General Height-Diameter Equation Depending on the Stand Variables, for <i>Eucalyptus benthamii</i>

Téo, Saulo Jorge; Silva, Tainá Carnera da

doi:10.1590/2179-8087-FLORAM-2018-0302

Saulo Jorge Téo

Universidade do Oeste de Santa Catarina, Xanxere, SC, Brasil

http://orcid.org/0000-0003-4279-2635

Tainá Carnera da Silva

Universidade do Oeste de Santa Catarina, Xanxere, SC, Brasil

CORRESPONDENCE TOTainá Carnera da Silva Universidade do Oeste de Santa Catarina, Rua: Dirceu Giordani, 696, Jardim Tarumã, Xanrere, Santa Catarina, Brasil e-mail: tainallemos@gmail.com

Associate editor: Emanuel José Gomes de Araújo http://orcid.org/0000-0002-2301-1031

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Figure 1
Location of the municipality of Irani in the state of Santa Catarina, Brazil.

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Figure 2
Analysis of studentized residuals for different versions of Harrison et al. (1986)Harrison WC, Burk TE, Beck DE. Individual tree basal area increments and total height equations for appalachian mixed hardwoods after thinning. Southern Journal of Applied Forestry, 1986; 10 (2): 99-104. equation, with the parameters expressed as linear function of stand variables, to represent height-diameter relationship of Eucalyptus benthamii Maiden et Cambage.

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Figure 3
Analysis of studentized residuals for Michailoff, Prodan and Stoffels & Van Soest equations, with the parameters expressed as linear function of stand variables, to represent height-diameter relationship of Eucalyptus benthamii Maiden et Cambage.

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Figure 4
Age and density effect on hypsometric relationship curves, represented by Harrison et al. (1986)Harrison WC, Burk TE, Beck DE. Individual tree basal area increments and total height equations for appalachian mixed hardwoods after thinning. Southern Journal of Applied Forestry, 1986; 10 (2): 99-104. model with the parameter “c” expressed as linear function of stand variables of Eucalyptus benthamii Maiden et Cambage stands, in the municipality of Irani - SC.

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Table 1
Candidate functions to model the height-diameter relationship of Eucalyptus benthamii Maiden et Cambage, in the municipality of Irani - SC.

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Table 2
Selection statistics of the equations to represent the hypsometric relationship of Eucalyptus benthamii Maiden et Cambage.

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Table 3
Validation statistics of the height-diameter equations for Eucalyptus benthamii Maiden et Cambage, in the municipality of Irani - SC.

(Equation 1)

(Equation 2)

(Equation 3)

(Equation 4)

(Equation 5)

(Equation 6)

(Equation 7)

(Equation 8)

(Equation 9)

(Equation 10)

(Equation 11)

(Equation 12)

n	Author	Models
1	Harrison et al. (1986)Harrison WC, Burk TE, Beck DE. Individual tree basal area increments and total height equations for appalachian mixed hardwoods after thinning. Southern Journal of Applied Forestry, 1986; 10 (2): 99-104.	$h = 1, 3 + \{h_{d o m} [1 + a e^{(b h_{d o m})}] [1 - e^{(- c (\frac{d}{h_{d o m}}))}]\}$
2	Michailoff modified by Tomé (1988)	$h = 1, 3 + \{h_{d o m} e [^{a (\frac{1}{d} - \frac{1}{d_{d o m}})}]\}$
3	Prodan modified by Tomé (1988)	$h = 1, 3 + \{h_{d o m} {[1 + a h_{d o m} (\frac{1}{d} - \frac{1}{d_{d o m}})]}^{- 1}\}$
4	Stoffels & Van Soest modified by Tomé (1988)	$h = 1, 3 + [h_{d o m} {(\frac{d}{d_{d o m}})}^{a}]$

Equation	R²ad	syx %	MD	MAD
Harrison_a	0,8408	8,82	-0,0146	1,6429
Harrison_b	0,8441	8,73	-0,0155	1,6222
Harrison_c	0,8408	8,82	-0,0125	1,6586
Michailoff_a	0,3697	17,55	2,1461	3,5167
Prodan_a	0,3818	17,38	2,1476	3,4282
Stoffels & Van Soest_a	0,3342	18,04	2,1529	3,6014

Equation	EM	MDPRESS	MADPRESS	P5	P95
Harrison_a	0,8633	-0,0058	1,5225	-3,45	3,19
Harrison_b	0,8755	-0,0071	1,4809	-3,02	2,99
Harrison_c	0,8940	-0,0081	1,3470	-2,78	2,50
Michailoff_a	0,4359	1,9059	3,2425	-3,81	6,95
Prodan_a	0,4661	1,8920	3,0840	-3,27	7,00
Stoffels e Van Soest_a	0,4354	1,9155	3,1978	-3,33	7,19

[1] CORRESPONDENCE TOTainá Carnera da Silva Universidade do Oeste de Santa Catarina, Rua: Dirceu Giordani, 696, Jardim Tarumã, Xanrere, Santa Catarina, Brasil e-mail: tainallemos@gmail.com

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General Height-Diameter Equation Depending on the Stand Variables, for Eucalyptus benthamii

Abstract