effects height-diameter models for loblolly pine (Pinus taeda L.) plantations. European Journal of Forest Research 126: 253-262.
CrossRef | Gscholar
(44)
Vonesh EF, Chinchilli VM (1997)
Linear and nonlinear models for the analysis of repeated measurements. Marcel Dekker Inc, New York, USA, pp. 560.
Gscholar
(45)
Zeide B, Vanderschaaf C (2002)
The effect of density on the height-diameter relationship. In: Proceedings of the “11th Biennial Southern Silvicultural Research Conference” (Outcalt KW ed). Knoxville (TN, USA), 20-22 March 2001. Gen. Tech. Rep. SRS-48, Southern Research Station, USDA Forest Service, Asheville, NC, USA, pp. 463-466.
Online | Gscholar
(46)
Zhang SA, Burkhart HE, Amateis RL (1997)
The influence of thinning on tree height and diameter relationships in loblolly pine plantations. Southern Journal of Applied Forestry 21: 199-205.
Online | Gscholar
 

This website uses cookies to ensure you get the best experience on our website. More info