Syllabus

Module 1: Introduction to Stochastic Hydrology (7 hours)
Definition/ Overview and types of stochastic processes, Importance in hydrology, Applications
in hydrological modeling, Sources of uncertainty in hydrological processes
Module 2: Fundamentals of Probability and Random Variables (7 hours)
Concepts of probability, Random variables and their properties, Moments and expectations,
Common probabilistic distributions, Estimation of distribution parameters, Goodness of fit tests
Module 3: Modeling Hydrologic Extremes (7 hours)
Modelling high and low hydrological extremes, Regional frequency analysis, Applications of
probability distributions in hydrology
Module 4: Stochastic Time Series Analysis (7 hours)
Stochastic processes in hydrology, Modeling and analysis of stochastic time series, Applications
of time series analysis in hydrological studies
Module 5: Markov Chains in Hydrology (8 hours)
Introduction to Markov Chains, Application of Markov Chains in hydrological modelling,
Modeling transitions in hydrological states, Probabilistic theory of reservoir storages

Introduce the principles of stochastic hydrology: Provide students with a foundational understanding of stochastic processes, their types, and their importance in hydrological modeling, along with an exploration of the sources of uncertainty in hydrological systems.

Develop proficiency in probability theory and random variables: Equip students with the necessary skills to understand probability concepts, random variables, and their properties, along with the ability to estimate distribution parameters and conduct goodness-of-fit tests.

Apply statistical methods to model hydrological extremes: Enable students to use probabilistic techniques, such as regional frequency analysis, to model and understand hydrological extremes, including both high and low extremes, in real-world hydrological applications.

Utilize stochastic methods for hydrological time series analysis and Markov Chains: Teach students to model and analyze stochastic time series data and apply Markov Chains in hydrological systems, focusing on state transitions and reservoir storage modeling.

CO1: Demonstrate a clear understanding of various types of stochastic processes and their significance in hydrological modeling, with a focus on sources of uncertainty in hydrological processes.
CO2: Master foundational concepts in probability and random variables: Gain proficiency in the core principles of probability theory, random variables, their properties, and commonly used probabilistic distributions, as well as estimation techniques and goodness-of-fit tests for distribution parameters.
CO3: Analyze and model hydrological extremes: Apply probability distributions and regional frequency analysis techniques to model high and low hydrological extremes, addressing the impact of these extremes in real-world hydrological scenarios.
CO4: Utilize stochastic time series analysis in hydrological studies: Develop the ability to model and analyze stochastic time series data in hydrology, integrating time series analysis techniques to understand hydrological processes and predict future trends.
CO5: Implement Markov Chains for hydrological modeling: Understand and apply the theory of Markov Chains to model transitions in hydrological states, with a focus on reservoir storage dynamics and other relevant hydrological systems.

C T Haan, Statistical Method in Hydrology, Macgrawhill

Bras, R.L. and Rodriguez-Iturbe, Random Functions and Hydrology, Macgrawhill

Brockwell, P. J., and Davis, R. A., Introduction to time series and forecasting, Mcgrawhill

Clarke, R.T., Clarke, R.T., "Statistical Models in Hydrology", Mcgrawhill