Laboratory for Remote Sensing 
Hydrology and Spatial Modeling (RSLAB)
Professor Ke-Sheng Cheng
Dept of Bioenvironmental Systems Engineering &
Master Program in Statistics
Email: rslab@ntu.edu.tw
RSLAB_BSE_NTU
No. 1, Section 4, Roosevelt Road
Bioenvironmental Syst. Eng., National Taiwan University
Hydrologic Frequency Analysis (HFA)
水文頻率分析
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).
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 separability7. 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