Stochastic Integral Equations and Rainfall-Runoff Models

ISBN-13: 9783642493119 / Angielski / Miękka / 2012 / 384 str.

Theodore V. Hromadka II; Robert J. Whitley

Opis

The subject of rainfall-runoff modeling involves a wide spectrum of topics. Fundamental to each topic is the problem of accurately computing runoff at a point given rainfall data at another point. The fact that there is currently no one universally accepted approach to computing runoff, given rainfall data, indicates that a purely deter ministic solution to the problem has not yet been found. The technology employed in the modern rainfall-runoff models has evolved substantially over the last two decades, with computer models becoming increasingly more complex in their detail of describing the hydrologic and hydraulic processes which occur in the catchment. But despite the advances in including this additional detail, the level of error in runoff estimates (given rainfall) does not seem to be significantly changed with increasing model complexity; in fact it is not uncommon for the model's level of accuracy to deteriorate with increasing complexity. In a latter section of this chapter, a literature review of the state-of-the-art in rainfall-runoff modeling is compiled which includes many of the concerns noted by rainfall-runoff modelers. The review indicates that there is still no deterministic solution to the rainfall-runoff modeling problem, and that the error in runoff estimates produced from rainfall-runoff models is of such magnitude that they should not be simply ignored."

Spis treści

1: Rainfall-Runoff Approximation.- 1.1. Introduction.- 1.1.1. An Analogy to Rainfall-Runoff Modeling.- 1.2. Stormflow Determination Methods.- 1.3. Method for Development of Synthetic Flood Frequency Estimates.- 1.4. Watershed Modeling Uncertainty.- 1.4.1. Some Concerns in Deterministic Rainfall-Runoff Model Performance.- 1.4.2. Runoff Hydrograph Generation Techniques (Linear vs. Nonlinear).- 1.4.3. On Predicting T-Year Return Frequency Values of a Criterion Variable.- 1.4.4. The Design Storm/Unit Hydrograph Approach.- 1.5. Hypothetical Floods, Balanced Floods, and Design Storm Methods.- 1.6. A Preview of the Rainfall-Runoff Model Prediction Problem.- 1.7. An Overview of Rainfall-Runoff Model Structures.- 1.7.1. Estimating Effective Rainfall.- 1.7.2. The Physical Processes Involved.- 1.7.3. The Phi-Index Method for Estimating Effective Rainfall.- 1.7.4. Constant Proportion Loss Rate.- 1.7.5. Coupled Phi-Index and Constant Proportion Loss Rate Function.- 1.7.6. Horton Loss Rate Function.- 1.7.7. Exponential Loss Rate Function.- 1.7.8. Initial Abstraction Considerations.- 1.7.9. SCS Loss Separation.- 1.7.10. SCS Hydrologic Soil Groups.- 1.7.11. Soil Cover Considerations.- 1.7.12. Generating Runoff Using the Unit Hydrograph Method.- 1.7.13. Forming Synthetic Unit Hydrographs.- 1.7.14. Synthetic Runoff Hydrograph Development (Convolution).- 1.7.15. Detention Basin Routing Procedure (Modified Puls Method).- 1.7.16. Flow-by Channel Model (Runoff Hydrograph Separation).- 1.7.17. The Modified Convex Channel Routing Method.- 1.7.18. Muskingum Channel Routing.- 1.7.19. A Pipeflow Routing Model.- 1.7.20. Hydrograph Translation.- 1.7.21. A Link-Node Rainfall-Runoff Model.- Study Problems.- 2: Probability and Statistics Review.- 2.1. Probability Spaces.- 2.2. Random Variables.- 2.3. Moments.- 2.4. Two Random Variables.- 2.5. Several Random Variables.- 2.6. Parameter Estimation.- 2.7. Confidence Intervals.- Study Problems.- 3: Introduction to Stochastic Integral Equations in Rainfall-Runoff Modeling.- 3.1. Introduction.- 3.2. Introduction to Analysis of Rainfall-Runoff Model Structures.- 3.2.1. Rainfall-Runoff Model #1.- 3.2.2. Rainfall-Runoff Model #2.- 3.3. Application of Stochastic Integral Equations to Rainfall-Runoff Data.- 3.4. Another Look at Probabilistic Modeling: Assuming Mutually Independent Parameters.- Study Problems.- 4: Stochastic Integral Equations Applied to a Multi-Linear Rainfall-Runoff Model.- 4.1. Stochastic Integral Equation Method.- 4.1.1. Rainfall-Runoff Model Errors.- 4.1.2. Developing Distributions for Model Estimates Using the S.I.E.M..- 4.1.3. Application 1: Coupling the S.I.E.M. to a Complex Model.- 4.1.3.1. Rainfall-runoff Model Description and Data Forms.- 4.1.3.2. Development of the Distribution [?M(·)].- 4.1.3.3. Functional Operator Distributions.- 4.2. Sensitivity of Functional Operator Distributions to Sampling Error.- 4.2.1. True Distributions.- 4.2.2. Application 2: Development of Total Error Distributions.- 4.2.2.1. A Translation Unsteady Flow Routing Rainfall-runoff Model.- 4.2.2.2. Multilinear Unsteady Flow Routing and Storm Classes.- 4.2.2.3. Multilinear Hydrologic Unsteady Flow Routing.- 4.2.2.4. Example.- 4.3. A Multilinear Rainfall-Runoff Model.- 4.3.1. Generalization of Model.- 4.3.2. Application 3 — Multilinear Rainfall-Runoff Model.- 4.4. An Application of the S.I.E.M..- Study Problems.- 5: Rainfall-Runoff Model Criterion Variable Frequency Distributions.- 5.1. Probabilistic Distribution Concept.- 5.2. The Distribution of the Criterion Variable.- 5.3. Sequence of Annual Model Inputs.- 5.4. Model Input Peak Duration Analysis.- 5.5. Criterion Variable Distribution Analysis.- 5.6. Estimation of T-Year Values of the Criterion Variable.- 5.7. T-Year Estimate Model Simplifications.- 5.8. Discussion of Results.- 5.9. Computational Problem.- 5.10. Computational Program.- Study Problems.- 6: Using the Stochastic Integral Equation Method.- 6.1. Introduction.- 6.2. Problem Setting.- 6.3. Stochastic Integral Equation Method (S.I.E.M.).- 6.4. Approximation of Criterion Variable Confidence Intervals, Using the S.I.E.M..- 6.5. Rainfall-Runoff Models, and the Variance in the Criterion Variable Estimates.- 6.6 Rainfall-Runoff Model Calibration.- 6.7. Confidence Interval Estimates.- 6.8. Unit Hydrographs as a Multivariate Normal Distribution.- 6.8.1. S.I.E.M. Formulation.- 6.8.2. Criterion Variable Value Estimation.- 6.8.3. Computational Problem.- 6.8.4. Discussion of Computational Problem Results.- 6.8.5. Computer Program 6.1.- Study Problems.- References.- Author Index.