# Reducing Forecast Errors of a Regional Climate Model Using Adaptive Filters
## 6 Conclusions  
This paper proposed a postprocessing approach to reduce forecast deviations of the Eta regional climate model by using adaptive filters. The correction of forecast deviation depends on comparisons between past model forecasts and reanalysis data. These data are applied to the well-known RLS (Recursive Least-Squares) algorithm to obtain the filter.  
There are many cells within the geographic domain of climate forecast. Each cell presents a set of climate variable time series. Therefore, the K-means clustering algorithm is employed to learn the number of filters adapted in the model domain. The criterion for the clusters is the average climate in the cells.  
The fraction of climate forecast cells where the error between the prognosis (Eta RCM) and the observed (NCEP) reduces the effectiveness rate (ER) is used to evaluate the proposal. One computes the ER for three error metrics: the normalized mean square error, the maximum absolute error, and the absolute normalized error.  
The proposed procedure was tested in a region comprising most of Brazil, within 6\({}^{\circ}\) S-30\({}^{\circ}\) S and 33\({}^{\circ}\) W-83\({}^{\circ}\) W. The results show that the proposed method can achieve high effectiveness rates (ER) in reducing forecast deviations of the Eta RCM, mainly with a four-coefficient filter that corresponds to a one-day time period. Moreover, at 500 hPa, we could obtain better ER performance than at 250 hPa. This is an important and useful result, as the 500-hPa level climate variables affect more closely the variables near the surface, where people live.  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline  & \multicolumn{2}{c}{**NMSE**} & \multicolumn{2}{c}{\(e_{\text{max}}\)} & \multicolumn{2}{c}{\(e_{\text{NR}}\)} \\ \hline
**Pressure Level** & **N** & **MER(\%)** & \(\sigma\) & **MER(\%)** & \(\sigma\) & **MER(\%)** & \(\sigma\) \\ \hline \multirow{4}{*}{250 hPa} & 4 & 93.14 & 9.60 & 81.14 & 12.42 & 91.78 & 7.03 \\  & 8 & 90.72 & 10.71 & 81.46 & 12.16 & 89.05 & 8.67 \\  & 16 & 87.24 & 14.63 & 75.16 & 17.47 & 85.37 & 9.03 \\  & 32 & 83.01 & 17.84 & 73.25 & 17.10 & 77.41 & 9.12 \\ \hline \multirow{4}{*}{500 hPa} & 4 & 99.42 & 1.33 & 88.12 & 9.36 & 97.23 & 1.22 \\  & 8 & 98.76 & 2.09 & 84.66 & 11.64 & 94.09 & 2.53 \\ \cline{1-1}  & 16 & 98.10 & 3.12 & 84.10 & 11.13 & 91.18 & 3.58 \\ \cline{1-1}  & 32 & 94.88 & 8.29 & 80.83 & 13.26 & 85.15 & 5.08 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Centroid (MER) and dispersion (\(\sigma\)) of effectiveness rates for different filter orders at 250 hPa and 500 hPa.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Pressure Level** & **Climate Variable** & **NMSE** & \(e_{\text{max}}\) & \(e_{\text{NR}}\) \\ \hline \multirow{4}{*}{250 hPa} & Meridional wind & 99 & 90 & 97 \\  & Zonal wind & 93 & 78 & 92 \\  & Geopotential height & 88 & 75 & 86 \\ \hline \multirow{4}{*}{500 hPa} & Meridional wind & 100 & 83 & 97 \\  & Zonal wind & 99 & 89 & 98 \\ \cline{1-1}  & Geopotential height & 99 & 92 & 97 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Mean effectiveness rates (%) of climate variables at 250 hPa and 500 hPa, considering a four-coefficient filter and 19 clusters.  
**Author Contributions:** Conceptualization, M.P.T., L.L. and S.C.C.; methodology, M.P.T., A.R.F. and L.L.; software, A.R.F. and M.P.T.; validation, A.R.F and M.P.T.; writing--original draft preparation, M.P.T. and L.L.; writing--review and editing, M.P.T., L.L. and S.C.C. All authors have read and agreed to the published version of the manuscript.  
**Funding:** This study was financed in part by Coordenacao de Aperfeicoamento de Pessoal de Nivel Superior--Brasil (CAPES) Finance Code 001, by Conselho Nacional de Desenvolvimento Cientifico e Tecnologico (CNPq) no. 306757/2017-6 and by Fundacao Carlos Chagas Filho de Amparo a Pesquisa do Estado do Rio de Janeiro (FAPERJ).  
**Institutional Review Board Statement:** Not applicable.  
**Informed Consent Statement:** Not applicable.  
**Conflicts of Interest:** The authors declare no conflict of interest.