Dynamic Linear Modeling for Characterizing and Predicting the Patterns of Summer Monsoon Rainfall in Northwest India

The Indian economy and food grain production are intricately tied to the spatial distribution and the amount of rainfall during the summer monsoon period (June to September). Numerous studies have delved into modeling methods for forecasting Indian summer monsoon rainfall. This paper utilizes monthly rainfall data spanning 72 years (1950–2021) to analyze, model, and predict the monsoon over Northwest India using Dynamic Linear Modeling (DLM). In view of this, the well-accepted dynamic linear model with significant components is selected from the parsimonious models of DLM based on Bayesian Information Criteria (BIC), significant tests, and statistical fit. The dynamic linear model comprises a significant linear time trend component, a deterministic trigonometric seasonal component, a deterministic cycle component, and a stochastic irregular component has been selected. The validation of the selected model passed through the normal and correlation diagnostics of model residuals. The analysis reveals a subtle decreasing trend in monsoon rainfall, showcasing consistent behaviour in deterministic seasonality, and highlighting the deterministic nature of cyclical component with a period of approximately 2.5 years, alongside irregular variations. Utilizing this model, future monsoon rainfall over Northwest India has been forecasted for the years 2022–2027, providing a 95% confidence interval.