Statistical methods for correcting forecast of NWP models

Due to its high uncertainties, the performances of the NWP models have to be improved. As stated by Wilks [14], the predictors are the input variables of a statistic black box model, which has the function to predict an output variable, named as predictand that is used for correction. The MOS can be categorized in two distinct methods that differ in its predictors. While the first method, which is applied in [11] and [13], utilizes as predictors the simulated weather variables of the NWP model, except the solar radiation, the second method utilizes as predictors a time series of the measured minus the forecasted variable as presented by Libonati [15]. The second method is thus

enabled for phase and amplitude corrections of a local weather forecast. The Multiple Linear Regression (MLR) as shown in [11] and [13] or an ANN [13] is used as statistic model for the first method and a Kalman Filter for the second method [12]. Correcting the non-hydrostatic model MM5, which has a resolution of (3 x 3) km, the author of [11] obtained for two different years an RMSE of 28 % and 30 % for the prediction of the total daily horizontal solar energy on a site in Germany. Correcting the hydrostatic model ETA, the author of [13] obtained an RMSE of

25.5 % and 25.6 % for the forecast of the same variable for two different sites in Brazil. At a particular day the radiation was predicted with 17 MJ/m2 (107% of the mean value), whereas the measured energy was only 2 MJ/m2. The author selected the used output variables of the ETA model by the application of a significance test based on the MLR. Substituting the MLR with an ANN model the author didn’t observe considerable improvements of the MOS using the selected variables as predictors. The author applied the obtained model to other sites to test the generality of model performance. For two different cases, he obtained 35.6% and 38.9%. The second MOS method, which utilizes the Kalman Filter model [15], wasn’t already applied for the forecast correction of the solar radiation. The Kalman Filter has the disadvantage that it cannot, in its standard version, handle nonlinear problems [16]. Even applied to strictly linear systems, this model has higher uncertainties compared to an ANN, as shown in [17].