## 4 Discussion
### Comparison between This Research and Existing Research  
The ANN-PM model of this study combines ML methods and the PM equation, and the remote sensing data of inputting into ANN contains a recently proposed NIRv index, which can be used to reflect the photosynthetic capacity and water status of the surface vegetation. Combining NIRv with ML and the PM equation shows great advantages in estimating cropland ET. [PERSON] et al. [19] used an ML method (ANN) and PM equation to estimate ET, but the study used soil moisture data that is difficult to obtain, which limits the application of the model in a large-scale and long-term series. [PERSON] and [PERSON] [59] combined the PM equation with three ML methods (K nearest neighbor algorithm, ANN, and Adaptive Boosting model) to estimate the ET using available weather input data with four different scenarios (temperature, solar radiation, wind speed, and relative humidity). They showed that using the combination of four data scenarios performs better than any other combinations. The above two studies are based on the theoretical framework of the PM equation and use ML methods. However, the first study uses soil moisture data that is not feasibly accessed on a regional scale, and the second uses only meteorological data, which is only applicable in a limited area. Compared with the above two studies, we combined meteorological data with remote sensing data to estimate ET. The fitting effect is better, and accuracy is improved. The model tested was applicable to a wide range of environmental gradients. [PERSON] et al. [60] used a process and PM-based ET model, the MOD16 algorithm, to estimate ET for cropland sites (US-Tw2, US-Tw3, and US-Twt). The results showed that the site US-Tw2 has a higher R\({}^{2}\) (0.72) than US-Tw3 and US-Twt. In our study, we evaluated the performance of our ET models at three cropland sites (US-Tw2, US-Tw3, and US-Twt), respectively. Compared with [PERSON] et al.'s [60] study, our models at the three sites all show higher accuracy (R\({}^{2}\) = 0.74-0.86). Our hybrid model, based on ML and PM, can perform better than the model based on the process and PM equation. [PERSON] et al. [61] used the PM equation to estimate ET in semi-arid areas by introducing a simple relationship between surface resistances (r\({}_{\text{c}}\)) and verified the model at flood and drip irrigation sites. The results showed that the R\({}^{2}\) of these two sites were 0.76 and 0.70, respectively, and the RMSEs were 22 and 23 W m\({}^{-2}\), respectively. [PERSON] et al. [62] compared the performance of the PM equation and self-optimizing nearest neighbor algorithm (CCA-k-NN) in estimating ET. The results showed that the performance of CCA-k-NN was comparable with PM (R\({}^{2}\) = 0.8, RMSE = 24.01 W m\({}^{-2}\), MAE = 18.06 W m\({}^{-2}\)). The above studies only used the PM equation to estimate cropland ET. Our study combines ML methods with the PM equation to estimate cropland ET (R\({}^{2}\) = 0.84, RMSE = 17.40 W m\({}^{-2}\), MAE = 12.41 W m\({}^{-2}\)), the estimating accuracy obtained in this study is better, and the physical mechanism of the PM equation can ensure that the simulation result is always within the range of potential evapotranspiration.