## 4 Methodology
### Crop Yield Parameters
#### 4.1.1 Indicators of Plant Growth in the Region  
MODIS indices that could be related to plant growth and crop yield--including gross primary production (GPP), enhanced vegetation index (EVI), leaf area index (LAI), fraction of photosynthetically active radiation (FPAR), normalized difference vegetation index (NDVI), and evapotranspiration (ET)--were obtained from the Terra satellite. Figure 2a-f show the averages of these induces for \(11\) counties in the study area for the period 2010-2017. It should be explained that the counties in the middle part of the province have a temperate climate, those in the northern part have a cold climate, and those in the western part have a hot and dry climate. NDVI, the map of which is illustrated in Figure 2a, is a simple graphical index developed for remote sensing analysis to assess the presence or absence of vegetation in an area. This index is computed based on the difference between near-infrared and red-light spectra. NDVI values close to zero (between \(-0.1\) and \(+0.1\)) usually indicate bare rock, sand, or snow surfaces. Higher positive NDVI values (about \(+0.2\) to \(+0.4\)) indicate shrub and grassland cover. EVI has been developed to cover some of the limitations of NDVI and particularly to minimize atmospheric effects and differences in blue and red reflectance [28]. The EVI map of the area is shown in Figure 2b. This index varies in the range of \(-1\) to \(+1.\) LAI, which is plotted in Figure 2c, is the fraction of the surface area of the vegetation canopy to the surface area of the ground it covers. To obtain LAI for farmlands, the leaf area of the plants in one square meter of land should be measured. Another key parameter for the analysis of plant structures in ecosystems and also in crop yield models is FPAR, which provides a lot of information about photosynthesis, energy exchange, and carbon exchange of vegetation covers [29]. The FPAR map of the study area is shown in Figure 2d. FPAR is the fraction of photosynthetically active radiation (light available for photosynthesis) that is absorbed by the plant canopy. ET, the map of which is shown in Figure 2e, is the sum of evaporation and transpiration. This index has been defined because the evaporation from the moist soil surface cannot be easily separated from the transpiration from the plant surface. It has been shown ET has a relationship with crop yield and could be effective in its estimation [30]. The GPP map of the area is shown in Figure 2f. GPP is the ratio of solar energy captured in the plant's sugar molecules during the photosynthesis process, which then plants use for their cellular metabolisms, such as respiration and growth. Soil moisture content is also a key parameter for plant growth. Figure 2g-h shows the surface soil moisture and subsurface soil moisture, whichboth have an impact on planting, germination, harvesting of rainfed plants. In general, soil moisture is the water content in the soil, which can be expressed in terms of mass and volume percentages. In rainfed farming, where crops are not irrigated by any water source other than rain, soil moisture is an important determinant of crop yield, although it is also affected by a wide range of variables. In this study, the soil moisture map of the study area was created using NASA-USDA SMAP Global soil moisture data.  
Figure 2: \(Cont\).  
The sources of the data used in the study and the temporal and spatial resolutions of the collected remote sensing data are given in Table 3. The indices related to plant growth were all obtained from MODIS data of the Terra satellite. The specifications of MODIS data products used in the study are also listed in the table. Given the differences in temporal and spatial resolutions, the satellite images were constructed using the monthly averages of the data.