Period characteristics of representative hydrologic series in the Yellow River in China using maximum entropy spectra analysis(MESA)

In the field of stochastic hydrology, hydrologic series is formed with the non- periodic component, the periodic component and the stochastic component. Here the period characteristics used include approximate periods in the non-periodic component, simple periods and complex periods in the periodic component. Spectral analysis is an essential and effective tool for extracting such stochastic characteristics of time series. In 1948, Shannon developed a mathematical theory of entropy and applied it in communications. Nearly a decade later, Jaynes formulated the Principle of Maximum Entropy (POME), which makes good winning in solution the ill-posed problem. Maximum Entropy Spectra Analysis (MESA), introduced by BURG in 1975 and based on POME,has certain advantages over the classical and other new methods. The statistical characteristics, which are used in stochastic model identification, can be estimated using MESA, thus permitting integration of spectral analysis and computations related to stochastic model development. It can also be used in analyzing short time series, since it resolves low-frequency characteristics of the data. It is clear that studies with the use of entropy, POME and MESA in hydrology, water resources and water environment have been relatively few. Nevertheless, they are promising and justify further research. The former studies provided motivation for our following work. Here MESA is used to detect the period characteristics of the annual runoff series, monthly runoff series, and annual maximum flood peak series of some stations in the Yellow River in China. The subsection technique is used to compare whether the obtained periods have consistency and stability. Such conclusions are drawn. (a) The 1st to 4th periods of monthly runoff series takes the value of 12 month, 6 month, 4 month and 3 month respectively; (b) The 1st to 2nd periods of annual runoff series takes the value of 3 year and 4 year respectively. (c) There is no significant period in the annual maximum flood peak series. Key words hydrologic series; maximum entropy spectra analysis (MESA); period characteristics; the Yellow River; China