摘要: 目的以林场或县森林资源总体为调查对象，及时、准确地调查监测总体平均每公顷蓄积量，对上级（如市、省）部门开展森林资源宏观管理、生态保护价值评价、森林碳储量计量、领导干部任期绩效考核等工作都有重要支撑作用。将卫星、无人机等多源遥感数据作为辅助数据，采用较少抽样调查样地数据，实现总体参数有效估测的新方法，已成为国内外重要的研究方向，但目前，国内尚无多种现有估计方法的比较评价研究。为了促进新一代遥感技术在森林资源调查业务中的应用，提高我国森林资源天空地一体化调查监测技术水平，亟需对现有林场或县总体参数估测方法进行比较评价研究、�/sec> 方法以内蒙古旺业甸实验林场主要人工林树种为总体，基�?019年在林场获取的无人机激光雷达（LiDAR）抽样数据、Sentinel-2A多光谱数据（全覆盖）和少量样地数据，针对样地（p）、样地−卫星（ps）、样地−抽样无人机LiDAR（pl）以及样地−抽样无人机LiDAR-卫星（pls�?种模式，利用适合�?种模式的概率抽样法（DB）、模型辅助法（MA）、模型法（MD）和混合法（HY�?类共5种估测方法（DB _p、MD _ps、MA _ps、HY _pl以及MD _pls）对总体森林蓄积量密度均值（MSVD）进行估计与对比分析、�/sec> 结果�?）DB _p、MD _ps、MA _ps、HY _pl、MD _pls5种方法估测的MSVD分别�?12.54�?02.09�?02.38�?10.07以及208.96 m ³/hm ²，精度分别为90.44%�?1.54%�?1.69%�?6.35%�?6.45%，方差依次减小。（2）其�?种方法相对于MD _pls方法的估计效率（RE）均大于1（RE _DBp,MDpls= 5.39，RE _MDps,MDpls= 3.82，RE _MAps,MDpls= 3.69，RE _HYpl,MDpls= 1.07）；HY _pl相对于MD _pls的RE略大�?，但几倍于其他3种方法（RE _DBp,HYpl= 5.02，RE _MAps,HYpl= 3.43，RE _MDps,HYpl= 3.56）。（3）包含LiDAR数据的HY _pl与MD _pls方法相对于包含Sentinel-2A数据的MD _ps与MA _ps方法均为正效率（RE _MAps,HYpl= 3.43，RE _MDps,HYpl= 3.56，RE _MDps,MDpls= 3.82，RE _MAps,MDpls= 3.69）；MD _ps与MA _ps方法之间的RE接近1，但MA _ps的效率微高于MD _ps（RE _MDps,MAps= 1.04）、�/sec> 结论和只利用样地数据的估计方法相比，将遥感数据作为辅助变量建立估测模型，无论是采用对蓄积量不够敏感的林场全覆盖Sentinel-2A多光谱遥感数据，还是采用对蓄积量很敏感的抽样式获取的LiDAR数据，都可有效提高林场总体MSVD的估测精度。涉及遥感数据应用的4种方法，估计精度最高的为MD _pls，其次为HY _pl，这2种方法都包含了LiDAR遥感抽样观测数据的应用，都是适应于林场总体MSVD估计的年度监测方法。可实现天空�?种观测数据协同应用的MD _pls估测精度和相对效率最高，可作为林场森林蓄积量年度监测的首选方法、�/sec>

关键诌�
• 森林资源调查/
• 林场/厾�/a> /
• 多源数据/
• 总体蓄积量密度均倻�/a>

Abstract: ObjectiveTaking the overall forest resources of forest farms or counties as the object of investigation, timely and accurately investigating and monitoring of the mean stock volume density（MSVD）will play an important supporting role in the macro management of forest resources, the evaluation of ecological protection value, the measurement of forest carbon reserves, and the performance evaluation of the tenure of leading cadres by the superior departments (such as cities and provinces). It has become an important research direction at home and abroad using remote sensing data, such as satellites and unmanned aerial vehicles, combining with less sampling plot to effectively estimate the overall parameters. At present, there is no comparative validation of several estimation methods for mean stock volume based on multi-source data in domestic. In order to promote the application of remote sensing technology in the forest resource survey, there is an urgent need to compare and evaluate the methods for estimating overall parameters of forest farms or counties. MethodThe main plantation tree species of Wangyedian Forest Farm in Inner Mongolia of northern China were taken as the research object. Based on the sampling UAV LiDAR (herringbone system distribution), Sentinel-2A data (full coverage) and a small amount of sample plot data obtained in 2019, four patterns of sample plot (p), sample plot-satellite (ps), sample plot-sampling LiDAR (pl), and sample plot-sampling LiDAR-full coverage satellite (pls) were estimated and compared with five methods, including DB _p, MD _ps, MD _pls, HY _pland MA _ps, which were suitable for these four patterns and belong to design-based method (DB), model-assisted method (MA), model-dependent method (MD) and mixed or hybrid method (HY). Result(1)The mean stock volume densities of DB _p, MD _ps, MA _ps, HY _pl, and MD _plswere 212.54, 202.09, 202.38, 210.07 and 208.96 m ³/ha, respectively. The accuracy ( P) was 90.44%, 91.54%, 91.69%, 96.35%, and 96.45%, respectively, with variances decreasing in turn. (2) The relative efficiency (RE) of other methods compared with MD _plswas greater than 1 (RE _DBp,MDpls= 5.39, RE _MDps,MDpls= 3.82, RE _MAps,MDpls= 3.69, RE _HYpl,MDpls= 1.07), and the RE of HY _plcompared with MD _plsmethod was greater than 1, but close to 1. Compared with the other three methods, HY _plwas more efficient (RE _DBp,HYpl= 5.02, RE _MAps,HYpl= 3.43, RE _MDps,HYpl= 3.56). (3) Both HY _pland MD _plsmethods containing LiDAR data had positive efficiency compared with MD _psand MA _psmethods containing Sentinel-2A data (RE _MAps,HYpl= 3.43, RE _MDps,HYpl= 3.56, RE _MDps,MDpls= 3.82, RE _MAps,MDpls= 3.69). The RE of MD _psand MA _pswas close to 1, but the efficiency of MA _pswas slightly higher than that of MD _ps(RE _MDps,MAps= 1.04). ConclusionCompared with the estimation method that only used the sample plot data, when the remote sensing data was used as an auxiliary variable to establish the estimation model, it can effectively improve the estimation accuracy of the MSVD of the forest farm, whether the Sentinel-2A multispectral remote sensing data, which is fully covered the forest farm but not sensitive enough to the stock volume, or the sampling LiDAR data which are sensitive to stock volume. Among four methods involving the application of remote sensing data, MD _plshas the highest estimation accuracy, followed by HY _pl. Both of these two methods including the application of LiDAR remote sensing sampling observation data are suitable for the MSVD estimation of forest farms. The MD _plsmethod has the highest estimation accuracy and relative efficiency, which can realize the synergistic application of the Space-Air-Earth multi-source observation data, and can be used as the preferred method for annual monitoring of forest stock in forest farms.

Key words:
• forest resource inventory/
• forest farm/county/
• multi resource data/
• mean value of total volume density

�?nbsp; 1研究区位置和覆盖范围

Figure 1.Location and coverage of the study area

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�?nbsp; 2无人机和样地数据抽样获取方案示意国�/p>

Figure 2.Schematic diagram of UAV and sample plot data sampling acquisition scheme

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�?nbsp; 3各估测方法所利用数据示意国�/p>

Figure 3.Schematic diagram of the data used by each estimation method

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�?nbsp; 4遥感特征选择

折线代表值的变化趋势。The broken line represents the trend of value.

Figure 4.Feature selection of remote sensing

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�?nbsp; 5遥感特征建模估测模型精度

实线�?�?验证线。图中RMSE和ME的单位均为m³/hm²。The solid line is 1�? verification line.The unit of RMSE and ME in the figure is m³/ha.

Figure 5.Remote sensing feature modeling to estimate model accuracy

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�?nbsp; 6各方法之间的相对效率

Figure 6.Relative efficiency (RE) between methods

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�?nbsp; 1S-2A卫星数据特征

Table 1.S-2A satellite data characteristics

特征名称 Feature name	特征符号 Feature symbol	计算公式 Calculation formula		特征名称 Feature name	特征符号 Feature symbol	计算公式 Calculation formula
光谱特征 Spectral feature	B2�?i>B3�?i>B4�?i>B5�?i>B6�?i>B7�?i>B8a�?i>B11�?i>B12			角二阶矩 Angular second moment	AN	$\displaystyle \sum \limits_{i,j = 1}^k {P_{i,j}^2}$
差值植被指�?br/>Difference vegetation index	DVI	${B_8} - {B_4}$		熴�br/>Entropy	EN	$\displaystyle \sum \limits_{i,j = 1}^k {P_{i,j}}\left( { - \ln {P_{i,j}}} \right)$
增强植被指数 Enhanced vegetation index	EVI	2.5 × (B8�B4)/(B8+ 6 ×B4� 7.5 ×B2+ 1)		对比�?br/>Contrast	CON	$\displaystyle \sum \limits_{i,j = 1}^k {\left( {i - j} \right)^2} \times {P_{i,j}}$
归一化植被指�?br/>Normalized difference vegetation index	NDVI	$({B_8} - {B_4})/({B_8} + {B_4})$		均倻�br/>Mean	ME	$\dfrac{1}{{{k^2}}}\displaystyle \sum \limits_{i,j = 1}^k {P_{i,j}}$
比值植被指�?br/>Ratio vegetation index	SR	${B_8}/{B_4}$		方差 Variance	VAR	$\displaystyle \sum \limits_{i,j = 1}^k {P_{i,j} }\left( {i,j - {\rm{ME}}} \right)$
转换归一化植被指�?br/>Transformed normalized difference vegetation index	TNDVI	$\sqrt {({B_8} - {B_4})/({B_8} + {B_4}) + 0.5}$		同质�?br/>Homogeneity	HOM	$\displaystyle \sum \limits_{i,j = 1}^k \dfrac{ { {P_{i,j} } } }{ {1 + { {\left( {i - j} \right)}^2} } }$
叶绿素指�?br/>Chlorophyll index	CIg	${B_8}/{B_3} - 1$		相关�?br/> Correlation	COR	$\displaystyle\sum\limits_{i,j = 1}^k {P_{i,j}^2} \left[ {\frac{{\left( {i - {u_i}} \right) - \left( {j - {u_j}} \right)}}{{\sqrt {\sigma _i^2\sigma _j^2} }}} \right]$
反向红边叶绿素指�?br/>Inverted red edge chlorophyll index	IRECI	$({B_7} - {B_4})/({B_5}/{B_6})$		相异�?br/>Dissimilarity	DIS	$\displaystyle\sum\limits_{i,j = 1}^k {{P_{i,j}}} |i - j|$
色素简单比值指�?br/>Pigment specific simple ratio	PSSRA	${B_7}/{B_4}$		修正叶绿素吸收反射指�?br/>Modified chlorophyll absorption in reflectance index	MCARI	[(B5�B4) � 0.2 × (B5�B3)] × (B5/B4)
S-2A 红边位置指数 S-2A red edge position	S2REP	705 + 35 × [(B4+B7)/2 �B5]/(B6�B5)		修正窄边红边简单比值指�?br/>Modified simple ratio red edge narrow	MSRren	$[({B_{8{\text{a}}}}/{B_5}) - 1]/\sqrt {({B_{8{\text{a}}}}/{B_5}) + 1} $
红边叶绿素指�?br/>Red edge chlorophyll index	CIgre1	$ {{B}}_{{5}}{/}{{B}}_{{3}}{-1} $		红边植被指数 Red edge vegetation index	NDVIre1	$ {(}{{B}}_{{8}}{-}{{B}}_{{5}}{)/(}{{B}}_{{8}}{ + }{{B}}_{{5}}{)} $
	CIgre2	${B_5}/{B_3} - 1$			NDVIre2	$ {(}{{B}}_{{8}}{-}{{B}}_{{6}}{)/(}{{B}}_{{8}}{ + }{{B}}_{{6}}{)} $
	CIgre3	$ {{B}}_{{7}}{/}{{B}}_{{3}}{-1} $			NDVIre3	$ {(}{{B}}_{{8}}{-}{{B}}_{{7}}{)/(}{{B}}_{{8}}{ + }{{B}}_{{7}}{)} $
注：$ {{B}}_{{2}} $�? {{B}}_{{3}} $�? {{B}}_{{4}} $�? {{B}}_{{5}} $�? {{B}}_{{6}} $�? {{B}}_{{7}} $�?i>B8�?{ {B} }_{ {8{\rm{a}}} }$�? {{B}}_{{11}} $�? {{B}}_{{12}} $代表S-2A数据对应的波段，${ {P} }_{ {i,j} }{=}{ {D} }_{ {i,j} }{/}\displaystyle{ \sum} _{ {i,j}{=1} }^{ {k} }{ {D} }_{ {i,j} }$�? {{D}}_{{i,j}} $丹�i>i衋�i>j列对应的像元值，k代表计算纹理时窗口大小。Notes: $ {{B}}_{{2}} $, $ {{B}}_{{3}} $, $ {{B}}_{{4}} $, $ {{B}}_{{5}} $, $ {{B}}_{{6}} $, $ {{B}}_{{7}} $,B8, ${ {B} }_{ {8{\rm{a}}} }$, $ {{B}}_{{11}} $ and $ {{B}}_{{12}} $ represent the bands corresponding to S-2A data; ${ {P} }_{ {i,j} }{=}{ {D} }_{ {i,j} }{/}\displaystyle {\sum} _{ {i,j}{=1} }^{ {k} }{ {D} }_{ {i,j} }$, $ {{D}}_{{i,j}} $ is the pixel value corresponding to theirow andjcolumn,krepresents the window size when calculating the texture.

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�?nbsp; 2LiDAR数据特征

Table 2.Feature of LiDAR data

特征名称 Feature name	特征符号 Feature symbol
均倻�br/> Mean	Hmean,Imean
方差和标准差 Variance and standard deviation	Hvar,Ivar,Hsd,Isd
最大值和最小倻�br/> Maximum value and minimum value	Hmax,Imax,Hmin,Imin
变异系数 Coefficient of variation	Hcv,Icv
四分距差 Interquartile distance	Hiq,Iiq
偏斜�?br/> Skewness	Hsk,Isk
百分位数 Percentile	Hp05,Hp10,Hp20,Hp25, ···,Hp95,Hp99 Ip05,Ip10,Ip20,Ip25,···,Ip95,Ip99
最小高度以上返回点 Count of return point above the minimum height	R1H, R2H,···, R8H, R9H
注：H代表高度＋�i>I代表强度，var代表方差，sd代表标准差，max与min分别代表最大值与最小值，cv、iq以及sk分别代表变异系数、四分距差以及偏斜度＋�i>p05–�i>p99代表对应的百分位数。Notes:Hrepresents height,Irepresents intensity, var represents variance, sd represents standard deviation, max and min represent maximum value and minimum value, respectively; cv, iq and sk represent coefficient of variation, interquartile distance and skewness, respectively;p05∑�i>p99 represent the corresponding percentiles.

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�?nbsp; 3材积计算公式

Table 3.Formula for volume calculation

树种 Tree species	材积计算公式 Formula for volume calculation
白桦 Betula platyphylla	$ {V}{=}{{10}}^{{0.000}\;{397}\;{507}\;{075}\;{980}\;{248 \;\times\; }{{d}}^{{2}}{ \;\times\; }{h}{ \;+\; 3.812}\;{138}\;{080}\;{735}\;{6 \;\times\; }{{10}}^{-{6}}{ \;\times\; }{{d}}^{{3}}{ \;\times\; }{h}\;-\;{0.000}\;{843}\;{446}\;{660}\;{194}\;{932 \;\times\; }{{d}}^{{2}}\;-\;{0.000}\;{290}\;{088}\;{083}\;{727}\;{618 \;\times\; }{{d}}^{{2}}{ \;\times\; }{h}{ \;\times\; }{\lg}\;{d}} $
黑桦 Betula davurica	$ {V}{=0.019}\;{921}\;{519}\;{389}\;{050}\;{9 \;+\; 0.000}\;{388}\;{145}\;{167}\;{080}\;{27 \;\times\; }{{d}}^{{2}}\;-\;{2.050}\;{596}\;{607}\;{769}\;{77 \;\times\; }{{10}}^{-{5}}{ \;\times\; }{{d}}^{{2}}{ \;\times\; }{h} -$ $ {0.000}\;{870}\;{310}\;{875}\;{746}\;{131 \;\times\; }{{h}}^{{2}}{ \;+\; 8.053}\;{621}\;{369}\;{495}\;{43 \;\times\; }{{10}}^{-{5}}{ \;\times\; }{d}{ \;\times\; }{{h}}^{{2}} $
落叶杽�br/>Larix gmelinii	$ {V}{=}{{10}}^{-{3.498}\;{903}\;{907}\;{280}\;{04 \;+\; 2.755}\;{048}\;{465}\;{025}\;{64 \;\times\; }{\lg}\;{d}\;-\;{0.394}\;{050}\;{839}\;{410}\;{844 \;\times\; }{\lg}\;{{d}}^{{2}}\;-\;{1.379}\;{153}\;{564}\;{042}\;{94 \;\times\; }{\lg}\;{h}{ \;+\; 1.145}\;{866}\;{814}\;{777}\;{51 \;\times\; }{\lg}\;{{h}}^{{2}}} $
樟子杽�br/>Pinus sylvestris	$ {V}{=0.000}\;{445}\;{504}\;{541}\;{007}\;{861 \;\times\; }{{d}}^{{1.663}\;{165}\;{237}\;{864}\;{29 \;\times\; \exp(0.098}\;{992}\;{935}\;{700}\;{498}\;{1 \;\times\; }{h}\;-\;{1.666}\;{816}\;{460}\;{562}\;{17/}{h}{)}} $
油松 Pinus tabuliformis	${V}{=2.533}\;{092}\;{907}\;{631}\;{68 \;\times\; }{ {10} }^{ {-5} }{ \;\times\; }{ {d} }^{ {2} }{ \;\times\; }{h}\;-\;{8.573}\;{788}\;{411}\;{603}\;{25 \;\times\; }{ {10} }^{ {-7} }{ \;\times\; }{ {d} }^{ {3} }{ \;\times\; }{h}\;-\;{6.000}\;{334}\;{292}\;{010}\;{54 \;\times\; }{ {10} }^{ {-5} }{ \;\times\; }{ {d} }^{ {2} } \;+\;$ ${ 2.937}\;{206}\;{772}\;{188}\;{84 \;\times\; }{ {10} }^{ {-5} }{ \;\times\; }{ {d} }^{ {2} }{ \;\times\; }{h}{ \;\times\; }{ {\lg} }\; {d}$
注：引自文献[40]、�i>V代表单木材积：�i>d代表单木胸径：�i>h代表单木树高。Notes: cited from reference [40].Vrepresents single tree stock volume,drepresents single tree DBH,hrepresents single tree height.

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�?nbsp; 4遥感特征优选后保留的特�?/p>

Table 4.Remotes sensing features selected after optimum feature selection

数据溏�br/> Data source	特征选择结果 Result of feature selection
S-2A	B2，MCARI＋�i>B2ME＋�i>B12COR
LiDAR	Hmean＋�i>Ip99，R2H

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�?nbsp; 55种方法的总体均值估计结果和精度

Table 5.Results and accuracy of total mean estimation of the five methods

方法 Method	总体均�?（m3·hm�?（�br/>Total mean/(m3·ha�?)	均值方�?（m3·hm�?（�br/>Mean variance/(m3·ha�?)	标准�?（m3·hm�?（�br/>Standard error/(m3·ha�?)	估测精度 Estimation accuracy
DBp	212.54	107.51	10.37	90.44%
MDps	202.09	76.18	8.72	91.54%
MAps	202.38	73.55	8.58	91.69%
HYpl	210.07	21.42	4.63	96.35%
MDpls	208.96	19.95	4.47	96.45%

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