## 4 Discussion  
In this study, we evaluated the predictive performance of the deep learning model architecture on county-level rice yields. Remote sensing data and climate data of the rice growing period from 2000 to 2019 in Hubei Province, China, were used. On this basis, the effect of spatial heterogeneity was taken into account by adding the dummy variable of county numbering together as an input variable for prediction. We converted the remote sensing images into normalized 32-bin histograms based on GEE, which can facilitate the input of deep learning models. We designed and trained three different deep learning model architectures: CNN, ConvLSTM and CNN-LSTM. We obtained the model architecture with the best prediction performance by tuning the parameters. Data from 2000 to 2016 were used for training and validation, and data from 2017 to 2019 were used to test the predictive power of the model. Among these model architectures, the CNN-LSTM hybrid model has the best prediction performance. The prediction effects of the three model architectures are given in Section 3.1. The CNN-LSTM hybrid model has the best performance in the three evaluation metrics of root mean square error RMSE, mean absolute error MAE and correlation coefficient R. Compared with the CNN model and the ConvLSTM model, the RMSE of the CNN-LSTM model was reduced by 20.4% and 46.5%, the MAE was reduced by 19.9% and 54.5%, and the correlation coefficient R was improved by 9.88% and 29.5%, respectively. The results showed that the prediction performance of all three model architectures was significantly improved by adding the dummy variable, which represents spatial heterogeneity. After adding the dummy variable, RMSE decreased by 27.5% and 20.4%, MAE decreased by 18.4% and 20.0%, and the correlation coefficient R improved by 7.6% and 16.1%, respectively. The inclusion of dummy variable is very effective in predicting yield. Deep learning model architectures are widely used in the field of crop yield prediction. Among the most frequently applied models are CNN models and LSTM models. Many studies have combined CNN and LSTM to improve the accuracy of crop yield prediction. Positive feedback has already been received. [PERSON] proposed a hybrid CNN-LSTM model architecture to predict U.S. county-level soybean yields using MODIS surface reflectance and surface temperature, as well as weather data. The CNN-LSTM hybrid model was superior in yield prediction for each year from 2011 to 2015. The average RMSE of the CNN-LSTM hybrid model was reduced by about 8.24% and 9.26%, respectively, compared to the single CNN and LSTM [31]. [PERSON] used the MODIS time series of surface reflectance, surface temperature and evapotranspiration as input datasets to test the prediction performance of three algorithms: random forest, 3D-CNN and CNN-LSTM. The results showed that for county-level analysis, the CNN-LSTM model had the highest accuracy. The average percentage error was 10.3% and 9.6% for corn and soybeans, respectively [48]. [PERSON] predicted crop yields for the Midwestern states of the United States. CNN, LSTM, CNN-LSTM and CNN-LSTM integrated model architectures were tested using MODIS surface reflectance, surface temperature and humidity as input data. The results showed that the model architecture of two CNN-LSTM ensembles performed best in predicting annual soybean yields. It improved RMSE by 31% [49]. [PERSON] used NDVI, EVI, surface temperature and soil moisture as feature variables to train and predict corn yields in the United States from 2001 to 2018 based on a CNN-LSTM hybrid model. The results showed that the hybrid model had the smallest prediction error [24]. In the comparison experiments, we found that the ConvLSTM model had the worst prediction effect, even inferior to the prediction effect of a single CNN model. [PERSON] used a CNN model to extract spatial features before using ConvLSTM, and the extracted features were passed to ConvLSTM to extract temporal features [30].