## 2 Materials and Methods
### Method
#### 2.3.2 Model Construction and Validation  
The machine learning method adopted here is DNN, one of the typical deep learning algorithms. The DNN has the advantage of learning complex, non-linear relationships and extracting intricate information effectively through the process of transforming raw inputs (satellite and climate data here) gradually towards a higher level of information [34; 76; 77], e.g., crop yields in this case. DNN used in this study is a feed-forward neural network (NN) with architectures of multiple fully connected layers. Layers in NN can be categorized into the input, hidden, and output layers, and each layer is composed of a certain number of neurons. The number of input neurons is equal to the number of inputs (three-year means of monthly EVI, SIF, and climate variables). DNN has a large number of hyper-parameters and weights, which require sufficient training data to prevent overfitting and to achieve good model performance. However, due to the low data availability of OCO-2 SIF, it is difficult to collect adequate training, validation, and testing to optimize hyperparameters while testing the trained DNN unbiasedly. Transfer learning (TL) between similar tasks, therefore, becomes desirable for overcoming this problem. Theoretically, this technique enables the leveraging of data and knowledge from a source domain to facilitate modeling in a related target domain, and thus alleviates difficulties and efforts of data collecting and model building [78]. Additionally, the TL technique, unlike the traditional machine learning methods, does not require the training and targeted data in the same feature space and have the same distribution [79]. Based on the rationale of TL, we selected NPP, EVI, and climate data as the source dataset considering the close link between crop NPP and yield. We then built DNNs by transferring the knowledge of employing EVI and climate data to predict NPP to our targeted task of using a similar dataset to predict crop yields. A detailed description of the transferring process is as follows: before the construction and validation of DNN models, all variables were standardized into features with zero mean and unit variance, including yields and NPP of maize and soybean (dependent variables), and three-year means of monthly SIF, EVI, and climate data from May to September (independent variables). Then, we pre-trained the structure of DNN using county-level mean annual NPP and monthly mean EVI from May to September in years 2013 and 2014 to determine hyper-parameters, such as the number of hidden layers and neurons in each layer (Appendix A). The trained network structure is shown in Figure S3. With the DNN architecture obtained above, the weights in each layer were optimized with the training subsets of the targeted dataset (the three-year-mean crop yield, SIF, EVI, and climate data) for corn and soybean, respectively. The repeated five-fold cross-validation (CV) technique [80] was used to separate the targeted dataset into training and testing groups. In each iteration, the targeted dataset was first shuffled randomly and then split into five equal-sized subsets, of which four subsets of data were used for training the model and the remaining one subset was used for testing the model. The training and testing processes were repeated until all five subsets of data had been used for model tests. All estimated corn and soybean yields in all five test processes were combined to produce a complete validation dataset for this iteration. This whole process of five-fold CV was then iterated 100 times. The validation scores of the 100 runs were averaged for further analysis.