Stochastic Hydrology

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The objective of this course is to introduce the concepts of probability theory and stochastic processes with applications in hydrologic analysis and design.
Modeling of hydrologic time series with specific techniques for data generation and hydrologic forecasting will be dealt with.
Case study applications will be discussed.
Contents:
Introduction to Random Variables (RVs).
Probability Distributions – One dimensional RVs.
Higher Dimensional RVs – Joint Distribution.
Conditional Distribution; Independence.
Properties of Random Variables.
Parameter Estimation.
Parameter Estimation.
Hydrologic Data Generation.
Introduction to Time Series – stationarity; ergodicity.
Purely stochastic Models; Markov Processes.
Spectral Density; Analysis in the Frequency Domain.
Auto Correlation and Partial Auto Correlation.
Auto Regressive Moving Average Models (Box – Jenkins models – model identification; Parameter estimation ; calibration and validation; Simulation of hydrologic time series ; Applications to Hydrologic Forecasting – case studies).

Course Curriculum

Introduction Details 54:48
Bivariate Distributions Details 57:23
Independence ; Functions of Random Variables Details 58:39
Moments of a Distribution Details 58:42
Normal Distribution Details 59:29
Other Continuous Distributions Details 1:22
Parameter Estimation Details 59:25
Covariance and Correlation Details 58:54
Data Generation Details 59:23
Time Series Analysis – I Details 57:42
Time Series Analysis – II Details 58:58
Time Series Analysis-III Details 57:38
Frequency Domain Analysis – I Details 57:53
Frequency Domain Analysis – II and ARIMA Models – I Details 58:55
ARIMA Models-II Details 57:38
ARIMA Models – III Details 57:3
ARIMA Models-IV Details 58:5
Case Studies – I Details 57:29
Case Studies – II Details 57:37
Case Studies -III Details 57:44
Case Studies- IV Details 57:8
Markov Chains – I Details 56:40
Markov Chains-II Details 56:14
Frequency Analysis – I Details 57:12
Frequency Analysis-II Details 57:8
Frequency Analysis – III and Probability Plotting – I Details 57:59
Probability Plotting – II Details 58:11
Goodness of Fit Details 59:26
IDF Relationships Details 57:52
Multiple Linear Regression Details 57:49
Principal Component Analysis Details 58:43
Regression on Principal Components Details 58:36
Multivariate Stochastic Models – I Details 58:25
Multivariate Stochastic Models – II Details 58:47
Multivariate Stochastic Models – III Details 59:11
Data Consistency Checks -I Details 58:33
Data Consistency Checks – II Details 57:49
Data Consistency Checks – III Details 56:54
Recent Applications: Climate Change Impact Assessment Details 59:24
Summary of the Course Details 57:43

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