# Mid-to-Long Range Wind Forecast in Brazil Using Numerical Modeling and Neural Networks

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## Abstract

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## 1. Introduction

## 2. Data Description

#### 2.1. Local Wind Characteristics and Data Screening

#### 2.2. Global Atmospheric Ensemble Forecast

## 3. Assessment of the Numerical Ensemble Forecast Data

## 4. Neural Networks for Post-Processing

- (i)
- Build one NN for each station, independently. Therefore, the datasets of neighboring stations are not included into the NN training and modeling, i.e., the inputs (ECMWF forecast) and outputs (residue of wind) are restricted to that specific station.
- (ii)
- Build a large NN where inputs are the information from all the stations inside the cluster (10 for Maranhão and 6 for Piauí) and the outputs are the residues of wind speed for the same stations. In this way, the dataset $D$ is expanded in ${{\rm X}}_{j}$, where ${{\rm X}}_{j}$ corresponds to the environmental variables at each station. The data space for this approach, for example at Maranhão with 10 stations, would be ${\mathbb{R}}^{d\times 10,n}$.
- (iii)
- Build one NN where inputs and outputs are variables for each station, which are one by one appended to generate a new dataset, where two new variables’ latitude and longitude are included to distinguish the stations. In this case, the training consists of an NN model passing through each station inside the cluster during the process. Note that the training data is constructed by appending the dataset of each station consecutively, so that the NN minimizes the error at the whole group of stations. Following the same example at Maranhão with 10 stations, the new space becomes ${\mathbb{R}}^{d+2,n\times 10}$. It is important to highlight that in (ii), the number of input variables and dimension $d$ is significantly augmented (10 times in Maranhão), whereas in (iii), the number of variables is just $d+2$, while the number of records is significantly expanded—following a similar approach of space/time trade proposed by the regional frequency analysis [53].

## 5. Results

#### 5.1. Neural Network Architecture and Ensemble

- The NNs with normalized bias above 10% are excluded, including the mean value (through forecast range) as well for each forecast lead time.
- The NNs with bias or RMSE worse than the ECMWF ensemble forecast are excluded, i.e., no NN model can risk deteriorating the original ECMWF prediction.
- Additionally, the algorithm analyzes each month of the year, excluding NNs with bias and RMSE worse than ECMWF.
- The algorithm runs the error metrics through the forecast lead time (1 to 46 days) excluding the worst NN at each forecast lead (day), which prioritize networks more consistent over the months.
- The last monthly swap is done at this stage, excluding the single worst network at each month.
- After the exclusions of steps one to five, the algorithm takes the remaining networks and builds two ranks with the best SI and CC, calculating the intersection of the two lists. The top 20 networks are finally selected to compose the ensemble of NNs.

#### 5.2. Evaluation of Results

## 6. Final Discussion

## 7. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 2.**Position of the atmospheric measurements located in the northeast of Brazil. The cold colors on the left indicate ten stations in the state of Maranhão, while the hot colors on the right indicate six stations in the state of Piauí. The same color standards will be used throughout this paper.

**Figure 3.**Wind speed (m/s) measured by 16 anemometers located in the northeast of Brazil (Figure 2) from September 2017 to August 2020. The observations are relative to 80 m height, the default level used in this paper for both observations and forecasts.

**Figure 4.**Cluster analysis of three years of atmospheric data from 16 stations in the northeast of Brazil. (

**a**) Elbow plot for the decision of the best number of clusters. (

**b**) Meridional wind component versus zonal wind component, where the colors represent each station showed in Figure 2. (

**c**) Correlation matrix (Pearson) among the 16 stations. (

**d**) Predictive Power Score among the 16 stations.

**Figure 5.**Chiclet charts of wind speed (m/s), where consecutive forecasts are plotted in the x-axis, being the forecast lead time (days) in the y-axis (panel (

**A**)). The wind speed observations have been collocated to the exact forecast times in panel B, calculating the difference between the arithmetic ensemble mean and the measurements. Hot colors in the bottom plot (

**B**) show overestimation of forecast winds while cold colors show underestimation. Both plots refer to station (302) at Maranhão/Brazil and the daily average is employed.

**Figure 6.**ECMWF forecast error as a function of the forecast time at Maranhão, where thin lines are the ensemble members, and the solid thick lines are the arithmetic ensemble mean. Plots on the left (

**A**,

**D**) show the scatter error through the scatter index (SI). Center plots (

**B**,

**E**) show the correlation coefficient. Plots on the right (

**C**,

**F**) show bias (in m/s and hPa). The top plots present the wind speed errors while the bottom plots present the atmospheric pressure errors. The same color standards of Figure 2, for each station, are retained.

**Figure 7.**ECMWF forecast error as a function of the forecast time at Piauí, where thin lines are the ensemble members, and the solid thick lines are the arithmetic ensemble mean. Plots on the left (

**A**,

**D**) show the scatter error through the scatter index (SI). Center plots (

**B**,

**E**) show the correlation coefficient. Plots on the right (

**C**,

**F**) show bias (in m/s and hPa). The top plots present the wind speed errors while the bottom plots present the atmospheric pressure errors. The same color standards of Figure 2, for each station, are retained.

**Figure 8.**Schematic of the hybrid model implemented. The ECMWF ensemble forecast (green) provides the arithmetic ensemble mean of the members that is added to the NN forecast (red, the residue). If the observations had no uncertainties and errors, one could describe that the NN predicts the error of the ECMWF ensemble forecast, which is added to the original prediction to compose the final forecast product, being the wind speed the final target variable.

**Figure 9.**Correlation results of four probabilistic moments (calculated using 51 ECMWF ensemble members) with the target variable of the NN model (residue of wind speed; in black). The first six bars on the left of the plot (blue and black) are related to NN outputs while the remaining bars are related to NN inputs.

**Figure 10.**Illustration of the cross validation with three cycles (

**A**) where the training set (green, blue, and black) and test set (red) are created. The bottom plot (

**B**) presents the data split of one year of validation set (red) from the training + test set (green, blue, and black), also with three cycles.

**Figure 11.**Analysis of the error as a function of the number of neurons at the intermediate layer. Despite the curve indicating the best number equal to 20, the differences among tests are small, as shown in the y-axis of the plots.

**Figure 12.**Scatter plots of NN simulations of wind speed (m/s) versus observations, comparing different numbers of neurons, in the training set (

**left**) and validation set (

**right**). The top-left box of each plot shows the number of neurons at one or two layers.

**Figure 13.**Wind speed (m/s) Bias (

**top**) and RMSE (

**bottom**) of the ensemble of NNs calculated for each month of the year (x-axis). NN_AY is the all-year approach (blue); NN_SWind refers to NNs trained during the strong wind season; NN_LWind refers to NNs trained during the light wind season; EM is the ECMWF ensemble mean (red) used as reference.

**Figure 14.**Assessment results of the ensemble of NNs when compared to the initial ECMWF forecast, for the forecast range from 1 to 15 days. Wind speed (m/s) Bias (lest), RMSE (center), and correlation coefficient (CC; right) are presented. Colors refer to: NN training set in dashed blue, NN test set in dashed-dotted cyan; NN validation set in green; the ECMWF forecast in red.

**Figure 15.**Assessment results of the ensemble of NNs when compared to the initial ECMWF forecast, for the forecast range from 16 to 46 days. Wind speed (m/s) Bias (lest), RMSE (center), and correlation coefficient (CC; right) are presented. Colors refer to: NN training set in dashed blue, NN test set in dashed-dotted cyan; NN validation set in green; the ECMWF forecast in red.

**Figure 16.**Chiclet chart presenting the reforecast results of wind speed (m/s) for the state of Piauí.

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## Share and Cite

**MDPI and ACS Style**

Campos, R.M.; Palmeira, R.M.J.; Pereira, H.P.P.; Azevedo, L.C.
Mid-to-Long Range Wind Forecast in Brazil Using Numerical Modeling and Neural Networks. *Wind* **2022**, *2*, 221-245.
https://doi.org/10.3390/wind2020013

**AMA Style**

Campos RM, Palmeira RMJ, Pereira HPP, Azevedo LC.
Mid-to-Long Range Wind Forecast in Brazil Using Numerical Modeling and Neural Networks. *Wind*. 2022; 2(2):221-245.
https://doi.org/10.3390/wind2020013

**Chicago/Turabian Style**

Campos, Ricardo M., Ronaldo M. J. Palmeira, Henrique P. P. Pereira, and Laura C. Azevedo.
2022. "Mid-to-Long Range Wind Forecast in Brazil Using Numerical Modeling and Neural Networks" *Wind* 2, no. 2: 221-245.
https://doi.org/10.3390/wind2020013