Calibration of volume equation in stands of <i>Acacia mearnsii</i> De Wild.

Santos, Amanda Pereira; Koehler, Henrique Soares; Sanquetta, Carlos Roberto; Péllico Netto, Sylvio; Behling, Alexandre

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Artigos • Ci. Fl. 33 (1) • 2023 • https://doi.org/10.5902/1980509864859 copy

Calibration of volume equation in stands of Acacia mearnsii De Wild.

Authorship SCIMAGO INSTITUTIONS RANKINGS

ABSTRACT

The fitting of volume models by the traditional method (data obtained by means of scaling several trees), is the most used way to obtain volume equations. This method requires a lot of effort and is quite costly, therefore some alternatives have been developed to decrease the sampling of the number of trees and obtain results of estimates similar to that obtained by the traditional method, highlighting the mixed modeling applied to calibrate equations. In this work, the general objective of the research was to calibrate the Schumacher-Hall volume model by predicting random effects at the stand level and comparing it with the equations obtained using the traditional approach. The database is made up of 670 trees with ages varying from 1 to 10.75 years. The calibrations tested in the mixed model were using: (i) the largest tree of variable d for each stand; (ii) the two largest trees of variable d for each stand; (iii) the three largest trees in d for each stand; (iv) the four largest trees in d for each stand; (v) the five largest trees in d for each stand; (vi) the median tree for variable d in each stand; vii) one random tree in each stand; viii) three trees, being the smallest tree, the mean tree and the largest tree for the variable d for each stand; ix) three trees, being the mean tree, the mean tree minus two standard deviations and the mean tree plus two standard deviations for the variable d in each stand. The statistics for evaluating the equations were the coefficient of determination, the standard error of the estimate, the analysis of residuals, and the graphical analysis of the observed and estimated values. The results show that the volume equations can be calibrated at the stand level by sampling three trees: the average tree, the average tree plus two standard deviations, and the average tree minus two standard deviations. Considering that in the traditional method, 50 trees on average are measured in the forest inventory, the reduction of sampling in a new stand would be 94%.

Keywords
Tree scaling; Mixed models; BLUP; Random effect

Grupos de idades	Idade do povoamento (anos)	Idade do povoamento (qualitativa)
1	1	Muito jovem
2	1,75 – 1,83	Jovem
3	2,33 – 3,08	Média – Inicial
4	5 – 5,75	Média – Avançada
5	9,83 – 10,75	Madura

Base de dados
	Média	Mínimo	Máximo	Desvio padrão
d (cm)	9,50	0,63	23,55	4,39
h (m)	12,17	1,60	21,90	4,94
v (m³)	0,0663	0,0002	0,4773	0,0665

Idade	${\hat{β}}_{0}$	${\hat{β}}_{1}$	${\hat{β}}_{2}$	R²	Syx	Sȳx	Idade	${\hat{β}}_{0}$	${\hat{β}}_{1}$	${\hat{β}}_{2}$	R²	Syx	Sȳx
1	-8,606	1,047	0,897	0,999	0,0001	13,14	5	-10,029	1,708	1,213	0,985	0,0047	6,11
1,75	-9,661	1,836	0,960	0,997	0,0026	13,74	5,25	-9,668	1,979	0,844	0,993	0,0040	5,09
1,83	-9,423	1,794	0,894	0,999	0,0009	7,05	5,75	-10,450	1,751	1,313	0,991	0,0077	6,06
2,33	-9,736	1,836	0,990	0,980	0,0045	6,54	9,83	-9,935	1,855	1,047	0,990	0,0108	7,90
2,75	-9,507	1,911	0,863	0,997	0,0016	4,73	10,08	-9,476	2,039	0,742	0,991	0,0072	7,09
3,08	-9,533	2,049	0,724	0,993	0,0031	8,84	10,75	-9,551	1,876	0,902	0,992	0,0074	6,27
Geral				0,992	0,0055	8,18

Parcela	Idade	${\hat{β}}_{0}$	${\hat{β}}_{1}$	${\hat{β}}_{2}$	R²	Syx	Sȳx
3	10,08	-10,190	1,827	1,726	0,976	0,0132	6,67
19	5,75	-9,413	1,879	0,837	0,998	0,0019	2,83
25	2,75	-9,248	2,022	0,651	0,991	0,0022	5,69
36	1	-8,041	1,823	-0,148	0,929	0,0001	11,51
42	1,83	-8,763	1,972	0,307	0,965	0,0013	6,31
Geral					0,995	0,0054	9,67

Matrizes		598 árvores				73 árvores
D			R²	Syx	Sýx		R²	Syx	Sýx
		Tradicional	0,992	0,0055	8,18	Tradicional	0,995	0,0054	9,67
R	0,007488	Fixo	0,981	0,0087	13,00	Fixo	0,984	0,0100	17,76

Idade	Tradicional		Calibrada (1A)		Calibrada (2A)		Calibrada (3A)		Calibrada (4A)
	R²	Sýx	R²	Sýx	R²	Sýx	R²	Sýx	R²	Sýx
1	0,930	12,261	0,791	21,154	0,773	22,005	0,768	22,256	0,780	21,692
1,83	0,965	6,786	0,954	7,835	0,952	7,979	0,954	7,849	0,953	7,876
2,75	0,992	6,093	0,991	6,442	0,993	5,683	0,993	5,815	0,993	5,645
5,75	0,999	3,064	0,998	3,521	0,999	3,082	0,999	3,207	0,999	3,076
10,08	0,976	7,375	0,965	8,975	0,977	7,175	0,978	7,108	0,978	7,101
Idade	Calibrada (5A)		Calibrada (6A)		Calibrada (7A)		Calibrada(8A)		Calibrada (9A)
	R²	Sýx	R²	Sýx	R²	Sýx	R²	Sýx	R²	Sýx
1	0,815	19,906	0,840	18,488	0,868	16,814	0,842	18,377	0,848	17,996
1,83	0,952	8,031	0,879	12,689	0,943	8,682	0,948	8,312	0,950	8,163
2,75	0,993	5,748	0,993	5,612	0,992	6,142	0,992	6,239	0,993	5,570
5,75	0,999	3,071	0,998	4,184	0,998	4,115	0,999	3,126	0,998	3,784
10,08	0,977	7,207	0,975	7,491	0,978	7,110	0,970	8,230	0,978	7,085

Grupo	Idade	${\hat{β}}_{0}$	${\hat{β}}_{1}$	${\hat{β}}_{2}$	${\hat{b}}_{1}$	${\hat{b}}_{2}$	R²	Syx	Sýx
1	1	-9,440	1,802	0,911	-0,936	0,789	0,848	0,0002	18,00
2	1,83	-9,440	1,802	0,911	-0,107	0,089	0,950	0,0018	8,16
3	2,75	-9,440	1,802	0,911	0,153	-0,127	0,993	0,0022	5,57
4	5,75	-9,440	1,802	0,911	0,200	-0,016	0,998	0,0025	3,78
5	10,08	-9,440	1,802	0,911	0,200	-0,167	0,978	0,0141	7,09
Tradicional							0,995	0,0054	9,67
Fixo		-9,444	1,802	0,911			0,984	0,0100	17,76
Calibrada							0,995	0,0053	9,39

Tratamento	Grupo 1	Grupo 2	Grupo 3	Grupo 4	Grupo 5
1	0,00127 a	0,02183	0,03897 a	0,06715 a	0,19910 a
2	0,00126 a	0,02192	0,03915 a	0,06714 a	0,19936 a
3	0,00107 b	0,0226	0,03665 b	0,06554 b	0,18098 b
4	0,00119 a	0,02217	0,03841 a	0,06640 ab	0,19859 a

Universidade Federal de Santa Maria Av. Roraima, 1.000, 97105-900 Santa Maria RS Brasil, Tel. : (55 55)3220-8444 r.37, Fax: (55 55)3220-8444 r.22 - Santa Maria - RS - Brazil
E-mail: cienciaflorestal@ufsm.br

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[1] Amanda Pereira Santos

Mestre em manejo florestal