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Course objectives

To introduce fundamental concept of random variables, random vector and random function, and
their applications in hydrology.
To demonstrate the stochastic nature of many hydrological variables and processes and how
hydrological parameters can be estimated by statistical methods.
To discuss the uncertainty involved in stochastic parameter estimation and introduce the techniques
of stochastic simulation for quantification of uncertainties.
To demonstrate how hydrological processes can be characterized using stochastic models.

Week

Specific topics

Remarks

Review of fundamental statistics (I)

Random variables and their probability
density functions
Joint and conditional probability
distributions

S THY0
STHY1

Review of fundamental statistics (II)

Sampling and sampling distributions
Parametric point estimation
Parametric interval estimation
Properties of estimators

STHY2 , HW1

Stochastic simulation (I) – Univariate
simulation

Pseudo random number generation
Frequency-factor-based generation
Rejection method

STHY3 , HW2

Hydrological Frequency Analysis (I)

Statistical considerations for data selection
Statistical distribution of design storm depth
Commonly used distributions
General equation for frequency analysis

STHY4 ,
HW3-1

Hydrological Frequency Analysis (II)

Test of hypotheses
Chi-square GOF test
Kolmogorov-Smirnov GOF test

STHY5 , HW4

Hydrological Frequency Analysis (III)

Moment-ratio-based GOF test
L-moment-ratio-diagram
Sample size issues and uncertainties of
sample moments
Confidence ellipses for LMRD GOF test

STHY6 , STHY6A,
HW5, MatlabCode

Stochastic simulation (II) – Bivariate simulation

Bivariate normal distribution
Bivariate exponential distribution
Bivariate gamma distribution
Frequency analysis based on bivariate
distributions

STHY7 , HW6

Introduction to random processes

Definition of a stochastic process
Characterizing a stochastic process
Markovian property
Exemplar stochastic processes

STHY8, STHY8_PPT, HW7
HW8 , HW8_AR2.xls

Modeling the time variation of storm rainfall

Simple scaling model
Design storm hyetographs

STHY9 , SSGM_PPT, HW9
SSGM_rainfall_data.xls
computer code

Stochastic simulation (III) – Simulation of
random processes

Gauss-Markov process
Conditional simulation
Continuous storm rainfall simulation model

STHY11 , HW9

Introduction to Geostatistics

Random function
Variogram modeling
Ordinary kriging

STHY12-1 , STHY12-2
HW10

Modeling the spatial variation

Contouring design storm depth
Raingauge network design

STHY13, PPT file, HW11

Hydrological forecasting (I)

Time series modeling
Time series forecasting

Or
Scaling issues in hydrology

STHY14 , HW12

Hydrological forecasting (II)

Realtime (adaptive) forecasting – Kalman
filtering
The issue of performance evaluation –
persistency

STHY15

Course description
Hydrology is a branch of earth science focusing on water-related study. It is also an engineering discipline which
deals with storage, discharge, and utilization of water. Almost all variables involved in hydrological processes
exhibit certain degree of randomness. Either from a scientific or engineering point of view, understanding and
characterizing the random nature of hydrological processes enable us to achieve sound water management
practices.
Stochastic hydrology is the study about characterizing the random nature of hydrological variables and
establishing models that describe the spatial and temporal variations of these hydrological variables. In this
course students will learn step by step from characterizing and simulating a single random variable to simulation
of a random field which is composed of many correlated random variables in space. Stochastic simulation will be
highly emphasized in class since it is the foundation for probability-based risk assessment. Familiarity of
stochastic simulation will open a wide window of potential research and application subjects to students.