## 2 Materials and Methods
### Methodology
#### 2.3.2 Remote Sensing Monitoring and Detection of Cropland Productivity  
(1) Remote sensing estimation of cropland productivity based on VPM  
The Vegetation Photosynthesis Model (VPM) is a light use efficiency model for estimating GPP based on satellite remote sensing data [34; 35]. Its theoretical basis is the light use efficiency theory proposed by [PERSON], which divides the vegetation canopy into photosynthetic and non-photosynthetic parts. NPP is part of GPP, and its formula is as follows:  
\[NPP=GPP\times CUE \tag{1}\]  
\[GPP=\varepsilon_{g}\times FPAR_{chl}\times PAR \tag{2}\]  
\[\varepsilon_{g}=\varepsilon_{max}\times T_{scalar}\times W_{scalar}\times P_ {scalar} \tag{3}\]  
\[T_{scalar}=\frac{(T-T_{min})\times(T-T_{max})}{(T-T_{min})\times(T-T_{max})- \left(T-T_{opt}\right)^{2}} \tag{4}\]  
\[W_{scalar}=\frac{(1+LSWI)}{(1+LSWI_{max})} \tag{5}\]  
\[P_{scalar}=\frac{1+LSWI}{2} \tag{6}\]  
where Carbon Use Efficiency (_CUE_) represents a strictly linear relationship between daytime cumulative photosynthesis and cumulative nighttime respiration based on observation data [36], \(\varepsilon_{g}\) is the light use efficiency, \(FPAR_{chl}\) is the fraction of photosynthetically active radiation (_PAR_) absorbed by leaf chlorophyll in the canopy, \(\varepsilon_{max}\) is the maximum light use efficiency and \(T_{scalar}\), \(W_{scalar}\), and \(P_{scalar}\) are scalars for the effects of temperature, water and leaf phenology on the efficiency of light use in vegetation, respectively [34; 35; 37]. \(T\) is the air temperature, \(T_{opt}\) is the optimal temperature for photosynthesis, \(T_{max}\) is the maximum temperature for photosynthesis and \(T_{min}\) is the minimum temperature for photosynthesis. \(LSWI\) is the land surface water index, while \(LSWI_{max}\) is the maximum LSWI during the growing season [34; 35; 37]. The temporal resolution of the model outputs was 8 days, and the spatial resolution was 500 \(\times\) 500 m.  
The NPP data simulated by the VPM were applied as a basic index that reflects the cropland productivity level. Based on the statistical data on the main crop souring areas in \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Project No.** & **Project Name** & **Construction Year** & **Construction Area (10,000 mu)** \\ \hline Project A & HSF construction project in Fengcun & 2012 & 1.00 \\  & Township, Fengqiu County & 2012 & 2.00 \\ Project B & HSF construction project in & 2012 & 2.00 \\  & Liuguang Town, Fengqiu County & 2012 & 2.00 \\  & HSF construction project in & & \\ Project C & Longtang town (Yegang township), & 2012 & 2.00 \\  & Minquan County & & \\  & MLPF transformation project in & & \\ Project D & Hongniwan Town, & 2011 & 1.00 \\  & Wancheng District & & \\  & HFS transformation project in & & \\ Project E & Hongniwan Town (South), & 2012 & 1.00 \\  & Wancheng District & & \\ Project F & HSF construction project in Jiangliji & 2011 & 2.00 \\  & Town, Xuchang County & & \\ Project G & HSF construction project in & 2012 & 1.00 \\  & Wunvdian Town, Xuchang County & 2013 & 1.00 \\  & HSF construction project in Yegang & & \\  & Township, Minquan County & 2013 & 1.00 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The project regions of sampling survey in Henan Province. counties of Henan Province, the main grain-producing counties with grain sowing areas larger than 80% of the total sowing area were selected as the sample counties. According to the statistics on main crop productivity and NPP data of each sample county, the regression relationship between the cropland productivity and the NPP per unit cropland area was established in order to calculate the cropland productivity (Figure 3) as follows (Cropland productivity = 0.9735 \(\times\) NPP).