Application of Neural Network for Estimating Mean Monthly Rainfall in the State of Ceará, Brazilian Northeast

Application of Neural Network for Estimating Mean Monthly Rainfall in the State of Ceará, Brazilian Northeast | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Application of Neural Network for Estimating Mean Monthly Rainfall in the State of Ceará, Brazilian Northeast Luigi Pereira de Paiva, Benito Moreira de Azevedo, Aldeney Andrade Soares Filho, and 1 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-9020912/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract This research assessed the predictive power of Long Short-Term Memory (LSTM) networks to forecast mean monthly precipitation in Ceará using data from 2002–2025. We implemented a 12-month walk-forward validation focused on high-variability periods associated with La Niña (2020–2023). LSTM performance was compared with XGBoost, SARIMA, and a seasonal persistence baseline. SARIMA achieved superior average performance and greater operational stability (NSE 0.771; RMSE 38.54 mm/month), outperforming LSTM on average. However, Wilcoxon tests indicated no statistically significant differences between the models and the baseline. The main contribution is the validation of LSTM’s conditional utility: despite higher average volatility, LSTM attained peak skill in specific high-predictability windows (NSE up to 0.903), demonstrating capacity to capture non-linear dependencies. We also produced an average monthly precipitation forecast for 2026, noting limitations in predicting values near zero. We recommend ensemble approaches combining SARIMA and LSTM and the inclusion of exogenous variables to improve accuracy for extreme precipitation events. Rainfall Deep Learning Precipitation Estimation Figures Figure 1 Figure 2 Figure 3 1.Introduction Prediction forecasting aids in decision-making in hydrological, agricultural, and economic sectors (Pirone et al., 2023 ). In the agricultural sector, accurate forecasts enable the optimization of planting, irrigation, and harvesting, which minimizes financial losses, ensuring food security (Ceppi et al., 2014 ). According to Tang, Chen & Gui (2022), forecasting plays a fundamental role in disaster prevention, mitigation, and water management. Due to the inconsistency of precipitation, raw forecasts have systematic bias and consequently errors, and therefore statistical processing is essential in mitigating errors (Zhang & Ye 2021 ). With technological advancement, Bouaziz, Medhioub & Csaplovisc (2021) highlight the use of advanced techniques with machine learning algorithms as a high-capacity tool for forecasting precipitation data. Barrera-Animas et al. ( 2022 ), Long-Term Memory (LTSM) networks have potential for use in precipitation forecasting. Long-Short-Term Memory is a type of recurrent neural network that uses recurrent information, gate techniques (Gonzalez; Yu, 2018 ). As reported by Akbari et al. (2018), long-term memory models provide the ability to efficiently understand spatial and temporal correlations. Focusing on long-term memory models, Graves ( 2012 ) highlights that the model stands out for its ability to use contextual information for input and output, which counteracts the problem of standard RNN models that face the problem of gradient vanishing. In the context of Ceará, Pinheiro & Ouarda ( 2025 ), it is a Brazilian region that stands out for being one of the most predictable in the world when related to seasonal forecasting. Furthermore, According to Rolim & Souza (2025) highlight the effectiveness of applying machine learning models focused on prediction as a tool to assist water managers and decision-makers. Despite the successful demonstration, the history of water challenges and the constant need for long-term planning make the demand for robust predictive validation something recurrent (Hong, 2008 ; Küllahcı & Altunkaynak, 2025 ). Although there is a limitation due to the scarcity and volatility of rainfall, the issue of prediction has become a fundamental part of the debate on precipitation (Li et al., 2022 ). Diez-Sierra & Jesus ( 2017 ) emphasize that precipitation analysis methodologies are integrated in various ways, including point statistics, which divides the analysis into spatial and point data. Considering the regional context and the size of the Brazilian semi-arid region, although there are models applied at the local scale with a high degree of robustness, the gap in studies of the entire state region is evident (Rolim & Souza, 2024; Pinheiro & Guarda, 2025). Complementarily, there is a significant presence of studies that prioritize usual error metrics (RMSE, R²) and do not present statistical significance analyses of the performance of benchmark models (He et al., 2021 ). This methodological limitation hinders the validation process of predictive models and the complete explanation of the superiority of Deep Learning (DL) models for long-term planning (Zhang, Ye, 2021 ). Wilks ( 2011 ) highlights the need for statistical tests to differentiate models and emphasize significance between them, advocating the use of Hypothesis Tests (Wilcoxon). The comparison of the use of various models highlights the effective use of bidirectional LSTM models for rainfall forecasting, and validation was performed using root mean square error (RMSE), Nash-Sutcliffe efficiency (NSE), mean absolute error (MAE), and root mean square logarithmic error (RMSELO) for model validation (Barrera-Animas et al., 2022 ; Nash & Sutcliffe, 1970 ). Murphy ( 1988 ) corroborates this, highlighting the gain in accuracy compared to the persistence benchmark model from the use of the Skill Score. In the context of regional literature, this study aims to develop a comprehensive validation framework based on a Walk-forward backtesting over a 12-month horizon, which will be complemented by the estimation of confidence intervals (bootstrap) to assess the uncertainty and stability of the metrics. Given the complexity of predicting monthly precipitation in semi-arid regions of Brazil, there is a growing demand for studies related to rainfall predictability in the state of Ceará (Silva et al., 2006 ; Pinheiro & Ouarda, 2023 ; Mello, 2003). With this in mind, the main objective of this work will be to develop and validate a neural network model capable of predicting precipitation for the state of Ceará, Brazilian Northeast. 2. Materials and Methods 2.1 Study Area Located in northeastern Brazil, the state of Ceará has latitudes between 2.5ºS and 10ºS and longitudes between 34ºW and 42ºW (Rodrigues, 2024). According to Silva et al. ( 2021 ), the state has a Koppen-Geiger climate classification as tropical with a dry summer season (Aw), characterizing most of the Ceará territory as semi-arid, with irregular precipitation activity and high rainfall intensity from February to May (Oliveira et al., 2022). Figure 1 below shows a representative map of the study area. The relevance of studying the semi-arid precipitation of Ceará stems from the historical challenge to water management, marked by significant water shortages due to high evapotranspiration rates, increased temperatures, and other extreme hydrological events (Rolim, Oliveira & Souza, 2022; Seigerman et al., 2024 ). 2.2.1 Data Acquisition and Preprocessing Precipitation data were obtained from the Ceará Foundation for Meteorology and Water Resources (FUNCEME), from which monthly average precipitation data were selected from January 2002 to September 2025, totaling 285 months. Feature engineering was applied through time series transformation, using lags to construct the dataset. The model configuration uses the immediately preceding 12 months (lags = 12) as predictor features (Xt), with the target variable (Yt) being the average monthly precipitation of the future month (Pt + 1). In this way, the LSTM network will have a strong capacity to capture the seasonal dependence inherent to the semi-arid regime. In order to mitigate scaling effects and optimize the learning process of the neural network, the data were subjected to normalization (scaling), concentrating the values ​​in the interval between 0 and 1 (Akbari Asanjan et al., 2018 ). The transformation process will be essential for LSTM networks to achieve rapid and efficient algorithm convergence. Training was based on available values, using data from January 2002 to December 2022 for training and January 2023 to September 2025 for testing and validation. 2.2.2 Predictive models and architectures For the methodological approach, a recurrent neural network (RNN) was used in a long-short-term memory (LSTM) architecture, which are designed to learn long-term dependencies on sequential data, making them suitable for precipitation analysis (Fouotsa Manfouo et al., 2023 ). The functional flow of an LSTM cell is based on three gates: Forget Gate, whose function determines which information will be discarded from the memory cell; Input Gate, which will determine which information will be stored; Output Gate, which estimates the value of the cell. This architectural morphology makes it possible to address the disappearance of gradients in patterns (Renteria-Mena; Giraldo, 2024 ). A sequential model will be formed using the Keras library, which is contained in TensorFlow (Kareem; Seong; Jung, 2021 ). The architecture consists of an LSTM layer made up of 100 neurons using the Rectified Linear Unit (ReLU) activation function. This LSTM layer is followed by a Dense Layer consisting of a single neuron containing the final prediction value (Ebtehaj; Bonakdari, 2024 ). For prediction, values ​​from the previous 12 months (lags) will be observed, aiming at learning the model for autocorrelation under the premise of the current value on past values ​​(Kumar et al., 2019 ). The model will be optimized using Adam and a loss function based on mean squared error (MSE). 2.2.3 Benchmark Models For robust, predictive validation of the LSTM architecture and to justify its computational cost, the model will be compared with benchmark models. The first benchmark model will be the Seasonal Persistence (Lag12) model. This model is considered the baseline in forecasting seasonal time series because it assumes that the trend in precipitation value in a given month (Pt) will be equal to the value observed in the previous month (Pt-12), providing a minimum acceptable performance baseline for the analyzed time series (Knoben, 2024 ; Isphording et al., 2024 ). For in-depth comparison, algorithmic models of different classes will be added. The Seasonal AutoRegressive Integrated Moving Average (SARIMA) model was selected because it is state-of-the-art in statistical time series models with seasonality, allowing for the evaluation of LSTM performance against traditional seasonally adjusted approaches (Kabbilawsh, Kumar & Chithra, 2022 ). In addition, the eXtreme Gradient Boosting (XGBoost) model was incorporated, representing machine learning models based on decision tree ensembles (Wang & Peng, 2024). This addition will be necessary for comparison with feature-based models. The joint evaluation of these benchmarks will allow for the isolation and quantification of the performance gain provided by the deep learning architecture. 2.2.4 Validation and Performance Evaluation Model validation will be performed through back testing using rigorous walk-forward validation in selected years (Díaz; Olarte; Jara, 2022; Islam et al., 2025 ). The test took place from 2020 to 2023, and the selection of these years was strategically aligned with the conditions of the La Niña climate phenomenon, under the premise of testing the generalization capacity of models in scenarios of high variability and extreme events. The use of this method is essential for realistic operational forecast simulation. After the forecast, the result of the models (benchmarks and LSTM) will return to non-normalized values ​​(mm/month), which will then be compared with real data. The performance metrics will be formulated by a broad set, including the Mean Squared Error (RMSE), coefficient of determination (R²), Mean Absolute Error (MAE), Nash-Sutcliffe efficiency index (NSE), and bias. The skill score will be used to quantify the accuracy gain in relation to the Seasonal Persistence baseline. Furthermore, the rigor of the study will be verified by hypothesis testing (Wilcoxon) and bootstrap confidence intervals to determine the statistical significance and stability of the metrics, according to Saplıoğlu & Güçlü ( 2022 ). Figure 2 below shows a flowchart representing the methodology and neural network used in this study. Source: Authors, 2025. 3. Results and discussion 3.1 Back testing performance and comparison between benchmarks The validation process was carried out by back testing in the period from 2020 to 2023, which encompasses cycles of the La Niña climatological phenomenon. This approach in scenarios of high variation ensures analytical robustness. Following the process, the SARIMA model presents itself as the most robust and stable model from the perspective of average performance. Table 1 , below, summarizes the consolidated results of the validation process, to which the XGBoost, SARIMA and LSTM models were subjected, in comparison with the Seasonal Persistence baseline. Table 1 – Average performance metrics (Progressive validation 2020–2023). Metric LSTM SARIMA XGBoost RMSE 42.51 38.54 46.01 R² / NSE 0.721 0.771 0.674 MAE 26.53 25.85 30.38 Bias (%) -10.05 -20.52 -8.5 Skill Score -0.567 -0.994 -0.798 Wilcoxon p-value 0.796 0.947 0.915 Shapiro p-value 0 0 0 Source: Authors (2025). The analysis in Table 1 confirms that the SARIMA model achieved better average performance and greater operational stability during periods of high variability (2020–2023). The average Nash-Sutcliffe efficiency (NSE) value of SARIMA was 0.771, approximately 6.93% higher than the LSTM model (0.721) and 14.39% higher than XGBoost (0.674). This superiority demonstrates a greater capacity for forecasting rainfall in rainfall events under different annual regimes (Li et al., 2024 ). Furthermore, the SARIMA model presented a lower mean squared error (RMSE = 38.54 mm/month), confirming its robustness compared to the other models. In addition to the operational superiority of the SARIMA model, the LSTM architecture demonstrated conditional utility based on its Peak Performance, which enhanced its predictive capacity, corroborating with Di Taranto et al. ( 2025 ). In scenarios of high predictability, the LSTM model recorded an absolute NSE (0.903) of the historical series, while the SARIMA model reached 0.849 in the same period, consistent with the work of Santos-Romero et al. ( 2024 ), where SARIMA also demonstrated superiority over the LSTM model. This particularity suggests that, although volatile, LSTM has a greater capacity to capture non-linear dependencies, corroborating the literature. According to the variance data, the analysis of the mean absolute error (MAE) and bias reinforces the robustness of SARIMA on average, given that it recorded the lowest MAE (25.85 mm/month). Despite this, SARIMA presented the highest negative bias (BIAS = -20.515), suggesting that on average, the model significantly underestimates the total volume of precipitation in the region, while LSTM presented a significantly lower bias. The skill score analysis corroborates this scenario, given that all models had negative results, which proves that the seasonal persistence baseline is the model with the greatest potential robustness for the period from 2020 to 2023 (Murphy, 1989 ). Under a complementary approach, Markovics & Mayer ( 2022 ) highlight the challenge of the validity of the skill score under different objects of study; however, in the present study, the use of the data presents itself as an excellent metric for forecasting measures. The statistical significance analysis complemented the performance data, using the Wilcoxon Signed-Rank Test to differentiate the accuracy of the models based on the Seasonal Persistence baseline. The rigor of the study requires the use of hypothesis tests to differentiate models. The high p-value obtained in the Wilcoxon test, which in all cases exceeded 0.7955, indicates that there is no statistically significant difference between the performance of the models tested. The result reinforces the conclusion that the high variability inherent in La Niña cycles imposed a limitation on generalization across all architectures, which, together with the results of the Wilcoxon test, complements Hamill's (1999) conclusion that the use of this type of metric is appropriate for evaluating forecasting ability. 3.2 Average monthly forecast for 2026 The results of applying the LSTM model, which underwent superior Peak Performance validation, are presented in Fig. 3 , which shows the forecast graph for 2026. Using the model trained with data up to September 2025, the forecast provides technical and strategic support to water managers in the state of Ceará. Source: Authors (2025). The values ​​obtained, while consistent with the official regime and capable of capturing the intrinsic behavioral seasonality of the state of Ceará, showed clear limitations in predicting the transition months (January to March) and periods of low rainfall. Furthermore, the model tends not to predict values ​​very close to zero during the dry months. These particularities indicate that, although the model is functional, there is a persistent problem of its adequacy to the behavioral dynamics of rainfall in the study area during extreme events (very low values). 4. Conclusion The premise of this work was to evaluate the predictive capacity of the LSTM (Long Short-Term Memory) model for forecasting average monthly precipitation at the state level, with the state of Ceará (Brazil) as the object of study, in the time interval from 2002 to 2025. Using a rigorous progressive evaluation (Walk-forward validation) in scenarios of high variability of the La Niña climate event (2020–2023), the evaluation was carried out using the SARIMA, XGBoost models and a Seasonal Persistence baseline as references. The results obtained demonstrate that although the SARIMA model presents a better average performance and greater operational stability (NSE 0.771 and RMSE 38.54 mm/month), the statistical superiority of the baseline was not maintained in the Wilcoxon test. Despite the average volatility, the main contribution of the study is conceived through the validation of the conditional utility of the LSTM architecture. In Peak Performance, the LSTM model demonstrated superiority over the SARIMA model during the same period. This particularity confirms the inherent potential of the LSTM architecture for trend non-linear dependencies, establishing it as a robust alternative for specific scenarios that demand events of greater magnitude in water planning. The 2026 average precipitation projection, which was the objective of this work, was achieved. The forecast using the LSTM architecture indicates a rainfall regime with high precipitation activity in the first quarter (February to March), consistent with the seasonality of the state. The limitations found in the discussion session suggest difficulty for the model in predicting values ​​very close to zero, which suggests the need for future refinement of the modeling, specifically aimed at improving performance in extreme precipitation circumstances (drought or flood). Finally, the use of ensemble learning techniques is recommended in combination with the SARIMA model and LSTM architecture, which will allow for the obtaining of more robust models with lower volatility. Furthermore, the integration of exogenous variables may provide valuable insights into the relationship of external factors on precipitation. The integration of current deep learning models may also corroborate the overcoming of generalization challenges present in the model used in this study and consequently improve accuracy in scenarios of high variability. Declarations Declaration of Competing 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. Author Contribution **Luigi Pereira de Paiva:** Writing – original draft, Validation, Software, Methodology, Data curation, Conceptualization. **Benito Moreira de Azevedo:** Conceptualization, Supervision, Project administration, Writing – review & editing. **Aldeney Andrade Soares Filho:** Investigation, Writing – review & editing. **Juvenaldo Florentino Canja:** Conceptualization, Visualization, Writing – review & editing. Data Availability The data used were collected from the website of the Ceará Foundation for Meteorology and Water Resources (FUNCEME) via the link: [https://chuvas.funceme.br/mensal/municipios/media/](https:/chuvas.funceme.br/mensal/municipios/media) . References Akbari Asanjan A, Yang T, Hsu K, Sorooshian S, Lin J, Peng Q (2018) Short-term precipitation forecast based on the PERSIANN system and LSTM recurrent neural networks. J Geophys Research: Atmos 123(22):12543–12563 Barrera-Animas AY, Oyedele LO, Bilal M, Akinosho TD, Delgado JMD, Akanbi LA (2022) Rainfall prediction: A comparative analysis of modern machine learning algorithms for time-series forecasting. Mach Learn Appl 7:100204 Bouaziz M, Medhioub E, Csaplovics E (2021) A machine learning model for drought tracking and forecasting using remote precipitation data and a standardized precipitation index from arid regions. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-9020912","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":606225649,"identity":"460ec02b-bb23-4fa0-80f7-b535c1e01f1b","order_by":0,"name":"Luigi Pereira de Paiva","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA/ElEQVRIiWNgGAWjYBACPgbGBoYEBgYeBgbmA3DRAw/waGFDaGEDUgwGEC0JeLXAAY8BXAsDXi0Syc0vHu6wkzE4fubb44qKP3LmYocfAm2xk9NtwKUlsc0i8Uwyj8GZ3O2GZ84YGFvOTjMAakk2NjuAW4tBYhszj2RD7jbJRiB7w+0EkJYDidvwa6nnkex/8wyqJf0DIS3NDxLbDvPwS+SwQbXkELCF52EbQ+KZ40Atz8wNG84YGxvczik4kGCA2y/87OmPP/7cUW3Pxp/87GFDhZycwe30zR8+VNjJ4dICdhswNsEMJEEDnMpBgPkDFi2jYBSMglEwChAAAHAqX/m+oBbFAAAAAElFTkSuQmCC","orcid":"","institution":"Universidade Federal do Ceará","correspondingAuthor":true,"prefix":"","firstName":"Luigi","middleName":"Pereira","lastName":"de Paiva","suffix":""},{"id":606225651,"identity":"5aaccf4b-ff17-43d6-b4f5-34739abaa6a0","order_by":1,"name":"Benito Moreira de Azevedo","email":"","orcid":"","institution":"Universidade Federal do Ceará","correspondingAuthor":false,"prefix":"","firstName":"Benito","middleName":"Moreira","lastName":"de Azevedo","suffix":""},{"id":606225653,"identity":"8fbf2c50-0775-4199-b95f-cbcf761c894d","order_by":2,"name":"Aldeney Andrade Soares Filho","email":"","orcid":"","institution":"Universidade Federal do Ceará","correspondingAuthor":false,"prefix":"","firstName":"Aldeney","middleName":"Andrade Soares","lastName":"Filho","suffix":""},{"id":606225654,"identity":"7ff22b44-cd1c-455f-a75a-2adac4b0080f","order_by":3,"name":"Juvenaldo Florentino Canja","email":"","orcid":"","institution":"Universidade Federal do Ceará","correspondingAuthor":false,"prefix":"","firstName":"Juvenaldo","middleName":"Florentino","lastName":"Canja","suffix":""}],"badges":[],"createdAt":"2026-03-03 13:53:26","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-9020912/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-9020912/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":104783268,"identity":"7c9d55a9-46e7-48eb-a468-e3adc7d74d05","added_by":"auto","created_at":"2026-03-17 07:58:30","extension":"jpg","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":15401,"visible":true,"origin":"","legend":"\u003cp\u003eIllustrative map of the study site, located in the state of Ceará, Brazil. Source: Authors, 2025.\u003c/p\u003e","description":"","filename":"Picture1.jpg","url":"https://assets-eu.researchsquare.com/files/rs-9020912/v1/15ebbc51b01da34293958eec.jpg"},{"id":104752039,"identity":"dcb9eaa2-e8f1-424f-a524-893959037901","added_by":"auto","created_at":"2026-03-16 20:20:07","extension":"jpg","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":21955,"visible":true,"origin":"","legend":"\u003cp\u003eMethodological Flowchart of the LSTM Prediction Model\u003c/p\u003e\n\u003cp\u003eSource: Authors, 2025.\u003c/p\u003e","description":"","filename":"Picture2.jpg","url":"https://assets-eu.researchsquare.com/files/rs-9020912/v1/1dc5491bbe6f6c09e7c12a82.jpg"},{"id":104752041,"identity":"f9d51587-7661-45ff-a518-7e47a9a65cbc","added_by":"auto","created_at":"2026-03-16 20:20:07","extension":"jpg","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":39727,"visible":true,"origin":"","legend":"\u003cp\u003eRainfall forecast for the state of Ceará for 2026.\u003c/p\u003e\n\u003cp\u003eSource: Authors (2025).\u003c/p\u003e","description":"","filename":"Picture3.jpg","url":"https://assets-eu.researchsquare.com/files/rs-9020912/v1/a83abce81feca6e295d2ea95.jpg"},{"id":106394457,"identity":"2077b711-b7bc-44e4-b273-70a33dd25d41","added_by":"auto","created_at":"2026-04-08 07:43:58","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":602703,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-9020912/v1/69ad9c06-4887-4318-a8cc-af4c564e0c90.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Application of Neural Network for Estimating Mean Monthly Rainfall in the State of Ceará, Brazilian Northeast","fulltext":[{"header":"1.Introduction","content":"\u003cp\u003ePrediction forecasting aids in decision-making in hydrological, agricultural, and economic sectors (Pirone et al., \u003cspan citationid=\"CR32\" class=\"CitationRef\"\u003e2023\u003c/span\u003e). In the agricultural sector, accurate forecasts enable the optimization of planting, irrigation, and harvesting, which minimizes financial losses, ensuring food security (Ceppi et al., \u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e2014\u003c/span\u003e). According to Tang, Chen \u0026amp; Gui (2022), forecasting plays a fundamental role in disaster prevention, mitigation, and water management.\u003c/p\u003e \u003cp\u003eDue to the inconsistency of precipitation, raw forecasts have systematic bias and consequently errors, and therefore statistical processing is essential in mitigating errors (Zhang \u0026amp; Ye \u003cspan citationid=\"CR43\" class=\"CitationRef\"\u003e2021\u003c/span\u003e). With technological advancement, Bouaziz, Medhioub \u0026amp; Csaplovisc (2021) highlight the use of advanced techniques with machine learning algorithms as a high-capacity tool for forecasting precipitation data.\u003c/p\u003e \u003cp\u003eBarrera-Animas et al. (\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2022\u003c/span\u003e), Long-Term Memory (LTSM) networks have potential for use in precipitation forecasting. Long-Short-Term Memory is a type of recurrent neural network that uses recurrent information, gate techniques (Gonzalez; Yu, \u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e2018\u003c/span\u003e). As reported by Akbari et al. (2018), long-term memory models provide the ability to efficiently understand spatial and temporal correlations. Focusing on long-term memory models, Graves (\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e2012\u003c/span\u003e) highlights that the model stands out for its ability to use contextual information for input and output, which counteracts the problem of standard RNN models that face the problem of gradient vanishing.\u003c/p\u003e \u003cp\u003eIn the context of Cear\u0026aacute;, Pinheiro \u0026amp; Ouarda (\u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e2025\u003c/span\u003e), it is a Brazilian region that stands out for being one of the most predictable in the world when related to seasonal forecasting. Furthermore, According to Rolim \u0026amp; Souza (2025) highlight the effectiveness of applying machine learning models focused on prediction as a tool to assist water managers and decision-makers. Despite the successful demonstration, the history of water challenges and the constant need for long-term planning make the demand for robust predictive validation something recurrent (Hong, \u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e2008\u003c/span\u003e; K\u0026uuml;llahcı \u0026amp; Altunkaynak, \u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e2025\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eAlthough there is a limitation due to the scarcity and volatility of rainfall, the issue of prediction has become a fundamental part of the debate on precipitation (Li et al., \u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e2022\u003c/span\u003e). Diez-Sierra \u0026amp; Jesus (\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e2017\u003c/span\u003e) emphasize that precipitation analysis methodologies are integrated in various ways, including point statistics, which divides the analysis into spatial and point data. Considering the regional context and the size of the Brazilian semi-arid region, although there are models applied at the local scale with a high degree of robustness, the gap in studies of the entire state region is evident (Rolim \u0026amp; Souza, 2024; Pinheiro \u0026amp; Guarda, 2025). Complementarily, there is a significant presence of studies that prioritize usual error metrics (RMSE, R\u0026sup2;) and do not present statistical significance analyses of the performance of benchmark models (He et al., \u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e2021\u003c/span\u003e). This methodological limitation hinders the validation process of predictive models and the complete explanation of the superiority of Deep Learning (DL) models for long-term planning (Zhang, Ye, \u003cspan citationid=\"CR43\" class=\"CitationRef\"\u003e2021\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eWilks (\u003cspan citationid=\"CR42\" class=\"CitationRef\"\u003e2011\u003c/span\u003e) highlights the need for statistical tests to differentiate models and emphasize significance between them, advocating the use of Hypothesis Tests (Wilcoxon). The comparison of the use of various models highlights the effective use of bidirectional LSTM models for rainfall forecasting, and validation was performed using root mean square error (RMSE), Nash-Sutcliffe efficiency (NSE), mean absolute error (MAE), and root mean square logarithmic error (RMSELO) for model validation (Barrera-Animas et al., \u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2022\u003c/span\u003e; Nash \u0026amp; Sutcliffe, \u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e1970\u003c/span\u003e). Murphy (\u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e1988\u003c/span\u003e) corroborates this, highlighting the gain in accuracy compared to the persistence benchmark model from the use of the Skill Score. In the context of regional literature, this study aims to develop a comprehensive validation framework based on a Walk-forward backtesting over a 12-month horizon, which will be complemented by the estimation of confidence intervals (bootstrap) to assess the uncertainty and stability of the metrics.\u003c/p\u003e \u003cp\u003eGiven the complexity of predicting monthly precipitation in semi-arid regions of Brazil, there is a growing demand for studies related to rainfall predictability in the state of Cear\u0026aacute; (Silva et al., \u003cspan citationid=\"CR41\" class=\"CitationRef\"\u003e2006\u003c/span\u003e; Pinheiro \u0026amp; Ouarda, \u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e2023\u003c/span\u003e; Mello, 2003). With this in mind, the main objective of this work will be to develop and validate a neural network model capable of predicting precipitation for the state of Cear\u0026aacute;, Brazilian Northeast.\u003c/p\u003e"},{"header":"2. Materials and Methods","content":"\u003cdiv id=\"Sec3\" class=\"Section2\"\u003e \u003ch2\u003e2.1 Study Area\u003c/h2\u003e \u003cp\u003eLocated in northeastern Brazil, the state of Cear\u0026aacute; has latitudes between 2.5\u0026ordm;S and 10\u0026ordm;S and longitudes between 34\u0026ordm;W and 42\u0026ordm;W (Rodrigues, 2024). According to Silva et al. (\u003cspan citationid=\"CR40\" class=\"CitationRef\"\u003e2021\u003c/span\u003e), the state has a Koppen-Geiger climate classification as tropical with a dry summer season (Aw), characterizing most of the Cear\u0026aacute; territory as semi-arid, with irregular precipitation activity and high rainfall intensity from February to May (Oliveira et al., 2022). Figure\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e below shows a representative map of the study area.\u003c/p\u003e \u003cp\u003eThe relevance of studying the semi-arid precipitation of Cear\u0026aacute; stems from the historical challenge to water management, marked by significant water shortages due to high evapotranspiration rates, increased temperatures, and other extreme hydrological events (Rolim, Oliveira \u0026amp; Souza, 2022; Seigerman et al., \u003cspan citationid=\"CR39\" class=\"CitationRef\"\u003e2024\u003c/span\u003e).\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cdiv id=\"Sec4\" class=\"Section3\"\u003e \u003ch2\u003e2.2.1 Data Acquisition and Preprocessing\u003c/h2\u003e \u003cp\u003ePrecipitation data were obtained from the Cear\u0026aacute; Foundation for Meteorology and Water Resources (FUNCEME), from which monthly average precipitation data were selected from January 2002 to September 2025, totaling 285 months. Feature engineering was applied through time series transformation, using lags to construct the dataset. The model configuration uses the immediately preceding 12 months (lags\u0026thinsp;=\u0026thinsp;12) as predictor features (Xt), with the target variable (Yt) being the average monthly precipitation of the future month (Pt\u0026thinsp;+\u0026thinsp;1). In this way, the LSTM network will have a strong capacity to capture the seasonal dependence inherent to the semi-arid regime.\u003c/p\u003e \u003cp\u003eIn order to mitigate scaling effects and optimize the learning process of the neural network, the data were subjected to normalization (scaling), concentrating the values ​​in the interval between 0 and 1 (Akbari Asanjan et al., \u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e2018\u003c/span\u003e). The transformation process will be essential for LSTM networks to achieve rapid and efficient algorithm convergence. Training was based on available values, using data from January 2002 to December 2022 for training and January 2023 to September 2025 for testing and validation.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec5\" class=\"Section3\"\u003e \u003ch2\u003e2.2.2 Predictive models and architectures\u003c/h2\u003e \u003cp\u003eFor the methodological approach, a recurrent neural network (RNN) was used in a long-short-term memory (LSTM) architecture, which are designed to learn long-term dependencies on sequential data, making them suitable for precipitation analysis (Fouotsa Manfouo et al., \u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e2023\u003c/span\u003e). The functional flow of an LSTM cell is based on three gates: Forget Gate, whose function determines which information will be discarded from the memory cell; Input Gate, which will determine which information will be stored; Output Gate, which estimates the value of the cell. This architectural morphology makes it possible to address the disappearance of gradients in patterns (Renteria-Mena; Giraldo, \u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e2024\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eA sequential model will be formed using the Keras library, which is contained in TensorFlow (Kareem; Seong; Jung, \u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e2021\u003c/span\u003e). The architecture consists of an LSTM layer made up of 100 neurons using the Rectified Linear Unit (ReLU) activation function. This LSTM layer is followed by a Dense Layer consisting of a single neuron containing the final prediction value (Ebtehaj; Bonakdari, \u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e2024\u003c/span\u003e). For prediction, values ​​from the previous 12 months (lags) will be observed, aiming at learning the model for autocorrelation under the premise of the current value on past values ​​(Kumar et al., \u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e2019\u003c/span\u003e). The model will be optimized using Adam and a loss function based on mean squared error (MSE).\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec6\" class=\"Section3\"\u003e \u003ch2\u003e2.2.3 Benchmark Models\u003c/h2\u003e \u003cp\u003eFor robust, predictive validation of the LSTM architecture and to justify its computational cost, the model will be compared with benchmark models. The first benchmark model will be the Seasonal Persistence (Lag12) model. This model is considered the baseline in forecasting seasonal time series because it assumes that the trend in precipitation value in a given month (Pt) will be equal to the value observed in the previous month (Pt-12), providing a minimum acceptable performance baseline for the analyzed time series (Knoben, \u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e2024\u003c/span\u003e; Isphording et al., \u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e2024\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eFor in-depth comparison, algorithmic models of different classes will be added. The Seasonal AutoRegressive Integrated Moving Average (SARIMA) model was selected because it is state-of-the-art in statistical time series models with seasonality, allowing for the evaluation of LSTM performance against traditional seasonally adjusted approaches (Kabbilawsh, Kumar \u0026amp; Chithra, \u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e2022\u003c/span\u003e). In addition, the eXtreme Gradient Boosting (XGBoost) model was incorporated, representing machine learning models based on decision tree ensembles (Wang \u0026amp; Peng, 2024). This addition will be necessary for comparison with feature-based models. The joint evaluation of these benchmarks will allow for the isolation and quantification of the performance gain provided by the deep learning architecture.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec7\" class=\"Section3\"\u003e \u003ch2\u003e2.2.4 Validation and Performance Evaluation\u003c/h2\u003e \u003cp\u003eModel validation will be performed through back testing using rigorous walk-forward validation in selected years (D\u0026iacute;az; Olarte; Jara, 2022; Islam et al., \u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e2025\u003c/span\u003e). The test took place from 2020 to 2023, and the selection of these years was strategically aligned with the conditions of the La Ni\u0026ntilde;a climate phenomenon, under the premise of testing the generalization capacity of models in scenarios of high variability and extreme events. The use of this method is essential for realistic operational forecast simulation. After the forecast, the result of the models (benchmarks and LSTM) will return to non-normalized values ​​(mm/month), which will then be compared with real data.\u003c/p\u003e \u003cp\u003eThe performance metrics will be formulated by a broad set, including the Mean Squared Error (RMSE), coefficient of determination (R\u0026sup2;), Mean Absolute Error (MAE), Nash-Sutcliffe efficiency index (NSE), and bias. The skill score will be used to quantify the accuracy gain in relation to the Seasonal Persistence baseline. Furthermore, the rigor of the study will be verified by hypothesis testing (Wilcoxon) and bootstrap confidence intervals to determine the statistical significance and stability of the metrics, according to Saplıoğlu \u0026amp; G\u0026uuml;\u0026ccedil;l\u0026uuml; (\u003cspan citationid=\"CR37\" class=\"CitationRef\"\u003e2022\u003c/span\u003e). Figure\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e below shows a flowchart representing the methodology and neural network used in this study.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eSource: Authors, 2025.\u003c/p\u003e \u003c/div\u003e \u003c/div\u003e"},{"header":"3. Results and discussion","content":"\u003cdiv id=\"Sec9\" class=\"Section2\"\u003e \u003ch2\u003e3.1 Back testing performance and comparison between benchmarks\u003c/h2\u003e \u003cp\u003eThe validation process was carried out by back testing in the period from 2020 to 2023, which encompasses cycles of the La Ni\u0026ntilde;a climatological phenomenon. This approach in scenarios of high variation ensures analytical robustness. Following the process, the SARIMA model presents itself as the most robust and stable model from the perspective of average performance. Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e, below, summarizes the consolidated results of the validation process, to which the XGBoost, SARIMA and LSTM models were subjected, in comparison with the Seasonal Persistence baseline.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab1\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003e\u0026ndash; Average performance metrics (Progressive validation 2020\u0026ndash;2023).\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"4\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eMetric\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eLSTM\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eSARIMA\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eXGBoost\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eRMSE\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e42.51\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e38.54\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e46.01\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eR\u0026sup2; / NSE\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.721\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.771\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.674\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eMAE\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e26.53\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e25.85\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e30.38\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eBias (%)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e-10.05\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e-20.52\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e-8.5\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSkill Score\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e-0.567\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e-0.994\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e-0.798\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eWilcoxon p-value\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.796\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.947\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.915\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eShapiro p-value\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eSource: Authors (2025).\u003c/p\u003e \u003cp\u003eThe analysis in Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e confirms that the SARIMA model achieved better average performance and greater operational stability during periods of high variability (2020\u0026ndash;2023). The average Nash-Sutcliffe efficiency (NSE) value of SARIMA was 0.771, approximately 6.93% higher than the LSTM model (0.721) and 14.39% higher than XGBoost (0.674). This superiority demonstrates a greater capacity for forecasting rainfall in rainfall events under different annual regimes (Li et al., \u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e2024\u003c/span\u003e). Furthermore, the SARIMA model presented a lower mean squared error (RMSE\u0026thinsp;=\u0026thinsp;38.54 mm/month), confirming its robustness compared to the other models.\u003c/p\u003e \u003cp\u003eIn addition to the operational superiority of the SARIMA model, the LSTM architecture demonstrated conditional utility based on its Peak Performance, which enhanced its predictive capacity, corroborating with Di Taranto et al. (\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e2025\u003c/span\u003e). In scenarios of high predictability, the LSTM model recorded an absolute NSE (0.903) of the historical series, while the SARIMA model reached 0.849 in the same period, consistent with the work of Santos-Romero et al. (\u003cspan citationid=\"CR38\" class=\"CitationRef\"\u003e2024\u003c/span\u003e), where SARIMA also demonstrated superiority over the LSTM model. This particularity suggests that, although volatile, LSTM has a greater capacity to capture non-linear dependencies, corroborating the literature.\u003c/p\u003e \u003cp\u003eAccording to the variance data, the analysis of the mean absolute error (MAE) and bias reinforces the robustness of SARIMA on average, given that it recorded the lowest MAE (25.85 mm/month). Despite this, SARIMA presented the highest negative bias (BIAS = -20.515), suggesting that on average, the model significantly underestimates the total volume of precipitation in the region, while LSTM presented a significantly lower bias. The skill score analysis corroborates this scenario, given that all models had negative results, which proves that the seasonal persistence baseline is the model with the greatest potential robustness for the period from 2020 to 2023 (Murphy, \u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e1989\u003c/span\u003e). Under a complementary approach, Markovics \u0026amp; Mayer (\u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e2022\u003c/span\u003e) highlight the challenge of the validity of the skill score under different objects of study; however, in the present study, the use of the data presents itself as an excellent metric for forecasting measures.\u003c/p\u003e \u003cp\u003eThe statistical significance analysis complemented the performance data, using the Wilcoxon Signed-Rank Test to differentiate the accuracy of the models based on the Seasonal Persistence baseline. The rigor of the study requires the use of hypothesis tests to differentiate models. The high p-value obtained in the Wilcoxon test, which in all cases exceeded 0.7955, indicates that there is no statistically significant difference between the performance of the models tested. The result reinforces the conclusion that the high variability inherent in La Ni\u0026ntilde;a cycles imposed a limitation on generalization across all architectures, which, together with the results of the Wilcoxon test, complements Hamill's (1999) conclusion that the use of this type of metric is appropriate for evaluating forecasting ability.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec10\" class=\"Section2\"\u003e \u003ch2\u003e3.2 Average monthly forecast for 2026\u003c/h2\u003e \u003cp\u003eThe results of applying the LSTM model, which underwent superior Peak Performance validation, are presented in Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e, which shows the forecast graph for 2026. Using the model trained with data up to September 2025, the forecast provides technical and strategic support to water managers in the state of Cear\u0026aacute;.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eSource: Authors (2025).\u003c/p\u003e \u003cp\u003eThe values ​​obtained, while consistent with the official regime and capable of capturing the intrinsic behavioral seasonality of the state of Cear\u0026aacute;, showed clear limitations in predicting the transition months (January to March) and periods of low rainfall. Furthermore, the model tends not to predict values ​​very close to zero during the dry months. These particularities indicate that, although the model is functional, there is a persistent problem of its adequacy to the behavioral dynamics of rainfall in the study area during extreme events (very low values).\u003c/p\u003e \u003c/div\u003e"},{"header":"4. Conclusion","content":"\u003cp\u003eThe premise of this work was to evaluate the predictive capacity of the LSTM (Long Short-Term Memory) model for forecasting average monthly precipitation at the state level, with the state of Cear\u0026aacute; (Brazil) as the object of study, in the time interval from 2002 to 2025. Using a rigorous progressive evaluation (Walk-forward validation) in scenarios of high variability of the La Ni\u0026ntilde;a climate event (2020\u0026ndash;2023), the evaluation was carried out using the SARIMA, XGBoost models and a Seasonal Persistence baseline as references. The results obtained demonstrate that although the SARIMA model presents a better average performance and greater operational stability (NSE 0.771 and RMSE 38.54 mm/month), the statistical superiority of the baseline was not maintained in the Wilcoxon test.\u003c/p\u003e \u003cp\u003eDespite the average volatility, the main contribution of the study is conceived through the validation of the conditional utility of the LSTM architecture. In Peak Performance, the LSTM model demonstrated superiority over the SARIMA model during the same period. This particularity confirms the inherent potential of the LSTM architecture for trend non-linear dependencies, establishing it as a robust alternative for specific scenarios that demand events of greater magnitude in water planning.\u003c/p\u003e \u003cp\u003eThe 2026 average precipitation projection, which was the objective of this work, was achieved. The forecast using the LSTM architecture indicates a rainfall regime with high precipitation activity in the first quarter (February to March), consistent with the seasonality of the state. The limitations found in the discussion session suggest difficulty for the model in predicting values ​​very close to zero, which suggests the need for future refinement of the modeling, specifically aimed at improving performance in extreme precipitation circumstances (drought or flood).\u003c/p\u003e \u003cp\u003eFinally, the use of ensemble learning techniques is recommended in combination with the SARIMA model and LSTM architecture, which will allow for the obtaining of more robust models with lower volatility. Furthermore, the integration of exogenous variables may provide valuable insights into the relationship of external factors on precipitation. The integration of current deep learning models may also corroborate the overcoming of generalization challenges present in the model used in this study and consequently improve accuracy in scenarios of high variability.\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003e \u003ch2\u003eDeclaration of Competing Interest\u003c/h2\u003e \u003cp\u003eThe 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.\u003c/p\u003e \u003c/p\u003e\u003ch2\u003eAuthor Contribution\u003c/h2\u003e\u003cp\u003e**Luigi Pereira de Paiva:** Writing \u0026ndash; original draft, Validation, Software, Methodology, Data curation, Conceptualization. **Benito Moreira de Azevedo:** Conceptualization, Supervision, Project administration, Writing \u0026ndash; review \u0026amp;amp; editing. **Aldeney Andrade Soares Filho:** Investigation, Writing \u0026ndash; review \u0026amp;amp; editing. **Juvenaldo Florentino Canja:** Conceptualization, Visualization, Writing \u0026ndash; review \u0026amp;amp; editing.\u003c/p\u003e\u003ch2\u003eData Availability\u003c/h2\u003e\u003cp\u003eThe data used were collected from the website of the Cear\u0026aacute; Foundation for Meteorology and Water Resources (FUNCEME) via the link: [https://chuvas.funceme.br/mensal/municipios/media/](https:/chuvas.funceme.br/mensal/municipios/media) .\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\u003cli\u003e\u003cspan\u003eAkbari Asanjan A, Yang T, Hsu K, Sorooshian S, Lin J, Peng Q (2018) Short-term precipitation forecast based on the PERSIANN system and LSTM recurrent neural networks. 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Stochastic Environmental Research and Risk Assessment, pp 2285\u0026ndash;2301. 8\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eSaplıoğlu K, G\u0026uuml;\u0026ccedil;l\u0026uuml; YS (2022) Combination of the Wilcoxon test and scatter diagram for trend analysis of hydrological data. J Hydrol 612:128132\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eSantos-Romero MA, Sanabria JMC, Trinidad JA\u0026Aacute;, Alvarado RC, Pinto AGR (2024), October Extreme Rainfall Time Series Prediction: A Comparative Analysis of SARIMA, Random Forest, LSTM and Prophet Models. In \u003cem\u003e2024 13th International Conference On Software Process Improvement (CIMPS)\u003c/em\u003e (pp. 364\u0026ndash;371). IEEE\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eSeigerman CK, Leite NS, Martins ESP, Nelson DR (2024) At the extremes: Interrelations among impacts and responses to extreme hydroclimatic events in Cear\u0026aacute;, Northeast Brazil. J Hydrol 632:130850\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eSilva GKD et al (2021) Spatio-temporal variability analysis of SPI: A case study of the Chor\u0026oacute; sub-basin, Cear\u0026aacute;, Brazil. Revista Brasileira de Meteorologia 36(3):539\u0026ndash;549\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eSilva MES, Carvalho LMV, Silva Dias MAF, Xavier TM (2006) Complexity and predictability of daily precipitation in a semi-arid region: An application to Cear\u0026aacute;, Brazil. Nonlinear Process Geophys 13(6):651\u0026ndash;659\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eWilks DS (2011) Statistical methods in the atmospheric sciences, vol 100. Academic\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eZhang Y, Ye A (2021) Machine learning for precipitation forecasts postprocessing: Multimodel comparison and experimental investigation. J Hydrometeorol 22(11):3065\u0026ndash;3085\u003c/span\u003e\u003c/li\u003e\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"Rainfall, Deep Learning, Precipitation Estimation","lastPublishedDoi":"10.21203/rs.3.rs-9020912/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-9020912/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eThis research assessed the predictive power of Long Short-Term Memory (LSTM) networks to forecast mean monthly precipitation in Cear\u0026aacute; using data from 2002\u0026ndash;2025. We implemented a 12-month walk-forward validation focused on high-variability periods associated with La Ni\u0026ntilde;a (2020\u0026ndash;2023). LSTM performance was compared with XGBoost, SARIMA, and a seasonal persistence baseline. SARIMA achieved superior average performance and greater operational stability (NSE 0.771; RMSE 38.54 mm/month), outperforming LSTM on average. However, Wilcoxon tests indicated no statistically significant differences between the models and the baseline. The main contribution is the validation of LSTM\u0026rsquo;s conditional utility: despite higher average volatility, LSTM attained peak skill in specific high-predictability windows (NSE up to 0.903), demonstrating capacity to capture non-linear dependencies. We also produced an average monthly precipitation forecast for 2026, noting limitations in predicting values near zero. We recommend ensemble approaches combining SARIMA and LSTM and the inclusion of exogenous variables to improve accuracy for extreme precipitation events.\u003c/p\u003e","manuscriptTitle":"Application of Neural Network for Estimating Mean Monthly Rainfall in the State of Ceará, Brazilian Northeast","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2026-03-16 20:20:02","doi":"10.21203/rs.3.rs-9020912/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"319634ce-e5fe-4e36-b9d0-d0d8db0fd7c3","owner":[],"postedDate":"March 16th, 2026","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[],"tags":[],"updatedAt":"2026-04-08T07:42:43+00:00","versionOfRecord":[],"versionCreatedAt":"2026-03-16 20:20:02","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-9020912","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-9020912","identity":"rs-9020912","version":["v1"]},"buildId":"XKTyCvWXoU3ODBz1xrDgd","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}