黄土高原刺槐人工林生长对立地质量和林分密度的响应

doi:10.11707/j.1001-7488.LYKX20240116

摘要/Abstract

摘要：

目的: 分析黄土高原刺槐人工林主要生长指标（平均树高、平均胸径和林分蓄积量）对林龄、林分密度及立地指数的响应规律，构建多因子耦合模型，准确模拟和预测立地质量等因子对刺槐生长的影响，为该地区刺槐人工林可持续经营提供科学依据。方法: 基于2021—2022年样地调查及文献收集数据，首先采用上外包线法确定平均树高和平均胸径对林龄、林分密度和立地指数的单因子响应关系和函数类型；然后，通过连乘构建多因子耦合生长模型的框架，并利用3/4和1/4的数据率定和验证树高与胸径生长的多因子耦合模型；最后，基于模型计算的平均树高和胸径数据，重新率定林分蓄积量生长模型，并用于林分密度管理的情景分析。结果: 1）随林龄增加，平均树高、胸径均先快速增大后缓慢增大；随密度增加，树高先缓慢降低后快速降低，胸径先快速降低后缓慢降低；随立地指数增加，树高和胸径均近线性增大。2）建立了耦合立地指数、林龄和密度影响的平均树高、平均胸径和林分蓄积量生长模型，精度均较高（R²分别为0.73、0.67和0.71）。3）模拟并分析了不同立地指数、林分密度和林龄时的平均树高、平均胸径及林分蓄积量生长，并提出了不同立地条件的刺槐人工林经营策略建议。在劣等（SI<7.5 m）和中等立地（SI为7.5~12.5 m），仅能生产小径级林木（胸径<13 cm），林分蓄积量较低，建议以土壤保持、水文调节等为主导功能，但可在中等立地上兼顾木材生产功能。在优等立地（SI≥12.5 m），林龄40 年前可生产小径级林木；林龄50 年时可生产中径级林木（胸径13~21 cm），林分蓄积量较高，建议以木材生产为主导功能，同时兼顾土壤保持、水文调节等生态功能。结论: 黄土高原刺槐人工林的生长同时受到立地质量和林分结构的影响，建立的包括立地指数、林分密度和林龄的多因子耦合生长模型，可准确地预测和解释不同立地条件下刺槐林生长对密度调控的响应，并据此制定不同经营策略，指导刺槐人工林的可持续经营。

关键词: 刺槐人工林, 多因子耦合生长模型, 立地指数, 林分密度, 黄土高原

Abstract:

Objective: This study aims to investigate the response of main growth parameters (mean tree height, mean DBH, and stand volume) of Robinia pseudoacacia plantations on the Loess Plateau of China to forest age, stand density and site index (SI) , and to establish multi-factor coupling growth models for providing scientific basis of sustainable management of R. pseudoacacia plantations in this study region. Method: Based on the data of sample plots collected from the field surveys in 2021—2022 and literature, the response relations and corresponding function types of mean tree height and mean DBH to the single-factors of forest age, stand density and site index were determined using the upper envelope line method. Then, a framework of multi-factor coupling growth models was established by a continuous multiplication of these function types, and the multi-factor coupling growth models of mean tree height and DBH were calibrated and verified using 3/4 and 1/4 of sample plots data. Thereafter, the growth model of stand volume was re-calibrated based on the model calculated data of mean tree height and DBH, and used to the scenario analysis of stand density management. Result: 1) Both the mean tree height and DBH increase first rapidly and then slowly with rising forest age; With rising stand density, the mean tree height decreases first slowly and then rapidly, while the DBH decreases first rapidly and then slowly; With rising SI, both the mean tree height and DBH increase near linearly. 2) The established growth models of mean tree height, DBH, and stand volume by coupling the effects of multiple factors (SI, forest age, and stand density) have high fitness (R² = 0.73, 0.67, 0.71). 3). The mean tree height, DBH and stand volume under different SI, stand density, and forest age were simulated and analyzed, and then management strategies of R. pseudoacacia plantations with different site conditions were proposed. At poor sites (SI < 7.5 m) and medium sites (SI = 7.5?12.5 m), only small sized timber (DBH < 13 cm) can be produced with lower stand volume. Therefore, it is recommended that the dominant function of forests at poor sites should be soil conservation, hydrological regulation, or other ecological services, but a low priority should be given to the function of timber production; while the recommended dominant function of forests at medium sites should be still soil conservation or hydrological regulation, but giving consideration to the timber production functions. At fertile sites (SI ≥ 12.5 m), small sized timber can be produced before the forest age of 40 years, while medium sized timber (DBH = 13?21 cm) can be produced at the forest age of 50 years with higher stand volume. Therefore, the recommended dominant function of forests at fertile sites is timber production, while considering the functions of soil conservation, hydrological regulation, and other ecological services. Conclusion: The growth of R. pseudoacacia plantations on the Loess Plateau is influenced by both site quality and stand structure. The established growth models coupling multi-factors (SI, stand density, and forest age) can accurately predict and explain the growth response of R. pseudoacacia plantations to density regulation under different site conditions, and formulate different management strategies accordingly, to guide the sustainable management of R. pseudoacacia plantations.

Key words: Robinia pseudoacacia plantation, multifactor-coupling growth model, site index, stand density, Loess Plateau

中图分类号:

李平平,王彦辉,于澎涛,王依瑞,段文标,万艳芳,韦小茶,史再军. 黄土高原刺槐人工林生长对立地质量和林分密度的响应[J]. 林业科学, 2025, 61(7): 192-207.

Pingping Li,Yanhui Wang,Pengtao Yu,Yirui Wang,Wenbiao Duan,Yanfang Wan,Xiaocha Wei,Zaijun Shi. Growth Response of Black Locust Plantations to Site Quality and Stand Density on the Loess Plateau of China[J]. Scientia Silvae Sinicae, 2025, 61(7): 192-207.

图/表 10

表1

刺槐林文献数据地点及作者调查的甘肃泾川官山林场基本情况"

省（自治区） Province （region）	调查地点 Study sites	年均气温 Mean annual temperature/℃	年均降水量 Mean annual precipitation / mm	林龄 Forest age/a	林分密度 Stand density/ （trees$ \cdot $hm^?2）	立地指数 Site index/m	平均树高 Mean tree height/m	平均胸径 Mean DBH/cm	单株材积 Single tree volume/m³	林分蓄积量 Stand volume/ （m³$ \cdot $hm^?2）	郁闭度 Canopy density	样地数Plot quantity	参考文献 References
甘肃省 Gansu Province	泾川县官山林场Guanshan Forest Farm of Jingchuan County	9.2~10.5	475~555	7~45	1 100~3 240	10.2~15.8	4.1~14.9	2.6~17.5	0.001~0.174	10.0~169.6	0.5~0.9	38	笔者调查 Author’s survey 张晓梅等， 2019；景贯阳等，2017；Schw?rzel et al.，2018
甘肃省 Gansu Province	庄浪、天水、通渭、环县Counties of Zhuanglang， Tianshui， Tongwei， Huan	7.5~11.0	408~548	8~28	3 330~6 990	8.5~11.3	4.9~6.7	3.4~6.3	0.003~0.014	20.8~47.5	0.7~0.8	4	柳洋， 2021；马玉玺等， 1990

陕西省 Shaanxi Province	安塞县纸坊沟流域Zhifanggou watershed， Ansai County	8.8	500~543	9~40	900~2 475	9.9~14.6	5.0~12.0	4.7~17.5	0.005~0.127	11.1~148.4	0.6~0.8	14	刘愿等， 2019；刘愿， 2019
	安塞县南沟流域Nangou watershed， Ansai County	8.8	505	2~9	675~2 800	10.5~13.1	2.2~7.8	3.2~16.7	0.001~0.077	1.4~58.2	0.5~0.8	9	刘建利等， 2008
	清涧、米脂、神木Counties of Qingjian， Mizhi， Shenmu	8.5~9.6	440~500	18~25	2 502~3 334	9.2~9.9	6.0~8.0	6.6~10.8	0.011~0.037	29.0~122.2	0.8~0.9	3	马玉玺等， 1990

山西省 Shanxi Province	吉县蔡家川流域 Caijiachuan watershed， Jixian County	10	576	18~36	667~1 625	10.4~13.6	7.2~9.0	7.3~11.9	0.007~0.038	7.9~61.5	0.6~0.8	8	朱悦， 2012；赵丹阳等， 2021
	方山县和吉县 Fangshan County and Jixian County	7.3~10.6	497~576	11~25	833~2 222	8.5~13.5	7.2~14.1	5.3~12.6	0.004~0.031	3.4~53.1	0.6~0.8	32	玉宝等，2011；2012；史振华， 2009
	偏关县以南的西部沿黄一带Western area along the Yellow River south of Pianguan County	8.0	500	2~18	3 193~3 433	8.1~12.0	2.3~9.3	2.6~9.8	0.001~0.025	1.3~84.4	0.3~0.9	48	卫三平等， 2002
	离石Lishi County	8.9	490	12	4 814	10.4	6.6	6.8	0.005	24.5	0.9	1	马玉玺等， 1990

宁夏回族自治区 Ningxia Hui Autonomous Region	固原、西吉 Counties of Guyuan and Xiji	6.0~6.2	435~478	11~23	1 665	4.6~7.9	4.6~7.1	7.1~8.9	0.025	41.5~41.9	0.7	2	马玉玺等， 1990

表1

图1

表2

图2

表3

图3

图4

表4

图5

表5

刺槐人工林不同经营情景下的生长差异①"

情景序列 Sequence of scenarios	生长指标 Growth indicators	劣等立地Poor sites （立地质量极差和差，SI<7.5 m。Very low and low site quality， SI<7.5 m）					中等立地Medium sites （立地质量中和良，7.5 m≤SI<12.5 m。Middle and high site quality， 7.5 m≤SI<12.5 m）					优等立地Fertile sites （立地质量优，SI≥12.5 m。Very high site quality， SI≥12.5 m）
		10 a	20 a	30 a	40 a	50 a	10 a	20 a	30 a	40 a	50 a	10 a	20 a	30 a	40 a	50 a
		1884~3 148 trees$ \cdot $hm^?2	1760~2 652 trees$ \cdot $hm^?2	1688~2 398 trees$ \cdot $hm^?2	1644~2 232 trees$ \cdot $hm^?2	1606~2 120 trees$ \cdot $hm^?2	4 034~4 302 trees$ \cdot $hm^?2	3 157~3 269 trees$ \cdot $hm^?2	2 767~2 796 trees$ \cdot $hm^?2	2 487~2 513 trees$ \cdot $hm^?2	2 293~2 323 trees$ \cdot $hm^?2	4168 trees$ \cdot $hm^?2	3093 trees$ \cdot $hm^?2	2609 trees$ \cdot $hm^?2	2308 trees$ \cdot $hm^?2	2099 trees$ \cdot $hm^?2
最大密度的1.0倍 1.0 times of the maximum density	平均树高Mean tree height /m	3.8~4.6	5.7~6.7	6.6~7.7	6.9~8.1	7.1~8.3	5.6~6.9	7.7~8.7	8.6~9.5	9.0~9.8	9.2~10	8.3	9.7	10.3	10.5	10.6
	平均胸径Mean DBH /cm	3.9~4.4	5.3~6.0	6.4~7.2	7.2~8.2	8.0~9.0	5.1~6.2	7.0~8.3	8.3~9.8	9.4~11.1	10.4~12.1	7.5	9.9	11.6	13.0	14.2
	林分蓄积量Stand volume / （m³$ \cdot $hm^?2）	2.15~5.53	6.12~14.17	11.05~24.12	16.66~34.84	22.76~46.21	12.51~25.79	28.81~53.96	46.42~82.28	64.54~110.01	82.88~138.02	50.03	95.06	137.55	177.90	216.77
	郁闭度 Canopy density	0.59~0.70	0.66~0.75	0.69~0.77	0.70~0.78	0.71~0.78	0.77~0.82	0.81~0.84	0.82~0.84	0.82~0.83	0.81~0.82	0.86	0.86	0.84	0.82	0.81

最大密度的0.9倍 0.9 times of the maximum density	平均树高Mean tree height /m	3.9~4.7	5.8~6.7	6.6~7.7	7.0~8.1	7.1~8.3	5.7~6.9	7.7~8.7	8.6~9.5	9.0~9.8	9.2~10.0	8.4	9.8	10.3	10.5	10.6
	平均胸径Mean DBH /cm	4.0~4.5	5.4~6.1	6.5~7.3	7.4~8.3	8.2~9.2	5.2~6.3	7.1~8.4	8.5~10.0	9.6~11.2	10.6~12.3	7.6	10.1	11.8	13.2	14.4
	林分蓄积量Stand volume / （m³$ \cdot $hm^?2）	2.07~5.32	5.91~13.62	10.66~23.16	16.05~33.44	21.92~44.33	11.98~24.60	27.57~51.43	44.39~78.36	61.70~104.74	79.20~131.37	47.50	90.20	130.47	168.70	205.53
	郁闭度 Canopy density	0.58~0.69	0.64~0.74	0.67~0.76	0.69~0.76	0.70~0.76	0.76~0.82	0.80~0.83	0.80~0.82	0.80~0.81	0.79~0.80	0.85	0.84	0.82	0.80	0.79

最大密度的0.8倍 0.8 times of the maximum density	平均树高Mean tree height /m	3.9~4.7	5.8~6.8	6.6~7.7	7.0~8.1	7.1~8.3	5.8~7.0	7.8~8.8	8.7~9.5	9.0~9.8	9.2~10.0	8.5	9.8	10.3	10.6	10.6
	平均胸径Mean DBH /cm	4.1~4.6	5.5~6.2	6.7~7.5	7.6~8.5	8.4~9.4	5.3~6.4	7.2~8.6	8.6~10.2	9.8~11.5	10.8~12.6	7.8	10.2	12.0	13.5	14.7
	林分蓄积量Stand volume / （m³$ \cdot $hm^?2）	2.00~5.09	5.68~13.03	10.23~22.13	15.39~31.93	21.01~42.32	11.42~23.33	26.25~48.73	42.23~74.21	58.66~99.14	75.28~124.32	44.81	85.06	122.98	158.97	193.64
	郁闭度 Canopy density	0.57~0.68	0.63~0.72	0.65~0.74	0.67~0.74	0.68~0.74	0.75~0.80	0.78~0.81	0.78~0.80	0.78~0.79	0.77~0.78	0.84	0.82	0.80	0.78	0.77

最大密度的0.7倍 0.7 times of the maximum density	平均树高Mean tree height /m	4.0~4.8	5.9~6.9	6.7~7.8	7.0~8.2	7.1~8.3	5.8~7.1	7.9~8.8	8.7~9.6	9.1~9.9	9.2~10.6	8.5	9.9	10.4	10.6	10.7
	平均胸径Mean DBH /cm	4.2~4.7	5.7~6.4	6.8~7.7	7.8~8.7	8.6~9.6	5.5~6.5	7.4~8.8	8.8~10.4	10.0~11.7	11.1~12.8	7.9	10.4	12.3	13.7	15.0
	林分蓄积量Stand volume / （m³$ \cdot $hm^?2）	1.91~4.85	5.43~12.39	9.76~21.02	14.68~30.30	20.03~40.15	10.82~21.97	24.83~45.84	39.90~69.76	55.40~93.15	71.07~116.78	41.96	79.58	115.00	148.62	180.99
	郁闭度 Canopy density	0.56~0.66	0.61~0.71	0.63~0.72	0.65~0.72	0.65~0.72	0.74~0.79	0.76~0.79	0.76~0.78	0.76	0.75	0.82	0.80	0.78	0.76	0.74

最大密度的0.6倍 0.6 times of the maximum density	平均树高Mean tree height /m	4.1~4.9	6.0~7.0	6.7~7.8	7.0~8.2	7.2~8.3	5.9~7.2	7.9~8.9	8.8~9.6	9.1~9.9	9.2~10.0	8.6	9.9	10.4	10.6	10.7
	平均胸径Mean DBH /cm	4.3~4.8	5.9~6.6	7.0~7.9	8.0~9.0	8.8~9.9	5.6~6.7	7.6~9.0	9.1~10.6	10.3~12.0	11.4~13.2	8.1	10.7	12.5	14.1	15.3
	林分蓄积量Stand volume / （m³$ \cdot $hm^?2）	1.82~4.58	5.15~11.69	9.25~19.80	13.89~28.53	18.95~37.77	10.16~20.49	23.28~42.71	37.38~64.95	51.85~86.68	66.49~108.63	38.88	73.69	106.44	137.49	167.40
	郁闭度 Canopy density	0.54~0.65	0.59~0.68	0.61~0.69	0.62~0.69	0.63~0.69	0.72~0.77	0.74~0.77	0.74~0.75	0.73~0.74	0.72	0.80	0.77	0.75	0.73	0.71

最大密度的0.5倍 0.5 times of the maximum density	平均树高Mean tree height /m	4.2~5.1	6.1~7.1	6.8~7.9	7.1~8.3	7.2~8.3	6.1~7.3	8.0~9.0	8.8~9.7	9.1~9.9	9.3~10.0	8.7	10.0	10.4	10.6	10.7
	平均胸径Mean DBH /cm	4.5~5.0	6.1~6.8	7.3~8.1	8.3~9.3	9.2~10.2	5.8~6.9	7.9~9.2	9.4~10.9	10.6~12.4	11.7~13.6	8.4	11.0	12.9	14.4	15.8
	林分蓄积量Stand volume / （m³$ \cdot $hm^?2）	1.71~4.29	4.84~10.91	8.68~18.45	13.02~26.56	17.75~35.14	9.43~18.87	21.57~39.29	34.59~59.68	47.94~79.60	61.45~99.72	35.53	67.28	97.12	125.40	152.64
	郁闭度 Canopy density	0.52~0.62	0.56~0.65	0.58~0.66	0.59~0.66	0.59~0.66	0.70~0.75	0.71~0.73	0.70~0.72	0.69~0.70	0.68~0.69	0.77	0.74	0.71	0.69	0.67

表5

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地点 Location	立地类型 Site type	计算公式 Equation	参考文献 Reference	公式编号 No. of equation
甘肃省 Gansu Province	阳面沟坡 Sunny gully slope	V=0.000 150 923×DBH^{2.541 458}	王云等，2007	（4）
	阴面沟坡 Shady gully slope	V=0.000 138 101×DBH^{2.485 315}		（5）
	梁坡中部 Middle part of ridge slope	V=0.000 148 933 3×DBH^{2.477 607}		（6）
	梁坡下部 Lower part of ridge slope	V=0.000 146 818×DBH^{2.504 261}		（7）
	沟底 Gully bottom	V=0.000 138 491×DBH^{2.516 521}		（8）

陕西省 Shaanxi Province	——	V=0.000 074 243 44×DBH^1.784737517×H^{0.938 449 377 8}	李玉明，1984	（9）
山西省 Shanxi Province	阴面沟坡Shady gully slope	V=0.088 3/（1+59.02e^?0.21×A）	卫三平等，2002	（10）
	阴面梁坡Shady ridge slope	V=0.044 5/（1+24.92e^?0.23×A）		（11）
	梁峁顶Hilly top	V=0.032 9/（1+89.89e^?0.27×A）		（12）
	阳面梁坡Sunny ridge slope	V=0.008 2/（1+119.91e^?0.44×A）		（13）
	阳面沟坡Sunny gully slope	V=0.025 5/（1+71.39e^?0.21×A）		（14）

生长指标 Growth parameters	模型 Model	R²	RMSE	公式编号 No. of equations
平均树高 Mean tree height /m	$ H=\left(4.69\times {\mathrm{S}\mathrm{I}}^{0.313}\right)\times {\left[1-\mathrm{e}\mathrm{x}\mathrm{p}(-0.439\times {N}^{-0.227}\times A)\right]}^{(1.362-0.073\times \mathrm{S}\mathrm{I})} $	0.73	1.16	（18）
平均胸径 Mean DBH/ cm	$ \mathrm{D}\mathrm{B}\mathrm{H}=\left(59.44\times {\mathrm{S}\mathrm{I}}^{0.10}\right)\times {\left[1-\mathrm{e}\mathrm{x}\mathrm{p}(-0.003 8\times {N}^{-0.452}\times A)\right]}^{(0.469-0.01\times \mathrm{S}\mathrm{I})} $	0.67	1.92	（19）
林分蓄积量 Stand volume / （m³$ \cdot $hm^?2）	V_s$ =(9.51\mathrm{E}-6)\times {\mathrm{D}\mathrm{B}\mathrm{H}}^{3.3}\times {H}^{0.23}\times N $	0.76	18.00	（20）

立地指数分组 Site index groups	林龄 Forest age/a	最大密度对应胸径 Maximum density corresponding DBH/cm	最大密度 Maximum density/ （trees$ \cdot $hm^?2）	经营情景密度（最大密度的倍数） Management density scenarios （multiple of maximum density）/（trees$ \cdot $hm^?2）
立地指数分组 Site index groups	林龄 Forest age/a	最大密度对应胸径 Maximum density corresponding DBH/cm	最大密度 Maximum density/ （trees$ \cdot $hm^?2）	0.9	0.8	0.7	0.6	0.5
极差 Very low （SI=4.0 m）	10	3.9	1 884	1 696	1 507	1 319	1 130	942
	20	5.3	1 760	1 584	1 408	1 232	1 056	880
	30	6.4	1 688	1 519	1 350	1 182	1 013	844
	40	7.2	1 644	1 480	1 315	1 151	986	822
	50	8.0	1 606	1 445	1 285	1 124	964	803

差 Low （SI=6.5 m）	10	4.4	3 148	2 833	2 518	2 204	1 889	1 574
	20	6.0	2 652	2 387	2 122	1 856	1 591	1 326
	30	7.2	2 398	2 158	1 918	1 679	1 439	1 199
	40	8.2	2 232	2 009	1 786	1 562	1 339	1 116
	50	9.0	2 120	1 908	1 696	1 484	1 272	1 060

中 Middle （SI=9.0 m）	10	5.1	4 034	3 631	3 227	2 824	2 420	2 017
	20	7.0	3 157	2 841	2 526	2 210	1 894	1 579
	30	8.3	2 767	2 490	2 214	1 937	1 660	1 384
	40	9.4	2 513	2 262	2 010	1 759	1 508	1 257
	50	10.4	2 323	2 091	1 858	1 626	1 394	1 162

良 High （SI=11.5 m）	10	6.2	4 302	3 872	3 442	3 011	2 581	2 151
	20	8.3	3 269	2 942	2 615	2 288	1 961	1 635
	30	9.8	2 796	2 516	2 237	1 957	1 678	1 398
	40	11.1	2 487	2 238	1 990	1 741	1 492	1 244
	50	12.1	2 293	2 064	1 834	1 605	1 376	1 147

优 Very high （SI=14.0 m）	10	7.5	4 168	3 751	3 334	2 918	2 501	2 084
	20	9.9	3 093	2 784	2 474	2 165	1 856	1 547
	30	11.6	2 609	2 348	2 087	1 826	1 565	1 305
	40	13.0	2 308	2 077	1 846	1 616	1 385	1 154
	50	14.2	2 099	1 889	1 679	1 469	1 259	1 050

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