## 2 Data and Methods
### Methods
#### 2.3.2 Contributions of Climate Factors and Human Activities to Forest Dynamics  
In the study, to better explore the impacts of human activities and climate changes on forests of different ages, forests were separated into two parts using the forest maps in 2000 and 2017. \(\mathrm{F_{old}}\) refers to the forests that have already existed during 2000-2019, while \(\mathrm{F_{new}}\) refers to those that only appeared after 2000. Figure 2 shows the separation of \(\mathrm{F_{old}}\) and \(\mathrm{F_{new}}\). Forests in YRB that are disturbed by anthropogenic factors from 2000 to 2019 are identified as \(\mathrm{F_{new}}\), including plantations and secondary forests and covering 62.17% of forest area in YRB. \(\mathrm{F_{old}}\) accounts for 37.83% of the forest area in YRB, and is mainly distributed in areas with rich primary forest. Secondly, NPP dynamic is the function of climate factors (including temperature, precipitation, and solar radiation) and other variables such as ecological projects, winds, natural disaster, etc. ; therefore, the contribution of each factor to the interannual variation rate of NPP can be estimated for each pixel using Equation (2). Equation (2), based on partial derivatives, has been widely employed to assess the effects of various climatic factors on evaporation or hydrological dynamics [12; 25; 26]. \[ \begin{split}\mathrm{slope}_{NPP}=\mathrm{C}_{\mathit{com}}+ \mathit{UIF}=\mathrm{T}_{\mathit{com}}+\mathrm{P}_{\mathit{com}}+\mathrm{R}_{ \mathit{con}}+\mathit{UIF}\\ =\partial\mathrm{NPP}/\partial\mathrm{T}\times\mathit{dT}/dn+ \partial\mathrm{NPP}/\partial\mathrm{P}\times\mathit{dP}/dn+\partial\mathrm{ NPP}/\partial\mathrm{R}\times\mathit{dR}/dn+\mathit{UIF}\end{split}  \tag{2}\]  
where \(\mathrm{slope}_{NPP}\) refers to the inter-annual variation trend of NPP. \(\mathrm{C}_{\mathit{com}}\), \(\mathrm{T}_{\mathit{com}}\), \(\mathrm{P}_{\mathit{com}}\), and \(\mathrm{R}_{\mathit{con}}\) represent the contributions of climate, temperature, precipitation, and solar radiation to the inter-annual NPP changes, respectively; \(\mathrm{C}_{\mathit{com}}\) is the sum of \(\mathrm{T}_{\mathit{com}}\), \(\mathrm{P}_{\mathit{com}}\), and \(\mathrm{R}_{\mathit{con}}\). \(\mathrm{T}_{\mathit{com}}\) can be calculated as \(\partial\mathrm{NPP}/\partial\mathrm{T}\) which is the partial correlation coefficient between NPP and temperature without the effects of precipitation and solar radiation. \(\mathit{dT}/dn\) is the inter-annual variation rate of temperature, and \(\mathrm{T}_{\mathit{com}}\) is calculated as the product of \(\partial\mathrm{NPP}/\partial\mathrm{T}\) and \(\mathrm{dT}/\mathrm{dn}\). The calculation of \(\mathrm{P}_{\mathit{com}}\) and \(\mathrm{R}_{\mathit{con}}\) is the same as \(\mathrm{T}_{\mathit{com}}\). \(\mathit{UIF}\) is equal to the residual between the \(\mathrm{slope}_{\mathit{NPP}}\) and \(\mathrm{C}_{\mathit{con}}\). In this study, \(\mathit{UIF}\) indicates the change rate of the contribution of unknown factors to NPP. Both human activities and some uncertain natural factors (such as wind, natural disaster, et al.) are contained in \(\mathit{UIF}\). As expressed in previous studies [12; 16], \(\mathit{UIF}\) of \(\mathrm{F_{new}}\) represents the impact of human activities on NPP, namely, \(\mathrm{H}_{\mathit{com}}\) (such as ecology projects and urbanization). Nevertheless, for \(\mathrm{F_{old}}\), disturbances of human activities are minimal and can be ignored by selecting an unaltered natural forest. Hence, \(\mathit{UIF}\) of \(\mathrm{F_{old}}\) represents the effects of other climatic factors (such as vapor pressure deficit, drought, and snowstorm) on forest dynamics, namely, \(\mathrm{O}_{\mathit{con}}\). Besides, the impacts of climate on all forest variations in YRB were achieved by adding the effects of climate factors to \(\mathrm{F_{old}}\) and \(\mathrm{F_{new}}\).