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eLibrary > Statistical Analysis of Hydrologic Variables - Methods and Applications >

Statistical Analysis of Hydrologic Variables - Methods and Applications, 2019

Contents
Preface
CHAPTER 1 [Go to Page]
Chapter 1: Introduction [Go to Page]
References
CHAPTER 2 [Go to Page]
Chapter 2: Statistical Analysis of Precipitation Extremes [Go to Page]
2.0 Introduction
2.1 Ground-, Radar-, and Satellite-based Measurements [Go to Page]
2.1.1 Systematic and Random Errors
2.1.2 Precipitation Measurements and Networks
2.1.3 Radar-Based Rainfall Estimates
2.1.4 Satellite-Based Precipitation Estimation
2.2 Fitting of Probability Distributions for Rainfall Extremes
2.3 Precipitation Frequency Analysis: Development of Cumulative Distribution Functions
2.4 Probability Distributions for Characterizing Precipitation Data [Go to Page]
2.4.1. Normal Distribution
2.4.2. Log-Normal Distribution
2.4.3 Three-Parameter Log-Normal Distribution
2.4.4 Extreme Value Type I Distribution
2.4.5 Extreme Value Type III Distribution
2.4.6 Generalized Extreme Value Distribution
2.4.7 Gamma Type III Distribution
2.4.8 Exponential Distribution
2.4.9 Other Distributions
2.5 Estimation of Distribution Parameters [Go to Page]
2.5.1 Method of Moments
2.5.2 Maximum Likelihood Estimation Method
2.5.3 L-Moments Approach
2.6 Frequency Factors
2.7 Goodness-of-Fit Tests for Normal Distributions
2.8 Goodness-of-Fit Tests for Other Distributions [Go to Page]
2.8.1 Quantitative Measures
2.8.2 L-Moment Diagrams
2.9 Regional Frequency Analysis
2.10 Illustrative Examples [Go to Page]
Example 2-1: Daily Precipitation Time Series
Example 2-2: Annual Extremes for Different Durations
2.11 Fitting of a Parametric Frequency Curve for Rainfall Extremes
2.12 Extreme Rainfall Frequency Analysis in the United States
2.13 Probable Maximum Precipitation
2.14 Rainfall Frequency Analysis: Uncertainty and Variability Issues [Go to Page]
2.14.1 Sample Adjustment Factors
2.14.2 Length of Historical Data
2.14.3 Missing Data and Rainfall Statistics Preservation
2.14.4 Missing Rainfall Records: Estimation Methods
2.14.5 Statistical Corrections of Spatially Interpolated Missing Precipitation Data Estimates
2.15 Stationarity Issues [Go to Page]
2.15.1 Trend Analysis
2.15.2 Spearman's Rank Correlation Coefficient (ρ) Test
2.15.3 Mann-Kendall Test
2.15.4 Application of Spearman's Rho and Mann-Kendall Tests
2.15.5 Parametric Trend Analysis: Regression
2.16 Homogeneity
2.17 Detection of Changes in Moments
2.18 Nonparametric Methods [Go to Page]
2.18.1 Kernel Density Estimation
2.18.2 Characterization of Extreme Precipitation Events
2.19 Nonparametric Test for Independence [Go to Page]
2.19.1 Runs Test
2.19.2 Ranked von Neumann Test
2.20 Partial Duration Series
2.21 Statistical Characterization of Interevent Time Definition of Storm Events
2.22 Incorporation of Climate Variability Cycles and Climate Change into Rainfall Frequency Analysis
2.23 Use of Future Data Sources for Frequency Analysis
2.24 Descriptive Indexes for Precipitation Extremes
2.25 Standard Precipitation Index
2.26 Trends Based on GCM Model Simulations
2.27 Hydrologic Design for the Future
2.28 Summary and Conclusions
References
Appendix: Cumulative Probility Plots of Precipitation Data Using Different Plotting Position Formulae
CHAPTER 3 [Go to Page]
Chapter 3: Evapotranspiration and Evaporative Demand [Go to Page]
3.0 INTRODUCTION [Go to Page]
3.0.1 Motivation
3.0.2 Chapter Contents
3.1 Evapotranspiration and Evaporative Demand: A Physical Primer [Go to Page]
3.1.1 Physical Measures of ET and E0
3.1.2 Drivers or Limits to ET: Introducing E0
3.2 Models and Observations of ET and E0 [Go to Page]
3.2.1 Penman's Legacy: Physical Models of E0
3.2.2 Energy and Water Limits to ET: The Budyko Framework
3.2.3 Complementarity of Regional ET and E0
3.2.4 Water-balance Estimates of ET
3.2.5 Eddy Covariance Estimates of ET and Global Observation Efforts
3.2.6 Remote Sensing and Energy Balance Modeling of ET
3.2.7 T-Based E0 Formulations: A Warning
3.2.8 Observed E0
3.3 The Reference Evapotranspiration Concept [Go to Page]
3.3.1 Penman-Monteith Approach to ET
3.3.2 The ASCE Standardized Reference ET Equation
3.3.3 Derivation of ETc from Reference ET
3.3.4 Sources of Uncertainty in ETc Estimation
3.3.5 Observed Sensitivity Analysis of ETrc
3.3.6 Method of Moments Variability Analysis of ETrc
3.4 Trends in ET and E0 [Go to Page]
3.4.1 Trend Analysis Techniques
3.4.2 Trends in ET and E0 and the Evaporation Paradox
3.5 Summary
Acknowledgments
References
CHAPTER 4 [Go to Page]
Chapter 4: Infiltration and Soil Water [Go to Page]
4.0 Scope and Introduction [Go to Page]
4.0.1 Central Role of Infiltration in Hydrology
4.0.2 Process Interactions Affecting Infiltration and Soil Water
4.0.3 Variability and Uncertainty of Infiltration and Soil Water
4.1 Infiltration and Soil-Water Dynamics: Description and Measurement [Go to Page]
4.1.1 History: Engineering Treatment of Rainfall Infiltration and Losses
4.1.2 Plant Canopy Interception of Rainfall
4.1.3 Local Processes of Soil Water and Infiltration
4.1.4 Infiltration Dynamics
4.1.5 Soil-Surface Sealing
4.1.6 Methods of Measuring Soil Water Content
4.1.7 Surface Flux Measurements
4.2 Spatial and Temporal Variability of Soil Water and Infiltration [Go to Page]
4.2.1 Vertical Soil Heterogeneity Effects on Infiltration
4.2.2 Observations of Space-Time Variability
4.2.3 Temporal Variability of Soil Hydraulic Properties
4.3 Scaling and Estimation of Soil Hydraulic Properties and Infiltration [Go to Page]
4.3.1 Pedotransfer Functions
4.3.2 Dimensionless Relationships in Infiltration Processes
4.3.3 Geostatistical Scaling Methods and Examples
4.3.4 Effective Parameters of Heterogeneous Soil
4.4 Uncertainty in Measurement and Space-Time Estimation [Go to Page]
4.4.1 Local Measurement Uncertainty
4.4.2 Inverse Methods and Parameter Estimation
4.4.3 Model Process Uncertainty and Preferential Flow
4.4.4 Statistical Inference
4.5 Links between Infiltration and Runoff at Different Scales [Go to Page]
4.5.1 Runoff, Run-On, and Process Interactions
4.5.2 Recent Advances in Simulating Space-Time Infiltration and Soil Water
4.6 Suggestions for Advancing Infiltration Science and Practice [Go to Page]
4.6.1 Advances in Measurement across Scales
4.6.2 Systems Approaches for Simulating Process Interactions
4.6.3 Computer Decision Aids and Risk Assessments
List of Terms [Go to Page]
Acronyms
Symbols
Acknowledgments and Caveat
References
CHAPTER 5 [Go to Page]
Chapter 5: Probability Distributions in Groundwater Hydrology [Go to Page]
5.0 General
5.1 Definitions [Go to Page]
5.1.1 Probability Density Function
5.1.2 Correlation Coefficient
5.1.3 Spatial Correlation
5.1.4 Correlation Scale
5.1.5 Statistical Homogeneity and Independence
5.2 Basic Notation and Key Statistics [Go to Page]
5.2.1 The Sample Average
5.2.2 The Geometric Mean
5.2.3 The Standard Deviation and Variance
5.2.4 The Coefficient of Skew
5.3 Frequently Used pdfs in Groundwater Hydrology [Go to Page]
5.3.1 The Log-Normal pdf
5.3.2 The Gamma pdf and Its Special Case the Exponential pdf
5.3.3 The Log-Gamma pdf
5.4 Illustrative Examples [Go to Page]
5.4.1 Application of the Log-Normal pdf to Hydraulic Conductivity Data
5.4.2 Application of the Log-Gamma pdf to Fit Hydraulic Conductivity Data
5.4.3 Application of the Exponential Function to Hydraulic Conductivity Data
5.4.4 Application of the Gamma pdf to Residence Time and Age of Groundwater
5.4.5 Application of the Gamma pdf to Model Water Quality of Springs: Correlated Gamma Variables
5.5 Conclusions
References
CHAPTER 6 [Go to Page]
Chapter 6: Modeling Streamflow Variability [Go to Page]
6.0 Introduction
6.1 Stochastic Features of Streamflow Time Series [Go to Page]
6.1.1 Autocorrelation
6.1.2 Seasonality
6.1.3 Storage-Related Statistics and Hurst Effect
Example 6-1: Analysis of Variability Features of Poudre River Streamflows
6.2 Modeling of Streamflow Time Series [Go to Page]
6.2.1 ARMA Models
6.2.2 Modeling of Seasonal Series
6.2.3 Product Models for Intermittent Flows
6.2.4 Modeling of Long-Term Variability
6.2.5 Modeling of Streamflows by Nonparametric Methods
6.3 Modeling of Complex River Systems [Go to Page]
6.3.1 Modeling of Multivariate Time Series
6.3.2 Disaggregation Models
6.3.3 Modeling Strategies for Complex River Systems
Example 6-2: Disaggregation Strategy for Modeling Upper Colorado River System
6.4 Software Tools
6.5 Further Remarks
References
CHAPTER 7 [Go to Page]
Chapter 7: Flood Frequency Analysis in the United States [Go to Page]
7.0 General
7.1 Evolution of Bulletin 17B
7.2 Characteristics of the LP3 Distribution [Go to Page]
7.2.1 Log Space Characteristics
7.2.2 Real Space Characteristics
7.2.3 LP3 Model for Annual Flood Series
7.2.4 L-Moments
7.3 Estimation Procedures for Complete Samples [Go to Page]
7.3.1 Log Space Method of Moments
7.3.2 Log Space Method of Moments with Regional Skew
Example 7.1
7.4 Estimation Procedures with Historical Information and Low Outliers [Go to Page]
7.4.1 Low Outliers
7.4.2 Historical Flood Information
7.4.3 Expected Moments Algorithm
Example 7-2
7.4.5 What's Next: Bulletin 17C
7.5 Incorporation of Climate Change and Climate Variability into Flood Frequency Analysis [Go to Page]
7.5.1 Block Adjustment versus Parametric Adjustment
7.5.2 Incorporation of ENSO Effects Using Parametric Relationships
Example 7-3
7.6 Closing Remarks
Appendix 7A: Plotting Positions for Use with Low Outliers and Historical Information
Appendix 7B: Expected Moments Algorithm
References
CHAPTER 8 [Go to Page]
Chapter 8: Low Flows and Droughts [Go to Page]
8.0 Introduction
8.1 Low Flow and Drought Definitions [Go to Page]
8.1.1 Definitions of Low Flows
8.1.2 Definition of Drought
8.2 Empirical Frequency Analysis of Low Flows
8.3 Probability Distribution of Low Flows [Go to Page]
8.3.1 Fitting of Univariate Distributions
8.3.2 Case of Intermittent Flows
8.4 Regional Analysis of Low Flows [Go to Page]
8.4.1 Methods for Selecting Homogeneous Regions
8.4.2 Methods for Regional Analysis and Estimation
8.5 Analysis of Autocorrelated Low Flows [Go to Page]
8.5.1 Modeling of Autocorrelated Low Flows
8.5.2 Return Period and Risk of Low Flows
8.6 Statistical Characterization of Multiyear Droughts [Go to Page]
8.6.1 Probability Distributions and Moments of Drought Characteristics
8.6.2 Return Period of Multiyear Droughts
8.7 Regional Analysis of Droughts
8.8 Effects of Hydraulic Structures on Low Flows
8.9 Closing Remarks
References
CHAPTER 9 [Go to Page]
Chapter 9: Probabilistic Models for Urban Stormwater Management [Go to Page]
List of Symbols
9.0 General
9.1 Analytical Probabilistic Stormwater Models [Go to Page]
9.1.1 Overview
9.1.2 Rainfall Characterization
9.1.3 Event-Based Rainfall-Runoff Transformation
9.1.4 Derived Probability Distributions of Runoff Characteristics
9.1.5 Example 9-1: Flood Quantile Estimation and Flood Control Detention Pond Design in Chicago, Illinois
9.2 Performance Modeling for BMP Pollutant Removal with Uncertainty Analysis [Go to Page]
9.2.1 Overview
9.2.2 BMP Performance Modeling
9.2.3 Methods for Uncertainty Analysis
9.2.4 Sensitivity Results
9.2.5 Example 9-2: Uncertainty Analysis of BMP Performance for TSS Removal in Los Angeles, California
9.3 Summary
Acknowledgments
References
CHAPTER 10 [Go to Page]
Chapter 10: Analysis of Water Quality Random Variables [Go to Page]
Glossary
10.0 General
10.1 Special Characteristics of Water Quality Random Variables
10.2 Practical Applications of Water Quality Distributions
10.3 The Normal Distribution
10.4 Tests for Normality and Transformations
10.5 The Log-Normal Distribution
10.6 Other Continuous Distributions: Gamma, Weibull, and Beta
10.7 The Binomial and Hypergeometric Distributions
10.8 Other Discrete Distributions and Microbiological Variables [Go to Page]
10.8.1 The Poisson Distribution
10.8.2 The Negative Binomial Distribution
10.8.3 The Multinomial Distribution
10.9 Nonparametric Representations [Go to Page]
10.9.1 Nonparametric Estimation of Quantiles and Proportions
10.9.2 Box-and-Whisker Plots
10.10 Censored Observations [Go to Page]
10.10.1 Empirical Distribution Functions and Summary Statistics for ROS and KM
10.10.2 Quantiles and Boxplots Using Censored Data
10.10.3 Avoidance of Censoring by Using All Measurements
10.11 Water Quality Populations of Interest Defined
10.12 Probability Sampling
10.13 Time Series and Stochastic Processes
10.14 Importance of Serial Correlation [Go to Page]
10.14.1 Serial Correlation and Probability Sampling
10.14.2 Serial Correlation and Stochastic Processes
10.14.3 Trend and Serial Correlation
10.14.4 Automated Sampling, Nearly Continuous Monitoring
10.15 Seasonality and Flow Effects
10.16 Multivariate Characterization
10.17 Summary
References
CHAPTER 11 [Go to Page]
Chapter 11: Multivariate Frequency Distributions in Hydrology [Go to Page]
11.0 General
11.1 Multivariate Distributions in Hydrology [Go to Page]
11.1.1 Hydrometeorological Applications
11.1.2 Hydrological Applications
11.2 Conventional Multivariate Distributions Used in Hydrology [Go to Page]
11.2.1 Bivariate Normal Distribution
11.2.2 Bivariate Log-Normal Distribution
11.2.3 Bivariate Exponential Distribution
11.2.4 Bivariate Largest Extreme Value or Gumbel Distribution
11.3 Copula Method and Its Use in Hydrology [Go to Page]
11.3.1 Copula Concept
11.3.2 Copula Classes
11.3.3 Dependence through Copulas
11.3.4 Parameter Estimation Methods
11.3.5 Copula-Based Random Generation
11.3.6 Copula Selection Process
11.4 Illustrative Examples [Go to Page]
11.4.1 Example 11-1: Peak Flow and Volume
11.4.2 Example 11-2: Storm Duration and Depth
11.4.3 Example 11-3: Regional Flood Risk Management
References
CHAPTER 12 [Go to Page]
Chapter 12: Hydrologic Record Events [Go to Page]
Glossary
12.0 General
12.1 Parametric Properties of Hydrologic Records [Go to Page]
12.1.1 The Probability Distribution, Quantile Function, and Moments of Record Floods
12.1.2 The Gumbel Distribution
12.1.3 The Generalized Extreme Value Distribution
12.1.4 The Exponential Distribution
12.1.5 Generalized Pareto Distribution
12.2 Nonparametric Statistical Properties of Hydrologic Records [Go to Page]
12.2.1 The Recurrence or Waiting Time of Record Floods
12.2.2 The Probability Distribution of the Number of Record Events
12.2.3 Moments of the Number of Record-Breaking Events
12.2.4 Multivariate Record Events
12.3 Flood Envelope Curves: Application of the Theory of Records [Go to Page]
12.3.1 Envelope Curves: Historical Background
12.3.2 Probabilistic Interpretation of Envelope Curves
12.3.3 Exceedance Probability of Empirical Envelope Curves
12.4 Applications of the Theory of Records: Case Studies [Go to Page]
12.4.1 Application of Probabilistic Regional Envelope Curves
12.4.2 Record-Breaking Properties of Floods in the United States
12.5 Conclusions
References
Index [Go to Page]

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