# Comparisons of Spatially Downscaling TMPA and IMERG over the Tibetan Plateau
## 3 Results
### Main Results in the Downscaling Procedure Using Random Forest  
Ntree and \(m_{try}\) were the key parameters that affected the predictive performances of the RF model. To determine the optimal selection of parameters, the OOB error rate, as defined in Equation (2), was applied. The OOB error rate was an internal estimate of the predictive performances provided by the bagging model. The values of OOB error usually correlated well with the assessment of the predictive performance obtained from a cross-validation or test set. In addition, using OOB error rate could decrease the computational time required to tune RF model. The RF was protected from overfitting [43], the model could not be adversely affected if a large number of trees were built for the forest. Figure 6a,b indicated that the OOB error in \(RF_{TMPA}\) and \(RF_{IMERG}\) decreased not significantly when _ntree_ increased from 900 to 1500. To balance the accuracy and computational burden, 1000 was finally selected as the value of _ntree_ for both \(RF_{TMPA}\) and \(RF_{IMERG}\). \begin{table}
\begin{tabular}{c c c c c c c c c c c c c} \hline  & & **Jan** & **Feb** & **Mar** & **Apr** & **May** & **Jun** & **Jul** & **Aug** & **Sep** & **Oct** & **Nov** & **Dec** \\ \hline Original IMPA & \(\mathbf{K}^{2}\) & 0.57 & 0.56 & 0.48 & 0.51 & 0.53 & 0.67 & 0.68 & 0.67 & 0.74 & 0.48 & 0.37 & 0.39 \\  & Bias (\%) & 6.29 & 46.54 & 65.57 & 14.30 & 29.40 & 16.86 & 19.99 & 18.35 & 21.25 & 47.02 & 81.07 & 53.79 \\  & MAE (mm) & 4.20 & 4.18 & 7.98 & 14.75 & 20.19 & 27.45 & 22.53 & 31.45 & 23.98 & 10.71 & 3.75 & 2.20 \\  & RMSE (mm) & 10.21 & 6.55 & 14.48 & 22.42 & 28.00 & 37.89 & 32.01 & 50.42 & 31.06 & 15.41 & 5.64 & 3.53 \\ Resampled IMERG & R\({}^{2}\) & 0.56 & 0.66 & 0.67 & 0.63 & 0.69 & 0.74 & 0.71 & 0.68 & 0.75 & 0.56 & 0.58 & 0.42 \\  & Bias (\%) & \(-13.02\) & 19.78 & 32.75 & -4.74 & 13.95 & 13.50 & 8.19 & 13.27 & 16.48 & 20.14 & 51.24 & 31.74 \\  & MAE (mm) & 3.43 & 3.02 & 5.50 & 12.10 & 15.35 & 23.20 & 18.30 & 27.97 & 21.00 & 8.32 & 2.65 & 1.87 \\  & RMSE (mm) & 9.96 & 5.00 & 9.84 & 19.60 & 19.79 & 30.67 & 27.30 & 42.45 & 28.00 & 11.27 & 3.50 & 3.20 \\ Original IMERG & R\({}^{2}\) & 0.55 & 0.69 & 0.58 & 0.59 & 0.72 & 0.74 & 0.72 & 0.67 & 0.74 & 0.62 & 0.57 & 0.48 \\  & Bias (\%) & \(-12.53\) & 17.59 & 38.85 & -4.27 & 12.14 & 14.23 & 7.60 & 13.31 & 16.22 & 16.86 & 45.86 & 26.04 \\  & MAE(mm) & 3.56 & 3.13 & 5.96 & 12.45 & 14.43 & 23.61 & 17.79 & 27.86 & 22.15 & 7.59 & 2.54 & 1.85 \\  & RMSE(mm) & 10.10 & 5.32 & 12.97 & 20.72 & 18.70 & 31.25 & 26.47 & 43.01 & 28.22 & 10.62 & 3.43 & 3.59 \\ \hline \end{tabular}
\end{table} 
Table 1: Coefficients of determination (R\({}^{2}\)), bias, mean absolute error (MAE) and root mean square error (RMSE) of the original TMPA data, the resampled IMERG data and the original IMERG data, compared with ground observations at each month in 2015. Figure 6: Graphs of the variation of the ’out of bag’ (OOB) error rate for (**a**) \(RF_{TMPA}\) and (**b**) \(RF_{IMERG}\) at different _ntree_ values. Note: OOB error denoted the ’out of bag’ error provided by the bagging model. \(RF_{TMPA}\) and \(RF_{IMERG}\) denoted the random forest models based on TMPA data and IMERG data, respectively. To specify the \(m_{try}\) parameter for \(RF_{TMPA}\) and \(RF_{IMERG}\), we tested five values of \(m_{try}\) that ranged from 2 to 10 and independently generated 1000 tree models at each \(m_{try}\) value. The boxplots of the OOB error for \(RF_{TMPA}\) and \(RF_{IMERG}\) were presented in Figure 7a,b, respectively. The upper and lower edges of the central box were the first and third quartiles (25% and 75%, respectively). The sign of band and circle inside the box represented the median and average value of OOB error, respectively. For \(RF_{TMPA}\), the OOB error decreased when the value of \(m_{try}\) increased from 2 to 6 and then increased with increasing values from 6 to 10. For \(RF_{IMERG}\), the OOB error decreased when \(m_{try}\) increased from 2 to 8.