Recursive Streamflow Forecasting

Abstract

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