An Improved InTEC Model for Estimating the Carbon Budgets in Eucalyptus Plantations

Abstract

Eucalyptus has become a major plantation crop in southern China, with a carbon sequestration capacity significantly higher than that of other species. However, its long-term carbon sequestration capacity and regional-scale potential remain highly uncertain due to commonly applied short-rotation management practices. The InTEC (Integrated Terrestrial Ecosystem Carbon) model is a process-based biogeochemical model that simulates carbon dynamics in terrestrial ecosystems by integrating physiological processes, environmental drivers, and management practices. In this study, the InTEC model was enhanced with an optimized eucalyptus module (InTEC_euc) and a data assimilation module (InTEC_DA), and driven by multiple remote sensing products (Net Primary Productivity (NPP) and carbon density) to simulate the carbon budgets of eucalyptus plantations from 2003 to 2023. The results indicated notable improvements in the performance of the InTEC_euc model when driven by different datasets: carbon density simulation showed improvements in R² (0.07–0.56), reductions in MAE (5.99–28.51 Mg C ha⁻¹), reductions in RMSE (8.1–31.85 Mg C ha⁻¹), and improvements in rRMSE (12.37–51.82%), excluding NPP_Lin. The carbon density-driven InTEC_euc model outperformed the NPP-driven model, with improvements in R² (0.28), MAE (−8.15 Mg C ha⁻¹), RMSE (−9.43 Mg C ha⁻¹), and rRMSE (−15.34%). When the InTEC_DA model was employed, R² values for carbon density improved by 0–0.03 (excluding ACD_Yan), with MAE reductions between 0.17 and 7.22 Mg C ha⁻¹, RMSE reductions between 0.33 and 12.94 Mg C ha⁻¹ and rRMSE improvements ranging from 0.51 to 20.22%. The carbon density-driven InTEC_DA model enabled the production of high-resolution and accurate carbon budget estimates for eucalyptus plantations from 2003 to 2023, with average NPP, Net Ecosystem Productivity (NEP), and Net Biome Productivity (NBP) values of 17.80, 10.09, and 9.32 Mg C ha⁻¹ yr⁻¹, respectively, offering scientific insights and technical support for the management of eucalyptus plantations in alignment with carbon neutrality targets.

1. Introduction

Extensive plantations across China play a vital role in carbon sequestration and contribute significantly to the nation’s climate change mitigation efforts [1]. Eucalyptus plantations exhibit carbon fixation rates 2.95 times higher than those of Pinus massoniana and 2.18 times higher than those of Cunninghamia lanceolata [2]. They represent 6.85% of China’s total plantation area and contribute over 17.96% to the national timber harvest [2]. Eucalyptus is typically managed under a short-rotation monoculture regime, with trees harvested every 5 to 9 years and all biomass removed from the ecosystem following harvest. This practice reduces residual carbon stock in the ecosystem, potentially lowering Net Biome Productivity (NBP) and even turning plantations into carbon sources [3]. Although eucalyptus plantations currently function as carbon sinks, the long-term effects of repeated short rotations on carbon storage remain poorly understood. The short-rotation management model introduces significant uncertainty into carbon stock estimates, complicating accurate assessments of their overall contribution to regional carbon sequestration.

Temporally, forest ecosystems may alternate between acting as carbon sinks and sources from year to year; however, they must function as net carbon sinks over longer timescales to contribute to long-term carbon sequestration [4]. Short-term or single-period carbon stock assessments (e.g., plot inventory and remote sensing estimation) are insufficient to accurately capture the carbon cycling dynamics in eucalyptus plantations. Spatially, the rapid growth of eucalyptus enables substantial CO₂ fixation. However, harvesting leads to the direct removal of biomass carbon from the forest carbon pool, with the carbon either stored or released through forest products. According to the seventh and eighth national forest resource inventories, eucalyptus plantations demonstrated a strong carbon sequestration capacity, with an annual carbon increment of 9.96 Tg C—the largest increase in carbon density among major species [5]. However, a study in Guangxi Province—where eucalyptus occupies the largest plantation area in China—reported that eucalyptus contributes only 6.67% to the provincial carbon stock, ranking eighth in carbon density among ten major forest types [6]. Thus, whether eucalyptus plantations can enhance regional forest carbon sinks remains uncertain. Time-series remote sensing offers a robust data foundation for the continuous monitoring of the dynamic changes in eucalyptus plantations [7], while process-based ecosystem models provide a methodological framework for investigating their carbon sink/source characteristics over extended periods. Integrating time-series remote sensing with ecosystem model simulations provides a scientific basis for the quantitative assessment of eucalyptus plantations’ contribution to regional carbon sinks.

Process-based ecosystem models effectively characterize carbon transfer among pools in response to disturbances and facilitate integrated assessments of climate change impacts on biogeochemical cycles. The Integrated Terrestrial Ecosystem Carbon budget model (InTEC) is among the few process-based models that incorporate the effects of climate, stand age, and forest disturbances on carbon cycling, while being driven by remote sensing data [8]. It has been widely applied to simulate carbon budgets at both regional and national scales [9,10,11]. However, a key limitation of the InTEC model is that it can only account for a single disturbance event within a time series [12,13]. It also assumes that each pixel remains continuously forested throughout the simulation period, thereby ignoring temporal changes in land cover. This static assumption hinders the model’s ability to capture the dynamic changes in forest structure and composition under multiple disturbance regimes. Therefore, to accurately represent the spatiotemporal dynamics of eucalyptus plantations and their carbon budgets, it is essential to update the disturbance and land cover modules of the InTEC model.

At the same time, the InTEC model also heavily relies on the Net Primary Productivity (NPP) value from a designated reference year. This reference-year NPP is critical to ensuring the accurate and realistic simulation of carbon dynamics. However, the limited availability of high-resolution and reliable NPP data for eucalyptus plantations significantly constrains the model’s applicability. Existing NPP datasets [14,15] tend to underestimate the actual productivity of eucalyptus forests [16,17,18]. Recently, high-resolution biomass [19] and carbon density [20] datasets have become more reliable, representing promising alternatives for driving the InTEC model. Therefore, leveraging high-resolution and accurate biomass and carbon density data to optimize the InTEC model—thereby reducing its dependency on reference-year NPP—offers a direct and effective approach to enhancing its capacity to simulate regional-scale carbon budgets in eucalyptus plantations. As more time-series carbon and biomass products become available, developing strategies to integrate these datasets will be key to further improving simulation quality.

To address uncertainties in input data, data assimilation techniques can integrate multi-year remote sensing observations with the InTEC model to optimize parameterization and improve the agreement between model outputs and observational datasets [21,22,23,24], thereby enhancing the accuracy of regional-scale carbon budget simulations for eucalyptus plantations.

This study aims to enhance the InTEC model by optimizing key modules and to assess the impact of various remote sensing-derived carbon monitoring products on simulation performance. The overarching objective is to evaluate the spatiotemporal patterns of carbon sources and sinks in eucalyptus plantations at the regional scale. The specific objectives are (1) to optimize the eucalyptus and data assimilation modules within the InTEC model by considering short rotation and forest dynamics; (2) to compare model outputs driven by NPP- and carbon density-based products; and (3) to evaluate the spatiotemporal dynamics of carbon budgets in eucalyptus plantations at the regional scale.

2. Methods

2.1. Study Area and Data

2.1.1. Study Area

A subtropical region in Fujian Province, southeastern China, was selected as the study area. Yunxiao County, situated in Zhangzhou City, experiences a subtropical monsoon climate, with an average annual temperature of 21.2 °C, annual precipitation of 1730.6 mm, approximately 2000 h of sunshine annually, and a frost-free period exceeding 347 days (Figure 1). Eucalyptus in this area grows rapidly on a 5–7-year rotation, and most stands have been harvested once or twice (Figure 1a). The forest coverage rate in the county is 67.81%, with eucalyptus plantations covering approximately 300,000 acres, accounting for 29% of the total forest area (Figure 1b).

2.1.2. Data Collection and Preprocessing

The input data for the InTEC model include climate data, soil data, eucalyptus data (e.g., spatial distribution, clear-cutting, and planting years), atmospheric data (CO₂ concentration and nitrogen deposition data), maximum leaf area index (LAI), reference-year NPP, and biomass/carbon density datasets. Detailed descriptions of these datasets are provided in

Table 1. Input data for the InTEC model.

Data	Name	Description	Time	Resolution	Source
Model Input Data	Climate Data	Monthly average temperature, total monthly precipitation, average monthly radiation, average monthly vapor pressure	1960–2023	30 m	This Study
	Soil Data	Soil depth, soil texture data	-	1 km	National Qinghai–Tibet Plateau Science Data Center
		Wetness index, Water table	-	30 m	This Study
	Eucalyptus Data	Eucalyptus distribution, harvest frequency, and harvest timing data	1986–2021	30 m	[7]
	CO2 Concentration	Station observation data	2013–2022	-	https://www.gml.noaa.gov accessed on 12 February 2024
		Satellite Data Inversion	1850–2013	1°	[25]
	Nitrogen Deposition	Simulated Data	1980–2013	0.5°	[26]
	LAI	Calculated using Sentinel-2 data	2020	30 m	This Study
	Reference-year NPP	MODIS NPP (NPPMODIS)	2020	500 m	[14]
		Lin GPP (NPPLin)	2020	30 m	[15]
	Reference-year Biomass/Carbon Density	Aboveground carbon density from Yang et al. (ACDYang)	2019	30 m	[19]
		Aboveground carbon density from Yan et al. (ACDYan)	2013–2021	30 m	[27]
		Carbon density from Jiang et al. (CDJiang)	2020–2021	30 m	[20]
Validation Data	Plot survey data (CDPlots)	15 plots, collected semi-annually	2021–2024	-	-

. All datasets, except atmospheric data, were projected and resampled (bilinear interpolation) to a 30 m spatial resolution using the UTM coordinate system, ensuring consistency for input into InTEC model simulations.

(1) The relationship between Fnpp and age

In InTEC model simulations, the relationship between forest NPP and stand age plays a critical role. The model incorporates a normalized NPP–age relationship (Fnpp-age curve) as an input variable to adjust NPP calculations throughout the simulation process. In this study, the Fnpp–age relationship specific to eucalyptus plantations was derived by analyzing observed NPP data and corresponding stand age information reported in previous studies [17,28], following the empirical formulations described in Equations (1) and (2) [29].

$$\mathrm{Fnpp}\left(\mathrm{age}\right) ={\displaystyle \frac{\mathrm{NPP}\left(\mathrm{age}\right)}{{\mathrm{NPP}}_{\max }}}$$

(1)

$$\mathrm{NPP}\left(\mathrm{age}\right)=\mathrm{a}*\left(1+{\displaystyle \frac{\mathrm{b}* {\left(\frac{\mathrm{age}}{\mathrm{c}}\right)}^{\mathrm{d}}- 1}{{\mathrm{e}}^{\left(\frac{\mathrm{age}}{\mathrm{c}}\right)}}}\right)$$

(2)

where $\mathrm{age}$ denotes the stand age of eucalyptus; $\mathrm{Fnpp}\left(\mathrm{age}\right)$ represents the normalized NPP at that age; and $\mathrm{NPP}\left(\mathrm{age}\right)$ indicates the actual NPP value corresponding to the same stand age. ${\mathrm{NPP}}_{\max }$ is the maximum NPP observed across all stand ages. The empirical coefficients a, b, c, and d were obtained by fitting the Levenberg–Marquardt nonlinear least-squares algorithm to NPP measurements from [28] for 0–6-year-old eucalyptus stands in Guangxi Province, China, and to NPP observations for the same species in stands older than 7 years from [17]. The resulting coefficients were 16.14, 0.55, 3.66, and 2.80 for a, b, c, and d, respectively.

(2) Carbon products for reference year

The InTEC model adjusts the initial NPP (NPP₀) using reference-year NPP data to accurately simulate long-term NPP dynamics. To this end, five types of reference-year carbon datasets were compared for model calibration. Specifically, two NPP datasets are employed: the MODIS NPP dataset [14] (NPP_MODIS, Figure 2a) and the NPP derived from the GPP product by Lin et al. (2022) [15] (NPP_Lin, Figure 2b). Additionally, three carbon density datasets are included: carbon density data from Jiang et al. (2023) [20] (CD_Jiang, Figure 2c), and aboveground carbon density data derived from Yang et al. (2023) [19] and Yan et al. (2023) [27] (ACD_Yang and ACD_Yan, Figure 2d,e).

The study applied the following preprocessing steps to the input datasets: Lin’s GPP product was converted to NPP by applying a GPP-to-NPP conversion factor of 0.5 [30], while the aboveground biomass data from Yang and Yan were converted to aboveground carbon density using a biomass-to-carbon factor of 0.5 [31]. The NPP_MODIS values were slightly lower than those of NPP_Lin (Figure 3a). The CD_Jiang dataset, which includes both aboveground and belowground carbon, ranges from 0 to 90 Mg C ha⁻¹. ACD_Yang values are primarily concentrated between 40 and 56 Mg C ha⁻¹, indicating relatively lower carbon densities. The ACD_Yan dataset spans a wider range, from 15 to 87 Mg C ha⁻¹, and shows a considerable proportion of higher values (Figure 3b).

2.2. InTEC Model and Improvement

2.2.1. Basic Principles and Key Parameters of InTEC Model

The InTEC model is a biogeochemical process-based model that simulates forest carbon and nitrogen cycles by incorporating inputs such as climate, soil, vegetation, atmospheric CO₂ concentration, and nitrogen deposition [32]. It incorporates multiple sub-models, including the Farquhar photosynthesis model, the CENTURY soil carbon and nitrogen model, a net nitrogen mineralization module, and the NPP–age relationship, to investigate the long-term impacts of climate change, atmospheric chemistry, forest disturbances, and regeneration on forest carbon and nitrogen dynamics [33]. Within this modeling framework, climate change and atmospheric chemical changes (e.g., CO₂ enrichment and nitrogen deposition) are classified as non-disturbance factors, and their influences on the carbon cycle are defined as non-disturbance effects. Conversely, disturbances such as logging, fire, pest outbreaks, and forest regrowth are defined as disturbance factors, with their associated impacts on the carbon cycle referred to as disturbance effects. The InTEC model evaluates the effects of both disturbance and non-disturbance drivers on vegetation through a carbon pool framework, which partitions the vegetation carbon pool into leaf, stem, fine root, and coarse root components.

Prior to model parameterization, it is essential to clarify the hierarchy of carbon fluxes: Gross Primary Productivity (GPP) represents the total carbon fixed by vegetation via photosynthesis; NPP is the net carbon remaining after subtracting plant autotrophic respiration from GPP; NEP further deducts soil microbial and other respiratory losses from NPP; and NBP then subtracts carbon losses due to disturbances (e.g., fire, logging, pests, and diseases), yielding the final net carbon accumulation. Based on this framework, model parameterization follows the NPP allocation scheme proposed by D. Li et al. (2016) [7] to determine the partitioning coefficients and turnover rates for different vegetation carbon pools—leaves, stems, fine roots, and coarse roots (see

Table 2. Allocation coefficients of NPP to leaf, stem, fine root, and coarse root carbon pools, and the turnover rates of the corresponding carbon pools [34].

Carbon Allocation		Turnover Rate
Allocation coefficient to stem	0.4624	Wood turnover rate	0.0288
Allocation coefficient to coarse root	0.2226	Coarse root turnover rate	0.0448
Allocation coefficient to leaf	0.1190	Leaf turnover rate	0.2948
Allocation coefficient to fine root	0.1960	Fine root turnover rate	1.0000

for details).

2.2.2. Optimizing Key Modules of InTEC Model

As a static vegetation model primarily driven by NPP data, the InTEC model traditionally accounts for only a single forest harvest event. Eucalyptus plantations, however, are managed under a short-rotation, monoculture system, for which existing NPP products often underestimate actual productivity or its dynamics (because NDVI saturates in high-LAI eucalyptus stands—typically above 0.8—preventing further increases in leaf area and photosynthetic activity from being captured in the light-use-efficiency model). To improve model fidelity, high-resolution and accurate carbon density datasets are therefore essential. In response to this limitation, we developed and integrated two key modules—a eucalyptus module and a data assimilation module—into the InTEC model, enabling a more accurate representation of the spatiotemporal dynamics and carbon budgets of eucalyptus plantations.

(1) The eucalyptus module (InTEC_euc)

The InTEC model currently lacks the ability to adequately account for the impacts of multi-rotation harvest cycles and forest type transitions on the carbon budgets of eucalyptus plantations. To overcome this limitation, we developed the eucalyptus module that incorporates historical eucalyptus harvest records and classification data spanning from 1986 to 2021, enabling accurate simulation of plantation carbon dynamics. In addition, recent improvements in biomass and carbon density estimation were leveraged to integrate high-resolution carbon density data, thereby enhancing the accuracy of carbon budget simulations. Within this module, carbon pools (leaf, stem, fine root, and coarse root) are reset to zero following each harvest event. NPP is computed using Equations (3)–(5), and carbon pool dynamics are calculated with Equation (6), where NPP₀ is determined via an iterative optimization process. After each iteration, convergence is evaluated using the criterion ($\left|{\mathrm{C}}_{\mathrm{t}}\left(\mathrm{i}\right) - {\mathrm{C}}_{\mathrm{ref}}\right| < {\mathrm{C}}_{\mathrm{ref}}*0.01$). If the condition is satisfied, the current NPP₀ is accepted; otherwise, the value is adjusted and the process is repeated until convergence is achieved.

$${\mathrm{NPP}}_{\mathrm{t}}\left(\mathrm{i}\right)=\left\{\begin{array}{ll}{\mathrm{NPP}}_0*{\phi }_{{\mathrm{NPPn}}_{\mathrm{t}}}\left(\mathrm{i}\right)* {\phi }_{{\mathrm{NPP}}_{{\mathrm{age}}_{\mathrm{t}}}}\left(\mathrm{i}\right)*{\phi }_{{\mathrm{NPP}}_{{\mathrm{cut}}_{\mathrm{t}}}}\left(\mathrm{i}\right),& \mathrm{t}\in \mathrm{f}\mathrm{o}\mathrm{r}\mathrm{e}\mathrm{s}\mathrm{t} \\ 0,& \mathrm{t}\notin \mathrm{f}\mathrm{o}\mathrm{r}\mathrm{e}\mathrm{s}\mathrm{t}\end{array}\right.$$

(3)

where $\mathrm{i}$ denotes the simulation year and $\mathrm{t}$ represents the tree species type. ${\mathrm{NPP}}_{\mathrm{t}}\left(\mathrm{i}\right)$ refers to the NPP for tree species t in the $\mathrm{i}$-th year; and ${\mathrm{NPP}}_0$ is the NPP in the initial year. ${\phi }_{{\mathrm{NPPn}}_{\mathrm{t}}}\left(\mathrm{i}\right)$ represents the non-disturbance impact factor on NPP for tree species t in the $\mathrm{i}$-th year, quantifying relative changes in NPP compared to the previous year due to variations in climatic conditions, atmospheric CO₂ concentration, and nitrogen deposition, among other environmental drivers. This factor is calculated following the methodology described in Chen et al. (2000) [35]. ${\phi }_{{\mathrm{NPP}}_{{\mathrm{age}}_{\mathrm{t}}}}\left(\mathrm{i}\right)$ denotes the effect of stand age on NPP for tree species t in the $\mathrm{i}$-th year. ${\phi }_{{\mathrm{NPP}}_{{\mathrm{cut}}_{\mathrm{t}}}}\left(\mathrm{i}\right)$ reflects the impact of harvesting events on NPP for tree species t in the $\mathrm{i}$-th year. It is set to 0 in years when harvesting occurs—indicating a reset of productivity—and to 1 otherwise.

$${\mathrm{NPP}}_0=\left\{\begin{array}{ll}{\mathrm{NPP}}_0,& \left|{\mathrm{C}}_{\mathrm{t}}\left(\mathrm{i}\right) - {\mathrm{C}}_{\mathrm{ref}}\right|<{\mathrm{C}}_{\mathrm{ref}}*0.01\\ {\mathrm{NPP}}_0*{\displaystyle \frac{{\mathrm{C}}_{\mathrm{ref}}}{{\mathrm{C}}_{\mathrm{ref}}+\left|{\mathrm{C}}_{\mathrm{t}}\left(\mathrm{i}\right) - {\mathrm{C}}_{\mathrm{ref}}\right|}},& \left|{\mathrm{C}}_{\mathrm{t}}\left(\mathrm{i}\right) - {\mathrm{C}}_{\mathrm{ref}}\right|\ge {\mathrm{C}}_{\mathrm{ref}}*0.01\end{array}\right.$$

(4)

where ${\mathrm{NPP}}_0$ denotes the initialized NPP. $\mathrm{i}$ refers to the simulation year, which is specifically designated as the reference year in this context; and $\mathrm{t}$ represents the tree species type. ${\mathrm{C}}_{\mathrm{t}}\left(\mathrm{i}\right)$ indicates the simulated vegetation carbon density for tree species $\mathrm{t}$ in the $\mathrm{i}$-th year; and ${\mathrm{C}}_{\mathrm{ref}}$ is the input vegetation carbon density corresponding to the reference year.

$${\phi }_{{\mathrm{NPP}}_{\mathrm{a}{\mathrm{ge}}_{\mathrm{t}}}}\left(\mathrm{i}\right) ={\displaystyle \frac{\mathrm{Fnpp}\left({\mathrm{age}}_{\mathrm{t}}\left(\mathrm{i}\right)\right)}{\mathrm{Fnpp}\left({{\mathrm{age}}_{\max }}_{\mathrm{t}}\right)}}$$

(5)

where $\mathrm{i}$ denotes the simulation year; and $\mathrm{t}$ represents the tree species type. ${\mathrm{A}\mathrm{ge}}_{\mathrm{t}}\left(\mathrm{i}\right)$ refers to the stand age for tree species $\mathrm{t}$ in the $\mathrm{i}$-th year and and ${{\mathrm{age}}_{\max }}_{\mathrm{t}}$ indicates the maximum stand age for tree species $\mathrm{t}$. $\mathrm{Fnpp}\left({\mathrm{age}}_{\mathrm{t}}\left(\mathrm{i}\right)\right)$ is the normalized NPP value (Fnpp) for tree species $\mathrm{t}$ at that stand age; and $\mathrm{Fnpp}\left({{\mathrm{age}}_{\max }}_{\mathrm{t}}\right)$ is the corresponding Fnpp value at the maximum stand age.

$${\mathrm{C}}_{{\mathrm{j}}_{\mathrm{t}}}\left(\mathrm{i}\right)=\left\{\begin{array}{ll}{\mathrm{C}}_{{\mathrm{j}}_{\mathrm{t}}}\left(\mathrm{i} - 1\right)+{\displaystyle \frac{{\mathrm{f}}_{{\mathrm{j}}_{\mathrm{t}}}\left(\mathrm{i}\right){\mathrm{NPP}}_{\mathrm{t}}\left(\mathrm{i}\right) - {\mathrm{k}}_{{\mathrm{j}}_{\mathrm{t}}}\left(\mathrm{i}\right){\mathrm{C}}_{{\mathrm{j}}_{\mathrm{t}}}\left(\mathrm{i} -1\right)}{1+{\mathrm{k}}_{{\mathrm{j}}_{\mathrm{t}}}\left(\mathrm{i}\right)}} - {\mathrm{Cut}}_{{\mathrm{j}}_{\mathrm{t}}}\left(\mathrm{i}\right),& \mathrm{t}=\mathrm{f}\mathrm{o}\mathrm{r}\mathrm{e}\mathrm{s}\mathrm{t}\\ 0,& \mathrm{t}\ne \mathrm{f}\mathrm{o}\mathrm{r}\mathrm{e}\mathrm{s}\mathrm{t}\end{array}\right.$$

(6)

where $\mathrm{i}$ denotes the simulation year; $\mathrm{j}$ indicates the specific vegetation carbon pool (e.g., leaf, stem, fine root, coarse root); and $\mathrm{t}$ represents the tree species type. ${\mathrm{C}}_{{\mathrm{j}}_{\mathrm{t}}}\left(\mathrm{i}\right)$ and ${\mathrm{C}}_{{\mathrm{j}}_{\mathrm{t}}}\left(\mathrm{i}-1\right)$ denote the carbon stocks in vegetation pool $\mathrm{j}$ for tree species $\mathrm{t}$ in the $\mathrm{i}$-th and ($\mathrm{i}-1$)-th years, respectively. ${\mathrm{NPP}}_{\mathrm{t}}\left(\mathrm{i}\right)$ is the NPP of tree species $\mathrm{t}$ in the $\mathrm{i}$-th year. ${\mathrm{f}}_{{\mathrm{j}}_{\mathrm{t}}}\left(\mathrm{i}\right)$ is the allocation coefficient of NPP allocated to vegetation carbon pool $\mathrm{j}$ for tree species $\mathrm{t}$ in the $\mathrm{i}$-th year; and ${\mathrm{k}}_{{\mathrm{j}}_{\mathrm{t}}}\left(\mathrm{i}\right)$ is the turnover rate of vegetation carbon pool $\mathrm{j}$ for tree species $\mathrm{t}$ in the $\mathrm{i}$-th year. ${\mathrm{Cut}}_{{\mathrm{j}}_{\mathrm{t}}}\left(\mathrm{i}\right)$ represents the carbon released from vegetation pool $\mathrm{j}$ by tree species $\mathrm{t}$ as a result of harvesting events occurring in the $\mathrm{i}$-th year. This release is defined as the total carbon accumulated in pool $\mathrm{j}$ since the previous harvest.

(2) The data assimilation module (InTEC_DA)

The incorporation of single-year carbon density data in the InTEC_euc model introduces notable uncertainty to simulation results. To mitigate this uncertainty, we developed a data assimilation module that integrates multi-year carbon density data and applies the four-dimensional variational assimilation (4DVar) [36] algorithm to optimize the key parameter, NPP₀. This approach improves the accuracy of simulating carbon budgets in eucalyptus plantations. NPP₀ is calculated based on Equations (7) and (8), where the optimization of NPP₀ is achieved through iterative computation. After each iteration, the convergence criterion ($\mathrm{J}\left(\mathrm{x}\right) = {\mathrm{J}\left(\mathrm{x}\right)}_{\min }$) is evaluated. If this criterion is satisfied, the prevailing NPP₀ value is accepted as the final result. Otherwise, NPP₀ undergoes further adjustment, and the iterative procedure continues until convergence is achieved. Loss minimization (Equations (9) and (10)) proceeds in three simple stages: first, a global search using SCE-UA with 50 complexes over 50 iterations [37,38] to locate promising ranges; next, 50 “jumping” iterations of Simulated Annealing to prevent trapping in local minima; and finally, a single Nelder–Mead iteration [39] for efficient, gradient-free fine-tuning.

$${\mathrm{NPP}}_0=\left\{\begin{array}{ll}{\mathrm{NPP}}_{\mathrm{DA}},& \mathrm{J}\left(\mathrm{x}\right)={\mathrm{J}\left(\mathrm{x}\right)}_{\min }\\ {\mathrm{NPP}}_0+\mathrm{r}\mathrm{a}\mathrm{n}\mathrm{d}\mathrm{o}\mathrm{m}\left(-2.0, 2.0\right),& \mathrm{J}\left(\mathrm{x}\right)\ne {\mathrm{J}\left(\mathrm{x}\right)}_{\min }\end{array}\right.$$

(7)

where ${\mathrm{NPP}}_0$ represents the initial NPP; and ${\mathrm{NPP}}_{\mathrm{DA}}$ is the final optimized initial NPP obtained through simulations incorporating the 4DVar algorithm. $\mathrm{J}\left(\mathrm{x}\right)$ denotes the cost function used in the 4DVar algorithm; and ${\mathrm{J}\left(\mathrm{x}\right)}_{\min }$ indicates the minimum value of the cost function achieved during the optimization process. $\mathrm{Random}\left(\right)$ is the stochastic function used to generate random values, which is used to apply random perturbations to ${\mathrm{NPP}}_0$ during the iterative optimization to explore a wider parameter space.

$$\mathrm{J}\left(\mathrm{x}\right)=0.1*{\left({\displaystyle \frac{{\mathrm{NPP}}_0 - {\mathrm{NPP}}_{\mathrm{BG}}}{{\mathrm{NPP}}_{\mathrm{SIGMA}}}}\right)}^2+ \sum _{\mathrm{i}}^{\mathrm{N}}{\mathrm{W}}_{\mathrm{i}}*{\left({\displaystyle \frac{{\mathrm{Sim}}_{\mathrm{i}} - {\mathrm{Obs}}_{\mathrm{i}}*{\alpha }_{\mathrm{i}}}{{\mathrm{Obs}}_{{\mathrm{SIGMA}}_{\mathrm{i}}}}}\right)}^2$$

(8)

where $\mathrm{J}\left(\mathrm{x}\right)$ denotes the cost function used in the 4DVar algorithm. ${\mathrm{NPP}}_0$ is the initial NPP to be optimized; ${\mathrm{NPP}}_{\mathrm{BG}}$ represents the background (a priori) value of initial NPP; and ${\mathrm{NPP}}_{\mathrm{S}\mathrm{IGMA}}$ signifies the standard deviation of the background error for the initial NPP. $\mathrm{i}$ is the simulation year; $\mathrm{N}$ represents the total number of simulated years; ${\mathrm{W}}_{\mathrm{i}}$ represents the weighting factor in the $\mathrm{i}$-th year, determining the relative importance of observations in that year; while ${\alpha }_{\mathrm{i}}$ is the correction coefficient used to adjust the observations in the $\mathrm{i}-\mathrm{th}$ year. ${\mathrm{Sim}}_{\mathrm{i}}$ refers to the carbon density value simulated by the InTEC_euc model in the $\mathrm{i}$-th year; ${\mathrm{Obs}}_{\mathrm{i}}$ denotes the observed carbon density value in the $\mathrm{i}$-th year; and ${\mathrm{Obs}}_{{\mathrm{SIGMA}}_{\mathrm{i}}}$ indicates the observation error (standard deviation) of the carbon density in the $\mathrm{i}$-th year.

$${\alpha }_{\mathrm{i}}=\left\{\begin{array}{cc}{\mathrm{E}}_{{\mathrm{H}}_{\mathrm{coef}}},& {\mathrm{Obs}}_{\mathrm{i}}/{\mathrm{Obs}}_{\mathrm{med}}>{\mathrm{E}}_{{\mathrm{HIGH}}_{\mathrm{RATIO}}}\hfill \\ {\mathrm{H}}_{\mathrm{coef}},& {\mathrm{HIGH}}_{\mathrm{RATIO}}<{\mathrm{Obs}}_{\mathrm{i}}/{\mathrm{Obs}}_{\mathrm{med}}\le {\mathrm{E}}_{{\mathrm{HIGH}}_{\mathrm{RATIO}}}\hfill \\ {\mathrm{N}}_{\mathrm{coef}} - {\displaystyle \frac{{\mathrm{Obs}}_{\mathrm{i}}/{\mathrm{Obs}}_{\mathrm{med}}- {{\mathrm{N}}_{\mathrm{HIGH}}}_{\mathrm{RATIO}}}{{\mathrm{HIGH}}_{\mathrm{RATIO}} - {{\mathrm{N}}_{\mathrm{HIGH}}}_{\mathrm{RATIO}}}}*{(\mathrm{M}}_{\mathrm{coef}} - {\mathrm{N}}_{\mathrm{coef}}),& {{\mathrm{N}}_{\mathrm{HIGH}}}_{\mathrm{RATIO}}<{\mathrm{Obs}}_{\mathrm{i}}/{\mathrm{Obs}}_{\mathrm{med}}\le {\mathrm{HIGH}}_{\mathrm{RATIO}}\hfill \\ {\mathrm{N}}_{\mathrm{coef}},& {\mathrm{Obs}}_{\mathrm{i}}/{\mathrm{Obs}}_{\mathrm{med}} \le {{\mathrm{N}}_{\mathrm{HIGH}}}_{\mathrm{RATIO}}\hfill \end{array}\right.$$

(9)

where i is the simulation year; ${\alpha }_{\mathrm{i}}$ is the correction coefficient applied in the i-th year; ${\mathrm{Obs}}_{\mathrm{i}}$ denotes the observed carbon density in year i; ${\mathrm{Obs}}_{\mathrm{med}}$ represents the median of all observed carbon density values across the entire period; ${\mathrm{E}}_{{\mathrm{H}}_{\mathrm{coef}}}$, ${\mathrm{H}}_{\mathrm{coef}}$, ${\mathrm{M}}_{\mathrm{coef}}$, and ${\mathrm{N}}_{\mathrm{coef}}$ are the correction coefficients corresponding to extreme overestimation, overestimation, normal values, and no correction, respectively; and ${\mathrm{E}}_{{\mathrm{HIGH}}_{\mathrm{RATIO}}}$, ${\mathrm{HIGH}}_{\mathrm{RATIO}}$, and ${{\mathrm{N}}_{\mathrm{HIGH}}}_{\mathrm{RATIO}}$ are the threshold coefficients used to classify extreme overestimation, overestimation, and normal fluctuation.

$${\mathrm{W}}_{\mathrm{i} }=\left\{\begin{array}{l} 1.0, {\mathrm{Obs}}_{\mathrm{i}}/{\mathrm{Obs}}_{\mathrm{med}}\ge \mathrm{H}\mathrm{I}\mathrm{G}{\mathrm{H}}_{\mathrm{RATIO}}\\ 2.0, {\mathrm{Obs}}_{\mathrm{i}}/{\mathrm{Obs}}_{\mathrm{med}}< \mathrm{H}\mathrm{I}\mathrm{G}{\mathrm{H}}_{\mathrm{RATIO}}\end{array} \right.$$

(10)

where i is the simulation year; ${\mathrm{W}}_{\mathrm{i}}$ is the correction weight for the i-th year; ${\mathrm{Obs}}_{\mathrm{i}}$ denotes the observed carbon density in the i-th year; ${\mathrm{Obs}}_{\mathrm{med}}$ represents the median of all observed carbon density values; and ${\mathrm{HIGH}}_{\mathrm{RATIO}}$ is the threshold coefficient for identifying overestimation.

In employing an optimization algorithm to minimize the loss function, the parameters of the data assimilation module are adjusted based on the model’s input carbon density observations to identify an optimal initial state that both closely fits the measurements and avoids excessive deviation from the background field. The module’s key parameters include the background NPP bounds for the eucalyptus plantation (${\mathrm{NPP}}_{\mathrm{BG}}$) as specified in Refs. [17,28]; the initial NPP bounds (${\mathrm{NPP}}_0$), the background NPP error standard deviations (${\mathrm{NPP}}_{\mathrm{SIGMA}}$), and the background carbon density observation error standard deviations (${\mathrm{Obs}}_{\mathrm{SIGMA}}$) all drawn from existing experiments (Model-input vs. field-measured carbon densities) and studies; and the experimentally calibrated correction coefficients (${\mathrm{E}}_{{\mathrm{H}}_{\mathrm{coef}}}$, ${\mathrm{H}}_{\mathrm{coef}}$, ${\mathrm{M}}_{\mathrm{coef}}$, ${\mathrm{N}}_{\mathrm{coef}}$) along with their corresponding threshold values (${\mathrm{E}}_{{\mathrm{HIGH}}_{\mathrm{RATIO}}}$, ${\mathrm{HIGH}}_{\mathrm{RATIO}}$, ${\mathrm{N}}_{{\mathrm{HIGH}}_{\mathrm{RATIO}}}$). Specific parameter values are detailed in

Table 3. Parameter settings in the data assimilation module [17,28].

Parameter	CDPlots	CDJiang	ACDYan	Parameter	CDPlots	CDJiang	ACDYan
${\mathrm{NPP}}_{\mathrm{SIGMA}}$ (Mg C ha−1 yr−1)	[10, 500]	[10, 500]	[10, 500]	${\mathrm{E}}_{{\mathrm{H}}_{\mathrm{coef}}}$	1.0	1.0	0.2
${\mathrm{Obs}}_{\mathrm{SIGMA}}$ (Mg C ha−1)	[0, 1]	[1, 10]	[1, 10]	${\mathrm{H}}_{\mathrm{coef}}$	1.0	1.0	0.3
${\mathrm{NPP}}_{\mathrm{BG}}$ (Mg C ha−1 yr−1)	[1000, 3000]	[1000, 3000]	[1000, 3000]	${\mathrm{M}}_{\mathrm{coef}}$	1.0	1.0	0.8
${\mathrm{NPP}}_0$ (Mg C ha−1 yr−1)	[100, 2500]	[100, 2500]	[100, 2500]	${\mathrm{N}}_{\mathrm{coef}}$	1.0	1.0	1.0
${\mathrm{E}}_{{\mathrm{HIGH}}_{\mathrm{RATIO}}}$	3.0	3.0	3.0	${\mathrm{HIGH}}_{\mathrm{RATIO}}$	2.0	2.0	2.0
${\mathrm{N}}_{{\mathrm{HIGH}}_{\mathrm{RATIO}}}$	1.0	1.0	1.0

.

The loss-minimization procedure is carried out in three consecutive stages to ensure robust convergence without the need for gradient information. First, the SCE-UA algorithm is used to generate 50 candidate solutions (“complexes”) in parameter space, with random initialization of ${\mathrm{NPP}}_0$,${\mathrm{NPP}}_{\mathrm{BG}}$,${\mathrm{NPP}}_{\mathrm{SIGMA}}$, and ${\mathrm{Obs}}_{\mathrm{SIGMA}}$. In each of 50 generations, the cost function is computed by comparing the carbon density simulated by the ecosystem model with the bias-corrected observed carbon density; candidates are then ranked in ascending order of cost, the top two elites are retained, and the remaining individuals are recombined via a strategy that couples simulated annealing with Nelder–Mead local search, thereby expanding global exploration while accelerating local convergence. Second, to avoid entrapment in local minima, the best solution from SCE-UA undergoes 50 “jump” simulated-annealing steps: at each step, small perturbations are added to ${\mathrm{NPP}}_0$,${\mathrm{NPP}}_{\mathrm{BG}}$,${\mathrm{NPP}}_{\mathrm{SIGMA}}$, and ${\mathrm{Obs}}_{\mathrm{SIGMA}}$, the cost is re-evaluated, and the new solution is accepted based on improvement in fit or with Metropolis probability exp[(Δcost)/T] (initial temperature T = 100, decay factor α = 0.99 per step). Finally, a Nelder–Mead simplex reflection is performed: taking the centroid of the two lowest-cost points as a reference, the third point is reflected to a new position; if the reflected point yields a lower cost, it replaces the worst vertex. After completion of these iterations, the individual with the lowest cost in the entire complex is selected as the final calibration output.

2.3. Accuracy Evaluation

To evaluate the plot-scale accuracy of the modified InTEC_euc and InTEC_DA models, we established 15 eucalyptus plots (20 m × 20 m) in Yunxiao County, Fujian Province, and conducted seven semi-annual DBH surveys from 2021 to 2024 to derive observed carbon densities (Mg C ha⁻¹). Individual DBH measurements were converted to dry biomass using a regional allometric equation [40], summed per plot, normalized by plot area, and multiplied by a biomass-to-carbon factor of 0.5. Observed carbon densities from 2020 to 2023 were then matched one to one in space and time with the corresponding model outputs to ensure consistency. Finally, we calculated the coefficient of determination (R²; Equation (11)), mean absolute error (MAE; Equation (12)), root mean square error (RMSE; Equation (13)), and relative RMSE (rRMSE; Equation (14)), where RMSE quantifies the average prediction error in original units and rRMSE expresses the error as a percentage of the observed mean. All metrics were then used to evaluate the simulation results with the InTEC model to highlight the performance improvements from our improvements.

$${\mathrm{R}}^2=1 - {\displaystyle \frac{{\sum }_{\mathrm{p}=1}^{\mathrm{n}}{\left({\mathrm{y}}_{\mathrm{p}}- {\widehat{\mathrm{y}}}_{\mathrm{p}}\right)}^2}{{\sum }_{\mathrm{p}=1}^{\mathrm{n}}{\left({\mathrm{y}}_{\mathrm{p}}- {\stackrel{\mathrm{-}}{\mathrm{y}}}_{\mathrm{p}}\right)}^2}}$$

(11)

$$\mathrm{M}\mathrm{A}\mathrm{E}={\displaystyle \frac{1}{\mathrm{n}}}{\sum }_{\mathrm{p}=1}^{\mathrm{n}}|{\mathrm{y}}_{\mathrm{p}}- {\widehat{\mathrm{y}}}_{\mathrm{p}}|$$

(12)

$$\mathrm{RMSE}=\sqrt{{\displaystyle \frac{1}{\mathrm{n}}}{\sum }_{\mathrm{p}=1}^{\mathrm{n}}{\left({\mathrm{y}}_{\mathrm{p}}- {\widehat{\mathrm{y}}}_{\mathrm{p}}\right)}^2}$$

(13)

$$\mathrm{rRMSE}=\sqrt{{\displaystyle \frac{1}{\mathrm{n}}}{\sum }_{\mathrm{p}=1}^{\mathrm{n}}{\left({\mathrm{y}}_{\mathrm{p}}- {\widehat{\mathrm{y}}}_{\mathrm{p}}\right)}^2}/{\sum }_{\mathrm{p}=1}^{\mathrm{n}}{\displaystyle \frac{{\mathrm{y}}_{\mathrm{p}}}{\mathrm{n}}}*100\%={\displaystyle \frac{\mathrm{RMSE}}{{\stackrel{\mathrm{-}}{\mathrm{y}}}_{\mathrm{p}}}} *100\%$$

(14)

where $\mathrm{p}$ indicates the plot; $\mathrm{n}$ denotes the total number of field plots; ${\mathrm{y}}_{\mathrm{p}}$ represents the observed carbon density at plot $\mathrm{p}$; ${\stackrel{\mathrm{-}}{\mathrm{y}}}_{\mathrm{p}}$ is the mean observed carbon density across all plots; and ${\widehat{\mathrm{y}}}_{\mathrm{p}}$ is the model’s simulated carbon density at plot $\mathrm{p}$.

2.4. Spatiotemporal Variation Characteristics Analysis

This study investigates temporal trends in carbon budgets by calculating annual average values across eucalyptus plantations. NPP, Net Ecosystem Productivity (NEP), and NBP were selected as key indicators to represent carbon dynamics. The Kruskal–Wallis (KW) significance test [41] was subsequently employed to assess statistical differences in the temporal means of the carbon budgets and to evaluate the influence of different carbon-driving data sources. Spatially, carbon budget distributions were analyzed by calculating their mean values over the period 2003–2023.

3. Results

3.1. Evaluation of Simulation Result

3.1.1. Accuracy Evaluation of InTEC_euc Model

The InTEC_euc model, when driven by NPP and carbon density data, demonstrated a significant improvement in simulating both carbon density and changes in it compared to the original InTEC model. Overall, the simulation accuracy for carbon density improved, with R² increasing by 0.07–0.56, MAE being reduced by 5.99–28.51 Mg C ha⁻¹, RMSE decreasing by 8.1–31.85 Mg C ha⁻¹, and rRMSE being improved by 12.37–51.82% (excluding NPP_Lin). The simulation error for carbon density change also decreased significantly, with R² increasing by 0.26–0.46, MAE being reduced by 2.17–3.3 Mg C ha⁻¹, RMSE decreasing by 2.0–4.3 Mg C ha⁻¹, and rRMSE being improved by 27.54–48.2%. Compared to the NPP-driven InTEC_euc model, the carbon density-driven model exhibited a superior performance.

Simulation results from the original InTEC model generally overestimated the carbon density values observed in plot surveys, with notable differences arising from the influence of various drive data sources on these outcomes. Simulations driven by CD_Jiang demonstrated a significantly higher accuracy compared to those driven by both ACD_Yang and ACD_Yan, and also outperformed NPP-driven simulations. Furthermore, models using ACD_Yang and ACD_Yan exhibited lower accuracy relative to the NPP-driven simulations (Figure 4a–e). The InTEC_euc model, in contrast, exhibited a distinct behavior: the NPP-driven simulations tended to slightly underestimate plot measurements, while carbon density-driven versions generally produced a mild overestimation. Nevertheless, the InTEC_euc model substantially outperformed the original InTEC model. Notable improvements included NPP_MODIS-driven results (R² increased by 0.44, MAE reduced by 7.65 Mg C ha⁻¹, RMSE decreased by 13.38 Mg C ha⁻¹, and rRMSE improved by 21.94%) and ACD_Yang-driven outcomes (R² increased by 0.56, MAE reduced by 28.51 Mg C ha⁻¹, RMSE decreased by 31.85 Mg C ha⁻¹, rRMSE improved by 51.82%) (Figure 4f–j).

In simulating carbon density change, the results of the InTEC model were significantly lower than the plot survey data (Figure 5a,b). However, the InTEC_euc model demonstrated improvements in simulating carbon density change. Although some deviations remained, it represented a substantial advancement compared to the original InTEC model. In the NPP-driven InTEC_euc model, the simulation accuracy improved significantly, particularly for simulations driven by NPP_MODIS, where R² increased by 0.36, MAE was reduced by 2.91 Mg C ha⁻¹, RMSE decreased by 3.22 Mg C ha⁻¹, and rRMSE was improved by 33.99% (Figure 5f,g). The carbon density-driven InTEC_euc model also demonstrated significant improvement, especially for simulations driven by ACD_Yang and ACD_Yan. Specifically, R² increased by an average of 0.45, MAE was reduced by 3.04 Mg C ha⁻¹, RMSE decreased by 4.02 Mg C ha⁻¹, rRMSE was improved by 44.79%, and the simulation performance clearly surpassed that of the NPP-driven InTEC_euc model (Figure 5h–j).

The simulation results for carbon density, obtained from the NPP- and carbon density-driven InTEC and InTEC_euc models, revealed distinct temporal trends. Specifically, the NPP- and carbon density-driven InTEC model exhibited continuous growth, whereas the InTEC_euc model displayed fluctuating dynamics. For the NPP-driven InTEC model, the simulated carbon density ranged from 7 to 107 Mg C ha⁻¹ (Figure 6a,b). The carbon density-driven InTEC model showed greater dispersion, particularly when driven by the ACD_Yang and ACD_Yan (resulting in a range of 8 to 153 Mg C ha⁻¹). These higher values and greater dispersion were primarily attributed to differences in the carbon density range of the respective input data (Figure 6c–e). In comparison, the InTEC_euc model demonstrated superior capabilities in capturing the dynamic changes in eucalyptus plantations. When driven by carbon density data, its simulated carbon density ranged from 0 to 138 Mg C ha⁻¹, a range that was slightly broader and had a higher maximum than the 0 to 107 Mg C ha⁻¹ range for the NPP-driven model (Figure 6f–j).

3.1.2. Accuracy Evaluation of InTEC_DA Model

The InTEC_DA model, driven by carbon density data, demonstrated improvement in simulating both carbon density and its change compared to the InTEC_euc model (Figure 7). The simulation accuracy of carbon density improved overall, with R² increasing by 0–0.03 (excluding ACD_Yan), MAE being reduced by 0.17–7.22 Mg C ha⁻¹, RMSE decreasing by 0.33–12.94 Mg C ha⁻¹, and rRMSE being improved by 0.51–20.22% (Figure 7a–d). The simulation error for carbon density change also decreased significantly, with R² increasing by 0.01–0.05, MAE being reduced by 0.02–0.07 Mg C ha⁻¹, RMSE decreasing by 0.12–0.18 Mg C ha⁻¹, and rRMSE being improved by 1.19–1.91% (excluding ACD_Yan) (Figure 7e–h).

Compared to the InTEC_euc model, the InTEC_DA model exhibited a significantly higher accuracy in simulating carbon density, with the results being more closely aligned with the plot survey data. The influence of different driving data on simulation performance was also evident. With the InTEC_DA model, simulations driven by CD_Plots and CD_Jiang produced notably higher accuracy than those driven by ACD_Yan. Nonetheless, the performance of the ACD_Yan-driven simulation also improved relative to the InTEC_euc model, with MAE being reduced by 7.22 Mg C ha⁻¹, RMSE decreasing by 12.94 Mg C ha⁻¹ and rRMSE being improved by 20.22% (Figure 4j or Figure 7d). In terms of simulating carbon density change, both the InTEC_euc and InTEC_DA models underestimated the plot survey data. However, the InTEC_DA model showed clear improvements, particularly when driven by CD_Jiang, with R² increasing by 0.05, MAE being reduced by 0.07 Mg C ha⁻¹, RMSE decreasing by 0.18 Mg C ha⁻¹, and rRMSE being improved by 1.91% (Figure 5h or Figure 7g). In contrast, simulations driven by ACD_Yan exhibited a slight decline in performance, with R² decreasing by 0.04, MAE increasing by 0.51 Mg C ha⁻¹, RMSE increasing by 0.88 Mg C ha⁻¹, and rRMSE increasing by 10.29% (Figure 5j or Figure 7h).

Simulations using the carbon density-driven model (InTEC_euc and InTEC_DA models) displayed fluctuating results, with CD_Plots producing the most accurate outputs (Figure 8a–d). Simulations driven by CD_Plots in both the InTEC_euc and InTEC_DA models showed nearly identical ranges (0–102 Mg C ha⁻¹), and those driven by CD_Jiang also showed nearly identical ranges (0–87 Mg C ha⁻¹), but the plot-level simulated values varied, as seen in Plot05. The ACD_Yan-driven simulations showed marked changes in output range, including a 32 Mg C ha⁻¹ decrease in the output range maximum values and pronounced plot-level variations, with InTEC_euc producing 0–138 Mg C ha⁻¹ and InTEC_DA 0–106 Mg C ha⁻¹. The simulations driven by CD_Jiang produced slightly elevated outputs compared to those using CD_Plots; ACD_Yan-driven InTEC_euc model simulations substantially exceeded the CD_Plots results, while the InTEC_DA simulations using the ACD_Yan data were modestly higher than the CD_Plots results (Figure 8a–d).

3.2. Spatiotemporal Variation Characteristics of Eucalyptus Carbon Budgets with InTEC_euc Model

3.2.1. Temporal Variation Characteristics of Carbon Budgets

Over the past two decades, the eucalyptus plantations in our study area have exhibited a strong carbon sequestration capacity and have consistently functioned as carbon sinks. The simulation outcomes from the carbon density-driven InTEC_euc model indicated upward trends in NPP, NEP, and NBP, whereas the NPP-driven InTEC_euc model displayed decreased trends in NPP, with increases in both NEP and NBP (Figure 9). Specifically, under NPP data driving, the multi-year averages of NPP, NEP, and NBP were 12.71 Mg C ha⁻¹ yr⁻¹, 6.93 Mg C ha⁻¹ yr⁻¹, and 6.41 Mg C ha⁻¹ yr⁻¹, respectively. In contrast, when driven by carbon density data, these averages for NPP, NEP, and NBP increased to 19.56 Mg C ha⁻¹ yr⁻¹, 10.52 Mg C ha⁻¹ yr⁻¹, and 9.68 Mg C ha⁻¹ yr⁻¹, respectively. The results from the carbon density-driven InTEC_euc model were generally higher and exhibited greater fluctuation, highlighting the significant impact of the driving data on the model output.

When using different data (NPP and carbon density) to drive the InTEC_euc model for simulating carbon budgets on an annual scale, notable differences were observed in the results, particularly between the NPP- and carbon density-driven simulations (Figure 10). However, within the same data, the simulation results exhibited certain regularities. Specifically, the NPP, NEP, and NBP in the results driven by NPP showed strong intercorrelations, reflecting the intrinsic relationships within the same data driving set (NPP-driven data). Similarly, the NEP and NBP results driven by carbon density also demonstrated correlations. Furthermore, significant differences were observed between the simulated NPP results driven by CD_Jiang and ACD_Yang and those driven by ACD_Yan. Nonetheless, the NPP results from the CD_Jiang and ACD_Yang data still showed some correlation, attributable to the inherent relationships between these datasets (carbon density-driven data).

3.2.2. Spatial Variation Characteristics

On the spatial scale, the eucalyptus plantations in our study area also exhibited a strong carbon sequestration capacity, although areas exhibiting carbon source phenomena were also observed. The carbon budget results (NPP, NEP, NBP) from the InTEC_euc model driven by carbon density were generally higher than those from simulations driven by NPP, particularly in the simulation of NPP (Figure 11). Specifically, the results from the NPP-driven InTEC_euc model indicated that spatially distributed NPP values were primarily concentrated in the range of 6 to 27 Mg C ha⁻¹ yr⁻¹, NEP values in the range of 0 to 18 Mg C ha⁻¹ yr⁻¹, and NBP values between −10 and 18 Mg C ha⁻¹ yr⁻¹. In contrast, the results from the carbon density-driven InTEC_euc model showed that NPP values primarily concentrated in the range of 12 to 30 Mg C ha⁻¹ yr⁻¹, NEP values in the range of 0 to 24 Mg C ha⁻¹ yr⁻¹, and NBP values between −10 to 24 Mg C ha⁻¹ yr⁻¹.

The spatial distributions of carbon budgets from the InTEC_euc model, when driven by carbon density data versus NPP data, showed a fundamental consistency. Regions of strong carbon sequestration (acting as high carbon sinks) and regions acting as high carbon sources were largely co-located and covered approximately 95% of the eucalyptus plantation area (Figure 12). The overall carbon sequestration capacity and the extent of carbon sink areas simulated by the NPP-driven InTEC_euc model were significantly lower than those derived from carbon density. The NPP-driven results exhibited a more widespread spatial distribution, which can be attributed to the resolution (resampled from 250 m to 30 m) of the input NPP data and associated differences in forest classification.

3.3. Spatiotemporal Variation Characteristics of Eucalyptus Carbon Budgets with InTEC_DA Model

3.3.1. Temporal Variation Characteristics

Simulations using the InTEC_DA model, driven by carbon density data, revealed upward trends in NPP, NEP, and NBP, with multi-year averages of 17.80 Mg C ha⁻¹ yr⁻¹, 10.09 Mg C ha⁻¹ yr⁻¹, and 9.32 Mg C ha⁻¹ yr⁻¹, respectively (Figure 13). Prior to 2012, carbon budget results (mean values and standard deviations) from the InTEC_DA model when driven by the CD_Jiang data versus the ACD_Yan data exhibited significant discrepancies; however, after 2012, the metrics derived from these two data-driven datasets became nearly identical.

Annual-scale carbon budget simulations using carbon density data-driven models exhibited progressively enhanced correlations, with NPP results showing significant differences, while NEP and NBP outputs were significantly correlated (Figure 14). The CD_Jiang-driven models showed correlation in NPP simulations, contrasting with the significant discrepancies observed in ACD_Yan-based outputs.

3.3.2. Spatial Variation Characteristics of InTEC_DA Model

When the InTEC_DA model was driven by different carbon density data, the resulting distribution patterns of carbon budgets were similar to each other, yet retained variations in their amplitude extremes (Figure 15). The relatively smaller differences in overall carbon budget outcomes (NPP, NEP, NBP) observed when the InTEC_DA model was driven by these various carbon density data were attributed to the model’s methodology, where NEP and NBP were primarily determined by the simulated NPP (which was more consistently estimated by InTEC_DA across these different carbon density inputs due to data assimilation) and partitioning coefficients.

The spatial patterns from the carbon density-driven InTEC_DA model showed consistency with those from the InTEC_euc model. The results also indicated that eucalyptus plantations with a high carbon sequestration capacity predominantly occurred in management-intensive areas (Figure 12 and Figure 16). Conversely, regions exhibiting lower carbon sequestration capacities were situated in areas receiving limited management interventions. While the spatial distribution of carbon sources showed no clear regularity, carbon sources were primarily concentrated where logging occurred after 2015, with these regions typically experiencing more than two deforestation events during the study period.

4. Discussion

4.1. The Performance of Improved InTEC Model

The NPP- and carbon density-driven InTEC models exhibited systematic overestimation and persistent growth trends in the simulated carbon density, coupled with underestimations of carbon density change, primarily due to unaccounted multi-rotation eucalyptus management cycles and discrepancies in input data accuracy. In contrast, the InTEC_euc model driven by NPP and carbon density data demonstrated closer alignment with plot-surveyed eucalyptus carbon stocks. The NPP-driven simulations slightly underestimated actual carbon stocks due to NPP product underestimation biases in eucalyptus plantations [15,16,17]. The carbon density-driven simulations achieved a superior accuracy, particularly when utilizing CD_Jiang data that incorporates age and carbon density relationships through established allometric equations. Conversely, ACD_Yang and ACD_Yan data—employing random forest algorithms for aboveground biomass prediction without age considerations—produced substantial carbon density overestimations. The carbon density–driven InTEC_DA model demonstrated superior accuracy (e.g., when using CD_Jiang data), because during parameter optimization InTEC_DA not only accounts for input data uncertainty but also introduces a calibration function to attenuate heterogeneity among different data sources, thereby further improving model performance; however, due to substantial errors in the ACD_Yan dataset, the simulation accuracy remains somewhat constrained.

Baseline discrepancies in carbon density data directly influence the calibration of the NPP₀ parameter, thereby altering the model’s carbon accumulation rate and overall budget trajectory. Although the InTEC_euc model achieved significant gains in simulating harvested pixels, it continued to overestimate carbon density and underestimate its change in non-harvested pixels; these biases were effectively corrected in the InTEC_DA model by applying functions to adjust the input carbon density, establish a more accurate baseline, and recalibrate NPP₀, markedly improving the precision and reliability of carbon budget simulations. Although the carbon density calculation carried out by the InTEC_DA model is relatively accurate, there are discrepancies in the growth rate of eucalyptus carbon density. For instance, Z. Yu et al. (2020) [42] reported eucalyptus carbon density growth ranging from 4.77 to 9.19 Mg C ha⁻¹ yr⁻¹ under different management intensities, while Wen et al. (2014) [43] found a range of 3.1 to 12.58 Mg C ha⁻¹ yr⁻¹, and Tao et al. (2011) [44] observed fluctuations between 2.68 and 31.62 Mg C ha⁻¹ yr⁻¹. The InTEC_DA model generally underestimates eucalyptus carbon density growth, particularly when the growth exceeds 15 Mg C ha⁻¹ yr⁻¹. This discrepancy may be attributed to site conditions, management practices, and measurement errors in eucalyptus plantations.

Compared to alternative models, the InTEC_DA model demonstrated superior performance in simulating carbon budgets for eucalyptus plantations at the plot scale, while maintaining robust spatial-scale predictive capabilities. Several process-based models have been used to simulate the carbon budgets of eucalyptus plantations, including the 3-PG model [45], the Forest-DNDC model [46], and the ECOSMOS model [47] (

Table 4. Comparison of the ability of four process-based models to predict carbon stock in eucalyptus plantations (rRMSE).

Model	Validated Variable	rRMSE (%)
3-PG	Aboveground carbon stocks	15.70
Forest-DNDC	Total aboveground C	17.88
InTECDA	Carbon density	18.25
ECOSMOS	Total stem biomass	29.57

). Although validation datasets preclude direct model comparisons, the 3-PG model achieved the highest accuracy through region-specific parameterization of eucalyptus growth dynamics and the incorporation of thinning practices. Forest-DNDC and InTEC_DA simulations showed marginally lower accuracy than 3-PG, primarily due to the exclusion of thinning operations and the absence of calibrated species-specific growth parameters for InTEC_DA. Although the ECOSMOS model has developed a dedicated module and adjusted its parameters, its results still require further optimization. Despite lacking specialized parameter calibration or thinning regime integration, the InTEC_DA model effectively simulates eucalyptus plantation carbon budgets using essential spatial inputs, maintaining sufficient predictive accuracy for Chinese plantations.

4.2. Carbon Budgets of Eucalyptus

The carbon density-driven InTEC_euc simulations (19.56 Mg C ha⁻¹ yr⁻¹) aligned closely with the measured NPP in Mozambican Manica eucalyptus plots (19.71 ± 1.30 Mg C ha⁻¹ yr⁻¹) [48], and were slightly lower than that in New South Wales, Australia (22.44 Mg C ha⁻¹ yr⁻¹) [17] while exceeding Guangxi plantation observations (16.89 Mg C ha⁻¹ yr⁻¹) [28]. The InTEC_DA simulations (17.80 Mg C ha⁻¹ yr⁻¹) moderately surpassed Guangxi’s field NPP values yet remained below both Mozambican Manica and New South Wales benchmarks. NPP-driven InTEC_euc simulations systematically underestimated multi-year NPP due to inherent input data biases (NPP values < 17 Mg C ha⁻¹ yr⁻¹) compared to empirical measurements.

Carbon budgets are influenced not only by vegetation cover and LAI but also by the combined effects of forest management practices, soil properties, and climatic factors. Cleverly et al. (2020) [49] likewise demonstrated that variation in NEP is influenced by multiple factors, including species, climate, under-story composition, and management. In Brazilian eucalyptus plantations with a 6-year rotation period, NEP increased from 9.93 Mg C ha⁻¹ yr⁻¹ to 14 Mg C ha⁻¹ yr⁻¹ between the second and third years [50]. Australian eucalyptus plantations in Victoria transitioned from carbon sources to sinks approximately two years post-establishment [51]. Although the carbon density-driven InTEC_euc and InTEC_DA simulations replicated NEP levels comparable to Brazilian observations and mirrored source–sink transition timelines similar to those in Victoria, under short-rotation harvest regimes NEP increases within individual rotations but declines markedly over successive rotations. In the short term, rapid return of residues—branches, leaves, and roots—temporarily enhances soil carbon inputs; however, frequent soil disturbances accelerate residue decomposition and carbon mineralization and amplify carbon losses via erosion and leaching, progressively undermining the soil’s carbon sequestration capacity and increasing soil carbon release [3,52]. This mechanism not only limits the sustained enhancement of long-term NEP but also constrains the growth of NBP. Simulated NBP consistently lagged behind NEP (by 0.84 Mg C ha⁻¹ yr⁻¹ for InTEC_euc and 0.77 Mg C ha⁻¹ yr⁻¹ for InTEC_DA, respectively), primarily due to harvesting. Both InTEC_euc and InTEC_DA identified multi-rotation eucalyptus plantations as persistent carbon sinks, aligning with findings by Tong et al. (2020) [53], who reported that forests with short rotation periods are carbon sinks. Eucalyptus plantations typically function as annual carbon sinks, though harvesting can reduce their carbon sink capacity, potentially transforming them into carbon sources, as noted by A. Rodrigues et al. (2011) [54].

4.3. Limitations and Potential Improvements

While the carbon density-driven InTEC_DA model’s outputs moderately aligned with field-measured eucalyptus carbon density, temporal changes in carbon stocks were consistently underpredicted. The observed biases originated from systemic inaccuracies in carbon density input data and potential flaws in data assimilation parameter configurations, collectively limiting the model’s ability to correct errors effectively. Previous studies have demonstrated that incorporating the Kalman filter algorithm can significantly improve soil respiration rate data accuracy, thereby enhancing the InTEC model’s performance in NEP estimation [55]. Future research should prioritize (1) establishing additional eucalyptus plots and eddy-covariance towers within the study area, integrating LiDAR point clouds and high-resolution UAV imagery to build a multi-scale, multi-source dataset, and performing systematic plot-to-regional scale validation to comprehensively improve the model’s applicability and generalizability and (2) integrating advanced data assimilation to refine biomass inputs and recalibrate InTEC_DA parameters based on data characteristics, thereby improving the accuracy of eucalyptus plantation carbon budget simulations (carbon density, NPP, NEP, NBP). (3) Although InTEC can simulate soil carbon dynamics, this study validated only aboveground carbon density, and future work should incorporate soil carbon monitoring data [56] and optimized the corresponding parameters [57] to fully evaluate the model’s performance in simulating the complete forest carbon budget.

5. Conclusions

We simulated the carbon budgets of eucalyptus plantations from 2003 to 2023 using distinct datasets (NPP and carbon density) to drive two models (InTEC_euc and InTEC_DA). The results revealed significant discrepancies in simulated NPP, NEP, and NBP between the NPP- and carbon density-driven models, with the fluctuation range strongly dependent on the driving data. NPP-driven InTEC model systematically underestimated carbon budgets, whereas carbon density-driven implementations exhibited pronounced overestimation. The InTEC_euc model partially mitigated these biases, with carbon density-driven model outperforming NPP-driven. InTEC_DA alleviated overestimation biases, achieving optimal carbon density simulations (R² = 0.72, MAE = 9.93 Mg C ha⁻¹, RMSE = 11.94 Mg C ha⁻¹, rRMSE = 18.25%), and yielding derived NPP, NEP, and NBP values of 18.36, 10.50, and 9.68 Mg C ha⁻¹ yr⁻¹ respectively. The InTEC_DA model enables high-resolution carbon budget simulations of eucalyptus plantations (2003–2023), providing a scientific basis and technical support for sustainable management that is aligned with carbon neutrality targets.