大兴安岭白桦削度方程

doi:10.11707/j.1001-7488.20201109

Abstract

Abstract:

Objective: Stem taper functions are important components in forest management and planning systems. Currently,there is no taper function for Betula platyphylla in northeast China,therefore,it is necessary to develop the taper function for this species. Eight commonly used taper functions in forestry were compared to evaluate which would provide a better prediction for diameter at a specific height and total volume for B. platyphylla in northeast China. Method: The data used in this study were collected from 253 destructively felled sample trees with 3 795 diameter/height measurements in the northwest of the northern slope of Yilehuli Mountains of northeast China. A first-order continuous autoregressive error structure was used to model the error term and account for autocorrelation. Multicollinearity was also evaluated with condition number. Coefficient of determination (R²),mean absolute bias (MAB),root mean square error (RMSE) and mean percentage of bias (MPB) were selected as evaluation criteria of models. Comparison of the taper models was carried out using goodness-of-fit statistics,box plots of diameter and volume residual distributions and validation statistics. Result: 1) In terms of model fitting statistics, the models of Kozak (2004)-2, Fang et al. (2000) and Max et al. (1976) were the top three models. The model of Sharma et al. (2001) showed the poorest performance. 2) Based on the box plots of diameter and volume residuals, the models of Bi (2000), Max et al. (1976), Kozak (2004)-2 and Fang et al. (2000) were more accurate in diameter and volume prediction with smaller errors and almost similar residual diameter and volume distribution. The models of Sharma et al. (2001), Sharma et al. (2004), Sharma et al. (2009) and Kozak (2004)-1 had non homogeneous distribution of the diameter residuals along different sections of the stem. 3) Model validation also confirmed that Max et al. (1976), Kozak (2004)-2 and Fang et al. (2000) showed better performances. In general, the model of Kozak (2004)-2 showed consistent performances and was superior to other taper models in predicting diameter and volume. Conclusion: Based on the evaluation statistics of fitting and validation,graphic analysis and condition number,the model of Kozak (2004)-2 was recommended for estimating diameter at a specific height,total volume and merchantable volume for B. platyphylla in northeast China.

Key words: Betula platyphylla, taper, volume, autocorrelation, multicollinearity

CLC Number:

S757

Muhammad Khurram Shahzad,Amna Hussain,Pei He,Lichun Jiang. Stem Taper Functions for Betula platyphylla in Daxing'anling[J]. Scientia Silvae Sinicae, 2020, 56(11): 87-96.

Figures/Tables 8

Model	Expression
Bi(2000)	$ d=D\left(\frac{\ln \sin \left(\frac{\pi}{2} q\right)}{\ln \sin \left(\frac{\pi}{2} t\right)}\right)^{b_{0}+b_{1} \sin \left(\frac{\pi}{2} q\right)+b_{2} \cos \left(\frac{3 \pi}{2} q\right)+b_{3} \sin \left(\frac{\pi}{2} q\right) / q+b_{4} D+b_{5} q \sqrt{D}+b_{6} q \sqrt{H}}$
Sharma et al. (2001)	${d = \sqrt {{D^2}{{\left({\frac{h}{{1.3}}} \right)}^{2 - {b_1}}}X} } $
Sharma et al.(2004)	$ {d = D\sqrt {{b_0}{{\left({\frac{h}{{1.3}}} \right)}^{2 - \left({{b_1} + {b_2}z + {b_3}{z^2}} \right)}}\left({\frac{{H - h}}{{H - 1.3}}} \right)} }$
Sharma et al.(2009)	$ {d = D\left[ {{b_0}\left({\frac{{H - h}}{{H - 1.3}}} \right){{\left({\frac{h}{{1.3}}} \right)}^{{b_1} + {b_2}z + {b_3}{z^2}}}} \right]}$
Max et al.(1976)	$d=\sqrt{D^{2}\left[b_{1}(q-1)+b_{2}\left(q^{2}-1\right)+b_{3}\left(a_{1}-q\right)^{2} I_{1}+b_{4}\left(a_{2}-q\right)^{2} I_{2}\right]} $ I₁=1, if q ≤ a₁; 0 otherwiseI₂ =1, if q ≤ a₂; 0 otherwise
Kozak (2004)-1	$d = {b_0}{D^{{b_1}}}{\left[ {\frac{{1 - {q^{1/4}}}}{{1 - {m^{1/4}}}}} \right]^{\left[ {{b_2} + {b_3}\left({1/{{\rm{e}}^{D/H}}} \right) + {b_4}D\left({\frac{{1 - {q^{1/4}}}}{{1 - {m^{1/4}}}}} \right) + {b_5}{{\left({\frac{{1 - {q^{1/4}}}}{{1 - {m^{1/4}}}}} \right)}^{D/H}}} \right]}} $
Kozak (2004)-2	${d = {b_0}{D^b}_1{H^{{b_2}}}{{\left[ {\frac{{1 - {q^{1/3}}}}{{1 - {t^{1/3}}}}} \right]}^{\left[ {{b_3}{q^4} + {b_4}\left({1/{{\rm{e}}^{D/H}}} \right) + {b_5}{{\left({\frac{{1 - {q^{1/3}}}}{{1 - {t^{1/3}}}}} \right)}^{0.1}} + {b_6}(1/D) + {b_7}{H^{1 - {q^{1/3}}}} + {b_8}\left({\frac{{1 - {q^{1/3}}}}{{1 - {t^{1/3}}}}} \right)} \right]}}} $
Fang et al.(2000)	$ \begin{array}{l}\begin{array}{*{20}{l}}{d = {c_1}\sqrt {{H^{\left({k - {b_1}} \right)/{b_1}}}{{(1 - z)}^{(k - b)/b}}q_1^{{I_1} + {I_2}}q_2^{{I_2}}} }\\{{c_1} = \sqrt {{a_0}{D^a}1{H^a}{2^{ - k/b}}1/\left[ {{b_1}\left({{t_0} - {t_1}} \right) + {b_2}\left({{t_1} - {q_1}{t_2}} \right) + {b_3}{q_1}{t_2}} \right]} }\end{array}\\{q_1} = {\left({1 - {p_1}} \right)^{\left({{b_2} - {b_1}} \right)k/{b_1}{b_2}}}\;\;{q_2} = {\left({1 - {p_2}} \right)^{\left({{b_3} - {b_2}} \right)k/{b_2}{b_3}}}\;\;\quad {t_0} = 1\quad {t_1} = {\left({1 - {p_1}} \right)^{k/{b_1}}}\\{t_2} = {\left({1 - {p_2}} \right)^{k/{b_2}}}\quad z = h/H\;\;\quad b = b_1^{1 - \left({{I_1} + {I_2}} \right)}b_2^{{I_1}}{b_3}^{{I_2}}\quad k = 0.000078539\\{\rm{ }}{I_1} = 1, \;{\rm{if }}~~{p_2} \ge z \ge {p_1}, 0{\rm{ }}\;\;{\rm{otherwise }}\;\;\;\;\;\;{I_2} = 1, {\rm{ if }}1 \ge z \ge {p_2}, 0{\rm{ }}\;\;{\rm{otherwise}}\end{array}$

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Data	Variable	Number of trees	Mean	Min.	Max.	SD
Fitting	D	191	18.18	5.0	43.8	8.26
Fitting	H	191	17.25	7.9	24.1	3.92
Validation	D	62	16.84	5.2	36.3	8.00
Validation	H	62	15.77	8.5	22.1	3.09

Models	b₀	b₁	b₂	b₃	b₄	b₅	b₆	b₇	b₈	a₀	a₁	a₂	p₁	p₂
Bi (2000)	0.339 4 (0.061 0)	0.339 4 (0.030 1)	0.339 4 (0.009 7)	0.339 4 (0.033 8)	0.339 4 (0.000 2)	—	—
Sharma et al. (2001)		2.037 6 (0.000 7)
Sharma et al. (2004)	1.011 2 (0.004 1)	2.033 4 (0.000 7)	—	0.363 7 (0.012 3)
Sharma et al. (2009)	1.010 8 (0.002 3)	-0.013 8 (0.000 3)	0.201 6 (0.014 7)	0.046 1 (0.021 4)
Max et al. (1976)		-3.919 8 (0.361 9)	1.878 8 (0.198 5)	-1.775 3 (0.176 7)	156.608 3 (12.162 7)						0.747 3 (0.027 6)	0.064 4 (0.002 4)
Kozak (2004)-1	1.353 7 (0.027 5)	0.945 8 (0.006 7)	0.346 9 (0.012 2)	0.357 4 (0.040 5)	0.008 3 (0.000 8)	-0.697 2 (0.062 3)
Kozak (2004)-2	0.892 2 (0.034 6)	0.967 2 (0.007 7)	0.076 6 (0.017 9)	0.432 4 (0.021 6)	0.154 0 (0.035 0)	0.365 9 (0.014 6)	—	0.011 8 (0.001 9)	-0.086 3 (0.025 3)
Fang et al. (2000)		6.62E-06 (1.8E-7)	0.000 035 (2.7E-7)	0.000 030 (6.0E-7)						0.000 048 (3.4E-6)	1.950 1 (0.015 1)	0.970 3 (0.034 4)	0.047 6 (0.001 3)	0.613 2 (0.034 1)

Models	RMSE	R²	Rank	CN
Bi (2000)	1.528 7	0.971 1	1.667	113.4 5
Sharma et al. (2001)	1.885 1	0.955 9	8.000	1.000 0
Sharma et al. (2004)	1.578 6	0.969 1	2.527	1.800 0
Sharma et al. (2009)	1.528 2	0.971 1	1.662	8.904 8
Max et al. (1976)	1.495 6	0.972 3	1.123	274.69
Kozak (2004)-1	1.630 6	0.967 1	2.905	30.220
Kozak (2004)-2	1.488 7	0.972 6	1.000	77.830
Fang et al. (2000)	1.492 4	0.972 4	1.074	83.083

Models	Diameter				Volume
Models	MPB	MAB	RMSE	Rank	MPB	MAB	RMSE	Rank
Bi (2000)	7.428 3	0.982 2	1.696 9	1.613	10.102 4	0.022 0	0.046 8	2.081
Sharma et al. (2001)	10.713 1	1.416 5	2.338 3	8.000	17.913 1	0.039 1	0.070 7	8.000
Sharma et al. (2004)	7.814 3	1.033 1	1.714 9	2.180	10.621 4	0.023 1	0.048 1	2.445
Sharma et al. (2009)	7.331 8	0.969 4	1.656 9	1.358	16.236 0	0.035 4	0.066 7	6.817
Max et al. (1976)	7.294 0	0.964 4	1.605 2	1.143	9.980 1	0.021 7	0.047 1	2.039
Kozak (2004)-1	8.463 2	1.119 0	1.811 4	3.342	8.771 7	0.019 1	0.041 8	1.000
Kozak (2004)-2	7.185 3	0.950 0	1.651 9	1.148	9.653 0	0.021 0	0.045 5	1.745
Fang et al. (2000)	7.249 5	0.958 5	1.634 9	1.179	10.078 3	0.022 0	0.046 4	2.043

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Stem Taper Functions for Betula platyphylla in Daxing'anling

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