Stochastic Hydrology (Lecture 13) - Notes - Civil Engineering (CE)

 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.