Estimating carbon fixation of plant organs for afforestation monitoring using a process‐based ecosystem model and ecophysiological parameter optimization

Abstract Afforestation projects for mitigating CO2 emissions require to monitor the carbon fixation and plant growth as key indicators. We proposed a monitoring method for predicting carbon fixation in afforestation projects, combining a process‐based ecosystem model and field data and addressed the uncertainty of predicted carbon fixation and ecophysiological characteristics with plant growth. Carbon pools were simulated using the Biome‐BGC model tuned by parameter optimization using measured carbon density of biomass pools on an 11‐year‐old Eucommia ulmoides plantation on Loess Plateau, China. The allocation parameters fine root carbon to leaf carbon (FRC:LC) and stem carbon to leaf carbon (SC:LC), along with specific leaf area (SLA) and maximum stomatal conductance (g smax) strongly affected aboveground woody (AC) and leaf carbon (LC) density in sensitivity analysis and were selected as adjusting parameters. We assessed the uncertainty of carbon fixation and plant growth predictions by modeling three growth phases with corresponding parameters: (i) before afforestation using default parameters, (ii) early monitoring using parameters optimized with data from years 1 to 5, and (iii) updated monitoring at year 11 using parameters optimized with 11‐year data. The predicted carbon fixation and optimized parameters differed in the three phases. Overall, 30‐year average carbon fixation rate in plantation (AC, LC, belowground woody parts and soil pools) was ranged 0.14–0.35 kg‐C m−2 y−1 in simulations using parameters of phases (i)–(iii). Updating parameters by periodic field surveys reduced the uncertainty and revealed changes in ecophysiological characteristics with plant growth. This monitoring method should support management of afforestation projects by carbon fixation estimation adapting to observation gap, noncommon species and variable growing conditions such as climate change, land use change.


| INTRODUC TI ON
Planted forests, including both forest plantations and rubber plantations but not oil-palm plantations or other agricultural plantations, account for 7% of global forest area (FAO, 2015). Although natural forest area declined from 3,961 Mha in 1990 to 3,721 Mha in 2015, planted forest area increased from 168 Mha to 278 Mha over the same period, helping to mitigate the annual rate of net forest loss (Keenan et al., 2015). Afforestation and reforestation could reduce the harvest pressure on natural forests by supplying timber (Fenning & Gershenzon, 2002) and reduce surface runoff and soil erosion in degraded landscapes through rainfall interception (Nunes, Almeida, & Coelho, 2011). Forest management using afforestation and reforestation is also an effective tool for promoting carbon dioxide (CO 2 ) absorption through plant regrowth (Keith, Mackey, & Lindenmayer, 2009;Noormets et al., 2015;Xu, Wen, Zhu, & He, 2017). Indeed, the recent promotion of afforestation and reforestation provides carbon storage, resulting in an increase of net CO 2 uptake by the forests in China (Streets et al., 2001). Afforestation and reforestation therefore are mitigation and adaptation strategies for climate change in the forest sector (Ravindranath, 2007).

Afforestation projects under market mechanisms in the Kyoto
Protocol and the Paris Agreement aim to reduce CO 2 while supporting sustainable development. The Clean Development Mechanism (CDM) is part of the emerging carbon market established under the terms of the Kyoto Protocol and aims to achieve sustainable development in developing countries and cost-effective reduction of greenhouse gases in developed countries (Olsen, 2007). Olsen (2007) classified CDM projects into a typology of four groups according to their key findings: forward-looking studies, sustainability impact studies, carbon forestry studies, and mixed studies.
Afforestation and reforestation are accepted as eligible activities in the carbon forestry studies of CDM projects. Globally, more than 760 Mha of land are identified as biophysically suitable for CDM afforestation and reforestation (CDM-AR) activities (Zomer, Trabucco, Bossio, & Verchot, 2008). In mid-2009, however, only four projects were registered as CDM-AR with the United Nations Framework Convention on Climate Change (UNFCCC) out of a total of 1,665 registered projects (Thomas, Dargusch, Harrison, & Herbohn, 2010). The bottlenecks in the development of CDM-AR projects can be attributed to both the length of time it takes to gain revenue from the project and a lack of the knowledge and technical capacity required to meet the demands of the CDM registration process (Thomas et al., 2010).
In the approved methodology for CDM-AR, it is stipulated that projects will monitor changes in carbon stocks in five pools after afforestation or reforestation-aboveground biomass, belowground biomass, dead wood, litter, and soil organic carbon-based on quality assurance/quality control (QA/QC) procedures for inventory operations (UNFCCC, 2013). The more advanced methods in the guide recommend the application of direct measurements of the carbon stock growth rate and its validation using modeling approaches (Penman et al., 2000), allowing an application to national circumstances by fine temporal and spatial scale and closer link between biomass and soil dynamics. However, this requires technical competence and scientific expertise (Palm, Ostwald, Berndes, & Ravindranath, 2009). Previous studies in general focused on the assessment of no-project-implemented carbon dynamics baselines based on empirical models or forest inventories (Dushku & Brown, 2003;Dutschke, Butzengeiger, & Michaelowa, 2006). Selection of the model used in a project and the model parametrization and calibration are critical issues for proper documentation of the validity and completeness of the data. Diagnostic biosphere models using remote-sensing data would be useful in CDM-AR projects because of the complete coverage of information in the subjective study area, which enables the interpretation of land use and plant phenology. However, most conventional diagnostic biosphere models demonstrate low predictive skill and show uncertainty in simulations according to the quality of available satellite observations, and stress factors without biophysical processes (Sasai, Ichii, Yamaguchi, & Nemani, 2005). Prognostic biosphere models, or process-based models, predict carbon dynamics in the biosphere based on biogeochemical processes in individual carbon components driven mainly by climate variability. Changes in carbon stocks in the five specified pools under various circumstances are predictable using process-based models, but applicability of the models to CDM-AR projects critically depends on appropriate model validation with ground observations. Several studies have investigated validation schemes for prognostic biosphere models (e.g., Braswell, Sacks, Linder, & Schimel, 2005;Fox et al., 2009;Mo, Chen, Ju, & Black, 2008;Santaren, Peylin, Viovy, & Ciais, 2007;Trudinger et al., 2007), although these studies were designed to examine carbon exchange rates between the atmosphere and the biosphere, not carbon pools and growth in plant organs and soil. Cienciala and Tatarinov (2006) estimated aboveground woody biomass in managed forests using adjusted ecophysiological and nitrogen parameters. Zhao, Xiang, Peng, and Tian (2009) performed sensitivity analysis and prediction for each plant organ in a managed forest, comparing long-term fir-stand data. These studies were performed in managed forests where long-term data reflect moderately stable conditions, which differ from the conditions under land use changes for recovering degraded ecosystems. Saito, Ito, and Maksyutov (2014) applied the assimilation scheme of a prognostic biosphere model to 10-years average aboveground biomass and CO 2 concentration data by combining it with an atmospheric tracer transport model, but they did not assess the temporal biomass changes or other carbon pools such as leaf and belowground biomass, the reporting of which is required in CDM-AR projects. Unfortunately, there are few studies on model validation for carbon-stock monitoring and growth processes based on field surveys.
In this study, we quantify the growth processes of carbon stocks in an afforestation project in China. This site has been implemented the "Grain for Green" program, which returns arable lands inappropriate for cultivation to forests, and restores degraded ecosystems to healthy condition. This program supplies increasing demands for timber in China and is expected to increase vegetation cover, leading to carbon sequestration (Liu, Li, Ouyang, Tam, & Chen, 2008).
The adaptive monitoring of carbon pools following afforestation is necessary to assess the potential of plantations as carbon sinks. By monitoring the carbon pools in an afforestation project, we aim to estimate carbon fixation with adapting to ecophysiological changes and to address the uncertainty in predicting carbon-stock changes and ecophysiological characteristics. We used an optimization scheme for biophysical parameters in a process-based model with field surveys to represent plant growth following afforestation.

| Study site and biomass data
The study site is an 11-year-old Eucommia ulmoides plantation in Loess Plateau, consisting mostly of silt soil, in Lingbao City, Henan Province, China (34°16′N, 110°40′E, 1,000 m a.s.l). Annual average air temperature and annual precipitation for 1981-2010 measured at Lushi station, 40 km southeast of the site, are 13.7°C and 686 mm, respectively. Eucommia ulmoides is one of the common deciduous broadleaf trees in central and southern China. The trees at the study site were planted in 1999 on an abandoned cornfield as part of the Grain for Green program (Cao, Chen, & Yu, 2009;Wang, Hu, Deng, Shangguan, & Deng, 2018). This forest had been surveyed as a candidate site for a new afforestation project by a joint enterprise between China and Japan (Hitz, 2010).
To obtain biomass data, we conducted a field survey at the E. ulmoides plantation in 2009. We measured trunk diameter at breast height (D; m) and tree height (H; m) of E. ulmoides trees (all 11 years old). Survey of D and H in four quadrats in the plantation was performed at the same time of biometric 7 model-tree survey. Sixtyfour samples from the four quadrats showed 10.5 ± 2.0 cm in D and 7.8 ± 1.8 m in tree height. By comparison of model and quadrat trees, averages of D and H of the model trees biased by 0.9 cm and 0.0 m from the averages of quadrat trees, respectively. These biases were enough small to decide these model trees as representatives in the plantation.
These seven model trees were harvested and separated into aboveground (trunks and branches) and belowground (coarse roots) woody parts, and leaves. The dry weight (kg) of each part was measured. We applied allometric relationships based on proportional relationships of biomass weight to D 2 and D 2 H (Niklas, 2004). In general, both the above-and belowground biomass have allometric relationships with D and H as follows: The relationship between leaf biomass and D is as follows: The parameters a, b, c, and d for E. ulmoides in the present study were obtained using the measurements from the harvested trees fitted by linear regression using least squares method. The leaves of one of the trees were extremely damaged because of drainage water from a nearby building, so the leaf biomass data from that tree were not included, and the parameters for Equation (2) were obtained from the data of six trees.
To estimate above-and belowground and leaf biomass in the years prior to the field survey, we estimated D for previous years from the tree rings of the seven harvested trees. The tree trunks were cut at breast height, and we assumed that the tree-ring diameter for each year was the same as D for that year. Measured average tree height of 1-11 year measured by trunk analysis was used for H. The above-and belowground and leaf biomass for each year were estimated from Equations (1) and (2) and the mean value for D of each year. The amounts of carbon in the aboveground (AC), belowground (BC), and leaf (LC) biomass were estimated by applying the measured percentage carbon content of 46% for above-and belowground biomass and 45% for leaves. The calculated mean carbon mass of cut trees (kg-C) was converted into carbon density per unit land area (kg-C/m 2 ) using the total of D 2 and D 2 H acquired from measured D and H of all tree in four 10 × 15 m quadrats (supplied in data repository).

| Model description
This study used the process-based ecosystem model Biome-BGC (Kimball, White, & Running, 1997;Running & Hunt, 1993;Thornton et al., 2002;Thornton & Rosenbloom, 2005;White, Thornton, Running, & Nemani, 2000) to simulate the biomass growth and carbon fixation of each plant organ. Biome-BGC predicts the carbon fixation of leaf, stem, and root associated with the carbon allocation of photosynthetic products to each plant organ for six plant functional types: deciduous broadleaf trees, deciduous needle-leaf trees, evergreen broadleaf trees, evergreen needle-leaf trees, C3 grasses, and C4 grasses. The photosynthetic productivity in the model has been investigated and verified by various studies (e.g., Pietsch, Hasenauer, & Thornton, 2005;Ueyama et al., 2010;Wang, Bauerle, & Reynolds, 2008). Biome-BGC allocates the photosynthetic production to each plant organ on the basis of carbon allocation parameters, and soil carbon is supplied through the litter from plant organs.
Biome-BGC was driven with ecophysiological parameters, initial site information, and climate-forcing data at a daily time-step with point simulation at the site. The input parameters for ecophysiological characteristics for this study are shown in Table 1. The initial site information included the site characteristics of elevation (m), latitude (degree N), albedo, effective soil depth (m), first-year maximum leaf and stem carbon (kg-C/m 2 ), atmospheric nitrogen deposition (kg-N/m 2 ), symbiotic and asymbiotic nitrogen fixation (kg-N/ m 2 ), soil carbon content of pools (kg-C/m 2 ), soil nitrogen content of the mineral pool (kg-N/m 2 ), and soil texture. The nitrogen input rate (1) y = aD 2 H + b (2) y = cD 2 + d from atmospheric deposition to the ecosystem at the site was fixed at 0.002 kg-N m −2 y −1 , which is the average value in broadleaf forests in various regions of China (Toda et al., 2010). Soil texture at the site was obtained from the literature (Li & Shao, 2006) as 5% sand, 68% silt, and 27% clay. The initial conditions for soil carbon and nitrogen density at the site were simulated by running the model over a 6,000-year period with the default plant ecophysiological parameters of C4 annual grass and a nitrogen supply to the soil of 0.03 kg m −2 y −1 by fertilization, which was obtained from a survey of plantation managers. In this spin-up simulation, 50% of the aboveground crop biomass was removed every year to represent harvest practice (Penman et al., 2003).  Thornton & Running, 1999)  in January. The peak monthly precipitation was 156 mm in July.
Vapor pressure deficit estimated from these meteorological values was highest in the summer. Estimated SRAD showed small variations around normal yearly values (210-484).

| Sensitivity of carbon pool simulations to ecophysiological parameters
To represent the carbon storage and growth of each plant organ adaptively, parameter adjustment was required. We therefore analyzed the sensitivity of AC and LC to ecophysiological parameters related to photosynthesis and carbon allocation to plant organs to select the parameters for adjustment by an optimization scheme.
The sensitivity of BC was not analyzed because BC is calculated by multiplying AC by the ratio of carbon allocation of coarse root carbon to stem carbon (CRC:SC) in Biome-BGC, so BC can be reproduced by using the appropriate AC and the CRC:SC ratio.
In Biome-BGC, the photosynthetic assimilation rate A (µmol CO 2 m −2 s −1 ) is simulated using Farquhar's photosynthesis model (Farquhar, Caemmerer, & Berry, 1980;De Pury & Farquhar, 1997): where A c (μmol CO 2 m −2 s −1 ) is the carboxylation-limited assimilation and A j (μmol CO 2 m −2 s −1 ) is the RuBP-regeneration-limited assimilation. A c and A j are calculated as follows: where V cmax (μmol CO 2 m −2 s −1 ) is the maximum carboxylation rate, J (μmol CO 2 m −2 s −1 ) is the actual electron transport rate and is related to the incident photosynthetic photon flux density (PPFD), and the maximum electron transport rate (J max ; μmol CO 2 m −2 s −1 ) (Kuehn & McFadden, 1969), C i (Pa) is the leaf intercellular CO 2 concentration (partial pressure), Γ * (Pa) is the CO 2 compensation point in the absence of photorespiration, K c and K o are the Michaelis-Menten constants of Rubisco for CO 2 and O 2 , respectively, and R d (μmol CO 2 m −2 s −1 ) is the photorespiration rate.
Biome-BGC calculates V cmax from leaf nitrogen data and Rubisco activity as follows: where lnc (kg-N/m 2 ) is the leaf nitrogen content per unit projected sunlight leaf area, flnr (kg-N/kg-N) is the proportion of leaf nitrogen content that is in Rubisco, fnr (kg-Rubisco/kg-N) is the weight ratio of Rubisco to its nitrogen content (=7.16), and act (μmol-CO 2 kg-Rubisco −1 s −1 ) is the Rubisco activity, which is adjusted for temperature and O 2 and CO 2 levels.
A in Equation (3) can also be determined by using the relationship between the photosynthetic assimilation, the stomatal conductance, and the atmospheric and leaf intercellular CO 2 concentrations as follows: where g (μmol-CO 2 m −2 s −1 Pa −1 ) is the leaf-scale conductance of CO 2 , and C a (Pa) is the atmospheric concentration of CO 2 . To represent the stomatal closure corresponding to environmental stresses, Biome-BGC scales the maximum stomatal conductance (g smax ) by a series of multipliers between 0 and 1 for stresses connected with the PPFD, soil-water potential, minimum temperature, and VPD (Körner, 1995;White et al., 2000). Biome-BGC represents the ecophysiological responses of stomata to the stresses of the light and water environment, and photosynthetic activity to nitrogen content, by these processes.
These processes are calculated for leaves both in sun and shade by daily steps. The actual photosynthesis can be calculated by solving the quadric expressions in Equations (3) and (7). In Biome-BGC, 39 ecophysiological parameters are used to represent photosynthetic production based on A and its allocation to each plant organ according to specified allocation parameters. We conducted a literature search for these parameters (e.g., Chiesi et al., 2007;Cienciala & Tatarinov, 2006;Hidy et al., 2012;Jarvis, 1976;Jarvis & McNaughton, 1986;Leuning, 1995;Pietsch et al., 2005;Warren, Livingston, & Turpin, 2004;White et al., 2000). We then arbitrarily selected seven parameters for sensitivity analysis to determine the critical parameters for variability in the carbon pools of each plant organ. For carbon allocation parameters, we used the ratios of fine root carbon to leaf carbon (FRC:LC), stem carbon to leaf carbon (SC:LC), and CRC:SC. We also selected the specific leaf area (SLA), g smax , VPD at the final reduction of stomatal conductance (VPD f ), and VPD at the initial reduction of stomatal conductance (VPD i ).
In the sensitivity analysis, we individually tested the sensitivity of predicted AC and LC to variations in parameter levels of ±30% and ±60% of default values.

| Model tuning
The seven parameters selected as described in Section 2.32.3 were optimized to represent the observed biomass growth using the Schematic diagram of the system for minimizing the object function using Dakota optimizer (Adams et al., 2013). The Dakota system provides the parameters generated by userspecified optimization methods to a model and then reads the object function estimated from model outputs. The system iterates this procedure until the object function is minimized Reading object function Providing input parameters Input file for controlling optimization the input parameters to minimize the object function and generate search-optimized parameters. The derivative-free global methods can search optimal parameters for the minimum object function even for black-box models or functions without derivatives, and these five methods were able to solve nonconvex functions such as the Rosenbrock function (Adams et al., 2013). Trudinger et al. (2007) compared optimization methods for data assimilation of terrestrial ecosystem models, and they reported that the design of the object function is more important for parameter optimization than selection of optimization methods. In this study, we simply adopted the algorithm showing the highest performance of the five tested to represent the measured carbon density of plant organs. The results of the tests of the five algorithms using measured biomass data and minimized object functions (described in Equation 8 below) are shown in Table A1.
As the object function to be minimized by Dakota, we defined the average yearly relative error between simulated and measured LC and AC pools over 11 years as follows: where f is the object function, i is stand age (years), n is the stand age at the last field survey (n = 11 in this study), AC i and LC i are the aboveground woody and leaf carbon densities in year i, respectively, and In addition to optimization using 11-year data, we also performed optimization using 1-to 5-year-old stand data to investigate parameter variability during the afforestation and plant growth phases of the project. We performed optimization at three different phases with different parameters to represent carbon fixation during each phase: (i) the phase before implementation of the afforestation project ("planning" phase), using the default parameters; (ii) the first monitoring phase at year 5, with parameters optimized using stand data for years 1-5; and (iii) an updated monitoring phase at year 11, with parameters optimized using stand data for years 1-11. The field survey at year 11 was performed as part of this study and yielded the tree-ring data and total D 2 and D 2 H for each quadrat; however, there was no field survey at year 5. Instead, we simply used the data for years 1-5 estimated from the allometric relationships and the tree-ring measurements from the 11-year-old stand.

| 30-year carbon fixation
In this study, we estimated the carbon fixation in each carbon pool over the project period (30 years as in some approved CDM-AR monitoring methodology). The goal was to assess total carbon fixation and the variability associated with ecophysiological parameters that are individually tuned to three different phases as described in Section 2.42.4: before implementation, year 5 monitoring, and year 11 updated monitoring. We estimated the variability in carbon fixation of above-and belowground woody biomass and leaf biomass at the site for 30 years after afforestation using climate-forcing data for 1981-2010. To reduce the impact of climate anomalies on plant carbon fixation in the simulation, the model was driven by repeating the 30-year climate-forcing data cyclically from the beginning of each year, with atmospheric CO 2 concentrations for 1981-2010, and then averaging the resulting ensemble of estimated carbon pools. In addition to the simulation using the model fully tuned by the observations of eleven years, we estimated the carbon fixation using default parameters and those tuned with observations from the stand at ages 1-5 years.
These processes yield simulations for the planning phase, with updated predictions for the implementation phase of an afforestation project.

| Biomass variability and meteorological conditions at the study site
We determined the allometric relationships between D and H and the dry weights of aboveground woody biomass (trunks and branches), belowground woody biomass, and leaf dry weight for E. ulmoides using the data from the biometric survey ( Figure 3). The relationships were well approximated by straight lines. The parameters a and b of Equation (1) for aboveground woody parts were 373.5 and 3.2, respectively; for belowground woody parts they were 162.6 and 1.2, respectively. The parameters c and d of Equation (2)  The mean ratio of the belowground carbon density to the aboveground carbon density (trunks and branches) over 11 years was 0.47.

| Sensitivity analysis of carbon pools to ecophysiological parameters
We investigated sensitivity of AC and LC to ecophysiological parameters by varying individual parameters by ±30% and ±60% from default values to select the parameters for optimization for reproducing

| Model tuning
We tested derivative-free global methods in Dakota to adjust the selected parameters to represent the measured biomass growth  Table 2 shows a comparison between the results using nonweighted and weighted object functions and AC and LC at 11 years. The minimized nonweighted (W A = W L = 1) object function in Equation (8) using 1-to 11-year-old stand data was 0.225, whereas the weighted

| 30-year carbon fixation
We estimated the carbon fixation for 30 years after planting at the afforestation site to assess the impact on carbon pool estimates of using ecophysiological parameters that were individually optimized for three different project phases (see Section 2.52.5; Figure 8 and Table 4). We also estimated the carbon fixation in the soil pool.

| Parameter variation with plant growth stage
The ecophysiological parameters FRC:LC, SC:LC, SLA, and g smax , having shown a high contribution to AC and LC, were optimized to reproduce the temporal changes in carbon pools for each plant organ. They also showed variability with plant growth stage. FRC:LC optimized using the data from years 1 to 5 was higher (2.36) than F I G U R E 7 Measured above-and belowground woody biomass carbon and leaf biomass carbon, and those simulated using (a) the default ecophysiologicalcharacteristic parameters, (b) parameters tuned by Dakota using the observed biomass in the first 5 years, and (c) parameters tuned using the entire 11-year period F I G U R E 8 Temporal changes in leaf, above-and belowground woody, and soil carbon density simulated using (a) the default ecophysiological-characteristic parameters, (b) those tuned using data from the first 5 years, and (c) those tuned using data from the entire 11-year period of the implementation phase of the plantation project (30 years). The values are the ensemble averages of simulation runs with cyclic use of 30-year meteorological data Values of SC:LC optimized using 1-to 5-year and 1-to 11-year data were both lower (1.23, 1.76, respectively) than the default value (2.20). These lower values mean that the proportional allocation of carbon to leaf compared to stem was higher than that for a generalized deciduous broadleaf forest in Biome-BGC. This observation might reflect the phenomenon where carbon allocation to leaf becomes higher in arid conditions (Orians & Solbrig, 1977). The mean SC:LC value and standard deviation of the collected data for Biome-BGC were 2.20 and 1.10, respectively . The optimized values in this study fell within this range. Several other studies reported similar values in deciduous broadleaf stands (e.g., Betula pubescens , Fagus crenata [Kakubari, 1977;White et al., 2000]).
BC was reproduced by using the ratio of BC to AC as CRC:SC (0.47) estimated from field survey data, which is higher than the default value (0.23). This demonstrated that the coarse root growth corresponded to a higher allocation of photosynthetic production in roots with the response of trees to water stress (Silva et al., 2004 Specific leaf area as optimized using 5-year and 11-year data showed a lower value (15 m 2 /kg-C) than the default value for deciduous broadleaf forests (30 m 2 /kg-C). In semi-arid and arid areas, leaves protect themselves from water stress and reduce transpiration by thickening (Orians & Solbrig, 1977). Eucommia ulmoides is known to accumulate trans-polyisoprene gum in its tissues (Nakazawa et al., 2009) and that could have influenced leaf thickness. The mean SLA and standard deviation from the collected data for Biome-BGC were 32 and 11 m 2 /kg-C, respectively . The optimized SLA in this study was somewhat lower than this range. This can be explained by the common tendency of leaf thickening in arid climates (Onoda et al., 2011). Specific leaf areas in deciduous broadleaf stands have been reported as 16.8 m 2 /kg-C in an Ulmus americana stand (Reich, Kloeppel, Ellsworth, & Walters, 1995) and 16.3 m 2 /kg-C in a Godmania macrocarpa stand (Holbrook, Whitbeck, & Mooney, 1995).
The g smax optimized using 5-year data was higher (0.008) than the default value (0.005) but lower than the default using 11-year data (0.003). There are few data for g smax , and just one reference (Kelliher, Leuning, Raupach, & Schulze, 1995) was used in Biome-BGC. Plants under semi-arid and arid conditions in general survive by reducing transpiration through lower stomatal conductance (Orians & Solbrig, 1977). In the 11-year-old stand, transpiration increased with increased LC and leaf area, so leaves may have reduced transpiration by decreasing g smax .
These results show that our optimized parameters fell within actual ranges reported by other studies, and the values at each phase reflect the behavior of plants in semi-arid and arid conditions. In this study, the parameters for reproducing the phenomena under semi-arid conditions were selected a priori for the sensitivity analysis. That selection contributed to the reproducibility of the carbon pools, but at the same time it might have been arbitrary.

| Monitoring method for afforestation projects in this study
We demonstrated a monitoring methodology for afforestation projects using process-based model and field surveys. Conventional monitoring (e.g., AR-ACM0003 of CDM [Methodology for Afforestation and Reforestation of Lands except Wetlands]; UNFCCC, 2013) includes field surveys every few years for monitoring plant carbon pools and enhanced QA/QC. This study used the TA B L E 4 Carbon density in the forest carbon pools at the end of the 30-year afforestation project, and average carbon fixation rates over the 30 years as estimated (i) using the default ecophysiological-characteristic parameters (as in the planning phase), (ii) using parameters tuned with data for the first 5 years after planting, and (iii) using parameters tuned using data from the entire 11-year period of the implementation phase

Average ± standard deviation of carbon density at the end of 30-year project (kg-C/m 2 )
Average carbon fixation rates for 30 years (kg-C m −2 y −1 ) mandatory field survey for model tuning, and the monitoring method that we propose is additionally applicable to conventional methods.
There are few studies using a process-based model in the forest management field because of the requirement for large amounts of information that are not readily available or easily obtained (Landsberg, Johnsen, Albaugh, Allen, & McKeand, 2001). It is therefore beneficial to have model parameter information to reproduce plant growth. The model, once tuned, would be reusable for the next project or another project with the same tree species and climate conditions. Adaptive monitoring by using a tuned model with field surveys could help obtain sustainable ecosystem services.
The model parameter optimization scheme demonstrated that it is possible to adaptively estimate each plant carbon pool in 1-to 11- year-old stands (Figure 7c). The parameters describing ecophysiological characteristics changed with the three phases of the project, and there was uncertainty in the prediction of carbon fixation for 30 years using the parameters optimized for each phase ( Figure 8 and The process-based approach can support forest inventory-and literature-based approaches adapting changes of growth condition, noncommon species, and observation gap. Zhou et al. (2014) demonstrated the relationship between the biomass carbon density and forest age on a plantation by using the forest inventory and estimated carbon storage well. However, they also mentioned some uncertainties. For example, using a relationship established at a provincial scale and the data from the national forest inventory for only one phase of forest growth can easily cause error. The other uncertainties arose because the calculation of carbon storage resulted from the hypothesis that plantation growth followed the growth equation, and some plantings were affected by geographic and climate conditions. Models incorporating climate as a driving force and ecophysiological processes can mitigate these problems because they accommodate environmental changes.
As the next step resulting from this study, the process-based approach could be used in conjunction with forest management models in assessing both CO 2 mitigation and other ecosystem services concerned with forest management strategy and human activity. Forest management models can simulate carbon storage, plant growth, timber volume, and management effects of thinning and cutting (Lemma, Kleja, Olsson, & Nilsson, 2007;Ooba, Hayashi, Machimura, & Matsui, 2014). The growth process in these models is estimated on the basis of yield tables and forest inventory without accounting for changes in climate and environmental conditions. We focused on required monitoring, and thus, we estimated carbon fixation and uncertainty by using a process-based model that calculated

| Limitations of this study
Most studies assessing carbon storage in CDM-AR projects have generally focused on no-project-implemented baseline carbon storage (e.g., Dushku & Brown, 2003), and there are no studies assessing CDM-AR with long-term monitoring using a process-based model.
Our approach requires regular field surveys to ensure the validation of the model, resulting in increases in the total cost of the project.
This is a bottleneck in our approach; it would be acceptable, however, in situations where the afforestation project is aimed at carbon fixation and field surveys are obligatory.
The object function using relative error and weighting coeffi- In this study, the available data were restricted to trunk diameter at breast height, tree height, and the dry weight of each carbon pool in an 11-year-old E. ulmoides stand. We estimated AC, BC, and LC using the allometric relationships based on these data, but the period for which biomass data were available was shorter than the project term (30 years in CDM-AR). This data limitation might also affect the spatial representativeness of our study. We focused mainly on our ability to reproduce carbon storage and changes in each plant organ during the afforestation monitoring phases by tuning the model, although the period with available data was insufficient to make this assessment over the project term. The growth rates and the ecophysiological conditions might change for years 12-30. Our methods were designed to estimate carbon fixation in the plantation after a land use change and to investigate the uncertainty in the model predictions by model tuning at each plant growth stage, but more observations over a longer period are needed to support our results.
Our method adaptively updates the prediction by observations every few years, which corresponds to long-term predictions under limited conditions that do not cause phenomena beyond the model representation (fire and wind disturbances, exceptional drought, forest fire, pest attack). Biome-BGC has no capacities responding to drastic environmental changes. For sustainable management and monitoring of afforestation, the incorporation of processes for above phenomena or the coupling with other management models is required.

| CON CLUS IONS
To meet the requirement of highly reliable monitoring of afforestation projects aimed at mitigating CO 2 levels, we have described a monitoring methodology that combines a process-based ecosystem model simulation with field surveys for monitoring different phases of a project. The requirements of the model for afforestation projects were that the model reproduces carbon storage and changes in each plant organ using adjustable parameters, as well as defining the uncertainty of prediction using adjusted parameters and environmental conditions.
We demonstrated that the model can reproduce carbon density for AC, BC, and LC using optimized ecophysiological model parame- This study shows how to estimate each plant carbon pool and understand the parameter changes with plant growth stages and the uncertainty of predicted carbon fixation in a plantation by an optimization scheme using field survey data. We expect the application of this monitoring method to support the management of afforestation projects by carbon fixation estimation adapting to observation gap, noncommon species, and variable growing conditions such as climate change, land use change.

ACK N OWLED G M ENTS
T. Miyauchi thanks Dr. Hibiki M. Noda of the National Institute for Environmental Studies, Japan, for carefully proofreading the manuscript. We thank Mr. Tadayuki Sada of Hitz Research Alliance Laboratory, Osaka University for helping with data processing of measurements from the E. ulmoides stand. We also thank Dr.

Yoshihisa Nakazawa of Hitz Research Alliance Laboratory, Osaka
University for coordinating the survey of sites in China.

CO N FLI C T O F I NTE R E S T
None declared.

AUTH O R CO NTR I B UTI O N S
T. Miyauchi and T. Machimura conceived the ideas and designed the study; T. Miyauchi performed model simulation and analysis, and implementation of optimization scheme; T. Miyauchi wrote the manuscript; M. Saito corrected the manuscript.

DATA ACCE SS I B I LIT Y
The biometric data for allometric relationships of E. ulmoides and the files related to optimization and simulation results are available