The performance of the NWP model ARPS and the proposed MOS procedure is verified for the site Florianopolis, localized in the south of Brazil with 48° 3ri5’’W longitude and 27° 36’ 76’’S latitude. The measured global horizontal radiation within the period from January 2000 to June 2006 was used to calculate the daily mean values. For daily mean values, the utilized pyranometer CM11 has a measurement uncertainty of 1 % for 95 % confidence as stated in [31]. For the quality control [32], [33] the measured radiation vales have to appear in the measurement range of (0 to 1367) W/m2. If this criterion was not fulfilled for a time interval larger than 10 min, the daily mean value was rejected as recommended in [33]. From the training-validation of 6.5 years, 119 days were excluded by the quality criterion, leading to the remaining data, which appears in 53 consistent time series. To facilitate the implementation, the data blocks of the training data set were chained, rather than is accomplished a specific DWT of each block, obtaining three equal length vectors with synchronized day numbers. The vector of residuals {sA} is obtained by subtraction of the measured {H} from the forecasted daily solar radiation means {HA}. The obtained predictors sAsi_1 to sAsi-k and predictands sAsi (eqn. 3), selected from the partially reconstructed sub-signals (eqn. 2, {sAS}), have to consider the limitations of each of the data blocks to avoid uncharacteristic modification of the ANN input pattern. As to see in eqn. 3, the data of the first k days of each block are used exclusively as predictors, thus a time series with the length nj provide (n-k) training samples for the ANN. Each sample has an input vector with the pattern length k, the predictors, and one output variable, the observed predictand, of the forecast at the considered time scale. The total number of training-validation samples ntv is obtained with expression (5).

ntv = YU (nj — k ) (5)

Where j = 1…nb defines the number of data blocks obtained by the data qualification, with block individual number of training samples nj. The resulting data set is subdivided in two subsets, the training and the validation set. As recommended in Kaastra [34], the validation set, which is independent from the training set has to represent (10 … 30) % of the data. This set may be selected randomly from the data or it follows immediately the training set [34]. From the data the last year, representing a validation set of 18 % was separated. Due to hardware improvements of the measurement system [35], the validation set was not exposed to system outages, which leads to its consistence.

4. Results

The average of the selected daily mean values of the measured solar radiation is 182.36 W/m2. For ARPS model simulations, based on the reanalysis dada, was obtained a RMSE of 70 W/m2 that corresponds to 38.4% of the measured average value. The maximal error of the daily mean solar radiation simulation is with 264.3 W/m2 higher than the measured average value (compare figure 3 — third chart and figure 4). If the correction is build up with data of twelve subsequent previous days (k = 12), a set of 1356 predictor vectors (sAs, (i-1) … sAs, (i-k) ) were selected. With the proposed MOS method the RMSE of the ARPS model reduces to 18.92 W/m2 for the training data set, which corresponds to 10.37 % of the measured average value of 182.36 W/m2. For the independent validation data set was obtained 9.06 % (see figure 3, fourth chart and figure 5). Worst performances were observed for the sub-signal di which contains the details of the higher frequency band (RMSE = 9.08 W/m2) and for the approximation sub-signal a1 (RMSE = 6.82 W/m2). The generalization performance of the ANN was verified with the validation data set. By arbitrary configured number of neurons in each layer with (k = 12), the best performance of the d1 sub-signal correction was observed, for 22 neurons at the first, and 12 neurons at the second hidden layer. This configuration of the neurons was used also for the other three ANN, whereby the one used for the approximation signal was configured as RNN, due to slight improvement in its performance. To access the probably higher boundary uncertainties under operation of the prediction model, it is necessary to accomplish ntv times (equation 5) the DWT for the data set having ntv predictor/predictand samples (see discussion in section 3.2). Avoiding numerical effort, the present article release only the results based on a single DWT of the data set as accomplished in

[9] .

Figure 3 — Daily mean values of the solar radiation — charts from the top to the bottom: (1) measured solar radiation H; (2) forecasted solar radiation with the ARPS model HA; (3) (H — HA); (4) (H — HA, corr), where HA, con — is the corrected ARPS forecast. The validation set appears from 2000 to 2500 days.