## Data
### Satellite Images  
The MODIS instrument is a satellite sensor operated by the National Aeronautics and Space Administration (NASA) for Earth environmental monitoring onboard the Terra and Aqua satellites with a sun-synchronous orbit. The satellites pass over a specific location at the same local time every day. Terra crosses the equator from north to south (descending path) at approximately 10:30 AM local time. Aqua crosses the equator from south to north (ascending path) at approximately 1:30 PM local time. We obtained the NDVI, LAI, and FPAR products as the indicators of vegetation vitality, biomass, and gross primary production (GPP), from the Aqua MODIS.  
NDVI is a commonly used vegetation index that represents the vitality and greenness of vegetation. We used the MYD13C2 monthly product that has a resolution of 0.05\({}^{\circ}\), instead of the MYD13A1 16-day product with a 500 m resolution because the 16-day 500 m product has many missing pixels due to clouds, particularly in summer. On the other hand, the monthly 0.05\({}^{\circ}\) product has almost no missing pixels through the spatial and temporal smoothing. In general, vegetation greenness changes gradually in the form of a cosine curve over a year, so we converted the monthly product to daily values using the cubic spline method. The LAI, which is calculated using a crop-specific growth coefficient and maximum GPP, can be used as a proxy of the leaf biomass. FPAR is the portion of photosynthetically active radiation absorbed by green vegetation. We obtained LAI and FPAR from the MCD15A2H 8-day  
Figure 1: Input variables for the machine learning (ML) model to retrieve the gridded reference evapotranspiration (ET\({}_{0}\)) in the croplands of South Korea, with the in situ point data from Korea Meteorology Administration (KMA).  
product with a resolution of 500 m, based on a combination of Terra and Aqua products, by choosing the best pixel available from all acquisitions of both sensors within the 8-day period.  
To extract croplands in South Korea, we used the MODIS land-cover type product (MCD12Q1), which was created by the supervised classification using the reflectance of multiple spectral bands, with an annual update over the 500 m grid [36]. According to the classification criteria released by the International Geosphere-Biosphere Programme (IGBP), we extracted the pixels associated with croplands, including type 12 (croplands) and type 14 (cropland/natural vegetation mosaic).  
The Global Precipitation Measurement (GPM) mission comprises an international satellite network that provides the next-generation global observations of rain and snow to elucidate Earth's water and energy cycles [37]. We used the TRMM_3B42_Daily version 7 product, which provides better rainfall estimates than previous versions, with significantly lower bias over complex topography [38]. Precipitation is the supply of water to the land surface, which can be infiltrated and evaporated by soil or transpired by vegetation. Because cumulative precipitation is generally more closely associated with ET\({}_{0}\) than daily precipitation, we used SPI3, which is calculated from the z-score of the empirical cumulative distribution function (ECDF) of 3-month accumulated precipitation.  
\[\mathrm{z}\ =\ \frac{x_{i}-\mu}{\sigma} \tag{2}\]  
where \(x_{i}\) is the ECDF of \(i\)-th day; \(\mu\) is the mean of the entire ECDF; \(\sigma\) is the standard deviation of the ECDF.  
Figure 2: Measurement locations for the reference evapotranspiration (ET\({}_{0}\)) by the Korea Meteorological Administration (KMA). The digits around the red points are the station identification number.