Page 1 STOCHASTIC HYDROLOGY Lecture -14 Course Instructor : Prof. P. P. MUJUMDAR Department of Civil Engg., IISc. INDIAN INSTITUTE OF SCIENCE Page 2 STOCHASTIC HYDROLOGY Lecture -14 Course Instructor : Prof. P. P. MUJUMDAR Department of Civil Engg., IISc. INDIAN INSTITUTE OF SCIENCE 2 Summary of the previous lecture •? Frequency domain analysis –? Spectral density –? Test for significance of periodicities –? Removing periodicities –? Standardizing the data Page 3 STOCHASTIC HYDROLOGY Lecture -14 Course Instructor : Prof. P. P. MUJUMDAR Department of Civil Engg., IISc. INDIAN INSTITUTE OF SCIENCE 2 Summary of the previous lecture •? Frequency domain analysis –? Spectral density –? Test for significance of periodicities –? Removing periodicities –? Standardizing the data Frequency Domain Analysis 3 •? Spectral density (I k ) is the amount of variance per interval of frequency •? Spectral analysis helps indentify the significant periodicities themselves •? A peak in the spectrum indicates an important contribution to variance at frequencies close to the peak •? Prominent spikes indicate periodicity •? Line spectrum - inconsistent estimate •? Power spectrum - consistent estimate ? k I(k) Page 4 STOCHASTIC HYDROLOGY Lecture -14 Course Instructor : Prof. P. P. MUJUMDAR Department of Civil Engg., IISc. INDIAN INSTITUTE OF SCIENCE 2 Summary of the previous lecture •? Frequency domain analysis –? Spectral density –? Test for significance of periodicities –? Removing periodicities –? Standardizing the data Frequency Domain Analysis 3 •? Spectral density (I k ) is the amount of variance per interval of frequency •? Spectral analysis helps indentify the significant periodicities themselves •? A peak in the spectrum indicates an important contribution to variance at frequencies close to the peak •? Prominent spikes indicate periodicity •? Line spectrum - inconsistent estimate •? Power spectrum - consistent estimate ? k I(k) Example – 1 (Spectral Analysis) 4 Monthly Stream flow (in cumec) statistics(1979-2008) for a river is selected for the study. (Part data shown below) Year Month S.No. Flow 1979 June 1 54.6 July 2 325.4 August 3 509.5 September 4 99.4 October 5 53.5 November 6 25.8 December 7 12.5 1980 January 8 5.6 February 9 3.1 March 10 2.2 April 11 0.9 May 12 0.81 N = 348 Page 5 STOCHASTIC HYDROLOGY Lecture -14 Course Instructor : Prof. P. P. MUJUMDAR Department of Civil Engg., IISc. INDIAN INSTITUTE OF SCIENCE 2 Summary of the previous lecture •? Frequency domain analysis –? Spectral density –? Test for significance of periodicities –? Removing periodicities –? Standardizing the data Frequency Domain Analysis 3 •? Spectral density (I k ) is the amount of variance per interval of frequency •? Spectral analysis helps indentify the significant periodicities themselves •? A peak in the spectrum indicates an important contribution to variance at frequencies close to the peak •? Prominent spikes indicate periodicity •? Line spectrum - inconsistent estimate •? Power spectrum - consistent estimate ? k I(k) Example – 1 (Spectral Analysis) 4 Monthly Stream flow (in cumec) statistics(1979-2008) for a river is selected for the study. (Part data shown below) Year Month S.No. Flow 1979 June 1 54.6 July 2 325.4 August 3 509.5 September 4 99.4 October 5 53.5 November 6 25.8 December 7 12.5 1980 January 8 5.6 February 9 3.1 March 10 2.2 April 11 0.9 May 12 0.81 N = 348 Example – 1 (contd.) (Spectral Analysis) 5 The time series plot 0 100 200 300 400 500 600 700 800 900 0 50 100 150 200 250 300 350 400 Flow in Cumec TimeRead More

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