Determination of Best-Fit Probability
Distribution of Rainfall Data in Sikkim,
India
S. Kiran and David Raj Micheal
Abstract Rainfall is an essential input in design of various hydraulic structures,
urban planning, disaster management, and agriculture. In this study, an attempt is
made to identify the probability distributions that best fits the rainfall data of Sikkim,
India. Monthly rainfall data is collected in four rain gauge stations in Sikkim and the
best-fit probability distributions of the rainfall data in each station in annual, dry, and
wet seasons are identified. Goodness-of-fit tests such as χ
2 , log-likelihood, Akaike
information criterion (AIC), and Bayesian information criterion (BIC) are used to
test the fit of probability distributions on the empirical data.
Keywords Sikkim · Rainfall · Probability distribution · Maximum likelihood
estimation
1 Introduction
In India, the spatial and temporal distribution of rainfall has predominantly been
dependent on the monsoons every year. This holds an adverse effect on irrigation
scheduling and crop productivity, posing acute challenges on livelihood. It also triggers extreme events like acute water scarcity, drought, and flood which cause changes
in land forms relating to the processes of mass movements. Knowledge of rainfall
pattern, its distribution, and variability is thus important and useful to forecast rainfall which in turn helps in crop practice, irrigation scheduling, drought and flood
management, and water supply.
The abrupt variation in the topography of Sikkim is a major factor that influences
the distribution of rainfall throughout the state. The unique rainfall pattern is also
influenced by the direction of wind, aspect of hill slopes, and complex orographic
S. Kiran (B)
Department of Civil Engineering, Sikkim Manipal Institute of Technology, Sikkim, India
e-mail: kiran.sriram@smit.smu.edu.in
D. R. Micheal
Department of Mathematics, Sikkim Manipal Institute of Technology, Sikkim, India
© Springer Nature Singapore Pte Ltd. 2021
C. Bhuiyan et al. (eds.), Water Security and Sustainability,
Lecture Notes in Civil Engineering 115,
https://doi.org/10.1007/978-981-15-9805-0_7
65
Distribution of Rainfall Data in Sikkim,
India
S. Kiran and David Raj Micheal
Abstract Rainfall is an essential input in design of various hydraulic structures,
urban planning, disaster management, and agriculture. In this study, an attempt is
made to identify the probability distributions that best fits the rainfall data of Sikkim,
India. Monthly rainfall data is collected in four rain gauge stations in Sikkim and the
best-fit probability distributions of the rainfall data in each station in annual, dry, and
wet seasons are identified. Goodness-of-fit tests such as χ
2 , log-likelihood, Akaike
information criterion (AIC), and Bayesian information criterion (BIC) are used to
test the fit of probability distributions on the empirical data.
Keywords Sikkim · Rainfall · Probability distribution · Maximum likelihood
estimation
1 Introduction
In India, the spatial and temporal distribution of rainfall has predominantly been
dependent on the monsoons every year. This holds an adverse effect on irrigation
scheduling and crop productivity, posing acute challenges on livelihood. It also triggers extreme events like acute water scarcity, drought, and flood which cause changes
in land forms relating to the processes of mass movements. Knowledge of rainfall
pattern, its distribution, and variability is thus important and useful to forecast rainfall which in turn helps in crop practice, irrigation scheduling, drought and flood
management, and water supply.
The abrupt variation in the topography of Sikkim is a major factor that influences
the distribution of rainfall throughout the state. The unique rainfall pattern is also
influenced by the direction of wind, aspect of hill slopes, and complex orographic
S. Kiran (B)
Department of Civil Engineering, Sikkim Manipal Institute of Technology, Sikkim, India
e-mail: kiran.sriram@smit.smu.edu.in
D. R. Micheal
Department of Mathematics, Sikkim Manipal Institute of Technology, Sikkim, India
© Springer Nature Singapore Pte Ltd. 2021
C. Bhuiyan et al. (eds.), Water Security and Sustainability,
Lecture Notes in Civil Engineering 115,
https://doi.org/10.1007/978-981-15-9805-0_7
65