Recursive Streamflow Forecasting: A State Space Approach

This textbook is a practical guide to real-time streamflow forecasting that provides a rigorous description of a coupled stochastic and physically based flow routing method and its practical applications. This method is used in current times of record-breaking floods to forecast flood levels by various hydrological forecasting services. By knowing in advance when, where, and at what level a river will crest, appropriate protection works can be organized, reducing casualties and property damage. Through its real-life case examples and problem listings, the book teaches hydrology and civil engineering students and water-resources practitioners the physical forecasting model and allows them to apply it directly in real-life problems of streamflow simulation and forecasting. Designed as a textbook for courses on hydroinformatics and water management, it includes exercises and a CD-ROM with MATLAB® codes for the simulation of streamflows and the creation of real-time hydrological forecasts.

Table of Contents:
1. Introduction 2. Overview of continuous flow routing techniques 2.1. Basic equations of the one-dimensional, gradually varied nonpermanent open channel flow 2.2. Diffusion wave equation 2.3. Kinematic wave equation 2.4. Flow routing methods 2.4.1. Derivation of the storage equation from the Saint-Venant equations 2.4.2. The Kalinin-Milyukov-Nash cascade 2.4.3. The Muskingum channel routing technique 3. State-space description of the spatially discretized linear kinematic wave 3.1. State-space formulation of the continuous, spatially discrete linear kinematic wave 3.2. Impulse response of the continuous, spatially discrete linear kinematic wave 4. State-space description of the continuous Kalinin-Milyukov-Nash (KMN) cascade 4.1. State equation of the continuous KMN-cascade 4.2. Impulse response of the continuous KMN-cascade and its equivalence with the continuous, spatially discrete linear kinematic wave 4.3. Continuity, steady state, and transitivity of the KMN-cascade 5. State-space description of the discrete linear cascade model (DLCM) and its properties: The pulse-data system approach 5.1. Trivial discretization of the continuous KMN-cascade and its consequences 5.2. A conditionally adequate discrete model of the continuous KMNcascade 5.2.1. Derivation of the discrete cascade, its continuity, steady state and transitivity 5.2.2. Relationship between conditionally adequate discrete models with different sampling intervals 5.2.3. Temporal discretization and numerical diffusion 5.3. Deterministic prediction of the state variables of the discrete cascade using a linear transformation 5.4. Calculation of system characteristics 5.4.1. Unit-pulse response of the discrete cascade 5.4.2. Unit-step response of the discrete cascade 5.5. Calculation of initial conditions for the discrete cascade 5.6. Deterministic prediction of the discrete cascade output and its asymptotic behavior 5.7. The inverse of prediction: input detection 6. The sample-data system approach 6.1. Formulation of the discrete cascade in a sample-data system framework 6.2. Discrete state-space approximation of the continuous KMN-cascade of noninteger storage elements 6.3. Application of the discrete cascade for flow routing with unknown rating curves 7. DLCM and stream-aquifer interactions 7.1. Accounting for stream-aquifer interactions in DLCM 7.2. Assessing groundwater contribution to the channel via input detection 8. Handling of model-error: the deterministic-stochastic model and its prediction updating 8.1. A stochastic model of forecast errors 8.2. Recursive prediction and updating 9. Some practical aspects of model application for real-time operational forecasting 9.1. Model parameterization 9.2. Comparison of a pure stochastic, deterministic (DLCM), and the deterministic-stochastic models 9.3. Application of the deterministic-stochastic model for the Danube basin in Hungary 10. Summary 11. Appendix 11.1. State-space description of linear dynamic systems 11.2. Algorithm of the discrete linear Kalman filter 12. References 13. Guide to the exercises