Analysis of the Wind Potential in the Mexican Republic and Prediction of Its Behavior through Dense Neural Networks

Climate change is a global issue that has driven the adoption of renewable energies due to their sustainability and environmental benefits. However, these energies face limitations, such as the lack of regional studies on wind or solar dynamics and the efficiency of energy systems. Tools that simulate and calculate energy potential while considering uncontrollable climatic variables are crucial for optimizing the design of these systems. Artificial intelligence, particularly multilayer neural networks, has proven effective in data prediction across industries. This paper focuses on training a 3-layer neural network using the ReLU activation function and quadratic error to predict wind potential density in Mexico, aiming to identify key areas for renewable energy development.

Keywords:

Subject: Environmental and Earth Sciences - Atmospheric Science and Meteorology

1. Introduction

Energy demand on our planet has increased at an alarming rate, which has caused a serious impact on our environment, the extraction of natural resources needed to satisfy energy demand are causing irreversible damage. As this energy consumption has become an indispensable part of our daily lives, it has become imperative to prioritize the implementation of sustainable energy systems. However, the challenge is twofold: meeting the growing energy demand and designing environmentally friendly systems to reduce the use of non-renewable resources such as coal, diesel and natural gas, since most of the world’s energy is still produced by these fuels [1,2].

Nevertheless, the implementing such systems requires that the conditions of the area are suitable for the application of these systems, therefore, comprehensive studies are needed to know the environmental behavior of the area for extended periods of time [3], to facilitate these studies have been used several tools, including climate prediction, these predictions give us a future vision of the climatic interactions of a region and help to calculate the electrical potential that the system can generate. However, making predictions for extended periods is a difficult task that requires powerful equipment to obtain relevant data; in the early 20th century, it took at least six weeks of work to predict weather patterns only six hours in advance [4].

To address this challenge, mathematical fluid mechanics models have been used to fine-tune weather prediction. These models allow us to predict the future state of the atmosphere from an initial state [5]. However, the analytical equations used in these models can be problematic to process by computers, as they require long processing times, so to overcome this, numerical weather prediction (NWP) has been developed, which eliminates the need to deal with the fluid mechanics equations analytically, and instead, treats them in the form of numerical integrals, using the previous state of the atmosphere to predict future states [6].

1.1. Renewable Energy in Mexico

The new laws in the Mexican Republic require a decrease in greenhouse gas emissions, it is expected that there will be a 50% reduction by 2050, a strategy to reduce dependence on fossil fuels, is the use of renewable energy sources, Mexico has a large amount of renewable energy sources (oceanic, hydroelectric, geothermal, biomass, wind and solar), so the projects to generate energy have great potential, however, this is still a hard work since the energy consumption in Mexico is 257 TW/h, of which 80% is generated by fossil fuels, 13% is produced by hydroelectric energy, 4% by nuclear energy, 2%. The north of the Mexican Republic has 5 states (Sonora, Chihuahua, Nuevo León and Tamaulipas) which represent 36.9% of the national territory, and have a great wind energy potential, however the use of wind energy is very low according to data collected by National Institute for Forestry, Agriculture and Livestock Research (INIFAP) and National Meteorological Service (SMN) [7].

The northern states of the republic, as well as Baja California Norte and Oaxaca in the south, are very important points for energy generation. Disadvantages of wind energy include its intermittent nature, meaning it can only generate electricity when the wind blows at certain speeds, making it less reliable than other energy sources. Wind turbines can also have negative impacts on wildlife, including birds and bats. Additionally, wind farms can be visually intrusive and noisy, which can cause issues for nearby residents [7,8,9]. However, the use of a neural network can help predict and optimize wind energy systems by analyzing large amounts of data on weather patterns, wind speeds, and energy production. This can allow for better decision-making on when and where to deploy wind turbines, as well as how to adjust their settings for optimal energy production.

1.2. Weather Prediction Using Neural Networks

Neural networks are an effective tool for modeling nonlinear systems, since they do not consider the mathematical relationship with natural phenomena that follow chaotic models of entropy [10], which has made them a powerful tool for scientific research, one of the areas where it has been most used is in meteorology, they are one of the most feasible and useful methods to perform modeling of different climate variables, which is important for the economic and energy development of the country.

Knowing the climatic behavior of the Mexican Republic area in the future would provide us with very relevant information when establishing energy and agricultural projects, which would allow us to know the best place for such projects, so that the benefit of these is greater, optimizing the consumption of resources for greater benefit, so the objective of this work is to design a tool that through supervised machine learning, in order to learn the wind behavior using historical databases from 1981 to 2022, which would give it the ability to model wind potential of the Mexican Republic in the future, which will allow us to know the most important points for wind power generation and how much energy could be obtained to support the energy demand.

2. Materials and Methods

2.1. Study Area

The study area was delimited at latitudes 35°N, 14°N, longitudes -86°W, -118°W, corresponding to the Mexican Republic (Figure 1), located in North America, with a territorial extension of 1.973 million km^2, has a great geographic and climatic diversity. This diversity, together with its extensive coastline and geographic position, make it a place with great wind potential. Among the areas with the greatest wind potential in Mexico are the Baja California Peninsula, the Isthmus of Tehuantepec in Oaxaca and the northern region of the country, in the states of Chihuahua, Coahuila and Nuevo León, these regions have constant and strong winds throughout the year [8].

2.2. Data Base

Two databases were used for this study, which provided us with the necessary data to carry out the training of our neural network, Livneh and ERA5.

Livneh hydrometeorological dataset provides us with daily and monthly climate variables such as maximum and minimum air temperature, and wind speed for the continental U.S., southern Canada and Mexico for the period 1950-2013. All represented on a grid with a horizontal resolution of 1/16° (~ 6 km), the data have been used as training data for downscaling GCMs, as validation for numerical weather prediction models, and as datasets for offline land surface models in support of various historical investigations. Temperature and precipitation data are from about 20,000 weather stations from GHCN-daily, Environment Canada, and the National Meteorological Service (Mexico). Wind data are from the NCEP-NCAR reanalysis [11].

(Available at: http://192.12.137.7/pub/dcp/archive/OBS/livneh2014.1_16deg/netcdf/daily/).

ERA5 reanalysis for the global climate and weather provided by ECMWF (“European Centre for Medium-Range Weather Forecasts”), which provides global information from 1950 to the present day, we took data from January 1st, 1981, to December 31st, 2022. The database provides information on different climate variables [12], but for this work we focused on reanalysis using the wind speed components at 100 meters (m/s), focusing on the territory of the Mexican Republic, which provides us with a data matrix of 85x129x15340, corresponding to -118° to -86° from east to west, 35° to 14° north to south, with a separation of 0.25° between each point, and 15340 days of observation.

(Available at: https://cds.climate.copernicus.eu/cdsapp#!/dataset/reanalysis-era5-single-levels?tab=overview).

2.3. Wind Power Density

Since the Livneh data has a period of recorded data from 1950 to 2013, for comparative purposes the most recent 20 years, corresponding to the period from 1994 to 2013 were taken for comparison with the same period of ERA5 data, the data provided by Livneh, being from a weather station are surface data, so they had to be extrapolated to 100m, this was done in order to be able to compare the data provided by Livneh with the data provided in ERA5, to bring them to the same spatial resolution, since ERA5 is a lower resolution database. the average height of a wind turbine, for which we used the power laws:

\frac{u_{2}}{u_{1}} = {(\frac{Z_{2}}{Z_{1}})}^{α}

(1)

where

u_{2}

and

u_{1}

represent the wind speeds at heights

Z_{2}

and

Z_{1}

, respectively, and α is the power law index equivalent to 1/7, for ideal conditions.

The wind potential density (WPD) provides information on how much energy can be generated in a specific location. We computed WPD [13] at 100 m as follows:

W P D = \frac{1}{2} ρ V^{3}

(2)

where

ρ

is air density in

k g / m^{3}

using a constant value of 1,255

k g / m^{3}

and

V

is the wind speed in m/s taken at 100m [14,15].

The Figure 2a corresponds to the average WPD value obtained through ERA5 reanalysis. We can observe that the maximum points are in Baja California peninsula, Oaxaca, part of Zacatecas, Chihuahua, Nuevo León, Tamaulipas, Yucatan, and Quintana Roo. On the other hand, in image 2b, which corresponds to the data obtained by Livneh for the same period, we can see that the maximum points are in Baja California peninsula, the northern part of Chihuahua, Coahuila, Nuevo León, Tamaulipas, Yucatan, and Quintana Roo, for the period from 1993 to 2013. Finally, image c represents the difference between these datasets, which indicates how similar their behavior is this is consistent with previous studies [16] shows maximums in Baja California Sur, Chihuahua, Tamaulipas, Yucatan, and Quintana Roo, with values ranging from 125 to 225

W / m^{2}

2.4. Perceptron Architecture and Operation

With the obtained data and using the wind power equation 1 we carried out the evaluation of the daily wind power potential of the Mexican Republic. With this data, we trained a neural network using data from 1981 to 2020 for training, and data from 2021 to 2022 for prediction testing. Python was used for the design of the network, along with the tensorflow and keras libraries, we used the workstation of the Autonomous University of Aguascalientes, which has 2 Intel Xeon Gold 5812R processors with 20 cores and 2 UPI (Ultra Path Interconnect) links, which are a high-speed point-to-point interconnect bus between processors that offer higher bandwidth and performance, with a frequency of 2.1 to 4 GHz. It also has 255 GB of RAM and an NVIDIA Quadro RTX4000 card. Using this architecture, we designed the neural network, and Python was used to develop the scripts, as this system has an extensive collection of libraries that facilitate the handling of large amounts of data, and has great support for Machine Learning programming and work.

The proposed architecture for this work was a dense multilayer perceptron Figure 3, with a configuration of 5 input neurons, corresponding to year, month, day, temperature, and atmospheric pressure, respectively, for each point in our data mesh. Internally, the network has 3 dense layers, the first with 512 neurons, the second with 256, and the last with 128, all with a ReLU (Rectified Linear Unit) activation function. The output layer has 10965 neurons, corresponding to each point in the mesh, achieving a prediction for the entire Mexican Republic.

The database used corresponds to January 1, 1981 to December 31, 2022, the data were separated into 2 sets (Figure 4), training data (1981-2020), validation data (2021-2022), the data was used a batch size of 30 days, and a validation split of 0.33 for the separation of training blocks, the training was completed at 200 epochs, the test data were never entered during the training.

By applying the mean square error (MSE) loss function to each neuron with a learning factor of 0.001 we ensure that it is possible to reach the learning level without overtraining by using the equations:

M S E = \frac{1}{n} \sum_{i = 1}^{n} {(y_{i} - \hat{y_{i}})}^{2}

(3)

3. Results

Different tests and training were carried out to find the behavior that best suited the overall training process for the different neural network’s configuration. The total training time was 486 hours, resulting in the outcomes shown in Table 1.

When carrying out the different tests with different optimizers, it can be observed that the best result was obtained by the Adam-RMS configuration, as shown in Figure 5. It can be observed that the best possible result was achieved by combining the Adam optimizer with the mean squared error correction function, after the learning process of 300 epoch, during which the network reached its maximum learning, obtained a 96% similarity with the validation data.

In Figure 6a, corresponding to the WPD data obtained with ERA5 for the period from 2021 to 2022, we can see that the points with the highest energy production correspond to Baja California South, the northern part of Nuevo León, Tamaulipas, Chihuahua, part of Zacatecas bordering San Luis Potosí, as well as the Isthmus of Tehuantepec with energies between 100 to 200

W / m^{2}

. We also have areas such as Yucatan, Quintana Roo, and the northern part of the country where we can observe wind potential between 50 to 125

W / m^{2}

. In Figure 6b, we can observe its standard deviation, where we can see its maximums in Chihuahua, Baja California north and south, as well as Oaxaca. Figure 6c presents a prediction for the same period of years obtained through the perceptron, once the training was done. The data obtained from this process was not used during the training of the network. We can observe its maximums in Nuevo León, Tamaulipas, Zacatecas, Chihuahua, Baja California, and the Isthmus of Tehuantepec, with values between 100 to 200

W / m^{2}

, as well as values between 50 to 125

W / m^{2}

in areas such as Yucatan and Quintana Roo. In Figure 6d, we can see that its standard deviation marks its maximums between Zacatecas, San Luis Potosí, Baja California north and south, Chihuahua, and part of Oaxaca. We can verify that the values reported by ERA5 are very similar to those obtained by the neural network. In Table 2, we can see that their average values are very similar, 69.35

W / m^{2}

for ERA5 and 68.35

W / m^{2}

for the neural network. The reported values are consistent with previous studies that analyzed wind behavior in different parts of the Mexican Republic [17].

Table 1. Mean values for perceptron, ERA5, standard deviation, and the coefficient of determination.

	MEAN	SD	R2
ERA5	69.352	78.776	0.845
PERCEPTRON	68.352	75.833	0.834

From the statistical test (Figure 7), it could be observed that the prediction made by the ADAM-RSM model is statistically significant, Different seasonal models were made for comparison, verifying that the learning of the network emulates the wind behavior in different seasons and not only in average values (Figure 8).

Figure 9 shows the seasonal behavior of wind power potential in Mexico. In Figure 8a, we have the WPD in winter, with the highest values in the northern region of Tamaulipas and Oaxaca, reaching up to 100 a 175

W / m^{2}

, followed by Zacatecas, Durango, Chihuahua, Baja California Sur, and Yucatan, with values ranging from 75 to 125

W / m^{2}

. In Figure 8b, corresponding to spring, we can see that this pattern of maxima continues. In summer, shown in Figure 8c, the reported wind is lower, resulting in potential maxima ranging from 25 to 75

W / m^{2}

. In autumn, shown in Figure 8d, the wind potential is even lower, with values ranging from 12.5 to 75

W / m^{2}

, Figure 8e corresponds to the data obtained by our neural network for the winter season of 2021 and 2022, where we can observe that the maximums are found in the isthmus of Tehuantepec, north of the states of Nuevo Leon and Tamaulipas, and the peninsula of Baja California with an energy density of between 75 to 200

W / m^{2}

, in Figure 8f, which corresponds to spring, we observe that this behavior is maintained with intensities of 50 to 125

W / m^{2}

, in Figure 8g corresponding to the summer season, the wind potential decreases with maximums of 25

W / m^{2}

, while in winter Figure 8h the energetic power is maintained between 12. 5

W / m^{2}

to 50

W / m^{2}

Figure 8i shows us the difference that exists between the data obtained by ERA5 and the prediction of our neural network in winter. It is observed that the difference between them is minimal with values very close to each other counting with an error of ±3. 795

W / m^{2}

between their data, for Figure 8j corresponding to spring the correlation between their data has an error of ±6.05

W / m^{2}

, for the image 8k corresponding to the summer season, the error is 0.09

W / m^{2}

, while for the autumn season 8l we have an error of ±3.46

W / m^{2}

With the proposed configuration we achieved a statistically acceptable accuracy when recreating observations with our neural network, both in annual average data and seasonal data, a new model was made, comparing it with the latest data provided by ERA5 to date Figure 9.

Figure 9 provides information on several important points, which would be of interest when proposing wind projects, among them we have the peninsula of Baja California, the northern part of the country, the isthmus of Tehuantepec, with values ranging between 100 to 200

W / m^{2}

, the annual average values for some of the points of interest for this study can be seen in Table 3, the data obtained by the neural network provide us with short- and long- term information, and agree with the data reported in specific studies for specific areas of Mexican Republic [7,8,18,19].

Table 2. Mexican states with the highest average wind power potential .

State	$W / m^{2}$	Speed Wind m/s	Altitude m
Aguascalientes	216	5.79	100
Baja California norte	719	7.79	100
Nuevo León	435	7.54	100
Tamaulipas	516	8.04	100
Chihuahua	359	6.69	100
Oaxaca	1009	8.87	100

5. Conclusions

This study presents a very innovative approach for the prediction of wind potential in the Mexican Republic, by using neural networks using a multilayer configuration together with the combination of the ReLu activation function and the Adam-RMS algorithm, this approach outperformed the different models, the ReLu activation function helps to solve the downward gradient problem, which allows a faster and more accurate training, which considering the size of the database is a significant benefit achieving an optimal learning for Deep Learning, The Adam-RMS algorithm, on the other hand, adapts the learning rate for each parameter, effectively balancing the convergence speed and accuracy of the model, this combination allows the model to reach a statistical similarity of 96% with the data obtained through satellite measurements, a quite significant level, given that weather forecasting is a very complex field and presents very big challenges both at a local and global scale, considering the chaotic nature of these weather systems.

The results help us to identify and corroborate strategic zones, which can be useful when developing wind energy projects in Mexico, such as the regions in the north of the country (Nuevo Leon, Tamaulipas, Chihuahua), Central (Zacatecas, San Luis Potos and Aguascalientes) and the southern zone (Oaxaca), these regions show a high potential for wind energy generation, with values ranging from 200 to 1000

W / m^{2}

In addition to detecting strategic zones, this level of detail in the predictions provides us with a very useful tool when planning and designing wind farm projects, thus optimizing the cost-benefit ratio of the project.

Another advantage that this study provides us is the obtaining of simulations in real time, which is fundamental for the planning of energy resources in the short and long term, also because of the way and the training model used and its data validation, it can be extrapolated to different regions not only within Mexico but also globally, by modifying the input data and the size of the training matrix, this makes that retraining is performed with each prediction and data validation, opening the door to future research that could focus on the integration of hybrid learning techniques to improve the models with other graphical and energetic contexts.

Finally, the results obtained align with global efforts towards an energy transition to mitigate climate change. The ability to identify potential areas and optimize the use of renewable energy sources is crucial to reduce dependence on fossil fuels and mitigate

C O_{2}

emissions in the atmosphere. Therefore, this study not only contributes to the field of artificial intelligence and neural networks, but also offers a practical tool to address the challenge we face with energy sustainability.

Author Contributions

Methodology, M.M-A; validation, M.M.-A, L.O.S.-S. and C.L.C.-M; formal analysis L.E.B.-G, E.G.-S and H.A.G.-O, supervision L.O.S.-S, project administration M.M.-A, L.O.S.-S. All authors contributed to the study conception and design. Material preparation, data collection and analysis were, the first draft of the manuscript was written by Mario Molina-Almaraz, and all authors commented on previous versions of the manuscript. All authors read and approved the final manuscript.

Funding

This research received no external funding.

Institutional Review Board Statement

Not applicable

Informed Consent Statement

Not applicable.

Data Availability Statement

The dataset used can be found at the following GitHub link: https://github.com/mm3227/WP. (accessed on 05 october 2024).

Acknowledgments

The authors are thankful to the support from CONACYT, Copernicus, European Centre for Medium-Range Weather Forecasts, and the National Oceanic and Atmospheric Administration, for providing the databases for this work and the University Autonomy of Aguascalientes they provided the equipment for the network training.

Conflicts of Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper

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Figure 1. Study area, Mexican Republic topography above sea level

(m) .

Figure 1. Study area, Mexican Republic topography above sea level

(m) .

Figure 2. a), WPD ERA5 in the period 1994-2013 (

W / m^{2}

), b) WPD Extrapolated for Livneh surface data from 10m to 100m for the period 1994-2013 (

W / m^{2}

Figure 2. a), WPD ERA5 in the period 1994-2013 (

W / m^{2}

), b) WPD Extrapolated for Livneh surface data from 10m to 100m for the period 1994-2013 (

W / m^{2}

Figure 3. Example diagram of fully connected multilayer perceptron, image taken from https://tikz.net/neural_networks/.

Figure 4. Diagram of the functioning and operation of the neural network.

Figure 5. Evaluation of the deviation between the predictions made by the NN and the actual values of the observations used during the learning process.

Figure 6. The 2-yr average of WPD (a), and the standard deviation (b) in W/m^2 according to ERA5 during 2021-2022. (c)–(d) like to (a)–(b) but for NN during the same period.

Figure 7. Two-Sample t-Test a) ERA5-NeuralNetwork Statistical distribution of data b) probability distribution, the blue line corresponds to the ERA5 data, the dotted lines correspond to its proximity to the straight line represented by R^2. (c)–(d) like (a)-(b) but for NN.

Figure 8. a-d) ERA5 seasonal period 2021-2022, (e-h) NN seasonal period 2021-2022, (i-l) Differences between ERA5-NN.

Figure 9. a-c) WPD reported for ERA5 in 2023, (d-f) NN predicted model.

Table 1. Optimizers and configuration of the perceptron, SGD (Stochastic Gradient Descent), AdaGrad (adaptive gradient algorithm), RMSprop (Root Mean Square Propagation), Adam (adaptive moment estimation).

Optimizer	Neurons	Activation	epoch	Predictors	Accuracy
SGD	896	ReLU	1000	5	65%
AdaGrad	896	ReLU	1000	5	68%
RMSprop	896	ReLU	1000	5	65%
Adam	896	ReLU	500	5	75%
Adam-RMS	896	ReLU	200	5	96%

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