Civil Engineering (CE) > Stochastic Hydrology (Lecture 13)

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Page 1 STOCHASTIC HYDROLOGY Lecture -13 Course Instructor : Prof. P. P. MUJUMDAR Department of Civil Engg., IISc. INDIAN INSTITUTE OF SCIENCE Page 2 STOCHASTIC HYDROLOGY Lecture -13 Course Instructor : Prof. P. P. MUJUMDAR Department of Civil Engg., IISc. INDIAN INSTITUTE OF SCIENCE 2 Summary of the previous lecture •? Data Generation – Serially Correlated Data –? First order Markov Model •? Annual flow generation –? First order Markov model with non-stationarity •? Thoma Fiering model for monthly and seasonal flow generation Page 3 STOCHASTIC HYDROLOGY Lecture -13 Course Instructor : Prof. P. P. MUJUMDAR Department of Civil Engg., IISc. INDIAN INSTITUTE OF SCIENCE 2 Summary of the previous lecture •? Data Generation – Serially Correlated Data –? First order Markov Model •? Annual flow generation –? First order Markov model with non-stationarity •? Thoma Fiering model for monthly and seasonal flow generation FREQUENCY DOMAIN ANALYSIS 3 Page 4 STOCHASTIC HYDROLOGY Lecture -13 Course Instructor : Prof. P. P. MUJUMDAR Department of Civil Engg., IISc. INDIAN INSTITUTE OF SCIENCE 2 Summary of the previous lecture •? Data Generation – Serially Correlated Data –? First order Markov Model •? Annual flow generation –? First order Markov model with non-stationarity •? Thoma Fiering model for monthly and seasonal flow generation FREQUENCY DOMAIN ANALYSIS 3 Frequency Domain Analysis 4 •? Auto correlation function or correlogram is used for analyzing the time series in the time domain. •? Time domain analysis X t = d t + e t k r k Correlogram t x t Periodic process with noise Page 5 STOCHASTIC HYDROLOGY Lecture -13 Course Instructor : Prof. P. P. MUJUMDAR Department of Civil Engg., IISc. INDIAN INSTITUTE OF SCIENCE 2 Summary of the previous lecture •? Data Generation – Serially Correlated Data –? First order Markov Model •? Annual flow generation –? First order Markov model with non-stationarity •? Thoma Fiering model for monthly and seasonal flow generation FREQUENCY DOMAIN ANALYSIS 3 Frequency Domain Analysis 4 •? Auto correlation function or correlogram is used for analyzing the time series in the time domain. •? Time domain analysis X t = d t + e t k r k Correlogram t x t Periodic process with noise Frequency Domain Analysis 5 •? Periodicities in data can best be determined by analyzing the time series in frequency domain. •? Spectral analysis or the frequency domain analysis: the time series is represented in the frequency domain instead of the time domain •? The observed time series is a random sample of a process over time and is made up of oscillations of all possible frequencies.Read More

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