Conventional time series, machine and deep learning approaches for rainfall forecasting in a bimodal climate in Embu County, Kenya: A comparative study of SARIMA, ANN, LSTM, CNN and hybrid models

Abstract Accurate rainfall forecasting is critical for agricultural planning, water resource management, and climate risk reduction in regions characterized by strong seasonal variability and nonlinear climatic behaviour. This study evaluates the predictive performance of statistical, machine learning, and hybrid deep learning models for monthly rainfall forecasting in Embu County, Kenya, using data from 1998 to 2025 obtained from the Kenya Meteorological Department. The rainfall series exhibits a bimodal structure with moderate variability (CV = 7.08%), slight negative skewness, and near-normal distributional characteristics. Stationarity and diagnostic tests confirm suitability for time series modelling. The optimal linear benchmark model is identified as SARIMA\(((1,1,1)(0,1,1)_{12})\) based on information criteria; however, its forecasting ability is limited in capturing nonlinear rainfall dynamics. To improve predictive accuracy, Artificial Neural Network (ANN), Long Short-Term Memory (LSTM), and hybrid models including SARIMA--ANN, SARIMA--LSTM, SARIMA--NNAR--LSTM, and SARIMA--CNN--LSTM are developed. Model evaluation is conducted using RMSE, MAE, and MSE under both training and testing frameworks, complemented by residual diagnostics and Diebold--Mariano tests. Results show that hybrid models consistently outperform standalone approaches. The SARIMA--CNN--LSTM model achieves the best performance with RMSE = 1.68, MAE = 1.30, and MSE = 2.82, along with the smallest training--testing gap, indicating strong generalization and minimal overfitting. Residual diagnostics confirm near white-noise behavior for hybrid models, while Diebold--Mariano tests indicate statistically significant improvements over SARIMA at the 5% level. Overall, the findings demonstrate that rainfall variability in Embu County is driven by interacting linear seasonal, nonlinear, and long-memory processes. Hybrid deep learning frameworks, particularly CNN--LSTM-based models, provide a robust and reliable approach for rainfall forecasting in bimodal climatic systems.