Investigation of stationarity of hydrologic and climatic time series

Khaled H Hamed, Purdue University

Abstract

The principle of stationarity plays an important role in time series analysis. A key assumption in classical time series theory is stationarity, that is, the time series properties do not change with time. Nonstationary time series can, however, be adequately modeled if the type of nonstationarity can be identified and isolated. Several methods are proposed for the detection of non-stationarity in time series. Time domain methods include statistical tests such as Mann's test, the cumulative deviation test, and Worsley likelihood ratio test. In the frequency domain, nonstationarity can be studied by using evolutionary spectral analysis, which involves studying the spectrum as it evolves in time, based on successive overlapping windows of finite length over the time series. This method, combined with improved spectral estimation methods, such as MTM and MEM, is a powerful tool for studying nonstationary time series as well as the underlying dynamics of the systems which produce such outputs. A newly developed technique that can be used for analyzing time series is wavelet analysis. Similar to frequency analysis which is used to study signals at different frequencies, wavelet analysis allows investigating signals at different scales. A number of flow, rainfall, and temperature time series as well as tree-ring time series as proxy to hydrologic data from Iowa, Illinois, Indiana and Ohio states are analyzed. Time domain, frequency domain, time-frequency, and time-scale analyses are performed on these time series in order to assess their stationarity. Time domain analysis indicates the existence of trends in many of the studied time series. These trends are not monotonic, but there is evidence that they are similar among different series. Frequency domain analysis reveals the existence of a number of cyclic components that are common to different time series. Some of these components account for 5 to 18% of the total variance in the time series. Time-frequency analysis indicates that there are nonstationarities in both the continuous part as well as the discrete part of the spectrum. Time-scale analysis supports the results from the time-frequency analysis and provides information about the structure of hydrologic and climatic time series at different time scales.

Degree

Ph.D.

Advisors

Rao, Purdue University.

Subject Area

Civil engineering

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