## 1 Introduction  
Evapotranspiration (ET) is the transport of water vapor to the atmosphere through the evaporation from soil and canopy surfaces and the transpiration from vegetation [1]. ET is an important component of the Earth's energy and water cycles via the interaction between the atmosphere and the land surface in the form of latent heat using net radiation [2]. ET is affected by many agrometeorological variables such as radiation, temperature, humidity, wind, precipitation, and soil moisture. The amount of water transported by ET is generally greater than that by runoff in most agricultural fields [3]. Thus, the amount of irrigation water for the cropland can be determined by the cumulative amount of ET. Potential evapotranspiration (PET) is the possible amount of ET according to climatic and meteorological conditions, assuming a sufficient supply of water [4]. Actual evapotranspiration (AET) is a substantial amount of ET, as the result of the effects of many factors such as vegetation type, the fraction of vegetation cover (FVC), phenological cycle, soil type, soil moisture, irrigation, and drainage, in addition to meteorological conditions [2]. Water management in the croplands includes the maintenance of a suitable level of soil moisture and the adjustment of irrigation water. The accurate information of AET is essential to determine the amount of irrigation water because the AET represents the loss of water in the croplands through soil evaporation and vegetation transpiration. The in situ AET is usually obtained from the eddy covariance [5] that can be measured by the energy and water exchanges between the land surface and the atmosphere on a micrometeorological tower [6]. It is the most scientifically reliable system for the in situ measurement of AET, but the installation and operation of the eddy covariance instruments on the micrometeorological tower require high costs and many efforts [7]. For the sake of convenience, the AET can be calculated by multiplying a crop coefficient (K\({}_{\text{c}}\)) by the reference evapotranspiration (ET\({}_{0}\)) defined as the ET of well-irrigated hypothetical grassland under a specific meteorological condition [2]. Hence, the K\({}_{\text{c}}\) is expressed as the ratio of AET to ET\({}_{0}\). The ET\({}_{0}\) can have a similar physical quantity as PET, but is in a more agricultural context, assuming the calculation of AET using the K\({}_{\text{c}}\)[8]. The ET\({}_{0}\) for a given point can be easily derived from the Food and Agriculture Organization (FAO) version of the Penman-Monteith (PM) equation only using meteorological parameters [3], without the hydrological and physiological factors such as soil moisture and stomatal resistance. While the meteorological input data for the PM equation is usually obtainable, the physiological and phenological properties of the crops are hard to quantify in detail. So, the K\({}_{\text{c}}\) can be a useful method for the estimation of AET in the croplands. Under considerations of the possible use for the AET estimation, an efficient calculation of ET\({}_{0}\) using meteorological data will be of help for many agrometeorological studies. Despite the usefulness of K\({}_{\text{c}}\) in the AET estimation, it is usually confined to a specific point because some of the input data are only obtainable from in situ point observations. However, individual point observations cannot fully represent spatially continuous areas, although ET can vary spatially according to the meteorological and cropland variables. To date, many efforts have been made to retrieve PET, ET\({}_{0}\), and AET over a continuous grid. Most of them tried to expand the point-based calculation of PET, ET\({}_{0}\), and AET to a continuous grid using satellite images and gridded meteorological data with the linkage to the PM equation [9; 10; 11; 12; 13; 14; 15; 16; 17] or the Priestley-Taylor (PT) equation with the empirically derived coefficients fitted for the study areas [18; 19; 20; 21; 22; 23; 24; 25; 26; 27; 28].