## Random Functions and HydrologyAdvanced-level view of the tools of random processes and field theory as applied to the analysis and synthesis of hydrologic phenomena. Topics include time-series analysis, optimal estimation, optimal interpolation (Kriging), frequency-domain analysis of signals, and linear systems theory. Techniques and examples chosen to illustrate the latest advances in hydrologic signal analysis. Useable as graduate-level text in water resource systems, stochastic hydrology, random processes and signal analysis. 202 illustrations. |

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### Contents

INTRODUCTION | 1 |

GENERALIZED UNIVARIATE TIMESERIES | 14 |

MULTIVARIATE TIMESERIES ANALYSIS | 91 |

FREQUENCYDOMAIN ANALYSIS | 155 |

LONGTERM PERSISTENCE IN HYDROLOGIC | 210 |

APPENDIX TO CHAPTER 5 THE BROKENLINE | 266 |

The Multivariate BrokenLine Model | 275 |

MULTIDIMENSIONAL HYDROLOGIC PROCESSES | 281 |

Sampling from the Spectrum | 288 |

ESTIMATION OF STATIC LINEAR HYDROLOGIC | 359 |

ESTIMATION OF DYNAMIC HYDROLOGIC | 425 |

ADDITIONAL DYNAMIC FILTERING CONCEPTS | 466 |

521 | |

545 | |

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### Common terms and phrases

algorithm analysis approximation assumed autocorrelation function autoregressive model average basin behavior Box and Jenkins broken line broken-line process Chapter computed correlation function correlation structure corresponding covariance function covariance matrix defined detrending discharge discrete distribution drift dynamic Eagleson equation example expected value Figure finite forecasting frequency given by Eq Hurst hydrologic Idem implies input iterative Kalman filter Kriging lag-one correlation linear system matrix mean square error multivariate nonlinear nonstationarity normal number of stations observations obtained optimal Orinoco River parameter estimation partial autocorrelation polynomial prediction problem procedure random field random process random variables represents reservoir residuals Restrepo-Posada River runoff sampling seasonal semivariogram sequence shown in Fig simulation skewness solution spatial spectrum standard deviation stationary stationary process statistics stochastic storm streamflow theory tion Variance reduction Variance reduction factor variogram vector Water Resources Res weights white noise yields zero mean