Machine learning for predicting offshore vertical wind profiles

The accurate characterization of the vertical wind profile over the sea that covers the rotor swept area of modern wind turbines is a key challenge for wind energy yield calculations. Since offshore wind measurements are scarce, early-phase projects tend to use numerical model outputs before planning a dedicated measurement campaign. This study aims to develop and validate a machine-learning model that can assimilate wind parameters measured at the first level of the meteorological masts as input and provide a wind speed profile covering the rotor swept area of modern turbines that is more accurate than numerical weather prediction models. The methodology is based on a random forest model implemented in the python package Scikit-Learn. Three offshore sites in the North Sea have been selected for this study, namely FINO3, IJmuiden and Nordsee Ost’s (NSO) met mast, which are 100 to 350 km apart. Each site has an instrumented 100-m meteorological mast along with a Doppler wind lidar measuring up to 300 m. The baseline selected for comparison was the Weather Research and Forecast (WRF) model. To assess the accuracy of the random forest model two models were trained at IJmuiden and FINO3 and tested at all three locations. Hence, we examine the model performance at the site of training, the so-called same site approach, as well as new sites, the so-called round robin approach. The same site approach quantifies the model consistency, while the round robin shows the degree of spatial robustness. The results show that the model is consistent, where the model trained and tested at FINO3 showed a mean absolute error (MAE) reduction of 68% compared to WRF. This model is also robust, when applied at IJmuiden, 350 km away with a MAE of 1.2 m/s, 8% improved compared to WRF outputs. This study therefore shows the potential to implement machine-learning methods in the prediction of vertical wind speed profiles over the sea. One potential application for the presented methodology is the extension of wind profiles measured by floating lidar systems to higher heights, where current wind lidar products have low availability and higher associated uncertainties, when measuring at a higher height.


Introduction
As wind energy grows with the third power of wind speed, the accurate characterization of the wind profile that covers the rotor swept area of ever growing modern wind turbines is a key challenge for wind energy yield calculations.The uncertainties in these estimations increase the investment risks [1].Since offshore wind measurements are scarce, and the existing ones being mostly proprietary, a systematic characterization of offshore profiles is hindered.As a result, early-phase projects tend to use numerical model outputs before planning a dedicated measurement campaign [2].These numerical models are not capable of accurately capturing local conditions and are known to have biases [3].Hence, new approaches can be complementary to the existing characterization methods, based on near surface measurements.The near surface wind parameters can be vertically extrapolated to the desired height [4].Recently, machine learning models were employed for this purpose, and have shown promising results in the wind energy literature as a predictive tool.This novel method is investigated in wind energy applications onshore [5,6] as well as offshore [7,8].In [9], deep neural networks were used to extrapolate variables between 100 and 200 m in both complex and offshore terrains using lower height measurements and showed this method can improve the accuracy of logarithmic and power law methods up to a 65% and 52%, respectively.Deep neural networks were also utilized by [5] to vertically extrapolate the wind speed up to 120 m over a flat terrain in Saudi Arabia with 15% accuracy improvement compared to power law predictions.
However, all the models developed in these studies were trained and tested at the same site.In [10], it is discussed that this data-driven approach is not practical as the wind profile is already known at the site.Furthermore, it is not fair to the other extrapolation methods, as they are generally applicable and not site-specific.They proposed training and testing the machine learning model at distinct sites, in an approach called round robin.The term "round robin" is derived from the concept of round robin tournaments, where each team plays against every other team in a cyclic manner.In this study, similar to [10], round robin refers to the approach of cross-testing the models by training them at one site and testing them at another, and then repeating the process for all the possible combinations of sites.Hence, four onshore sites were chosen in [10], all within 50-100 km from each other, to implement this approach and predict the wind speed at 143 m.The study used wind speed, turbulent kinetic energy and the Obukhov length at 4 m plus the time and wind speed at 65 m as model inputs.Their round robin results showed that the MAE increased by 11% on average, when compared with the same site approach, but still improved by 14% and 20% compared to logarithmic and power law profiles, respectively.Random Forest was also used in a study by [8] to extrapolate the wind speed up to 200 m from 2 m data offshore, outperforming the WRF model, logarithmic profile, and a one-dimensional single column model, simplified with horizontal homogeneity.In a recent study [7], random forest was utilized to extrapolate the satellite wind retrievals at 10 m up to 100 m in the North Sea, using near surface parameters.The predictions of the random forest trained at 91 m at FINO3 yielded an R-squared value of 0.93, which dropped to 0.84, when applied at FINO1 (136 km away).Here, the developed model was given the wind speed and direction and sea surface temperature inputs at FINO1, and air temperature, pressure and relative humidity were assumed to be homogeneous in space [7].
With modern offshore wind turbines reaching a rotor diameter of 250 m, the need to characterize the vertical wind profile above 300 m is called-for to cover the entire rotor swept area.However, none of the aforementioned studies on vertical extrapolation of wind speed cover the entire rotor swept area of modern offshore wind turbines.This can be traced back to the sparsity of measurements at these heights offshore.As shown by [10], the MAE doubles, if the prediction height is increased from 100 m to 160 m.Their study also indicates that the MAE grows, as the horizontal distance between training and testing location increases.Moreover, there is a research gap in the application of machine learning based models trained for the North Sea metocean conditions.
This study focuses on vertical wind speed profile characterization using random forest models in the North Sea.Here, the same site approach will quantify how accurate and precise the model is, whereas the round robin approach will test how generic is the model when applied within the North Sea region.Furthermore, the sensitivity of the model to the inputs is to be addressed.The paper is structured as follows: in section 2, we introduce the collected data, used to develop and validate the random forest models, as well as the benchmark, namely the WRF model.Afterwards, the proposed extrapolation method is compared against the lidar profiles and WRF outputs in section 3, where the results are also discussed.Section 4 provides a summary and concludes the study, followed by future perspectives.

Materials and Methods
To develop and validate the random forest models, based on the same site and round robin approach, we chose three distinct offshore locations in the North Sea with a horizontal distance between 90 to 350 km.As baseline, we take the wind profiles provided by the Weather Research and Forecast (WRF) model [11].The measurements are 10-minutes averaged and the WRF outputs are stamped instantaneously every 10 minutes, both of which are down-sampled to 30 minutes.

Experimental data
Wind parameters are measured at the three locations in the North Sea: • Meteorological station near IJmuiden in the Netherlands [12] • Forschungsplattform in Nord-und Ostsee, Nr. 3 (FINO3) station near Sylt in Germany [13] • The meteorological mast in the Nordsee Ost (NSO) wind farm, north of the Heligoland island in Germany, hereafter referred to as IJmuiden, FINO3 and NSO.The first two sites are research meteorological stations maintained and operated by the Dutch and German governments, respectively.The NSO met mast is part of an operating wind farm in the German North Sea.The data from FINO3 and IJmuiden are publicly available, whereas the NSO met mast data is proprietary.IJmuiden and FINO3 stations are 326 and 93 km away from NSO, respectively (see Fig. 1).At all sites, the devices installed on the platform or the first level of the met mast (between 20 to 30 m) provided the random forest models with features, whereas the wind speed between 100 m and 300 m captured by a lidar close-by was used to train and test the models.The flow distortion induced by the booms have been removed from the met mast data by filtering out the affected wind sector, in case of having only one boom at the height.If multiple booms were available, their signals were combined to capture all wind directions.Moreover, since NSO is located inside a wind park, the wind was filtered for the sector without wind farm wake effects (225°to 315°).The data collected by the WindCube pulsed lidar system installed on the FINO3 platform was filtered for CNR (Carier-to-noise ratio) greater than -29 dB, as used by [14].IJmuiden and NSO platforms are equipped with continuous wave lidar systems from ZX lidars.The lidar profiles at FINO3 were filtered to have a minimum of 75% data availability.
Table 1 provides an overview of the three sits and the measured data used in this study.
From the long-term wind roses in Figure 1, it is worth noticing that the NSO and FINO3 sites are closer and share a similar climatology between them, when compared to IJmuiden.Due to this fact, the wind profile at IJmuiden is expected to be more dissimilar and harder to predict using NSO and FINO3 data.Table 2: Mean wind parameters at 100 m for the three sites, derived from 42 years of ERA5 data.k is the shape parameter and A the scale parameter of the Weilbull distribution.

Mean wind speed [m/s] Mean wind direction [°] k [-]
A

Model data -Baseline
To evaluate the accuracy of the random forest model predictions, we established a baseline for comparison.After analyzing the outputs from NEWA, ERA5, and our in-house WRF simulations, we determined that our own simulations exhibited superior performance in predicting average profiles, having a finer temporal and spatial grid resolution.This down-scale model setup is the same for all three sites and utilizes version 4.0.1 of the Weather Research and Forecasting (WRF) model.It incorporates the ERA5 data [15] and OSTIA sea surface temperature [16] for the boundary conditions.The one-way nesting strategy includes domains with resolutions of 18, 6 and 2 km centered at the met mast with 150 grid points for each domain and grid nudging above level 25.The vertical resolution can be obtained from Table 5.The model outputs are time-stamped at intervals of 10 minutes, capturing instantaneous data.For a more comprehensive understanding of the specific configuration setup for this model, please refer to [17].

Setup of the random forest model
An ensemble-based regression tree model known as random forest was adopted to extrapolate the wind speeds vertically [18].The modeling was implemented by the RandomForestRegressor estimator from ensemble module of Scikit-Learn in Python 3 [19].A random forest takes the average of the regression trees prediction, forming the forest.A decision tree searches for the best feature to split the training data, which is by definition the feature that yields the minimum error criteria, i.e., the minimum mean squared error herein.Each tree in a random forest is built on randomly chosen training samples and randomly selected features, which makes a forest more robust than a single tree.The random forest models developed for this study were tuned using a five-fold cross  The two random forests were built using 75% randomly chosen data at IJmuiden and FINO3.The remaining 25% of the data at these sites, and the whole period of NSO were used to validate the two random forests.The downside of using randomly selected timestamps to train and test in the same site approach is the fact that it introduces an auto-correlation, which can artificially improve of the model accuracy.However, the focus of this study lies on the round robin implementation, which does not carry any prior knowledge at the heights of prediction.Moreover, this splitting method enables us to study the model's capability of gap filling.
The measured parameters listed in Table 4 were given to the random forest models together with the timestamp and the height of prediction as inputs.As the prediction height is considered as an input, the random forest models are designed to be multiple input single output models.The time of day and month, as well as the wind direction were transformed into sine and cosine of these parameters, to maintain their periodic characteristics.Figure 2 shows how the MAE drops, when the features are fed progressively to the model, using the same site approach.The final set of features can be found in Fig. 3.
Wherever the height of predictions is different than the measured ones, a logarithmic interpolation function is adopted.The second order function proposed by [20] is simplified to a linear logarithmic function for the interpolation herein.Table 5 presents available heights for lidar measurements and WRF outputs at each location.

Results
In this section, the wind profiles extrapolated by the proposed methodology are presented and compared to the profiles predicted by WRF simulations.To implement both the same site and round robin approaches, two random forest models were trained at IJmuiden and FINO3 using 75% of the 30-min periods.These two models were applied at all three locations, namely IJmuiden, FINO3 on the remaining 25% of data and NSO for the whole period, creating six case studies in total.

Model sensitivity
As shown by [7,8], the temperature difference between air and sea improves the accuracy of random forest wind speed predictions, when considered among the features.Our analysis showed that when the air temperature is replaced with the temperature gradient in the input parameters, MAE of the same site validated random forest drops by 13% at IJmuiden as a result of including the thermal stratification in the modeling process.However, this study does not include the temperature gradient as an input due to low data availability at FINO3 and NSO. Figure 3 shows the importance of each input for the two random forests.The importance is calculated as the total reduction of the mean squared error brought by that feature normalized to 1.As in [10,8], the near surface wind speed is the most determining feature with 70% importance.Moreover, among the time-related inputs, the time of the day is not as determining as the month.This is expected, since the seasonal changes are more dominant than the diurnal ones in offshore locations.
As a next step, we investigated how the height of the input wind speed, as the most important feature, influences the accuracy.Replacing the wind speed at 30 m with the wind speed at around 100 m reduces the MAE of the same site implemented random forests by 22% and 24% in IJmuiden and FINO3, respectively.

Model performance
To assess the random forest model performance, the output and the baseline (WRF) are validated against the lidar observations using the testing dataset.We assessed the model performance using as metrics the bias, mean absolute error (MAE) and the square of correlation coefficient Figure 4a compares the modeled wind profiles with the measured ones at the three locations.The plots show that the same site random forest wind profiles are in best agreement with the measurements, whereas the wind profiles predicted by WRF show an underestimation at all locations.We see a difference in the accuracy of the round robin implementation of the random forest, depending on the training location.The random forest developed at IJmuiden generally underestimates the wind profile at FINO3 and NSO, even more drastically than WRF.While the random forest developed at FINO3 captures the average wind profiles at IJmuiden and NSO more accurately than WRF.At the NSO site the predictions of the random forest model trained at FINO3 match the measurements better than the other two models, especially at lower heights, but it has increasingly larger bias towards higher heights.
To rank the performance of the models in predicting wind speed timeseries, the MAE profiles are plotted in Fig. 4b.It can be seen that the same site random forest models posses the lowest MAE among all.The plots also suggest that the MAE of random forest models grows with height more rapidly than WRF.In all three locations, both implementations of random forest yield a lower MAE than WRF.
The difference between the performance of the random forest model trained at IJmuiden in predicting wind profiles and wind speed timeseries at NSO can be traced back to its error distribution.The error is defined such that a negative error is an indication of underestimation of the prediction.When tested at NSO, the error distribution of the IJmuiden random forest is less scattered compared to WRF, with a dominant peak close to zero.This is also true for the random forest trained at FINO3, leading to a smaller MAE of the random forests, compared to WRF.However, contrary to the non-skewed WRF error distribution, the error distribution of the random forest trained at IJmuiden is negatively skewed, leading to a thicker tail on the negative side.This explains the negative bias and the underestimation of the modeled wind profile.The error distribution of the random forest trained at FINO3 also shows a negative skewness, when tested at NSO.But this distribution peaks at a greater positive value compared to the IJmuiden model, which balances the thicker negative tail, leading to a smaller bias.
Figure 4: Predicted and measured wind profiles and MAE profiles at IJmuiden using 6978 samples (left), FINO3 using 3350 samples (middle) and NSO using 3337 samples (right).The wind profiles are shaded with standard error of the mean, which is calculated as the standard deviation divided by the square root of the sample size.
In fact, the asymmetrical error distribution of the random forest models, and its negative thicker tail stem from higher wind speeds.Figure 5 shows the average error in each binned wind speed exemplarily at 274 m, where the NSO testing wind speeds are binned into 1 m/s groups from 0 to 36 m/s, using the lidar measurements at this height.The underestimation of both random forest models takes place mostly at higher wind speeds, which explains the negative skewness of the error distribution.It can also be concluded that extreme events are not accurately reconstructed by the random forests.One could confine the application of the According to Fig. 5 both random forests seem to have a closer to zero error at the wind speeds, which appeared more frequently during training.The lager model error at higher wind speeds can therefore be associated with the small number of training samples at these wind speeds.However, the total number of training samples is not the only influential parameter.Although the total number of training samples seen by the the random forest model developed at IJmuiden is double the amount at FINO3, but it performs less accurately at NSO.It can be concluded that a training wind speed distribution similar to the testing one, can result in more accurate predictions.The superiority of the random forest trained at FINO3 can be attributed to the similarity in the wind speed distribution between the training site (FINO3) and testing (NSO), as well as the analogy between the wind roses shown in Fig. 1.This indicates the limitation of the horizontal distance from the training location, where the random forest is applicable.
Finally, the performance metrics are presented in Table 6, which are averaged across all heights.Table 6 shows that the best performance is achieved by the same site implementation of the random forest models, with the results highlighted in bold font.This finding is consistent with the results reported by [10].The round robin implementation of the random forests improves the WRF MAE and R 2 , by 15% and 5% on average, respectively.The bias of the round robin random forests depends on the training location.The random forest trained at FINO3 improves the WRF bias by 63%, corresponding to an average bias of 0.17 m/s when round robin is accounted.The random forest developed at IJmuiden proves an average bias of 0.57 m/s, when implemented based on round robin.

Conclusions
In this study, we performed a characterization of the wind profile at heights covering the rotor swept area of modern offshore wind turbines.For this, two random forest models were developed, based on a data-driven machine learning algorithm.The random forest models are validated using two approaches.Firstly, they are tested at the location of training using 25% of the data not used during training process, the so-called same site approach.Our analysis showed that by adding every feature, the model accuracy was improved.Furthermore, the most important input considered by the model was the input wind speed at 30 m. Increasing the height of this input to 100 m improved the the MAE of the same site implemented models by 23 % on average.Our study showed that replacing the air temperature with the air-sea temperature gradient in the features, leads to 13% MAE reduction, when validated at the location of training.
The main focus of this study was related to the performance of the random forest model trained and tested at distinct locations via a round robin.This approach was validated at NSO, and could reach 14% and 5% improvement in MAE and R 2 on average, compared to the WRF model outputs, respectively.The analysis showed that the error distribution of the random forest models have a lower variance than WRF, leading to more accurate time series predictions.However, the random forest predictions also were negatively skewed, causing an underestimation of the wind profiles at higher heights.One reason for this underestimation was the low sample size at higher wind speeds.A broader range of training wind speeds, as well as incorporating physical parameters at higher elevations, such as the geostrophic wind or the atmospheric boundary layer height, could help improve the model performance at higher altitudes.
In summary, the random forest trained at FINO3 outperformed WRF at the NSO site (93 km away), both in timeseries and wind profile predictions, which was not the case for the random forest developed at IJmuiden (326 km away).This can be attributed to the training dataset but mainly, to a more similar climatology between FINO3 and NSO, when compared to IJmuiden.This implies that the random forest model may be more applicable to locations with similar climatology to the training location, and its performance may degrade beyond a certain distance or dissimilarity in climatology.To further investigate this dependency, future studies could deploy more sites at different distances.
The results presented here point towards the potential to use machine learning methods for vertical wind profiles characterization.The negatively skewed results could be mitigated in a future work using a bigger training and testing datasets, also covering a broader wind speed range.Moreover, the relation between the random forest model performance and the atmospheric stability can be studied.Finally, the proposed approach could be used in an industry application to extrapolate the wind profiles observed by floating lidars to higher heights, where current solutions have low data availability and higher associated uncertainties.

Figure 1 :
Figure 1: Map with the location of the sites and the wind roses, derived from 42 years of ERA5 data at 100 m.The contours indicate the wind speed ranging from 0 to 40 m/s with a 1 m/s interval.

Figure 2 :
Figure 2: The MAE of the same site random forests, when features are added progressively

Figure 3 :
Figure 3: Normalized importance of each feature considered by the random forests, developed at IJmuiden (a) and at FINO3 (b)

Figure 5 :
Figure 5: The error dependency of the two random forest models to the wind speed at 274 m, when tested at NSO.The error curves are shaded with the standard error of the mean.

Table 1 :
Summary of the sites and their measurement periods used in this study.

Table 3 :
The default hyperparameters and the grid tried out to tune the models.'sqrt' stands for the squared root of the total number of features.

Table 4 :
Measured features for the random forests.u and dir are acronyms for wind speed and wind direction and the heights are above mean sea level.

Table 5 :
Heights where lidar measurements and WRF outputs are available at each site

Table 6 :
Performance metrics of the two random forests and WRF model at the studied sites