Khder Alakkari ¹*; Okan Mert Katipoğlu ²

1, Department of Statistics and Programming, Faculty of Economics, Latakia University, Latakia, P.O. Box 2230, Syria

2, Department of Civil Engineering, Erzincan Binali Yıldırım University, Erzincan, Turkey

 

Manuscript link
http://dx.doi.org/10.30493/DAS.2025.012612

Abstract

This paper proposes a hybrid deep learning framework for predicting monthly rainfall in Latakia, Syria, using historic data from 1993 to 2023 and utilizing three deep learning architectures: Convolutional Neural Network (CNN), Convolutional Long Short-Term Memory network (ConvLSTM), and CNN–Fourier. For that purpose, the rainfall data was preprocessed and normalization techniques were applied to ensure model convergence. Each model was then trained on a partitioned dataset (training, validation, and testing) and optimized through early stopping and regularization. It was noted that CNN model captured underlying rainfall patterns but was less robust in predicting extreme rainfall events. On the other hand, the ConvLSTM model accurately predicted upper-bound variability during periods of heavy rainfall. The CNN-Fourier model incorporated frequency domain features to reduce noise and enhance forecast stability. A statistical comparison of the models showed that CNN-Fourier demonstrates the effectiveness of combining Fourier noise removal and deep learning to address rainfall variability through hybridization. To inform environmental planning, the forecasts were extended to 2027 using three scenarios: minimum, average, and maximum. These scenarios may offer valuable insight for stakeholders in preparing for evolving climatic conditions by incorporating spectral filtering and hybridizing spatio-temporal modeling within a robust statistical framework.

Keywords: Rainfall forecasting, Deep learning, CNN, Fourier, LSTM, Climate

Introduction

Rainfall forecasting has become a key objective in meteorological research, particularly under the increasingly variable climatic conditions of arid and semi-arid regions [1]. Preliminary predictions of annual precipitation can support decision-making across multiple sectors, including agricultural policy, flood mitigation, and water resource management. In this context, deep learning-assisted statistical learning have revolutionized time series forecasting, especially in complex and nonlinear domains such as rainfall forecasting. Traditional statistical models often struggle with capturing intricate spatiotemporal dependencies, abrupt regime changes, and seasonal variations characteristic of meteorological data. In contrast, hybrid deep learning architectures such as Convolutional Neural Networks (CNN), Convolutional Long Short-Term Memory networks (ConvLSTM), and CNN–Fourier integrations offer data-driven flexibility, enabling the extraction of both local features and global structures. These models leverage the strengths of statistical preprocessing, spectral analysis, and neural representation learning, thus providing scalable and adaptable frameworks for forecasting under climate variability.

Numerous studies have demonstrated the effectiveness of deep learning models in meteorological forecasting. LSTM and CNN were evaluated in rainfall prediction and showed a superior performance over support vector regression [1]. Another study employed multi-step deep learning for rainfall forecasting, highlighting its scalability across time horizons [2]. GCM data were integrated in another research with deep learning for daily rainfall prediction, demonstrating robustness in multi-step ahead forecasts [3]. Furthermore, the combination of non-parametric and ML techniques was also utilized for trend analysis across Indian rainfall data [4]. Hybrid models such as CNN–Fourier are also supported by various studies [5][6] where spectral and climatic variables were incorporated for improved accuracy. The use of ensemble strategies, scenario-based forecasts, and probabilistic interpretations has been recommended by more researches to account for epistemic uncertainties and model variability [7-9], which might be of great importance under shifting climate regimes.

The main objective of this study is to develop a probabilistic rainfall forecasting framework based on three hybrid deep learning models (CNN, ConvLSTM, and CNN–Fourier) and generate three distinct predictive scenarios (minimum, average, and maximum) to better capture uncertainty. Unlike previous models that provide point forecasts, this approach incorporates statistical heterogeneity by comparing structurally diverse neural networks and using the output extremes to define forecast envelopes. By embedding statistical learning theory into model selection and validation, this study offers a robust and transparent methodology for rainfall prediction in the Eastern Mediterranean under conditions of climate variability.

Material and Methods

Software and datasets

The development of the forecasting models in this study relied on an integrated deep learning framework composed of essential Python libraries and tools designed for statistical computing, signal transformation, and neural network training. The foundational data handling and preprocessing tasks were carried out using Pandas and NumPy, which facilitated efficient time series structuring and array operations. To normalize the rainfall data and improve model convergence, the MinMaxScaler from Scikit-learn was employed, ensuring that input features remained within a bounded numerical range. For error assessment and validation, standard metrics such as RMSE, MAE, MAPE, and the R-squared coefficient were calculated using the metrics module from Scikit-learn, which provided an objective evaluation of model performance across the training, validation, and test sets [10].

The deep learning architecture was implemented using TensorFlow and its high-level Keras API, which enabled the rapid construction of sequential models incorporating layers like Conv1D, ConvLSTM2D, Dense, Dropout, and BatchNormalization. These layers were selected to optimize the learning process for spatiotemporal dependencies inherent in rainfall patterns. The ConvLSTM2D layer, in particular, was critical for modeling sequential dependencies while preserving spatial structure in a time-aware context. Training optimization was achieved using the Adam optimizer, while EarlyStopping and ReduceLROnPlateau callbacks were used to prevent overfitting and dynamically adjust the learning rate, respectively. For the CNN–Fourier model, Fast Fourier Transform (FFT) was used to denoise the rainfall series by filtering high-frequency components before feeding the cleaned signals into the CNN layers, demonstrating a hybrid statistical–deep learning approach. Matplotlib was used to visualize loss functions and prediction results, aiding in the interpretability and monitoring of the training process.

Monthly rainfall data for Lattakia city during the period 1993-2023 was used as a case study and proxy for the Eastern Mediterranean region. This data was obtained from rainfall stations in Lattakia. The exploratory information for the data includes the monthly rainfall time series for Latakia from 1993 to 2023 (Fig. 1). First, there is a clearly observable seasonal periodicity, characterized by regular peaks and troughs within each annual cycle, consistent with Mediterranean climatic patterns that produce rainfall concentrated in winter months. However, interannual variation in peak rainfall intensity is substantial, particularly after 2010, where episodes of extreme rainfall exceeding 400 mm appear more frequently, suggesting an increased variance and heavier right-tail behavior. This pattern is statistically consistent with non-stationary variance (heteroskedasticity), potentially driven by external climatic forces such as ENSO-related teleconnections or regional warming effects. the clustering of dry periods, especially between 1999–2002 and 2007–2009, may indicate shifts in the mean or prolonged anomalies, supporting the hypothesis of regime shifts rather than random fluctuations. The alternation of such dry and wet spells aligns with the concept of structural breaks in the time series, which challenge linear modeling and underscore the appropriateness of non-linear deep learning methods. The background shading further emphasizes periodic climate phases, and the post-2010 period notably shows higher frequency and amplitude fluctuations, reflecting potential intensification of climate variability.

The descriptive statistics (Table 1) offer clear insights into the dynamic rainfall regime of Latakia over the past three decades. The average monthly rainfall of 61.77 mm, combined with a high standard deviation of 81.73 mm, reflects a strongly variable hydroclimatic environment, where precipitation is neither stable nor uniformly distributed across months or years. The range from 0.00 mm to 473.90 mm highlights the presence of extreme rainfall events, particularly in winter months, and prolonged dry periods, especially in the summer. The median value of 31.05 mm, notably lower than the mean, confirms a positively skewed distribution, which is a well-established feature of precipitation datasets in semi-arid and Mediterranean regions. The observed amplitude of interannual variability and the presence of extreme values (especially after 2010) suggest an increasing frequency and intensity of anomalous events, consistent with findings from global climate change assessments [11]. These changes could be linked to warmer sea surface temperatures in the Eastern Mediterranean, which enhance convective activity and atmospheric moisture capacity, thus amplifying rainfall extremes. low 25^th percentile (0.58 mm) indicates a high frequency of near-zero or dry months, while the long tail toward higher values implies the need for non-Gaussian modelling approaches. data exhibit features of heteroscedasticity, seasonal non-stationarity, and volatility clustering. These features justify the application of hybrid deep learning models capable of learning nonlinear, long-term, and high-order dependencies. This is illustrated in Figures 2 and 3 through the probability distribution of precipitation data and its main components.

Hybrid deep learning framework

This Framework integrates advanced statistical learning principles with deep neural architectures to enhance forecasting accuracy in complex time series data. This approach leverages the complementary strengths of multiple model types to capture different temporal patterns, from short-term fluctuations to long-term seasonal shifts. By combining convolutional neural networks (CNNs), convolutional long short-term memory networks (ConvLSTMs), and Fourier-transformed CNNs, following sections describe each model in detail, highlighting its architecture, training performance, and role within the ensemble forecasting strategy.

Convolutional Neural Network (CNN)

Convolutional Neural Networks (CNNs) were originally developed for image recognition tasks, but their ability to capture local patterns has led to successful applications in one-dimensional time series forecasting. The underlying premise is that the convolutional layers can extract local temporal dependencies and features within a L fixed-length input window. Suppose X=[x₁,x_2,…,x_T] be a univariate time series, and let denote the look-back window used to forecast the next observation x_T+1. The CNN takes as input the sub-series [12]:

A 1D convolution operation applies a set of filters [w¹,w²,…,w^F] where each filter w^f ∈ R^k to sliding windows of size across the input. For each filter f the output feature map, h_i^(f) is given by:

where: σ is the activation function (ReLU in this case), b^(f) is the bias term and i∈[1,L-k+1]. In the first convolutional layer, 64 filters of kernel size 3 are applied, resulting in 64 feature maps of length L₁=L-3+1. This is followed by a second convolutional layer with 32 filters and the same kernel size, further reducing the sequence length to L₂=L₁-3+1. The output of the second convolutional layer is a tensor of shape (L₂, 32) which is flattened into a vector of length L₂×32 A dropout layer with rate 0.2 is applied for regularization to prevent overfitting by randomly setting 20% of the units to zero during training. A dense (fully connected) layer is used to map the flattened feature vector to the output scalar x̂_t+1 representing the forecasted value:

where: z∈R^(L2.32) is the flattened feature vector, w_fc and b_fc are the weights and bias of the dense layer.

Convolutional Neural Network with Fourier Transform Integration (CNN–Fourier)

The CNN–Fourier model integrates signal processing concepts with deep learning by applying a frequency-domain transformation to the input time series prior to the convolutional layers. This hybrid approach is designed to capture both local temporal dependencies and global frequency-based patterns, which are often present in climatological time series such as rainfall data. The first layer applies the Discrete Fourier Transform (DFT) to each input segment using [13]:

This transformation projects the temporal sequence into the complex frequency domain. Since the neural network requires real-valued inputs, only the real part of the transformed signal is retained:

This representation captures harmonic components, periodic patterns, and signal energy distribution across frequencies. Following the Fourier transform, the sequence z^(t) is passed through two 1D convolutional layers h_i^(f).  First Conv1D layer 64 filters, kernel size 3, ReLU activation and Output shape: (L−2,64). Second Conv1D layer: 32 filters, kernel size 3, ReLU activation and Output shape: (L−4,32). The convolutional layers operate on the frequency-transformed input, allowing the model to learn spectral patterns over local windows. After flattening, a dropout regularization layer with a rate of 0.2 is applied to reduce overfitting. The dense layer produces the final forecast x̂_t+1:

Convolutional Long Short-Term Memory Network (ConvLSTM)

The Convolutional Long Short-Term Memory (ConvLSTM) model is designed to capture both spatial and temporal dependencies in structured sequences. While initially proposed for spatiotemporal data such as video frames, its architecture also proves effective for one-dimensional time series where temporal structures are dominant. In this study, the ConvLSTM model is adapted for univariate rainfall forecasting by reshaping the time series into a five-dimensional tensor to match the input requirements of the ConvLSTM2D layer [14]. the univariate rainfall sequence be denoted by:

where n is the number of previous time steps (look-back window). For ConvLSTM2D input, this sequence is reshaped into:

where: B batch size, T: number of time steps, H=1,W=1: spatial dimensions, C=1: number of input channels, Thus, the input per sample becomes R^n×1×1×1, The ConvLSTM replaces matrix multiplications in traditional LSTM with convolutions, suitable for grid-structured data. The key cell operations are defined as:

where: *: 2D convolution, σ: sigmoid activation, ∘: element-wise multiplication, i_t, f_t, o_t input, forget, and output gates and C_t cell state, H_t hidden state (output), W,b learnable convolutional kernels and biases. Given the spatial dimensions H=W=1, the convolution acts effectively as a fully connected operation, but with the memory cell dynamics preserved.

Models architectural configurations

Table 2 shows the architectural configurations of the three hybrid deep learning models (CNN, ConvLSTM, and CNN-Fourier), including output shapes and the total number of trainable parameters. These specifications are essential for understanding the computational complexity and learning capacity of each model, as they directly influence convergence behavior and generalization ability in forecasting tasks. The subsequent analysis builds on this architecture summary to interpret the model performances across training, validation, and testing stages:

Each model has distinct structural characteristics and parameter loads that correspond to its functional design and learning objective. The CNN model starts with two successive one-dimensional convolutional layers that progressively extract temporal features, followed by flattening and dense layers, accumulating 6,689 trainable parameters. The ConvLSTM model includes a ConvLSTM2D layer capable of modeling temporal dependencies with spatial correlations, supplemented by batch normalization and dense layers, resulting in a slightly lower trainable parameter count of 6,181. The CNN-Fourier model incorporates bandwidth transformation via Fourier filtering before applying the CNN architecture, including a max-pooling layer for dimensionality reduction. It exhibits the highest trainable parameter count (21,801), reflecting its greater complexity and representational power. The total data was partitioned into training (70%), validation (20%), and testing (10%) data sets, which were used to train and optimize the developed models.

Loss and optimization

During training, the models were assessed using the Mean Squared Error (MSE) loss function:

Adam optimization algorithm was used, which adapts learning rates per parameter to accelerate convergence.  Two callbacks are applied during training: stops training if no improvement in validation loss after 15 epochs and ReduceLROnPlateau: reduces learning rate by a factor of 0.5 if validation loss stagnates for 10 epochs. Performance indicators for evaluating models include the following framework [15][16]:

These outputs allow comparison of the difference between actual and estimated values y_i, ŷi.

Results and Discussion

The CNN model achieved its optimal performance at epoch 19, with a training loss of 0.0125 and a higher validation loss of 0.0407, indicating overfitting while capturing the upper bounds of the variance of the precipitation series. The ConvLSTM model improved this performance, stabilizing at epoch 46 with a validation loss of 0.0266 and a comparable training loss of 0.0141, indicating better retention of temporal dependencies and lower variance between the training and validation sets. The CNN-Fourier model demonstrated superior performance, achieving convergence at epoch 100 with a negligible training loss (0.000083) and validation loss (0.000161), with near-parallel training and validation curves throughout the training process. From a statistical learning perspective, the CNN-Fourier model exhibits the lowest bias and variance, reflecting a well-fitted model with high prediction accuracy. The use of frequency-domain filtering before convolution enhanced signal-to-noise separation, reduced overfitting, and improved the model’s ability to generalize beyond the training data. The comparative gaps between the training and validation losses of CNN and ConvLSTM indicate sensitivity to noise and seasonal variations, further justifying the ensemble strategy adopted in the hybrid framework (Table 3 and Fig. 4).

Performance analysis (Table 4) for the tested models showed that CNN-Fourier model demonstrating superior performance across all datasets achieving the lowest RMSE and MAPE, along with the highest R² scores, particularly on the validation (0.8108) and test (0.7602) sets. These results indicate the model’s high accuracy and generalizability, with minimal error dispersion and excellent explanatory power. This justifies its selection as the average scenario in the ensemble forecast, as it provides the most stable and reliable predictions, assuming a well-trained model in a quasi-static environment. The CNN model exhibits average accuracy with a lower RMSE on both the training (5.89) and test (6.58) sets, but exhibits a relatively higher MAPE (2.52–2.55%) and lower R² values, especially in the validation (0.4596). These results suggest that although the CNN efficiently captures short-term features, it performs poorly at generalizing unobserved seasonal shifts, leading to under- or overestimates in the upper boundary periods. This behavior supports its use as a minimum scenario, especially in months when conservative rainfall estimates are preferred for policy and planning. Although the ConvLSTM model has a slightly better mean squared coefficient (RMSE) (7.64) than the CNN, it yields the highest MAPE value on the test set (4.50%) and the lowest R² value (0.4906), indicating wider variance and less consistent fit across datasets. These results are attributed to ConvLSTM’s sensitivity to temporal dynamics and the potential for overfitting to local sequential patterns. Therefore, ConvLSTM captures upswings and anomalies that the more stable CNN-Fourier model does not, making it suitable as an extreme scenario, especially for stress tests under heavy rainfall assumptions.

Based on previous results, scenario building effects can be obtained, including the average scenario, which relies on CNN-Fourier and provides more balanced and accurate forecasts under typical conditions. The lower scenario, which relies on CNN, reflects a conservative estimate of rainfall and is suitable for drought planning. The ConvLSTM-based extreme scenario, taking into account extremes and potential anomalies in the upper bound, provides a defensible statistical framework for probabilistic ensemble forecasting, captures model uncertainty, enhances decision support, and is consistent with best practices in climate risk analysis.

decision was made statistically to construct three predictive scenarios (minimum, average, and maximum) (Table 5 and Fig. 5) using hybrid deep learning models (CNN, ConvLSTM, and Fourier-CNN). This approach was motivated by the need to capture the uncertainty and variability inherent in the nonlinear and nonstationary climate rainfall time series in Lattakia. Rainfall is subject to high temporal variability, structural seasonality, and regime shifts due to climatic factors (El Nino), making point forecasts insufficient for policy- and risk-sensitive applications. Scenario-based forecasting enables a probabilistic framework for potential futures [7], supporting effective decision-making under uncertainty. The rationale for this includes:

• Model diversity and structural variability: CNN, ConvLSTM, and Fourier-CNN models exhibit distinct structures, each capturing different temporal and frequency characteristics. The ensemble literature supports the aggregation of structurally different learners to improve generalization and reduce overfitting [8].
• Approximating the prediction interval: Rather than producing formal confidence intervals (which are complex for deep learning models), ensemble min/max provides empirical bounds that approximate the envelopes of the prediction intervals and are particularly effective in the absence of distributional assumptions [17].
• Error distribution considerations: The asymmetric and heavy-tailed residuals observed in rainfall prediction models indicate that variance is not constant over time, reinforcing the need to report more than just the average prediction. The average scenario, derived from Fourier-CNN (the most accurate and stable model), is surrounded by outliers from CNN and ConvLSTM to reflect the uncertainty in the cognitive model [9].
• Policy and operational relevance: Rainfall-based planning (agriculture, flood control) benefits from viewing forecasts within ranges and the identification of lower and upper bounds supports scenario analysis, sensitivity testing, and contingency planning, which are standard practices in climate-informed risk assessment [7].

The CNN-Fourier model yields the mean (most expected) scenario. This model consistently predicts rainfall amounts that align with historical climatological patterns and exhibits temporal stability across seasons. The CNN model’s minimum scenario is a conservative estimate that can be used for planning water resources and dealing with drought. In this scenario, prolonged dry spells (or complete absence of rainfall) occur frequently, particularly during the summer months. This reflects the typical dry season characteristic of the Eastern Mediterranean climate. In contrast, the extreme scenario derived from ConvLSTM outputs indicates a non-negligible probability of pronounced rainfall anomalies. This model includes time-dependent trends that amplify peak rainfall intensities, particularly during the winter season. This feature enhances its utility in assessing flood likelihood.

The shaded area in Figure 5 shows the minimum and maximum scenarios and demonstrate the range of monthly expected rainfall. This multi-scenario forecasting framework supports adaptive decision-making in the fields of hydrology, agriculture, and infrastructure planning. It is also consistent with contemporary approaches in climate modeling that recommend probabilistic outputs to accommodate the deep uncertainty in long-term environmental forecasts.

The analysis of the forecasting results from the current study indicates a significant statistical advancement over prior models examined in the literature. Unlike traditional machine learning models or simple deep networks, the hybrid deep learning architectures applied here (CNN, ConvLSTM, and CNN–Fourier) exhibit superior performance, particularly in capturing the temporal and nonlinear dynamics of rainfall data. Compared to other studies, where classical time series models often failed to preserve pattern fluctuations [18], the CNN–Fourier model in this research showed enhanced accuracy with a remarkably low RMSE and MAPE across all datasets. This confirms the claims that hybrid models are better suited for chaotic and seasonal data [19]. Furthermore, the incorporation of spectral filtering before the CNN layer, as seen in the CNN–Fourier model, aligns with the previously suggested enhancement strategies [20], which emphasized the benefit of combining frequency-based signal processing with deep learning. Studies stressed the need for more generalizable models under climate variability [21][22], a gap this study addresses by validating all models across train, test, and validation sets with minimal overfitting, especially under CNN–Fourier. The dynamic learning adaptation of ConvLSTM also supported the claim that memory-based architectures can improve long-range dependencies in rainfall forecasting [23]. However, unlike the less stable performances reported in [24], the proposed models (especially CNN–Fourier) demonstrated consistent predictive strength. The reliability of hybrid models in operational forecasting are questioned due to their complexity [25]; however, the structured methodology presented in this study and scenario generation show that these limitations can be overcome with careful model design and evaluation.

Conclusions

This study demonstrated the effectiveness of a hybrid deep learning framework for monthly rainfall forecasting in the Eastern Mediterranean, with a focus on Latakia, Syria. By integrating three models (CNN, ConvLSTM, and CNN-Fourier) in a scenario-based forecasting architecture, the research addressed both the deterministic and probabilistic nature of climate variability. The CNN-Fourier model provided more accurate and stable forecasts, as evidenced by the lowest RMSE and MAPE and the highest R² across all datasets. CNN captured the underlying rainfall patterns but tended to underestimate extreme events, while ConvLSTM reflected the upper-bound variability, particularly during periods of heavy rainfall. This diversity in model behavior therefore justified the construction of minimum, average, and maximum forecast scenarios, allowing for a more complete representation of potential outcomes. According to the statistical results, the proposed framework captures nonlinearity, seasonality, and structural variability in rainfall time series more effectively than traditional methods. The average scenario can be used as a basis for monthly water resource allocations, while incorporating the maximum scenario for infrastructure stress testing and the minimum scenario for drought preparedness. The hybrid model can be further improved by integrating it into nowcasting systems, with monthly updates and retraining using the latest observations to improve accuracy. The hybrid deep learning framework presented here is expected to provide a scalable and interpretable statistical method for rainfall forecasting, providing practical value to decision-makers and researchers in climate-sensitive sectors.

Acknowledgment

The authors acknowledge the use of AI-assisted tools for language editing and fluency enhancement; all edits were rigorously reviewed and validated by the authors to preserve scientific accuracy and intended meaning.

Conflict of interest statement
The authors declared no conflict of interest.
Funding statement
The authors declared that no funding was received in relation to this manuscript.
Data availability statement
The author declared that all used datasets will be available upon reasonable request from the corresponding author. Furthermore, the codes developed in this study can be obtained from: https://github.com/khder90/research-codes/blob/main/README.md?plain=1

References

1. Al-Samrraie LA, Abdalla AM, Alrawashdeh KA, Bsoul AA, Awad MA, Alzboon K, Al-Taani AA. Deep Learning Models Based on CNN, RNN, and LSTM for Rainfall Forecasting: Jordan as a Case Study. Math. Model. Eng. Probl. 2025;12(7):2456-66. DOI
2. Narejo S, Jawaid MM, Talpur S, Baloch R, Pasero EGA. Multi-step rainfall forecasting using deep learning approach. PeerJ Comput. Sci. 2021;7:e514. DOI
3. Khan MI, Maity R. Hybrid Deep Learning Approach for Multi-Step-Ahead Daily Rainfall Prediction Using GCM Simulations. IEEE Access. 2020;8:52774-84. DOI
4. Praveen B, Talukdar S, Shahfahad, Mahato S, Mondal J, Sharma P, Islam ARMT, Rahman A. Analyzing trend and forecasting of rainfall changes in India using non-parametrical and machine learning approaches. Sci. Rep. 2020;10(1):10342. DOI
5. Ha J, Lee H. Enhancing Rainfall Nowcasting Using Generative Deep Learning Model with Multi-Temporal Optical Flow. Remote Sens. 2023;15(21):5169. DOI
6. Qiu D, Wu C, Mu X, Zhao G, Gao P. Spatial-temporal Analysis and Prediction of Precipitation Extremes: A Case Study in the Weihe River Basin, China. Chin. Geogr. Sci. 2022;32(2):358-72. DOI
7. Wilks DS. Statistical methods in the atmospheric sciences. Academic press; 2011.
8. Wang Y, Yuan Z, Liu H, Xing Z, Ji Y, Li H, Fu Q, Mo C. A new scheme for probabilistic forecasting with an ensemble model based on CEEMDAN and AM-MCMC and its application in precipitation forecasting. Expert Syst. Appl. 2022;187:115872. DOI
9. Gal Y, Ghahramani Z. Dropout as a bayesian approximation: Representing model uncertainty in deep learning. In: International conference on machine learning.  2016:1050-9.
10. Goodfellow I, Bengio Y, Courville A, Bengio Y. Deep learning. Cambridge: MIT press. 2016.
11. IPCC. Climate Change 2013: The Physical Science Basis. Cambridge: Cambridge University Press. 2013.
12. Bai S. An Empirical Evaluation of Generic Convolutional and Recurrent Networks for Sequence Modeling. arXiv preprint arXiv:1803.01271. 2018.
13. Brice R. Digital signal processing. In: Newnes Guide to Digital TV. Elsevier. 2003. DOI
14. Hochreiter S, Schmidhuber J. Long Short-Term Memory. Neural Comput. 1997;9(8):1735-80. DOI
15. Hyndman RJ, Athanasopoulos G. Forecasting: principles and practice. OTexts. 2018.
16. Willmott C, Matsuura K. Advantages of the mean absolute error (MAE) over the root mean square error (RMSE) in assessing average model performance. Clim. Res. 2005;30:79-82. DOI
17. Lakshmanan V, Smith T, Stumpf G, Hondl K. The Warning Decision Support System–Integrated Information. Weather Forecast. 2007;22(3):596-612. DOI
18. Gerbelot C, Karagulyan A, Karp S, Ravichandran K, Stern M, Srebro N. Applying statistical learning theory to deep learning. J. Stat. Mech: Theory Exp. 2024;2024(10):104003. DOI
19. Adewoyin RA, Dueben P, Watson P, He Y, Dutta R. TRU-NET: a deep learning approach to high resolution prediction of rainfall. Mach. Learn. 2021;110(8):2035-62. DOI
20. Allawi MF, Abdulhameed UH, Adham A, Sayl KN, Sulaiman SO, Ramal MM, Sherif M, El-Shafie A. Monthly rainfall forecasting modelling based on advanced machine learning methods: tropical region as case study. Eng. Appl. Comput. Fluid Mech. 2023;17(1):2243090. DOI
21. Baudhanwala D, Mehta D, Kumar V. Machine learning approaches for improving precipitation forecasting in the Ambica River basin of Navsari District, Gujarat. Water Pract. Technol. 2024;19(4):1315-29. DOI
22. Mondini AC, Guzzetti F, Melillo M. Deep learning forecast of rainfall-induced shallow landslides. Nat. Commun. 2023;14(1):2466. DOI
23. Harris L, McRae ATT, Chantry M, Dueben PD, Palmer TN. A Generative Deep Learning Approach to Stochastic Downscaling of Precipitation Forecasts. JAMES. 2022;14(10):e2022MS003120. DOI
24. Latif SD, Alyaa Binti Hazrin N, Hoon Koo C, Lin Ng J, Chaplot B, Feng Huang Y, El-Shafie A, Najah Ahmed A. Assessing rainfall prediction models: Exploring the advantages of machine learning and remote sensing approaches. Alexandria Eng. J. 2023;82:16-25. DOI
25. Wani OA, Mahdi SS, Yeasin M, Kumar SS, Gagnon AS, Danish F, Al-Ansari N, El‑Hendawy S, Mattar MA. Predicting rainfall using machine learning, deep learning, and time series models across an altitudinal gradient in the North-Western Himalayas. Sci. Rep. 2024;14(1):27876. DOI

Cite this article:

Alakkari K., Okan M.K. Hybrid deep learning for probabilistic rainfall forecasting in a changing climate. DYSONA-Applied Science. 2026;7(1):176-188. doi: 10.30493/DAS.2025.012612