# Entropy Theory in Hydrologic Science and Engineering

by: Vijay P. Singh, Ph.D., D.Sc., D.Eng. (Hon.), Ph.D. (Hon.), P.E., P.H., Hon.D.WRE

**Abstract:**A thorough introduction to entropy theory and its applications in hydrologic science and engineering. This comprehensive volume addresses basic concepts of entropy theory from a hydrologic engineering perspective. The application of these concepts to a wide range of hydrologic engineering problems is discussed in detail. The book is divided into sectionsâ€”preliminaries, rainfall and evapotranspiration, subsurface flow, surface flow, and environmental conditions. Helpful equations, solutions, tables, and diagrams are included throughout this practical resource.

Full details

## Table of Contents

**A.**About the Author**B.**Dedication**C.**Preface**D.**Acknowledgments**A.**PART I: Preliminaries**1.**Introduction to Entropy Theory**2.**Maximum Entropy Production Principle**3.**Performance Measures**4.**Morphological Analysis**5.**Evaluation and Design of Sampling and Measurement Networks**B.**PART II: Rainfall and Evapotranspiration**6.**Precipitation Variability**7.**Rainfall Frequency Distributions**8.**Evaluation of Probabilistic Precipitation Forecasting**9.**Assessment of Potential Water Resources Availability**10.**Evaporation**C.**PART III: Subsurface Flow**11.**Infiltration**12.**Soil Moisture**13.**Groundwater Flow**D.**PART IV: Surface Flow**14.**Rainfall-Runoff Modeling**15.**Stream Flow Simulation**16.**Hydrologic Frequency Analysis**17.**Stream Flow Forecasting**E.**PART V: Environmental Conditions**18.**River Flow Regime Classification**19.**Sediment Yield**20.**Eco-Index

## Tools & Media

## Expanded Table of Contents

**A.**About the Author**B.**Dedication**C.**Preface**D.**Acknowledgments**A.**PART I: Preliminaries**1.**Introduction to Entropy Theory- Concept of Entropy
- Entropy Theory
- Types of Entropies
- Approximate Entropy and Sample Entropy
- Principle of Maximum Entropy
- Methodology for Application of POME
- Concentration Theorem
- Principle of Minimum Cross Entropy
- Application of POMCE to Continuous Variables
- Application of POMCE with Fractile Constraints
- Comparison between POME and POMCE
- Entropy Scaling
- Partial and Constrained Entropy
- Entropy under Transformation of Variables
- Types of Hydrologic Problems
- Hypothesis on Cumulative Distribution Function
- Questions
- References
- Further Reading

**2.**Maximum Entropy Production Principle**3.**Performance Measures**4.**Morphological Analysis- Basic Terminology
- Distribution of Stream Elevations
- Entropy and Potential Energy
- Longitudinal Channel Profile
- Law of Average Stream Fall
- Entropy, Horton-Strahler Order, Magnitude, and Fractal Dimension
- Scaling Properties
- Horton-Strahler Equations
- Streambed Profile
- Stream Meandering
- Stream Order as a Measure of Sample Source Uncertainty
- Watershed Surface Description
- Case Study
- Questions
- References
- Further Reading

**5.**Evaluation and Design of Sampling and Measurement Networks**B.**PART II: Rainfall and Evapotranspiration**6.**Precipitation Variability- Measures of Variability
- Trend and Persistence
- Entropy Measures
- Comparison of Entropy and Diversity Indices
- Comparison of Entropy and Variance
- Rainfall Disaggregation
- Rainfall Complexity
- Entropy Scaling
- Case Study 1: Precipitation Variability
- Case Study 2: Rainfall Disaggregation
- Questions
- References
- Further Reading

**7.**Rainfall Frequency Distributions- Factors Affecting Rainfall Frequency Distributions
- Derivation of Annual Maximum Rainfall Distributions
- Three Generalized Distributions
- Case Study 1: Evaluation of Entropy-Based Distributions and Comparison Using Observed Rainfall Data
- Frequency Analysis and IDF Curves
- Case Study 2: Evaluation of Entropy-Based Distributions and Comparison Using Synthetic Data
- Questions
- References
- Further Reading

**8.**Evaluation of Probabilistic Precipitation Forecasting**9.**Assessment of Potential Water Resources Availability**10.**Evaporation**C.**PART III: Subsurface Flow**11.**Infiltration**12.**Soil Moisture**13.**Groundwater Flow**D.**PART IV: Surface Flow**14.**Rainfall-Runoff Modeling- Runoff Volume by SCS-CN Method
- Instantaneous Unit Hydrograph
- Volume-Peak Discharge Relation
- Derivation of Peak Discharge Rating Curve
- Rational Method
- Linear Reservoir Model
- Appendix 14A: Derivation of a General Probability Distribution
- Appendix 14B: Derivation of Exponential, Gamma, and Lognormal Probability Distributions
- Questions
- References
- Further Reading

**15.**Stream Flow Simulation- Simulation Models
- Stream Flow Simulation at a Single Site
- A Case Study: Testing with Synthetic Data
- A Case Study: Simulation of Monthly Stream Flow
- Entropy-Copula Method for Single-Site Stream Flow Simulation
- Entropy-Copula Method for Multisite Stream flow Simulation
- Appendix 15A: Bivariate Copulas and Their Corresponding Conditional Distributions
- Appendix 15B: Trivariate Copulas and Their Corresponding Conditional Distributions
- Questions
- References
- Further Reading

**16.**Hydrologic Frequency Analysis**17.**Stream Flow Forecasting**E.**PART V: Environmental Conditions**18.**River Flow Regime Classification**19.**Sediment Yield**20.**Eco-Index

**Book Details**

**Title: **Entropy Theory in Hydrologic Science and Engineering

**Publisher: **McGraw-Hill Education: New York, Chicago, San Francisco, Athens, London, Madrid, Mexico City, Milan, New Delhi, Singapore, Sydney, Toronto

**Copyright / Pub. Date: **2015 McGraw-Hill Education

**ISBN: **9780071835466

**Authors:****Vijay P. Singh, Ph.D., D.Sc., D.Eng. (Hon.), Ph.D. (Hon.), P.E., P.H., Hon.D.WRE**
is a Distinguished Professor in the Department of Biological and Agricultural Engineering at Texas A&M University. He specializes in surface-water hydrology, groundwater hydrology, hydraulics, irrigation engineering, environmental quality, and water resources. Dr. Singh has published more than 20 textbooks.

**Description: **
A thorough introduction to entropy theory and its applications in hydrologic science and engineering.
This comprehensive volume addresses basic concepts of entropy theory from a hydrologic engineering perspective. The application of these concepts to a wide range of hydrologic engineering problems is discussed in detail. The book is divided into sectionsâ€”preliminaries, rainfall and evapotranspiration, subsurface flow, surface flow, and environmental conditions. Helpful equations, solutions, tables, and diagrams are included throughout this practical resource.