# Reducing Forecast Errors of a Regional Climate Model Using Adaptive Filters
## 5 Experiments
### Results  
Regarding the experimental setup, we compute ER (see Equation (14)) for three deviation metrics, considering data from years 2001 to 2010 (\(N_{\rm Y}=10\)), at two pressure levels (250 hPa and 500 hPa), while designing/adapting filters of different lengths \(N=4\), 8, 16, and 32 (1, 2, 4, and 8 days, respectively, as discussed in Section 5.3). The number of clusters used in K-means is fixed at 19 (as discussed in Section 5.2). The combination of these setup variables generates an amount of ER data spread in a three-dimensional domain associating an axis to each one of the deviation metrics considered herein. Let **NMSE**, \(\mathbf{e_{\rm max}}\), and \(\mathbf{e_{\rm NR}}\) be the ordered series containing the ER data of the corresponding deviation metric in the different years of each time series, at each pressure level of each climate variable and value of \(N\). By computing the correlation coefficient among the ER values of **NMSE**, \(\mathbf{e_{\rm max}}\), and \(\mathbf{e_{\rm NR}}\), we can verify that since their correlation is around 0.5 and 0.6, as shown in Table 1, these results reveal different aspects. Remark that the poor cross-correlation among these error metrics proves that none of them should to be discarded in the proposed framework performance evaluation, since they evaluate distinct aspects of the systematic error between Eta RCM and the observational data. \begin{table}
\begin{tabular}{c c c c} \hline \hline  & **NMSE** & \(\mathbf{e_{\rm max}}\) & \(\mathbf{e_{\rm NR}}\) \\ \hline
**NMSE** & 1 & 0.63 & 0.62 \\ \(e_{\rm max}\) & 0.63 & 1 & 0.51 \\ \(e_{\rm NR}\) & 0.62 & 0.51 & 1 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Correlations between effectiveness rates for **NMSE**, \(\mathbf{e_{\rm max}}\), and \(\mathbf{e_{\rm NR}}\). Figure 7: Meridional wind time series at 250 hPa produced by the Eta RCM (_Eta-original_), its filtered version (_Eta-filtered_), and the NCEP reference data. To assess the performance of the proposed strategy for RCM deviation reduction, we plot the obtained ER data by combining simulation years and filter orders with respect to these three deviation metrics, as illustrated in Figures 8 and 9. These three-dimensional graphs present the ERs for each of the deviation metrics considered for the four filter lengths. The graph analysis is carried out separately at each pressure level, 250 hPa and 500 hPa. The more the cloud points are concentrated in the top-right corner, the better is the performance on reducing the RCM forecast deviation according to the three error metrics simultaneously. The better performance at 500 hPa than at 250 hPa is an important result. Variables at 500 hPa are closer to the surface than 250 hPa; therefore, the improvement of the 500-hPa variables can contribute more to the improvement of the forecasts near the surface. At the 250-hPa level, the climate variables exhibit longer wavelengths than at 500-hPa [33]; therefore, the filter acted more effectively at the 500-hPa level where more climate variability is found. Figure 8: Effectiveness rate of RCM forecast deviation reduction at 250 hPa with different filter orders (above), and a larger view with values greater than 50%. In addition, at both pressure levels, the ER performance decreases as the filter order increases. This becomes evident when we compute the centroids (averages) and dispersion of the cloud points separated by filter order. Table 2 contains the MER (%) and the standard deviation (\(\sigma\)) of the error metrics for each pressure level and filter order (\(N\)). Note that the larger MER and the smaller dispersion (marked in boldface) occur for the four-coefficient filter at the two pressure levels. It is important to highlight that the filter performs the convolution over the entire time series produced by the Eta RCM; therefore, it is applied for error correction. The filter does not produce a forecast.