Predicting Karnataka’s Average Annual Precipitation Through Arma Time-Series Modelling and Exceedance Probability Estimation

Abstract

The state of Karnataka receives significant amount of precipitation, strongly influenced by its varied topography and distinct climatic zones. The seasonal concentration of precipitation, with over 70% occurring during the southwest monsoon that is from June to September and there is also impact by the extreme events such as El Nino induced deficits and cyclonic surpluses on annual totals. The state comprises four major agro-climatic regions with 31 districts:

1. Coastal Karnataka, receiving the highest average annual rainfall, often surpassing 3,500 mm, driven by orographic lifting, which is a weather process where a moving air mass is forced to rise over a geographical obstacle, such as mountain range of Western Ghats;
2. Malnad (Hilly region), averaging around 2,000 mm, benefiting from southwest monsoon intensity;
3. North Interior Karnataka and South Interior Karnataka, both semi-arid/dry zones with average annual rainfall near 700 mm, largely dependent on monsoon progression and local convection (it is the method of heat transfer in fluids by the movement of the matter).

In order to create strong rainfall forecasts and calculate exceedance probabilities in Karnataka, this study uses verified time-series data to examine yearly average rainfall patterns from 1989 to 2023 using an Auto Regressive Moving Average (ARMA) model.

These findings deliver evidence-based guidance for:

• Policy formulation on drought mitigation and flood control;
• Agricultural planning, including crop diversification and water-efficient practices;
• Sustainable reservoir management and groundwater sustainability initiatives.

By integrating time-series analytics with probability-based modelling, this research paper establishes a scientific foundation for interpreting historical rainfall behavior and enhances predictive capacity for future climate variability in the state of Karnataka.