Recursive Streamflow Forecasting: A State Space Approach

 Content: 1.Introduction --
 2.  Overview Of Continuous Flow-Routing Techniques  --
 2.1.  Basic equations of the one-dimensional, gradually varied non-permanent 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.  Kalinin[-]Milyukov[-]Nash cascade --
 2.4.3.  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.  conditionally adequate discrete model of the continuous KMN-cascade  --
 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.  inverse of prediction: input detection  --
 6.  Linear Interpolation (LI) Data System Approach  --
 6.1.  Formulation of the discrete cascade in the LI-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  --
 6.4.  Detecting historical channel flow changes by the discrete linear cascade  --
 7.  DLCM And Stream[-]aquifer Interaction --
 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.  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, a deterministic (DLCM), and deterministic[-]stochastic models  --
 9.3.  Application of the deterministic[-]stochastic model for the Danube basin in Hungary  --
 A.I.1.  State[ --
 ]space description of linear dynamic systems  --
 A.I.2.  Algorithm of the discrete linear Kalman filter  --
 A.II.1.  Sample MATLAB scripts.