## 2 Materials and Methods
### Methodology
#### 2.3.2 NEP, WUE, and CUE  
The net ecosystem productivity (NEP) was proposed by [PERSON] [42] in 1978, considering the NEP as the NPP minus heterotrophic respiration.  
\[NEP=NPP-R_{H} \tag{5}\]  
where \(NEP\) is the net ecosystem productivity, \(NPP\) is the net primary productivity, and \(R_{H}\) is the heterotrophic respiration.  
Heterotrophic respiration is calculated by the temperature- and precipitation-based carbon emission regression equation proposed by [PERSON] et al. [43]. This equation model has been widely validated in Northwest China and Central Asia [8; 44; 45], so it is used in this study. The equations are as follows:  
\[R_{H}=0.22\times(\exp(0.0913\times TEM)+\ln(0.3145\times PRE+1))\times 30\times 46.5\% \tag{6}\]  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Form** & **Degree (Level or Extent)** & **DSI** \\ \hline D5 & Extreme drought & \(<\)\(-\)1.50 \\ D4 & Severe drought & \(-\)1.50—1.20 \\ D3 & Moderate drought & \(-\)1.19—0.90 \\ D2 & Mild drought & \(-\)0.89—0.60 \\ D1 & Incipient drought & \(-\)0.59—0.30 \\ WD & Near normal & \(-\)0.29–0.29 \\ W1 & Incipient wet & 0.30–0.59 \\ W2 & Slightly wet & 0.60–0.89 \\ W3 & Moderately wet & 0.90–1.19 \\ W4 & Very wet & 1.20–1.50 \\ W5 & Extremely wet & \textgreater{}1.50 \\ \hline \hline \end{tabular}
\end{table}
Table 2: DSI classification.  
where _TEM_ is temperature, _PRE_ is precipitation, 30 is because monthly data were used, and 46.5% is the fraction of carbon emissions released by microbial respiration.  
In this study, the CUE is the ecosystem carbon use efficiency [21]. Therefore, the WUE is also calculated by the NEP. The formula is as follows:  
\[CUE=\frac{NEP}{GPP} \tag{7}\]  
\[WUE=\frac{NEP}{ETa} \tag{8}\]  
where _CUE_ is the carbon use efficiency, _WUE_ is the water use efficiency, _GPP_ is the gross primary productivity, and _ETa_ is the actual evapotranspiration.  
For the MODIS productivity data, [PERSON] et al. [46] deployed a close-path eddy covariance (CPEC) flux tower in the eastern foothills of the Taihang Mountains in the MRYR, and found that the CPEC-observed GPP correlates well with the MODIS GPP (R\({}^{2}\) = 0.69, \(p\) < 0.01); for the MODIS evapotranspiration data, [PERSON] et al. [47] used measured data for the Han River basin near the MRYR for a correlation analysis with MOD16 products, and the correlation coefficients were all above 0.87. Therefore, we believe that the MODIS data are reliable for use in this study area. In addition, to give more credibility to our findings, relevant studies of NEP, WUE, and CUE based on MODIS products are summarized [8; 44; 45; 46; 47; 48; 49; 50; 51; 52; 53] (Table 3). MODIS satellite data can be effectively used in studies related to NEP, WUE, and CUE due to its high spatial and temporal resolution. Thus, MODIS productivity and evapotranspiration products are used in this study.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Study** & **Model Used** & **Location** & **Study Period** & **Key Results** \\ \hline [PERSON] et al. [48] & NEP = NPP \(-\) R\({}_{\rm H}\) & Yellow River Basin & 2000–2020 & (1) & The total amount of NEP shows a general upward trend; \\  & & Yellow Basin & 2000–2020 & There is uncertainty about the development of NEP. \\  & & & & (1) & The NEP in the QLM significantly increased during the study period; \\  & & & & (2) & Natural environmental factors (e.g., elevation and soil type) and climatic factors (e.g., temperature and precipitation) are the main determinants of the spatial distribution of NEP. \\  & & & & (1) \\ [PERSON] et al. [45] & Vegetation production model; NEP = NPP \(-\) R\({}_{\rm H}\) & China Grassland & 2010–2020 & \\  & & & & (2) \\ [PERSON] et al. [8] & CASA model; NEP = NPP \(-\) R\({}_{\rm H}\) & Central Asia & 2001–2019 & (2) \\  & & & & (1) \\ [PERSON] et al. [49] & WUE = GPP/ETa; BESS model & Global & 2000–2014 & \\ \hline \hline \end{tabular}
\end{table}
Table 3: NEP/WUE/CUE-related research.