Abstract
Accurate rainfall forecasting is crucial for optimising agricultural planning and managing water resources, especially in regions characterised by spatially heterogeneous monsoon dynamics and data scarcity. This study presents a hybrid framework that synergistically combines Kalman filtering (KF) with the Autoregressive Integrated Moving Average (ARIMA) model to improve the accuracy of univariate rainfall predictions across the eleven agroclimatic zones (ACZs) of Madhya Pradesh, Central India. Using long-term monthly rainfall data (1994–2023) obtained from the India Meteorological Department (IMD) and the Climate Hazards Group InfraRed Precipitation with Station Data (CHIRPS), time series were initially denoised through KF-based smoothing before model training and forecasting. The training window spanned from 1994 to 2020, with validation conducted from 2021 to 2023. To enhance the filter’s performance, four global and local optimisation algorithms, simulated annealing (SANN), Nelder–Mead, conjugate gradient (CG) and Broyden–Fletcher–Goldfarb–Shanno (BFGS), were assessed, with Nelder–Mead showing the most consistent convergence in noise reduction. Forecast accuracy was evaluated using root mean square error (RMSE), bias, and coefficient of determination (R2) metrics. CHIRPS generally surpassed IMD in areas such as GRID (RMSE: 51.4 mm versus 78.0 mm) and Nimar, while IMD produced better results in CNV and Satpura. Notably, CHIRPS exhibited a greater capacity for bias correction, reducing the negative bias in Satpura from –65.5 mm (IMD) to –13.8 mm. Rather than seeking absolute accuracy in observations, this study emphasises predictive reliability and regional applicability. The integrated KF–ARIMA framework effectively captures both long-term trends and short-term rainfall variations, providing a robust and scalable approach for monsoon forecasting in climate-sensitive zones. The insights gained can aid in data-driven irrigation scheduling, climate risk adaptation, and crop modelling strategies, strengthening the foundation for anticipatory decision-making in agrometeorological systems.