**Professor Ke-Sheng Cheng**

**Dept of Bioenvironmental Systems Engineering**** &**

**Email:** rslab@ntu.edu.tw

RSLAB_BSE_NTU

No. 1, Section 4, Roosevelt Road

Bioenvironmental Syst. Eng., National Taiwan University

**Hydrologic frequency analysis (HFA)** is the most fundamental work of all designs and engineering practices of water resources projects. Hydrologic processes are governed by physical laws while at the same time also exhibit natural variabilities both in space and in time. Statistics and stochastic models are widely used to characterize hydrologic variables and processes. Hydrologic frequency analysis is the study of hydrological extremes (for examples, droughts and floods). Although statistical theories form the basis of hydrologic frequency analysis, a good understanding of spatial and temporal variations of hydrologic processes is also essential. This course aims to conduct a comprehensive and thorough study of hydrologic frequency analysis with emphasis on balancing the statistical theories and hydrologic practices.

Hydrologic frequency analysis requires data analysis, computation, and simulation using computers. R is perhaps the most powerful computer language for statistical computing and graphics. R is not just a computer language, it is also a community of users of many different disciplines. Many R packages have been developed and can be used to aid in hydrologic frequency analysis. One of the goals of this course is to guide students to develop R codes that can be used in real-world practical applications of hydrologic frequency analysis.

**1. Introduction of Hydrological Frequency Analysis [PPT-1]**Hydrologic processes which are relevant to frequency analysis

The random nature of hydrologic processes

Spatial and temporal variations

Examples of hydrological frequency analysis

**2. Collecting & Extracting Data for Rainfall Frequency Analysis [****PPT-2****]****Extracting data for hydrological frequency analysis**- Complete duration series
Partial duration series (or peak-over-threshold series)

- Annual exceedance series
- Extreme value series
- Annual max/min series
- Block maximum series

**The concept of durational events and their occurrences****Geometric distribution and the return period****3. Probability Distributions Commonly Used in Hydrologic Frequency Analysis [PPT-3]**Normal and log-normal

Extreme value type I (Gumbel) distribution

Pearson type III and log Pearson type III

Generalized extreme value (GEV)

Random number simulation - frrquency factor

Random number simulation using R

### 4. Parameter Estimation [PPT-4]

The method of moments

The maximum likelihood method

The method of L-moments [ Ref-1, Ref-2 ]

Evaluating performance of different estimators (Why do we care about the performance of estimators?) [Example R code]

### 5. Test for randomness, Trend Detection, and Goodness-of-fit test [ PPT-5A, PPT-5B ]

The runs test

The Mann-Kendall test

The Mann-Whitney-Pettitt (MWP) test

The Q-Q plot [Probability plotting demo]

The Chi-square test

The Kolmogorov-Smirnov test

The L-moment-ratio-diagram test [R code for LMRD plotting]

Evaluating power of different tests [

**GOF Power Comparison**]**References**- Wu, Y.C., Liou, J.J., Cheng, K.S., 2012. Establishing acceptance regions for
*L*-moments based goodness-of-fit tests for the Pearson type III distribution.*Stochastic Environmental Research and Risk Assessment*, 26: 873-885, DOI 10.1007/s00477-011-0519-z. - Liou, J.J., Wu, Y.C., Cheng, K.S., 2008. Establishing acceptance regions for L-moments-based goodness-of-fit test by stochastic simulation.
*Journal of Hydrology*, Vol. 355, No.1-4, 49-62. (doi:10.1016/j.jhydrol.2008.02.023).

- Wu, Y.C., Liou, J.J., Cheng, K.S., 2012. Establishing acceptance regions for
### 6. Model Selection - Criterion of Information Losses [PPT-6]

Information-criteria-based model selection

Rationale of the information criteria

KL Divergence

Divergence as a measure of class separability### 7. Rainfall Frequency Analysis Using the Scaling properties (PPT-7)

Design duration vs event duration

The simple scaling property

Simple scaling modeling of storm events

IDF curves and the simple scaling property

Simple scaling in the dimensionless hyetograph

Simple scaling DDF

### 8. Presence of Outliers and Regional Frequency Analysis (PPT-8)

Fundamental concept of regional frequency analysis

The index-flood approach

The frequency factor approach

Demonstrating the advantage of RFA using simulated data

### 9. The Extremal Type Theorem

Annual maximal and order statistics

Block maximum

A mixture distribution model of the annual maxumum rainfalls

### 10. Rainfall Frequency Analysis Based on Event Maximum Rainfalls (PPT-9)

Definition of the event-maximum rainfalls

Modeling event occurrences

Probability distribution modeling of the event-maximum rainfalls

Derivation of the distribution of the annual-maximum rainfalls from event-maximum rainfalls

### 11. Hydrologic Frequency Analysis From the Perspective of Individual Storm Events

Design duration vs event duration

Correlation of the event duration and event total rainfall

Bivariate frequency analysis

### 12. Spatial Correlation of Multi-site Rainfall Extremes (PPT-10)

Spatial correlation of event-maximum rainfalls

Stochastic simulation of multi-site event maximum rainfalls

Estimating the return period of a multi-site extreme event (What is the return period of the Typhoon Morakot ?)

**References**Stochastic simulation of bivariate gamma distribution (SERRA article, PPT)

Stochastic simulation of the gamma random field - Covariance matrix conversion approach (SERRA article, PPT)

### 13. Spatiotemporal Stochastic Simulation of Event-maximum Typhoon Rainfalls (PPT-11A, PPT-11B, PPT-11C)

The flood inundation maps and their interpretation and usage

Toward the probabilstic inundation maps

Spatiotemporal modeling of event-maximum typhoon rainfalls

Spatiotemporal stochastic simulation of event-maximum typhoon rainfalls

Probabilistic flood inundation maps

### 14. Stochastic simulation of a random vector field (PPT-12A, PPT-12B)

**RSLAB - NTU**

**Prof. Ke-Sheng Cheng **

RSLAB_BSE_NTU

No. 1, Section 4, Roosevelt Road

Bioenvironmental Syst. Eng., National Taiwan University