Generalized additive models as an alternative approach to the modelling of the tree height-diameter relationship
Z. Adamec, K. Drápelahttps://doi.org/10.17221/14/2015-JFSCitation:Adamec Z., Drápela K. (2015): Generalized additive models as an alternative approach to the modelling of the tree height-diameter relationship. J. For. Sci., 61: 235-243.
Generalized additive models were tested using three types of smoothing functions as an alternative for modelling the height curve. The models were produced for 23 forest stands of Norway spruce (Picea abies [L.] Karst.) in the territory of the Training Forest Enterprise Masaryk Forest Křtiny. The results show that the best evaluated and recommended for practical use at the level of forest stand was the LOESS function (locally weighted scatterplot smooting) when using a greater width of the bandwidth. Due to the frequent overfitting and the associated unrealistic behaviour of the function, smoothing by spline functions cannot be recommended for modelling the height curve at the level of forest stand. It was validated that the resulting model must be assessed not only according to the calculated quality criteria, but also depending on the graphic pattern of the model which must ensure that the height curve pattern is realistic. The quality of the resulting models (with LOESS function) was assessed to be high, mainly due to the very precise determination of model heights.Keywords:loess; nonparametric method; Norway spruce; Petterson function; smoothing function; splineReferences:
Adame Patricia, del Río Miren, Cañellas Isabel (2008): A mixed nonlinear height–diameter model for pyrenean oak (Quercus pyrenaica Willd.). Forest Ecology and Management, 256, 88-98 https://doi.org/10.1016/j.foreco.2008.04.006Aertsen W., Kint V., Muys B., Van Orshoven J. (2012): Effects of scale and scaling in predictive modelling of forest site productivity. Environmental Modelling & Software, 31: 19–27.Akaike H. (1973): Information theory and an extension of the maximum likelihood principle. In: Petrov B.N., Csaki F. (eds): Proceedings 2nd International Symposium on Information Theory, Budapest, Sept 2–8, 1973: 268–281.Albert M., Schmidt M. (2010): Climate-sensitive modelling of site-productivity relationships for Norway spruce (Picea abies (L.) Karst.) and common beech (Fagus sylvatica L.). Forest Ecology and Management, 259, 739-749 https://doi.org/10.1016/j.foreco.2009.04.039Arabatzis A.A., Burkhart H.E. (1992): An evaluation of sampling methods and model forms for estimating height-diameter relationships in loblolly pine plantations. Forest Science, 38: 192–198.Austin M.P (2002): Spatial prediction of species distribution: an interface between ecological theory and statistical modelling. Ecological Modelling, 157, 101-118 https://doi.org/10.1016/S0304-3800(02)00205-3Byun J. G., Lee W. K., Kim M., Kwak D. A., Kwak H., Park T., Byun W. H., Son Y., Choi J. K., Lee Y. J., Saborowski J., Chung D. J., Jung J. H. (): Radial growth response of Pinus densiflora and Quercus spp. to topographic and climatic factors in South Korea. Journal of Plant Ecology, 6, 380-392 https://doi.org/10.1093/jpe/rtt001Castaño-Santamaría Javier, Crecente-Campo Felipe, Fernández-Martínez Juan Luis, Barrio-Anta Marcos, Obeso José Ramón (2013): Tree height prediction approaches for uneven-aged beech forests in northwestern Spain. Forest Ecology and Management, 307, 63-73 https://doi.org/10.1016/j.foreco.2013.07.014Curtis R.O. (1967): Height-diameter and height-diameter-age equations for second-growth douglas-fir. Forest Science, 13: 365–375.Dobson A.J. (2002): Introduction to Generalized Linear Models. Boca Raton, Chapman & Hall/CRC Press: 221.Drápela K. (2011): Regresní modely a možnosti jejich využití v lesnictví. [Habilitation Thesis.] Brno, Mendel University in Brno: 235.Falk Wolfgang, Mellert Karl H. (2011): Species distribution models as a tool for forest management planning under climate change: risk evaluation of Abies alba in Bavaria. Journal of Vegetation Science, 22, 621-634 https://doi.org/10.1111/j.1654-1103.2011.01294.xFang Zixing, Bailey R.L. (1998): Height–diameter models for tropical forests on Hainan Island in southern China. Forest Ecology and Management, 110, 315-327 https://doi.org/10.1016/S0378-1127(98)00297-7Frescino Tracey S., Edwards Thomas C., Moisen Gretchen G. (2001): Modeling Spatially Explicit Forest Structural Attributes Using Generalized Additive Models. Journal of Vegetation Science, 12, 15- https://doi.org/10.2307/3236670Huang Shongming, Price Daryl, J. Titus Stephen (2000): Development of ecoregion-based height–diameter models for white spruce in boreal forests. Forest Ecology and Management, 129, 125-141 https://doi.org/10.1016/S0378-1127(99)00151-6Huang Shongming, Titus Stephen J., Wiens Douglas P. (1992): Comparison of nonlinear height–diameter functions for major Alberta tree species. Canadian Journal of Forest Research, 22, 1297-1304 https://doi.org/10.1139/x92-172Husch B., Beers T.W., Kershaw J.A. (2003): Forest Mensuration. 4th Ed. Hoboken, John Wiley & Sons: 443.Kouba Yacine, Alados Concepción L. (2012): Spatio-temporal dynamics of Quercus faginea forests in the Spanish Central Pre-Pyrenees. European Journal of Forest Research, 131, 369-379 https://doi.org/10.1007/s10342-011-0509-1Kramer H., Akça A. (1995): Leitfaden zur Waldmesslehre. Frankfurt am Main, Sauerländer J.D.: 298.Kuželka K., Marušák R. (2014): Use of nonparametric regression methods for developing a local stem form model. Journal of Forest Science, 60: 464–471.Lehmann Anthony, Overton Jacob McC, Leathwick John R (2003): GRASP: generalized regression analysis and spatial prediction. Ecological Modelling, 160, 165-183 https://doi.org/10.1016/S0304-3800(02)00354-XLu J., Zhang L. (2013): Evaluation of structure specification in linear mixed models for modeling the spatial effects in tree height-diameter relationships. Annals of Forest Research, 56: 137–148.Martin F., Flewelling J. (1998): Evaluation of tree height prediction models for stand inventory. Western Journal of Applied Forestry, 13: 109–119.Mehtätalo Lauri (2004): A longitudinal heightdiameter model for Norway spruce in Finland. Canadian Journal of Forest Research, 34, 131-140 https://doi.org/10.1139/x03-207Moisen Gretchen G., Freeman Elizabeth A., Blackard Jock A., Frescino Tracey S., Zimmermann Niklaus E., Edwards Thomas C. (2006): Predicting tree species presence and basal area in Utah: A comparison of stochastic gradient boosting, generalized additive models, and tree-based methods. Ecological Modelling, 199, 176-187 https://doi.org/10.1016/j.ecolmodel.2006.05.021Moisen Gretchen G., Frescino Tracey S. (2002): Comparing five modelling techniques for predicting forest characteristics. Ecological Modelling, 157, 209-225 https://doi.org/10.1016/S0304-3800(02)00197-7Nanos Nikos, Calama Rafael, Montero Gregorio, Gil Luis (2004): Geostatistical prediction of height/diameter models. Forest Ecology and Management, 195, 221-235 https://doi.org/10.1016/j.foreco.2004.02.031Peng C. (1999): Nonlinear height-diameter models for nine boreal forest tree species in Ontario. OFRI – Report No. 155. Sault St. Marie, Ontario, Ontario Forest Research Institute, Ontario Ministry of Natural Resources: 28.Peng C., Zhang L., Liu J. (2001): Developing and validating nonlinear height-diameter models for major tree species of Ontario’s boreal forests. Northern Journal of Applied Forestry, 18: 87–94.Petterson H. (1955): Barrskogens volymproduktion. Meddelanden från Statens skogsforskningsinstitut, 45: 1–391.Pretzsch H. (2009): Forest Dynamics, Growth and Yield: From Measurement to Model. Berlin, Heidelberg, Springer-Verlag: 664.R Development Core Team (2013): R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria. Available at http://www.R-project.org (accessed March 1, 2013).Robinson Andrew P., Lane Stephen E., Thérien Guillaume (2011): Fitting forestry models using generalized additive models: a taper model example. Canadian Journal of Forest Research, 41, 1909-1916 https://doi.org/10.1139/x11-095Schmidt Matthias, Kiviste Andres, von Gadow Klaus (2011): A spatially explicit height–diameter model for Scots pine in Estonia. European Journal of Forest Research, 130, 303-315 https://doi.org/10.1007/s10342-010-0434-8Šmelko Š. (2007): Dendrometria. Zvolen, Technická univerzita vo Zvolene: 400.Trincado G., VanderSchaaf C.L., Burkhart H.E. (2007): Regional mixed-effects height-diameter models for loblolly pine (Pinus taeda L.) plantations. European Journalof Forest Research, 126: 253–262.Van Laar A., Akça A. (2007): Forest Mensuration. Managing Forest Ecosystems. Vol. 13. Dordrecht, Springer: 383.Vargas-Larreta B., Castedo-Dorado F., Alvarez-Gonzalez J. G., Barrio-Anta M., Cruz-Cobos F. (): A generalized height-diameter model with random coefficients for uneven-aged stands in El Salto, Durango (Mexico). Forestry, 82, 445-462 https://doi.org/10.1093/forestry/cpp016Wang Yonghe, Raulier Frédéric, Ung Chhun-Huor (2005): Evaluation of spatial predictions of site index obtained by parametric and nonparametric methods—A case study of lodgepole pine productivity. Forest Ecology and Management, 214, 201-211 https://doi.org/10.1016/j.foreco.2005.04.025Wood S.N. (2006): Generalized Additive Models: An Introduction with R. Boca Raton, Chapman and Hall/CRC: 410.Yue Chaofang, Kohnle Ulrich, Kahle Hans-Peter, Klädtke Joachim (2012): Exploiting irregular measurement intervals for the analysis of growth trends of stand basal area increments: A composite model approach. Forest Ecology and Management, 263, 216-228 https://doi.org/10.1016/j.foreco.2011.09.007ZHANG L (): Cross-validation of Non-linear Growth Functions for Modelling Tree Height–Diameter Relationships. Annals of Botany, 79, 251-257 https://doi.org/10.1006/anbo.1996.0334Zhang L., Ma Z., Guo L. (): Spatially assessing model errors of four regression techniques for three types of forest stands. Forestry, 81, 209-225 https://doi.org/10.1093/forestry/cpn014Zhang L., Gove J.H. (2005): Spatial assessment of model errors from four regression techniques. Forest Science, 51: 334–346.Zuur A.F., Ieno E.N., Walker N.J., Saveliev A.A., Smith G.M. (2009): Mixed Effects Models and Extensions in Ecology with R. New York, Springer: 574.