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Probabilistic assessment of one-step-ahead rainfall variation by Split Markov Process


Rajib Maity, Department of Civil Engineering, Indian Institute of Technology Kharagpur, Kharagpur, 721302 West Bengal, India.



In this paper, Split Markov Process (SMP) is developed to assess one-step-ahead variation of daily rainfall at a rain gauge station. SMP is an advancement of general Markov Process and specially developed for probabilistic assessment of change in daily rainfall magnitude. The approach is based on a first-order Markov chain to simulate daily rainfall variation at a point through state/sub-state transitional probability matrix (TPM). The state/sub-state TPM is based on the historical transitions from a particular state to a particular sub-state, which is the basic difference between SMP and general Markov Process. The cumulative state/sub-state TPM is represented in a contour plot at different probability levels. The developed cumulative state/sub-state TPM is used to assess the possible range of rainfall in next time step, in a probabilistic sense. Application of SMP is investigated for daily rainfall at four rain gauge stations – Khandwa, Jabalpur, Sambalpur, and Puri, located at various parts in India. There are 99 years of record available out of which approximately 80% of data are used for calibration, and 20% of data are used to assess the performance. Thus, 80 years of daily monsoon rainfall is used to develop the state/sub-state TPM, and 19 years data are used to investigate its performance. Model performance is assessed in terms of hit rate (HR), false alarm rate (FAR), and percentage captured. It is found that percentage captured is maximum for Khandwa (70%) and minimum for Sambalpur (44%) whereas hit rate is maximum for Sambalpur and minimum for Khandwa (73%). FAR is around 30% or below for Jabalpur, Sambalpur, and Puri. FAR is maximum for Khandwa (37%). Overall, the assessed range, particularly the upper limit, provides a quantification possible extreme value in the next time step, which is a very useful information to tackle the extreme events, such as flooding, water logging and so on. Copyright © 2011 John Wiley & Sons, Ltd.