Abstract
 Top of page
 Abstract
 1. Introduction
 2. Methodology
 3. Results and discussion
 4. Conclusions
 Acknowledgements
 References
Seven adaptive approaches to postprocessing wind speed forecasts are discussed and compared. Forecasts of the wind speed over 48 h are run at horizontal resolutions of 7 and 3 km for a domain centred over Ireland. Forecast wind speeds over a 2 year period are compared to observed wind speeds at seven synoptic stations around Ireland and skill scores calculated. Two automatic methods for combining forecast streams are applied. The forecasts produced by the combined methods give bias and root mean squared errors that are better than the numerical weather prediction forecasts at all station locations. One of the combined forecast methods results in skill scores that are equal to or better than all of its component forecast streams. This method is straightforward to apply and should prove beneficial in operational wind forecasting. Copyright © 2011 Royal Meteorological Society
1. Introduction
 Top of page
 Abstract
 1. Introduction
 2. Methodology
 3. Results and discussion
 4. Conclusions
 Acknowledgements
 References
Wind energy is a growing industry, and is supplying electricity to national grids worldwide. Wind energy cannot be generated on demand, in the manner of traditional electricity generation. Forecasting methods are required for the efficient management of wind energy. Reliable forecasts of wind energy production would reduce the costs of running the grid. They could also benefit wind farm operators by allowing a higher price to be obtained on the electricity spot market (Barthelmie et al., 2008). The purpose of this paper is to assess methods of reducing the errors in wind speed forecasts. Adaptive postprocessing methods that can easily be applied to wind forecasts produced by Numerical Weather Prediction (NWP) models are compared, and the advantage of combining forecast streams is investigated.
Ireland has a target of 40% renewable electricity generation by 2020. Most of this is expected to come from wind power. This will result in the Irish power system having one of the highest levels of wind penetration in the world by 2020. The highest penetration on the Irish power system to date was achieved on 5 April 2010. During this day, wind generation reached a peak of 1260 MW, which was 42% of the system demand at that time (EirGrid, 2010). Integrating this level of nonsynchronous generation on the power system will materially affect the way the electricity system is operated. A key factor in managing this variability is the development of improved forecasting methods.
Reviews of wind power forecasting methods are available from different authors (Giebel, 2003; Costa et al., 2008; Lei et al., 2009), and only a selection of different methods are considered here. One common approach in wind speed forecasting uses recent meteorological data. This is usually available from anemometers on the site of the wind farm. The data may then be analysed with different statistical models, such as autoregressive processes (Brown et al., 1984; Torres et al., 2005), and artificial intelligence techniques (Sfetsos, 2000; Cadenas and Rivera, 2010; Li and Shi, 2010). These techniques are only of use for forecasts of an hour or so into the future. This paper considers a forecast range of 48 h, and so it is important to use NWP model data.
All NWP forecasts contain errors, due in part to the quality of the data used to drive the model and in part to computational limitations in solving the governing equations with finite resolution. Some NWP errors are systematic and it is hoped that these can be reduced by applying statistical postprocessing methods.
Model Output Statistics (MOS) is a commonly used statistical postprocessing technique. It uses multiple linear regressions with forecast data and observations to attempt to remove forecast errors (Glahn and Lowry, 1972). However, MOS needs a long record of data for its training. This may cause difficulties when changing or updating the NWP model or the observing network.
It may be possible to equal or exceed MOS skill using adaptive shortterm postprocessing methods. Simple shortterm biascorrection has been shown to produce ensemble mean forecasts of 2 m temperature, 2 m dew point temperature, and 10 m wind speed that are competitive with or better than those available from MOS (Stensrud and Yussouf, 2005). Another study showed that MOS outperforms postprocessing with a Kalman filter or shortterm biascorrection when model biases change dramatically, performs worse during quiescent cool season patterns, and that all three are comparable at other times (Cheng and Steenburgh, 2007).
Kalman filtering (Kalman, 1960) is also used as a postprocessing tool for wind forecasting and has been shown to reduce systematic errors in a consistent manner (Crochet, 2004; Louka et al., 2008). Artificial Neural Networks (ANNs) are another popular method for postprocessing wind forecasts. They have shown good results when downscaling NWP wind speed, such as at a wind farm in Spain (SalcedoSanz et al., 2009a).
Previous studies have shown that wind power forecasts produced by combining individual forecasts can perform better than any of the individual forecasts (Nielsen et al., 2007). Two methods of combining forecast data are compared in this paper. One method uses ANNs to combine the forecasts, similar to SalcedoSanz et al. (2009b). The other method is a simple scheme using weights based on recent forecast skill, an updated version of the method used in Sweeney and Lynch (2011).
In this paper, seven different adaptive postprocessing methods are applied to NWP data produced at two horizontal resolutions (7 and 3 km) to produce 48 h wind speed forecasts. The training period is limited to 30 days to allow forecast data streams to be updated or replaced without requiring a large leadin period. Two different methods are then used to combine the forecast data. All 48 h wind speed forecasts are compared to the actual wind speeds observed at seven stations around Ireland over 2 years (June 2008 to June 2010). The skill scores considered are the bias and the Root Mean Square Error (RMSE).
Section '2. Methodology' concerns the COSMO NWP model, the forecast verification, and the statistical postprocessing methods, and methods used to combine the forecasts. The results of applying the different postprocessing and forecast combination methods are given in Section '3. Results and discussion'. Conclusions are presented in Section '4. Conclusions'.
3. Results and discussion
 Top of page
 Abstract
 1. Introduction
 2. Methodology
 3. Results and discussion
 4. Conclusions
 Acknowledgements
 References
A simple score often used to test forecast skill is the bias. The overall bias is calculated as the forecast wind speed minus the observed wind speed, averaged over all days (1 June 2008 to 31 May 2010) and forecast hours (+01 to + 48) at each station. Figure 7 shows the wind speed bias of the COSMO forecasts at the two model resolutions used. The higherresolution (3 km) bias is smaller than the 7 km bias at three stations, larger at another three stations, and similar at the remaining station.
All seven postprocessing methods used in this paper reduce the wind speed bias at all stations and both forecast resolutions to under 0.1 m s^{−1}, with the exception of the DIR 7 km forecast, which results in a bias of 0.127 m s^{−1} at Mullingar. Therefore all methods are considered to be effective at reducing overall bias.
To investigate the skill of the forecasts further, Figure 8 shows the average wind speed bias for each forecast hour at Dublin Airport. The 7 km COSMO forecast shows an overall negative bias, as well as a diurnal signal in the error. The STB forecast applies a single biascorrection to all forecast hours for each forecast. It can be seen that the STB forecast has reduced the overall bias, but still contains a diurnal signal. The DRL forecast applies a different correction to each forecast hour, and it can be seen to do a good job of reducing not only the overall bias, but also the bias at each forecast hour.
The COSMO forecasts produce average hourly biases ranging from − 1.972 to 2.656 m s^{−1} across all stations. The STB forecasts reduce these hourly biases to between − 0.514 and 0.620 m s^{−1}, and the DRL forecasts reduce them further to between − 0.041 and 0.118 m s^{−1}. The DRL forecast reduces the diurnal signal in the wind speed bias, as was hoped. Bias, however, is not a reliable measure of forecast skill on its own, as it may be hiding balanced negative and positive errors. To obtain another indicator of forecast skill, the RMSE of the forecast was calculated.
Figure 9 shows the RMSE, averaged over 2 years, for each forecast hour at Dublin Airport for the COSMO, STB and DRL forecasts. Although DRL has reduced the diurnal signal in the bias, it has not produced any improvement in the RMSE of the forecast compared to the simpler STB forecast. This is true for all stations.
The aim of the LLS forecast is to exploit the quasilinear relationship between forecast and observed wind speeds. Figure 10 shows the LLS 7 km forecast and observed wind speeds at Mullingar over the 2 year period. It can be seen that the LLS forecast has corrected the DMO forecast (shown in Figure 4) so that it is in better agreement with the 1:1 line. This does result in an improved RMSE score. The RMSE scores for the 7 km COSMO, STB and LLS forecasts at Mullingar are 2.873, 1.389 and 0.981 m s^{−1} respectively.
The LLS forecast only produces an improvement over STB if there is a weak linear relationship to start with. The 7 km COSMO forecast for Casement, for example, has a strong linear relationship with observed wind speeds, and the LLS forecast does not improve the RMSE of the STB forecast for that case.
The KAL forecast, produced using the Kalman filter described in Section '2.3. Statistical postprocessing methods', also seeks to find the optimal linear relationship to correct forecast data. It does a good job, and produces data that are in close agreement with the 1:1 fit, but not quite as close as those of the LLS forecasts. The RMSE score of the LLS forecast is always better than that of the KAL forecast, for both resolutions at all stations.
The MAV forecast seeks to correct the distribution of forecast wind speeds so that their mean and variance agree with those of the observed wind speeds. Figure 11 shows the 3 km COSMO, MAV and observed wind speeds at Malin Head. The MAV forecast has successfully corrected the COSMO forecast so that it is in better agreement with the observed wind speed distribution. However, the RMSE of the MAV forecast is worse than that of the simple STB forecast at five of the seven stations.
The DIR forecast uses the forecast wind direction to apply a correction to the forecast wind speed. Figure 12 shows the wind speed error binned by forecast wind speed for the 3 km COSMO and DIR forecasts at Belmullet. It is clear that the DIR forecast has substantially reduced the dependence of wind speed error on forecast direction. This also results in a lower RMSE. The RMSE for the 3 km COSMO, STB and DIR forecasts at Belmullet are 2.199, 2.114 and 2.006 m s^{−1} respectively. This improvement of DIR RMSE over STB RMSE happens at stations where there is a clear dependence of the wind speed forecast error on wind direction. Many wind farms are in hilly terrain, where the flow is strongly influenced by orography, and there is likely to be a strong dependence of model forecast error on wind direction.
The ANN forecasts were effective at reducing the RMSE at all stations to less than the COSMO forecasts, and improved on the STB RMSE for 8 of the 14 cases (seven stations at two resolutions).
Table 1 shows the overall RMSE of the wind speed forecasts for all postprocessing methods, with the best RMSE scores in bold. There is no single postprocessing method that produces the best score at all stations. Indeed, it is often the case that the best method for the 7 km forecast at a station is different to the best method for the 3 km forecast at the same station. The direct model output (COSMO) never produces the lowest RMSE. STB is best in one case, ANN is best in four cases, LLS is best in four cases, and DIR is best in five cases. The LLS forecast produces the best RMSE averaged over all cases.
Table 1. Wind speed forecast RMSE (m s^{−1}) for seven postprocessing methodsStation  km  COSMO  STB  DRL  LLS  KAL  DST  DIR  ANN 


Belmullet  7  1.954  1.953  1.964  1.956  2.005  2.032  1.915  1.947 
 3  2.199  2.114  2.131  2.100  2.156  2.192  2.006  2.043 
Valentia  7  1.648  1.600  1.622  1.580  1.647  1.645  1.630  1.615 
 3  1.762  1.716  1.738  1.720  1.773  1.788  1.652  1.730 
Cork Airport  7  1.530  1.483  1.500  1.436  1.503  1.506  1.478  1.480 
 3  1.612  1.560  1.573  1.506  1.566  1.587  1.500  1.480 
Dublin Airport  7  1.910  1.526  1.533  1.525  1.578  1.599  1.539  1.550 
 3  1.883  1.602  1.605  1.606  1.663  1.683  1.607  1.615 
Malin Head  7  2.219  2.149  2.164  2.127  2.188  2.231  2.113  2.147 
 3  2.709  2.126  2.146  2.106  2.182  2.202  2.149  2.146 
Casement  7  1.555  1.513  1.524  1.518  1.577  1.579  1.508  1.531 
 3  1.681  1.668  1.651  1.579  1.603  1.660  1.599  1.564 
Mullingar  7  2.873  1.389  1.398  0.981  0.994  1.019  1.408  0.969 
 3  2.422  1.285  1.287  1.007  1.016  1.048  1.278  0.971 
Average  7  1.956  1.659  1.672  1.589  1.642  1.659  1.656  1.606 
 3  2.038  1.724  1.733  1.661  1.708  1.737  1.684  1.650 
The fact that no single method is consistently the best provides the motivation for the combined forecasts, ANNCOM and MSECOM. The RMSE scores for these forecasts are shown in Table 2, with the best scores in bold. There is a clear advantage in combining forecast streams. Both combined forecasts outperform the COSMO forecast for all 14 test cases. ANNCOM gives better RMSE scores than its constituent forecast streams for 12 of the 14 test cases, but performs slightly worse than the Valentia 7 km LLS and the Dublin 7 km LLS forecasts. MSECOM, however, gives better RMSE scores than any of its constituent forecast streams for 13 of the 14 test cases and equals the RMSE skill in the 14^{th} case.
Table 2. COSMO and combined wind speed forecast RMSE (m s^{−1}). The best forecast in each row is in boldStation  COSMO 7 km  COSMO 3 km  ANNCOM  MSECOM 

Belmullet  1.954  2.199  1.905  1.890 
Valentia  1.648  1.762  1.588  1.554 
Cork Airport  1.530  1.612  1.427  1.410 
Dublin Airport  1.910  1.883  1.526  1.478 
Malin Head  2.219  2.709  2.097  2.029 
Casement  1.555  1.681  1.477  1.422 
Mullingar  2.873  2.422  0.934  0.969 
Average  1.956  2.038  1.565  1.536 
4. Conclusions
 Top of page
 Abstract
 1. Introduction
 2. Methodology
 3. Results and discussion
 4. Conclusions
 Acknowledgements
 References
Seven different postprocessing methods have been applied to NWP output at seven locations around Ireland over a period of 2 years. All of the postprocessing methods reduce the model bias. Average DMO bias over all stations varies from − 1.64 to 2.47 m s^{−1}. All postprocessing methods reduce this average bias to between − 0.08 and 0.13 m s^{−1}. All of the methods are, therefore, considered to be effective at reducing model bias.
The adaptive postprocessing methods are effective at reducing the errors for which they were designed. The STB forecast (and, indeed, every other postprocessed forecast) reduces the overall model bias. The DRL forecast reduces the diurnal signal in forecast error. The LLS and KAL forecasts correct the linear relationship between forecast and observed wind speeds. The MAV forecast improves the match between the forecast and observed wind speed distributions. The DIR forecast reduces the dependence of forecast error on wind speed direction.
Bias scores can hide a balance between positive and negative errors, therefore the RMSE should also be considered. When comparing postprocessing methods it has been found important to include a simple method in the comparison, such as the STB forecast used here. It is often difficult for other postprocessing methods, even comparatively advanced ones, to improve on the RMSE scores achieved by the basic STB forecast. Although different methods are effective at reducing model RMSE at different locations and model resolutions, there is no single method that produces the best RMSE score for all cases.
Combining forecasts not only allows the performance of the method with the best RMSE to be automatically achieved at each station, but can also result in RMSE scores that are better than all of the available forecasts. The best overall forecast is produced by the MSECOM combined forecast: that gives better RMSE scores than any of its constituent forecast streams for 13 of the 14 test cases and equals the RMSE skill in the 14^{th} case. The MSECOM forecast gives a 17% improvement in RMSE over the 7 km COSMO forecast, a 23% improvement in RMSE over the 3 km COSMO forecast, and keeps average bias below 0.1 m s^{−1} in all cases.
It is noted that the programming effort required to implement the postprocessing schemes presented here is very small compared to that required to develop an NWP model. Moreover, the computational overhead is negligible compared to the computation required for the model integration. Therefore, the methods described in this study can yield substantial improvements in forecast accuracy at relatively small cost.
There are many different requirements that users may have from a forecast and many different ways of measuring skill. Warning systems for extreme events, for example, would require representation of outliers, and may be best served by probabilistic methods. This study considers deterministic forecasts, and the bias and RMSE scores are used as indicators of forecast error. Future work will consider the benefit of postprocessing and combining ensembles of forecasts to provide improved probabilistic forecasts.