Stochastic characteristics of environmental and hydrologic time series

Huey-Long Chen, Purdue University

Abstract

Stochastic models in conventional time series analysis are mainly based on three key assumptions: stationarity, Gaussianity and linearity. Due to the fact that non-stationary time series are often encountered in practice, stationary stochastic models cannot be directly applied without modifying stationary stochastic models or making changes to non-stationary time series. The primary objective of this study is to investigate stochastic characteristics of environmental and hydrologic time series. Four fundamental studies are conducted in this thesis, including: (1) segmentation of synthetic non-stationary time series; (2) estimation of turbulent kinetic energy dissipation by using synthetic data; (3) segmentation of observed time series; and (4) linearity and Gaussianity analyses. In this study, a modified segmentation algorithm is used to identify and partition non-stationary series into stationary segments. Five tests are applied to the segmentation algorithm, including four tests based on AR models and a new test based on wavelet analysis. Environmental and hydrologic time series analyzed in this study include: temperature gradient profiles, monthly streamflow, temperature, precipitation and Palmer's drought severity index (PDSI) series. A modified Batchelor curve fitting method is used to estimate the kinetic energy dissipation rate from the multitaper spectra of stationary segments of temperature gradient profiles. The stationary segments partitioned from these environmental and hydrologic time series are all tested for Gaussianity and linearity. General results show that: (1) the modified segmentation algorithm with two stages of boundary optimization detects both starting and ending boundaries of stationary segments at closer locations to the actual boundaries; (2) the multitaper spectral estimator has less bias than the Hamming-window smoothed spectral estimator and the periodogram at high frequencies in the estimated Batchelor spectra; (3) the Batchelor curve fitting method using the weighted chi-square distributed error function has better performance than that using the unweighted chi-square error function or that using the error in log-log space; (4) high numbers of stationary segments are identified in temperature gradient profiles, which indicate strong intermittency in temperature gradient profiles; (5) most of the standardized hydrologic monthly series, either differenced or not, are non-stationary; (6) more stationary segments of temperature gradient profiles are identified as non-linear than those identified as linear, despite which test is used in the segmentation algorithm; and (7) the conventional assumption of linear models of Gaussian-distributed variables may not be valid for all standardized monthly streamflow and PDSI series.

Degree

Ph.D.

Advisors

Rao, Purdue University.

Subject Area

Civil engineering

COinS