Markov Chain Analysis and Incomplete Gamma Probability Function for Rainfall Distribution in the Plain and Hill Zones of Uttarakhand, India

Abstract

The rainfall data for the two stations i.e., Pantnagar (1981-2020) and Ranichauri (1985-2020) have been utilized to study the climate suitable for the growth and development of the crops in the plain and hill zones of Uttarakhand by using Weathercock software. Ranichauri experiences more frequent wet spells in the early weeks, whereas Pantnagar witnesses a sharp increase during peak monsoon (SMW 26–28), reaching up to 85% probability. This study is conducted to assess the rainfall variability in the plain and hill zones of Uttarakhand to support climate-resilient agricultural planning and water resource management. Markov Chain analysis indicates that the probability of consecutive wet weeks extends beyond monsoon into winter, particularly in the hills, making it suitable for off-season vegetable cultivation. The annual rainfall assessment confirms that Pantnagar receives higher total rainfall across all probability levels, with a 33.4% difference at the 10% probability level, highlighting greater monsoonal intensity in the plains. The weekly rainfall at different probability levels (10% to 90%) by incomplete gamma probability function showed that Ranichauri receives more consistent but moderate rainfall, whereas Pantnagar experiences intense, concentrated monsoonal precipitation. Rainfall at 75% probability (1166.2 mm in Pantnagar and 1047.7 mm in Ranichauri) is considered assured rainfall, crucial for crop planning and irrigation management. Policy makers should implement region-specific water conservation strategies, such as rainwater harvesting in the plains and micro-irrigation systems in the hills, to optimize water availability. Additionally, adaptive crop planning based on assured rainfall probabilities can enhance resilience to climate variability in both zones.