With a growing concern about a future climate crisis and a continuously increasing demand for electrical power, a greater penetration of renewable energy sources in the power supply system becomes crucial to meet the climate goals e.g.,. In the last 20 years, more and more attention has been directed to wind power, and as new technical inventions have enabled construction of larger and more efficient turbines, this technique now also accounts for a bigger share of the total power production .

As wind power production is highly dependent on the weather, a deep understanding of the climate for a site is needed when assessing the optimal location for a new wind farm, taking both the average and extreme conditions into account. Once the farm is in operational use, the meteorological focus shifts from site climatology to weather forecasting, to be able to predict the instantaneous power production. Accurate forecasts, especially for the short perspective (minutes to hours) but also for longer timescales (weeks to seasons), are requested by the grid operators, power production companies and traders on the electricity market to balance the power in the grid, to plan ahead and to maximize the revenue e.g.,.

When it comes to planning for new wind power farms, offshore sites have recently gained more attention . The main reason for this is simple: as the wind speed is generally higher over water than over land, constructing a new wind farm offshore allows for higher production. However, similar to when planning for a wind farm onshore, there are many aspects that must be considered before a new farm can become a reality, such as noise and visual disturbances e.g.,, military restricted areas, natural resources and animal life e.g.,, topography/bathymetry, and costs for grid connection e.g.,.

The Baltic Sea is in many ways ideal for establishing new offshore wind power farms, and with nine countries surrounding the semi-enclosed sea there are many stakeholders. Today, mostly the southwestern parts of the basin have been utilized for wind energy purposes (mainly by Denmark and Germany), but also other countries have well advanced plans for wind power expansion in the Baltic Sea in the coming decades e.g.,.

In general, forecast performance is better offshore than onshore as the sea surface is rather homogeneous and since diurnal cycles are less pronounced . Still, forecasts struggle with accurate timing and magnitude of wind ramps (in connection to convective cells or passing front zones), extreme wind speeds, extreme wind shear and low-level jets (LLJs), a phenomenon that is very common over the Baltic Sea during spring and summer .

With a close proximity to a coastline almost everywhere in the Baltic Sea there are many frequently occurring mesoscale meteorological events affecting the wind conditions to a varying extent, such as the sea breeze–land breeze circulation, LLJs and pronounced internal boundary layers . Also, upwelling and wave–air interaction affects the lower part of the wind profiles .

In order to create an accurate forecast, usually numerical weather prediction (NWP) models are applied using clusters of supercomputers to calculate the evolution of the weather, although other methods also exist see, e.g.,. As a starting point for the calculations in an NWP model, a background field of assimilated initial conditions with observations from multiple sources is used. The quality of this field is crucial for the quality of the forecast, together with the model setup regarding horizontal and vertical resolution as well as the parameterizations used to describe different physical processes. To improve the forecasts further, different post-processing techniques can be applied to the output from the NWP model; see, e.g.,  for a recent review.

This study presents a comparison of six commonly used post-processing methods to improve short-term deterministic wind power production forecasts for a site in the Baltic Sea, using data from an operational high-resolution NWP model and comparing with observations from a lidar (light detection and ranging). To provide a deeper understanding of the characteristics that distinguish the methods, they were all implemented in their basic form. The performance of the methods under different conditions were evaluated together with an overview of their general performance.

As of today, one of the most popular post-processing methods is to apply machine learning (ML) algorithms to the NWP data. The number of studies on different ways to implement ML methods and their relative strengths and weaknesses have grown rapidly during the last decade see, e.g.,. Common for all ML methods is that, using supervised or unsupervised learning, the algorithm finds patterns in the data and uses these patterns to make predictions based on data that were not in the training set. Among the most popular ML algorithms applied to post-processing of NWP data are neural networks, support vector regression algorithms and random forests (RFs). In this study, we limited ourselves to test only the RF to highlight the benefits and limitations of using ML as a post-processing method. This particular method has been successfully applied to improve wind power forecasts by, e.g.,  and .

The paper is structured as follows. After the introduction in Sect. , a description of the site location, the lidar observations and the NWP model is presented in Sect. . In Sect.  the six post-processing methods are described together with a brief overview of the metrics applied to evaluate forecast performance. The results are presented in Sect.  and followed by a discussion in Sect. . A summary and concluding remarks can be found in Sect. . To simplify for the reader, a list of all abbreviations used throughout the text is presented at the end of the paper.

In this section the different metrics used to evaluate the performance of the post-processed forecasts are presented, together with a detailed description of the different methods applied.

In this section, the general meteorological conditions and theoretical power production at Utö during the 2 years of measurements and forecasts are presented, followed by an overview of the performance of the original and the post-processed forecasts. Also, the forecast performance in different weather situations is presented. For the RF, details about the optimization of the features and settings in the algorithm are given.

Even though NWP forecasts for offshore wind power production are relatively good compared to forecasts for wind conditions in complex terrain, there is still room for improvement. The post-processing methods tested in this study are all commonly used and are implemented as they would be used operationally and in basic formulations, to allow a clean analysis of their respective advantages and disadvantages.

The methods tested are all general and could be applied to longer forecast lead times, to other variables than wind speed and onshore as well as offshore. However, as most methods require a substantial amount of training, they are sensitive to model updates and would need retraining from scratch in case of a major update that affects the NWP performance for the variable of interest. For AROME, there was a major update in February 2020, which is the reason that we did not include more recent forecasts. Also, if the observations are prone to systematic errors or large uncertainties that are not removed or minimized through quality control, there is a substantial risk of making the forecast worse when applying the above techniques, as the forecast will be adjusted to these erroneous values. The D1 / D2 MIX, the NBH method and smoothing (except for the first time step) are less sensitive to observational errors than the other methods. Furthermore, the training data have to be representative for the conditions at the site, including both seasonality and different types of synoptic and mesoscale situations. As suggested by Fig. d, at least 6 months of training data are needed for the RF method, but preferably 1 to 2 years or more. It is likely that the number of training data needed for the other methods is similar. However, some methods (such as the smoothing method) do not require any training data at all.

Even though the methods were only tested for one site, we believe that the main findings in the study are not site specific and will generalize to other parts of the Baltic Sea and possibly also to other (offshore) areas . Since lidar observations are scarce in the Baltic Sea, the post-processing methods might as well be trained using wind speed data from, e.g., a nacelle-mounted anemometer on an offshore wind turbine. More data in the test period would open up for a more detailed analysis of the performance of the post-processing methods, for example how the methods perform in different wind speed bins given the LWT. Also, a detailed analysis of the representativeness of the years analyzed in this study would contribute to assessing the uncertainty in the results. Building on this study, we suggest for future work to compare the performance of the different post-processing methods for other offshore (and potentially also onshore) locations as well as testing other NWP models and using a longer time series of observations and forecasts. Although the post-processing methods have been applied to mimic how they could be used in operational forecasting, a real-time test of the methods in fully operational mode would be of interest.

In order to better represent the operational use of the AROME forecast, the delay of the forecast could be included in the analysis. In reality, the AROME forecast is available approximately at 03:00 UTC, and thus forecasts could be evaluated for 04:00 to 03:00 UTC the following day, using the same forecast lengths as in our analysis. With observations available close to real time it is then possible to assess the quality of the first 3 h of the forecast and use this information in the subsequent correction. All methods can be implemented on a laptop, and runtime is usually not an issue for small problems (one site, short forecasts). For the RF, the runtime increases when adding more training features, increasing the number of trees or the training length, or when decreasing the MLS. The reason for the lower performance for MLS of 1 (as seen in Fig. c) is probably overfitting of the data, using too many splits of the branches in the decision trees. More training features could be added to the RF to increase performance, but it is clear from Table  that training features have to be relevant and not contain redundant information. Examples of training features that provide additional information and could be tested are for example turbulent kinetic energy and wave parameters.

The chain of adding training features one by one is implemented to provide as much insight as possible into the importance of the individual training features. No more training features were added when the MAE skill score for the optimization period started to decrease, but this does not guarantee an optimal final set of features. For examples of other ways to arrive at an optimal set of training features, we refer to , , , and . To perfectly mimic how the RF could be optimized in a wind power forecasting company, the optimization period could be selected from the historical data to be, e.g., the same season, continuously adapting the training features and the settings in the algorithm to the seasonal variations.

Although only the RF was tested here, there are many other possible ML methods that could be applied, and the promising result for the RF method should be interpreted as yet another indicator of the great potential benefit of applying ML methods for post-processing .

As the wind field offshore is rather homogeneous, differences in wind speed at a specific time between grid points that are close to each other are small, which explains the small changes to the forecast when applying the NBH method (Fig. ). Onshore, where spatial variation is higher, or if a model with a lower horizontal resolution is used, the method might still be important to consider . The NBH method smooths the forecast, and just as for temporal smoothing it decreases the risk of double penalty, e.g., in cases of wind ramps in connection with a passing front zone or squall line. The increased skill resulting from spatial smoothing of a NWP model is well studied, e.g., by , and also temporal smoothing has been shown to be beneficial for offshore wind power production before .

The reduced risk for double penalty is probably also the reason why the smoothing method performs best when the air flow is from N or NE (Fig. ), since winds from those directions typically are gusty due to the often unstable conditions related to advection of cooler air. However, comparing different stabilities (Fig. ) the smoothing method has similar performance in all categories. It should also be mentioned that all post-processing methods that apply averaging (that is, all methods except the LR) reduce the variability in the data and thus increase the risk of underestimating the occurrence of extreme conditions.

Comparing diurnal averages of wind power production data instead of hourly production, the correlation coefficient increases to 0.97 and the CRMSE decreases to 300 kWh for the deterministic 0–23 h forecast. Using the post-processing methods based on hourly data, only the NBH and smoothing methods result in positive MAE skill scores (0.007 and 0.005 respectively). However, the performance of most methods could probably be improved if diurnal data instead of hourly data were used for training.

The major improvement for the smoothing method is due to the interpolation of the observations at 23:00 UTC, as real-time observations and short interpolations are the best way to increase forecast improvement for short forecasts. To develop the smoothing function further, a running average with a longer block length duration could be used, and time steps within the block could be given different weights.

Applying smoothing directly to the power production forecast (instead of smoothing the wind speed forecast first and then calculating the production) does not result in a higher MAE skill score for the test period, even though the correlation coefficient and the CRMSE both slightly improve; see Fig. . Due to the shape of the power curve, error propagation in the wind speed forecast is non-linear, and using the smoothing method based on the forecasted power is better for wind speeds around cut-in and the rated wind speed. In the ranges 2.5–5.0 and 15.0–17.5 m s-1, the MAE skill scores for the smoothed method based on power production are 0.24 and 0.10 respectively, to be compared with the results for the smoothing method based on wind speed in Fig. . For the other wind speed bins, smoothing the wind speeds in the forecast is more beneficial than smoothing the forecasted power production.

The synoptic classification using LWTs is beneficial compared to other synoptic classification methods as it simplifies the meteorological reasoning and understanding of the forecast behavior for different classes. One drawback with LWTs is, however, that it is less strict from a mathematical perspective than for example principal component analysis (PCA) . Also, the JC method has a tendency to classify the synoptic situation as anticyclonic or cyclonic too often, and hybrid classes and pure directional flow are less common. To get a sufficient number of data in each class, we used the reduced set of 11 LWTs instead of the original 27 classes . As a consequence of this, the variability of the pressure field within a class is quite large.

The D1 / D2 MIX combines the D1 and D2 forecasts using a mix of approximately 60 % of the data from the new forecast and 40 % from the old. Only forecasts issued at 00:00 UTC have been used in this study, but the method is general and directly applicable to all earlier forecasts that overlap in lead times.

It is well known that NWP models struggle with resolving strongly stable stratification . This can also be seen in Fig. b where this stability class has the highest CRMSE. Improving data assimilation and schemes for turbulent mixing under these conditions are key to improve the forecasts and would be beneficial for the representation of, e.g., low-level jets and the extent of turbine wakes. It is a promising result that some of the post-processing methods tested, primarily smoothing and RF, managed to improve the forecasts under these conditions.

The result in Fig. a was expected, as Utö is a pure offshore location in the AROME model (Fig. c) and stable (unstable) stratification is known to be dominant in spring and summer (fall and winter) . However, in contrast to these results, using tower data from Utö and calculating the stability for the 2–50 m layer, the stability varies with a pattern typical for boundary layers over land with a clear diurnal cycle during the summer months (stable during night and unstable during day) and mostly stable conditions during winter (results not shown). Even though the horizontal resolution in the model is high, many islands in the Finnish archipelago (such as Utö) are not resolved by the model as illustrated by the land–sea mask presented in Fig. b, and the issue with the stability is most probably a consequence of this.

As the RF and smoothing are the methods with the best general performance (Fig. ) it might be interesting to combine the two methods to see if this would further improve the forecast. This can be performed in two ways: either the RF is run as before and the resulting forecast is smoothed or the training features are smoothed before the RF is applied. Both these methods were tested, and the result is presented in Fig. . For the RF only the wind speed training features for D1 and D2 for the four grid points (see Table ) were smoothed. The RF was optimized in the same manner as described in Sect. .

Figure  shows that none of the two setups managed to perform better than the smoothed forecast presented before. Still, smoothing the RF gave an improvement over the original RF method. It can also be seen that smoothing the training features for the RF improved the performance, but not as much as when applying smoothing afterwards. This is probably due to the fact that smoothing decreased the variability in the training data too much. The features selected in the optimization procedure turned out to be the same as for the RF “wind speed to wind speed” setup (Table ) with the exception of the final feature, which was Z for D2 instead of persistence. Since influence from the 23:00 UTC observation was embedded in the smoothed training features, it is reasonable that the persistence forecast was of secondary importance for this RF setup.

Assuming that we would have known in advance that the RF was the best selection in case of an LLJ (Fig. ), that the D1 / D2 MIX excelled during weak synoptic flow (U) (Fig. ) and that smoothing was the best method in general (Fig. ), we could have combined these methods accordingly. The result is presented in Fig. . Since the combination of methods is based on how well the methods performed for data in the test period and was then evaluated for the same period, we know that this will improve the MAE skill score but not by how much. To properly investigate the effect of the combined forecast, an independent test period is needed. Thus, the result in Fig.  can only be seen as an indicator of to what degree this combined method could have improved the forecast. The change in the MAE skill score is noticeable. Using the smoothing method based on power production for wind speeds forecasted in the ranges 2.5–5.0 and 15.0–17.5 m s-1 resulted in an additional minor improvement of the MAE skill score. For comparison with the results in Fig. , this combined forecast resulted in an EMD value of 331 kWh compared to a perfect forecast and was superior to the AROME D1 forecast 31 % of the time. A more detailed investigation of the wind speed ranges where the smoothing method based on power production is better than the original smoothing and adjustment of the wind speed ranges when it is applied would likely result in further improvement of the final forecast.

Six commonly used post-processing methods were applied to the 0–23 h AROME forecasts for wind speed at an offshore location in the Baltic Sea and evaluated in terms of performance in forecasting power production during 1 year.

Applying smoothing to the forecast or using a RF algorithm were the most promising methods to improve the forecast, with the best performance in MAE skill score, highest correlation and lowest CRMSE. The smoothing method performed slightly better than the RF and had a lower bias. Combining the two techniques by smoothing the RF forecast or by smoothing the training features before applying the RF algorithm improved the performance of the RF but did not surpass the original smoothing method.

Even though the smoothing and RF methods improved the forecast for approximately 30 % of the time, almost equally often the methods deteriorated the forecast. For 40 %–50 % of the time, the changes compared to the original forecast are small, and in terms of forecast superiority and EMD the performance is only slightly better than what could be achieved by chance. However, the MAE skill score for the forecast with added noise is lower than for the smoothing method and RF.

The major improvement for the smoothing method is for the first time step of the forecast as interpolation of the 23:00 UTC observation was used. Both the smoothing and the RF worked well for intermediate wind speeds, but for the RF both lower and higher wind speeds were problematic. Smoothing improved the forecast in all stability classes, while the RF mainly improved the forecast in stable and neutral stratification. Similarly, smoothing increased the performance for all synoptic situations, while the RF struggled primarily with easterly winds, probably because the number of training data for these situations was inadequate. RF improved the forecast substantially when a LLJ was forecasted but gave almost no improvement otherwise.

Among the other methods tested, the D1 / D2 MIX, using a combination of the new forecast and the forecast from the previous day, resulted in improvement under some conditions but mainly when the synoptic flow was weak and/or neutral stratification. The best MAE skill score was achieved using smoothing and switching to RF in case of a LLJ and to D1 / D2 MIX during weak synoptic forcing (and no LLJ). Further, if smoothing applied to the forecasted power production (instead of the wind speed) was used in the combined method for wind speeds in the ranges 2.5–5.0 and 15.0–17.5 m s-1, an additional small improvement of the MAE skill score was achieved.

As the forecasted wind speeds for neighboring grid points offshore are similar in a high-resolution NWP model, combining nearby grid points in a NBH method gave only minor changes compared to using the forecast from the closest grid point. Applying LR to improve the forecast was in general not a successful method.

The different post-processing methods applied in this study are all general and can be applied to any NWP model, any parameter and any forecast length offshore as well as onshore. For further studies, we suggest comparing state-of-the-art ML methods in combination with nudging techniques to include real-time observations in the forecasts. Different methods to smooth the forecast or the training features for ML should be investigated. Also, an overview of different methods to improve probabilistic forecasts for offshore wind energy in the Baltic Sea would be of interest to the community.