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Journal of Geographical Sciences >

2016 , Vol. 26 >Issue 5: 568 - 584

DOI: https://doi.org/10.1007/s11442-016-1286-z

Orginal Article

Uncertainty of forest biomass carbon patterns simulation on provincial scale: A case study in Jiangxi Province, China

  • WANG Yifu , 1, 2 ,
  • *YUE Tianxiang , 1, 2 ,
  • LEI Yuancai 3 ,
  • DU Zhengping 1 ,
  • ZHAO Mingwei 4
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  • 1. State Key Laboratory of Resources and Environment Information System, Institute of Geographic Sciences and Natural Resources Research, CAS, Beijing 100101, China
  • 2. University of Chinese Academy of Sciences, Beijing 100049, China
  • 3. Chinese Academy of Forestry, Beijing 100091, China
  • 4. Anhui Center for Collaborative Innovation in Geographical Information Integration and Application, Chuzhou University, Chuzhou 239012, Anhui, China

Author: Wang Yifu (1990-), PhD Candidate, specialized in ecological modeling and system simulation. E-mail:

*Corresponding author: Yue Tianxiang (1963-), PhD and Professor, E-mail:

Received date: 2015-09-23

  Accepted date: 2015-12-29

  Online published: 2016-05-25

Supported by

National Fundamental R&D Program of the Ministry of Science and Technology of the People’s Republic of China, No.2013FY111600-4

Copyright

Journal of Geographical Sciences, All Rights Reserved
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Abstract

Forest vegetation carbon patterns are significant for evaluating carbon emission and accumulation. Many methods were used to simulate patterns of forest vegetation carbon stock in previous studies, however, uncertainty apparently existed between results of different methods, even estimates of same method in different studies. Three previous methods, including Atmosphere-vegetation interaction model 2 (AVIM2), Kriging, Satellite-data Based Approach (SBA), and a new method, High Accuracy Surface Modeling (HASM), were used to simulate forest vegetation carbon stock patterns in Jiangxi Province in China. Cross-validation was used to evaluate methods. The uncertainty and applicability of the four methods on provincial scale were analyzed and discussed. The results showed that HASM had the highest accuracy, which improved by 50.66%, 33.37% and 28.58%, compared with AVIM2, Kriging and SBA, respectively. Uncertainty of simulation of forest biomass carbon stock was mainly derived from modeling error, sampling error and statistical error of forest area. Total forest carbon stock, carbon density and forest area of Jiangxi were 288.62 Tg, 3.06 kg/m2 and 94.32×109 m2 simulated by HASM, respectively.

Key words： forest carbon stock; HASM; AVIM2; Kriging; Satellite-data Based Approach (SBA)

Cite this article

WANG Yifu , *YUE Tianxiang , LEI Yuancai , DU Zhengping , ZHAO Mingwei . Uncertainty of forest biomass carbon patterns simulation on provincial scale: A case study in Jiangxi Province, China[J]. Journal of Geographical Sciences, 2016 , 26(5) : 568 -584 . DOI: 10.1007/s11442-016-1286-z

1 Introduction

Forest is the largest carbon pool of terrestrial ecosystem, containing more than 80% of global above-ground carbon (Dixon, 1994). However, it is controversial that forest is a carbon sink or a carbon source. As accumulating carbon from atmospheric CO2 via photosynthesis, forest is a carbon sink; on the other hand, climatic warming, deforestation and land use change make forest a major carbon source in some areas (IPCC, 2007). Consequently, simulating dynamic forest biomass carbon patterns accurately is significant for demonstrating forest carbon sink and source worldwide and regionally.
Estimation of forest vegetation carbon stock is the basis of simulation of forest biomass carbon patterns. Methods for estimating forest vegetation biomass carbon stock on national and regional scale have been developed, e.g. mean biomass density method (Brown and Lugo, 1984, 1992), volume-derived method (Fang et al., 1998; Wang et al., 2001) and Satellite-data Based Approach (Piao et al., 2005; Tan et al., 2007; Yao et al., 2015). The volume-derived method is regarded as the reasonable and reliable method so far, which has been widely applied (Fang et al., 2001, 2007; Pan et al., 2004; Xu et al., 2007; Wang et al., 2009; Ren et al., 2011). Fang et al. (2001) declared that forest of China was a carbon source during 1949 to the late 1970s, yet a carbon sink during the late 1970s to the late 1990s. Improving the parameters based on Fang’s study, Zhang et al. (2013) demonstrated Fang et al. overestimated China’s forest biomass carbon stock, with a result of 6.24 Pg during 2004 to 2008. Li H K et al. (2011) and Li X et al. (2011) estimated national and provincial carbon stock, with substituting for detailed carbon content values of different tree species.
In previous studies, the methods for simulating forest biomass or carbon patterns could be generalized as four forms:
(1) Vegetation dynamic models (e.g. CENTURY (Parton, 1987; Parton, 1993), FOREST- BGC (Running, 1994), CEVSA (Cao and Woodward, 1998), LPJ-DGVM (Sitch et al., 2003; Zhao et al., 2014), and AVIM2 (Huang, 2005; Huang et al., 2008). These models simulate photosynthesis, respiration and carbon accumulation of vegetation and cycles of water, heat and nitrogen, based on relationships between growth and climatic factors, soil properties, and so on. Dynamic vegetation carbon stock on large temporal and spatial scale could be monitored accurately by vegetation dynamic models.
(2) Geo-statistical methods (e.g. Kriging (Sales et al., 2007)), is based on the fact that the carbon density of adjacent patterns are correlative. These methods are appropriate to simulate forest carbon stock in the case of adequate even-distributed sampling. Sales et al. (2007) simulated forest carbon stock pattern in Brazilian Amazon region by Kriging with external drift, with accuracy improved.
(3) Satellite-data Based Approach (Piao et al., 2005; Tan et al., 2007), is a method for simulating patterns of forest vegetation carbon stock via empirical models derived from measured biomass carbon samples and satellite data. Foody et al. (2003) developed empirical models derived from vegetation indexes (from Landsat TM data) for tropic forest biomass estimation at sites in Brazil, Malaysia and Thailand, and declared that the relationship between predicted and measured biomass differed markedly among sites. Piao et al. (2005) developed a regression model derived from NDVI (from the NOAA/AVHRR land dataset) and National Forest Resource Inventory database, and simulated national forest biomass carbon patterns in China.
(4) HASM (Yue, 2011), a new method of surface modelling based on the fundamental theorem of surfaces, has been successfully applied to DEM construction (Yue et al., 2007, 2010; Chen and Yue, 2010; Chen et al., 2013a,b), filling voids in the Shuttle Radar Topography Mission (SRTM) dataset (Yue et al., 2012), simulation of mean annual temperature and precipitation (Yue et al., 2011, 2013a, b; Zhao and Yue, 2014a, b) and modelling soil properties (Shi et al., 2011), soil pollution (Shi et al., 2009) and drivers of soil change (Shi et al., 2012). Sun et al. (2013) and Zhao et al. (2014) applied HASM to forest biomass and carbon stock monitoring, with improved accuracy.
However, the difference apparently existed between results of different methods, even results of the same method in different studies. In this study, four methods, including AVIM2, SBA, Kriging and HASM, were used to simulate patterns of forest vegetation carbon stock of Jiangxi Province of China. The uncertainty and applicability of the four methods on a provincial scale were analyzed and discussed.

2 Data

2.1 Statistic data

The statistic data is from Jiangxi Province section of National Forest Resource Inventory (NFRI) database for China, collected from 2004 to 2008. Forest stands biomass was estimated by a volume-derived method. The area weighted mean forest stands biomass of each forest stand type was calculated by Eq. (1):
W = a•V + b(1)
where W is area weighted mean forest stands biomass (Mg/ha), V is area weighted mean forest volume (m3/ha), a (Mg/m3) and b (Mg/ha) are parameters related to biomass expression factor. Parameters a and b of all forest stand types are listed in Appendix 1 in Fang et al., 2007.
Biomass of economic forests, bamboo, woodlands and shrub forests were calculated by the mean biomass density method. The mean biomass density of economic forests was assumed to be 23.70 Mg/ha (Fang et al., 1996); the mean biomass density of woodlands and shrub forests was assumed to be 19.76 Mg/ha (Fang et al., 1996); the mean biomass of single bamboo was assumed to be 22.5 kg (Nie, 1994), and the number per hectare was assumed to be 1831 (Li X et al., 2011).
Biomass of trees on non-forest lands were calculated as volume multiplied the ratio of biomass and volume, and the ratio was calculated as total biomass divided to total volume of forest stands.
Carbon stock of all forest types were calculated by Eq. (2):
BCD = W·CC (2)
where BCD is forest biomass carbon density (Mg/ha); CC is carbon content. CC of all forest stand types are listed in Table 1, and CC of other forest types are assumed to be 0.5.
Table 1 C content of tree species (Li and Lei, 2010)
Tree species CC
Pinus massoniana 0.4596
Pinus densata 0.5009
Pinus elliottii 0.4596
Pinus taeda 0.4596
Cunninghamia lanceolata 0.5201
Coniferous mixed forest 0.5101
Broad-leaved and coniferous mixed forest 0.4978
Cinnamomum camphora 0.4916
Schima superba 0.4916
Liquidambar formosana 0.4916
Oaks 0.5004
Sassafras tzumu 0.4848
Eucalyptus robusta 0.5253
Populus 0.4956
Broad-leaved mixed forest 0.49
Finally, the total forest biomass carbon stock of Jiangxi was calculated by Eq. (3):
(3)
where CS is total forest vegetation carbon stock of Jiangxi (Tg); Ai (ha) and BCDi (Mg/ha) are area and biomass carbon density of the ith forest type, respectively; n is the number of forest type in Jiangxi.

2.2 Measured data

Measured dataset was collected from 2004 to 2008, for SBA, Kriging and HASM and vali-dation, including 1674 sample plots. The plots, whose area was 667 m2, were even-distributed across Jiangxi. The tree species was identified and the diameter at breast height (dbh, cm) was measured for every tree with a dbh > 5 cm, and tree height was measured for 3 to 5 average trees in each plot. Heights were estimated by height- iameter equations, for trees haven’t measured in height. Biomass of each tree in plots was calculated via tree biomass empirical models (Table 2). Carbon stock of each tree was calculated as biomass multiplied by carbon content (Table 1).The carbon stock of each plot was the sum of carbon stock of all trees in the plot.
Table 2 Biomass empirical models for each tree species (Li et al., 2010). WA, WR, WS, WBa, WBr and WL are biomass of aboveground, root, stem, bark, branch and leaf, respectively (kg); D (cm) and H (m) are diameter at breast height and tree height, respectively; a and b are parameters.

2.3 Forest type map

The forest type map (Figure 1) applied in this study was obtained from 2 datasets: 1) GlobCover global land cover map for the period from December 2004 to June 2006, at a spatial resolution of 300 m×300 m, includes 6 forest types and 4 mosaic types which might contain forest; 2) GLC2000 global land cover map for the period from November 1999 to December 2000, at a spatial resolution of 1 km×1 km, includes 9 forest types and 2 mosaic types which might contain forest (Table 3). Dataset 1 was used as primary data, while dataset 2 was used to extract forest patterns from mosaic in dataset 1.
Figure 1 Location and distribution of forest in Jiangxi Province
Table 3 The forest types contained by two land cover maps (of China)
GlobCover 2009 land cover map GLC2000
Class Class name Class Class name
20 Mosaic cropland (50%-70%) / vegetation (grassland/shrubland/forest) (20%-50%) 1 Tree cover: broad-leaved, evergreen
30 Mosaic vegetation (grassland/shrubland/forest) (50%-70%) / cropland (20%-50%) 2 Tree cover: broad-leaved, deciduous, closed
40 Closed to open (>15%) broad-leaved evergreen or semi-deciduous forest (>5 m) 3 Tree cover: broad-leaved, deciduous, open
50 Closed (>40%) broad-leaved deciduous forest (>5 m) 4 Tree cover: needle-leaved, evergreen
60 Open (15%-40%) broad-leaved deciduous forest/woodland (>5 m) 5 Tree cover: needle-leaved, deciduous
70 Closed (>40%) needle-leaved evergreen forest (>5 m) 6 Tree cover: mixed-leaved type
90 Open (15%-40%) needle-leaved deciduous or evergreen forest (>5 m) 7 Tree cover: regularly flooded, fresh water
100 Closed to open (>15%) mixed broad-leaved and
needle-leaved forest (>5 m)		 8 Tree cover: regularly flooded, saline water
110 Mosaic forest or shrubland (50%-70%) / grassland (20%-50%) 9 Mosaic: Tree cover / Other natural vegetation
120 Mosaic grassland (50%-70%) / forest or shrubland (20%-50%) 10 Tree cover: burnt

3 Methods

3.1 AVIM2

Atmosphere-vegetation interaction model 2 (AVIM2) contains 3 modules, including physical process module (PHY), physiological plant growth module (PLT) and soil carbon and nitrogen dynamics module (SOM). SOM can be coupled directly and timely with modules PHY, and PLT.
The climatic dataset used in the model was generated by HASM interpolation method (Yue et al., 2013a), based on the data collected at 49 climate stations located in Jiangxi with a 100-kilometer-buffer area, from 1951 to 2008. The forest type dataset used in the model was the forest type map obtained in 2.3 which contained 5 types: evergreen needle-leaved forest, deciduous needle-leaved forest, evergreen broad-leaved forest, deciduous broad-leaved forest and mixed-leaved forest. The soil texture dataset used in the model was Soil Texture Type Map of China, at a scale of 1:4,000,000. Vegetation respiration parameters and loss parameter for each vegetation type have been adjusted to forests of this province.

3.2 Kriging

Kriging (Krige, 1951) is a fundamental method in geostatistics, including Simple Kriging, Ordinary Kriging, Co-Kriging, Universal Kriging and Disjunctive Kriging (Kleijnen, 2009). Ordinary Kriging is the method used in this study, whose prediction equation expressed by Eq. (4):
(4)
where V0 is the value to be estimated; Vi is the value of the ith available sample; ωi is the weight to be estimated; n is the number of available samples; and =1.
The difference between true value and the estimated value (R0) could be calculated by Eq. (5):
(5)
where ci,j is the covariance of Vi and Vj; c0,0 is the variance of V0; ci,0 is the covariance of Vi and V0.
Introducing the Lagrange parameter, μ, into Eq. (5) and taking the first order derivative with respect to ω and μ, respectively, the constrained minimization problem can be expressed by Eq. (6):
(6)
The weight matrix ω could be obtained by solving Eq. (6), then V0 can be calculated by Eq. (4).
The available samples used in the method were the measured data described in 2.2.

3.3 Satellite-data Based Approach (SBA)

An empirical model was developed derived from vegetation indexes, spectral reflectance and topographical factors in this study. The satellite-data applied was from Landsat TM5 (bands 1 to 5 and 7), obtained from 2004 to 2008, at a spatial resolution of 30 m. The spectral reflectance was expressed by image intensity of each band which ranges from 0 to 255. The DEM data used was from ASTER GDEM dataset, at a spatial resolution of 30 m. Independent variables in the empirical model contains TM5 bands 1 to 5 and 7 (B1, B2, B3, B4, B5, B7), normalized differential vegetation index (NDVI), ratio vegetation index (RVI), altitude (unit: m), slope (unit: degree) and aspect (unit: degree). The value of NDVI was calculated as (B4 - B3) / (B4 + B3). The RVI was calculated as B4 / B3. The values of altitude, slope and aspect were generalized from DEM dataset by ArcGIS software. The empirical model can be expressed as Eq. (7),
BCD = -115.9485 - 6.6195 B1 + 8.8045 B2 - 5.8455 B3 + 1.646 B4 - 0.248 B5
-0.563 B7 + 84.849 NDVI + 81.5795 RVI - 0.033 Altitude + 0.007 Aspect
-0.4825 Alope, R2 = 0.309, P < 0.001 (7)

3.4 High Accuracy Surface Modeling (HASM)

HASM is a more complex approach than the previous ones. If the surface can be expressed as , then the first fundamental coefficients can be formulated as:
(8)
The second fundamental coefficients can be formulated as:
(9)
These two coefficient sets must satisfy the following Gauss equation set,
(10)
where
and are the second kind of Christoffel symbols.
If {(xi, yj)} is an orthogonal division of a computational domain and h the simulation step length, the central point of lattice (xi, yj) could be expressed as (0.5 h + (i-1) h, 0.5 h + (j-1) h), in which i = 0, 1, 2, …, I, I+1 and j = 0, 1, 2, …, J, J+1. If (n ≥ 0) represents the iterants of f(x, y) at (xi, yj) in the nth iterative step, in which { } are interpolations based on sampling values { }. In terms of numerical mathematics (Quarteroni et al., 2000), the iterative formulation of the HASM master equation set can be expressed as (Yue et al., 2013b; Zhao and Yue, 2014a),
(11)
(12)
(13)
where , and are the iterants of the first fundamental coefficients at the nth iterative step; , and represent the iterants of the second fundamental coefficients at the nth iterative step; , , and are the iterants of the Christoffel symbols of the second kind at the nth iterative step, which depend only upon the first fundamental coefficients and their derivatives.
The matrix formulation of HASM master equations can be respectively expressed as,
(14)
(15)
(16)
where A, B and C represent coefficient matrixes of the first equation, the second equation and the third equation; d(n), q(n) and p(n) are right-hand side vectors of the three equations respectively; is the value of the nth iteration of f(x, y) at grid cell (xi, yi); for , .
If is value of z = f(x, y) at the pth sampled point (xi, yi), There is only one non-zero element, 1, in every row of the coefficient matrix, S, making it a sparse matrix. The solution procedure of HASM, taking the sampled points as its constraints, can be transformed into solving the following linear equation set in terms of least squares principle
(17)
The parameter λ is the weight of the sampling points and determines the contribution of the sampling points to the simulated surface. λ can be a real number, which means all sampling points have the same weight, or a sector, which means each sampling point has its own weight. An area affected by a sampling point in a complex region is smaller than in a flat region. Therefore, a smaller value of λ is selected in a complex region and a bigger value of λ is selected in a flat region.
Let and, ,then HASM has the following formulation,
(18)
In terms of Gauss-Codazii equation set, iteration stopping criterion of HASM is formulated as,
(φ1y -ϕ2x -φ2 P - ϕ2Q)2+(φ2x -ϕ1y - φ1 Q - ϕ1P)2 +(Qx+Py +φ1φ2-ϕ1ϕ2)2<EI (19)
where, φ1= φ2= P= Q= ϕ1= ϕ2= EI is the iteration stopping criterion of HASM determined by an application requirement for accuracy.
The steps of HASM for forest carbon stock simulation are summarized as follows: (1) build forest carbon density surface as an initial surface for HASM iteration process, derived from satellite-data and measured data; (2) calculate the first fundamental coefficients and the second fundamental coefficients as well as the Christoffel symbols of the second kind; (3) solve HASM equations via an iteration process, and obtained an approximate distribution surface of forest carbon; (4) repeat the iteration process until simulation accuracy is satisfied.

3.5 Model evaluation

Cross-validation was applied for validation of Kriging, SBA and HASM in this study, which was comprised of four steps: (1) 5% of the sample points were removed for validation prior to model creation; (2) the patterns of forest carbon stock in Jiangxi were simulated at a spatial resolution of 300 m×300 m using the remaining 95% of the sample points; (3) mean absolute error (MAE) and mean relative error (MRE) were calculated using the 5% validation dataset; and (4) the 5% validation dataset was returned to the pool of the available station for the next iteration, and another 5% validation dataset was removed. This process was repeated until all of the sample points were used for validation at least one time. Cross-validation was not essential for validation of AVIM2, because no sample point was required in simulation process of AVIM2. MAE and MRE of AVIM2 were calculated using all sample points. The simulation error statistics for each sample point can be calculated by Eqs. (20)-(21):
(20)
(21)
where n is the number of validation samples, oi and si are measured value and simulated value of the ith validation sample.

4 Result

4.1 Validation

Comparison of measured and simulated forest carbon densities was displayed in Figure 2. The range of forest carbon densities simulated by AVIM2 (0.54-8.64 kg/m2) was seriously different from measured data (0.03-243.25 kg/m2). It was mainly caused by the fact that forests were assumed as mature forest in physiological plant growth module (PLT) and the difference caused by age was overlooked. Forest carbon density simulated by SBA was accordant to measured data when it was less than 150 kg/m2, however, it was underestimated when greater than 150 kg/m2. A good coincidence was found between measured data and results of Kriging and HASM.
Figure 2 Comparison between observed and simulated results of forest vegetation C density (a. AVIM2; b. SBA; c. Kriging; d. HASM)
The results of cross-validation were display in Table 4. The MAE and MRE of AVIM2 method were 2.63 kg/m2 and 79.79%, respectively. The MAE and MRE of SBA method were 1.90 kg/m2 and 57.71%, respectively. The MAE and MRE of Kriging method were 2.06 kg/m2 and 62.50%, respectively. The MAE and MRE of HASM method were 0.96 kg/m2 and 29.13%, respectively.
Table 4 The accuracy of the four methods for forest vegetation C stock pattern simulation of Jiangxi Province in China
Methods MAE (kg/m-2) MRE (%)
AVIM2 2.63 79.79
Kriging 2.06 62.5
SBA 1.9 57.71
HASM 0.96 29.13
The accuracy of AVIM2 was lower than SBA, Kriging and HASM. The simulated distribution by AVIM2 was consistent with potential distribution of forest carbon stock, taking into account that the simulation process strongly related to climate and soil properties. In other words, the result simulated on large scale would be more accurate than that on provincial scale. The accuracies of SBA and Kriging approximated to each other, being about 60% of the MRE. HASM had the highest accuracy. Comparing with AVIM2, Kriging and SBA, the accuracy of HASM had improved by 50.66%, 33.37% and 28.58%, respectively.
The carbon stocks and carbon density of Jiangxi calculated by the four simulation methods were compared with the result calculated by volume-derived method (Table 5). The results of simulation methods, except for AVIM2, were close to the results of volume-derived method. Particularly, the bias of SBA and HASM were less than 10%.
Table 5 Comparison of forest vegetation C stocks of Jiangxi Province estimated by different methods (Tg =1012 g). Forest vegetation C stocks include C stocks of forest stands, economic forests, woodlands, shrub forests, bamboos and trees in non-forest. C stocks of forest stands include C stocks of needle-leaved forests, broad-leaved forests and mixed-leaved forests.
Methods Components Area
(109 m2)		 Carbon density
(kg/m2)		 Carbon stock
(Tg)		 Periods References
Volume-derived Forest stands 78.93 2.72 214.70 2001-2005 Li X et al., 2011
Volume-derived Forest 100.33 2.63 263.87 2001-2005 Li X et al., 2011
Volume-derived Forest stands 3.00 2004-2008 Li H K et al., 2011
Volume-derived Forest 289.07 2004-2008 Li H K et al., 2011
Volume-derived Forest 99.80 2.67 297.97 2004-2008 This study
Volume-derived Forest stands 76.81 3.02 231.97 2004-2008 This study
Volume-derived Needle-leaved forests 47.05 2.60 122.33 2004-2008 This study
Volume-derived Broad-leaved forests 21.83 3.84 83.82 2004-2008 This study
Volume-derived Mixed-leaved forests 7.94 3.25 25.82 2004-2008 This study
Volume-derived Economic forests 12.03 1.19 14.26 2004-2008 This study
Volume-derived Bamboos 8.52 2.06 17.54 2004-2008 This study
Volume-derived Woodlands 0.45 0.99 0.44 2004-2008 This study
Volume-derived Shrub forests 1.99 0.99 1.96 2004-2008 This study
Volume-derived Trees in non-forest 31.80 2004-2008 This study
Volume-derived Forest stands 72.78 2.86 208.15 1999-2003 This study
AVIM2 Forest 94.32 3.71 349.93 2004-2008 This study
Kriging Forest 94.32 3.04 286.73 2004-2008 This study
SBA Forest 94.32 3.25 306.54 2004-2008 This study
HASM Forest 94.32 3.06 288.62 2004-2008 This study
HASM Forest 94.32 2.88 271.64 1999-2003 This study

4.2 Total forest carbon stock of Jiangxi

In previous studies, the definitions of forest vegetation carbon stock were inconsistent. In some studies, e.g. Fang et al. (2001), forest vegetation carbon stock was regarded as the carbon stock of forest stands; while in other studies, e.g. Zhang et al. (2013), it was treated as a sum of carbon stocks of forest stands, economic forests, bamboo, special shrubbery, woodlands and trees on non-forest lands. In this study, to avoid confusion, the first definition was considered as forest stand vegetation carbon stock (SCS), and the second definition was considered as forest vegetation carbon stock (CS), which contains SCS. Accordingly, the area weighted mean carbon stocks of forest and forest stand were forest vegetation carbon density (CD) and forest stand vegetation carbon density (SCD), respectively.
According to the results of volume-derived method, CS, CD and forest area of Jiangxi were 297.97 Tg, 2.67 kg/m2 and 99.80 ×109 m2, respectively; SCS, SCD and forest stand area of Jiangxi were 231.97 Tg, 3.02 kg/m2 and 76.81×109 m2, respectively. C stocks of needle-leaved forests, broad-leaved forests and mixed-leaved forests were 122.33, 83.82 and 25.82 Tg, respectively. C density of these three forest types were 2.60, 3.84 and 3.25 kg/m2, respectively. Needle-leaved forest was the largest C pool, and broad-leaved forest had the highest C density in forest ecosystem in Jiangxi. C stock of economic forests, bamboos, woodlands, shrub forests and trees in non-forest were 14.26, 17.54, 0.44, 1.96 and 31.80 Tg, respectively.
Distribution of forest vegetation carbon stocks simulated by HASM was showed in Figure 3. Forest carbon stocks were equably distributed in hilly and mountainous areas in eastern, western and southern parts of Jiangxi, while forest carbon density was low in basin areas, such as Ganzhou Basin and Yudu Basin.
Figure 3 Forest vegetation C stock patterns simulated by HASM

5 Discussion

5.1 Comparison with other studies

SCD of Jiangxi Province in period from 2001 to 2005 was 2.72 kg/m2, calculated by volume-derived method in Li X et al. (2011), which was lower than that both in period from 2004 to 2008 and in period from 1999 to 2003, calculated by the same method in this study. The difference was mainly due to inconsistency of the datasets used in two studies. The forest inventory data used in Li X et al. (2011) was from Provincial Forest Resource Inventory (PFRI), while that was from National Forest Resource Inventory (NFRI) in our study. For the different criterions, some woodlands, economic forests and trees in non-forest lands might be summed into forest stand in PFRI, causing that the area of forest stand of Jiangxi in PFRI (78.93×109 m2 in 2001 to 2005) was larger than that in NFRI (76.81×109 m2 in 2004 to 2008 and 72.78×109 m2 in 1999 to 2003). On the account of lower carbon densities of woodlands, economic forests and trees in non-forest lands, SCD was underestimated in Li X et al. (2011). CD of the period from 2004 to 2008 calculated in our study (3.02 kg/m2) was close to that in Li H K et al. (2011) (3.00 kg/m2), because of the same method and same data applied in both studies.
In previous studies (Huang, 2005; Ji et al., 2008), AVIMs were applied in simulation of NPP, NEP and biomass carbon stock on global and national scale. In Huang (2005), the simulated biomass of each forest type of China (including deciduous needle-leaved forests, evergreen needle-leaved forests, deciduous broad-leaved forests, evergreen broad-leaved forests and mixed-leaved forests) was consistent with CEVSA (Li et al., 2003) and Fang et al. (1996). However, it was insufficient in forest carbon stock pattern simulation on provincial scale in this study, which might be caused by the fact that the real distribution of forest carbon stock in Jiangxi deviated from the potential distribution, which the result of AVIM2 was consistent with. Forest distribution and forest carbon stock patterns obviously changed in some regions or provinces of China in the past 65 years. During 1949 to the late 1970s, forest was felled for reestablishment, which caused that the percentage of forest cover of Jiangxi decreased from 40.36% to 32.80%. Since the late 1970s, forest conservation and restoration projects were beginning to implement, as a result, the percentage of forest cover of Jiangxi increased to 58.32% in the early 21st century. However, afforestation and introduction of exotic tree species disturbed the ecological succession, making the potential relationship between distribution of forest carbon stock and ecological factors indistinct. The dominant factors on forest growth changed from ecological factors (e.g. temperature, precipitation, soil properties) to management tactics (e.g. felling, forestation, introduction of exotic tree species) in Jiangxi.
Simulated CD by SBA (3.25 kg/m-2) was overestimated in our study. The critical source of bias might be the empirical model which had a low accuracy (R2=0.309). In Piao et al. (2005), the R2 of empirical model was 0.64, and the simulated CD of China was very close to estimates in Fang et al. (2001) which was calculated by volume-derived method. The difference of Piao et al. (2005) and our study was mainly due to the difference of datasets. In our study, satellite data was from TM dataset, at a spatial resolution of 30 m × 30 m, and the measured data was from sampling plots; while in Piao et al. (2005), satellite data was from the NOAA/AVHRR Land dataset, at a spatial resolution of 8 km × 8 km, and the measured data was from statistic data. The low resolution of satellite data and statistic data eliminate some variance. In Foody (2003), empirical models were built for tropical forest carbon stocks simulation of Thailand, Brazil and Malaysia, based on TM data and measured samples. The values of R2 of empirical models were 0.300, 0.318 and 0.251 for Thailand, Brazil and Malaysia, respectively. The accuracies of Foody (2003) were close to our study, due to the similar dataset and same method.

5.2 Uncertainties in simulations of forest carbon stock patterns

5.2.1 Mechanism of SBA, Kriging and HASM
SBA is based on the relationship between biomass C density and factors, while Kriging is based on spatial autocorrelation of samples. Regarding longitude, latitude and C density as x, y and z axes, C stock patterns could be regarded as a surface in three-dimensional space. The relationship between biomass C density and factors and the spatial autocorrelation of samples might be the external and internal characteristic of the surface, respectively.
Table 6 showed that C density was significant related to satellite data and geographic factors, which approved that SBA was a competent method for simulation of forest vegetation carbon stock patterns in macroscopic way. Predicted semi-variance (Eq. 22) indicated that spatial autocorrelation of samples was conspicuous, which approved that Kriging could be an appropriate method for simulation of forest vegetation carbon stock patterns in microscopic way. HASM considered both external characteristic (derived from satellite data and geographic factors) and internal characteristic (derived from samples) of the surface, and improved accuracy of simulation by fusing macroscopic and microscopic information.
Table 6 Correlation coefficient (R) between biomass C density and factors. ** means the factor was significantly correlated to biomass C density, P < 0.01.
Factors B1 B2 B3 B4 B5 B7 NDVI RVI Altitude Aspect Slope
R -0.210** -0.266** -0.254** 0.242** -0.175** -0.213** 0.219** 0.229** -0.349** 0.004 -0.331**
R2=0.399 (22)
Even the accuracy of HASM had improved due to fusion of satellite data and sampling data, the models and the mechanism of HASM for simulation of forest carbon stock patterns should be further improved.
5.2.2 Uncertainties in estimates of volume-derived method
The estimates of volume-derived method were regarded as true values for simulations of forest carbon stock patterns. However, uncertainties confirmedly existed in field biomass data, empirical biomass-volume equations and assumed carbon contents (Zhang et al., 2013), which might induce errors in simulations. Even we collected carbon content of each species for carbon calculation, the main errors would still descend to simulations.
5.2.3 Effect of forest area on estimated CS
The difference in calculated forest area was a significant cause of uncertainty of CS (or SCS) calculation. Comparing with Li X et al. (2011), forest stand area in period from 2004 to 2008 calculated in our study was underestimated. As a result, the SCS calculated in our study was lower than that in Li X et al. (2011), although the SCD was higher.
On the other hand, the confusion of area was a critical cause of the difference between the results of simulation methods and estimates of volume-derived method. Generally, the area in forest carbon stock patterns simulation contained the area of forest stand, bamboo, economic forests and some woodlands, while the measured sampling plots were only located at forest stands. In other words, bamboo, economic forests and some woodlands which have lower carbon density were regarded as forest stand in the process of simulation. Due to this reason, the simulated CD by HASM (3.06 kg/m-2) was overestimated, while it was close to SCD calculated by volume-derived method (3.02 kg/m-2).

6 Conclusions

This study simulated forest vegetation carbon stock patterns of Jiangxi Province using four simulation methods, including AVIM2, Kriging, SBA and HASM. The results were validated through cross-validation, and were compared with the estimates of volume-derived method. The main conclusions can be drawn as follows:
(1) HASM was the method which had the highest accuracy for forest vegetation carbon stock patterns simulation, followed by SBA, Kriging and AVIM2. AVIM2 is an appropriate method for simulating forest carbon stock distribution on large scale, yet not applicable for that on provincial scale. HASM improved accuracy by fusing macroscopic information from satellite data and microscopic information from measured data.
(2) CS, CD and forest area of Jiangxi calculated by volume-derived method were 267.31 Tg, 2.76 kg/m-2 and 97.36×109 m2, respectively. They were 288.62 Tg, 3.06 kg/m-2 and 94.32×109 m2 by HASM, respectively. Compared with volume-derived method, the CS and CD were overestimated by HASM, due to confusing economic forests and bamboos with forest stands.
(3) Simulation errors of methods or models were the main source of uncertainty of forest carbon stock patterns simulation. In addition, two more causes induced the uncertainty: a) errors in estimates of volume-derived method which were regarded as true values in simulations descend to simulations; b) forest type maps were different in each study, causing inconsistence of forest area. And forest was confused with forest stands in some studies, causing inconsistence of forest carbon density.

The authors have declared that no competing interests exist.

References

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Chen Chuanfa, Yue Tianxiang, Dai Hongleiet al., 2013b. The smoothness of HASM.International Journal of Geographical Information Science, 27: 1651-1667.To smooth noises inherent in uniformly sampled dataset, the smoothness of high accuracy surface modeling (HASM) was explored, and a smoothing method of HASM (HASM-SM) was developed based on a penalized least squares method. The optimal smoothing parameter of HASM-SM was automatically obtained by means of the generalized cross-validation (GCV) method. For an efficient smoothing computation, discrete cosine transform was employed to solve the system of HASM-SM and to estimate the minimum GCV score, simultaneously. Two examples including a numerical test and a real-world example were employed to compare the smoothing ability of HASM-SM with that of GCV thin plate smoothing spline (TPS) and kriging. The numerical test indicated that the minimum GCV HASM-SM is averagely more accurate than TPS and kriging for noisy surface smoothing. The real-world example of smoothing a lidar-derived Digital Elevation Model (DEM) showed that HASM-SM has an obvious smoothing effect, which is on a par with TPS. In conclusion, HASM-SM provides an efficient tool for filtering noises in grid-based surfaces like remote sensing鈥揹erived images and DEMs.

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Fang Jingyun, Chen Anping, Peng Changhuiet al., 2001. Changes in forest biomass carbon storage in China between 1949 and 1998.Science, 292(5525): 2320-2322.The location and mechanisms responsible for the carbon sink in northern mid-latitude are uncertain. Here, we used an improved estimation method of forest biomass and a 50-year national forest resource inventory in China to estimate changes in the storage of living biomass between 1949 and 1998. Our results suggest that Chinese forests released about 0.68 petagram of carbon between 1949 and 1980, for an annual emission rate of 0.022 petagram of carbon. Carbon storage increased significantly after the late 1970s from 4.38 to 4.75 petagram of carbon by 1998, for a mean accumulation rate of 0.021 petagram of carbon per year, mainly due to forest expansion and regrowth. Since the mid-1970s, planted forests (afforestation and reforestation) have sequestered 0.45 petagram of carbon, and their average carbon density increased from 15.3 to 31.1 megagrams per hectare, while natural forests have lost an additional 0.14 petagram of carbon, suggesting that carbon sequestration through forest management practices addressed in the Kyoto Protocol could help offset industrial carbon dioxide emissions.

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Fang Jingyun, Guo Zhaodi, Piao Shilonget al., 2007. Terrestrial vegetation carbon sinks in China, 1981-2000.Science in China Series D-Earth Sciences, 50(9): 1341-1350.Using China’s ground observations, e.g., forest inventory, grassland resource, agricultural statistics, climate, and satellite data, we estimate terrestrial vegetation carbon sinks for China’s major biomes between 1981 and 2000. The main results are in the following: (1) Forest area and forest biomass carbon (C) stock increased from 116.5×10ha and 4.3 Pg C (1 Pg C = 10g C) in the early 1980s to 142.8×10ha and 5.9 Pg C in the early 2000s, respectively. Forest biomass carbon density increased form 36.9 Mg C/ha (1 Mg C = 10g C) to 41.0 Mg C/ha, with an annual carbon sequestration rate of 0.075 Pg C/a. Grassland, shrub, and crop biomass sequestrate carbon at annual rates of 0.007 Pg C/a, 0.014–0.024 Pg C/a, and 0.0125–0.0143 Pg C/a, respectively. (2) The total terrestrial vegetation C sink in China is in a range of 0.096–0.106 Pg C/a between 1981 and 2000, accounting for 14.6%–16.1% of carbon dioxide (CO) emitted by China’s industry in the same period. In addition, soil carbon sink is estimated at 0.04–0.07 Pg C/a. Accordingly, carbon sequestration by China’s terrestrial ecosystems (vegetation and soil) offsets 20.8%–26.8% of its industrial COemission for the study period. (3) Considerable uncertainties exist in the present study, especially in the estimation of soil carbon sinks, and need further intensive investigation in the future.

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Fang Jingyun, Liu Guohua, Xu Songling, 1996, Biomass and net production of forest vegetation in China.Acta Ecologica Sinica, 16(5): 497-508. (in Chinese)Method for estimating biomass and net production of forest vegetation from stem volume of stand was proposed in this paper, and biological production all over China was estimated by using this methed. As a result, average biomass was smaller, and mean net preduction was higher in China than mean values of the world. Total biomass in Chinese forest vegetation was 9102. 9 × 106 t, of which 8592. 1 × 106 t for stands, 325. 7 × 106 t for economic forest, 185. 0 × 106 t for bamboo forests and 790. 5 × 10' t for scrub forest. The total net production was 1177. 3 × 106 t· a-1 for forest vegetation and 458. 2 × 106 t. a-1 for forests and scrub forests. Volume-derived biomass was smaller than that estimated by mean biomass method.Analyzing the contribution of Chinese forest carbon pool to the global terrestrial carbon pools,it was found that biomass of Chinese forest was small, with below 1% of the global forest biomass.

11
Fang Jingyun, Wang G Geoff, Liu Guohuaet al., 1998. Forest biomass of China: An estimate based on the biomass-volume relationship.Ecological Applications, 8(4): 1084-1091.In this study, a method was developed to estimate the forest biomass of China based on the relationship between stand biomass and volume. Biomass-volume relationships were quantified for all the main forest types in China using 758 sets of data obtained from direct field measurements. These relationships were used to convert volume measurements into total biomass values (above- and belowground dry masses) based on 1984-1988 forest inventory data for China. The latter had been compiled from more than 250000 permanent and temporary field plots across the country. This data contained information on forest area and timber volume for each ape class and site class for all forest types at the provincial level. As a result, the total forest biomass of China was estimated as 9103 Tg (1 Tg 10(12) g), with 8592, 326, and 185 Tg from forests, special product plantations, and bamboo Forests, respectively. The area-weighted mean biomass density was 84 Mg/ha (1 Mg = 10(6) g). For comparison, two additional estimates, one based on the mean biomass density method and another based on the mean ratio of biomass to stem volume, were also derived. Compared to the biomass-volume relationship method, the mean biomass density method considerably overestimated the forest biomass of China (by 59.6%), while the mean ratio of biomass to stem volume method slightly underestimated it (by 12.1%). Despite the small forest biomass value due to a low forest cover, the area-weighted mean biomass density was comparable to those of other regions in the middle and high latitudes except in the United States. We believe that our study provided not only an appropriate estimate of forest biomass for China, but also an improved methodology for estimating forest biomass at the regional, national, and global level.

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Ji Jinjun, Huang Mei, Li Kerang, 2008. Prediction of carbon exchanges between China terrestrial ecosystem and atmosphere in 21st century.Science in China, Series D-Earth Sciences, 51(6): 885-898.The projected changes in carbon exchange between China terrestrial ecosystem and the atmosphere and vegetation and soil carbon storage during the 21st century were investigated using an atmosphere-vegetation interaction model (AVIM2). The results show that in the coming 100 a, for SRES B2 scenario and constant atmospheric CO(2) concentration, the net primary productivity (NPP) of terrestrial ecosystem in China will be decreased slowly, and vegetation and soil carbon storage as well as net ecosystem productivity (NEP) will also be decreased. The carbon sink for China terrestrial ecosystem in the beginning of the 20th century will become totally a carbon source by the year of 2020, while for B2 scenario and changing atmospheric CO(2) concentration, NPP for China will increase continuously from 2.94 GtC center dot a(-1) by the end of the 20th century to 3.99 GtC center dot a(-1) by the end of the 21st century, and vegetation and soil carbon storage will increase to 110.3 GtC. NEP in China will keep rising during the first and middle periods of the 21st century, and reach the peak around 2050s, then will decrease gradually and approach to zero by the end of the 21st century.

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Li Haikui, Lei Yuancai, Zeng Weisheng, 2011. Forest carbon storage in China estimated using forestry inventory data.Scientia Silvae Sinicae, 47(7): 7-12. (in Chinese)<p>In this study, we used biomass regression model to estimate biomass of arbor forest, took carbon-included rate in different tree species as the transferring coefficient from biomass to carbon stock, and further summed a single tree to plot and weighted means to province level. The carbon storage of arbor forests in China were estimated based on original data of 7th national forest continuous inventory. In the same time, carbon storage of open forests, scatted trees and &quot;four-sides&quot; trees were estimated by weighted mean conversion factors, and carbon storage of bamboo and shrubbery were estimated by regression model. The results showed that most of the forest carbon storage was distributed in the southwestern and northeastern China. Arbor forests were a main body of forest carbon storage in China. Carbon storage of plantations was more than 15% of total arbor forests in China, and carbon storage and density of broad leaf trees were higher than that of conifer trees.</p>

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Li Kerang, Wang Shaoqiang, Cao Mingkui, 2003. Vegetation and soil carbon stock of China.Science in China, Series D-Earth Sciences, 33(1): 72-80. (in Chinese)

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Li Xin, Ouyang Xunzhi, Liu Qijing, 2011. Carbon storage of forest vegetation and its geographical pattern in China’s Jiangxi Province during 2001-2005.Journal of Natural Resources, 26(4): 655-665. (in Chinese)Based on the second-class forest inventory data of Jiangxi Province during the Tenth Five-year Plan period (2001-2005), the carbon storage of forest ecosystems was estimated by regression equations between biomass and timber volume for dominant tree species, and its spatial pattern was analyzed. The total carbon storage of forest vegetation (including understory) was 263.87 Tg C (0.26387 billion tons), including 214.70 Tg C of forest stands (tree layer only). Among the 11 prefectures or cities,Ganzhou City possessed the largest amount of 70.11 Tg C, followed by Ji&rsquo;an, Shangrao and Yichun counties in sequence. The average carbon densities of forest vegetation and forest stands were 26.27 t/hm<sup>2</sup> and 27.20 t/hm<sup>2</sup> respectively. The densities varied among districts, with the highest in Jingdezhen city, 31.65 t/hm<sup>2</sup> followed by Yichun, Ji&rsquo;an and Yingtan, in sequence. Among the forest categories, <em>Cunninghamia lanceolata</em> plantation had the largest storage of 73.77 Tg C or 34.36% of the total carbon storage. The carbon density of broad-leaved forest was 42.64 t/hm<sup>2</sup>1.5 times of the average value of the whole province. Increasing with developing stage, the carbon storage of young and middle age forest stands accounted for 81.95% of the total storage in the province.

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Nie Daoping, 1994. Structural dynamics of bamboo forest stands.Scientia Silvae Sinicae, 30(3): 201-208. (in Chinese)During 1985-1990 a continuous investigation was carried out in the bamboo (<I>Phyllostachys pubescens</I>) forests at the Dagangshan Experimental Centre, CAF, located in Jiangxi Province,to monitor the structural dynamics of stands. The research results showed that the correlations between DBH(<I>D</I>)and the culm length(<I>H</I>), clear length(<I>HL</I>), crown length(<I>L</I>) and total weight (<I>W</I>) could be expressed in power function,<I>D<SUP>b</SUP> = H (H<SUB>L</SUB>L,W)</I>where the parameter, <I>a</I> varies with stem stocking (<I>N</I>)<SUP>a</SUP> of bamboo stands. As the stem stocking rises, the stand productivity will go up, thus the age class distribution within the stand will tend to even out. The differentiation of diameter class generally followed weibull distribution in the stands, however, it would become a normal distribution in some stands with higher productivity.

22
Pan Yude, Birdsey Richard A, Fang Jingyunet al., 2011. A large and persistent carbon sink in the world’s forests.Science, 333(6045): 988-993.The terrestrial carbon sink has been large in recent decades, but its size and location remain uncertain. Using forest inventory data and long-term ecosystem carbon studies, we estimate a total forest sink of 2.4 ± 0.4 petagrams of carbon per year (Pg C year(-1)) globally for 1990 to 2007. We also estimate a source of 1.3 ± 0.7 Pg C year(-1) from tropical land-use change, consisting of a gross tropical deforestation emission of 2.9 ± 0.5 Pg C year(-1) partially compensated by a carbon sink in tropical forest regrowth of 1.6 ± 0.5 Pg C year(-1). Together, the fluxes comprise a net global forest sink of 1.1 ± 0.8 Pg C year(-1), with tropical estimates having the largest uncertainties. Our total forest sink estimate is equivalent in magnitude to the terrestrial sink deduced from fossil fuel emissions and land-use change sources minus ocean and atmospheric sinks.

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Pan Yude, Luo Tianxiang, Birdsey Richard Aet al., 2004. New estimates of carbon storage and sequestration in China’s forests: Effects of age-class and method on inventory-based carbon estimation.Climatic Change, 67(2/3): 211-236.

24
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25
Parton W J, Scurlock J M O, Ojima D Set al., 1993. Observations and modeling of biomass and soil organic-matter dynamics for the grassland biome worldwide.Global Biogeochemical Cycles, 7(4): 785-809.The Century model for plant-soil ecosystems, developed under a Scientific Committee on Problems of the Environment (SCOPE) project, has been modified by a grasslands modelling group so it can be applied to a wide range of tempeate and tropical grasslands worldwide. This study was developed to meet the overall aims of the SCOPE project to review and identify models with wide application and predictive ability, in order to link plant ans soil responses to the large scale modelling of global change. The Century model is reviewed and compared with other models. The model simulated differences between wet and dry years well, but was unable to simulate more subtle differences between years with similar precipitation. The model substantially underestimated live biomass for unusually high production years. 44 refs., 15 figs., 2 tabs.

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Piao Shilong, Fang Jingyun, Zhu Biaoet al., 2005. Forest biomass carbon stocks in China over the past 2 decades: Estimation based on integrated inventory and satellite data.Journal of Geophysical Research-Biogeosciences, 110(G1): 12.Forests are major contributor of terrestrial ecosystem carbon (C) pools, and are thus crucial components for assessing the global C budget. On the basis of forest inventory data for three inventory periods of 1984-1988, 1989-1993, and 1994-1998, and synchronous NDVI (Normalized Difference Vegetation Index) data, we developed a satellite-based approach for estimating China's forest total biomass C stocks. Using this approach, we analyzed the changes in forest C stocks over the last 2 decades to identify the size and distribution of C sinks/sources in the forests. The total forest biomass of China averaged 5.79 Pg C (1 Pg = 10g) during the study period, with an average biomass density of 45.31 Mg C/ha (1 Mg = 10g). The forest biomass C density showed a large spatial heterogeneity: high in southwestern and northeastern areas, and low in the eastern coastal regions. Over the past 2 decades, the total forest biomass C stock increased from 5.62 Pg C in the early 1980s (average for 1981-1983) to 5.99 Pg C by the end of the 1990s (average for 1997-1999), giving a total increase of 0.37 Pg C and an annual sequestration rate of 0.019 Pg C/yr. The C sink appeared mainly in regions with lower C density. Both environmental changes and human activities are likely major drivers of such spatiotemporal patterns.

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Ren Yin, Wei Xiaohua, Zhang Liet al., 2011. Potential for forest vegetation carbon storage in Fujian Province, China, determined from forest inventories.Plant and Soil, 345(1/2): 125-140.Carbon storage in forest vegetation of Fujian Province plays a significant role in the terrestrial carbon budget in China. The purposes of this study are: (1) to evaluate how the afforestation and reforestation programs established in Fujian Province influence carbon storage in forest ecosystems; (2) to assess the influence of tree species, forest age and ownership changes on vegetation carbon storage; and (3) to explore strategies for increasing vegetation carbon potentials. Data from seven Chinese Forest Resource Inventories and 5,059 separate sample plots collected between 1978 and 2008 were used to estimate vegetation carbon storage in the whole province. In addition, uncertainty analysis was conducted to provide the range of our estimations. Total forest vegetation carbon storage increased from 136.51 in 1978 to 229.31 Tg C in 2008, and the forest area increased from 855.27 10

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Running Steven W, 1994. Testing forest: BGC ecosystem process simulations across a climatic gradient in Oregon.Ecological Applications, 4(2): 238-247.Field measurements from the Oregon Transect Ecological Research project (OTTER) were used to validate selected process simulations in the FOREST-BGC ecosystem model. Certain hydrologic, carbon, and nitrogen cycle process simulations were tested in this validation, either comparatively across sites, or seasonally at single sites. The range of simulated ecosystem-process rates across the OTTER sites was large; annual evapotranspiration (ET) ranged from 15 to 82 cm, net photosynthesis (as carbon) from 2.2 to 22.8 Mg/ha, and decomposition (as carbon) from 1.0 to 7.2 Mg.ha-1.yr-1. High correlations between predicted and measured data were found for: aboveground net primary production, R2 = 0.82; 100-yr stem biomass, R2 = 0.79; and average leaf nitrogen concentration, R2 = 0.88. However, correlations for pre-dawn leaf water potential and equilibrium leaf area index (LAI) were much lower, because successful simulation of these variables requires accurate data for soil water-holding capacity. Defining the water-holding capacity of the rooting zone and the maximum surface conductance for photosynthesis and transpiration rates proved to be critical system variables that defied routine field measurement. Although many other processes are simulated in FOREST-BGC, no other processes had repeated field data sets for validations. Problems in parameterizing the model from disparate data sets are also evaluated, with suggestions for using ecosystem modeling in future integrated research programs.

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Sales Marcio H, Souza Carlos M, Kyriakidis Phaedon Cet al., 2007. Improving spatial distribution estimation of forest biomass with geostatistics: A case study for Rondonia, Brazil.Ecological Modelling, 205(1/2): 221-230.Mapping aboveground forest biomass is of fundamental importance for estimating CO 2 emissions due to land use and land cover changes in the Brazilian Amazon. However, existing biomass maps for this region diverge in terms of the total biomass estimates derived, as well as in the spatial patterns of mapped biomass. In addition, no regional or location-specific measure of reliability accompanies most of these maps. In this study, 330 one-hectare plots from the RADAMBRASIL survey, acquired over and along areas adjacent to the state of Rond00nia, were used to generate a biomass map over the entire region using geostatistics. The RADAMBRASIL samples were used to generate a biomass map, along with a measure of reliability for each biomass estimate at each location, using kriging with external drift with elevation, vegetation type and soil texture considered as biomass predictor variables. Cross-validation was performed using the sample plots to compare the performance of kriging against a simple biomass estimation using the sample mean. Overall, biomass varied from 225 to 48602Mg02ha 611 , with a local standard deviation ranging from 62 to 20202Mg02ha 611 . Large uncertainty values were obtained for regions with low sampling density, in particular in savanna areas. The geostatistical method adopted in this paper has the potential to be applied over the entire Brazilian Amazon region to provide more accurate local estimates of biomass, which would aid carbon flux estimation, along with measures of their reliability, and to identify areas where more sampling efforts should be concentrated.

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Shi Wenjiao, Liu Jiyuan, Du Zhengpinget al., 2009. Surface modelling of soil pH.Geoderma, 150(1/2): 113-119.In addition to classical methods, namely kriging, Inverse Distance Weighting (IDW) and splines, which have been frequently used for interpolating the spatial patterns of soil properties, a relatively more accurate surface modelling technique is being developed in recent years, namely high accuracy surface modelling (HASM). It has been used in the numerical tests, DEM construction and the interpolation of climate and ecosystem changes. In this paper, HASM was applied to interpolate soil pH for assessing its feasibility of soil property interpolation in a red soil region of Jiangxi Province, China. Soil pH was measured on 150 samples of topsoil (0-20&nbsp;cm) for the interpolation and comparing the performance of HASM, kriging, IDW and splines. The mean errors (MEs) of interpolations indicate little bias of interpolation for soil pH by the four techniques. HASM has less mean absolute error (MAE) and root mean square error (RMSE) than kriging, IDW and splines. HASM is still the most accurate one when we use the mean rank and the standard deviation of the ranks to avoid the outlier effects in assessing the prediction performance of the four methods. Therefore, HASM can be considered as an alternative and accurate method for interpolating soil properties. Further researches of HASM are needed to combine HASM with ancillary variables to improve the interpolation performance and develop a user-friendly algorithm that can be implemented in a GIS package. &copy; 2009 Elsevier B.V. All rights reserved.

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Shi Wenjiao, Liu Jiyuan, Du Zhengpinget al., 2011. Surface modeling of soil properties based on land use information.Geoderma, 162: 347-357.High accuracy surface modelling (HASM) is a spatial interpolation technique based on the fundamental theorem of surfaces. This study proposed a modified HASM method based on the incorporation of ancillary land use information (HASM_LU) for improved interpolation of soil properties. To assess its feasibility, a total of 150 samples were collected in different land use types (woodlands, croplands and grasslands) of a typical red soil region in the middle part of Jiangxi Province, China. Observations on soil pH, alkali-hydrolyzable N (AN), total C, N, K, Al, Ca, Mg and Zn were interpolated. To evaluate the performance of HASM_LU, it was compared with four other interpolators: HASM, ordinary kriging with land use information (OK_LU), stratified kriging (SK) and regression-kriging using a generalized linear model (RK_GLM). To do so, predicted and measured values were compared using the mean error (ME), mean absolute error (MAE), root mean square error (RMSE) and prediction efficiency (PE). The results have shown that HASM_LU generally performs better than HASM, OK_LU, SK and RK_GLM with a lower estimation bias, MAE and RMSE as well as greater PE. In particular, the RMSE of HASM_LU for AN was smaller than that of HASM by 33.4%; that of OK_LU, 1.6%; that of SK, 41.5%; and that of RK_GLM, 67.6%. The largest difference in PE occurred when comparing HASM_LU with HASM for N (57.95%), with OK_LU (7.18%) for K, with SK (125.16%) for Zn and with RK_GLM (100.21%) for AN. The HASM_LU maps of soil properties present more details and more accurate spatial patterns. The good performance of HASM_LU can be attributed to the adequate surface modelling ability of HASM, combined with incorporation of information on abrupt spatial boundaries introduced by land use.

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Shi Wenjiao, Liu Jiyuan, Du Zhengping et al., 2012. Development of a surface modeling method for mapping soil properties.International Journal of Geographical Information Science, 2012, 22(4): 752-760.HASM ) 高精确性表面建模是能被使用玷污性质插值的一个方法。在这份报纸，我们在场 HASM 的一个方法联合了地理信息让土壤性质插值(HASM-SP ) 改进精确性。把类型，陆地使用类型和父母岩石基于土壤， HASM-SP 被使用插入内推在典型红土壤玷污可得到的 P，李， pH， alkali-hydrolyzable N，全部的 K 和 Cr 多山的区域。评估 HASM-SP 的表演，我们把它的表演与作比较平常的 kriging (好) ，平常的 kriging 联合了地理信息(OK-Geo ) 并且成层 kriging (SK ) 。结果证明方法包括 HASM-SP 与地理信息结合了， OK-Geo 获得了更低的评价偏爱。HASM-SP 也看了更少的 MAE 和 RMSE 它什么时候与另外的三个方法(OK-Geo，好和 SK ) 相比。更多细节由于为土壤性质的空间变化给了突然的边界的地理信息的不同类型的联合为土壤性质在 HASM-SP 地图被介绍。因此， HASM-SP 不能仅仅减少预言错误而且能与地理信息的分发一致，它做土壤性质的空间模拟更合理。HASM-SP 让充实不仅高精确性表面当模特儿土壤性质的理论，而且在资源管理并且环境计划为申请提供了一个科学方法。

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Sitch S, Smith B, Prentice I Cet al., 2003. Evaluation of ecosystem dynamics, plant geography and terrestrial carbon cycling in the LPJ Dynamic Global Vegetation Model.Global Change Biology, 9(2): 161-185.ABSTRACT

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Sun Xiaofang, Yue Tianxiang, Wang Qing, 2013. High accuracy surface modeling of grassland aboveground biomass.Journal of Remote Sensing, 17(5): 1060-1076. (in Chinese)The mapping of grassland biomass is of fundamental importance for estimating carbon budgets and the optimal use of grassland resources. The High Accuracy Surface Model for Grassland Biomass Simulation (HASM-GB) model was developed to estimate grassland aboveground biomass in Inner Mongolia, China. The ground truth biomass data and Normalized Difference Vegetation Index (NDVI) were used to predict maximum growing season biomass maps using the HASM-GB model. To evaluate the performance of HASM-GB, it was compared with three other methods: Satellite-Based Regression Model (REG), Ordinary Kriging (OK), and Regression Kriging (RK). As expected from theory, HASM-GB generally performs better than REG, OK, and RK, with a lower estimation bias, mean absolute error, root mean square error and higher correlation coefficient for measured and simulated values. From the predicted grassland biomass maps, the aspatial method vegetation index-biomass relationship technique was directly used with the variable NDVI to estimate biomass, and the precision of the results depend largely on how closely the primary and secondary variables are related. The spatial variation of the biomass produced by this method is very similar to the spatial variation of NDVI, so the simulation result is sensitive to errors in NDVI data. The OK method cannot factor information regarding vegetation index. However, HASM-GB can consider both the spatial structure of the measured biomass values and the NDVI data affecting local spatial trends, and it also had a higher precision of interpolation than RK. Consequently, HASM-GB is shown to be relatively effective for simulating spatial patterns of grassland biomass.

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Tan Kun, Piao Shilong, Peng Changhuiet al., 2007. Satellite-based estimation of biomass carbon stocks for northeast China’s forests between 1982 and 1999.Forest Ecology and Management, 240(1-3): 114-121.Northeast China maintains large areas of primary forest resource and has been experiencing the largest increase in temperature over the past several decades in the country. Therefore, studying its forest biomass carbon (C) stock and the change is important to the sustainable use of forest resources and understanding of the forest C budget in China. In this study, we use forest inventory datasets for three inventory periods of 1984–1988, 1989–1993 and 1994–1998 and NOAA/AVHRR Normalized Difference Vegetation Index (NDVI) data from 1982 to 1999, to estimate forest biomass C stock and its changes in this region over the last two decades. The averaged forest biomass C stock and C density were estimated as 2.1002Pg02C (102Pg02=0210 15 02g) and 44.6502Mg02C02ha 611 over the study period. The forest biomass C stock has increased by 7% with an annual rate of 0.008202Pg02C. The largest increase in the C density occurred in two humid mountain areas, Changbai Mountains and northern Xiaoxing’anling Mountains. Climate warming is probably the key driving force for this increase, while anthropogenic activities such as afforestation and deforestation may contribute to variations in the C stocks.

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Wang Bin, Liu Moucheng, Zhang Biao, 2009. Dynamics of net production of Chinese forest vegetation based on forest inventory data.Forest Resource Management, 1: 35-43. (in Chinese)According to the net primary productivity data of 1?266 samples about different forest types in China,the functional relationship between biomass,volume,community growth and annual litter fall about Chinese major forest types were established and the net production and dynamic changes about Chinese forest ecosystems were studied by using the data from six NFIs of China from 1973 to 2003.The results showed that the net production of Chinese forest vegetation was 1?360.64 106t/a during the 6th NFI,and the average net primary productivity was 9.53 t/hm2.a.The net production was composed mainly of young and middle-age forests and had some differences between different regions with the net production higher in northeast and southwest,and lower in other regions.From 1973 to 2003,the net production of Chinese forest vegetation increased from 790.13 106t/a to 1?360.64 106t/a.The net production was the lowest before 1970s and then increased gradually.Whereas the average net primary productivity of Chinese forest vegetation was higher before 1970s and decreased until the end of 1990s and then increased again.

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Wang Xiaoke, Feng Zongwei, Ouyang Zhixun, 2001. The impact of human disturbance on vegetative carbon storage in forest ecosystems in China.Forest Ecology and Management, 148(1-3): 117-123.Carbon (C) density (carbon mass per hectare) is a critical variable in determining the extent of the effect of human activity on ecosystems and our environment, because many ecological processes depend on the C cycle. Quantifying the human impact on C density of forest ecosystems is very important for reducing the uncertainties pertaining to C emission from terrestrial ecosystems. Using the volume-derived method, we have estimated the total vegetative C pool and density in the forest ecosystems for every province in China, and then analyzed the relationship between the C density and population density. In China, forest C storage was 3255.71Tg, of which 59% was located in remote regions including Helongjiang, Sichuan, Yunnan, and Inner Mongolia Provinces. The area-weighed vegetative C density is 32Mg/ha with a range of 5-75Mg/ha on a provincial scale. A good negative correlation was found between the C densities and population densities at a significant level (carbon density=-9.84. In (population density)+75.13, r=0.64). It can be concluded that, apart from changes in land use, forest degradation also causes significant carbon release to the atmosphere, and that existing forest ecosystems can sequester a considerable amount of carbon if effective management systems are applied.

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Xu Xinliang, Cao Mingkui, Li Kerang, 2007. Temporal-spatial dynamics of carbon storage of forest vegetation in China.Progress in Geography, 26(6): 1-10. (in Chinese)<p>Forest is the first major form of terrestrial ecosystem and plays an important dominant role in global carbon cycle. In this study, we developed an age - based volume - to - biomass method to estimate the carbon storage of Chinese forests between 1973 and 2003 by using inventory data of six periods and forest biomass data obtained from direct field measurements. The results show that the total vegetation carbon storage of Chinese forests in the six periods (1973～ 1976, 1977～1981, 1984～1988, 1989～1993, 1994～1998 and 1999～2003) is 3.8488 PgC, 3.6960 PgC, 3.759 PgC, 4.1138 PgC, 4.6563 PgC and 5.5064 PgC, respectively. Although the results of different periods is fluctuates their trends are an increase with the time. Especially, since 1980s the total vegetation carbon storage of Chinese forests has increased 1.8104PgC and accumulated about 0.0823PgC per year. It means that Chinese forests play a role as a significant sink of atmospheric carbon dioxide in that period. On the other hand, the mean carbon density of Chinese forests has increased 3.001Mgha<sup>- 1</sup> since 1970s, and that of young and middle- aged forests has increased 5.2871 and 0.6022Mgha <sup>- 1</sup> respectively, but that of mature forests has decreased by 0.7581Mgha<sup>- 1</sup>. This phenomenon suggests that the carbon fixation ability of Chinese forests primarily derives from forest plantation and it would be enhanced with carbon storage and carbon density increasing of young and middle- aged forests. The carbon stocks and densities of Chinese forests vary greatly in space. The larger carbon storage is primarily found in north eastern and south western regions, and higher C density mostly occurs in north eastern, south western and north western regions. These spatial distribution characteristics of carbon storage and mean C density in Chinese forests are prominently determined by human activities.</p>

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Yao Z Y, Liu J J, Zhao X Wet al., 2015. Spatial dynamics of aboveground carbon stock in urban green space: A case study of Xi’an, China.Journal of Arid Land, 7(3): 350-360.Greenhouse gas emission of carbon dioxide (CO2) is one of the major factors causing global climate change. Urban green space plays a key role in regulating the global carbon cycle and reducing atmospheric CO2. Quantifying the carbon stock, distribution and change of urban green space is vital to understanding the role of urban green space in the urban environment. Remote sensing is a valuable and effective tool for monitoring and estimating aboveground carbon (AGC) stock in large areas. In the present study, different remotely-sensed vegetation indices (VIs) were used to develop a regression equation between VI and AGC stock of urban green space, and the best fit model was then used to estimate the AGC stock of urban green space within the beltways of Xi&rsquo;an city for the years 2004 and 2010. A map of changes in the spatial distribution patterns of AGC stock was plotted and the possible causes of these changes were analyzed. Results showed that Normalized Difference Vegetation Index (NDVI) correlated moderately well with AGC stock in urban green space. The Difference Vegetation Index (DVI), Ratio Vegetation Index (RVI), Soil Adjusted Vegetation Index (SAVI), Modified Soil Adjusted Vegetation Index (MSAVI) and Renormalized Difference Vegetative Index (RDVI) were lower correlation coefficients than NDVI. The AGC stock in the urban green space of Xi&rsquo;an in 2004 and 2010 was 73,843 and 126,621 t, respectively, with an average annual growth of 8,796 t and an average annual growth rate of 11.9%. The carbon densities in 2004 and 2010 were 1.62 and 2.77 t/hm<sup>2</sup> respectively. Precipitation was not an important factor to influence the changes of AGC stock in the urban green space of Xi&rsquo;an. Policy orientation, major ecological greening projects such as &ldquo;transplanting big trees into the city&rdquo; and the World Horticultural Exposition were found to have an important impact on changes in the spatiotemporal patterns of AGC stock.

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Yue Tianxiang, Du Zhengping, Song Dunjianget al., 2007. A new method of surface modeling and its application to DEM construction.Geomorphology, 91: 161-172.A new method of surface modelling based on the fundamental theorem of surfaces (SMTS) is presented. Eight different test surfaces are employed to comparatively analyze the simulation errors of SMTS and the classical methods of surface modeling in GIS, including TLI (triangulated irregular network with linear interpolation), SPLINE, IDW (inverse distance weighted) and KRIGING. Numerical tests show that SMTS is much more accurate than the classical methods. SMTS theoretically gives a solution to the error problem that has long troubled DEM construction. As a real-world example, SMTS is used to construct a DEM of the Da-Fo-Si coal mine in Shaan-Xi Province, China. Its root mean square error (RMSE) is compared with those of DEMs constructed by the four classical methods. The results show that although SMTS also has a higher accuracy in the real-world example, the improvement of accuracy is less distinct than that expected from the numerical tests. The accuracy loss seems to be caused by location differences between sampling points and the central points of lattices of the simulated surfaces. Two alternative ways are proposed to solve this problem.

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Yue Tianxiang, Tian Yongzhong, Liu Jiyuanet al., 2008. Surface modeling of human carrying capacity of terrestrial ecosystems in China.Ecological Modelling, 214(2-4): 168-180.Surface models are developed for simulating the food provision capacities of cropland, grassland, woodland, and aquatic ecosystems. Based on these models, it appears that China's current agricultural structure is responsible for the shortage of food. If the agricultural production structure was improved so as to result in balanced nutritional value, the human carrying capacity would be 2029, 1914, and 1794 million individuals, living under the standards of the primary well-to-do life, full well-to-do life, and well-off life, respectively, taking into account the threshold of the human carrying capacity and an 11% production drop caused by natural disasters. If 57 billion m3 of water were transferred from southern to northern China by a south-to-north water diversion project and 17.3 billion m3 of water were diverted into agriculture, the human carrying capacity would be 2058, 1940, and 1817 million individuals, respectively, under the three living standards. 2008 Elsevier B.V. All rights reserved.

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Yue Tianxiang, Song Dinjiang, Du Zhengpinget al., 2010. High-accuracy surface modelling and its application to DEM generation.International Journal of Remote Sensing, 31(8): 2205-2226.Chinese Academy of Science [kzcx2-yw-429, kzcx2-yw-308, KZCX0504]; Ministry of Science and Technology of the People's Republic of China [2006BAC08B04, 2006AA12Z219]; International Cooperation Program for Science and Technology [2006DFB919201]

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Yue Tianxiang, 2011. Surface Modelling: High Accuracy and High Speed Methods. New York: CRC Press.

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Yue Tianxiang, Fan Zemeng, Chen Chuanfaet al., 2011. Surface modelling of global terrestrial ecosystems under three climate change scenarios.Ecological Modelling, 222(14): 2342-2361.A high accuracy and speed method (HASM) of surface modelling is developed to find a solution for error problem and to improve computation speed. A digital elevation model (DEM) is established on spatial resolution of 13.5 km x 13.5 km. Regression formulations among temperature, elevation and latitude are simulated in terms of data from 2766 weather observation stations scattered over the world by using the 13.5 km x 13.5 km DEM as auxiliary data. Three climate scenarios of HadCM3 are refined from spatial resolution of 405 km x 270 km to 13.5 km x 13.5 km in terms of the regression formulations. HASM is employed to simulate surfaces of mean annual bio-temperature, mean annual precipitation and potential evapotranspiration ratio during the periods from 1961 to 1990(T(1)), from 2010 to 2039 (T(2)), from 2040 to 2069 (T(3)), and from 2070 to 2099 (T(4)) on spatial resolution of 13.5 km x 13.5 km. Three scenarios of terrestrial ecosystems on global level are finally developed on the basis of the simulated climate surfaces. The scenarios show that all polar/nival, subpolar/alpine and cold ecosystem types would continuously shrink and all tropical types, except tropical rain forest in scenario A1Fi, would expand because of the climate warming. Especially at least 80% of moist tundra and 22% of nival area might disappear in period T(4) comparing with the ones in the period T(1). Tropical thorn woodland might increase by more than 97%. Subpolar/alpine moist tundra would be the most sensitive ecosystem type because its area would have the rapidest decreasing rate and its mean center would shift the longest distance towards west. Subpolar/alpine moist tundra might be able to serve as an indicator of climatic change. In general, climate change would lead to a continuous reduction of ecological diversity. (C) 2010 Elsevier B.V. All rights reserved.

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Yue Tianxiang, Zhao Na, Ramsey R Douglaset al., 2013a. Climate change trend in China, with improved accuracy.Climatic Change, 120(1/2): 137-151.中国科学院机构知识库(中国科学院机构知识库网格（CAS IR GRID）)以发展机构知识能力和知识管理能力为目标，快速实现对本机构知识资产的收集、长期保存、合理传播利用，积极建设对知识内容进行捕获、转化、传播、利用和审计的能力，逐步建设包括知识内容分析、关系分析和能力审计在内的知识服务能力，开展综合知识管理。

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Yue Tianxiang, Zhao Na, Yang Haiet al., 2013b. The multi-grid method of high accuracy surface modelling and its validation.Trans GIS, 17(6): 943-952.

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Zhang Chunhua, Ju Weimin, Chen Jing Met al., 2013. China’s forest biomass carbon sink based on seven inventories from 1973 to 2008.Climatic Change, 118(3/4): 933-948.

48
Zhao Mingwei, Yue Tianxiang, Zhao Naet al., 2014. Combining LPJ-guess and HASM to simulate the spatial distribution of forest vegetation carbon stock in China.Journal of Geographical Sciences, 24(2): 249-268.lt;p>It is very important in accurately estimating the forests' carbon stock and spatial distribution in the regional scale because they possess a great rate in the carbon stock of the terrestrial ecosystem. Yet the current estimation of forest carbon stock in the regional scale mainly depends on the forest inventory data,and the whole process consumes too much labor,money and time. And meanwhile it has many negative influences on the forest carbon storage updating. In order to figure out these problems,this paper,based on High Accuracy Surface Modeling (HASM),proposes a forest vegetation carbon storage simulation method. This new method employs the output of LPJ-GUESS model as initial values of HASM and uses the inventory data as sample points of HASM to simulate the distribution of forest carbon storage in China. This study also adopts the seventh forest resources statistics of China as the data source to generate sample points,and it also works as the simulation accuracy test. The HASM simulation shows that the total forest carbon storage of China is 9.2405 Pg,while the calculated value based on forest resources statistics are 7.8115 Pg. The forest resources statistics is taken based on a forest canopy closure,and the result of HASM is much more suitable to the real forest carbon storage. The simulation result also indicates that the southwestern mountain region and the northeastern forests are the important forest carbon reservoirs in China,and they account for 39.82% and 20.46% of the country's total forest vegetation carbon stock respectively. Compared with the former value (1975-1995),it manifests that the carbon storage of the two regions do increase clearly. The results of this research show that the large-scale reforestation in the last decades in China attains a significant carbon sink.</p>

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Zhao Na, Yue Tianxiang, 2014a. A modification of HASM for interpolating precipitation in China.Theoretical and Applied Climatology, 116: 273-285.Based on the spatial distribution of precipitation in China, this study gives a modification of High Accuracy Surface Modeling (HASM) method for improving interpolation of precipitation. To assess the feasibility of this modified model, namely, HASM-PRE, we use precipitation data measured at 712 stations for the period 1951鈥2010, using 605 stations for function development and reserving 107 for validation tests. The performance of HASM-PRE is compared with those of HASM and other classical methods: kriging, inverse distance weighted (IDW) method and spline. Results show that HASM-PRE has less root mean square error (RMSE) and mean absolute error (MAE) than the other techniques tested in this study. The precipitation map obtained from HASM-PRE is better than that obtained using other methods. Therefore, HASM-PRE can be seen as an alternative to the popular interpolation techniques, particularly if we focus on simulation accuracy. In addition, the effective way to combine the strengths of both human expert and differential geometry in this study can be applied for calculating precipitation for other areas in other temporal scales. For better improvement, HASM-PRE can be combined with ancillary variables and implemented in parallel environments.

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Zhao Na, Yue Tianxiang, 2014b. Sensitivity studies of a high accuracy surface modelling method.Science China-Earth Sciences, 57: 1-11.The sensitivities of the initial value and the sampling information to the accuracy of a high accuracy surface modeling (HASM) are investigated and the implementations of this new modeling method are modified and enhanced. Based on the fundamental theorem of surface theory, HASM is developed to correct the error produced in geographical information system and ecological modeling process. However, the earlier version of HASM is theoretically incomplete and its initial value must be produced by other surface modeling methods, such as spline, which limit its promotion. In other words, we must use other interpolators to drive HASM. According to the fundamental theorem of surface theory, we modify HASM, namely HASM.MOD, by adding another important nonlinear equation to make it independent of other methods and, at the same time, have a complete and solid theory foundation. Two mathematic surfaces and monthly mean temperature of 1951-2010 are used to validate the effectiveness of the new method. Experiments show that the modified version of HASM is insensitive to the selection of initial value which is particular important for HASM. We analyze the sensitivities of sampling error and sampling ratio to the simulation accuracy of HASM.MOD. It is found that sampling information plays an important role in the simulation accuracy of HASM.MOD. Another feature of the modified version of HASM is that it is theoretically perfect as it considers the third equation of the surface theory which reflects the local warping of the surface. The modified HASM may be useful with a wide range of spatial interpolation as it would no longer rely on other interpolation methods.

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