# Desertification Mitigation in Northern China Was Promoted by Climate Drivers after 2000
## 2 Dataset and Methodology
### Methods  
In this study, we studied desertification using trends in three NPP factors that were representative of the roles of different factors. A flowchart of the methodological approach is shown in Figure S1. The CASA model was employed to calculate the actual NPP (ANPP). The CASA model is an ecological model that utilizes satellite, meteorological, and surface data to estimate light-use efficiency [62; 63]. This model has been extensively employed in China [64; 65; 66]. ANPP represents NPP from climatic factors and human activities and is essentially equivalent to the NPP from the GLASS based on [PERSON] scores [67], [PERSON]'s correlation coefficient, linear fitting, etc. (Figure S3).  
In the CASA model, ANPP is calculated by converting the absorbed photosynthetically active radiation (_APAR_, g C MJ\({}^{-1}\)) into plant biomass:  
\[ANPP(x,t)=APAR(x,t)\times\varepsilon(x,t) \tag{1}\]  
where \(\varepsilon(x,t)\) denotes light-use efficiency, the spatial location is denoted by \(x\), and \(t\) denotes time. More detailed calculations of _APAR_ and \(\varepsilon\) and the parameter settings can be found in the Supplementary Materials (Method S1).  
This study calculated a potential NPP (PNPP) that was generated only from climate drivers using the modified Thornthwaite memorial model [68; 69]. The calculation of PNPP was expressed as follows:  
\[PNPP(x,t)=3000\times\left[1-e^{-0.0009695(V(x,t)-20)}\right] \tag{2}\]  
where \(V(x,t)\) stands for the average annual actual evapotranspiration (mm). A detailed calculation of PNPP is presented in the Supplementary Materials (Method S2).  
The human-induced loss of NPP (HNPP), which reflects the impacts of human activities on vegetation productivity, is defined as the difference between _PNPP_ and _ANPP_:  
\[HNPP=PNPP-ANPP \tag{3}\]  
A flowchart of the implementation details of the CASA and modified Thornthwaite models used to calculate ANPP, PNPP, and HNPP can be seen in the Supplementary Materials (Figure S2).  
The impacts of climate drivers and human activity on NPP can be attributed according to the linear trends (\(S\)) of NPP, i.e., ANPP (\(S_{ANPP}\)), PNPP (\(S_{PNPP}\)), and HNPP (\(S_{HNPP}\)), which are calculated as follows:  
\[S=\frac{(\sum_{i=1}^{n}i\times NP_{i})-\sum_{i=1}^{n}i\times\frac{1}{2}\sum_{ i=1}^{n}NP_{i}}{\sum_{i=1}^{n}i^{2}-n\left(\frac{1}{n}\sum_{i=1}^{n}NP_{i} \right)^{2}} \tag{4}\]  
where \(i\) represents the sequential numbering of years, commencing with 1 for the year 1984, 2 for the year 1985, and so on (\(i=1,2,\ldots 31\)), aligning with the study period. \(NPP_{i}\) symbolizes the NPP value for the \(i\)th year.  
Generally, a positive trend in ANPP (\(S_{ANPP}>0\)) means that desertification mitigation occurred, while a negative \(S_{ANPP}\) (\(S_{ANPP}<0\)) indicates that vegetation degradation and desertification exacerbation occurred. A positive \(S_{PNPP}\) (\(S_{PNPP}>0\)) indicates that climate drivers benefited vegetation growth and contributed to desertification mitigation, whereas a negative \(S_{HNPP}\) (\(S_{HNPP}<0\)) means a decrease in human-induced vegetation deterioration; in other words, human activity contributed to desertification mitigation and vice versa. Detailed criteria for assessing desertification mitigation or exacerbation and the contributions of climate drivers and human activity are outlined in Table 2.