## 2 Materials and Methods
### Methods
#### 2.3.4 Simulating Potential LAI and Yp  
Temporal variations in LAI of crops fully depend on simulations in CGMs; thus, it is feasible to simulate Yp using a calibrated crop model by removing all field management limits for crop growth in the model. However, not all management factors in an RS-based yield model can be adjusted to the optimum because RS-LAI, as a critical input of the RS-based model, does include environmental stress on crop growth. However, it is still possible to use an RS-based model to simulate Yp if the stress on crop growth represented by actual LAI is removed. Here, we define the LAI time series, representing no environmental stress on crops and leading to potential yielding, as potential LAI (LAI\({}_{\text{P}}\)). RS-LAI derived from the MODIS VI (Equation (1)) may fail in representing the magnitude of LAI\({}_{\text{P}}\) but could capture the variation trend of LAI\({}_{\text{P}}\) in time because the DVS of crops, including maize, primarily depends on the effective accumulative temperature rather than field managements, as represented by existing CGMs [41; 42; 44]. Figure 2 is a scatter plot, with 45 data pairs, for maize yield vs. peak LAI observed during the growing season (PLAI). These data were collected from 21 published and 8 unpublished super-high yield experiments over China. These experiments attempted to optimize all field managements, and the growth of maize was primarily limited by air temperature and solar radiation. Under optimum field managements, maize yield positively correlates with PLAI. When PLAI is greater than 6.6, maize yield tends to saturate at a high level, -20 t hm\({}^{-2}\), and the correlations between PLAI and maize yield become insignificant (Figure 2). This implies that a PLAI greater than 6.6 may be adequate for maize yielding. Based on the above analyses, we proposed using the following steps to calculate LAI\({}_{\text{P}}\) and Yp:  
1. Derive a reference curve (\(C_{\text{RF}}=\left\{\text{LAI}_{\text{RF}}^{(0)},\text{ LAI}_{\text{RF}}^{(2)},\,\ldots,\,\text{ LAI}_{\text{RF}}^{(I_{\text{HV}})}\right\}\)) from the LAI time series within the reference region (Figure 1), where \(I_{\text{HV}}\) denotes the number of days from EM to HV, LAI\({}_{\text{RF}}\) denotes a reference LAI value of a given day. \(C_{\text{RF}}\) has a PLAI greater than 6.6, representing the roughly temporal variation in LAI\({}_{\text{P}}\). We obtain \(C_{\text{RF}}\) using two procedures: (i) Average the LAI time series of all maize pixels retrieved  
Figure 2: Maize yield against growing season maximum leaf area index (LAI\({}_{\text{max}}\)) over China. Red circles denote data retrieved from 21 published [45; 46; 47; 48; 49; 50; 51; 52; 53; 54; 55; 56; 57; 58; 59; 60; 61; 62; 63; 64; 65; 66; 67; 68; 69; 70; 71; 72; 73; 74; 75; 76; 77; 78; 79; 80; 81; 82; 83  
from MODIS VI-based LAI (Equation (1)) by date in 2010 within the reference region (Figure 2) to obtain an LAI curve (\(C_{0}=\left\{\text{LAI}_{0}^{(0)},\text{ LAI}_{0}^{(2)},\text{ }\ldots,\text{ LAI}_{0}^{(h_{\text{HV}})}\right\}\)) for maize; (ii) calculate \(C_{\text{RF}}\) from \(C_{0}\) as \(C_{\text{RF}}=\text{PLAI}_{\text{opt}}\times\frac{C_{0}-\min(C_{0})}{\max(C_{0} )-\min(C_{0})}\), where \(\text{PLAI}_{\text{opt}}\) denotes the optimum PLAI for maize potentially yielding and is expected to be greater than 6.6. In this study, we made a conservative estimate for \(\text{PLAI}_{\text{opt}}\) and set it to 7.5, and this estimate was supported by [PERSON], [PERSON], [PERSON], [PERSON], [PERSON], [PERSON], [PERSON], [PERSON] and [PERSON] [50], who reported \(\text{PLAI}=7.53\) of the maize plants, achieving the highest maize yield (22.5 \(\text{t}\text{h}\text{m}^{-2}\)) record in China. 2.