## 3 Results  
### Model Development and Validation  
#### 3.1.1 Performance Validation of the Models  
We built 82 local downscaling models for 82 10 km 16-day aggregated TROPOSIF data corresponding to 82 dates. Figure 2 shows the determination coefficient R\({}^{2}\), RMSE of TROPOSIF and TSIF for training and validation and TROPOSIF mean within the MODIS tile H27V05. For training, there were 34 models with R\({}^{2}\) > 0.85, 34 models with R\({}^{2}\) > 0.75, and 10 models with R\({}^{2}\) > 0.65. For validation, there were 32 models with R\({}^{2}\) > 0.85, 29 modelswith R\({}^{2}\) > 0.75, and 19 models with R\({}^{2}\) > 0.65. Most RMSE were below 0.07 for both training and validation. In general, the R\({}^{2}\) and RMSE for validation were very close to those for training indicating no overfitting occurred. Interestingly, the RMSE has a strong seasonality similar to those of TROPOSIF. RMSE peak in July or August and reach a valley in November or December. One possible reason is that sufficient precipitation in the growing season reduces our models' prediction performance, but in general, our models perform well. We calculated the probability distribution of _SIF_ prediction residuals (Figure 3). We found that the residuals between our TSIF and TROPOSIF were within \(\pm\)0.05 mWm\({}^{-2}\)sr\({}^{-1}\)nm\({}^{-1}\) for the majority of the pixels and the distribution was approximate to the normal distribution. The results suggest that our models predict _SIF_ well. To further estimate the overall accuracy of our method, we then pooled all training data and all validation data, respectively, and drew the scatterplots of TROPOSIF and predicted SIF. As shown in Figure 4, we had a good prediction accuracy with the determination coefficients R\({}^{2}\) = 0.958 and RMSE = 0.053 for training and R\({}^{2}\) = 0.956 and RMSE = 0.054 for validation. For the universal model, R\({}^{2}\) = 0.937 and RMSE = 0.065 were used for both training and validation. Moreover, we also re-aggregated the predicted _SIF_ to 10 km and drew the scatterplots of TROPOSIF and the re-aggregated SIF. As shown in Figure 5, we also had a good prediction accuracy with R\({}^{2}\) = 0.951 and RMSE = 0.058 for our local models and R\({}^{2}\) = 0.933 and RMSE = 0.067 for the universal model. This means that our local models only performed slightly better than the universal model. A similar comparison made by [PERSON] [14] also showed a similar R\({}^{2}\) for the universal and the local models. Figure 2: **(a)** The determination coefficient R\({}^{2}\) and (b) RMSE of TROPOSIF and predicted TSIF for training and validation; (c) The TROPOSIF mean of all _SIF_ pixels within MODIS tile grid H27V05. Figure 4: The scatterplots of TROPOSIF and predicted TSIF for training and validation; (**a,b**) for our local models and (**c,d**) for the universal model. Figure 3: The probability distribution of residuals (TROPOSIF minus predicted TSIF). To further explore the performance advantage of our local models over that of the universal model, we also calculated the temporal correlations of each pixel between TROPOSIF and TSIF, and TROPOSIF and USIF. As shown in Figure 6a, for TSIF, 85% of the pixels have a temporal correlation with R\({}^{2}>\)0.9 and 92% of pixels with R\({}^{2}>\) 0.85. However, for USIF, 79% of pixels R\({}^{2}>\) 0.9 and 92% of pixels had R\({}^{2}>\)0.85; 80% of R\({}^{2}\) of TSIF are greater than R\({}^{2}\) of USIF. This finding suggests that our local models can capture better temporal information in TROPOSIF than the universal model for almost all land cover types within the MODIS tile grid H27V05; a reasonable explanation is that the universal model learns the data features only from the value distribution of the samples and learns the temporal features indirectly from the value changes of samples. In Figure 6a,b, only a small portion of TSIF pixels exhibit slightly lower correlations in the lower left of the images where we found many data gaps caused by cloud contamination.