Estimation Theory in Hydrology and Water SystemsBy
- K. Nacházel, Faculty of Civil Engineering, Technical University, Prague, Czechoslovakia
Methodological procedures of the theory of estimation of statistical parameters of time series and their application to hydrology and water engineering, particularly the sphere of reservoir-controlled runoffs, are dealt with in this volume. For estimates use is made of random sequences generated for various probability properties. This methodological approach enables examination of the properties of random and systematic errors of the parameters estimated even for the asymmetrical probability distributions, which are frequent in hydrology and water engineering. This book will be of interest to stochastic hydrologists.
Developments in Water Science
Published: June 1993
- Preface. Symbols and units. Part I: Foundations of Estimation Theory. 1. Essence of the Role of Estimation and the Fundamental Problems of Estimation Theory. 2. Development of Estimation Theory and its Application to Hydrology and Water Engineering. Basic methods of the theory of estimation. Methods of examination of the representativeness of sample characteristics based on comparative analysis. Methods of parameter estimation based upon simulation models of random sequences. 3. Sample Characteristics. Their Distribution. Definition of characteristics. Their fundamental relationship to parameters. Problems of the distribution of characteristics. Estimators of autocorrelation function and spectral density. Problems of filtration. Computation of point interval estimates of parameters. 4. Estimation of Parameters by the Moments Method. Principles of the moments method and the application of simulation models of random sequences to estimation. Estimation of parameters of populations with various probability distributions. Mutual relationships between the random, probable and systematic errors of parameter estimation. Effect of extreme sample elements on parameter estimation. 5. Estimation of Parameters by Method of Maximum Likelihood. Brief review of the development of the method. Principle of the method of maximum likelihood and the application of simulation models of random sequences to estimation. Estimation of parameters of populations with various probability distributions. Properties of parameter estimates of populations with various probability distributions. 6. Estimation of Parameters by the Quantiles Method. Principle of quantiles method and the application of simulation models of synthetic sequences to estimation. Properties of parameter estimates of populations with various probablilty distributions. 7. Analysis of Time Series, and Their Mathematical Modelling. Fundamental problems of the analysis of time series. Basic models of time series. Part II: Application of Estimation Theory to Hydrology and Water Engineering. 8. Parameter Estimation of Series of Maximum Flood Flows. Fundamental problems of processing N-year flows. Probability properties of intervals between culminating flows. 9. Estimation of Parameters of Average Annual Flow Series. Estimation of parameters of probabilty distribution. Problems of estimation of the autocorrelation function. 10. Estimation of Parameters of Average Monthly Flow Series. Estimation of parameters of probability distribution. Problems of estimation of the autocorrelation function. Estimation of the coefficients of correlation between the average flow series in calendar months. Problems of generating random samples from flow series. 11. Automated Parameter Estimation and Computer-Aided Modelling of Random Hydrological Series. Automated computer-aided estimation of parameters. The linear regression stochastic model and its modifications. Modelling of random hydrological series with respect to the bias of the characteristics of the real given example. 12. Application of the Theory of Estimation to the Design of Storage Reservoirs. Long-term stationary function of storage reservoirs. Designing storage reservoirs using sets of short realizations of flow series. Effect of the estimation of the autocorrelation function of flow series on the computation of the design parameters of storage reservoirs. Relationship between estimation theory and optimum control of reservoirs in real time. Estimation of future climatic changes and their effect upon hydrologic regimes and water management in water resource systems. 13. Prospect of the Development of Estimation Theory. Bibliography. Subject index.