## 2 Materials and Methods
### Model Development and Validation  
In this paper, we used Neural Networks (NN) to downscale TROPOSIF. NN is a classical machine learning method that has been successfully used for downscaling SIF, land surface temperature, and soil moisture [13; 14; 16; 26]. NN are a series of computational nodes (called neurons) structured in a single or multi-layer architecture. Every node is connected with all nodes in the previous layer and the next layer. The node values are derived using the activation function (e.g., ReLu) with a pre-activated value, i.e., the weighted sum of all nodes in the previous layer and biases. The NN downscaling model is trained to minimize the loss function to get the best weights and biases [2]. We built local downscaling models for each 10 km 16-day aggregated TROPOSIF using the aggregated MODIS data within the MODIS tile grid of H27V05 which covers the entire Henan Province. The 500 m 16-day aggregated MODIS data were used for _SIF_ prediction. We used the data within the MODIS tile grid of H27V05 rather than only within our study area to ensure an adequate sample size. For each local downscaling model, the training data were normalized by their mean and standard deviation. The validation data and prediction data were also normalized by the same mean and standard deviation. Because our method uses \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Site ID** & **Site Name** & **Longitude** & **Latitude** & **Vegotation Type** \\ \hline US-Bi2 & Bouldin Island Corn & 121.5350 & 38.1090 & cropland \\ US-Ion & Tonzi Randn & 120.9660 & 38.4316 & woody savannas \\ US-Var & Varia Ranch & 120.9507 & 38.4133 & grasslands \\ US-Tw1 & Twitchell Island West Pond & 121.6469 & 38.1074 & permanent wetlands \\ US-Tw4 & Twitchell Island East End & 121.6414 & 38.1030 & permanent wetlands \\ US-Tw5 & Twitchell Island East Pond & 121.6426 & 38.1072 & permanent wetlands \\ \hline \hline \end{tabular}
\end{table} 
Table 1: AmeriFlux eddy covariance sites used in this paper [24]. the data in the same area and time for training and prediction, and the training data and validation data are from the aggregation of data used for prediction, such data have similar features which can reduce the errors introduced by data with different spatiotemporal features and distribution. We used the classic machine learning framework Tensorflow ([[https://tensorflow.google.cn/](https://tensorflow.google.cn/)]([https://tensorflow.google.cn/](https://tensorflow.google.cn/)) (accessed on 25 December 2021)) and set the NN models as a 4-layer network with each hidden layer containing 16 neurons, RMSE as the loss function, Adam as the gradient descent function, learning rate as 0.001, and 40 epochs. In order to prevent overfitting, we also set mindelta = 0.002 and patience = 5 as the early stopping conditions. We first trained a universal model using all TROPOSIF and MODIS data; then, we used it as a pre-trained model to initialize our local models. To train a local model, only TROPOSIF and MODIS data of specific dates were used to generate samples; for example, to train the local model on 12 July 2019, we used the aggregated TROPOSIF and MODIS data on 12 July 2019 (here the date is the first day of 16-day aggregation). We then divided samples into a training dataset (70%) and a validation dataset (30%). Finally, we built the local downscaled models based on these training datasets and validation datasets. We verified the performance of our downscaling models by calculating R\({}^{2}\) and RMSE for training and validation and the probability distribution of our _SIF_ estimation errors following [PERSON] et al. [12]. We also calculated the mean and the 5 th and 95 th percentile of _SIF_ of all pixels from TROPOSIF and TSIF. We also made a pixel-by-pixel comparison of TSIF with TROPOSIF to validate their temporal correlation. In addition, we tested the robustness of our method against overfitting by setting the numbers of the hidden layers from 1, 2, 3, 4, and the numbers of neurons of the hidden layers 8, 16, 32, 64.