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, 0(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

References 27

[1]	李瑛萍, 赵玉文, 姚祺, 等. 雅鲁藏布江中游巨柏种群立地分类研究[J]. 林业资源管理, 2020(3):78-84.
[2]	郭艳荣, 吴保国, 刘洋, 等. 立地质量评价研究进展[J]. 世界林业研究, 2012,25(5):47-52.
[3]	杜雨菲. 桉树立地质量评价与适宜性研究[D]. 北京:北京林业大学, 2019.
[4]	刘东兰, 周宁, 郑小贤. 杉木人工林地位指数表简捷编制方法研究[J]. 林业资源管理, 2012(1):61-65.
[5]	Monserud R A. Height growth and site index curves for inland Douglas-fir based on stem analysis data and forest habitat type[J]. Forest Science, 1984,30(4):943-965.
[6]	王冬至, 张冬燕, 蒋凤玲, 等. 塞罕坝华北落叶松人工林地位指数模型[J]. 应用生态学报, 2015,26(11):3413-3420.
[7]	曹元帅, 孙玉军. 基于广义代数差分法的杉木人工林地位指数模型[J]. 南京林业大学学报:自然科学版, 2017,41(5):79-84.
[8]	Diéguez-Aranda U, Burkhart H E, Rodríguez-Soalleiro R. Modeling dominant height growth of radiata pine(Pinus radiata D.Don) plantations in north-western Spain[J]. Forest Ecology and Management, 2005,215(1):271-284.
[9]	相聪伟. 杉木人工林立地指数方程的研究[D]. 北京:中国林业科学研究院, 2010.
[10]	Clutter J L. Compatible growth and yield models for loblolly pine[J]. Forest Science, 1963,9(3):354-371.
[11]	倪成才, 刘春梅, 丁俊峰, 等. 差分生长模型预测误差的分析[J]. 北京林业大学学报, 2009,31(4):1-6.
[12]	倪成才, 于福平, 张玉学, 等. 差分生长模型的应用分析与研究进展[J]. 北京林业大学学报, 2010,32(4):284-292.
[13]	Bailey R L, Clutter J L. Base-age invariant polymorphic site curves[J]. Forest Science, 1974,20(2):155-159.
[14]	赵磊, 倪成才, Gordon N. 加拿大哥伦比亚省美国黄松广义代数差分型地位指数模型[J]. 林业科学, 2012,48(3):74-81.
[15]	Cieszewski C J, Bailey R L. Generalized algebraic difference approach:Theory based derivation of dynamic site equations with polymorphism and variable asymptotes[J]. Forest Science, 2000,46(1):116-126.
[16]	Cieszewski C J. Three methods of deriving advanced dynamic site equations demonstrated on inland Douglas-fir site curves[J]. Canadian Journal of Forest Research, 2001,31(1):165-173. doi: 10.1139/x00-132
[17]	Cieszewski C J. Comparing fixed-and variable-base-age site equation having single versus multiple asymptotes[J]. Forest Science, 2002,48(1):7-28.
[18]	Cieszewski C J, Mike S. Generalized algebraic difference approach derivation of dynamic site equations with polymorphism and variable asymptotes from exponential and logarithmic functions[J]. Forest Science, 2008,54(3):303-315.
[19]	牛亦龙, 董利虎, 李凤日. 基于广义代数差分法的长白落叶松人工林地位指数模型[J]. 北京林业大学学报, 2020,42(2):9-18.
[20]	Richards F J. A flexible growth function for empirical use[J]. Journal of Experimental Botany, 1959,10(2):290-300. doi: 10.1093/jxb/10.2.290
[21]	赵贝贝, 翟文元, 郝克嘉, 等. Richards生长函数在107-杨树速生丰产林生长预测上的应用[J]. 山东农业大学学报:自然科学版, 2010,41(1):23-26.
[22]	魏晓慧, 孙玉军, 马炜. 基于Richards方程的杉木树高生长模型[J]. 浙江农林大学学报, 2012,29(5):661-666.
[23]	童佳鸣, 何强, 苏小飞, 等. 金佛山方竹不同冠层枝叶生长动态模拟模型[J]. 江西农业大学学报, 2019,41(6):1130-1141.
[24]	董晨, 吴保国, 张瀚. 基于冠幅的杉木人工林胸径和树高参数化预估模型[J]. 北京林业大学学报, 2016,38(3):55-63.
[25]	范阔, 苏晓慧, 张艺超, 等. 运用改进Richards模型预测马尾松人工林立地指数—以广西高峰林场为例[J]. 东北林业大学学报, 2019,47(9):48-51.
[26]	李斌成, 杜超群, 袁慧, 等. 基于理论模型及其差分方程的湖北省杉木立地指数表研制[J]. 中南林业科技大学学报, 2019,39(7):56-64.
[27]	段爱国, 张建国. 杉木人工林优势高生长模拟及多形地位指数方程[J]. 林业科学, 2004(6):13-19. doi: 10.11707/j.1001-7488.20040603

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