## 1 Introduction  
Net ecosystem productivity (NEP) represents the net primary productivity minus the photosynthetic carbon product consumed by heterotrophic respiration and is an important feature of the carbon cycle of forest ecosystems. Given that carbon can also be sent to the atmosphere via combustion, NEP can underestimate the total exchange between the forest and atmosphere when disturbances associated with combustion occur. Further, NEP does not account for the fate of carbon removed from forests via harvest, erosion, or leaching. Nonetheless, NEP is an important component of the net carbon exchange between terrestrial ecosystems and the atmosphere. In recent years, research on forest ecosystem NEP has attracted more and more attention [1; 2; 3; 4]. However, the relationship between the spatiotemporal patterns of NEP and climate change remains uncertain [5; 6; 7; 8]. The impact of climate change on the spatiotemporal patterns of NEP is different in different regions [3; 7; 9]. Therefore, it is important to precisely simulate forest ecosystem NEP and analyze its response to environmental factors. There are many research methods for carbon budgets in forest ecosystems including sample plots [10], micrometeorology [11], remote sensing [12], and simulation models [13]. Model simulation is an important method to study forest ecosystem NEP. Commonly used models include the empirical model, parametric model, and process model [14]. Process models such as integrated terrestrial ecosystem carbon cycle (InTEC), boreal ecosystem productivity simulator (BEPS), biome biogeochemical cycles model (BIOME-BGC), and so forth are based on developing an understanding of ecosystems by simulating the effects of biological processes such as canopy photosynthesis, absorption, transpiration, and soil moisture on net primary productivity (NPP) to reveal the growth of biomass, the interaction of vegetation with environment, and the response mechanism of ecosystems to climate change [15]. Therefore, process model results are more reliable than those of other models. On the other hand, due to the advantages of stability and reliability of repeated measurements, as well as wide-scale and even global coverage, remote sensing technology is one of the most important macroscopic research methods of the carbon cycle [16]. Therefore, remote sensing technology combined with process models, with the advantage of reflecting both the ecological and physiological processes of vegetation, can achieve large-scale simulation of the carbon cycle process, reflect the spatial distribution and dynamic changes of the carbon cycle at regional and even global scales, and effectively solve the problems of spatiotemporal heterogeneity and scale complexity of forest ecosystems, which greatly improves the reliability of terrestrial vegetation carbon cycle estimation [8; 17; 18]. Based on the physiological and biochemical processes of the carbon cycle, InTEC model takes the effects of forest disturbances and changes in forest age into consideration. Forest age has a very important impact on the productivity of forest ecosystems [19; 20], which makes InTEC one of the most advanced models to simulate the spatiotemporal changes of forest ecosystem NEP. Furthermore, the InTEC model can reconstruct the characteristics and driving mechanisms of carbon cycling in past forests and predict the spatiotemporal evolution of carbon cycles in the future [21]. The InTEC model is an integrated model of terrestrial ecosystem carbon cycles which combines the Farquhar photosynthetic model [22], the canopy radiation transfer model, the CENTURY soil model [23], the nitrogen cycle model, the net nitrogen mineralization model of [PERSON] et al. [24], and the _NPP-age_ model [25; 26].