Modeling diameter distribution of Austrian black pine (Pinus nigra Arn.) plantations: a comparison of the Weibull frequency distribution function and percentile-based projection methods

Abstract

The main purpose of the present investigation is to examine and compare three methods for diameter distribution modeling in terms of their fitness to predict from stand level variables the diameter distributions of even-aged Austrian black pine (Pinus nigra Arn.) plantations in Bulgaria. The percentile-based projection method involving empirical probability density function based on 12 percentiles was the first method tested. A new modified approach based on the first method was proposed as the second alternative. The third method was the 2-parameter Weibull functional model in which parameters were recovered from the first and the second raw moments and the second central moment of the empirical distributions. The KolmogorovSmirnov test was applied to compare the experimental distributions with the predicted ones, and estimation of the error indices was employed to evaluate the total absolute deviation of the predicted numbers from the actual ones by diameter class. The two-parameter Weibull function proved superior to the examined alternative percentile-based projection methods and the newly proposed percentile method, without a driver percentile showed improved precision compared to the classical percentile method (with a driver percentile). The parameters of the Weibull frequency distribution function can be easily recovered from the stand quadratic mean diameter. Consequently, this diameter distribution model could be incorporated as a sub-model for stand horizontal structure characterization within the Stand Density Management Diagram modeling framework.

Estimation of Weibull function parameters for modelling tree diameter distribution using least squares and artificial neural networks methods

“…Among many PDFs, the two-parameter Weibull distribution is the most commonly chosen for modelling diameter distributions in forestry practices (Bailey & Dell, 1973;Borders, Souter, Bailey, & Ware, 1987;Calzado-Carretero & Torres-Alvarez, 2013;Cao, 2004;Gorgoso et al, 2007Gorgoso et al, , 2012Jiang & Brooks, 2009;Liu et al, 2009;McGarrigle, Kershaw, Lavigne, Weiskittel, & Ducey, 2011;Palahí et al, 2006Palahí et al, , 2007Qin, Cao, & Blouin, 2007;Stankova & Zlatanov, 2010;Zhang & Liu, 2006). The advantages of the Weibull distribution include its flexibility to fit shapes commonly found in both uneven-aged and even-aged stands and its easiness of computing probabilities without the need for numerical integration (Cao & McCarty, 2006).…”

“…The two-parameter Weibull function has therefore been reported to be the most simple and accurate for modelling diameter distributions for several tree species worldwide, such as birch (Betula alba) stands in northwestern Spain (Gorgoso, 2003;Gorgoso, Alvarez-Gonzalez, Rojo, & Grandas-Arias, 2007), sitka spruce (Picea sitchensis) and other conifer species in Great Britain (Rennolls, Geary, & Rollinson, 1985), Scots Pine (Pinus sylvestris) and Norway Spruce (Picea abies) stands in Finland (Maltamo, Puumalainen, & Paivinen, 1995), Maritime Pine (Pinus pinaster) in Spain ( Alvarez-Gonz alez, 1997), Common Birch (Betula alba) in northwestern Spain (Gorgoso, 2003;Gorgoso et al, 2007), Loblolly Pine (Pinus taeda) in USA (Bullock & Burkhart, 2005), the eight most common tree species of Catalonia in Spain (P. sylvestris, Pinus uncinata, Pinus pinea, Pinus halepensis, Pinus nigra, Abies alba, Quercus ilex, and Quercus suber) (Palahí, Pukkala, & Trasobares, 2006), Austrian Black Pine (P. nigra) in Bulgaria (Stankova & Zlatanov, 2010), and Cork Oak (Q. suber L.) in Spain (Calzado-Carretero & Torres-Alvarez, 2013).…”

A comparison of estimation methods for fitting Weibull, Johnson’s SB and beta functions to Pinus pinaster, Pinus radiate and Pinus sylvestris stands in northwest Spain

“…The method of moments (Shifley and Lentz, 1985;Nanang, 1998;Río, 1999;Stankova and Zlatanov, 2010) is based on the relationship between the parameters of the Weibull function and the first and second moments of the diameter distribution (arithmetic mean diameter and variance, respectively):…”

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

“…Such method has been previously applied (Nanang 1998, Del Río 1999, Stankova & Zlatanov 2010, Gorgoso et al 2012, and is based on the relationship between the parameters of the Weibull function and the first and second moments of the diameter distribution (mean diameter and variance, respectively -eqn. 13, eqn.…”