*2.2. Data*

#### 2.2.1. Remotely Sensed Crop Information

The remotely sensed crop information we used in this study includes maize distribution maps and vegetation indices (VIs) data. We used annual maize cultivation areas over the study region in the period 2010 to 2015, which were estimated by Xun, et al. [37] and have users' accuracies greater than 80%. The remotely sensed VIs were required in the RS crop model to simulate the actual yield. We used the Moderate Resolution Imaging Spectroradiometer (MODIS) normalized difference vegetation index (NDVI), enhanced vegetation index (EVI), and LAI in this study. NDVI and EVI data with 1 km and 16- day resolution, retrieved from MOD13A2 and MYD13A2 products (available through https://earthdata.nasa.gov/, accessed in 3 May 2020), were used. As the study area is large enough and the typical maize planted region is usually larger than 1 km2, the used images with 1 km resolution could capture the main spatial characteristics of maize in the study area. The retrieved data were preprocessed in terms of the following procedures before use to remove unreliable data and noise:


**Figure 1.** The study region (North China Plain) and reference region (Rongcheng county and Dingxing county). The reference region is a county, where most of the croplands were cultivated with summer maize, and we obtained a reference LAI time-series curve by averaging the LAI time series of all maize pixels retrieved from MODIS products in the reference region (Section 2.3.4). The reference LAI time series was an important factor for computing the Yp of maize (Section 2.3.4).

The LAI of maize was not directly retrieved from the MODIS product as crop LAI was reported to be significantly underestimated by the MODIS product. In this study, maize LAI was calculated using empirical equations, calibrated by Bai, et al. [38], in terms of EVI. This method was calibrated with samples collected from the US, Europe, and China. Thus,

$$\text{LAI} = \begin{cases} 24.805 \text{EVI}^2 - 15.444 \text{EVI} + 2.382 & \text{before EVI peaking} \\ 2.49 \text{EVI} - 1.236 & \text{after EVI peaking} \end{cases} \tag{1}$$

where LAI was calculated in two ways during one growing season, and we used a quadratic equation before EVI peaking and a linear equation after it.

All the computations involving gridded MODIS data were carried out using the GDAL (the Geospatial Data Abstraction Library) package under the Python2.7 environment.
