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Probabilistic assessment of one‐step‐ahead rainfall variation by Split Markov Process
Author(s) -
Maity Rajib
Publication year - 2012
Publication title -
hydrological processes
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.222
H-Index - 161
eISSN - 1099-1085
pISSN - 0885-6087
DOI - 10.1002/hyp.8245
Subject(s) - rain gauge , markov chain , probabilistic logic , statistics , mathematics , state (computer science) , markov model , environmental science , markov process , stochastic matrix , meteorology , computer science , algorithm , precipitation , geography
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.