System-Theoretical Modelling in Surface Water Hydrology

1 Introduction.- 2 Preparation of Hydrological Variables for Modelling.- 2.1 Mean Areal Precipitation.- 2.2 Baseflow and Runoff.- 2.3 Effective Rainfall.- 3 Treatment of Hydrological Variables in Linear System Models.- 3.1 System-Theoretical Elements.- 3.2 Concepts in Linear Systems.- 3.3 Treatment of Variables in the Time Domain.- 3.3.1 Impulse and Step Function.- 3.3.2 Resolution of System Input Functions.- 3.3.3 System Response Function.- 3.3.4 Synthesis of System Output Functions by Convolution.- 3.4 Treatment of Variables in the Frequency Domain.- 3.4.1 Fourier, Laplace and Z-Transformations.- 3.4.2 Convolution Theorem.- 3.4.3 Synthesis of System Output Functions by Convolution.- 3.5 Particular Linear Systems (Conceptional Models).- 3.5.1 Model of Linear Reservoir.- 3.5.2 Model of Linear Cascade.- 3.5.3 Model After Clark.- 3.6 Identification of Linear Systems.- 3.6.1 Method of Differentiation.- 3.6.2 Method of Transform Technique.- 3.6.3 Method of Matrix Approach.- 3.7 Linear Systems with Stochastic Inputs.- 3.7.1 Random Processes and Linear Systems.- 3.7.2 Equations Wiener-Hopf and Yule-Walker.- 3.7.3 Common Random Processes as System Input.- 3.7.4 Random Processes of the ARMA Type.- 3.7.5 Whitening and Innovation Filters.- 3.7.6 Filters of Smoothing and Prediction.- 4 Treatment of Hydrological Variables in Non-Linear Systems.- 4.1 Volterra Series Model.- 4.2 Composition of Parallel Submodels.- Appendix 1 Program: PMSB1.- Appendix 2 Program: PMSB2.- Appendix 3 Program: PMSB3.- Appendix 4 Program: PMSB4.- Appendix 5 Program: PMSB5.- Appendix 6 Program: PREF1.- Appendix 7 Program: PREF2.- Appendix 8 Program: PREF3.- Appendix 9 Program: VAZAO1.- Appendix 10 Program: VAZAO2.- Appendix 11 Program: VAZAO3.- Appendix 12 Program: VAZAO4.- Appendix 13 Program: IDENT1.- Appendix 14 Program: IDENT2.- Appendix 15 Program: PCORR.