Laboratory for Remote Sensing Hydrology and Spatial Modeling
Professor Ke-Sheng Cheng (Email: rslab@ntu.edu.tw)
RSLAB_BSE_NTU
No. 1, Section 4, Roosevelt Road
Bioenvironmental Syst. Eng., National Taiwan University
Stochastic Hydrology 2017
- 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 uncertainties involved in parameter estimation and introduce the techniques of stochastic simulation for quantification of uncertainties.
- To demonstrate how hydrological processes can be characterized using stochastic models.
Datasets
(1) Extreme rainfall data
Event-max rainfall data in Taiwan
24-hour annual-max rainfall data in Taiwan
(2) Streamflow data
40-year (1964 - 2003) flow data at the Xia-Yun station (Xia_Yuan_DailyFlow.csv)
(3) Reservoir inflow data
(4) Hourly rainfalls of storm events (hourly_rainfall_depths.xlsx) (Hourly typhoon rainfall data at Bamboo Lake, BambooLake_Typhoon_Rainfall.xslx)
(5) Daily rainfall data
1. Stochastic simulation of univariate random variables
Random Number Generation in R
Pseudo Random Number Generator (PRNG)
Probability Integral Transformation
Acceptance/Rejection Method
Frequency-factor-based Method
2. Hydrological frequency analysis - 1
PPT - 03062017 [Updated on March 22, 2017]
General concept
General equation for frequency analysis
Data series for frequency analysis
Parameter estimation
Techniques for goodness-of-fit test
Selection of best-fit distribution
IDF curve fitting
3. Hydrological frequency analysis - 2
Goodness-of-fit test using moment ratios diagram
L-moments and L-moment ratios diagram (LMRD)
Establishing acceptance region for L-moment ratios
- Normal distribution
- Gumbel distribution
- Pearson Type III distribution
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).
R code for LMRD-GOF plotting (LMRD-GOF_Plotting.R)
4. Hydrological frequency analysis - 3 (Simple scaling)
Annual maximum events
Simple scaling and multiple scaling
IDF Curves and the Scaling Property
Theoretical Basis for Usage of Dimensionless Hyetographs
Simple scaling DDF (skipped)Multiple scaling DDF (skipped)
5. Hydrological frequency analysis - 4 (Regional Frequency Analysis, RFA)
Fundamental concept of regional frequency analysis
The index-flood approach
General procedures of regional frequency analysis
Situations for application of RFA
Regional frequency analysis with presence of extraordinary rainfalls6. Design storm hyetograph
Alternating block hyetograph
Average rank hyetograph
Simple scaling Gauss-Markov hyetograph (SSGM)
7. Stochastic simulation of bivariate distributions
Bivariate normal distribution
Bivariate gamma distribution
Working problems - WP-88. Random process and stochastic convergence
Random (stochastic) process
Characterizing a random process
Stationary random process
Equality of random processesStochastic convergence
- Sure convergence (convergence everywhere)
- Almost-sure convergence (convergence with probability 1)
- Mean-square convergence
- Convergence in probability
- Convergence in distribution
Ergodic theorem
Examples of stochastic processes
- iid random process
- Random walk process
- Gaussian process
- Autoregressive (AR) random process
- The 1-D Brownian motion
9. Introduction to time series model - the autoregressive (AR) model
Autogressiove model - general form
Characteristics of AR(1) and AR(2) models
Time series modeling in R (A good reference book: Time Series Analysis and Its Applications With R Examples by RH Shumway and DS Stoffer. Springer)
AR(1), Gauss-Markov process, and bivariate normal distribution
Stream flow series modelingWorking problems - WP-9 [Uploaded May 31, 2017] (R code for WP-9)
Flow persistence and the Hurst phenomenon
Flow duration curve
10. Hydrological time series
PPT
Stream flow series
10-day-period (TDP) rainfall series
Standardized Precipitation Index (SPI) for drought monitoring, early warning, and forecasting
11. Gamma random field simulation
PPT - Gamma Random Field Simulation
Characterizing a random field
Sequential Gaussian Random Field Simulation (SGS)
Gamma random field simulation
Potential applications
12. Multisite stream flow simulation
13. Rainfall frequency analysis with consideration of spatial correlation - Estimating the return period of a multisite-extreme event
14. Stochastic storm rainfall simulation model
15. Assessing the impact of climate change on rainfall extremes
16. Statistical downscaling of GCM outputs
17. Hydrological forecasting and model performance evaluation
PPT - Evaluation of hydrological model performance considering uncertainties
Sources of uncertainty and uncertainty in model performance
Persistence in flood flow series
Criteria for model performance evaluation (MPE)
Coefficient of efficiency (CE), coefficient of persistence (CP), and bench coefficient
Theorectial asymptotic relationship between CE and CP
Misuse of CE and CP for MPE of realtime flood forecasting
Theoretical CE-CP relationships of the AR(1) and AR(2) models
Demonstration of MPE using model-based bootstrap samples
18. Bootstrap resampling
19. Event-based rainfall frequency analysis (PPT)
RSLAB - NTU
Prof. Ke-Sheng Cheng
RSLAB_BSE_NTU
No. 1, Section 4, Roosevelt Road
Bioenvironmental Syst. Eng., National Taiwan University