## 1 Introduction  
The terrestrial ecosystem carbon fluxes include gross primary productivity (GPP), ecosystem respiration (RE), and net ecosystem productivity (NEP). Forest vegetation absorbs carbon dioxide (CO\({}_{2}\)) from the atmosphere through photosynthetic productivity and functions as a huge carbon sink [1]. NEP was originally defined by [PERSON] and [PERSON] as the difference between the organic matter fixed by GPP and the total respiration of the ecosystem [2]. Therefore, the impact of the environment on NEP is determined by the different influences of GPP and RE on environmental factors [3, 4]. Differences in the response of carbon fluxes (GPP, RE, and NEP) to different environmental conditions will lead to shifts in the ecosystem carbon balance from sink to source or source to sink [5]. When GPP and NEP are consistent, they exhibit synchronized changes. This consistency usually reflects a balance between photosynthesis and respiration processes. In such an ecosystem, plants have a higher amount of carbon fixed by GPP, while respiration results in a lower amount of carbon loss, leading to an increase in NEP. However, when GPP and NEP are decoupled, they no longer exhibit synchronized changes [6]. GPP may increase while NEP does not, or even decreases. This is usually due to an increase in ecosystem respiration that offsets the gains in GPP. In a cold temperate climate, the sensitivity of forest ecosystem carbon fluxes to environmental changes, especially temperature and precipitation, makes it an important indicator of broader climate trends. Consequently, it is crucial to understand the carbon cycle and its changes in cold temperate forest terrestrial ecosystems to study carbon dynamics and their influencing factors in these ecosystems quantitatively. In recent decades, several quantitative studies of carbon fluxes in terrestrial ecosystems have been conducted using various approaches, such as inventory methods, eddy covariance (EC) techniques, remote sensing models, terrestrial ecosystem carbon cycle models, and atmospheric inversion methods [7; 8; 9]. Among these, an EC flux tower is a key observation system for the direct monitoring of ecosystem carbon fluxes [10]. The AmeriFlux and FLUXNET networks have been established based on this technique [11]. FLUXNET sites cover most climate zones and biome types, making their observations crucial for the parameterization of process models and the accurate estimation of uncertainties in each component of the carbon cycle [12; 13; 14]. [PERSON] et al. [15] examined net ecosystem exchange data from 15 European forests and confirmed that many of the forest ecosystems were significant carbon sinks, with RE determining the net ecosystem carbon exchange. [PERSON] et al. found that the increase in growing season productivity by spring warmth could be counteracted by water stress resulting from higher evapotranspiration in the summer and carbon loss resulting from higher respiration in the autumn. [PERSON] et al. [16] analyzed the observed flux data in the Qianyanzhou region from 2003 to 2008 and showed that the main factors controlling the interannual variation of NEP in this region were low temperatures from January to March and that GPP was more sensitive to water deficit stress than RE. [PERSON] et al. [17] found that the annual NEP of subtropical and tropical forests in southern China was closely related to variations in annual precipitation, with annual precipitation being the fundamental driver of annual NEP. A longer time series study confirmed that the vapor pressure deficit (VPD) is an important regulator of vegetation carbon fluxes in many ecosystems [18]. [PERSON] et al. [19] found that the vegetation growth process is jointly limited by the combination of air temperature, soil moisture, solar radiation, and atmospheric CO\({}_{2}\), but with varying degrees of influence.