## 4 Discussion
\begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Method**} & \multirow{2}{*}{**Mean**} & \multicolumn{6}{c}{**Forward**} & \multicolumn{6}{c}{**Backward**} \\ \cline{3-10}  & & & **Season 1** & **Season 2** & **Season 3** & **Season 4** & **Season 1** & **Season 2** & **Season 3** & **Season 4** \\ \hline \multirow{3}{*}{ASDMTE} & \(R^{2}\) & 0.758 & 0.857 & 0.831 & 0.728 & 0.628 & 0.595 & 0.851 & 0.802 & 0.770 \\  & (0.443) & (0.593) & (0.381) & (0.396) & (0.174) & (0.360) & (0.496) & (0.653) & (0.488) \\  & RMSE & 0.067 & 0.051 & 0.061 & 0.074 & 0.058 & 0.088 & 0.069 & 0.043 & 0.094 \\  & (0.021) & (0.010) & (0.013) & (0.017) & (0.014) & (0.018) & (0.014) & (0.005) & (0.075) \\  & \(R^{2}\) & 0.735 & 0.890 & 0.810 & 0.642 & 0.588 & 0.576 & 0.851 & 0.790 & 0.732 \\  & (0.431) & (0.656) & (0.371) & (0.394) & (0.185) & (0.313) & (0.415) & (0.616) & (0.494) \\  & RMSE & 0.068 & 0.045 & 0.062 & 0.077 & 0.057 & 0.089 & 0.064 & 0.045 & 0.106 \\  & (0.020) & (0.008) & (0.013) & (0.012) & (0.012) & (0.016) & (0.010) & (0.007) & (0.078) \\  & \(R^{2}\) & 0.313 & 0.425 & 0.198 & 0.268 & 0.422 & 0.239 & 0.211 & 0.412 & 0.332 \\ SRDRN & (0.088) & (0.177) & (0.067) & (0.063) & (0.123) & (0.075) & (0.040) & (0.094) & (0.067) \\  & RMSE & 0.088 & 0.177 & 0.067 & 0.063 & 0.123 & 0.075 & 0.040 & 0.094 & 0.067 \\  & (0.083) & (0.131) & (0.060) & (0.060) & (0.108) & (0.067) & (0.046) & (0.098) & (0.098) \\  & \(R^{2}\) & 0.106 & 0.199 & 0.139 & 0.056 & 0.040 & 0.079 & 0.070 & 0.143 & 0.124 \\ dissever GAM & (0.046) & (0.155) & (0.055) & (0.015) & (0.013) & (0.018) & (0.009) & (0.068) & (0.038) \\  & RMSE & 0.213 & 0.359 & 0.130 & 0.161 & 0.280 & 0.172 & 0.131 & 0.293 & 0.181 \\  & (0.039) & (0.058) & (0.012) & (0.030) & (0.055) & (0.052) & (0.014) & (0.045) & (0.044) \\  & \(R^{2}\) & 0.095 & 0.173 & 0.108 & 0.067 & 0.031 & 0.087 & 0.062 & 0.121 & 0.113 \\ dissever LM & (0.040) & (0.133) & (0.047) & (0.015) & (0.013) & (0.017) & (0.008) & (0.048) & (0.037) \\  & RMSE & 0.214 & 0.362 & 0.130 & 0.161 & 0.279 & 0.170 & 0.131 & 0.295 & 0.181 \\  & (0.039) & (0.059) & (0.012) & (0.031) & (0.055) & (0.051) & (0.013) & (0.045) & (0.044) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Image-wise \(R^{2}\) and RMSE from downscaling (by method); \(R^{2}\) is presented as Max (Mean), and RMSE is presented as Mean (SD). predictions. Essentially, the target fine-scale variable can be estimated by the coarse-scale variable as well as its own temporal lagging, adjusting for geographic features, location and time. By defining the downscaling problem as above, the ASDM/ASDMTE approach was able to take advantage of both the within-scale temporal associations in the fine-scale data, and between-scale spatial associations, which allow it to have more information with which the neural network can learn better than just using the between-scale spatial relationships. This richness in predictive information is especially important in a situation where data are limited, since it can enable the model to be trained on a short period of overlapping data without requiring point-to-point matching of the fine- and coarse-scale images. This setting also enabled the use of transfer learning (through ASDMTE) by leveraging the within-scale temporal associations in the coarse-scale data, which had a much longer time series. Typically in downscaling only the temporally overlapping coarse- and fine-scale data can be used for modeling. However, in our case we wanted to downscale a longer time series, and we were able to use transfer learning to learn from all (2000-2018) coarse-scale MERRA-2 data by training \(\hat{g}\) and transferring it to enhance the downscaling model. ASDM/ASDMTE suffers from the same assumption of stationarity as other downscaling methods, that is it assumes the statistical association between coarse- and fine-scale data does not change outside of the model training time [51; 52]. In addition, we may need to further assume stationary of within-scale temporal associations (i.e., temporal lags) used in the model.