## Materials and Methods
### Remote Sensing Data  
We used remote sensing images from two satellites, i.e., the COMS with the medium ground resolution of 500 m and the RapidEye with the high ground resolution of 6.5 m. The COMS developed by the Korea Aerospace Research Institute (KARI) and launched on 27 June 2010, is a geostationary satellite stationed at an altitude of 3600 km above the Earth's equator and at a longitude of 128.2\({}^{\rm{\textdegree}}\)E. The COMS loads two typical sensors of the GOCI and the MI (Table 2). The GOCI can observe the Korean landscape eight times a day, with eight spectral wavebands mounted on the system. The primary objectives of the GOCI sensor are: (1) to detect, monitor and forecast short-term biophysical phenomena; (2) to analyse the bio-geochemical variables and the cycles; and (3) to identify information on the yellow dust and land classification. The GOCI was predominantly considered to monitor the ocean phenomena, with a Sea-Viewing Wide Field-of-View Sensor (SeaWiFS) spectral band [34]. However, its  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Vegetation Index1** & **Equation2** \\ \hline NDVI [30] & \((R_{800}-R_{660})/(R_{800}+R_{660})\) \\ RDVI [31] & \((R_{800}-R_{660})/\sqrt{R_{800}+R_{660}}\) \\ OSAVI [32] & \((R_{800}-R_{660})/(R_{800}+R_{860}+0.16)\) \\ MTVII [33] & \(1.2(1.2[R_{800}-R_{560}]-2.5[R_{660}-R_{560}])\) \\ \hline \hline \end{tabular}  
* NDVI = Normalized Difference Vegetation Index, RDVI = Re-normalized Difference Vegetation Index, OSAVI = Optimized Soil-Adjusted Vegetation Index, and MTVI = Modified Triangular Vegetation Index. \({}^{I}\)\(R_{800}\), \(R_{660}\), and \(R_{560}\) represent the reflectance values of each waveband (800 nm, 660 nm, and 560 nm).  
\end{table}
Table 1: Vegetation indices used for rice growth phenological stage monitoring and leaf area index estimation.  
high temporal resolution of the observations and vegetation-sensitive spectral wavebands are mostly suitable for land surface-based applications and, more specifically, for monitoring various types of crop information and conditions [23]. In this study, the GOCI is used to determine the cumulative vegetation indices (VIs) in South Korea, since the setup is responsive to vegetation bands (i.e., red and near infrared, NIR).  
RapidEye [35] collects 4 million square kilometres of data per day (Table 2). RapidEye satellite images comprise five spectral wavebands (red, green, blue, red edge, and near-infrared) and are provided commercially using three processing levels: \"Level 1B\" geometrically uncorrected images, \"Level 3A\" ortho-rectified tile images with radiometric, geometric, and terrain corrections, and \"Level 3B\" ortho-rectified, bundle-adjusted images that are larger than the Level 3A products [35]. The Gimje and Buan sites were selected, along with the availability of the RapidEye satellite images (Plant Labs, Inc., CA, USA) for 2014, to perform simulations at the regional scale. For the present study, we obtained radiometrically and geometrically corrected Level 3A images, including the Buan and Gimje sites that were acquired on DOY 149 (29 May), 198 (17 July), 221 (9 August), and 256 (13 September) in 2014. These images contained reflectance values with four different wavebands at 11,700 \(\times\) 7900 pixels with a size of 5 m. The image data were further processed to classify rice paddy field areas using a digitized paddy coverage map from the Korea Ministry of Environment.  
Likewise in the model evaluation procedure, four different VIs (Table 1) were determined and used to project spatiotemporal productivity of paddy rice using the developed crop modelling design discussed in the following section.