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Article

Rainfall Projections for the Brazilian Legal Amazon: An Artificial Neural Networks First Approach

by
Luiz Augusto Ferreira Monteiro
1,*,
Francisco Ivam Castro do Nascimento
1,
José Francisco de Oliveira-Júnior
2,
Dorisvalder Dias Nunes
1,
David Mendes
3,
Givanildo de Gois
4,
Fabio de Oliveira Sanches
5,
Cassio Arthur Wollmann
6,
Michel Watanabe
1 and
João Paulo Assis Gobo
1,*
1
Departament of Geography, Federal University of Rondônia (UNIR), Porto Velho 76801-059, Rondônia, Brazil
2
Institute of de Atmospheric Sciences (ICAT), Federal University of Alagoas (UFAL), Maceió 57072-900, Alagoas, Brazil
3
Department of Atmospheric and Climatic Sciences (DCAC), Federal University of Rio Grande do Norte (UFRN), Natal 59078-970, Rio Grande do Norte, Brazil
4
Environmental Sciences Postgraduate Program (PPGCA), Campus Floresta, Federal University of Acre (UFAC), Cruzeiro do Sul 69895-000, Acre, Brazil
5
Departament of Geosciences, Federal University of Juiz de Fora (UFJF), Juiz de Fora 36036-900, Minas Gerais, Brazil
6
Department of Geosciences, Federal University of Santa Maria (UFSM), Santa Maria 97105-900, Rio Grande do Sul, Brazil
*
Authors to whom correspondence should be addressed.
Climate 2024, 12(11), 187; https://doi.org/10.3390/cli12110187
Submission received: 4 October 2024 / Revised: 11 November 2024 / Accepted: 12 November 2024 / Published: 15 November 2024
(This article belongs to the Special Issue Addressing Climate Change with Artificial Intelligence Methods)

Abstract

:
Rainfall in the Brazilian Legal Amazon (BLA) is vital for climate and water resource management. This research uses spatial downscaling and validated rainfall data from the National Water and Sanitation Agency (ANA) to ensure accurate rain projections with artificial intelligence. To make an initial approach, Recurrent Neural Networks (RNNs) with Long Short-Term Memory (LSTM) were employed to forecast rainfall from 2012 to 2020. The RNN model showed strong alignment with the observed patterns, accurately predicting rainfall seasonality. However, median comparisons revealed fair approximations with discrepancies. The Root Mean Square Error (RMSE) ranged from 6.7 mm to 11.2 mm, and the coefficient of determination (R2) was low in some series. Extensive analyses showed a low Wilmott agreement and high Mean Absolute Percentage Error (MAPE), highlighting limitations in projecting anomalies and days without rain. Despite challenges, this study lays a foundation for future advancements in climate modeling and water resource management in the BLA.

1. Introduction

Rainfall in the Brazilian Legal Amazon (BLA) has a fundamental importance for climate scenarios [1,2], strategic scenarios [3], water resources [4,5], and climate change [6]. Several research studies in the BLA have already been conducted; for example [7], explore the use of observational data from traditional meteorological stations, whereas [8] discuss the use of automated stations. Several studies have used data from environmental satellites [9], grid products [10,11], and numerical simulations [12,13].
The Amazon Forest plays a significant role in the interchange of energy, water, and carbon with the planet’s atmosphere; hence, there is a need to better understand its rainfall regime and climate [13,14]. The water balance of the area can change over time due to human actions (e.g., deforestation and fires) and extreme natural events (e.g., droughts and floods) caused by El Niño (droughts) and La Niña (increased rainfall). Other climate anomalies can also impact the BLA [15,16].
According to [17], air humidity created by the BLA has an impact on rainfall in numerous locations in Brazil and Argentina. Deforestation within the limits of the BLA has been identified as a factor that can lead to a reduction in rainfall in these areas, as shown in research carried out by [18], being the result of several elements, such as the absence of adequate government policies and the increase in agricultural and livestock activities, as highlighted by [19,20].
In addition to the previously listed variables, those associated with climate change, such as decreasing rainfall, higher air temperature, and the dry season, also play a key influence, producing an exacerbation of drought conditions in the BLA, affecting each region differently according to its climatic variability, as pointed out by [21,22].
Rainfall data from Brazilian meteorological stations net are known to be prone to failure, particularly in the BLA. However, such issues did not prevent the BLA from conducting rainfall research, some of which included gap-filling approaches such as simple linear regression (RLS), data imputation, and outlier treatment [23,24]. RLS is the gap-filling method used by the World Meteorological Organization (WMO) [25,26].
Time series data imputation is required and acceptable for future analyses [27]. On the other hand, the treatment of outliers might uncover outliers, which can have a detrimental impact on statistical analyses or predictive modeling [28].
There are observational studies, such as [7], which have examined rainfall in the BLA using observational data, with data quality control based on data imputation techniques and outlier removal. They discovered tendencies of increased rainfall in various areas. Furthermore [29], examined rainfall data from the BLA on a monthly and yearly basis, as well as their features. They examined the National Water and Sanitation Agency (ANA) database, with 2029 stations; however, only 591 stations were constantly working over a period of 30 years. They determined that rainfall in the BLA is not homogenous and is nevertheless impacted by multiscale meteorological systems.
Due to discrepancies in the rainfall data, climate modeling was used to assess the historical and future rainfall in the BLA [30,31]. To estimate rainfall features, the models consider a variety of input variables, including Sea Surface Temperature (SST), winds, soil humidity, relief, and atmosphere–ocean interactions [32]. However, it is vital to emphasize that the use of climate modeling is prone to uncertainty [33].
Other investigations have employed satellite data and numerical simulations [12,34,35]. The benefit of employing these sorts of data is their worldwide coverage, which provides for access to locations that would otherwise need in-person observation. However, such data are indirect measures that must be validated with in situ data [36]. Ref. [37] emphasize the trustworthiness of rainfall estimations using the TRMM 3B42 satellite, which reliably reproduced observed rainfall data. The seasonal variability in rainfall was well captured, and while there were discrepancies between point measurements, the averages throughout the basin produced values that were extremely close to those derived from rainfall data. Ref. [38] add to this perspective, demonstrating that, while satellite data are a helpful tool and can come close to data acquired in situ, equivalency between the two is unusual.
Ref. [32] analyzed data from the Tropical Rainfall satellite. The Rainfall Measuring Mission (TRMM) used data from the Legal Amazon Project’s Satellite Monitoring of Deforestation (PRODES) to investigate the link between rainfall and deforestation. In the stations studied, variety was detected in the rainfall trend, with some showing a reduction in rainfall and others an increase. Furthermore, according to [32], these fluctuations can be linked not just to deforestation, since much of the decline happens in places with a high rate of deforestation, but also to other variables, such as the impact of climatic anomaly modes. Furthermore [39], demonstrated that atmospheric circulation, deforestation, and land use and occupation, using data from the Climate Hazards product Group Infrared Precipitation with Stations (CHIRPS) and ERA5-Land, impact rainfall dynamics in the BLA.
In addition to the studies that use a variety of data sources, artificial intelligence (AI) has emerged as a valuable complement to research, using Artificial Neural Network (ANN) algorithms to forecast climate events [40,41,42]. A key property of AI is the capacity to handle massive amounts of data and detect complex patterns [43].
Ref. [44] used observational data to illustrate the capability of forecasting rainfall variability in the BLA. Furthermore [45], employed an ANN to examine the connection between rainfall and flow in the Guamá River sub-basin in Pará, using ANA data. They employed two distinct RNA architectures: (i) Multilayer Perceptron (MLP) and (ii) Nonlinear Autoregressive with Exogenous Inputs (NARX). They determined that the NARX architecture allowed for the reliable prediction of data from micro and medium river basins in the Amazon.
To gain a better understanding of rainfall in the Brazilian Legal Amazon (BLA), this research concerns analyzing 124 sets of daily rainfall data gathered by the spatial downscaling approach using bilinear interpolation and a Convolutional Neural Network (CNN). In addition, as an initial approach, a Recurrent Neural Network (RNN) model was developed to project rainfall in the BLA based on different datasets, considering a 40-year period (1981–2020). This projection aims to provide a perspective on possible scenarios for a 9-year period in the region, considering rainfall patterns, trends, and anomalies.

2. Materials and Methods

2.1. Study Area

The BLA (Figure 1) comprises 5 million km2, or 58.93% of the Brazilian territory, and was established by Law No. 1806 on 6 January 1953, to accomplish the Amazon Economic Valorization Plan [46]. The area is separated into western and eastern portions [47], and includes the states of Amazonas (AM), Amapá (AP), Acre (AC), Mato Grosso (MT), Pará (PA), Rondônia (RO), Roraima (RR), and Tocantins (TO). Only a portion of Maranhão (MA) is considered part of the Amazon biome—west of the 44th meridian [48,49].
Within this panorama, it is possible to identify the main climatic types present in the BLA according to the Köppen classification, also described in the research by [50]: the monsoon climate (Am), predominant in the region; the equatorial climate (Af), with no dry season and a monthly rainfall of no less than 60.0 mm; the tropical climate with dry winter (Aw), marked by a rainy summer and a dry winter; and the tropical climate with dry summer (As). Refs. [22,51] provided detailed descriptions of these climatic profiles, emphasizing the complexity and variety of climate in the BLA.

2.2. Data Control and Quality

ANA data were used to check around 300 rainfall stations in the BLA area. During this research, a significant prevalence of missing and null data was detected, above the level considered acceptable by studies such as [7], which defined a 10% data quality threshold. Ref. [23] applied an even tougher 5% criterion, identifying just 5 rainfall stations with this feature in data from the National Institute of Meteorology (INMET). However, during the investigation of the time series received using ANA, it was discovered that the proportion of missing data substantially surpassed 20%.
To collect rainfall data, it was decided to apply a spatial downscaling strategy based on linear interpolation and Convolutional Neural Networks (CNNs) [52]. Based on this approach, 122 databases were created, as illustrated by the dots in Figure 1. The databases acquired were separated into two groups: one for the years 1981 to 2000 and the other for the years 2001 to 2020. Then, an algorithm was devised to merge these two bases for usage in the Recurrent Neural Network (RNN).
To confirm data dependability, the bias test, which measures the systematic disparity between observed and simulated values, was performed using the HydroGof package, version 0.6-0.1, in R. The bulk of the findings were regarded as good, with positive values near zero. Only a few examples had values that surpassed 20, indicating that the estimations are trustworthy for time series analysis and may be utilized in predictions created using the RNN method.

2.2.1. Bilinear Interpolation

Bilinear interpolation, used to create the spatial downscaling database, is a resizing technique that estimates the pixel value at a given position by using the four pixels nearest to it. When a point (x, y) in an image does not match to a specific pixel, the values of the four nearest nearby pixels are utilized to determine the value at the point. According to [53], the mathematical description of this technique is as follows:
Let the four pixels be (x1, y1), (x1, y2), (x2, y1), and (x2, y2), with corresponding values l(x1, y1), l(x1, y2), l(x2, y1), and l(x2, y2). The bilinear interpolation value l(x, y) is calculated according to Equation (1):
l x , y = l x 1 , y 1 x 2 x 1   y 2 y 1   x 2 x   y 2 y + l x 1 , y 2 x 2 x 1   y 2 y 1   x 2 x   y y 1 + l x 2 , y 1 x 2 x 1   y 2 y 1   x x 1   y 2 y + l x 2 , y 2 x 2 x 1   y 2 y 1   x x 1   y y 1

2.2.2. Convolutional Neural Networks (CNNs)

The use of CNNs for analyzing rainfall data in the Amazon is justified by the several advantages this method offers over other Neural Networks, especially when dealing with spatiotemporal data and precipitation time series.
Advantages of using CNNs for rainfall data analysis in the Amazon:
-
Efficiency in processing large volumes of data;
-
Ability to handle complex data: CNNs can address the complexity of Amazon rainfall data, which include spatial and temporal variability, seasonality, and extreme events;
-
Automatic feature extraction: CNNs automatically learn the relevant features from rainfall data without the need for manual feature engineering, which simplifies the analysis process and improves model accuracy.
CNNs, employed to improve the quality of the spatial downscaling database, process pictures using many layers of convolution and pooling. Convolution, a type of interpolation, computes the value of a pixel as a weighted sum of nearby pixels using weights (or kernels) learnt during training [54].
The generated picture is compared to the original high-resolution image during training using bilinear interpolation and CNNs [55]. The difference between pictures is utilized as a loss function, such as a mean squared difference, to update the CNN weights [56]. This update allows the network to learn to improve the original estimate provided via bilinear interpolation, hence enhancing its prediction accuracy [55].
Convolutional Neural Networks (CNNs) are powerful tools for analyzing rainfall data in the Amazon, but their use requires attention to some limitations. Data availability is a crucial factor, as the vastness of the region and access difficulties can result in sparse data with gaps, impacting model accuracy. Data quality is also vital. Moreover, the complexity of the Amazon’s climate system, with its variability, extreme events, and ongoing climate change, demands the robust and adaptable use of CNNs.

2.3. Applied Statistics

In this study, Pearson’s correlation coefficient [57] was used, and it is represented by Equation (2), to evaluate the similarity between the data obtained by spatial downscaling and those produced by the algorithm in question.
r = n x y x y n x 2 x 2 n y 2 y 2
where
  • n is the number of data pairs;
  • x and y are the variables;
  • ∑ represents the sum;
  • xy is the sum of the products of x and y;
  • x and ∑y are the sums of the variables x and y;
  • x2 and ∑y2 are the sums of the squares of the variables x and y.
Furthermore, the Willmott concordance index was used, allowing an additional comparative analysis between the statistical methodologies applied to the databases, being represented by Equation (3):
d = 1 i = 1 n O i M i 2 i = 1 n O i O ¯ + M i O ¯ 2
where
  • i is the value observed at position i;
  • Mi is the modeled value at position I;
  • Ō is the average of the observed values;
  • n is the total number of observations.
The coefficient of determination, known as R2, was another important metric applied, but restricted to data generated by the RNN. Its formula (Equation (4)) is given as
R 2 = 1 i = 1 n y i y ^ i 2 i = 1 n y i y ¯ 2
where
  • n is the number of observations;
  • y i is the observed values of the dependent variable;
  • y i is the values predicted by the model;
  • y ¯   is the average of the observed values.
To measure the accuracy of the predictions, according to [58], the Mean Absolute Percentage Error (MAPE) was used, with Equation (5):
M A P E = 1 n i = 1 n A i F i   A i   ×   100 %
where
  • n is the total number of observations;
  • A i   is the actual value observed at position I;
  • F i   is the predicted (or estimated) value at position I;
  • ∣⋅∣ represents the absolute value.
Finally, the Root Mean Square Error (RMSE) was computed to determine the discrepancy between the model estimates and the actual data. According to [59], the RMSE is especially useful, as it highlights bigger mistakes when squaring differences before computing the mean. It is represented by Equation (6):
R M S E = 1 n i = 1 n A i F i 2
where
  • n is the total number of observations;
  • A i is the real value observed at position I;
  • F i is the predicted (or estimated) value at position i.

2.4. Data Grouping

The clustering analysis was based on the K-Means algorithm, using the scikit-learn library in Python. The process can be summarized in the following steps:
  • Access to the database: The manipulation of the method needed access to a database built by spatial downscaling, which includes information such as the position of each point, expressed as geographic coordinates;
  • Application of K-Means: The K-Means algorithm was used to perform the clustering task, and the number of clusters was determined to be 9 after applying techniques such as the elbow method, as illustrated in Figure 2, and the silhouette method (Silhouette Method), as shown in Figure 3 [60,61]. This option proved to be more suited for representing the BLA.
  • Model Training: The K-Means model was trained on the spatial downscaling database, and the cluster centroids (Figure 4) were determined as each group’s midpoints. Each color represents a set of coordinates within each ALB state. When the midpoint of each group was returned, no coordinates from the database were supplied; thus, the coordinate closest to the results obtained from the centroids was picked.

2.5. Artificial Neural Networks

The ANN algorithm was implemented using the Python programming language, version 3.13.0, and the PyCharm Community IDE, version 2024.3. The first step of processing the data into the ANN comprises loading important Python libraries such as Pandas, NumPy, scikit-learn, and Matplotlib.
Pandas is critical in making files easier to access and visualize [62]. Furthermore, it simplifies the data format transition to make them manipulable and turns these data into numeric values, which is especially important when the data are originally in “.txt” format [63]. In turn, NumPy oversees transforming the Pandas database into arrays, which are collections of items of the same type that may be easily manipulated [64]. Scikit-learn is required for the development and use of ANNs [65]. Finally, the results are shown using Matplotlib [66].
The major activation key in the devised method is Long Short-Term Memory (LSTM) [67]. The initial stage was to access and manipulate the database so that it could be processed by the ANN. Following this phase, the data needed to be normalized, which involved placing them on a standard scale to minimize unintended distortions. After the data processing and correction phase, a function was used to effectively prepare the database for LSTM.
The database was then separated into two sets: training and testing. The ANN was then developed using the LSTM design, which included a thick layer and 100 cycles of feedback. Following that, predictions were constructed using both the training and test datasets. After completion, the normalization was reversed to allow the display of the output data, and a correlation calculation was also conducted for further study.
Setting the right hyperparameters for a CNN that analyzes rainfall time series is like fine-tuning the gears of a complex clock. Each parameter—such as the number of layers, the quantity of filters, and the kernel size—affects the network’s ability to capture the intricate rainfall patterns in the Amazon. The learning rate and optimizer guide the learning process, while regularization techniques prevent the model from getting lost in details and missing the bigger picture.
We used five layers in our CNN, even with just one filter, to explore the hierarchical representations of rainfall patterns in the data. This architectural depth allowed the network to learn complex and abstract features, capturing subtle nuances in the temporal and spatial variability of precipitation. The choice of a single filter proved to be suitable for the dataset’s characteristics, simplifying the architecture and reducing computational demand without compromising the CNN’s ability to extract the relevant information.

3. Results

3.1. Scattering Diagram

The RNN algorithm’s rainfall estimates follow a pattern that is extremely similar to the surface data (Figure 5). In many cases, the prediction can properly predict the quantity of rain forecast for each day. This constancy is crucial because it permits a decent modeling of rainfall patterns in the BLA over a substantial time since mid-2012.
The precision of the estimates may be proved by comparing the medians of the observed data to the forecasts generated. For example, in the municipality of Feijó (AC), the actual data show a median rainfall of about 8.0 mm in January 2013, but the estimates show a number closer to 6.0 mm. This minor gap between the medians remains consistent throughout the period, demonstrating the algorithm’s ability to predict rainfall in the BLA.
Arenápolis (MT), Palmas (TO), and Reserva Nacional de Mulata (PA) are excellent examples of how the RNN captures rainfall patterns in the BLA. Over time, fluctuations in the frequency of rain may be seen, allowing the identification of dry and wet seasons in the BLA region.
It is interesting to look at the intervals between years, such as the time between 2012 and 2013, when the predicted data replicate the BLA dry spells, as seen in the downscaling base. The research demonstrates a poor connection between the two time series, namely the actual and predicted data. Nonetheless, the predictions’ ability to replicate rainfall patterns in the region indicates how the RNN might be effective for projecting rainfall data for the BLA.
The downscaling data show abnormal points (outliers) that are attributed to heavy rain during these times, particularly owing to La Niña. Although these outliers may explain the low correlation between the time series, it is worth noting that a previous normalization of the data was performed before processing by the RNN, limiting the influence of the outliers on the data projection.

3.2. Recurrent Neural Network

Downscaling points were accessed; however, the analysis was conducted based on the centroids defined in the grouping stage, which comprised Arenápolis (MT), Feijó (AC), Mirante da Serra (RO), Missão Catrimani (RR), Palmas (TO), Mulata National Reserve (PA), Serra do Navio (AP), Tefé (AM), and Vitória do Mearim (MA) (Figure 6).
The algorithm’s performance ranged from 0.15 (a poor correlation) to 0.48 (the greatest correlation). It should be mentioned that in Palmas (TO), the correlation reached 0.51; however, this was only noticed during the algorithm training phase. This phase is focused solely on understanding the variations contained in the base time series and replicating them in the projection.
In Tefé (AM), both during training and testing, the algorithm showed a poor generalization and agreement with the real data. The forecast values do not approach zero, which explains the lack of rain in this location. However, by the end of the testing session, an improvement is noted, showing that the algorithm tends to project rainfall data in a more consistent manner with the trend of the real data, although weakly. These findings indicate that the algorithm’s performance may vary across different time series.
At other points, the algorithm demonstrated a higher performance, with a good correlation, such as 0.51 in Palmas (TO) and 0.49 in Serra do Navio (AP), throughout training and after the testing phase, with a trend that approximates the actual data. It is noteworthy that, even with a substantial part of the data used to train the algorithm, the municipality of Palmas (TO) achieved good results in the testing phase, maintaining the correlation and rainfall trend almost constantly.
The RMSE of the examined downscaling points ranged from 6.7 mm to 11.2 mm of rain. When the RMSE variances between the forecast rainfall and average rainfall in the real data were analyzed, it was discovered that the algorithm can execute rainfall projections well while avoiding mistakes to the greatest extent feasible. In addition to the minimum RMSE value (6.7 mm), the coefficient of determination (R2) at the Mulata National Reserve (PA) reaches 26%, indicating that a significant proportion of the projections agree with the actual data.
Although the first results were promising, a more extensive examination utilizing the Wilmott concordance index and Mean Absolute Percentage Error (MAPE) revealed less optimism. The correlation created between the observational data and the model’s forecasts did not show a significant link, as evidenced by an agreement index of about 0.01 across all datasets. At the same time, the MAPE found high values, signifying a significant disagreement between the studied datasets, particularly for null values, which represent days without rain.

4. Discussion

Refs. [40,41,42] demonstrate the importance of AI in climatology. In this context, RNNs can be successful in projecting rainfall data, with LSTM being responsible for these projections.
Refs. [68,69] used this architecture to make rainfall data forecasts. However, with the BLA, other forms of RNN have been applied. For example [40], employed backpropagation to forecast floods in the River Acre, considering the SST and monthly average pressure in Darwin and Tahiti. Meanwhile, in this research, LSTM is utilized to conduct out predictions in the BLA utilizing rainfall data collected using a spatial downscaling method.
This process was seen in [41] research, which demonstrated effectiveness in processing and learning RNNs. These foundations were established using bilinear interpolation, a typical approach for scaling photos, and CNNs, capable of learning complicated representations of data, were incorporated.
Obtaining rainfall data using the spatial downscaling method in the BLA proved to be a highly effective strategy, sparking interest in a more detailed analysis of the dispersion of these data to achieve a more precise and individualized characterization of the states that make up the region [70,71]. During the experimental phase, the development of groups ranging from six to nine was investigated, ending in the finding that the construction of nine clusters gave the most sufficient and refined depiction of the states that make up the BLA [61,72]. This choice was based on the innovation of constructing homogenous groupings of rainfall stations in the BLA, in this case using the points obtained by the spatial downscaling method.
Throughout the investigation, considerable barriers arose, mostly owing to the physical closeness of the coordinates, with a higher frequency on state boundaries [60]. This occurrence resulted in point overlap in select places, as seen in the example of Amazonas state, where a point was categorized in the Acre state cluster [73]. Despite these anomalies, the method was able to efficiently represent the data due to the prevailing spatial structure of the points and the acceptable distance between them. These findings underscore the significance of a strategy that takes into account regional features and local specificities when modeling climate data in extremely complex locations, such as the BLA.
This precise technique not only improves our understanding of regional climatic patterns, but it also gives useful insights for future research into climate change and its influence in this area. This study demonstrates that rigorous investigation and correct modeling are crucial to understanding BLA climatic trends.
For this reason, the RNN algorithm was created, which has a single input layer consisting of four units in the hidden layer. It uses the Mean Squared Error (MSE) approach to handle errors. Although this model is simpler than the one employed by [41], the LSTM architecture performed well in predicting BLA rainfall data. Ref. [74] demonstrate the efficiency of LSTM in rain runoff estimates for the Dadu River Basin (China). Following the study findings of [75], the algorithm underwent 100 training epochs to further enhance its performance.
The forecasts performed successfully in capturing rainfall trends in the BLA, properly identifying periods of rain and drought, particularly in areas with seasonal rainfall. Despite using the same technique for different sets of data, the findings were consistent, as seen by the statistics utilized [76].
Given these results, investigating additional machine learning and RNN methods may provide fresh views on spotting tiny patterns in data that are difficult to detect using standard methodologies. This comprehensive technique promises to enhance prediction accuracy while also contributing to a deeper knowledge of the mechanisms driving rainfall events, opening the path for substantial advancements in climate modeling and weather forecasting.

5. Conclusions

This study addressed the necessity of data management and quality by applying spatial downscaling techniques such as linear interpolation and CNN to capture precise and detailed data. Furthermore, the rainfall data acquired using this method adequately replicates the records of in situ rainfall stations, as evidenced by the results of the bias test, which numerically approach zero.
This study gives insights into how rainfall forecasts function in the BLA, laying a strong platform for future research. Although statistically it was not possible to achieve a satisfactory value in the projections, this study proves valuable in providing a starting point for long-term projection research in the BLA. In addition, the algorithm provides a consistent projection of the behavior of rainfall patterns in this region. Potential applications, such as the development of an app or website for highly accurate long-term rainfall forecasting, can be pursued to complement water resource management and environmental planning.
To create a more realistic depiction of rainfall changes found in real data, the model must be modified. One drawback was the algorithm’s inability to forecast days without rain. Additionally, tweaking the hyperparameters for each time series or pursuing a more complete combination might boost the outcomes.
Although the projections made by the RNR enabled an excellent visualization of the rainfall patterns in the BLA, the R2 value obtained was not satisfactory, highlighting one of the limitations of this study. This result is due to the large amount of data being projected, the limited computing power, and, consequently, the limitations on the algorithm’s running time.
Furthermore, with increased processing capabilities, running additional rounds of the technique might result in considerable gains. Finally, the integration of modern machine learning approaches with an extensive analysis of climate data opens the way for breakthroughs in climate modeling and rainfall forecasts in the region.

Author Contributions

Conceptualization, L.A.F.M., J.F.d.O.-J. and J.P.A.G.; Data curation, L.A.F.M., J.F.d.O.-J., D.M., M.W. and J.P.A.G.; Formal analysis, L.A.F.M., J.F.d.O.-J. and J.P.A.G.; Funding acquisition, J.P.A.G.; Investigation, L.A.F.M., J.F.d.O.-J. and J.P.A.G.; Methodology, L.A.F.M., J.F.d.O.-J. and J.P.A.G.; Project administration, J.F.d.O.-J. and J.P.A.G.; Resources, J.F.d.O.-J. and J.P.A.G.; Software, L.A.F.M., J.F.d.O.-J., D.M. and J.P.A.G.; Supervision, J.F.d.O.-J. and J.P.A.G.; Validation, L.A.F.M., F.I.C.d.N., J.F.d.O.-J. and J.P.A.G.; Visualization, L.A.F.M., J.F.d.O.-J. and J.P.A.G.; Writing—original draft, L.A.F.M.; Writing—review and editing, L.A.F.M., F.I.C.d.N., J.F.d.O.-J., D.D.N., D.M., G.d.G., F.d.O.S., C.A.W., M.W. and J.P.A.G. All authors have read and agreed to the published version of the manuscript.

Funding

This research received no external funding.

Data Availability Statement

Data will be made available on request.

Acknowledgments

The authors would like to thank the Rondônia Foundation for Supporting the Development of Scientific and Technological Actions and Research—FAPERO. The first author would like to thank the Postgraduate Development Program (PDPG) of the Coordination for the Improvement of Higher Education Personnel (CAPES) and FAPERO for awarding him a master’s scholarship. The second, fourth, sixth, seventh, and ninth authors thank CNPq for the design of the productivity grants.

Conflicts of Interest

The authors declare that they have no conflicts of interest.

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Figure 1. Downscaling points in the Brazilian Legal Amazon.
Figure 1. Downscaling points in the Brazilian Legal Amazon.
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Figure 2. Elbow method for the coordinates of the BLA.
Figure 2. Elbow method for the coordinates of the BLA.
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Figure 3. Silhouette method for the coordinates of the BLA.
Figure 3. Silhouette method for the coordinates of the BLA.
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Figure 4. Representation of clusters and centroids of the BLA.
Figure 4. Representation of clusters and centroids of the BLA.
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Figure 5. Annual distribution between spatial downscaling data and rainfall projection.
Figure 5. Annual distribution between spatial downscaling data and rainfall projection.
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Figure 6. Recurrent Neural Network for the centroids of the BLA.
Figure 6. Recurrent Neural Network for the centroids of the BLA.
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Monteiro, L.A.F.; do Nascimento, F.I.C.; de Oliveira-Júnior, J.F.; Nunes, D.D.; Mendes, D.; de Gois, G.; Sanches, F.d.O.; Wollmann, C.A.; Watanabe, M.; Gobo, J.P.A. Rainfall Projections for the Brazilian Legal Amazon: An Artificial Neural Networks First Approach. Climate 2024, 12, 187. https://doi.org/10.3390/cli12110187

AMA Style

Monteiro LAF, do Nascimento FIC, de Oliveira-Júnior JF, Nunes DD, Mendes D, de Gois G, Sanches FdO, Wollmann CA, Watanabe M, Gobo JPA. Rainfall Projections for the Brazilian Legal Amazon: An Artificial Neural Networks First Approach. Climate. 2024; 12(11):187. https://doi.org/10.3390/cli12110187

Chicago/Turabian Style

Monteiro, Luiz Augusto Ferreira, Francisco Ivam Castro do Nascimento, José Francisco de Oliveira-Júnior, Dorisvalder Dias Nunes, David Mendes, Givanildo de Gois, Fabio de Oliveira Sanches, Cassio Arthur Wollmann, Michel Watanabe, and João Paulo Assis Gobo. 2024. "Rainfall Projections for the Brazilian Legal Amazon: An Artificial Neural Networks First Approach" Climate 12, no. 11: 187. https://doi.org/10.3390/cli12110187

APA Style

Monteiro, L. A. F., do Nascimento, F. I. C., de Oliveira-Júnior, J. F., Nunes, D. D., Mendes, D., de Gois, G., Sanches, F. d. O., Wollmann, C. A., Watanabe, M., & Gobo, J. P. A. (2024). Rainfall Projections for the Brazilian Legal Amazon: An Artificial Neural Networks First Approach. Climate, 12(11), 187. https://doi.org/10.3390/cli12110187

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