Construction of Difference Site Index Model for Larix Principis-rupprechtii Plantation

doi:10.13466/j.cnki.lyzygl.2021.01.020

Abstract

Abstract:

In the paper,the Larix principis-rupprechtii plantation in Sumu Mountain forest farm of Yin Mountain was taken as the research object.Based on the data of 43 analytic trees,the difference site index models were constructed based on Richards equation.The results showed that the difference model fitting results were significantly better than the basic model,with R² above 0.96,RMSE between 0.86 and 0.96,and MAE below 0.42.The model derived by ADA method,the fitting result with b or c as free parameter is better than that with a as free parameter.In the model derived by GADA method,it is more reasonable to assume a linear relationship between the free a parameter and the variable X₀.Through such methods as statistical analysis,residual analysis and site index curve cluster comparison,by applying GADA method,the difference model derived by free parameters $a=e^{X_{0}}$,$c=c_{1}+c_{2} X_{0}$ is the best model,which meets the requirements of biology and statistics.Higher site index has the greater extreme value of tree height and annual growth of dominant trees,and the earlier the curve reaches the inflection point.The results can provide basis for the scientific evaluation of site quality of Larix principis-rupprechtii plantation.

Key words: site index model, Richards equation, algebraic difference approach, generalized algebraic difference approach, Larix principis-rupprechtii plantation

CLC Number:

S758.5

WANG Zhibo, JI Meng, LI Yongle, LI Yinxiang, MA Shiming, ZHANG Haidong. Construction of Difference Site Index Model for Larix Principis-rupprechtii Plantation[J]. FOREST RESOURCES WANAGEMENT, 2021, (1): 156-163.

Figures/Tables 7

Tab.1

Tab.2

The ADA equations

自由参数	X的解	差分方程	编号
$a$	$X = h 1 (1 - e - b t 1) c$	$h 2 = h 1 (1 - e - b t 2 1 - e - b t 1) c$	E1
$b$	$X = ln (1 - (h 1 a) 1 c) t 1$	$h 2 = a (1 - (1 - (h 1 a) 1 c) t 2 t 1) c$	E2
$c$	$X = ln (h 1 a) ln (1 - e - b t 1)$	$h 2 = a (h 1 a) ln (1 - e - b t 2) ln (1 - e - b t 1)$	E3

Tab.2

Tab.3

The GADA equations

自由参数	$X 0$ 的解	差分方程	编号
$a = e X 0$	$X 0 = ln h 1 - c 1 ln (1 - e - b t 1) 1 + c 2 ln (1 - e - b t 1)$	$h 2 = e X 0 (1 - e - b t 2) (c 1 + c 2 X 0)$	E4
$c = c 1 + c 2 X 0$		$h 2 = e X 0 (1 - e - b t 2) (c 1 + c 2 X 0)$	E4
$a = e X 0$	$X 0 = 12 (F + F 2 - 4 c 2 ln (1 - e - b t 1))$	$h 2 = e X 0 (1 - e - b t 2) (c 1 + c 2 X 0)$	E5
$c = c 1 + c 2 / X 0$	$F = ln h 1 - c 1 ln (1 - e - b t 1)$	$h 2 = e X 0 (1 - e - b t 2) (c 1 + c 2 X 0)$	E5

Tab.3

Tab.4

Parameter estimates and relevant statistical indicators of difference site index models for Larix principis-rupprechtii plantation

模型	参数	估计值	标准误	P值	R²	RMSE	MAE
E0	$a$	38.9943	12.5491	0.0021	0.8915	1.7353	0.7726
	$b$	0.0161	0.0080	0.0440
	$c$	1.1550	0.1261	<0.0001
E1	$b$	0.0330	0.0037	<0.0001	0.9671	0.9530	0.4011
E1	$c$	1.3670	0.0777	<0.0001	0.9671	0.9530	0.4011
E2	$a$	27.2526	1.1755	<0.0001	0.9728	0.8669	0.3569
E2	$c$	1.3217	0.0535	<0.0001	0.9728	0.8669	0.3569
E3	$a$	40.3098	4.3032	<0.0001	0.9678	0.9436	0.4127
E3	$b$	0.0145	0.0025	<0.0001	0.9678	0.9436	0.4127
E4	$b$	0.0313	0.0034	<0.0001	0.9719	0.8832	0.3828
	$c 1$	4.6150	0.9143	<0.0001
	$c 2$	-1.002	0.2787	0.0004
E5	$b$	0.0292	0.0042	<0.0001	0.9679	0.9467	0.4041
	$c 1$	1.3024	0.0790	<0.0001
	$c 2$	0.0072	0.0034	0.0360

Tab.4

Fig.1

Fig.2

Fig.3

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变量	全部数据(n=43)				建模数据(n=32)				检验数据(n=11)
变量	最大值	最小值	均值	标准差	最大值	最小值	均值	标准差	最大值	最小值	均值	标准差
林龄/a	49	16	35.05	9.80	49	16	35.31	9.93	47	19	34.27	9.86
胸径/cm	29.70	10.70	20.43	4.89	29.70	10.70	20.20	5.01	28.00	14.30	21.09	4.82
树高/m	22.90	7.60	14.92	4.32	22.90	7.60	14.83	4.58	21.00	10.50	15.20	3.69