Introduction

Across Africa, rainfall plays a significant role not just as a weather event but as a major driver of food production, energy generation, economic stability, and the normal functioning of both humans and even animals. In recent times, African countries have faced remarkable climate change as evidenced in sudden floods, severe drought, and unpredictable rainfall pattern1,2,3,4. Despite the availability of arable lands in Africa, the shift in climate undermines food security through reduced agricultural productivity, exacerbates poverty, and increases the vulnerability of millions of Africans to food insecurity and hunger5,6,7. This undoubtedly hampers the attainment of the Sustainable Development Goals 1, 2, and 3, which focus on alleviating poverty, eradicate hunger, and ensuring good health and wellbeing, respectively. Therefore, accurate and reliable prediction of rainfall in view of this variability goes beyond a mere academic research but a societal necessity for strategic agriculture planning, creation of early warning systems for climate actions, and disaster risk reduction2,8,9.

Despite the societal importance of understanding rainfall dynamics in Africa, accurate prediction of daily rainfall remains highly challenging due to inherent complexities in rainfall patterns across African cities. Africa, as a continent, suffers from an unevenly distributed meteorological observation network, which results in significant data gaps that hinder the performance of traditional statistical such as time series models, which have been used by researchers10 and physics-based numerical weather prediction (NWP) models. This variability has also been compounded by interactions among local convection, land–atmosphere feedbacks, and large-scale climate drivers. This therefore, has introduced spatial heterogeneity, temporal non-stationarity, and high nonlinearity in rainfall patterns, which the conventional models will not be able to adequately capture. The highly nonlinear and stochastic nature of precipitation processes makes daily rainfall prediction, in particular, a complex task despite its considerable value in short-term agricultural planning, early warning systems, and disaster risk reduction11,12,13,14,15. Predictability of rainfall and its successful incorporation into climate adaptation decision-making frameworks are further complicated by the growing frequency of extreme weather events such as flash floods, protracted droughts, and shifting wet and dry seasons16. The variability in the rainfall as a result of human environmental activities has also been underscored by17 while the effect of rainfall on waste management and environmental degradation has been stressed by1,18. These studies reaffirm how climate variability is linked to sustainable development priorities, such as water supply, sanitation, agriculture, and health19,20. Even though these studies are useful, they relied on traditional statistical models or empirical models that frequently fail to capture the complexities and non-linearity in rainfall patterns, particularly at finer temporal scales like daily intervals.

As a result of the evolutionary trend brought about by the use of Artificial Intelligence (AI) tools in prediction, deep learning models, have emerged as powerful alternatives. This is due to their ability to learn complex patterns in data, as well as capture the nonlinearity and spatial–temporal patterns in data which the conventional model cannot adequately capture21,22. Prominent among the Deep Learning (DL) algorithms that have played a significant role in forecasting climate data, particularly rainfall, are the Long Short-Term Memory (LSTM) networks, Convolutional Neural Networks (CNNs), Recurrent Neural Networks (RNNs), and Gated Recurrent Units (GRUs), among others. These Deep Learning algorithms are single architecture. The LSTMs, for instance, are adept at capturing temporal dependencies within sequential data while CNNs are very versatile at extracting spatial features from gridded datasets23,24,25,26,27,28.

The LSTM networks are ideally suited for rainfall forecasting tasks because of their exceptional ability to capture temporal dependencies in sequential data. Predictive accuracy has also been demonstrated to be improved by hybrid models that integrate CNNs and LSTM, utilizing both spatial and temporal data, particularly in meteorological applications where both kinds of dependencies are crucial29. The CNNs, LSTM networks, and their hybrid variants are examples of deep learning models that have proven to be more effective at modeling complex time-series data because they can automatically uncover hidden patterns without requiring a lot of feature engineering8,29. Despite their strength in capturing complexities in dataset, they also have limitations. The CNNs, for instance, often struggle with long-term temporal dependencies, whereas LSTMs may not be able to capture the localized spatial patterns, which is critical for rainfall events30,31. Even with these encouraging advancements, there is still little use of pure and hybrid deep learning models for predicting daily rainfall in African cities. Most of the current literature either ignores the spatial–temporal richness of climate data or concentrates on monthly or seasonal rainfall estimates2,20,23. Additionally, context-specific models that are adapted to the distinct topography, urban dynamics, and climatic patterns of African regions are required, as environmental complexity and data scarcity may make it difficult for global models to be transferred there1.

To address these challenges associated with these single models, the hybrid deep learning models, which combine the complementary strengths of different architectures on forecasting, have been explored30,31,32,33,34,35,36,37. For example, a hybrid of CNN + LSTM can improve its performance by leveraging the strengths of the individual models. The CNN can be used in extracting the salient spatial features from the data, while the LSTM will then capture the temporal dependencies over time. This approach has been proven to improve prediction accuracy when there is a complexity in the data set, which is typical of rainfall pattern in Africa. Gupta et al.35 explored the application of a hybrid deep learning model combining Bidirectional LSTM (Bi-LSTM) and standard LSTM networks for rainfall prediction in Mumbai, India. Similarly, Khan et al.34 proposed a hybrid approach integrating a one-dimensional CNN (Conv1D) with a Multi-Layer Perceptron (MLP) for daily rainfall forecasting. Their findings showed that the Conv1D-MLP model was more effective in capturing the complex nonlinear relationships between causal variables and daily rainfall variability. In Iraq, Alqahtani et al.30 introduced an optimized LSTM along with hybrid deep learning architectures to enhance the forecasting of average monthly rainfall. Their hybrid model, which combined Convolutional Neural Networks with stacked Bidirectional LSTM layers (CNN-BDLSTM), outperformed single models. Zhou et al. (2023) used a hybrid of self-attention (SA), CNN, and LSTM to form a hybrid SA-CNN-LSTM in predicting hourly streamflow in the Mazhou Basin, China. Compared to single models, the SA-CNN-LSTM demonstrated robust and better predictive performance across different flood magnitudes and lead times.

Yet, despite this growing interest in the use of hybrid models in climate forecasting, there are limited studies in Africa that carry out comparative studies systematically evaluating single and hybrid deep learning models for daily rainfall prediction. This kind of evaluation is very critical, given that single models may still outperform hybrid models, especially when the data is not complex. Without a clear, comprehensive evaluation, it is difficult to identify which modelling strategy is most suitable for African regions in view of climatic conditions and limited data infrastructure. Therefore, a comprehensive comparative analysis of single and hybrid deep learning models for daily rainfall prediction, using African climatic data, is carried out in this study. This study intends to advance research in data-driven rainfall forecasting in Africa which could help in developing robust prediction systems that reflect African climate data.

Materials and methods

Research area

Data used in this study came from the Modern-Era Retrospective Analysis for Research and Applications, Version 2 (MERRA-2), a global reanalysis dataset created by NASA that offers hourly temporal resolution and high-resolution outputs at 0.5° latitude × 0.625° longitude. The stations considered in this study are Nairobi, Abuja, Pretoria, Rabat, and Libreville chosen to represent various parts of Africa. These cities were selected because of their diverse geographic locations, reliance on agriculture, and varied climates.

The map in Fig. 1 shows the geographical representation of the study area and this graph was created by the authors using Python 3.0 with the Matplotlib library (version 3.8.0; https://matplotlib.org/) and the Basemap Toolkit (version 1.3.8; https://matplotlib.org/basemap/).

Fig. 1
figure 1

Map of the selected stations showing the study area. Figure created using Python 3.0 using Matplotlib 3.8.0.

Full size image

Data collection process and data preprocessing

Data used in this study came from the Modern-Era Retrospective Analysis for Research and Applications, Version 2 (MERRA-2), a global reanalysis dataset created by NASA that offers hourly temporal resolution and high-resolution outputs at 0.5° latitude × 0.625° longitude. The data collection spans from January 1, 1980, to December 31, 2024. The data collection and preprocessing steps were guided by established approaches reported in previous studies11,14,20. Preliminary inspection of the MERRA-2 dataset indicated that it contained no missing values, therefore, no missing-value treatment was necessary. Consistent with11,20, the input features included relative humidity, temperature, and pressure as predictors of rainfall. Additionally, lagged rainfall values from previous days were incorporated to capture temporal persistence in rainfall patterns, in line with the finding by14. To handle outliers in the data set, the Winsorizing method was used and the features in training these algorithms are the relative humidity, wind speed, and pressure which are continuous features while both the day and the month were treated as categorical variables and label-encoded with numbered from 1 (January) to 12 (December) and days of the week numbered from 1 (first day) to 7 (last day). The previous 10 days were included as individual discrete features, and this approach allows the models to learn distinct relationships for rainfall on each of the preceding days. The target feature was the daily rainfall and the data was divided into training and testing, with 80% as training and 20% as testing. The standard scaler was used in scaling the data, and Heatmap was used as exploratory data analysis to visualize the relationship in daily rainfall among the selected African cities.

Hyperparameter tuning was carried out using the Keras Tuner’s Random Search strategy with the main goal of minimizing validation loss, with a maximum of 10 hyperparameter trials conducted. Each model was trained for up to 50 epochs, and early stopping was employed to avoid overfitting if the validation loss did not improve for 5 consecutive epochs. The limited number of trials was chosen due to computational constraints and the high dimensionality of the models. Although this search space provided a reasonable balance between model performance and computational feasibility, future studies may explore a higher number of trials and the hyperparameter ranges to further improve model generalization and predictive accuracy. For the purpose of explainability, the permutation feature importance was used. The summary of the hyperparameters tuned and their range of values is presented in Table 1.

Table 1 Summary of the hyperparameters range used in training.
Full size table

Description of the deep learning algorithms

The following Deep Learning (DL) algorithms were used: LSTM, ANN, RNN, and CNN.

The LSTM is a deep learning algorithm that is efficient in understanding patterns in the data over time, making it suitable for time series data such as rainfall. Unlike other models that could not remember the past data, the LSTM has the ability to adequately recall previous data and use the information contained in the previous data to make future predictions. The LSTM model makes use of gates to determine what to ignore and what to remember. There are three gates in LSTM, which are input gate, forget gate, and output gate. The input gate controls the information to be included in the memory cell while output gate focuses on the information to be added to the memory cell. The forget cell on the other hand, focuses on what information to be removed from the memory cell. The diagrammatic representation of the LSTM architecture is shown in Fig. 2.

Fig. 2
figure 2

LSTM architecture.

Full size image

The ANN: The ANN deep learning algorithm comprises interconnected nodes, also known as neurons which are organized in layers. It is capable of learning complex and non-linear relationships in data set. The ANN algorithms comprise three layers namely: input layer, which receives the input features, the hidden layers, where complex computation of the input data and extraction of meaningful features and patterns take place, and the output layer which produces the output based on information processed in the hidden layers.

The structure of the ANN is described as follows:

Let \(z = \left( {z_{1} ,z_{1} ,...,z_{n} } \right)^{T}\) be the input features and y be the target feature then:

$$y = f\left( {\sum\limits_{j = 1}^{P} {w_{j}^{\left( 2 \right)} .\lambda \left( {\sum\limits_{{}}^{{}} {w_{ji}^{\left( 1 \right)} z_{i} + \gamma_{j}^{\left( 1 \right)} } } \right) + \gamma^{\left( 2 \right)} } } \right)$$
(1)

where, \(w_{ji}^{\left( 1 \right)}\) represents the weights from the input node i to hidden node j, \(w_{j}^{\left( 2 \right)}\) represents the weights from the hidden node j to the output, \(\gamma_{j}^{\left( 1 \right)}\) and \(\gamma^{\left( 2 \right)}\) are the bias terms, \(\lambda \left( . \right)\) is the activation function of the hidden layer which could be Sigmoid, Rectified Linear Unit (ReLU) or Tanh as defined in (2), (3) and, (4). The f (.) is the activation function of the output and p is the number of neurons in the hidden layer.

$$\text{Sigmoid}; \; \; \lambda \left( u \right) = \frac{1}{{1 + e^{ - u} }}$$
(2)
$$\text{ReLu}; \;\; \lambda \left( u \right) = \max \left( {0,u} \right)$$
(3)
$$\text{Tanh}; \;\; \lambda \left( u \right) = \frac{{e^{u} - e^{ - u} }}{{e^{u} + e^{ - u} }}$$
(4)

The RNN: The RNN deep learning algorithm has the ability to identify patterns in time series data. The RNN also has an internal memory to process these sequences of inputs. This makes the algorithm very suitable for time series data. At each time step i, the RNN receives the input feature, then updates the hidden state \(R_{i}\) and generates the desired output \(y_{i}\).

$$R_{i} = \lambda_{h} \left( {w_{h} z_{i} + s_{h} h_{i - 1} + \gamma_{h} } \right)$$
(5)
$$y_{i} = \lambda_{y} \left( {w_{y} h_{i} + \gamma_{y} } \right)$$
(6)

where, \(z_{i}\) is the input vector in the case past daily rainfall, \(h_{i}\) is the hidden state at time i, \(w_{h} ,s_{h}\) and \(w_{y}\) are matrices of the weights, \(\gamma_{h}\) and \(\gamma_{y}\) are the bias vectors, \(\lambda_{h}\) and \(\lambda_{y}\) are the activation function while \(y_{i}\) is the output.

The CNN: This is a type of deep learning that has the ability to learn directly from the data. This algorithm is very effective in finding patterns in data and has been widely used in image recognition. The architecture of the Convoluted Neural Network is illustrated in Fig. 3. It learns spatial hierarchies of features through non-linear activation, convolutions, and pooling. The structure of the CNN can be represented as:

$$\pi_{ij}^{\left( l \right)} = \sum\limits_{p = 1}^{P} {} \sum\limits_{r = 1}^{R} {w_{p,r}^{{\left( {l - 1} \right)}} } z^{{\left( {l - 1} \right)}}_{i + p,j + n} + \gamma^{\left( l \right)}$$
(7)

where, \(\pi_{ij}^{\left( l \right)}\) is the output at location (i,j) in layer l, \(w_{p,r}^{{\left( {l - 1} \right)}}\) are the learnable filter weights, \(z^{{\left( {l - 1} \right)}}\) is the input of the previous layer and \(\gamma^{\left( l \right)}\) is the bias.

Fig. 3
figure 3

Architecture of the convoluted neural network.

Full size image

Hybrid model of deep learning algorithms

A hybrid model of deep learning is a combination of two or more deep learning algorithms leveraging on the strength of these DL algorithms. It is usually more robust than single models as it combines the strength to improve the performance. In this study, we focus on the hybridization of RNN + ANN, LSTM + ANN and LSTM + RNN.

Forecasting performance metrics

The forecasting performance of these deep learning algorithms was compared using the Mean Square Error (MSE), Root Mean Square Error (RMSE), Mean Absolute Error (MAE) and Huber loss.

Results and discussion

The descriptive analysis of the daily rainfall in the five selected African cities is presented in Table 2. Result shows that Libreville has the highest average daily rainfall (11.67 mm) which, indicates that it is the wettest of all the locations. The lowest daily rainfall was reported in Rabat (0.99 mm), indicating that Rabat receives less rainfall than other cities indicating a generally drier climate. Daily rainfall extreme was also more pronounced in Libreville and Abuja compared with other African cities considered, and this is also corroborated by the result of standard deviation, which also indicates highest variability in rainfall in these locations. Result also reveals highest skewness (7.76) and kurtosis (91.39) indicating that though average daily rainfall is low, this location is more prone to rare but intense rainfall events. All the cities show positive skewness, indicating that extreme rainy days are rare but when they occur, it is always significant. The high kurtosis values ranging from 52.40 in Libreville to 91.39 in Pretoria suggest that the distribution of rainfall in these cities are highly peaked with heavy tails, indicating evidence of occasional extreme rainfall events followed by many days of little or no rain (Table 1). Based on this result, it is evident that rainfall in these cities is non-linear and this underscores the need to use a non-linear model to capture the variability in the rainfall patterns in these African cities confirming the need to use non-linear model such as RNN, LSTM, CNN as well as hybrid models. These variations in daily rainfall pattern in these locations as well as the non-linear pattern observed in these locations necessitate the need to use deep learning algorithms in predicting daily rainfall dynamics in these locations as well as the use of location -specific modelling. The non-linear pattern obtained in daily rainfall in this study is corroborated by that of Djibo et al.38 and Falayi et al.39 which also established non-linearity pattern in rainfall patterns in West Africa countries. This non-linearity is rainfall pattern has been established by Wani et al.31 and Bosson-Amedenu et al.37 where non-linear models including ANN and LSTM that account for non-seasonality in rainfall have been advocated. Wani et al.31 specifically stressed the inability of linear models such as the Autoregressive Integrated Moving Average (ARIMA) in rainfall modelling.

Table 2 Descriptive statistics for daily rainfall in the selected African cities.
Full size table

The result in Fig. 4 shows heatmap of the relationship among the selected cities in terms of their daily rainfall distribution. Figure 2 reveals that there is a weak correlation between daily rainfall patterns of the selected African cities suggesting that each of these African cities has a unique rainfall pattern. This weak correlation is an indication that daily rainfall in these cities is largely driven by local and regional atmospheric conditions rather than a single, shared continental-scale weather system. This is also consistent with that of other similar studies40,41. This emphasizes the use of city-specific deep learning in predicting rainfall dynamics for sustainable environmental management and climate action in these African cities.

Fig. 4
figure 4

Heatmap for the correlation between daily rainfalls in the selected African cities.

Full size image

The performance evaluation results for these algorithms based on the out-of-sample daily rainfall data is presented in Table 3. In Nairobi, the RNN was found to perform better than other algorithms with the least MSE (18.6225), RMSE (4.3154), and MAE (2.3688) as well as the least value of Huber loss (1.9688) compared with other models. The RNN algorithm also shows dominance in Pretoria (MSE = 16.8059, RMSE = 4.0995, MAE = 2.7239, Huber loss = 2.2545) and Rabat (MSE = 13.5506, MAE = 3.6811, MAE = 2.7192, Huber loss = 2.7192), outperforming the hybrid models. The hybrid of LSTM-ANN shows superiority in Abuja (MSE = 50.0173, RMSE = 7.0723, MAE = 2.5242, Huber loss = 2.2478) with ANN out performing other competing DL algorithms in Libreville (MSE = 184.1970, RMSE = 13.5719, MAE = 8.4073, Huber loss = 7.8178). This implies that despite the variability in rainfall, the single DL model still outperformed the hybrid models in most of the selected African cities. This finding is not consistent with other similar studies where hybrid model was found to perform better than single models25,26,27. The performance of deep learning algorithms differs significantly by location and this can be a result of the influence of the underlying complexity and variability of rainfall patterns.

Table 3 Performance evaluation of the different deep learning algorithms for rainfall in African countries.
Full size table

Despite the capabilities of the hybrid DL model to account for the complexity in rainfall patterns, this study has shown that the single model performed better in most of the cities. This could be a result of the fact that single DL models have fewer parameters and are less likely to be prone to overfitting. The hybrid DL models, though more powerful theoretically than the single models, could become overly complex and may fail to adequately capture city specific rainfall pattern. This finding is corroborated by previous studies that simpler model architectures could perform better than more complex models when predicting rainfall42,43. The ability of the RNN model to perform better than other DL models despite being conceptually simpler compared with others points towards the fact that model complexity does not always translate into superior forecasting performance, especially when dealing with highly localized and noisy meteorological datasets such as rainfall.

For the purpose of explainability, the permutation feature importance was used and the plot for the best model for each of the African cities is shown in Figs. 5, 6, 7, 8, 9. Different features were found to be significant factors in influencing rainfall in the different cities, with relative humidity being the most importance features in most of the cities (Abuja, Libreville, and Nairobi). This is expected because it is a key indicator of atmospheric moisture content which has a direct positive effect on precipitation formation most especially in the tropical regions. For Pretoria, the impact of the previous day rainfall was the most important feature, while in Rabat, it was the previous two days’ rainfall which is an indication that temporal rainfall persistence played a larger role in these two locations. This kind of temporal autocorrelation is not unusual in semi-arid or Mediterranean climates, consistent with Rabat’s climate. In all the cities, the impact of temperature on rainfall was positive but this was not the case in Rabat where temperature was found to have very high negative contribution to rainfall. The positive impact of temperature on rainfall in most cities is not unexpected and this is consistent with the general meteorological principles. However, Rabat exhibited a contrasting pattern and this could be due to Rabat’s Mediterranean climate, which is usually characterized by dry, hot summers where there is a coincidence between higher temperatures and low rainfall.

Fig. 5
figure 5

Permutation feature importance plot for Nairobi based on RNN.

Full size image
Fig. 6
figure 6

Permutation feature importance plot for Abuja based on LSTM-ANN.

Full size image
Fig. 7
figure 7

Permutation feature importance plot for Pretoria based on RNN.

Full size image
Fig. 8
figure 8

Permutation feature importance plot for Rabat based on RNN.

Full size image
Fig. 9
figure 9

Permutation feature importance plot for Libreville based on ANN.

Full size image

Conclusion

This study compared the performance of deep learning models and its hybridization in predicting daily rainfall in the five selected African cities. These models were found to be very competitive in their performances but in most of the cities, the single models were found to outperform hybrid models. The study also established variation in the rainfall pattern in these selected African cities as different models were found to be most suitable for each of the locations. This study highlighted notable spatial variability in rainfall dynamics. The findings show that single deep learning models, particularly the RNN, generally performed better than other DL algorithms, offering more reliable predictions than hybrid models across most of the cities. The hybrid model achieved superior accuracy, suggesting that hybrid models still play a significant role in rainfall, especially when dealing with highly complex rainfall patterns. Furthermore, relative humidity was found to be the most influential predictor of rainfall in most cities, while in Pretoria and Rabat, rainfall persistence from previous days played a more significant role.