## 5 Discussion
Improved results of DAM and yield estimation were obtained in Hengshui City in 2017 after utilizing the modified GPP estimation model (ACPM). Compared with the DAM and yield results based on GPP1 and GPP2 models, the results based on the ACPM model were significantly increased. Compared with the field data, the simulated DAM and yield results were consistent with the actual distribution in Hengshui City. The error of DAM was <10%, and the error of yield was <12%. Similarly, based on the GPP estimation in Boreal Ecosystem Productivity Simulator (BEPS), [PERSON] et al. (2017) simulated the winter wheat yield with mean relative error of 4.6% in the North China Plain, but this model hardly satisfied the practical production, owing to many input parameters (e.g., weather condition). A biomass relative error of 28% was reported in Southwest France after coupling formosat-2 data with a light-use-efficiency algorithm for the yield estimate ([PERSON] et al., 2017). In comparison with this result, the DAM results in the current study showed an improved accuracy to some extent. Simultaneously, other empirical models from the MODIS NDVI or EVI time series data forecasted a winter wheat yield in the USA or Hungary within 10% of the official reported yield, 2-6 weeks prior to harvest or 7-10 days before the corn silking stage, which was comparable with our results ([PERSON] et al., 2017; [PERSON] et al., 2017; [PERSON] et al., 2017). However, those approaches were hard to apply in other regions. Introducing the crop growth monitoring system into the China Agriculture Remote Sensing Monitoring System, [PERSON] et al. (2017) reported a more than 88% accuracy of the yield forecasting for the winter wheat in the North China Plain. This result was comparable with our result of the yield estimation. [PERSON] et al. (2017) performed the comparative analysis of MODIS EVI and NDVI time series data for the rice yield estimation and the EVI-based model obtained the higher accuracy with a RMSE of 6.9-8.1%, which was a little better than our result. However, the accuracy of the forecasting method for county or state areas would become less reliable for small areas, and few literature focussed on the quantitative estimation of the yield at the field scale using the satellite data ([PERSON] et al., 2017; [PERSON] et al., 2017). In the current study, our results were verified by in situ yield data, and the accuracy was comparable to the aforementioned studies with acceptable estimation yields. [PERSON] et al. (2017) used the difference water index (RDWI) from the land satellite thematic map (TM) and the NIR band from the MODIS images to predict the winter wheat yield in the North China Plain, and the average relative error between the situ yield and the estimated yield was 10.11%,which was comparable with our results. [PERSON] et al. (2018) compared the performance of three modeling algorithms, namely, the Random Forest (RF) machine-learning algorithm, the RF algorithm with support vector regression (SVR), and artificial neural network (ANN) machine-learning algorithms, for the wheat-biomass estimation based on the 15 VIs from the environment and disaster reduction small satellites (H)-CCD) images, the RF model obtained the more accurate estimation. [PERSON] et al. (2018) compared the accuracy of the narrow band vegetation indices and red-edge position for the winter wheat biomass estimation and the partial least square regression method, based on the combination of the band depth ratio (BDR), and the optimal NDVI-like obtained the best estimation result with a RMSE of 1.77 t/ha, which was clearly higher than our result. Using the step-wise regression, [PERSON] et al. (2018) compared the accuracy of different indexes (e.g., SAVI, EVI, NDVI and MSAVI from MODIS images) for the wheat yield-estimation in the irrigated Indus Basin, and the SAVI obtained the best estimation result with a R2 of 0.63, which was slightly higher than our result. However, these models were hard to apply in other regions as a result of a lack of the physical mechanism.