Laboratory for Remote Sensing Hydrology and Spatial Modeling

 

Professor Ke-Sheng Cheng (Email: rslab@ntu.edu.tw)

Department of Bioenvironmental Systems Engineering

National Taiwan University

RSLAB_BSE_NTU
No. 1, Section 4, Roosevelt Road
Bioenvironmental Syst. Eng., National Taiwan University

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    • Stochastic Hydrology 2017
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Stochastic Hydrology 2017

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 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  

    BambooLake_AMS.csv   

    (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

    PPT - 02212017

    Random Number Generation in R

    Pseudo Random Number Generator (PRNG)

    Probability Integral Transformation

    Acceptance/Rejection Method

    Frequency-factor-based Method

    Working problems WP-1   

  • 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

    Working problems WP-2   

     

  • 3. Hydrological frequency analysis - 2

    PPT - 03062017

    Goodness-of-fit test using moment ratios diagram

    L-moments and L-moment ratios diagram (LMRD)

    Establishing acceptance region for L-moment ratios

    1. Normal distribution
    2. Gumbel distribution
    3. Pearson Type III distribution

     References

    1. 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.
    2. 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).

    Working problems WP-3

     R code for LMRD-GOF plotting (LMRD-GOF_Plotting.R)  

    Working problems WP-4   

    Working problems WP-5   


  • 4. Hydrological frequency analysis - 3  (Simple scaling)

    PPT - 03222017    

    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)

    Working problems WP-6   

  • 5. Hydrological frequency analysis - 4 (Regional Frequency Analysis, RFA)

    PPT - 03292017   

    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 rainfalls

  • 6. Design storm hyetograph 

    PPT - 04112017   

    Alternating block hyetograph

    Average rank hyetograph

    Simple scaling Gauss-Markov hyetograph (SSGM)

    Executable code of SSGM   

    Working problems - WP-7   

    水文設計應用手冊 (下載1, 下載2, 下載3)   

  • 7. Stochastic simulation of bivariate distributions   

    PPT - 04182017  

    Bivariate normal distribution  

    Bivariate gamma distribution  

    Working problems - WP-8   

    Stochastic simulation of bivariate gamma distribution:a frequency-factor based approach (SERRA, 2011)  

  • 8. Random process and stochastic convergence

    PPT - 04262017    

    Random (stochastic) process

    Characterizing a random process

    Stationary random process

    Equality of random processes  

    Stochastic convergence

    1. Sure convergence (convergence everywhere)
    2. Almost-sure convergence (convergence with probability 1)
    3. Mean-square convergence
    4. Convergence in probability
    5. Convergence in distribution

    Ergodic theorem

    Examples of stochastic processes

    1. iid random process
    2. Random walk process
    3. Gaussian process
    4. Autoregressive (AR) random process
    5. The 1-D Brownian motion
  • 9. Introduction to time series model - the autoregressive (AR) model

    TSA-1,  TSA-2   

    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 modeling

    Working 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   

    PPT-1,  PPT-2 - Statistical downscaling & stochastic storm rainfall simulation   

    GCM Emission Scenarios

    Climate Change Scenarios

    Downscaling Techniques

    Richardson Type Weather Generators

    Bias Correction Spatial Disaggregation (BCSD) method

    Stochastic storm rainfall simulation

  • 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