## 2 Materials and Methods
### Methodology
#### 2.3.2 Remote Sensing Monitoring and Detection of Cropland Productivity
Time series linear fitting model  
For the project region of the sampling survey, the time series fitting method is used to integrate spatial accuracy information of Landsat-OLI data with a spatial resolution of 30 m and the high temporal information of MODIS data with a spatial resolution of 500 m and a time step of 8 days. Accordingly, the cropland productivity data with a spatial resolution of 30 m and a time step of 8 days were produced [30; 31; 38]. The input data include one pair of coarse resolution (500 \(\times\) 500 m) NPP and fine resolution vegetation index (30 \(\times\) 30 m) calculated from Landsat at time \(k_{1}\) and one coarse resolution NPP at time \(k_{2}\). The output data are predicted as fine resolution NPP at time \(k_{2}\). The time series linear fitting model includes three main steps: (1) Extraction of pure pixels based on a vegetation type map with a resolution of 30 m at time \(k_{1}\); (2) based on pure pixels, the fitting relationship between NPP and EVI at time \(k_{1}\) was obtained; and (3) based on the constructed fitting relationship, we used Landsat EVI to calculate the fine resolution NPP at times \(k_{1}\) and \(k_{2}\). Based on the assumption that the temporal trends of vegetation productivity are similar in the same period for the same type of vegetation and with the same spatial resolution, the formula can be obtained:  
\[m NPP_{30}(k2)=\frac{m NPP_{30}(k1)\times m NPP_{500}(k1)}{m NPP_{500}(k2)} \tag{7}\]  
where \(m NPP_{30}(k2)\) and \(m NPP_{30}(k1)\) represent fine resolution NPP at times \(k_{1}\) and \(k_{2}\), while \(m NPP_{500}(t2)\) and \(m NPP_{500}(t1)\) represent coarse resolution NPPs at times \(k_{1}\) and \(k_{2}\). For more details, see [PERSON] et al. (2018) [31] and Figure 4.  
Figure 3: Relationship between NPP of farmland ecosystems and cropland productivity in Henan Province. 2.3.3. Indicators and Algorithms for Remote Sensing and Evaluation of HSF Construction Effectiveness  
(1) Improvement of cropland productivity level (CPL)  
Increasing the productivity of cropland refers to improving the output capacity of grain or cash crops in the region. It is a direct indicator for measuring the effectiveness of HSF projects. In this study, the change in cropland productivity before and after the construction of the HSF project was selected as an index to measure the level of cropland productivity improvement. The formula for changing cropland productivity is as follows:  
\[\Delta P=P_{2}-P_{1} \tag{8}\]  
where \(\Delta P\) represents the change in farmland productivity, \(P_{2}\) refers to the averaged multi-year farmland productivity of the project area after the HSF project (3 years, not counting the year of project construction) and \(P_{1}\) refers to the averaged multi-year farmland productivity of the project area before the HSF project (3 years, not counting the year of project construction). A positive value of \(\Delta P\) indicates an increase in cropland productivity in the project region, and a negative value indicates a decrease in cropland productivity in the project region. (2) Improvement of disaster resistance ability (DRA)  
The stability of cropland production can reflect the range of cropland productivity fluctuations between years and seasons. It is an index to evaluate the ability of cropland to resist disasters and achieve a stable and high yield after the HSF construction. In this  
Figure 4: The process diagram of estimate 30 m NPP using time series fitting method. study, the difference in improvement level of cropland production stability between normal years and disaster years after the HSF construction is selected as an index to evaluate the improvement level of DRA of cropland after construction.