methodsinecologyandevolution 2015 doi:10.1111/2041-210x ... et al_2015_mee.pdf · bon sequestration...

Correcting the overestimate of forest biomass carbon on

the national scale

Xiaolu Zhou1*, XiangdongLei2, Changhui Peng1,WeifengWang3, Carl Zhou4, Caixia Liu5 and

ZhenggangLiu6

1Ecological Modeling andCarbon Science, Department of Biology Science, University of Quebec atMontreal, Montreal, QC

H3C 3P8, Canada; 2Institute of Forest Resource Information Techniques, Chinese Academy of Forestry, Beijing 100091,

China; 3Department of Geography,McGill University, Montreal, QCH3A 0B9, Canada; 4Faculty of Health Sciences, University

of Ottawa,Ottawa,ONK1N 6N5, Canada; 5State Key Laboratory of Remote Sensing Science, Jointly Sponsored by the

Institute of Remote Sensing andDigital Earth of Chinese Academy of Sciences andBeijing Normal University, Beijing 100101,

China; and 6School of Geomatics, Institute for Remote Sensing Science and Application, Liaoning Technical University, Fuxin,

Liaoning 123000, China

Summary

1. For decades, researchers have thought it was difficult to remove the uncertainty from the estimates of forest

carbon storage and its changes on national sales. This is not only because of stochasticity in the data but also the

bias to overcome in the computations. Most studies of the estimation, however, ignore quantitative analyses for

the latter uncertainty. This bias primarily results from the widely used volume-biomass method via scaling up

forest biomass from limited sample plots to large areas. This paper addresses (i) the mechanism of scaling-up

error occurrence, and (ii) the quantitative effects of the statistical factors on the error.

2. The error compensators were derived, and expressed by ternary functions with three variables: expectation,

variance and the power in the volume-biomass equation. This is based on analysing the effect of power-law func-

tion convexity on scaling-up error by solving the difference of both sides of the weighted Jensen inequality. The

simulated data and the national forest inventory of China were used for algorithm testing and application,

respectively.

3. Scaling-up error occurrence stems primarily from an effect of the distribution heterogeneity of volume density

on the total biomass amount, and secondarily from the extent of function nonlinearities. In our experiments, on

average 94�2% of scaling-up error can be reduced for the statistical populations of forest stands in a region. Chi-

na’s forest biomass carbon was estimated as approximately 6�0 PgC or less at the beginning of the 2010s after on

average 1�1% error compensation.

4. The results of both the simulated data experiment and national-scale estimation suggest that the biomass is

overestimated for young forests more than others. It implies a necessity to compensate scaling-up error, espe-

cially for the areas going through extensive afforestation and reforestation in past decades.

5. This study highlights the importance of understanding how both the function nonlinearity and the statistics of

the variables quantitatively affect the scaling-up error. Generally, the presented methods will help to translate

fine-scale ecological relationships to estimate coarser scale ecosystem properties by correcting aggregation errors.

Key-words: aggregation error, allometric equation, error compensation, expectation of function,

extrapolation, nonlinear function, Scaling-up error, volume-biomass equation

Introduction

Many countries have made great efforts on enhancing the car-

bon sequestration capacity of forests to control the CO2 con-

centration in the atmosphere. High hopes have been placed on

these efforts (Bonan 2008; IPCC, 2013). However, for decades,

researchers have thought it was difficult to remove the uncer-

tainty regarding this capacity from the estimates of forest car-

bon storage (FCS) and its change (Brown & Lugo 1984;

Goodale, Quere & Raupacha 2002; Houghton 2005; Pan,

Birdsey & Fang 2011; IPCC, 2013). This uncertainty has a

direct impact on the quantification of the carbon balance in

some areas, especially in the countries with vast forested areas.

For instance, the afforestation campaigns carried out in China

over the past four decades have caused the forest volume to

continuously grow at the annual average rate of 2% remark-

ably (CMF 1999, 2004, 2009, and 2013). Yet, a number of

studies (Guo, Fang & Pan 2010; Li, Zhao & Lei 2012; Ni

2013), which used different methodologies, have yielded results

with great differences where the gap between estimates on Chi-

na’s FCS (i.e. living forest biomass carbon stock hereinafter)*Correspondence author. E-mail: [email protected]

© 2015 The Authors. Methods in Ecology and Evolution © 2015 British Ecological Society

Methods in Ecology and Evolution 2015 doi: 10.1111/2041-210X.12505

approximates 26% over the same period. Hence, it is necessary

to conduct fundamental research directly related to the estima-

tion methods for the management of global terrestrial ecosys-

tems to mitigate the CO2 growth rate, as well as for purely

academic studies in global forest ecosystem response under

climate change.

Unless remote sensing or other technical progresses can be

applied to monitor forest biomass accurately, the realistic esti-

mation is still considered to infer forest biomass indirectly from

living stock volume at the national scale. Two indirectmethods

were summarized by Somogyi, Cienciala &Makipaa (2007) to

estimate FCS using forest inventories. One is to use the volume

data and multiply it with a constant factor, e.g., biomass

expansion factors (BEF); another is through a volume-biomass

equation that predicts biomass as a function of some stand

variables (e.g. volume). Comparing both methods, using con-

stant factors can lead to large biases (Smith, Heath & Jenkens

2002). Although the volume-biomass equations have been pro-

ven to describe forest biomass dynamicsmore realistically than

constant BEF, many studies have analysed and suggested that

this type of equation may produce the scaling-up error that

leads to overestimates of large-scale forest biomasses (e.g. Cale

& Odell 1980; Brown & Lugo 1984; Rastetter, King & Cosby

1992; Fang, Chen&Zhao 2001b; Jenkins, Chojnacky&Heath

2003). The disadvantage on volume-biomass equations,

methodologically speaking, results from an assumption that

large-scale biomass can be converted using volume-biomass

equations depending on fieldmeasurements of a few study sites

(Brown & Lugo 1984). Eventually, all these biases translate

into an uncertainty of global carbon balance, raising the ques-

tion: how can bias be eliminated in forest biomass estimation

on the national scale?

To answer this question, two advances in quantifying the

error of FCS estimates are needed. First, an error analysis

should be carried out to identify the mechanism of scaling-up

error occurrence, and to clarify quantitative effects of the sta-

tistical factors on the error. Second, a practical algorithm

should be developed to correct scaling-up error for limiting the

bias. In order to achieve these two advances, we set two objec-

tives: to present an algorithm based on the error analysis for

solving the systematic error, and to prove that this algorithm

can further approach the ‘true value’ of FCS at the national

scale. In addition, a case study of China’s FCS estimation was

performed to illustrate how the statistics of forest area and vol-

ume influence the overestimates. Our analyses do not involve

any statistical uncertainty in the data of forest inventories and

biomassmeasurements.

Materials andmethods

VOLUME-BIOMASS EQUATIONS

Most volume-biomass equations come from allometric functions,

which describe the nonlinear relationship between forest biomass and

volume or the more easily measured diameter at breast height and tree

height (Parresol 1999; Zianis, Muukkonen & Makipaa 2005). These

equations are a type of convex function (defined as convex upwards or

convex caps hereinafter), which plays an important role in many areas

of mathematics, for example, the probability issue analysed below. One

of these volume-biomass equations is the widely used power-law func-

tion. It can be employed to convert regional forest biomass from two

different volume data, obtained on either the stand or regional scales.

Corresponding to the two different data sources, the biomass (Mg) can

be counted using the following twoways

Y1 ¼X

i

aiyi

Y2 ¼ ArXk

where ai (ha), yi (yi ¼ rxki ) (Mg ha�1) and xi (m3 ha�1) represent the

area, biomass density and volume density of the ith stand;A (ha) andX

(m3 ha�1) denote total forested area in a region and regional volume

density; r and k are parameters in the power function. Technically, Y1

andY2 can be understood as: (i) the precisemethod, which accumulates

biomass from all individual stands on which we actually lack volume

data; (ii) the extrapolation method, which is to convert large-scale bio-

mass directly from the regionalmean volume density.

MECHANISM OF SCALING-UP ERROR OCCURRENCE

SinceY1 is from all unobserved stands,Y1 could be viewed as a conven-

tional true value of the total stand biomass for component tree species.

Unfortunately, this true value is incomputable as the biomass (aiyi) is

unknown for each single stand. A regional biomass cannot be counted

stand by stand. Therefore, a lot of effort has been made to use regional

mean volume density for biomass estimation (it can be understood as a

data aggregate). This is to calculate Y2 instead of Y1 by taking advan-

tage of the regional volume density (X), which is the referable statistical

data from the national scale inventories in many countries for the time

being. BecauseX can be obtained easily, the secondway (Y2) is realistic

and realizable.

However, this commonly used way (Y2) does not help to accurately

compute the national FCSs in a mathematical sense. Comparing with

the true value (Y1),Y2 may contain an error resulting from the convex-

ity of the power function. An example of an extremely simplified calcu-

lation is shown in Fig. 1. Even if there were only two stands in a region,

the results from Y1 and Y2 should be different. Clearly, the calculation

is accurate when a volume-biomass equation is used for individual

stand estimations, since this equation is based on the regression data set

collected from measurements of some plots (refer to the Appendix S3,

Supporting information).Whereas, we will have a biased estimate once

the equation is applied only for a regional estimation. That is, the error

occurs through scaling up forest biomass from limited sample plots to

the large areas. This error (Y2 � Y1) can be simply called scaling-up

error. Figure 1 illustrates the theoretical necessity of the overestimate

in FCS estimations at large scales. The only case that causes no scaling-

up error is if all stands in a large area become identical in volume den-

sity with a zero variance (D), otherwise, the error always exists. In addi-

tion to the power function, other convex functions may result in the

same issue.

A detailed analysis in the Appendix S3 describes the scaling-up error

on the cause, magnitude and compensation. The analysis mathemati-

cally attributes the scaling-up error to Jensen inequality problem. It

explains the mechanism of error control and proves the nonnegative-

ness of the error. The essence of scaling-up error is to estimate a nonlin-

ear system based on the extrapolation by expected values. This is the

problem with using the ‘average’. The effect of using averages is most

likely to be random on an extrapolation. Consequently, scaling-up

error has characteristics of stochastic systematic errors, which are

© 2015 The Authors. Methods in Ecology and Evolution © 2015 British Ecological Society, Methods in Ecology and Evolution

2 X. Zhou et al.

vulnerable to the randomness of stand volume density. In other words,

the distribution of volume density determines the error level in the scale

expansion. In regards to national FCS estimation, we adopted the term

of stochastic systematic errors to distinguish this type of error from rel-

ative bias, which is caused by both function nonlinearity and the distri-

bution of volume density.

ALGORITHM OF ERROR COMPENSATION AND

ALGORITHM TEST

The key point of correcting overestimates of FCS on large scale is to

quantify the scaling-up error (Y2 �Y1). In view of this, we derived error

compensators as two ternary functions. To simplify the problemmath-

ematically, the power functionwas selected for volume-biomass expres-

sion. The detailed descriptions are provided in the Appendix S3. To

test the error compensator, the simulated data (dummydata) were used

to understand its ability to reduce the bias. This data set was designed

with 300 stands each with different areas and volume densities on nor-

mal and uniform distributions. All data were generated from the pseu-

dorandom number generator for carrying out a Monte-Carlo error

analysis. The detailed data description and an example of data

sampling are provided inAppendix S2.

FCS ESTIMATION

On the basis of the measurements cross China, we developed a set of

regression equations (Table 2) to convert the total biomasses including

stems, barks, branches and roots from provincial volume densities for

different tree species or forest types. To determine the parameters of the

equations, robust regressionwas conducted (Appendix S2) correspond-

ing to the classification of tree species in the forest inventories. The field

data pairs were collected from the data base (Luo et al. 2013) of Chi-

na’s forest biomass (Appendix S1) for 621 species observed from 520

field studies (Fig. 2) since 1978. The total forest biomass was calculated

by summing the biomasses of each forest types in each province, and

by compensating scaling-up errors for all these biomasses. Carbon con-

vert factor was set to 0�5. All forest volume data were collected from

the Forest Resource Inventory of China (FRIC) (CMF 1999, 2004,

2009, and 2013,) for the estimation experiment of China’s FCS.

Results

By considering the functional relation between the error and

different factors, we proposed an error compensation formula

derived and expressed as a ternary function withX,D and k as

the variables (X, regional volume density, m3 ha�1; D, vari-

ance of the volume density; r and k, parameters of the power

functionY = rXk;Y, biomass density,Mg ha�1):

UðX;D;kÞ ¼ 0�5rkð1� kÞXk�2D eqn 1

In form, obviously, this function elucidates that greater

error may occur under the conditions of small X or large D.

The curvature of the curved surface, namely k, also affects the

magnitude of the error (Fig. 3). Thus, eqn (1) can be the error

compensator to comprehensively reflect the effects of the three

factors (volume density, variance and nonlinearity) that deter-

mine the scaling-up errors.

An algorithm test and error analysis based simulated data

revealed that on average 83�7% (Fig. 4) of the errors have been

corrected after compensation, even though only second-order

Taylor series expansion was applied to the compensator. Fur-

thermore, applying fourth-order Taylor series expansion

derived anothermore precise function

UðX;D;kÞ ¼ 0�417rkð1� kÞXk�4D½Qðk� 2Þðk� 3ÞDþ 12X2�eqn 2

It corrected on average 94�2% (Fig. 4) of the errors in the

test. Q equals 3 for normal and 1�8 for uniform distribution

(see theAppendix S3).

Our test also demonstrated (Table 1) that the uniformdistri-

bution makes greater error than the normal distribution

because of greater variance. This has a significant consequence

on the results of biomass estimations in some areas where the

forest ages are extensively distributed. On the other side, the

lower volume density results in larger errors than the higher

density does if having same variance. Moreover, the sensitivity

3

1st stand x 1

2nd stand x 2

rXk

X = w ix i

Σwi rxik

Bio

mas

s de

nsity

(Mg

ha–1

) yi = rxik

y1

A(ha)

Y 2= ArX

k

Y 1= AΣw i

rx ik

Volume density (m ha–1)

Overestimatey2

For example, for the function y = 1·95x0·8119, if a region includes 1st stand (1 ha, 200 m3) and 2nd stand (2 ha, 100 m3) , the biomass should be:

Y1 = [1/(1+2)*1·95*(200/ 1)0·8119+2/(1+2)*1·95*(100/2)0·8119]*(1+2) = 237 (t ha–1) But we only know total amounts (3 ha, 300 m3), the biomass can only become:

Y2 = [1·95*(300/3)0·8119]*3 = 246 (t ha–1)

Fig. 1. Scaling-up error resulting from mean

average of two stands. Y1 and Y2 express

regional forest biomasses calculated from two

different ways, which show a gap existing in

the scaling-up from stand to regional scale. A,

area of a region; X, the mean regional average

volume; r and k, parameters in the biomass-

volume equation; xi, average volume of the ith

stand; yi, biomasses corresponding to xi; wi,

weighted area of the ith stand; i = 1, 2 in this

example. Symbols have the same definitions as

in Table S1.


Correcting the overestimates of forest biomass 3

of D can be inferred from Fig. 3 to assess how sensitive the

compensation is to misspecification of the volume density dis-

tribution. If X and k are known butD is not,g(X, D, k) becomes

g(D) and varies only with varianceD (Appendix S2).

To use the algorithm on a vast country’s forests, we esti-

mated China’s FCS based on the provincial statistics in FRIC

(CMF 1999, 2004, 2009, and 2013) as an example. China’s for-

ests cover 14% of the country. The total volume has increased

Fig. 2. Geographical distribution of China’s

sample plots (803), at which both the forest

biomass and volume were measured simulta-

neously in 520 field studies published during

1978–2008 (Luo et al. 2013; Appendix S1).

Fig. 3. The percentage and its scope of scaling-up error compensation for Pinus koraiensis and other temperate pines. (a) The surface intersection

and themaximum variance.g is the error compensation percentage given by eqn (A6).X is the weightedmean of xi (volume density of the ith stand),

and is also the mean regional volume density ranging from xmin (15 m3 ha�1) to xmax (500 m3 ha�1).D is the variance of xi. The parabolic cylinder

shows themaximum variance expressed by eqn (A7). (b) The comparison of compensation percentages between uniform (crossmark) and other dis-

tributions. For the uniform distribution,D = (xmax � xmin)2/12 withmedium compensation. Note: The curvature of surface corresponds the power

function (y = rxk, r = 1�95 and k = 0�8119, see Table 2). If k = 1 leads to a linear function y = rx + c (c, adjustable or regressed coefficient), then the

surface becomes a plane with no error compensation (g = 0). The distribution interval of xi was set up from 10 to 500 (m3 ha�1).


4 X. Zhou et al.

by 47% since the early 1900s. Our results indicate that FCS of

the country was approximately 6�0 PgC or less at the begin-

ning of the 2010s (Table 3). We suggest an increase rate of

21% (average is 0�12 PgC year�1) over the last decade for the

carbon fixation, which is roughly equivalent to 5% of the

country’s carbon emission (2�5 PgC year�1 in 2010) (UNSD

2010).

Discussions

Of our particular interest is the error compensation in Fig. 5,

which illustrates how the distributions of the volume densities

of different tree species affect the level of scaling-up errors

corresponding to different species in each province of China.

In our computation, the maximum compensation dosage

reached 16�3% (Fig. 5). Merely judging from the characteris-

tic of eqn (1), if the volume density X is lower (e.g.

X < 30 m3 ha�1) within a range of variance D, the error

should be greater. The comparison of estimates (Table 3)

indicates that the compensation rates are higher for the for-

ests with lower volume density than others are. It implies that

FCS may be overestimated more for young forests than for

Fig. 4. The probability densities for the percentages of compensated

value to scaling-up error, based on the simulated data analysis. The for-

est conditions were designed to be the same as the stands under uniform

distribution (with high expectation) in Table 1. This experimental

result is based on a Monte-Carlo error analysis. The convergence of

mathematical expectation (l) stabilized after 3000 samplings. The

curve a and b indicate two l convergences corresponding to eqns (1)

and (2), respectively. The curve ca (l = 83�7%, SD = 8�3%, n = 5000)

and cb (l = 94�2%, SD = 9�2%, n = 5000) represent the distributions

using eqns (1) and (2), separately.

Table 1. A calculation example of error compensation based on the analysis using the volume-biomass equation in power function form* and the

simulated data†

Low expectation High expectation

UnitNormal Uniform Normal Uniform

Distribution of stand volume density:

Region area (A) including 300 stands 618 618 618 618 ha

Total volume 93 309 93 279 184 456 186 260 m3

Expectation(X) of stand volume densities (e.g. regional volume density) 151 151 298 301 m3 ha�1

Variance(D) of stand volume densities 2299 7721 7619 29 973 –Calculationwithout error compensation:

Total biomass accumulated from stand biomasses (Y1) 70 205 68 526 122 240 120 565 Mg

Total biomass directly converted from regional volume density (Y2) 70 811 70 793 123 140 124 117 Mg

Error (Y2 � Y1) 606 2267 900 3552 Mg

Relative error (Y2 � Y1)/Y1 (%) 0�9 3�3 0�7 2�9 –After error compensation:

Total compensation‡ (ΦA) 545 1832 804 3127 Mg

Relative error‡ (Y2 � Y1 � ΦA)/Y1 (%) 0�09 0�63 0�08 0�35 –Total compensation§ ((ΦA) 581 2074 849 3530 Mg

Relative error§ (Y2 � Y1 � ΦA)/Y1 (%) 0�03 0�27 0�04 0�02 –

*Parameters of y = rxk are forPinus koraiensis and other temperate pines: r = 1�95 and k = 0�8119.†The simulated data are listed inAppendix S2.‡,§The results are found by using eqns (1) and (2), separately. Note that any type of regression function, not only the power function, can be tested to

evaluate the calculation’s accuracy using the simulated data.

Fig. 5. The compensator values for China’s forest biomass estimation.

n = 658 (percentages range from 0�0 to 16�3) for all available combina-

tions of species and provinces (Fig. 6) in the data from FRIC during

2008–2012. Symbols have the same definitions as in Table S1.



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31

No.

Province:

Species:

Bei

jing

Tian

jinH

ebei

Sha

nxi

Nei

mon

gLi

aoni

ng Jilin

Hei

long

jiang

Sha

ngha

iJi

angs

uZh

ejia

ngA

nhui

Fujia

nJi

angx

iS

hand

ong

Hen

anH

ubei

Hun

anG

uang

dong

Gua

ngxi

Hai

nan

Cho

ngqi

ngS

ichu

anG

uizh

ouY

unna

nX

izan

gS

hanx

iG

ansu

Qin

ghai

Nin

gxia

Xin

jiang

Equ

atio

n no

.

1 Other hard broadleaved trees 152 Other soft broadleaved trees 133 Quercus spp. 104 Mixed broadleaved trees 165 Populus spp. 116 Salix babylonica 137 Other Birchs 158 Ulmus pumila 109 Robinia pseudoacacia 1010 Cinnamomum camphora 1511 Paulownia 1312 Liquidambar formosana 1513 Tilia 1314 Betula platyphylla 1515 Eucalyptus 1216 Schima superba 1517 Phoebe zhennan 1518 Decaspermum 1319 Juglans mandshurica 1020 Betula costata 1521 Acacia spp. 1222 Astronium graveolens 1523 Quercus variabilis 1024 Fraxinus chinensis 1025 Fraxinus mandshurica 1026 Casuarina 1227 Sassafras tzumu 1328 Ginkgo biloba 1529 Castanopsis fargesii 1330 Castanopsis sclerophylla/carlesii 1331 Phellodendron amurense 1032 Castanea henryi 1533 Cyclobalanopsis glauca 1534 Typical deciduous trees 1035 Choerospondias axillaris 1536 Michelia spp. 1537 Elaeocarpus 1538 Eucommia ulmoides 1539 Vernicia fordii 1340 Mixed conifer and broadleaved trees 1441 Cupressus funebris 242 Mixed conifer trees 1443 Larix 344 Cunninghamia lanceolata 745 Pinus tabulaefomis 546 Picea 147 Pinus massoniana 848 Other pines 549 Pinus armandii 550 Metasequoia glyptostroboides 951 Abies 152 Keteleeria 953 Pinus elliottii 654 Pinus thunbergii 1455 Pinus sylvestris var. mongolica 556 Tsuga 1457 Pinus yunnanensis 658 Pinus taiwanensis 559 Pinus taeda 660 Pinus densiflora 561 Exotic pines 662 Pinus koraiensis 563 Pinus densata 564 Taxodium ascendens 965 Cryptomeria 1466 Taxus chinensis 167 Pinus griffithii 568 Pinus kesiya 669 Other firs 970 Cortex Phellodendri Chinensis 2

0 20 40 60 80 100+N/A


6 X. Zhou et al.

old. After all, any scaling-up error cannot be over the maxi-

mum limit calculable with eqn (A7 in Appendix S3) (also

refer to the parabolic cylinder in Fig. 3).

In practice, how much the information can be provided by

forest inventories could affect the magnitude of scaling-up

error in a FCS estimation. If volume information is available

for each age group, it can help to reduce more scaling-up error.

This is because the distribution ranges are divided by age

groups, as a result, the domain of xi is divided and redefined

for each age group. This processing accordingly lowers D and

then g for the stands of each age group. We reckon that to

count China’s FCS based on age group’s volume densities

would be relatively accurate for applying volume-biomass

equations in power form even without scaling-up compensa-

tion. Our experiment tested the scaling-up errors in China’s

FCS estimation by utilizing provincial volume densities of each

age group (see an example of provincial estimation in

Appendix S2). The scaling-up errors for the country are less

than 1% of the national FCS. But a critical problem is con-

cerning the distribution intervals and the variances, which were

tentatively presupposed by subjective judgment for each age

group of every species.

Overall, the scaling-up error on average is not significant

using the volume-biomass equations in the estimation of Chi-

na’s FCS (refer to Table 3). This is mainly because most

variances (D) are smaller (Fig. 6) and partly because of the tree

species in China’s forest ecosystems. These species were mea-

sured and modelled by the volume-biomass curves with low

curvature. Their powers are greater than 0�85 for most func-

tions (Table 2). Several powers are higher than 0�9, for

instance, Pinus massoniana and broadleaved trees. The former

is largely planted in south China, and the latter grows widely

across the country. They occupied 38% of the country’s total

volume. These forest conditions imply that, to compute Chi-

na’s FCS using power volume-biomass equations would not

introduce considerable scaling-up error at the current stage.

However, this does not mean that no compensation is needed

in national FCS estimations. There would be different age

structures and distributions of volume density in different

countries. The tree species and climates would be changed to

influence the parameters of volume-biomass equations in dif-

ferent ecosystems. The forested areas would be hugely different

between countries. Additionally, a certain ecosystemmay con-

tain special species, which were modelled by concave upward

functions (k > 1�0 slightly) for above-ground biomass (Mon-

tagu, Duttmer & Barton 2005) and perhaps for total biomass

as well, in which case, underestimates could be produced (refer

to eqns 1 and 2). All these changing conditions require detec-

tions of how large the scaling-up errors could be.

The repeatability and confirmability of the computation

with respect to the verification of FCS estimation needs to be

considered asmuch as possible.Whether or not the experimen-

tal result for a large-scale FCS estimation can be repeated

hinges on a key condition: the correspondence between the tree

species classified in forest inventories and the tree species

described by volume-biomass equations. This correspondence

Fig. 6. The standard deviation of mean volume density estimated for all tree species and forest types categorized by FRIC. A total of 658 standard

deviations (r ¼ ffiffiffiffiD

p, m3 ha�1; see theAppendix S3) were computed responding to all available combinations of species and types (70) and provinces

(31). The volume data were collected fromFRIC (2008–2012). Type no. 1–39 are broadleaved trees, and the rest are conifer ormixed trees. Themed-

ian and mode of standard deviations are 24�2 and 18�9 (m3 ha�1) separately. Twenty-six standard deviations are greater than 100 (m3 ha�1). The

available equation numbers (in the rightmost column) for each species or type correspond to the equation number in Table 2.

Table 2. Parameters to calculate the live-biomass density of tree layer for China’s major forest types. Biomass density y (Mg ha�1) is expressed as

the power function of stand volume density x (m3 ha�1), y = rxk, where r and k are coefficients determined by robust regression analysis. The total

biomass y includes stem, bark, branch and root. SEE are standard errors of the estimate. n andR2 denote plot number and determination coefficient,

respectively

Equation no. Forest type r k R2 SEE n

1 Abies andPicea 1�19 0�8790 0�88 29�4 25

2 Cupressus 1�87 0�8259 0�75 35�4 28

3 Larix 1�56 0�8617 0�88 25�5 38

4 Pinus tabulaeformis 1�55 0�8615 0�89 18�9 77

5 Pinus koraiensis and other temperate pines 1�95 0�8119 0�83 26�8 62

6 Pinus yunnanensis and other subtropical pines 1�44 0�8591 0�79 28�4 34

7 Cunninghamia lanceolata 1�26 0�8497 0�95 17�9 194

8 Pinusmassoniana 1�09 0�9154 0�87 30�1 63

9 Other conifer trees 1�37 0�8225 0�81 25�3 17

10 Oaks and other deciduous trees 1�80 0�8744 0�96 24�7 32

11 Populus 1�10 0�8969 0�78 24�5 56

12 Eucalyptus and other fast-growing trees 1�13 0�9277 0�76 29�7 20

13 Soft broadleaved trees 0�86 0�9523 0�80 38�4 12

14 Mixed conifer and deciduous trees 1�74 0�8350 0�82 30�3 64

15 Other hard broadleaved trees 1�57 0�9128 0�81 53�2 81

16 Other broadleaved trees 1�22 0�9125 0�81 42�1 93

The data of each volume-biomass pair are from 803 field sample plots (Fig. 3). All data were collected and published in 2013 (Luo et al. 2013;

Appendix S1). We did not list the equation for tropical forests not included in the categories by the FRIC. The parameter set is not necessarily

unique, but it needs to bementioned that this parameterization is subjected to the constraint conditions for restricted regressions.



needs to be indicated explicitly (Fig. 6), otherwise it is very dif-

ficult to verify the estimates for reproducibility. Another point

is regarding the observed data. An estimate may be influenced

considerably by volume-biomass equations upon these mea-

surements. We noticed that our results are on average roughly

13% lower than other estimates (Table 3). The causes may

include two factors. Besides the effect of scaling-up error on

the estimates, another possible reason could be the use of dif-

ferent field data sets for finding regression equations on vol-

ume-biomass relations. This is a verification issue on the

regression model itself. Actually, measured data pairs of both

volume and biomass have been lacking at best for many domi-

nant tree species in China. The data base that we usedwas pub-

lished by Luo et al. (2013). This has both systematized the

measurements of China’s forest biomass and brought them

into the public for the first time.

To a certain extent, rather than discussing the importance of

the error compensation per se, it can be said that whether the

compensation is possible or not makes a more significant dif-

ference to the method selection for estimating FCS on the

national scale. The difficulty of quantifying the scaling-up error

has promoted the development and application of some alter-

native methods. The big gaps between the estimates mentioned

in the opening of this paper might have been caused by differ-

ent magnitudes of scaling-up errors by applying the alternative

methods. Those gaps could be narrowed after conducting the

compensation of scaling-up error into thosemethods. A priori-

tized recommendation in experiments of FCS estimation is to

use the simulated data as an utilizable measure to realize the

true value and to compare different algorithms. Logically

speaking, because applying the power function definitely

overestimates biomass, the first target should be to reduce the

error to approach the true value as much as possible. Once the

error is compensated, a ‘reference value’ will be established for

the second target. It will be used to find a better method (e.g.

different forms of volume-biomass equation, including linear

equations) and see if it estimates more accurately between the

reference value and true value.

As IPCC suggested, ‘[the] approach for biomass carbon

stock change estimation allows for a variety of methods’

(IPCC, 2006). Researchers may be interested in the effects of

different methods on the estimations (IPCC, 2003; Woodbury,

Smith & Heath 2007; Ni 2013; MacLean, Ducey & Hoover

2014). Experience shows that in studies of climate-vegetation

interaction on national and global scales, the unfortunate real-

ity is that despite the fact that various methods and techniques,

including different BEFs and volume-biomass equations, have

been developed for FCS estimations, we are still facing the

issue of method evaluation because true value is immeasurable

for a country’s FCS. Nonetheless, a reference value can be cre-

ated for evaluating different estimations if we understand how

far away an estimate is to the true value. From that, quantify-

ing scaling-up error is the first and foremost step.

From a broader view in ecosystem analyses, scaling-up error

is the aggregation error producedby translating ecological rela-

tionshipsacrossscales(Rastetter,King&Cosby1992;Cushman

et al., 2010). The presentedmethodswill help to apply, inmany

aspects, the knowledge embodied in the fine-scale to coarser

scale models by correcting aggregation errors analytically.

Although thederivationmight be little lengthy in theAppendix,

thecompensatorscanbeappliedconvenientlyonanylarge-scale

FCSestimation.Thismethod isapplicable for thecountries that

provide the volume data in their forest inventories. After sub-

tractingthecompensatedamount, thenationalFCSscanbecor-

rected to theoretically approach the true value in each country.

As the sum of national FCSs, the global FCS should be lower

than the estimation without error compensation and, more

importantly,notbesignificantlyoverestimated.

Conclusion

In summary, the bias for estimating FCS at the national scale

can be reduced by selecting proper regression equations and

compensating scaling-up errors. Although volume-biomass

equations constructed with the power-law function yield errors

over 16% in some cases of FCS estimations in China, on aver-

Table 3. The forest carbon storage (FCS) estimates of China’s forests with the error compensation based on national forest inventories. The forest

inventory datawere collected fromFRIC (CMF1999, 2004, 2009, and 2013). The scaling-up errors were calculated using eqn (1)

Period

Forest inventory Estimated FCS

Area (106 ha) Inc. (%) Volume (106 m3) Inc. (%)

Before

compensation

(PgC)

After

compensation

(PgC) Rate (%)

1994–1998 129 – 10 086 – 4�20 0�160* 4�14 0�155* 1�5 2�9*4�040† 3�982† 1�4†

1999–2003 143 11 12 098 20 4�97 0�066* 4�91 0�064* 1�3 2�5*4�907† 4�844† 1�3†

2004–2008 156 9 13 363 10 5�46 0�080* 5�40 0�078* 1�2 2�9*5�381† 5�318† 1�2†

2009–2012 165 6 14 779 11 6�02 0�102* 5�96 0�099* 1�1 2�6*5�920† 5�875† 1�1†

China’s FCS has been estimated by applying different methods. Recently 12 studies carried out in last two decades were reviewed on the estimations

of China’s FCS, whichwas reported to be ranging from 4�6 to 6�4 PgC during 1994–2008 (Guo, Fang&Pan 2010).*For younger forests (volume densityX ≤ 30 m3 ha�1).†For other forests (volume densityX > 30 m3 ha�1).


8 X. Zhou et al.

age 94�2% of the errors can be corrected. As for the average of

the country, scaling-up errors were not compensated signifi-

cantly in our estimation. Nevertheless, the compensation is

completely necessary as a technical guarantee to reduce the

overestimations. Arguably, FCS estimations, especially for

young forests, without scaling-up error compensation will not

assure the rationality of the estimates whether or not they are

on the regional, national or global scale. The risk of overesti-

mation indicates the importance of understanding the stochas-

tic systematic error, which is caused by using nonlinear

volume-biomass equations or other alternative BEF methods.

The concept and methodology of the error compensation have

general implications for scaling up issues. A better understand-

ing could be achieved by analysing and creating the functional

relations between the errors and major factors that may affect

results of scaling-up biomass of sample plots to large areas.

Acknowledgements

We thank Yunjian Luo for the comments and discussions of field data and vol-

ume-biomass regression equations. We thank Terry Lee and Lori Lee for their

many valuable suggestions to the manuscript. This work was supported in part

by State Key Laboratory of Remote Sensing Science (OFSLRSS201404), Insti-

tute of Remote Sensing and Digital Earth, Chinese Academy of Sciences, Beijing

NormalUniversity.

Data accessibility

The data used in this study include: (i) the field data of biomass and volume (refer

to Luo et al. 2013, and Appendix S1); (ii) The forest volume data (refer to http://

cfdb.forestry.gov.cn/lysjk/indexJump.do?url=view/moudle/index). For the

details describing China’s forest inventories, it refers to CMF 1999, 2004, 2009,

and 2013, Fang, Chen & Peng (2001a), Guo, Fang & Pan (2010) and Fang, Guo

&Hu (2014).

Authorship

XZ conceived this study, performed mathematical analysis, and wrote the manu-

script; XZ and XL performed the forest growth, statistical model and result anal-

yses; XL, CP, WW, CZ, CL and ZL conducted the data collection and

computation. All authors contributed to the data analysis, result discussion and

manuscript preparation.

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Received 1 July 2015; accepted 25October 2015

Handling Editor: SeanMcMahon

Supporting Information

Additional Supporting Information may be found in the online version

of this article.

Appendix S1.Measurements of volume and biomass.

Appendix S2. Details of equations, derivations, analyses, and simula-

tion data.

Appendix S3.The derivation of the compensators.

Table S1. Symbols and their descriptions.



http://cfdb.forestry.gov.cn/lysjk/indexJump.do?url=view/moudle/index

http://cfdb.forestry.gov.cn/lysjk/indexJump.do?url=view/moudle/index

http://dx.doi.org/10.1007/978-4-431-87771-4_3

http://mdgs.un.org/unsd/mdg/Default.aspx

Notes:These data were measured in 803 field sample plots. All data were collected from a published data set: Luo, Y., Wang, X., Zhang, X., & Lu, F. Biomass and its allocation of forest ecosystems in China (Chinese forestry publishing house, 2013).A part of stand volumes were not measured, but can be calculated based on DBH, height, and tree density using the approach introduced in above reference (page 9).

Plot number Species 1 Species 2 Species 3 Species 4 Lat (e)d.m Long (n)d.mMean annualtemperature(d.c)

Mean annualprecipitation(mm)

Mean DBH(cm)

Mean treeheight (m)

Tree density(trees/ha)

Standvolume(m3/ha)

Total biomass(t/ha, above-and below-ground)

3 Abies fabri (Mast.) Craib 103.05 28.74 7.6 1585 10.6 8.3 2800 - 110.644 Abies fabri (Mast.) Craib 103.05 28.74 7.6 1585 14.1 11.9 2834 337.8 173.085 Abies fabri (Mast.) Craib 103.00 29.57 4 1900 19.56 15.26 1708 - 257.376 Abies fabri (Mast.) Craib 103.00 29.57 4 1900 50.78 31.86 209 - 321.00

7Picea likiangensis (Franch.) E.Pritz. var. Balfouriana (Rehder et E.H. Wilson) Hillier

102.72 32.15 6.5 783 10.4 10.5 3460 125.2 107.82

12 Picea asperata Mast.AbieschensiensisTiegh.

105.54 34.16 9.7 629 - - - 143.53 94.37

14 Picea asperata Mast. 103.77 32.58 7.5 697 18.92 14.53 1096 180.1 212.7715 Picea koraiensis Nakai 128.04 47.77 -0.4 700 11.3 10.65 2858 - 151.1316 Picea koraiensis Nakai 128.04 47.77 -0.4 700 11 9.04 2150 - 89.4017 Picea koraiensis Nakai 128.04 47.77 -0.4 700 11.3 10.38 2550 - 130.8518 Picea koraiensis Nakai 128.04 47.77 -0.4 700 7.7 6.79 1925 - 40.9719 Picea koraiensis Nakai 128.04 47.77 -0.4 700 8.3 6.3 3950 - 84.3620 Picea koraiensis Nakai 128.04 47.77 -0.4 700 2.7 2.9 3300 - 9.3421 Picea koraiensis Nakai 128.04 47.77 -0.4 700 3.1 3.05 3975 - 14.3622 Picea koraiensis Nakai 117.22 43.52 -1.6 404 15.92 10.32 765 91.4 97.68

23Picea likiangensis (Franch.) E.Pritz. var. linzhiensis W. C. Chenget L. K. Fu

95.89 29.93 8.5 877 114 65.1 - 3831 1564.30

31 Picea crassifolia Kom. 99.90 38.45 0.6 437 19.55 17.65 917 - 145.7032 Picea crassifolia Kom. 99.90 38.45 0.6 437 19.45 18.03 1182 - 177.8233 Picea crassifolia Kom. 99.90 38.45 0.6 437 26.43 23.37 657 - 232.8834 Picea crassifolia Kom. 99.90 38.45 0.6 437 19.9 17.1 938 - 180.4837 Picea crassifolia Kom. 101.80 37.03 3.8 454 18.9 12.7 1263 - 142.1038 Picea wilsonii Mast. 108.45 33.43 8.8 937 - - - 197.61 133.25

43Picea brachytyla (Franch.) E. Pritz.var. complanata (Mast.) W. C.Cheng ex Rehder

103.05 28.74 7.6 1585 13.4 12.5 3050 285.79 174.96

Appendix S1. Measurements of volume and biomass


99.67 28.08 5.4 625 11.23 18 1580 - 128.46


99.67 28.08 5.4 625 33.74 25 384 - 311.69

50 Sabina przewalskii (Kom.) Kom. 99.90 38.45 0.6 437 25.9 8.3 725 - 216.1251 Sabina przewalskii (Kom.) Kom. 99.90 38.45 0.6 437 29.54 10.4 975 - 328.7152 Sabina przewalskii (Kom.) Kom. 99.90 38.45 0.6 437 38.88 12.75 300 - 137.2353 Sabina przewalskii (Kom.) Kom. 99.90 38.45 0.6 437 31.44 10.48 667 - 182.1154 Larix olgensis A. Henry 128.00 42.28 1.7 719 17.5 17.03 1598 357.63 283.6181 Larix principis-rupprechtii Mayr. 100.65 37.23 2.4 570 11.28 5.88 1550 - 36.2583 Larix principis-rupprechtii Mayr. 112.18 38.71 4.7 472 7.1 6.8 5300 - 52.8784 Larix principis-rupprechtii Mayr. 112.18 38.71 4.7 472 6.3 7.4 3825 - 51.4985 Larix principis-rupprechtii Mayr. 111.67 38.53 4.7 493 5.6 6.7 4250 - 55.0587 Larix principis-rupprechtii Mayr. 111.44 37.83 3.5 700 17.62 20 1429 255 213.5088 Larix principis-rupprechtii Mayr. 111.44 37.83 3.5 700 12.92 13.55 2178 142 92.8889 Larix principis-rupprechtii Mayr. 111.44 37.83 3.5 700 16.14 19.8 1650 284 188.5190 Larix principis-rupprechtii Mayr. 111.44 37.83 3.5 700 14.72 15.8 2670 287 189.9991 Larix principis-rupprechtii Mayr. 113.60 38.98 3 800 5.1 5.85 2700 - 21.6292 Larix principis-rupprechtii Mayr. 113.60 38.98 3 800 6.3 6 2700 - 25.8193 Larix principis-rupprechtii Mayr. 113.60 38.98 3 800 10.4 7.1 2700 - 112.1294 Larix principis-rupprechtii Mayr. 113.60 38.98 3 800 7.65 7.1 2700 - 51.5095 Larix principis-rupprechtii Mayr. 113.60 38.98 3 800 8.6 7.45 2700 - 64.3396 Larix principis-rupprechtii Mayr. 113.60 38.98 3 800 11.4 9.5 2700 - 132.8097 Larix principis-rupprechtii Mayr. 113.60 38.98 3 800 8.7 8.9 2700 - 65.7798 Larix principis-rupprechtii Mayr. 113.60 38.98 3 800 12.3 11.5 2450 - 150.7999 Larix principis-rupprechtii Mayr. 113.60 38.98 3 800 9.8 10.15 2450 - 90.09

100 Larix principis-rupprechtii Mayr. 113.60 38.98 3 800 13.1 10.7 2450 - 196.50101 Larix principis-rupprechtii Mayr. 113.60 38.98 3 800 18 16 1560 - 238.56102 Larix principis-rupprechtii Mayr. 113.60 38.98 3 800 21.5 16.1 1350 - 247.98104 Larix kaempferi (Lamb.) Carrière 105.54 34.16 9.7 629 - - - 91.05 67.37108 Larix kaempferi (Lamb.) Carrière 111.32 33.71 12 900 9.7 10.9 3167 - 98.92109 Larix kaempferi (Lamb.) Carrière 111.32 33.71 12 900 13.6 14.6 2350 - 165.26110 Larix kaempferi (Lamb.) Carrière 111.32 33.71 12 900 22.1 22.2 1083 - 249.43111 Larix kaempferi (Lamb.) Carrière 111.32 33.71 12 900 24.4 25.5 738 - 228.79112 Larix kaempferi (Lamb.) Carrière 110.03 30.80 9.4 1411 15.4 13.8 714 - 53.18118 Larix kaempferi (Lamb.) Carrière 124.08 41.83 6.2 782 8.97 9.5 3066 97.19 109.91129 Larix kaempferi (Lamb.) Carrière 102.80 31.68 4.7 1194 17.35 14.5 1940 344.36 191.56131 Larix gmelinii Rupr. 127.52 45.28 2.6 649 17.07 16.4 1158 173.58 168.79132 Larix gmelinii Rupr. 127.52 45.28 2.6 649 15.75 15.16 1300 168.87 162.59133 Larix gmelinii Rupr. 127.52 45.28 2.6 649 14.85 14.6 1358 152.87 132.90

134 Larix gmelinii Rupr. 127.52 45.28 2.6 649 13.1 14.07 1475 119.03 133.96135 Larix gmelinii Rupr. 127.52 45.28 2.6 649 13.4 13.5 1450 - 142.36165 Larix gmelinii Rupr. 121.50 50.87 -4.9 466 24.6 24.3 792 450 249.21166 Larix gmelinii Rupr. 121.50 50.87 -4.9 466 17.3 17.4 811 163.66 117.34167 Larix gmelinii Rupr. 121.50 50.87 -4.9 466 8 8.1 2934 75.1 60.43

168 Larix mastersiana Rehder et E. H.Wilson 103.13 31.08 10.9 1100 17.02 13.75 1359 - 113.57

172 Pinus tabuliformis Carrière 116.21 40.01 11 651 13.6 4.7 1125 - 67.95173 Pinus tabuliformis Carrière 116.21 40.01 11 651 12.6 7.3 1550 - 85.45174 Pinus tabuliformis Carrière 116.21 40.01 11 651 16.3 9.6 850 - 83.11175 Pinus tabuliformis Carrière 116.21 40.01 11 651 8.1 5.2 2367 41.6 54.09176 Pinus tabuliformis Carrière 116.21 40.01 11 651 9.3 5.36 2071 43.6 53.61177 Pinus tabuliformis Carrière 116.21 40.01 11 651 11.7 6.8 1754 75.19 74.49183 Pinus tabuliformis Carrière 105.40 34.15 7.1 791 11.9 6.5 2479 - 96.80184 Pinus tabuliformis Carrière 105.40 34.15 7.1 791 12.5 7.2 2058 - 90.67185 Pinus tabuliformis Carrière 105.40 34.15 7.1 791 13 7.1 1877 - 83.29186 Pinus tabuliformis Carrière 105.40 34.15 7.1 791 11.3 6.4 1692 - 80.50187 Pinus tabuliformis Carrière 105.40 34.15 7.1 791 12.2 6.7 1500 - 77.39188 Pinus tabuliformis Carrière 105.40 34.15 7.1 791 13.9 7.8 1520 - 78.53189 Pinus tabuliformis Carrière 105.40 34.15 7.1 791 14.2 7.9 1380 - 68.69190 Pinus tabuliformis Carrière 105.40 34.15 7.1 791 14.5 8.1 1285 - 61.76191 Pinus tabuliformis Carrière 105.54 34.16 9.7 629 - - - 92.94 60.70192 Pinus tabuliformis Carrière 104.68 33.38 10 625 20.48 15.35 428 - 113.54193 Pinus tabuliformis Carrière 108.45 35.28 9.7 603 - - - 89.41 89.44199 Pinus tabuliformis Carrière 117.15 41.73 7 500 11.5 8.8 2033 104.79 82.33200 Pinus tabuliformis Carrière 117.56 41.67 4.7 472 6.24 4.98 5201 - 37.40201 Pinus tabuliformis Carrière 118.65 41.24 6.4 558 17.64 13.58 1348 - 208.95202 Pinus tabuliformis Carrière 118.77 41.22 7 557 8.79 7.3 3226 - 70.35203 Pinus tabuliformis Carrière 124.10 41.92 7.6 768 8.29 7.95 3482 - 77.27204 Pinus tabuliformis Carrière 124.10 41.92 7.6 768 12.08 10.93 2452 - 133.07205 Pinus tabuliformis Carrière 124.10 41.92 7.6 768 16.16 14 1248 - 184.22206 Pinus tabuliformis Carrière 124.10 41.92 7.6 768 19.16 15.19 1159 - 232.28207 Pinus tabuliformis Carrière 124.10 41.92 7.6 768 22.52 16.47 843 - 248.16208 Pinus tabuliformis Carrière 121.86 41.22 9.3 600 6.26 3.99 3472 - 27.22209 Pinus tabuliformis Carrière 121.86 41.22 9.3 600 7.43 4.95 3200 - 40.82210 Pinus tabuliformis Carrière 121.86 41.22 9.3 600 10.12 6.69 2430 - 72.59229 Pinus tabuliformis Carrière 118.45 41.42 5.3 537 18 11.7 1530 - 192.40230 Pinus tabuliformis Carrière 118.45 41.42 5.3 537 12.49 9.73 2010 - 107.45231 Pinus tabuliformis Carrière 118.45 41.42 5.3 537 24.35 18.19 603 - 182.48232 Pinus tabuliformis Carrière 118.45 41.42 5.3 537 10.57 8 2474 - 72.41233 Pinus tabuliformis Carrière 117.11 36.26 7.6 970 8.15 5.34 1700 - 27.54234 Pinus tabuliformis Carrière 117.11 36.26 7.6 970 11.09 6.57 1557 - 63.66

235 Pinus tabuliformis Carrière 113.17 36.20 8.1 619 9.23 5.68 1800 - 35.68241 Pinus tabuliformis Carrière 111.91 36.80 5.8 578 5.7 4.57 7246 - 45.78242 Pinus tabuliformis Carrière 111.91 36.80 5.8 578 7.3 6.25 6235 - 79.88243 Pinus tabuliformis Carrière 111.91 36.80 5.8 578 11.26 8.86 2444 - 125.47244 Pinus tabuliformis Carrière 111.91 36.80 5.8 578 13.07 7.83 1249 - 86.18245 Pinus tabuliformis Carrière 111.91 36.80 5.8 578 16.2 9.82 794 - 79.75246 Pinus tabuliformis Carrière 112.05 36.72 4.5 758 18.45 11.65 1035 - 117.07258 Pinus tabuliformis Carrière 109.10 35.69 9 550 4.27 3.1 2355 8.55 14.68259 Pinus tabuliformis Carrière 109.10 35.69 9 550 4.2 3.28 5955 21.32 20.90260 Pinus tabuliformis Carrière 109.10 35.69 9 550 3.38 2.86 2415 5.29 9.28261 Pinus tabuliformis Carrière 109.10 35.69 9 550 6.13 4.38 4305 38.06 38.84262 Pinus tabuliformis Carrière 109.10 35.69 9 550 4.89 3.62 1695 8.7 11.84263 Pinus tabuliformis Carrière 109.10 35.69 9 550 3.95 2.67 1950 5.71 9.39264 Pinus tabuliformis Carrière 109.10 35.69 9 550 5.36 3.56 2445 15.06 22.63265 Pinus tabuliformis Carrière 109.10 35.69 9 550 5.49 4.02 2445 16.75 22.47266 Pinus tabuliformis Carrière 109.10 35.69 9 550 6.4 4.44 1755 17.23 22.81267 Pinus tabuliformis Carrière 109.00 35.54 9.4 631 10.1 8.2 2150 - 61.81268 Pinus tabuliformis Carrière 109.00 35.54 9.4 631 8.1 6.5 2250 - 33.67269 Pinus tabuliformis Carrière 109.00 35.54 9.4 631 8 8.7 4330 - 77.47272 Pinus tabuliformis Carrière 109.42 34.15 13.7 626 8.88 7.2 2415 - 47.64273 Pinus tabuliformis Carrière 109.42 34.15 13.7 626 9.9 7.7 2708 - 85.17274 Pinus tabuliformis Carrière 109.42 34.15 13.7 626 8.3 8.6 3295 - 84.30275 Pinus tabuliformis Carrière 107.87 34.81 9.2 640 10.2 7.4 2200 89.7 74.82276 Pinus tabuliformis Carrière 107.87 34.81 9.2 640 13.4 8.3 1910 145.3 106.96277 Pinus tabuliformis Carrière 110.43 34.15 11.1 758 7.2 7.1 3549 - 59.16278 Pinus tabuliformis Carrière 108.45 33.43 8.8 937 - - - 157.36 107.90279 Pinus tabuliformis Carrière 108.45 33.43 8.8 937 10.7 8.9 1887 - 69.18281 Pinus tabuliformis Carrière 109.26 35.58 12.1 547 17.75 13.35 695 - 114.29282 Pinus tabuliformis Carrière 109.26 35.58 12.1 547 28.27 15.29 520 - 209.04283 Pinus tabuliformis Carrière 109.26 35.58 12.1 547 29.4 16.01 430 - 228.46284 Pinus tabuliformis Carrière 108.82 35.06 11.7 585 9.32 6.22 2136 - 72.61285 Pinus tabuliformis Carrière 108.82 35.06 11.7 585 13.01 10.63 1065 - 85.77286 Pinus tabuliformis Carrière 108.82 35.06 11.7 585 16.28 13.06 799 - 104.37287 Pinus tabuliformis Carrière 108.13 34.82 10.8 600 12.3 10 2233 - 67.12288 Pinus tabuliformis Carrière 108.88 36.60 7.8 528 7.6 8.1 5300 - 86.57289 Pinus tabuliformis Carrière 108.88 36.60 7.8 528 6.7 7.1 5070 - 59.75290 Pinus tabuliformis Carrière 108.88 36.60 7.8 528 6.8 6.3 5830 - 68.61292 Pinus tabuliformis Carrière 106.11 32.63 12 919 15.94 12.97 1177 - 158.30293 Pinus tabuliformis Carrière 106.11 32.63 12 919 11.92 9.95 2810 - 250.08295 Platycladus orientalis(L.) Franco 116.21 40.01 11 651 9.9 5.8 1750 - 54.99296 Platycladus orientalis(L.) Franco 116.21 40.01 11 651 11.48 8.3 1440 - 61.04297 Platycladus orientalis(L.) Franco 116.21 40.01 11 651 13.2 8.5 1025 - 66.91

298 Platycladus orientalis(L.) Franco 116.21 40.01 11 651 10.3 7.03 1520 35.32 46.26300 Platycladus orientalis(L.) Franco 107.87 34.81 9.2 640 4.7 5.5 2300 18.1 55.18301 Platycladus orientalis(L.) Franco 107.87 34.81 9.2 640 5.8 6.4 1950 24.1 76.05

309 Pinus sylvestris L.var.sylvestriformis (Taken.) W.C. 125.42 42.52 4.2 665 12 10.8 2100 - 101.91

315 Pinus densiflora Siebold et Zucc. 129.21 42.27 4.4 520 18.4 10.9 875 - 66.19316 Pinus densiflora Siebold et Zucc. 129.21 42.27 4.4 520 15.6 11.3 1325 - 103.31317 Pinus densiflora Siebold et Zucc. 129.21 42.27 4.4 520 16.4 9.7 1165 - 87.12318 Pinus densiflora Siebold et Zucc. 129.33 42.68 4.4 520 22 13.6 460 - 65.26319 Pinus densiflora Siebold et Zucc. 129.33 42.68 4.4 520 18.3 12.7 855 - 79.61320 Pinus densiflora Siebold et Zucc. 129.53 42.68 4.4 520 13.8 13.8 1150 - 86.31321 Pinus densiflora Siebold et Zucc. 129.53 42.68 4.4 520 15.5 14.1 1315 - 95.93322 Pinus densata Mast. 100.53 29.42 -0.7 783 10 4.5 2500 - 63.61323 Pinus densata Mast. 99.67 28.08 5.4 625 17.5 18 1050 - 293.52324 Pinus densata Mast. 99.67 28.08 5.4 625 23.2 15 600 - 231.00326 Pinus thunbergii Parl. 121.18 37.57 12.4 652 6.3 5.5 2130 22.9 38.06327 Pinus thunbergii Parl. 121.71 37.44 11.3 805 10.6 6.8 1395 - 88.34328 Pinus thunbergii Parl. 121.68 36.84 12.3 706 6.9 5.3 1560 19.03 31.14329 Pinus armandii Franch. 106.34 34.31 7.1 852 - - - 45.45 56.86330 Pinus armandii Franch. 106.34 34.31 7.1 852 - - - 107.23 96.34331 Pinus armandii Franch. 106.34 34.31 7.1 852 - - - 46.25 51.73332 Pinus armandii Franch. 105.54 34.16 9.7 629 - - - 91.87 67.98333 Pinus armandii Franch. 108.45 33.43 8.8 937 - - - 77.91 60.45334 Pinus armandii Franch. 108.45 33.43 8.8 937 - - - 142.24 98.87335 Pinus armandii Franch. 108.45 33.43 8.8 937 - - - 116.41 81.32336 Pinus armandii Franch. 108.45 33.43 8.8 937 - - - 116.75 84.72337 Pinus armandii Franch. 103.40 26.45 12.7 861 6.1 5 4900 - 42.84

346 Pinus sylvestris L. var. mongholicaLitv. 122.49 42.74 6.5 499 7.6 6 1800 29.7 39.63

347 Pinus sylvestris L. var. mongholicaLitv. 122.49 42.74 6.5 499 7.6 4.4 1659 28.6 30.26



350 Pinus tabuliformis CarrièrePlatycladusorientalis(L.)Franco

116.21 40.01 11 651 11.42 6.81 1365 - 66.83

351 Pinus tabuliformis CarrièrePlatycladusorientalis(L.)Franco

116.21 40.01 11 651 11.43 7.39 1333 48.11 60.42

352 Cunninghamia lanceolata (Lamb.)Hook. 116.18 31.10 15.2 1600 7.1 4.22 4545 40.24 49.12



357 Cunninghamia lanceolata (Lamb.)Hook. 118.64 27.16 18.7 1694 7.8 7.1 - 55.83 42.93

358 Cunninghamia lanceolata (Lamb.)Hook. 118.13 27.14 16.5 1880 8.2 5.48 2710 - 59.08

359 Cunninghamia lanceolata (Lamb.)Hook. 118.50 27.25 16 1890 3.89 2.02 3000 - 9.96





364 Cunninghamia lanceolata (Lamb.)Hook. 118.59 27.09 18.7 1670 10.63 7 3090 97.64 55.13
















384 Cunninghamia lanceolata (Lamb.)Hook. 117.95 26.47 20.1 1636 10.6 9.9 2625 126 48.60







391 Cunninghamia lanceolata (Lamb.)Hook. 117.95 26.47 20.1 1636 11.7 8.63 3600 137.57


393 Cunninghamia lanceolata (Lamb.)Hook. 118.12 26.57 20.2 1639 17 14.8 1129 - 95.74







400 Cunninghamia lanceolata (Lamb.)Hook. 116.80 26.25 17 1794 7.13 - 3025 43.26 33.36










410 Cunninghamia lanceolata (Lamb.)Hook. 117.54 26.16 19.8 1604 18 15.9 1500 299.73 130.83
















430 Cunninghamia lanceolata (Lamb.)Hook. 117.90 26.80 19.5 1728 12.9 12 3625 - 139.73





























472 Cunninghamia lanceolata (Lamb.)Hook. 111.83 23.13 21.7 1537 13 11 2160 178.42 88.93











485 Cunninghamia lanceolata (Lamb.)Hook. 107.18 25.07 20 1371 25.5 20.3 475 247.02 136.80

















505 Cunninghamia lanceolata (Lamb.)Hook. 109.63 26.78 17.4 1284 23 21.5 1665 817 328.60











554 Cunninghamia lanceolata (Lamb.)Hook. 111.24 28.90 16.5 1443 - - 3000 101.5 54.90

555 Cunninghamia lanceolata (Lamb.)Hook. 111.24 28.90 16.5 1443 - - 2565 110 58.80

556 Cunninghamia lanceolata (Lamb.)Hook. 111.24 28.90 16.5 1443 - - 3000 91.5 52.30
















688 Cupressus funebris Endl. 108.18 28.21 17 1161 12.1 10 818 - 32.72694 Cupressus funebris Endl. 105.21 31.75 16.5 992 9.8 9 3182 - 124.02702 Cupressus funebris Endl. 119.02 29.62 17 1430 10.4 9 1890 69.72 81.06703 Cupressus funebris Endl. 119.02 29.62 17 1430 13.7 12.05 1440 120.82 161.33704 Cupressus funebris Endl. 119.02 29.62 17 1430 17.1 15.2 1200 207.29 187.28

705 Fokienia hodginsii (Dunn) A. Henryet H. H. Thomas 117.68 24.86 17.4 1940 8.59 6.43 1344 - 27.60




716 Fokienia hodginsii (Dunn) A. Henryet H. H. Thomas 117.54 26.16 19.8 1604 21.6 21.4 1000 379.57 223.90

717 Fokienia hodginsii (Dunn) A. Henryet H. H. Thomas 117.54 26.16 19.8 1604 17 14.3 1750 289.25 164.75



720 Fokienia hodginsii (Dunn) A. Henryet H. H. Thomas 117.54 26.16 19.8 1604 17.4 12 1867 274.24 163.52

721 Fokienia hodginsii (Dunn) A. Henryet H. H. Thomas 117.79 26.38 20 1627 13.4 7.72 2150 118.25 103.61



737Fokienia hodginsii (Dunn) A. Henryet H. H. Thomas f. columnarisZ.F.Li et D.X.Zhou、 forma nov.

117.79 26.38 20 1627 12.9 8.26 2595 131.31 114.42

747 Pinus massoniana Lamb. 118.42 32.45 14.9 1020 18.7 10.8 960 - 120.60749 Pinus massoniana Lamb. 118.32 27.05 18 1630 5.73 4.13 936 6.41 9.60750 Pinus massoniana Lamb. 118.32 27.05 18 1630 5.73 4.05 1349 8.38 12.86751 Pinus massoniana Lamb. 118.32 27.05 18 1630 5.89 4.18 1784 12.25 16.96752 Pinus massoniana Lamb. 118.32 27.05 18 1630 6.41 4.39 2335 19.2 23.77753 Pinus massoniana Lamb. 118.32 27.05 18 1630 6.01 4.46 3009 24.61 28.72754 Pinus massoniana Lamb. 118.32 27.05 18 1630 4.81 4.14 4088 19.18 28.87755 Pinus massoniana Lamb. 118.32 27.05 18 1630 8.01 7.15 3525 - 71.05756 Pinus massoniana Lamb. 118.32 27.05 18 1630 10.01 10.02 2500 - 93.36757 Pinus massoniana Lamb. 118.32 27.05 18 1630 14.62 15.3 1450 - 143.33758 Pinus massoniana Lamb. 118.32 27.05 18 1630 20.55 18 1025 - 212.17759 Pinus massoniana Lamb. 118.32 27.05 18 1630 23.24 19.06 875 - 236.19763 Pinus massoniana Lamb. 117.95 26.63 19.4 1800 23.5 18.6 930 332.28 340.74764 Pinus massoniana Lamb. 117.95 26.63 19.4 1800 22.5 19.8 1095 383.16 330.74765 Pinus massoniana Lamb. 117.95 26.63 19.4 1800 19.8 17.4 1350 329.31 240.79766 Pinus massoniana Lamb. 117.95 26.63 19.4 1800 16.2 17 1845 303.34 169.11767 Pinus massoniana Lamb. 116.51 26.24 17.8 1769 9.9 9.53 1610 - 55.25768 Pinus massoniana Lamb. 116.51 26.24 17.8 1769 16.15 15.38 840 - 81.30771 Pinus massoniana Lamb. 117.54 26.16 19.8 1604 28.1 20.1 456 - 201.46772 Pinus massoniana Lamb. 117.54 26.16 19.8 1604 14.5 11.5 1630 - 160.60779 Pinus massoniana Lamb. 117.49 27.35 18.8 1789 5.31 3.97 2220 7.07 14.96780 Pinus massoniana Lamb. 117.49 27.35 18.8 1789 5.14 3.9 2760 13.25 14.87781 Pinus massoniana Lamb. 117.49 27.35 18.8 1789 4.08 3.48 1440 4.03 6.86782 Pinus massoniana Lamb. 117.76 26.93 19.4 1738 6.4 5.2 1590 - 33.45783 Pinus massoniana Lamb. 117.76 26.93 19.4 1738 15.1 13.9 1068 - 96.24784 Pinus massoniana Lamb. 117.76 26.93 19.4 1738 19.2 16.5 813 - 138.82789 Pinus massoniana Lamb. 118.20 26.10 18.2 1625 6.6 5.2 3225 31.51 47.35790 Pinus massoniana Lamb. 116.43 25.67 19 1628 8.2 7.5 2972 62.24 61.12791 Pinus massoniana Lamb. 116.43 25.67 19 1628 7.2 6.95 2075 30.67 29.75792 Pinus massoniana Lamb. 116.43 25.67 19 1628 11.3 12.78 1700 112.15 76.47793 Pinus massoniana Lamb. 116.43 25.67 19 1628 9 10.95 3425 124.74 124.61797 Pinus massoniana Lamb. 113.71 23.22 21.6 1905 19 14.9 906 177.19 140.43798 Pinus massoniana Lamb. 109.95 23.38 21 1712 6.97 5.3 - 36.16 40.09799 Pinus massoniana Lamb. 108.93 24.88 20.7 1371 13.8 14.1 1250 - 78.63803 Pinus massoniana Lamb. 109.67 23.75 21.1 1418 5.2 5.4 8010 72.1 32.00804 Pinus massoniana Lamb. 109.67 23.75 21.1 1418 12.8 9.8 3000 206.1 108.00805 Pinus massoniana Lamb. 109.67 23.75 21.1 1418 19 14.7 1635 328.2 186.60

806 Pinus massoniana Lamb. 109.67 23.75 21.1 1418 32.3 19 435 290.3 197.40807 Pinus massoniana Lamb. 108.69 24.43 19.2 1260 25 24.1 838 558 260.13808 Pinus massoniana Lamb. 108.18 28.21 17 1161 7.2 6.8 2033 - 29.92809 Pinus massoniana Lamb. 108.18 28.21 17 1161 12.7 14.5 2030 - 100.95810 Pinus massoniana Lamb. 108.18 28.21 17 1161 15.2 14.4 2120 - 155.17811 Pinus massoniana Lamb. 106.98 26.45 14.8 1089 11.75 11.96 2730 176.69 131.82812 Pinus massoniana Lamb. 106.98 26.45 14.8 1089 16.5 15.85 1830 291.11 217.60813 Pinus massoniana Lamb. 106.98 26.45 14.8 1089 19.95 19.04 1035 279.08 251.72814 Pinus massoniana Lamb. 106.98 26.45 14.8 1089 16.7 14.8 1365 208.66 173.74815 Pinus massoniana Lamb. 106.98 26.45 14.8 1089 19.4 18 1140 276.58 233.87816 Pinus massoniana Lamb. 106.98 26.45 14.8 1089 10.5 7.95 850 30.21 23.78817 Pinus massoniana Lamb. 106.98 26.45 14.8 1089 10.86 8 1750 66.61 46.84818 Pinus massoniana Lamb. 106.98 26.45 14.8 1089 9.48 8.75 2725 87.82 57.11819 Pinus massoniana Lamb. 106.98 26.45 14.8 1089 7.67 8.5 6425 135.95 86.90820 Pinus massoniana Lamb. 106.98 26.45 14.8 1089 5.28 4.9 6700 41.86 33.94821 Pinus massoniana Lamb. 106.98 26.45 14.8 1089 10.69 11.58 4600 242.23 204.52822 Pinus massoniana Lamb. 106.98 26.45 14.8 1089 11.3 12.4 4600 - 200.85826 Pinus massoniana Lamb. 110.97 30.87 17.5 1016 6.71 5.75 - 108.85 69.01827 Pinus massoniana Lamb. 110.97 30.87 17.5 1016 5.07 5.16 - 76.74 46.69828 Pinus massoniana Lamb. 110.17 29.50 16 1400 12.22 9.15 1455 - 75.44829 Pinus massoniana Lamb. 109.63 26.78 17.4 1284 13.83 12.2 1752 175.1 100.62830 Pinus massoniana Lamb. 113.54 27.74 17.6 1432 10.62 10.5 2250 - 79.47831 Pinus massoniana Lamb. 113.54 27.74 17.6 1432 9.18 8.3 2680 - 56.61832 Pinus massoniana Lamb. 113.54 27.74 17.6 1432 8.36 7.7 3225 - 53.05844 Pinus massoniana Lamb. 113.08 28.26 17.1 1486 14.2 12.5 1200 117.83 51.12857 Pinus massoniana Lamb. 106.68 29.63 18 1100 17.1 14.1 1120 - 127.72858 Pinus taiwanensis Hayata 116.18 31.10 15.2 1600 14.2 11.5 2340 238.7 171.42859 Pinus taiwanensis Hayata 115.87 31.22 15 1295 14.1 9.1 2418 - 203.53860 Pinus taiwanensis Hayata 119.47 27.48 14.9 1898 6.8 6.05 7500 98.1 76.06861 Pinus taiwanensis Hayata 119.47 27.48 14.9 1898 7.8 6.6 4500 83.2 61.94862 Pinus taiwanensis Hayata 119.47 27.48 14.9 1898 8.2 6.75 3600 71.6 53.62863 Pinus taiwanensis Hayata 119.47 27.48 14.9 1898 8.1 6.75 3000 59.4 44.69864 Pinus taiwanensis Hayata 119.47 27.48 14.9 1898 10.8 8.3 3600 - 74.12865 Pinus taiwanensis Hayata 119.47 27.48 14.9 1898 13.3 8.33 2565 - 74.10866 Pinus taiwanensis Hayata 115.32 31.40 15.2 1390 7.12 5.07 6085 81.27 65.42867 Pinus taiwanensis Hayata 114.12 28.39 13.7 2000 7.72 5.2 1530 23.49 16.74868 Pinus fenzeliana Hand.-Mazz. 106.10 28.53 18.1 1300 11.64 9.71 2566 - 149.35869 Pinus taeda L. 118.05 31.53 16 1189 16.2 8.5 450 33.12 46.42870 Pinus taeda L. 118.05 31.53 16 1189 23.6 9.9 450 114.98 159.32871 Pinus taeda L. 117.49 27.35 18.8 1789 7.65 4.33 1820 20.03 26.27872 Pinus taeda L. 119.22 32.12 15.2 1042 10 5.3 2505 54.05 49.28873 Pinus taeda L. 119.22 32.12 15.2 1042 10.8 5.4 2565 65.69 61.61

874 Pinus taeda L. 119.22 32.12 15.2 1042 9.3 5.5 3585 67.7 62.23875 Pinus taeda L. 119.22 32.12 15.2 1042 9.9 5.5 3900 84.06 78.79876 Pinus taeda L. 119.22 32.12 15.2 1042 9.1 5.4 4425 78.73 72.23877 Pinus taeda L. 119.22 32.12 15.2 1042 12.8 7.3 3333 155.69 145.25878 Pinus taeda L. 119.22 32.12 15.2 1042 14.9 8.3 1667 110.51 103.61879 Pinus taeda L. 119.22 32.12 15.2 1042 16.5 8.5 1250 105.6 99.90882 Pinuds elliottii Engelm. 117.41 23.67 20.8 1186 11.55 7.94 2393 - 141.89883 Pinuds elliottii Engelm. 117.49 27.35 18.8 1789 6.88 4.05 1403 11.93 15.58885 Pinuds elliottii Engelm. 109.67 23.75 21.1 1418 16 12.9 2220 273.06 174.99886 Pinuds elliottii Engelm. 109.67 23.75 21.1 1418 14.5 12.7 2745 273.95 174.50887 Pinuds elliottii Engelm. 109.67 23.75 21.1 1418 14.7 12.7 3255 312.48 200.57888 Pinuds elliottii Engelm. 109.67 23.75 21.1 1418 14.2 12.7 3750 360 197.54898 Pinuds elliottii Engelm. 115.14 27.22 18.3 1500 13.94 8.3 1620 100.86 69.90899 Pinuds elliottii Engelm. 115.72 28.79 16.1 1825 12.5 6.16 1330 59.5 52.72

909Pinus kesiya Royle ex Gordon var.langbianensis (A. Chev.) Gaussen exBui

99.45 24.33 16.1 1177 10.26 11 2390 - 85.66


99.45 24.33 16.1 1177 26 24 725 - 204.50


100.85 23.20 19.4 1250 14.99 13 1070 - 92.29


100.85 23.20 19.4 1250 17.55 22 792 - 119.20

913 Pinus rigida Mill. var. serotina(Michx.) Loudon ex Hoopes 119.76 31.33 15.7 1167 23.08 15.82 1050 396.17 234.85

918 Cryptomeria fortunei Hooibr. exOtto et Dietrich 121.00 32.50 14.8 1029 16.5 10.4 1168 - 111.87

919 Cryptomeria fortunei Hooibr. exOtto et Dietrich 103.37 29.91 12.5 2515 14.9 12.2 2235 254 123.31



922 Cryptomeria japonica (Thumb. ExL.f.) D. Don 114.12 28.39 13.7 2000 23.3 14.3 1575 489 239.50

923 Metasequoia glyptostroboides Hu etW. C. Cheng 114.12 28.39 13.7 2000 21.6 15.8 1300 - 157.46





943 Taiwania flousiana Gaussen 116.80 26.25 17 1794 8.25 - 2925 61.13 57.57949 Taiwania flousiana Gaussen 107.49 24.99 16.9 1498 8.6 10.7 2100 - 59.64950 Taiwania flousiana Gaussen 107.49 24.99 16.9 1498 13.3 14.1 1767 - 109.90951 Taiwania flousiana Gaussen 107.49 24.99 16.9 1498 15.8 17.9 2000 - 246.27952 Taiwania flousiana Gaussen 109.12 30.05 12.8 1300 15 10.58 1078 - 81.28

954 Keteleeria davidiana (C. E.Bertrand) Beissn. 112.05 30.95 16.4 1001 15.8 11 1320 174.09 140.55

955 Cupressus funebris Endl.Cunninghamialanceolata(Lamb.) Hook.

108.18 28.21 17 1161 14.4 13.2 744 - 71.10

957 Cunninghamia lanceolata (Lamb.)Hook.

Fokieniahodginsii(Dunn) A.Henry et H. H.Thomas

113.08 27.35 18.1 1614 12.45 9.32 2301 146.3 79.58


PinusmassonianaLamb.

106.82 22.13 21.1 1350 13.61 9.82 1971 - 85.35



106.82 22.13 21.1 1350 13.22 9.9 2342 - 101.13



106.82 22.13 21.1 1350 13 10.78 2129 - 95.00


PinustaiwanensisHayata

116.18 31.10 15.2 1600 15.73 11.29 2160 289.67 179.88



116.18 31.10 15.2 1600 6.94 5.15 4890 68.98 61.74



116.18 31.10 15.2 1600 14.14 10.08 2310 188.78 128.27


TaiwaniaflousianaGaussen

116.80 26.25 17 1794 8.64 - 3000 70.66 59.47

977 Robinia pseudoacacia L. 116.21 40.01 11 651 16.2 14.3 883 - 98.45978 Robinia pseudoacacia L. 116.21 40.01 11 651 17.7 12.7 733 - 83.17979 Robinia pseudoacacia L. 108.45 35.28 9.7 603 - - - 137.32 142.49983 Robinia pseudoacacia L. 114.25 34.43 14.4 670 17.4 19.91 855 192.81 179.92984 Robinia pseudoacacia L. 114.25 34.43 14.4 670 10.9 13.6 1500 113.83 100.82985 Robinia pseudoacacia L. 114.25 34.43 14.4 670 10.9 7.7 4065 81.42 81.35986 Robinia pseudoacacia L. 121.00 32.50 14.8 1029 16.2 13.6 555 - 87.75998 Robinia pseudoacacia L. 108.64 34.84 9.6 601 10.55 7.6 1775 - 74.27999 Robinia pseudoacacia L. 107.82 35.05 9.1 584 6.9 8.8 2783 - 48.95

1004 Quercus wutaishanica Mayr 108.45 35.28 9.7 603 - - - 126.31 131.101012 Quercus wutaishanica Mayr 108.55 35.08 9 600 8.4 7.4 1136 27.67 32.801013 Quercus wutaishanica Mayr 103.27 31.50 10 864 35.5 17 550 - 484.70

1018 Quercus mongolica Fisch. exLedeb.

TiliamongolicaMaxim

Acer monoMaxim. 117.52 40.55 7.6 720 18.8 11 895 104.46 122.66

1023 Quercus mongolica Fisch. exLedeb. 127.52 45.28 2.6 649 13.2 14.5 1960 156.4 192.47

1026 Quercus aliena Bl. var. acutiserrataMaxim. ex Wenz. 105.54 34.16 9.7 629 - - - 96.87 81.84

1027 Quercus aliena Bl. var. acutiserrataMaxim. ex Wenz. 111.94 33.48 15.1 886 11.25 11.8 1636 - 122.13

1029 Quercus aliena Bl. var. acutiserrataMaxim. ex Wenz. 107.83 34.15 9.4 589 - - 1072 499.61 515.75

1030 Quercus aliena Bl. var. acutiserrataMaxim. ex Wenz. 108.45 33.43 8.8 937 - - - 229.03 231.91

1031 Quercus aliena Bl. var. acutiserrataMaxim. ex Wenz. 108.45 33.43 8.8 937 - - 2650 305.61 365.29

1033 Quercus variabilis Bl. 116.21 40.01 11 651 8 7.6 1880 40.39 52.841034 Quercus variabilis Bl. 116.21 40.01 11 651 11.6 9.5 1050 - 66.901035 Quercus variabilis Bl. 116.21 40.01 11 651 11.2 8.6 817 - 43.691036 Quercus variabilis Bl. 116.21 40.01 11 651 12.7 11.7 983 - 94.891037 Quercus variabilis Bl. 105.54 34.16 9.7 629 - - - 75.2 79.801038 Quercus variabilis Bl. 111.94 33.48 15.1 886 17 16.4 807 - 158.83

1039 Quercus variabilis Bl.QuercusacutissimaCarruth.

119.22 32.12 15.2 1042 13.9 13.2 1225 168.5 194.60

1040 Acer truncatum Bunge 116.21 40.01 11 651 13.5 9.9 810 - 72.321041 Acer truncatum Bunge 116.21 40.01 11 651 9.87 7.48 1487 - 64.341042 Fraxinus mandshurica Rupr. Acer spp. Tilia spp. 105.51 34.16 9.7 629 - - - 97.94 96.551043 Fraxinus mandshurica Rupr. 127.52 45.28 2.6 649 22.2 16.6 620 - 174.04

1044 Fraxinus mandshurica Rupr.JuglansmandshuricaMaxim.

127.52 45.28 2.6 649 11.6 11 1170 75.3 91.76

1045 Fraxinus mandshurica Rupr. Tilia spp. Acer monoMaxim. 128.00 42.28 1.7 719 29.98 - 352 256.48 197.32

1048 Populus davidiana DodePhellodendronamurenseRupr.

JuglansmandshuricaMaxim.

TiliaamurensisRupr.

127.52 45.28 2.6 649 12 14.6 1590 120.5 99.62

1049 Tilia amurensis Rupr.PopulusdavidianaDode

UlmusdavidianaPlanch. var.japonica(Rehder)Nakai

JuglansmandshuricaMaxim.

127.52 45.28 2.6 649 15.4 15.6 1050 149.8 134.44

1052 Betula platyphylla Suk.PopulusdavidianaDode

127.52 45.28 2.6 649 12 16.5 1280 200 196.71

1057 Betula platyphylla Suk. 118.45 41.42 5.3 537 13.7 14.8 1980 - 103.581058 Betula platyphylla Suk. 100.65 37.23 2.4 570 12.31 10.6 513 - 26.531059 Betula platyphylla Suk. 101.37 36.68 3 502 10.9 10.7 1050 58.23 63.401060 Betula platyphylla Suk. 101.37 36.68 3 502 12.1 13.1 1090 74.43 76.581062 Betula platyphylla Suk. 92.86 29.78 5.4 542 7.7 7 1700 - 33.171066 Betula albosinensis Burkill 108.45 33.43 8.8 937 - - - 133.38 109.30

1070 Betula alnoides Buch.-Ham. ex D.Don 101.09 22.43 20.1 1655 4.89 5.37 2900 - 55.57

1071 Populus canadensis Moench 'N47' 119.45 42.07 7.4 415 15.6 12.9 556 49.63 37.611072 Populus canadensis Moench 'N51' 119.45 42.07 7.4 415 13.6 11.5 556 39.89 37.021073 Populus canadensis Moench 'N64' 119.45 42.07 7.4 415 15.6 13.1 556 70.4 43.711074 Populus canadensis Moench 'I-214' 116.75 36.62 13.7 650 - - - 247.05 149.441075 Populus canadensis Moench 'I-69' 116.75 36.62 13.7 650 - - - 234 138.791080 Populus canadensis Moench 'I-72' 116.75 36.62 13.7 650 - - - 278.4 183.05

1095 populus × xiaozhannica'Balizhuangyang' 116.75 36.62 13.7 650 - - - 143.7 89.05

1096 Populus xiaohei T.S.Hwang et Liang'Baicheng' 119.45 42.07 7.4 415 8.9 8.7 556 13.58 14.73

1106 Populus canadensis Moench 116.75 36.62 13.7 650 - - - 99.9 74.241107 Populus canadensis Moench 116.75 36.62 13.7 650 - - - 266.4 158.11

1108 Populus canadensis Moench'Robusta' 116.75 36.62 13.7 650 - - - 213.3 134.21

1116 Populus davidiana DodeBetulaplatyphyllaSuk.

105.54 34.16 9.7 629 - - - 89.4 75.39

1117 Populus davidiana Dode 111.00 40.78 4.6 349 9.7 9 1995 - 42.591143 Populus simonii Carr. 109.23 37.83 8.6 398 16.16 12.1 856 72.07 106.80

1148 Populus alba L. × P. berolinensisDippel 123.85 47.38 3.7 418 19.8 15.23 1250 - 188.39


1152 Populus alba L. × P. berolinensisDippel 124.45 48.05 2.2 455 16.9 15 833 - 69.72


1154 Populus alba L. × P. berolinensisDippel 124.45 48.05 2.2 455 18.62 15 500 - 54.08


1159 Zenia insignis Chun 117.80 26.80 19.5 1724 19.8 22.4 525 - 95.171160 Zenia insignis Chun 112.75 24.47 20.7 1700 - - - 9.93 10.31

1162 Liriodendron chinense (Hemsl.)Sarg. 114.63 27.67 17.8 1527 11.26 12.5 1450 - 60.28

1163 Liquidambar formosana Hance 118.64 27.16 18.7 1694 3.61 3.89 2500 5.82 15.141165 Liquidambar formosana Hance 118.79 29.72 17 1430 10 8.43 1470 50.35 60.891168 Paulownia fortunei(Seem.) Hemsl. 117.20 25.97 18 1578 16.5 8.3 400 34.96 21.171169 Alnus cremastogyne Burkill 109.40 28.49 15.8 1345 10.85 11.5 1533 69.72 51.231170 Alnus cremastogyne Burkill 109.40 28.49 15.8 1345 11.02 13.3 1697 120.82 70.051171 Alnus cremastogyne Burkill 109.54 28.38 14.6 1394 13.34 14.7 2000 207.29 95.311172 Alnus cremastogyne Burkill 113.09 28.80 17 1345 7.94 9.8 2283 - 51.991173 Alnus cremastogyne Burkill 103.40 26.45 12.7 861 5.5 5 3400 - 23.221174 Alnus formosana (Burkill) Makino 117.95 26.63 19.4 1800 19.2 18.4 1520 - 266.48

1177 Liquidambar formosana HanceLiriodendronchinense(Hemsl.) Sarg.

118.64 27.16 18.7 1694 5.26 5.14 2925 18.45 28.11

1178 Sassafras tzumu (Hemsl.) Hemsl.LiquidambarformosanaHance

110.03 28.76 15.8 1444 23.3 17 780 252 215.55

1179 Sassafras tzumu (Hemsl.) Hemsl.QuercusacutissimaCarruth.

110.54 28.69 16.9 1434 20.3 14.4 1230 292 258.90

1186 Betula alnoides Buch.-Ham. ex D.Don

Cinnamomumcassia (L.) C.Presl

101.09 22.43 20.1 1655 12.2 11.19 1050 - 103.17

1189 Castanopsis hystrix Miq. 117.48 24.74 20.8 1582 24.4 27.1 600 483 500.771190 Castanopsis hystrix Miq. 117.48 24.74 20.8 1582 22.3 21.4 645 342 354.65

1191 Castanopsis hystrix Miq.

Cyclobalanopsis glauca(Thunb.)Oerst.

MachiluspauhoiKaneh.

109.63 26.78 17.4 1284 22.11 13.99 - 592.61 426.88

1192 Castanopsis lamontii Hance 117.54 26.16 19.8 1604 20.5 14.4 887 203.4 150.28

1193 Castanopsis carlesii (Hemsl.)Hayata 117.54 26.16 19.8 1604 19.4 10.6 367 62.51 71.40

1198 Castanopsis carlesii (Hemsl.)Hayata 118.20 26.10 18.2 1625 14.49 17.43 2130 296.86 229.31

1201 Castanopsis fissa (Champ. exBenth.) Rehd. et E.H. Wils. 117.54 26.16 19.8 1604 12.7 10.7 2513 189.98 160.51


1203 Castanopsis fissa (Champ. exBenth.) Rehd. et E.H. Wils. 117.54 26.16 19.8 1604 11.3 11.3 1530 - 76.06

1204 Castanopsis fissa (Champ. exBenth.) Rehd. et E.H. Wils. 117.79 26.38 20 1627 18.5 12.2 692 110.79 101.06

1205 Castanopsis fissa (Champ. exBenth.) Rehd. et E.H. Wils. 117.79 26.38 20 1627 19.3 14.8 725 152.54 108.34


1209 Castanopsis kawakamii Hayata 117.54 26.16 19.8 1604 42.2 24.3 255 398.31 512.501210 Castanopsis kawakamii Hayata 117.54 26.16 19.8 1604 24.2 18.9 875 412.43 379.801211 Castanopsis kawakamii Hayata 117.54 26.16 19.8 1604 12.8 10.5 1476 100.32 105.461212 Castanopsis kawakamii Hayata 117.54 26.16 19.8 1604 18.6 15.2 813 163.35 168.671213 Castanopsis kawakamii Hayata 117.54 26.16 19.8 1604 18.79 17.4 1100 233.2 247.411222 Schima superba Gardner et Champ. 118.62 25.60 17.7 1479 8.4 7.8 2300 52.98 63.571223 Schima superba Gardner et Champ. 119.11 26.15 20.1 1700 17.1 16.7 1230 242.3 188.871224 Schima superba Gardner et Champ. 119.11 26.15 20.1 1700 22.6 23 825 382.8 300.851225 Schima superba Gardner et Champ. 117.95 26.63 19.4 1800 17.1 16.7 1168 230.1 180.771226 Schima superba Gardner et Champ. 117.95 26.63 19.4 1800 22.6 23 736 341.5 271.451227 Schima superba Gardner et Champ. 118.35 25.30 19.5 1700 8.62 8.38 2358 61.31 77.091232 Phoebe bournei (Hemsl.) Yang 118.48 26.43 19.3 1699 24 17.3 670 229.22 182.951233 Phoebe bournei (Hemsl.) Yang 117.54 26.16 19.8 1604 11.5 8.55 1533 72 77.951234 Phoebe bournei (Hemsl.) Yang 117.76 26.93 19.4 1738 9.4 8.3 1675 - 39.461235 Phoebe bournei (Hemsl.) Yang 117.76 26.93 19.4 1738 11.2 10.6 1579 - 79.031236 Phoebe bournei (Hemsl.) Yang 117.76 26.93 19.4 1738 12.5 11.5 1523 - 146.131237 Phoebe bournei (Hemsl.) Yang 117.76 26.93 19.4 1738 10.2 10.71 2302 - 98.591238 Phoebe bournei (Hemsl.) Yang 117.76 26.93 19.4 1738 11.95 11.4 2734 - 111.211239 Phoebe bournei (Hemsl.) Yang 117.35 25.97 19.1 1626 14.3 13.8 1872 - 96.291240 Phoebe bournei (Hemsl.) Yang 118.20 26.10 18.2 1625 4.1 4.8 2155 - 47.631241 Phoebe bournei (Hemsl.) Yang 118.20 26.10 18.2 1625 14.7 13.1 1360 - 111.89

1242 Phoebe bournei (Hemsl.) Yang 118.20 26.10 18.2 1625 23.5 18.5 832 - 173.381243 Phoebe bournei (Hemsl.) Yang 118.20 26.10 18.2 1625 9 8.41 2255 53.23 66.091244 Phoebe bournei (Hemsl.) Yang 103.57 31.02 15.2 1243 18 15.6 833 - 166.77

1245 Machilus pingii W. C. Cheng ex YenC. Yang

AceroblongumWall. ex DC.

CeltissinensisPers.

110.17 29.50 16 1400 14.42 9.87 1244 - 85.26

1254 Cyclobalanopsis elevaticostata Q.F. Zheng 119.02 26.47 14.4 1944 7.5 7.1 2400 40.61 50.84



1257 Cyclobalanopsis elevaticostata Q.F. Zheng 119.02 26.47 14.4 1944 6.2 6 4050 40.1 44.36

1259 Eucalyptus robusta Smith 118.25 25.50 18 1724 8.3 8.3 1425 - 41.811260 Eucalyptus robusta Smith 118.25 25.50 18 1724 9.1 11.6 1425 - 57.861261 Eucalyptus robusta Smith 118.25 25.50 18 1724 10.2 12.2 1425 - 73.771264 Eucalyptus camaldulensis Dehnh. 110.21 20.41 22.7 1578 - - - 166.56 97.841265 Eucalyptus camaldulensis Dehnh. 101.83 25.77 21.9 614 4.57 5.9 2871 - 23.511266 Eucalyptus camaldulensis Dehnh. 101.83 25.77 21.9 614 5.6 7.27 3861 - 40.661267 Eucalyptus camaldulensis Dehnh. 101.83 25.77 21.9 614 9.2 8.8 2871 - 88.321276 Eucalyptus '12ABL' 110.21 20.41 22.7 1578 - - - 136.99 83.041278 Eucalyptus grandis Hill 110.21 20.41 22.7 1578 - - - 135.69 77.131279 Eucalyptus grandis Hill 104.59 28.47 18.1 1022 7.05 10.41 2490 52.04 31.651280 Eucalyptus grandis Hill 104.59 28.47 18.1 1022 7.41 11.71 2280 57.91 39.671281 Eucalyptus grandis Hill 104.59 28.47 18.1 1022 7.49 11.94 2070 54.44 36.141282 Eucalyptus grandis Hill 104.59 28.47 18.1 1022 8.25 11.59 1860 58.03 39.341283 Eucalyptus grandis Hill 104.59 28.47 18.1 1022 10.11 11.02 1665 74.93 48.42

1285 Eucalyptus grandis Hill × E.urophylla S.T. Blakely 110.21 20.41 22.7 1578 - - - 101.86 73.23

1289 101.43 25.22 12.4 995 11.8 13.1 798 - 61.301294 Eucalyptus saligna Smith 110.21 20.41 22.7 1578 - - - 65.68 41.281297 Eucalyptus exserta F. V. Muell. 109.70 21.58 23 1589 6.8 9.1 2639 - 49.391298 Eucalyptus exserta F. V. Muell. 109.70 21.58 23 1589 8.2 11.5 2201 - 70.481299 Eucalyptus exserta F. V. Muell. 109.47 19.80 23.5 1418 7.6 9 1667 - 38.411301 Eucalyptus citriodora Hook.f. 110.06 21.58 23.5 1453 16.7 20.7 780 184.08 178.501302 Eucalyptus citriodora Hook.f. 110.06 21.58 23.5 1453 15.7 17.9 826 136.54 135.881303 Eucalyptus citriodora Hook.f. 110.06 21.58 23.5 1453 14.3 18.2 690 87.7 89.59

1317 Eucalyptus urophylla S. T. Blakely× E. grandis Hill ex Miaden 107.84 22.33 21.8 1200 11.53 18.56 1315 - 88.95

1318 Eucalyptus urophylla S. T. Blakely× E. grandis Hill ex Miaden 107.84 22.33 21.8 1200 11.27 18.47 1410 - 94.29

1319 Eucalyptus urophylla S. T. Blakely× E. grandis Hill ex Miaden 107.84 22.33 21.8 1200 11 15.3 1097 - 71.37

1320 Eucalyptus urophylla S. T. Blakely× E. grandis Hill ex Miaden 107.84 22.33 21.8 1200 9.23 14.33 1380 59.06 47.03



1332 Eucalyptus urophylla S. T. Blakely 110.21 20.41 22.7 1578 - - - 217.43 154.901343 Eucalyptus urophylla S. T. Blakely 109.47 19.80 23.5 1418 11.6 14.5 1667 - 108.661344 Eucalyptus urophylla S. T. Blakely 109.47 19.80 23.5 1418 13.2 17.5 1667 - 149.341346 Eucalyptus tereticornis Smith 110.21 20.41 22.7 1578 - - - 139.72 102.32

1348 Acacia auriculiformis A. Cunn. exBenth. 118.91 24.91 19.8 1100 9.4 9.5 2375 82.48 155.73

1350 Acacia auriculiformis A. Cunn. exBenth. 110.21 20.41 22.7 1578 - - - 128.34 91.33

1351 117.40 24.36 20.9 1472 13.5 14.7 1000 - 56.93

1353 Acacia crassicarpa A.Cunn. exBenth. 117.41 23.67 20.8 1186 20.6 13.86 835 - 144.85

1354 Acacia crassicarpa A.Cunn. exBenth. 118.91 24.91 19.8 1100 17.6 14.9 2300 409.63 308.28

1356 Acacia crassicarpa A.Cunn. exBenth. 108.51 23.03 21.2 1552 14 13 830 - 68.24

1357 Acacia cincinnata F. Muell. 117.40 24.36 20.9 1472 15.6 15.5 900 - 68.511358 Acacia mangium Willd. 118.91 24.91 19.8 1100 15.2 13.8 2325 373.47 267.191359 Acacia mangium Willd. 117.40 24.36 20.9 1472 12.9 12.4 875 - 41.981364 Acacia mangium Willd. 112.90 22.68 21.7 1800 11.4 12 1600 - 196.941365 Acacia mangium Willd. 112.90 22.68 21.7 1800 10.1 7.1 1600 - 49.081368 Acacia mangium Willd. 110.21 20.41 22.7 1578 - - - 146.35 81.891369 Acacia mangium Willd. 108.51 23.03 21.2 1552 14 12 1140 - 59.751370 Acacia mangium Willd. 108.51 23.03 21.2 1552 18.3 17.7 930 - 161.121371 Acacia mangium Willd. 108.51 23.03 21.2 1552 23.5 19 775 - 209.071374 Acacia dealbata Link 103.40 26.45 12.7 861 6.12 6 3000 - 39.591375 Acacia dealbata Link 102.78 25.15 13.8 1030 10.18 10.07 2200 - 130.42

1376 Casuarina equisetifolia J. R. Forst.et G. Forst. 118.91 24.91 19.8 1100 8.6 9 2500 67.74 127.48

1377 Casuarina equisetifolia J. R. Forst.et G. Forst. 118.91 24.91 19.8 1100 3.8 6.4 3045 19.18 36.52






1390 Casuarina junghuhniana Miq. 110.21 20.41 22.7 1578 - - - 85.22 83.61

1395 Gordonia axillaris (Roxb. ex KerGawl.) D. Dietr 106.35 29.87 18.7 1068 24.36 16.92 750 - 176.62

1396 Elaeocarpus sylvestris (Lour.) Poir. 118.46 27.82 17.4 1782 9.01 6.9 2700 62.1 58.821398 Tsoongiodendron odorum Chun 117.54 26.16 19.8 1604 12.88 9.8 2100 99.29 53.041401 Michelia macclurei Dandy 118.20 26.10 18.2 1625 7.2 6.87 2400 37.14 47.761402 Michelia macclurei Dandy 109.78 21.85 22 1600 12.3 9.6 945 55.2 74.201403 Michelia macclurei Dandy 109.88 22.58 20.2 1430 13.3 12.6 2505 208 197.94

1405 Ormosia hasiei Hemsl. et E. H.Wilson 117.54 26.16 19.8 1604 16.4 12.2 1113 120.8 118.62

1406 Ormosia xylocarpa Merr. et L.Chen 117.54 26.16 19.8 1604 17.15 18.37 1117 209.1 223.201407 Ormosia xylocarpa Merr. et L.Chen 117.54 26.16 19.8 1604 13.4 9.8 2070 162.5 161.571408 Sloanea sinensis (Hance) Hemsl. 117.54 26.16 19.8 1604 14.5 13.3 2384 262.93 250.581409 Quercus pannosa Hand.-Mazz. 99.67 28.08 5.4 625 20.53 20 1219 - 344.861411 Mytilaria laosensis Lecomte 117.31 26.33 18 1737 14.3 14.2 1785 186.83 194.781412 Manglietia hainanensis Dandy 108.83 18.71 22.1 2300 13.2 11.1 1923 - 113.531413 Manglietia yuyuanensis Y. W. Law 117.20 25.97 18 1578 4.8 4.5 2042 9.42 35.921414 Lindera communis Hemsl. 117.54 26.16 19.8 1604 17.8 16.9 2042 421.88 303.671416 Altingia gracilipes Hemsl. 118.20 26.10 18.2 1625 21.98 15.5 650 183.04 131.741417 Cinnamomum camphora (L.) Presl. 117.54 26.16 19.8 1604 12.1 10.6 1170 80 64.231418 Cinnamomum camphora (L.) Presl. 112.90 27.83 17.4 1431 14.5 8.47 1025 - 91.97

1419 Manglietia yuyuanensis Y. W. LawPaulowniafortunei(Seem.) Hemsl.

117.20 25.97 18 1578 8.77 6.16 2493 74.81 70.44

1430 Engelhardtia roxburghiana Wall.

SchimasuperbaGardner etChamp.

109.63 26.78 17.4 1284 14.6 12.7 1530 - 152.83

1441 Trema orientalis (L.) Blime 101.29 21.88 21.5 1557 5.7 6.95 2475 - 24.88

1449 Mallotus paniculatus (Lam.)Mull.Arg Litsea spp.

Scheffleraoctophylla(Lour.)Harms

101.29 21.88 21.5 1557 8 8.3 1311 - 37.72

1451 Litsea spp.

Cinnamomumglanduliferum(Wall.)Meisener

Polyalthiacheliensis Hu 101.29 21.88 21.5 1557 7.5 8.7 1267 - 53.72

1452 Macaranga denticulata (Blume) Müll. Arg. 101.29 21.88 21.5 1557 5.5 7 4575 - 29.71

1461 Pinus koraiensis Siebold et Zucc. 130.05 45.15 3.5 550 8.7 6.4 2713 - 53.391462 Pinus koraiensis Siebold et Zucc. 130.05 45.15 3.5 550 7.38 5.5 4275 - 54.961463 Pinus koraiensis Siebold et Zucc. 130.05 45.15 3.5 550 7.1 5.55 4275 - 50.031464 Pinus koraiensis Siebold et Zucc. 130.05 45.15 3.5 550 6.4 4.8 3700 - 33.511465 Pinus koraiensis Siebold et Zucc. 130.05 45.15 3.5 550 7.1 5.35 3175 - 36.541466 Pinus koraiensis Siebold et Zucc. 127.52 45.28 2.6 649 12.4 10.4 2475 159.6 106.881467 Pinus koraiensis Siebold et Zucc. 127.52 45.28 2.6 649 13.2 7.98 1775 - 85.491468 Pinus koraiensis Siebold et Zucc. 127.52 45.28 2.6 649 13 7.7 2025 - 93.901469 Pinus koraiensis Siebold et Zucc. 127.52 45.28 2.6 649 12.3 7.3 2140 - 88.451470 Pinus koraiensis Siebold et Zucc. 127.52 45.28 2.6 649 7.1 5.8 1950 - 28.171471 Pinus koraiensis Siebold et Zucc. 127.52 45.28 2.6 649 8.4 6.45 3670 - 69.611472 Pinus koraiensis Siebold et Zucc. 127.52 45.28 2.6 649 8.2 6.6 4030 - 72.641473 Pinus koraiensis Siebold et Zucc. 127.52 45.28 2.6 649 8.2 6.75 4590 - 81.241474 Pinus koraiensis Siebold et Zucc. 127.52 45.28 2.6 649 11.1 7.5 1420 - 46.221475 Pinus koraiensis Siebold et Zucc. 123.91 40.88 6.2 935 10.2 9.2 3900 164.62 97.831476 Pinus koraiensis Siebold et Zucc. 123.91 40.88 6.2 935 18.2 17.3 1660 313.65 264.061477 Pinus koraiensis Siebold et Zucc. 123.91 40.88 6.2 935 10.6 8.6 2800 120.01 78.121478 Pinus koraiensis Siebold et Zucc. 123.91 40.88 6.2 935 11 9.1 2430 117.39 77.371479 Pinus koraiensis Siebold et Zucc. 123.91 40.88 6.2 935 12.4 9.2 2070 125.78 88.771480 Pinus koraiensis Siebold et Zucc. 123.91 40.88 6.2 935 19.8 17.1 1490 404.73 210.691481 Pinus koraiensis Siebold et Zucc. 123.91 40.88 6.2 935 21.1 17.5 1170 367.3 185.831482 Pinus koraiensis Siebold et Zucc. 123.91 40.88 6.2 935 22.7 18.5 950 361.87 208.541483 Pinus koraiensis Siebold et Zucc. 123.91 40.88 6.2 935 20.9 19.5 1280 341.55 236.811484 Pinus koraiensis Siebold et Zucc. 123.91 40.88 6.2 935 23.3 19.9 1020 361.79 229.391485 Pinus koraiensis Siebold et Zucc. 123.91 40.88 6.2 935 24.5 20.1 820 325.93 224.481486 Pinus koraiensis Siebold et Zucc. 123.91 40.88 6.2 935 28.4 21.2 505 316.89 189.791487 Pinus koraiensis Siebold et Zucc. 123.91 40.88 6.2 935 7.3 5.53 3233 44.29 40.001488 Pinus koraiensis Siebold et Zucc. 123.91 40.88 6.2 935 8.9 6.95 3100 79.36 63.811489 Pinus koraiensis Siebold et Zucc. 123.91 40.88 6.2 935 11 8.68 3005 143.64 105.051490 Pinus koraiensis Siebold et Zucc. 123.91 40.88 6.2 935 16 13.35 1545 215.06 142.741491 Pinus koraiensis Siebold et Zucc. 123.91 40.88 6.2 935 18.3 14.1 1298 243.25 156.781492 Pinus koraiensis Siebold et Zucc. 123.91 40.88 6.2 935 29.7 20.4 450 316.35 165.791493 Pinus koraiensis Siebold et Zucc. 123.91 40.88 6.2 935 24.9 17.58 710 317.8 171.03

1500 Pinus koraiensis Siebold et Zucc.BetulaplatyphyllaSuk.

FraxinusmandshuricaRupr.

127.52 45.28 2.6 649 4.77 4.86 4600 50.54 36.94

1501 Pinus koraiensis Siebold et Zucc.PhellodendronamurenseRupr.

128.77 47.22 0.5 655 10.6 9.9 2200 - 63.87

1503 Pinus koraiensis Siebold et Zucc.TiliaamurensisRupr.

Acer monoMaxim.

QuercusmongolicaFisch. exLedeb.

128.00 42.28 1.7 719 42.34 - 358 607.64 369.54

1504 Pinus koraiensis Siebold et Zucc. Acer monoMaxim.

TiliaamurensisRupr.

BetulacostataTrautv

128.00 42.28 1.7 719 39.03 - 319 441.53 287.21

1505 Pinus koraiensis Siebold et Zucc. Acer monoMaxim.

TiliaamurensisRupr.

FraxinusmandshuricaRupr.

128.00 42.28 1.7 719 32.81 - 313 278.41 206.95

1512 Larix kaempferi (Lamb.) CarrièreBetulaluminifera H.Winkl.

124.08 41.83 6.2 782 9.82 11.09 2898 117.93 131.32

1513 Larix gmelinii Rupr.BetulaplatyphyllaSuk.

120.61 48.59 -5.1 450 14.7 16.05 690 - 58.20

1514 Pinus tabuliformis Carrière Quercusvariabilis Bl. 116.21 40.01 11 651 7.64 5.93 2494 42.4 64.53

1515 Pinus tabuliformis CarrièreAcertruncatumBunge

116.21 40.01 11 651 10.12 6.21 1937 67.12 69.94

1519 Quercus fabrei HanceCunninghamialanceolata(Lamb.) Hook.

Sassafrastzumu(Hemsl.)Hemsl.

110.54 28.69 16.9 1434 9.9 10.2 2820 - 112.65

1530 Cupressus funebris Endl.AlnuscremastogyneBurkill

105.47 31.27 17.3 880 7.66 8.81 4700 - 107.93

1532 Fokienia hodginsii (Dunn) A. Henryet H. H. Thomas


118.35 25.30 19.5 1700 9.9 7.81 2350 104.51 82.40

1535 Pinus massoniana Lamb.

Gordoniaaxillaris(Roxb. ex KerGawl.) D.Dietr

106.35 29.87 18.7 1068 13.58 12.87 2470 - 150.34

1536 Pinus massoniana Lamb.Cunninghamialanceolata(Lamb.) Hook.

Gordoniaaxillaris(Roxb. exKer Gawl.)D. Dietr

104.33 29.50 17.8 982 12.83 11.12 1740 158.5 105.16



104.33 29.50 17.8 982 14.71 14.67 1310 208.38 154.19



104.33 29.50 17.8 982 13.15 13.21 1500 159.89 104.30

1539 Pinus massoniana Lamb.EucommiaulmoidesOliver

118.42 32.45 14.9 1020 10.98 8.66 1920 - 129.56

1540 Pinus massoniana Lamb.LiquidambarformosanaHance

118.64 27.16 18.7 1694 3.29 3.21 3400 5.95 14.50

1541 Pinus massoniana Lamb.CastanopsiskawakamiiHayata

117.54 26.16 19.8 1604 17.34 13.25 1232 - 214.34

1543 Pinus massoniana Lamb.MicheliamacclureiDandy

117.54 26.16 19.8 1604 14.29 12.72 1575 - 209.94


Castanopsissclerpphylla(Lindl.)Schottky

117.54 26.16 19.8 1604 16.91 14.32 1250 - 215.07

1545 Pinus massoniana Lamb.CastanopsislamontiiHance

117.54 26.16 19.8 1604 18.16 13.78 1042 - 194.06


Castanopsisfissa (Champ.ex Benth.)Rehd. et E.H.Wils.

117.54 26.16 19.8 1604 17.02 17.76 1544 - 251.39


Castanopsisfissa (Champ.ex Benth.)Rehd. et E.H.Wils.

113.71 23.22 21.6 1905 12.44 11.62 2493 234.75 205.55

1554 Pinus massoniana Lamb.Cyclobalanopsis myrsinifolia(Bl.) Oerst.

117.54 26.16 19.8 1604 17.3 14.84 1260 - 238.84


Lithocarpusglaber(Thunb.)Nakai

113.08 28.26 17.1 1486 13.09 10.11 2205 153.82 144.97


MagnoliaofficinalisRehder et E.H. Wilsonsubsp.Biloba(Rehderet E.H.Wilson)Y.W.Law

117.23 26.22 18 1744 10.46 9.4 3066 - 74.98



117.23 26.22 18 1744 9.33 8.4 2866 - 60.61



117.23 26.22 18 1744 11 9.56 3000 - 67.62



110.03 28.76 15.8 1444 12.7 10.9 2085 134 117.03



110.03 28.76 15.8 1444 12.7 10.1 2865 174 141.75



110.03 28.76 15.8 1444 13.2 10.9 2970 213 156.92


Ormosiahasiei Hemsl.et E. H.Wilson

117.79 26.38 20 1627 18.55 16.66 2265 494.27 235.51


LiquidambarformosanaHance

118.64 27.16 18.7 1694 5.39 4.22 2525 14.46 21.33



118.79 29.72 17 1430 12.99 8.73 2040 131.15 83.04



118.79 29.72 17 1430 13.4 8.51 2115 134.94 85.08


Tsoongiodendron odorumChun

117.54 26.16 19.8 1604 13 12 2080 185.44 102.37


Tsoongiodendron odorumChun

117.54 26.16 19.8 1604 22.41 19.86 1357 518.52 251.40


MicheliamacclureiDandy

117.95 26.47 20.1 1636 11.18 9.36 3600 194.46 145.56


MicheliamacclureiDandy

118.20 26.10 18.2 1625 9.48 7.19 2400 66.83 46.42


Eucalyptusgrandis Hill ×E. urophyllaS.T. Blakely

117.76 24.77 21.1 1447 11.99 10.6 2474 151.89 112.67


Nyssa sinensisOliv. 115.08 27.04 18.2 1457 7.73 7.53 3000 59.87 49.89


Phoebebournei(Hemsl.) Yang

117.35 25.97 19.1 1626 16.5 15.05 1524 - 153.31



118.62 25.60 17.7 1479 9.76 8.13 2334 76.1 67.42


Phoebebournei(Hemsl.) Yang

118.20 26.10 18.2 1625 14.89 12.97 1785 245.43 149.76


Choerospondias axillaris(Roxb.) B. L.Burtt et A. W.Hill

117.54 26.16 19.8 1604 17.93 16.88 1650 355.11 168.74


Alniphyllumfortunei(Hemsl.)Makino

118.64 27.16 18.7 1694 7.73 7.53 - 59.87 49.89


Manglietiayuyuanensis Y.W. Law

117.78 26.56 19.7 1682 9.43 8.33 2918 91.02 127.50


Manglietiayuyuanensis Y.W. Law

117.99 26.53 18.5 1700 15.65 10.66 2432 123.1 77.99


Elaeocarpussylvestris(Lour.) Poir.

118.46 27.82 17.4 1782 9.25 6.12 3000 67.94 59.32


AltingiagracilipesHemsl.

117.46 26.26 19.4 1654 10 9.9 2933 128.93 128.05


AltingiagracilipesHemsl.

118.20 26.10 18.2 1625 18.1 14.87 990 186.8 120.06


Vernicia fordii(Hemsl.) Airy-Shaw

118.13 27.14 16.5 1880 8.34 6.03 3140 - 65.05



118.20 26.10 18.2 1625 6.11 4.41 4230 32.99 54.39



118.20 26.10 18.2 1625 7.76 5.6 5310 82.7 94.24

1604 Pinuds elliottii Engelm.


115.14 27.22 18.3 1500 10.97 8.51 2118 68.97 75.78

1

Appendix S2. Details of equations, derivations, analyses, and simulation 1

data. 2

3

1. Regression of volume-biomass equations 4

Stand biomass density y (Mg ha-1) is expressed as a power function (y=rxk ) of stand volume 5

density x (m3ha-1). The r and k are coefficients (denoted by ^ ) determined by robust regression 6

analysis. In the least squares estimation, the coefficients are obtained by minimizing i=1

n ei

2, where 7

ei=yi-j=1

t jxij, and M-estimation of is the solution of

i=1

n ixij=0 (i is sample number, and j is variable 8

number; t=2 in this study). is calculated based on Tukey's biweight (Beaton, et al., 1974; Press, et al., 9

1992) as follows, 10

i = 0 for Ji>1(1-Ji

2)

2 for Ji<1 11

where Ji=|ui/c|, ui=ei/s, c is set as 4.685, and s represents residual scale. The results are summarized in 12

Table 2, and scatter plots are shown in Fig. S2-1. The data of volume-biomass pairs were collected 13

from the publication (Luo et al., 2013; also see Supporting information 1). 14

15

Reference 16

Beaton, A.E., and Tukey, J.W. 1974. The fitting of power series, meaning polynomials, illustrated on 17

band-spectroscopic data. Technometrics, 16, 147-185. 18

Luo, Y., Wang, X., Zhang, X. & Lu, F. (2013) Biomass and its allocation of forest ecosystems in China, 19

Chinese Forestry Publishing House Press, Beijing. 20

Press, W.H., Flannery, B.P., Teukolsky, S.A., Vetterling, W.T. (1992) Numerical Recipes in FORTRAN: 21

The Art of Scientific Computing, 2nd ed. Cambridge, England: Cambridge University Press, p. 697. 22

2

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

Fig. S2-1. The scatter plots for 16 regression equations (B=rVk ) listed in Table 4. Solid lines are 17

regression curves of the equations. 18

. 19

1) CD=0.88

0

500

0 500

2) CD=0.75

0

500

0 500

3) CD=0.88

0

500

0 500

4) CD=0.89

0

500

0 500

5) CD=0.83

0

500

0 500

6) CD=0.79

0

500

0 500

7) CD=0.95

0

500

0 500

8) CD=0.87

0

500

0 500

9) CD=0.81

0

500

0 500

10) CD=0.96

0

500

0 500

11) CD=0.78

0

500

0 500

12) CD=0.76

0

500

0 500

13) CD=0.8

0

500

0 500

14) CD=0.82

0

500

0 500

15) CD=0.81

0

500

0 500

16) CD=0.81

0

500

0 500

Tota

l bio

mas

s B

(t/ha

)

Mean volume V (m3/ha)

3

2. Sensitivity of variance to the compensation ratio 1

The Sensitivity of variance to the compensation ratio can be reflected in Fig S2-2, which shows 2

how sensitive the compensation is to misspecification of the volume density distribution. If we only 3

know a provincial mean volume density X but do not know the distribution, we have many choices to 4

set up a variance (D) along with the line (seeD in Fig. S2-2). The real variance must be somewhere on 5

this line. In case we made a misspecification, the function X, D, k) will express what percentage we 6

missed in compensation. 7

For example in Fig. S2-2, D=0.00076%*D under the conditions (X=100, k=0.8119), so if we 8

miscalculate D=20000 instead of D=10000, then 7.6% of the compensation will be neglected. From Fig. 9

S2-2b, It can be seen that the compensation ratio is less when X>200m3ha-1, and the deviations (D) 10

become more important as volume density (X) is lowered. 11

12

Fig. S2-2. An example to assess the sensitivity of variance to the compensation ratio. Symbols have the 13

same definitions as in Fig. 3. 14

4

3. Some details in the derivation 1

(1) Expanding Eq. (A1) 2

To expand Equation (A1) 3

g ≈E{q=0

4

[(1/q!)g(q)()(x-)q]}, 4

we have 5

g ≈E[g()]+E[g(1)( )(x-)]+E[

12g(2)

( )(x-)2]+E[16g(3)

( )(x-)3]+E[124g(4)

( )(x-)4] 6

g ≈g()+g(1)()E[x-]+

12g(2)

()E[(x-)2]+16g(3)

()E[(x-)3]+124g(4)

()E[(x-)4] (S1), 7

where E[(x−)s] can be expressed by sth central moment of a real-valued random variable x, 8

s= E[(x−)s]= j=0

s ( s

j )(xj) (-s-j

. 9

where s=1, 2, 3, and 4. We have 10

1= E[x−]= E[x]-E[]=-=0 11

2= E[(x−)2]= (x2)-2= 12

3= E[(x−)3]=(x3)-3-3 (S2) 13

4= E[(x−)4]= (x4)-4(x3)+62(x2)-34 (S3). 14

15

(2) Expressing (x3) and (x4) 16

For symmetrical distributions, skewness is zero, i.e., 3=0. From Equation (S2), we have 17

(x3)=+3 (S4). 18

Substituting Equation (S4) into Equation (S3), we see that 19

4=(x4)-4(x3)+62(x2)-34=(x4)-4+3+62+2-34 20

4 =(x4)--6 (S5). 21

To calculate (x4) we can use kurtosis (4

) to express 4 as 22

4=Q 23

5

where Q indicates the 4th origin moment and Q=kurtosis+3. Substitute 4 to Equation (S5), it leads to1

(x4)=+6+Q (S6).2

Notice that, for several well-known symmetric distributions, kurtosis value and Q can be: 3

Uniform distribution, −1.2 and 1.8; 4

Wigner semicircle distribution, −1 and 2; 5

Raised cosine distribution, −0.5938 and 2.4062; 6

Normal distribution, 0 and 3; 7

Logistic distribution, 1.2 and 4.2; 8

Hyperbolic secant distribution, 2 and 5; 9

Laplace distribution (double exponential distribution), 3 and 6. 10

11

(3) Rewriting and simplifying g 12

Substitute Equation (S4) and (S6) into Equation (S2) and (S5), respectively, we see that 13

E[(x-)3]=(x3)-3-3=+3-3-3=0 14

E[(x-)4]=(x4)--6=+6+Q--6=Q.15

Note that in a symmetric distribution all odd moments equal zero. Here, E[x-] and E[(x-)3] are 16

derived as an analysis example. Now we solved all four moments, 17

E[x−]=0 (S7)18

E[(x−)2]= (S8)19

E[(x−)3]=0 (S9)20

E[(x-)4]=Q (S10).21

In addition, for g(x)=xk, we have 22

g(1)( )=k

k-1 23

g(2)( )= k(k-1)

k-2 24

g(3)( )= k(k-1)(r-2)

k-3 25

g(4)( )=k(k-1)(k-2)(k-3)

k-4. 26

6

Substitute Equation (S7), (S8), (S9), (S10), and g(q)( ) for q=1, 2, 3, 4 into Equation (S1), this 1

gives 2

g ≈k+(1/2)k(k-1)k -2+(1/24)k(k-1)(k-2)(k-3)k -4Q. 3

4

(4) Maximum variance 5

For a distribution between xmin and xmax, the definition of variance implies that a variance will be 6

largest for a given expectation while all samples (xi ) are either xmin or xmax. Assuming n samples start to 7

move from xmin to xmax one by one, the samples that are present at the point of xmin and xmax at any time 8

are n-np and np respectively. p is the percentage of the samples that have moved to the point of xmax. 9

Thus, we have 10

= (n-np)xmin+np xmax

n 11

(x2) = (n- np)(xmin)2+np(xmax)2

n . 12

Expanding them and simplifying, we can see 13

= (1-p)xmin +p xmax (S11) 14

(x2) = (1-p)(xmin)2+p(xmax)2 (S12). 15

Substitute Equation (S11) and (S12) into the variance formula D=(x2) - 2, it leads to 16

D= -(-xmin)2+(-xmin)(xmax-xmin). 17

The maximum variance can be expressed as 18

Dm= -(X-xmin)2+( X-xmin)(xmax-xmin). 19

where X represents the regional mean volume density. 20

21

7

4. Simulated data sets 1

The simulated data can be called dummy data from the pseudorandom number generator. This 2

data set was designed consisting of 300 stands each with different areas and volume densities on two 3

distributions. The stand areas are assumed as 1, 2, and 3 ha, which are randomly distributed. Total 4

forest area becomes 618 ha. The stand volume densities range from 4 to 603 m3ha-1 randomly. The 5

simple sampling method was applied in this experiment. Total stochastic samplings were set up 5000 6

times for a Monte-Carlo error analysis. Fig. S2-3 illustrates the distributions for one of the 5000 7

sampling sets. The simulated data for of this example are listed in Table S2-1, which corresponds to the 8

calculation results in Table 1. 9

10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26

27

Fig. S2-3. Distributions of the simulated data set in Table S2-1. The unit of volume density is m3ha-1. a, 28

b, c, and d denote two expectations for the two distributions (see Table S2-1). 29

a

0

100

200

300

400

0 100 200 300

Stand number

Volu

me

dens

ity

b

0

100

200

300

400

0 100 200 300

Stand number

Volu

me

dens

ity

c

0

200

400

600

800

0 100 200 300

Stand number

Volu

me

dens

ity

d

0

200

400

600

800

0 100 200 300

Stand number

Volu

me

dens

ity

8

Table S2-1. An example of simulated data set, which is one of the 5000 sampling sets from the 1

pseudorandom number generator 2

Volume density（m3ha-1） Low expectation High expectation

No Stand area (ha) a. Normal b. Uniform c. Normal d. Uniform 1 1 161.08 7.66 243.21 456.88 2 3 39.28 182.58 208.20 68.30 3 2 84.46 55.16 293.98 583.82 4 3 139.59 121.41 262.86 87.62 5 3 167.48 110.24 195.85 280.75 6 1 109.46 201.47 282.89 248.19 7 1 156.89 287.47 400.05 290.93 8 2 82.18 157.54 260.09 243.95 9 2 113.01 228.66 374.50 16.82

10 3 143.83 124.62 365.23 293.55 11 2 69.90 212.24 409.70 405.92 12 2 124.42 107.48 360.70 248.14 13 1 144.54 81.12 162.30 107.79 14 2 167.70 110.29 282.85 449.61 15 1 190.97 85.94 272.25 455.58 16 3 157.40 14.17 277.41 593.41 17 1 22.81 124.65 253.62 270.00 18 2 195.34 148.86 428.12 169.15 19 3 189.71 191.30 337.02 542.35 20 2 84.10 189.51 144.86 209.79 21 1 179.98 186.29 351.09 386.11 22 1 153.34 82.19 443.67 185.22 23 1 140.42 239.78 190.73 317.16 24 2 164.83 216.11 156.65 212.55 25 1 130.38 255.27 332.96 409.71 26 3 177.96 10.62 360.32 586.01 27 3 243.98 52.86 250.22 276.18 28 2 177.98 208.27 434.07 73.27 29 2 160.25 249.34 333.43 411.46 30 2 114.66 204.65 179.48 87.61 31 3 159.63 185.71 259.93 365.10 32 3 69.72 110.09 254.63 256.15 33 3 200.56 79.50 371.36 251.03 34 1 209.22 302.04 218.37 115.94 35 2 183.07 121.14 431.67 48.00 36 3 205.16 207.19 209.73 92.77 37 1 94.35 76.22 455.86 535.16

9

38 2 205.13 48.32 224.19 554.37 39 3 146.66 213.40 294.83 527.16 40 3 140.59 113.26 301.80 527.39 41 1 206.36 293.01 311.72 229.80 42 3 179.44 152.29 317.59 340.23 43 3 149.21 205.25 242.75 48.90 44 3 170.60 217.67 276.52 67.38 45 3 205.43 130.68 432.53 163.38 46 2 182.24 23.56 374.66 208.44 47 2 157.57 177.51 164.28 454.83 48 2 208.69 266.51 262.51 192.53 49 3 94.85 284.90 273.93 207.50 50 1 128.03 103.29 288.36 557.07 51 1 125.60 279.75 348.36 513.80 52 2 196.97 117.90 136.03 575.09 53 2 190.48 193.12 378.30 449.54 54 1 119.03 245.91 220.57 511.63 55 2 77.55 219.78 245.63 598.54 56 3 131.92 203.16 524.80 367.39 57 1 155.46 178.11 327.55 225.22 58 3 190.80 151.70 419.62 385.03 59 2 140.72 84.88 234.63 331.64 60 3 161.62 157.25 289.06 405.09 61 2 115.26 295.48 423.35 122.06 62 2 54.69 37.73 241.55 317.65 63 3 216.62 108.86 205.95 287.38 64 3 218.63 238.82 342.10 316.78 65 2 138.20 226.02 282.50 479.44 66 1 151.20 274.78 317.00 52.90 67 1 118.35 14.27 265.98 518.20 68 3 112.27 280.75 161.58 364.26 69 1 162.60 133.24 323.66 507.58 70 3 123.49 253.84 399.80 284.57 71 1 103.86 11.31 327.70 11.17 72 3 94.74 33.67 275.66 66.99 73 3 179.02 180.12 208.09 453.07 74 3 138.51 148.13 225.58 202.99 75 1 149.48 265.59 280.80 105.39 76 1 122.19 19.63 457.63 92.67 77 1 97.25 206.86 308.46 507.68 78 1 226.36 31.30 193.49 541.64 79 2 145.60 137.66 256.52 427.64 80 1 191.59 251.60 372.77 128.40

10

81 2 153.28 6.93 179.52 157.62 82 1 179.38 113.13 226.22 101.89 83 3 176.20 123.31 384.42 145.17 84 3 169.92 184.08 176.74 562.60 85 3 154.57 231.52 252.08 390.91 86 3 152.94 28.65 495.30 63.94 87 1 103.60 27.79 238.87 132.68 88 3 78.65 29.59 311.99 69.55 89 3 144.81 183.62 333.53 453.14 90 1 129.18 234.50 383.86 294.47 91 3 157.98 168.84 350.20 458.79 92 3 153.72 278.24 343.67 160.82 93 2 181.56 110.79 428.46 473.12 94 2 138.91 223.04 354.40 353.42 95 3 45.73 231.27 370.01 11.97 96 1 156.58 229.91 93.23 52.59 97 1 140.36 273.16 339.47 244.36 98 3 192.92 110.80 544.45 429.92 99 1 132.01 172.86 288.19 64.00

100 3 149.88 94.52 199.00 381.97 101 3 133.92 137.92 461.84 578.56 102 1 172.79 118.89 307.50 448.12 103 2 149.01 189.27 287.76 206.32 104 2 195.41 17.69 194.81 284.48 105 3 202.31 234.79 311.31 370.94 106 2 113.57 182.58 437.17 538.38 107 2 190.03 22.49 259.44 351.57 108 2 98.14 131.98 360.46 141.52 109 2 140.30 20.91 447.96 90.40 110 1 171.47 223.91 342.50 274.07 111 3 126.57 244.66 383.35 41.39 112 3 106.52 26.56 486.27 203.54 113 1 167.86 158.90 329.53 72.73 114 3 158.24 17.20 196.36 108.64 115 2 181.96 160.89 333.47 452.10 116 2 188.65 107.87 21.17 262.33 117 3 195.45 40.82 216.79 280.99 118 3 147.25 38.45 358.15 530.66 119 1 154.78 186.40 307.87 62.52 120 3 211.28 25.64 310.09 350.01 121 1 188.64 58.98 215.66 102.12 122 1 260.07 218.11 198.34 196.55 123 2 216.03 11.01 339.51 578.37

11

124 2 180.38 247.87 331.41 506.97 125 2 185.17 123.87 343.33 520.48 126 3 231.06 46.11 194.68 242.58 127 3 174.00 290.46 306.67 295.94 128 2 151.84 19.47 331.67 9.52 129 1 208.59 302.82 232.58 531.07 130 3 193.41 158.35 172.86 164.93 131 3 55.73 30.22 327.10 142.14 132 1 105.82 89.96 224.42 111.30 133 3 92.68 215.11 304.17 271.46 134 2 201.26 256.46 336.31 173.07 135 3 130.25 143.70 259.98 206.00 136 3 158.57 284.52 432.64 260.05 137 3 182.63 12.53 340.23 576.70 138 3 256.33 208.52 236.82 117.26 139 3 89.15 49.29 176.70 259.49 140 2 199.10 125.83 225.25 242.29 141 2 225.36 96.66 526.63 38.59 142 2 146.42 169.97 224.42 266.06 143 3 130.30 85.79 237.28 359.22 144 1 183.35 92.22 275.51 468.10 145 3 185.77 108.78 258.14 296.51 146 2 204.87 96.98 320.13 138.33 147 1 71.75 270.06 219.99 218.78 148 2 191.59 210.15 470.99 176.14 149 1 187.08 149.31 266.89 416.30 150 1 115.56 156.63 459.94 512.09 151 2 173.39 253.94 326.74 352.16 152 1 147.35 83.00 208.75 560.79 153 1 268.39 124.17 390.74 74.98 154 3 115.15 68.14 329.76 32.11 155 1 138.30 63.34 224.32 515.50 156 3 148.23 260.35 239.91 111.67 157 3 203.18 160.74 224.12 216.35 158 3 155.99 86.12 371.77 507.71 159 3 146.62 228.08 384.03 594.93 160 2 88.63 210.89 327.72 103.68 161 3 90.90 121.39 272.77 542.15 162 1 164.79 45.94 424.04 99.09 163 2 206.73 146.32 346.70 224.69 164 2 222.08 23.64 311.56 237.85 165 2 119.80 302.76 229.09 588.90 166 1 209.90 145.57 372.97 365.44

12

167 1 91.63 79.30 216.96 406.63 168 1 228.41 253.11 289.04 26.02 169 3 159.67 23.18 229.46 81.29 170 1 90.07 46.19 239.34 117.05 171 2 157.78 191.25 291.51 33.01 172 3 171.96 20.90 365.97 311.96 173 3 179.84 175.98 294.44 502.53 174 3 159.70 7.75 360.08 92.06 175 1 167.52 269.96 391.89 538.26 176 2 202.20 218.83 183.37 235.70 177 3 148.13 31.12 374.86 198.38 178 1 172.49 298.14 336.20 521.54 179 2 192.68 258.67 258.94 188.18 180 2 223.18 78.34 41.10 290.34 181 1 98.05 80.72 364.48 598.31 182 3 155.43 26.01 176.29 175.19 183 2 33.63 65.04 243.02 316.62 184 3 115.50 112.79 344.02 78.19 185 1 174.53 145.15 245.23 46.00 186 2 132.53 209.77 323.57 581.46 187 2 127.54 138.35 382.77 236.24 188 2 13.85 220.40 446.86 179.30 189 1 116.69 233.35 225.35 558.62 190 1 201.37 280.28 291.77 565.91 191 2 144.92 133.67 264.16 246.85 192 2 90.23 19.69 201.31 94.86 193 3 149.51 94.53 334.88 73.14 194 2 105.26 199.12 255.47 24.01 195 1 149.28 32.26 252.13 308.74 196 1 194.30 140.41 303.45 438.55 197 2 163.52 72.62 349.65 426.19 198 2 118.59 293.18 430.03 485.99 199 3 38.36 302.31 83.04 130.54 200 1 160.59 223.37 313.55 102.72 201 1 205.66 119.47 275.71 253.40 202 3 118.04 4.77 264.64 568.02 203 3 193.61 268.25 294.93 310.84 204 1 107.40 141.22 310.83 520.10 205 3 272.04 127.40 462.64 287.09 206 3 177.85 298.93 281.29 475.95 207 1 113.95 92.20 269.64 441.08 208 2 94.89 115.96 261.72 13.81 209 1 138.43 299.26 300.79 146.75

13

210 2 110.56 249.49 338.70 46.89 211 1 262.65 241.28 451.32 393.19 212 2 119.98 172.79 314.20 506.91 213 2 191.54 259.69 344.97 306.05 214 1 104.62 180.74 224.34 11.62 215 2 204.62 126.41 377.92 35.24 216 1 102.30 149.24 285.79 339.99 217 2 97.16 259.48 227.02 267.32 218 1 133.66 272.82 240.85 110.84 219 2 88.84 292.66 404.18 404.56 220 2 92.84 167.06 228.87 427.37 221 1 144.62 162.74 424.67 127.72 222 2 133.85 283.92 150.45 181.45 223 3 127.97 203.78 206.75 452.18 224 1 236.78 4.11 366.40 528.47 225 1 158.92 7.96 273.40 421.67 226 3 153.71 269.74 278.32 510.61 227 1 110.66 160.58 283.99 367.39 228 3 178.38 118.75 294.46 200.15 229 2 99.41 236.73 331.69 518.52 230 2 186.34 87.31 168.49 385.53 231 2 63.03 60.41 366.35 43.33 232 2 67.01 216.67 351.80 386.24 233 1 158.02 201.79 286.11 557.87 234 1 130.26 13.26 277.61 494.50 235 3 124.76 135.72 293.75 339.06 236 2 180.73 164.66 43.17 439.07 237 3 221.57 226.80 251.44 602.58 238 1 217.27 183.23 289.91 297.04 239 3 144.72 25.42 392.22 243.48 240 2 169.92 266.39 300.52 560.21 241 1 85.78 154.48 257.99 235.53 242 3 217.62 296.56 175.14 506.49 243 2 231.23 144.18 245.24 461.95 244 3 135.67 231.52 305.90 110.66 245 2 204.26 268.71 253.77 506.08 246 2 79.19 201.50 342.47 228.33 247 2 163.72 270.77 288.65 89.12 248 3 85.97 266.87 256.52 446.09 249 2 50.93 233.59 273.12 337.51 250 1 238.31 210.93 346.65 54.32 251 3 155.29 90.23 321.64 429.45 252 3 130.04 23.43 408.80 173.82

14

253 3 192.84 296.89 426.63 471.48 254 2 218.74 29.37 318.44 118.11 255 2 90.56 260.89 274.14 349.22 256 1 117.58 135.98 248.74 393.30 257 3 138.56 279.45 349.04 456.36 258 2 126.60 149.65 258.76 152.80 259 1 82.30 89.57 405.85 407.76 260 3 190.79 174.36 458.08 117.29 261 2 142.02 259.12 393.61 136.29 262 2 74.17 169.89 334.48 405.84 263 3 173.20 234.83 200.46 436.02 264 1 185.85 293.06 347.72 168.24 265 2 185.54 166.78 245.01 511.47 266 2 127.83 138.69 446.17 534.45 267 2 229.24 42.82 277.94 507.59 268 1 140.83 154.40 157.75 282.40 269 2 179.80 228.80 328.52 225.89 270 1 85.14 198.89 266.84 21.61 271 2 181.22 28.27 276.44 66.28 272 1 115.93 241.21 226.31 418.76 273 1 111.69 211.75 126.10 518.51 274 3 100.49 34.31 366.37 252.69 275 2 99.25 40.37 202.64 522.27 276 3 121.94 280.67 236.67 59.12 277 3 173.61 42.38 265.54 291.65 278 3 236.57 124.98 324.09 569.95 279 3 128.30 127.95 276.91 181.75 280 1 172.25 15.84 294.86 117.74 281 1 177.26 222.51 340.70 539.41 282 1 134.24 36.66 355.24 364.61 283 2 144.16 216.54 180.11 50.96 284 2 129.88 255.89 214.52 471.05 285 2 58.34 124.50 472.45 113.35 286 1 86.67 119.29 172.09 147.06 287 2 126.38 23.44 194.93 535.19 288 2 131.72 9.67 367.39 341.30 289 3 147.82 200.63 250.51 99.89 290 3 114.70 129.72 424.16 358.47 291 2 81.72 63.82 230.74 271.35 292 3 272.66 175.63 330.76 413.04 293 3 209.68 10.35 301.74 210.34 294 3 163.53 258.47 181.55 424.42 295 3 93.03 13.66 159.56 519.61

15

296 3 186.07 127.64 376.42 410.02 297 2 161.93 191.25 303.15 161.48 298 3 53.23 120.28 308.53 286.72 299 3 155.45 78.36 130.21 371.92 300 1 143.62 296.31 370.09 361.10

1

2

3

5. An example of estimation based on age groups 4

We tested scaling-up errors in the FCS estimation by utilizing provincial values of each age group 5

for Hubei province in China. The total biomass is 248,795 (kt) (Table S2-2) after compensating the 6

scaling-up errors based on averaged values of all age group. This has compensated more than 83.7% of 7

scaling-up error (Fig. 4). However, if the volumes from the biomasses are calculated and converted 8

separately based on each age group, the total biomass is 249,187 (kt) (Table S2-4) before the 9

compensation. This result indicates that the estimates would be relatively accurate based on each age 10

group’s volume density even without scaling-up compensation. After compensation, the total biomass 11

becomes lower (247,725 kt) with a fairly low rate of compensation (0.6%) (Table S2-4). Note that this 12

compensated value may be controversial owing to the assumption of the distribution forms and their 13

intervals (Table S2-3). 14

15

16

17

16

Table S2-2. An example of provincial FCS estimation (Hubei province) based on the averages for all age groups. Equation (1) was used for error compensation. r and k are parameters of 1

the power law function. The variances (D) were computed (see the appendix) responding to 27 available species and types in the province. 2

Species Parameters Biomass (kt)

Variance of volume density distribution r k Before After compensation Rate

Abies 1492 1.19 0.8790 1,181.23 1,176.55 0.4% Larix 2 1.56 0.8617 1,781.20 1,781.09 0.0% Pinus thunbergii 4 1.95 0.8119 37.31 37.17 0.4% Pinus tabuliformis 226 1.55 0.8615 389.48 386.79 0.7% Pinus armandii 577 1.95 0.8119 558.48 546.79 2.1% Pinus massoniana 316 1.09 0.9154 49,166.63 48,970.66 0.4% Exotic pines 92 1.95 0.8119 266.74 265.78 0.4% Pinuds elliottii 240 1.44 0.8591 1,013.52 1,004.99 0.8% Other pines 3722 1.44 0.8591 1,767.01 1,731.47 2.0% Cunninghamia lanceolata 735 1.26 0.8497 9,527.49 9,271.75 2.7% Cryptomeria fortunei 13026 1.37 0.8225 1,988.56 1,937.60 2.6% Metasequoia glyptostroboides 2386 1.37 0.8225 589.16 585.48 0.6% Taxodium ascendens 1813 1.37 0.8225 674.26 671.95 0.3% Cupressus funebris 176 1.87 0.8259 2,282.42 2,239.01 1.9% Quercus 902 1.80 0.8744 26,960.24 25,963.33 3.7% Betula 29885 1.57 0.9128 1,413.94 1,334.21 5.6% Cinnamomum longepaniculatum 41 1.57 0.9128 110.22 110.01 0.2% Robinia pseudoacacia 19 1.80 0.8744 363.44 359.09 1.2% Liquidambar formosana 10 1.57 0.9128 523.41 522.65 0.1% Other hard broadleaved trees 1439 1.57 0.9128 11,187.81 11,039.37 1.3% Tilia spp. 115 0.86 0.9523 113.50 113.38 0.1% Populus 350 1.10 0.8969 8,820.38 8,703.53 1.3% Salix babylonica 220 0.86 0.9523 154.70 154.53 0.1% Paulownia 4 0.86 0.9523 23.15 23.13 0.1% Soft broadleaved trees 260 0.86 0.9523 2,432.39 2,417.84 0.6% Other conifer trees 1066 1.74 0.8350 23,141.67 22,828.16 1.4% Other broadleaved trees 451 1.19 0.9325 76,076.66 75,642.25 0.6% Mixed conifer and deciduous trees 211 1.74 0.8350 29,160.28 28,976.56 0.6% Total 251,705 248,795 1.2%

3

17

Table S2-3. An example of the variance calculation for each age group of every species at the provincial scale (Hubei province). The maximum volume densities were tentatively 1

presupposed as the middle values between neighbouring age groups. The distributions were assumed as uniform to calculate variances (D), where D=(Dmax-Dmin)2/12 for uniform 2

distribution. For example, (108-0)2/12=966 for young Abies, and (127-108)2/12=31 for minddle-aged Abies, etc. 3

Assumed maximum volume densities (m3ha-1) Variances of each age group Species Young Middle-aged Near mature Mature Over-mature Young Middle-aged Near mature Mature Over-mature Abies 108 127 151 222 400 966 31 49 419 2631 Larix 44 58 86 130 234 163 15 69 156 898 Pinus thunbergii 11 17 25 38 69 11 3 6 13 77 Pinus tabuliformis 25 50 82 123 221 53 49 87 140 805 Pinus armandii 44 61 47 64 114 164 23 16 22 215 Pinus massoniana 44 68 72 83 150 162 48 1 12 371 Exotic pines 55 83 124 187 336 255 64 143 322 1856 Pinuds elliottii 28 35 51 74 133 64 5 20 44 289 Other pines 9 50 124 188 326 7 140 456 342 1586 Cunninghamia lanceolata 36 74 97 123 222 106 120 45 59 811 Cryptomeria fortunei 38 152 270 381 685 123 1079 1151 1028 7733 Metasequoia glyptostroboides 89 148 221 332 598 653 290 454 1021 5880 Taxodium ascendens 26 114 246 369 664 57 644 1449 1259 7251 Cupressus funebris 34 62 94 141 253 98 66 81 183 1054 Quercus 69 146 159 151 250 395 495 15 5 805 Betula 17 29 43 221 585 25 11 17 2629 11032 Cinnamomum longepaniculatum 37 55 83 125 224 114 28 64 144 830 Robinia pseudoacacia 6 15 26 38 68 3 6 10 12 75 Liquidambar formosana 17 25 38 57 103 24 6 13 30 173 Other hard broadleaved trees 74 120 121 141 255 453 177 0 34 1067 Tilia spp. 37 62 93 139 250 115 51 80 179 1031 Populus 25 52 69 94 169 54 57 24 53 472 Salix babylonica 26 39 59 69 103 57 14 32 10 92 Paulownia 12 17 26 39 71 11 3 6 14 82 Soft broadleaved trees 26 45 67 48 37 55 32 38 28 11 Other conifer trees 64 97 140 216 388 338 90 160 472 2479 Other broadleaved trees 65 95 130 150 211 353 75 104 33 302 Mixed conifer and deciduous trees 51 69 85 120 216 221 25 21 104 771 Average 49.5 76.5 95.4 138.6 262.0 204.2 60.9 29.5 155.4 1269.0

18

Table S2-4. An example of provincial FCS estimation (Hubei province) based on the volume densities (provided by China’s forest inventories) and variances (Table S2-3) of each age 1

group. Equation (1) was used for error compensation. r and k used for this calculation are the same as the values in Table S2-2. 2

Biomass for each age group (t) Total biomass for all age groups (kt) Young Middle-aged Near mature Mature Over-mature

Species Before

compensation Compensated Before compensation Compensated Before

compensation Compensated Before compensation Compensated Before

compensation Compensated Before compensation After compensation Rate

Abies 190,843 1,322 - - 264,078 44 721,338 510 - - 1,176 1,174 0.2% Larix 1,509,451 8,211 271,638 116 - - - - - - 1,781 1,773 0.5% Pinus thunbergii 37,306 371 - - - - - - - - 37 37 1.0% Pinus tabuliformis - - 204,916 535 182,046 220 - - - - 387 386 0.2% Pinus armandii 42,771 4,702 215,123 62 134,620 83 151,736 98 - - 544 539 0.9% Pinus massoniana 7,343,954 56,801 23,023,262 12,032 14,823,676 100 3,757,891 377 - - 48,949 48,879 0.1% Exotic pines 266,736 2,652 - - - - - - - - 267 264 1.0% Pinuds elliottii 155,818 826 243,709 92 - - 605,498 464 - - 1,005 1,004 0.1% Other pines 25,322 200 - - 872,879 3,019 357,844 293 468,450 951 1,724 1,720 0.3% Cunninghamia lanceolata 2,458,948 46,197 4,075,914 11,437 1,159,463 367 1,596,636 613 - - 9,291 9,232 0.6% Cryptomeria fortunei 22,404 3,791 143,349 2,334 780,181 1,189 966,396 781 - - 1,912 1,904 0.4% Metasequoia glyptostroboides - - 443,153 674 - - - - - - 443 442 0.2% Taxodium ascendens - - - - 674,256 1,843 - - - - 674 672 0.3% Cupressus funebris 1,335,897 27,384 910,094 1,739 - - - - - - 2,246 2,217 1.3% Quercus 19,997,557 537,077 2,443,509 5,559 2,186,404 55 1,271,022 20 504,303 804 26,403 25,859 2.1% Betula - - 175,301 145 - - - - 1,160,359 3,355 1,336 1,332 0.3% Cinnamomum longepaniculatum 110,220 571 - - - - - - - - 110 110 0.5% Robinia pseudoacacia - - 249,619 1,319 83,589 102 112,714 80 - - 446 444 0.3% Liquidambar formosana 431,379 2,236 - - - - - - - - 431 429 0.5% Other hard broadleaved trees 4,196,895 55,127 3,667,971 2,123 1,681,362 1 1,501,415 160 - - 11,048 10,990 0.5% Tilia spp. - - 113,498 54 - - - - - - 113 113 0.0% Populus 841,147 22,201 5,843,253 9,190 1,149,408 333 851,722 371 - - 8,686 8,653 0.4% Salix babylonica - - - - - - - - 154,699 69 155 155 0.0% Paulownia 23,151 68 - - - - - - - - 23 23 0.3% Soft broadleaved trees 998,915 2,568 483,168 403 554,245 130 325,925 39 58,162 25 2,420 2,417 0.1% Other conifer trees 6,105,804 78,775 11,791,844 10,126 2,498,183 2,348 2,458,451 2,687 - - 22,854 22,760 0.4% Other broadleaved trees 51,861,325 351,560 17,692,739 5,159 4,488,413 1,459 1,303,366 53 383,648 185 75,729 75,371 0.5% Mixed conifer and deciduous trees 16,418,079 167,716 9,710,352 4,120 1,608,751 432 1,257,697 975 - - 28,995 28,822 0.6%

Total 249,187 247,725 0.6% 3

Appendix S3. The derivation of compensators. 1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

The derivation of error compensator is described as follows. All symbols and descriptions

refer to Table S1.

Based on the assumed allometric relation between y and x in a stand, a monotonically

increasing power-law function can be derived as y=rxk (0.6≤k≤1 for volume-biomass conversion).

Therefore, rationally we have

Y1 =∑aiyi =∑ai(rxik)

to express a regional biomass. However, this expression is not applicable since both ai and xi are

unknown for each single stand. Instead, we have

Y2 =ArXk

to meet the demand of practicing national FCS estimation, because A (e.g., total forested area for

a species in a province) and X (e.g., provincial mean volume density for a species) are two

available inputs provided by national forest inventories. Thus, it is necessary to compare if Y2=Y1.

For an easier analysis, Y1 and Y2 can be converted to similar forms:

Y1 =∑aiyi = ∑[A(aiA)(xi

k)]=Ar∑wixik16

17

18

19

20

21

22

23

24

25

26

Y2 =ArXk = Ar(∑wixi)k

where the random variable x is discrete with wi. Through the weighted Jensen inequality, we can

prove that ∑(wixik)≤(∑wixi)k and Y1≤Y2, i.e., an error (error=Y2-Y1) does exist. This error is a

non-negative value. It is caused by scaling up forest biomass from stand to large scale. To solve

the error, we can rewrite it as error=Ar(μk-μg). If forest inventories provide sufficient information

to calculate μg directly, the error can be solved easily, whereas we need to express unknown μg

using known μ and σ2 as shown by the following derivation.

Assuming that the fourth derivatives of continuous g(x) exists in a neighbourhood of x=μ,

and μg exists as well, g(x) can be approximated at x=μ as

g(x)≈∑q=0

4

[(1/q!) g(q)(μ)( x-μ)q]

1

by using a fourth-order Taylor series expansion and omitting the remainder term. Taking

expectations on both sides, then we see that

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

μg ≈E{∑q=0

4

[(1/q!)g(q)(μ)(x-μ)q]} (A1).

For a symmetrical distribution, we have the following expressions based on the variance

definition and central moment equations (Supporting information 2):

μ(x3)= μ3+3μσ2 (A2)

μ(x4)= μ4+6μ2σ2+ σ4Q (A3).

After expanding the right side of Equation (A1) and substituting g=xk, Equation (A2), and

Equation (A3) gives

μ g ≈μk+(1/2)k(k-1)μk -2σ2+(1/24)k(k-1)(k-2)(k-3)μk -4σ4Q

and then error becomes

error≈0.417Ark(1-k)μk -4σ2[(k-2)(k-3)σ2Q +12μ2]

where Q=3 for normal distribution (i.e., ν2=σ2, ν3=0, ν4=3σ4), and Q=1.8 for uniform

distribution (i.e., ν2=σ2, ν3=0, ν4=1.8σ4). If we accept an approximation to express the stochastic

systematic error, then the compensator (Mg ha-1) can be written as a ternary function

Φ(X, D, k)=0.417rk(1-k)Xk-4 D[Q(k-2)(k-3)D +12X2] (A4)

where Φ(X, D, k) is expressed as a composite function, X and k are independent variables, D is an

intermediate variable that is also the function of X. By omitting the terms of Taylor series

expansion higher than second-order, it leads to a simple form

error ≈0.5Ark(1-k) μ k -2σ2

for any distribution. Statistically, errorAr is the approximate difference of both sides of the

aforementioned Jensen inequality. Then we have simple forms as

21

22

23

24

25

Φ(X, D, k)=0.5rk(1-k)Xk -2D (A5)

and the ratio of Φ(X, D, k) to the biomass density (before compensation) as

η(X, D, k)=0.5k(1-k)X-2D (A6)

2

where domains are xmin≤X≤xmax, 0≤D≤Dm, and 0.8≤k≤1 (in this study). Notice that Dm is derived

by assuming that x

1

2

3

i has largest variance for a given expectation if and only if xi equals either xmin

or xmax (Supporting information 2). Thus, we have

μ = (n-np)xmin+np xmax

n and μ(x2) = (n- np)(xmin)2+np(xmax)2

n . 4

5

6

7

8

9

Then we see that

Dm=μ(x2) - μ2= -(X-xmin)2+(X-xmin)(xmax-xmin) (A7)

for any distribution where xmin and xmax are known. This is a parabolic cylinder function on the

XD plane (Fig. 3).

The variance can be calculated based on the forest inventory data (from FRIC) as follows

D=∑j=1

5

(xj-X)2( aj A ) 10

11

12

13

14

where j, age group number ranging from 1 to 5 for young, middle-aged, near mature, mature, and

over-mature forest, respectively. D represents the variance for each combination of species and

provinces.

3

1

Table S1. Symbols and their descriptions 1

2

Symbol Description Unit A Total forested area in a region, A=∑ai. Ha ai The area of ith stand. ha D Variance of x. - Dm The maximum variance, which is a function of expectation X. - E The mathematical expectation operator. - g(x) The function of random variable x, g(x)=xk. - i Stand number, i=1, 2, …, n. - k Parameter in power-law function (y=rxk). - n The number of stands. - p Intermediate parameter (0～1), the percentage of the samples at the point of

xmax to total samples. -

q Derivative order, q is set up to 4 in this study. - r Parameter in the power-law function. - wi Weight or the probability of occurrence of ith stand, wi =ai /A. - x Volume density of a stand. m3 ha-1 X Weighted mean of stand volume densities, or regional volume density,

X=∑wixi . m3 ha-1

xi Volume density of ith stand. m3 ha-1 xmax The maximum possible volume density in the forest inventory. m3 ha-1 xmin The minimum possible volume density in the forest inventory. m3 ha-1 yi Biomass density of ith stand or sample plot. Mg ha-1 Y1 Regional biomass ideally supposed to accumulate from all stands. Mg Y2 Regional biomass calculated from A and X, Y2 =ArXk. Mg (X, D, k) The compensator of scaling-up error. Mg ha-1 (X, D, k) The compensation rate;

(X, D, k)=(X, D, k)/(Y2/A) =(X, D, k)/(rXk) =0.5k(1-k)X-2D. -

(xs) The expectation of xs, (xs)=E(xs), s=1, 2, 3, 4. - The expectation of x, =E(x). m3 ha-1 g The expectation of g(x), g=E[g(x)]. - s sth-order central moment, s=1, 2, 3, 4. - Variance of x, =D. -

Note: These descriptions are applicable to different species. 3

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methodsinecologyandevolution 2015 doi:10.1111/2041-210x ... et al_2015_mee.pdf · bon sequestration...

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