Maximum entropy spectral analysis of hydrologic data

Abstract

Determination of periodicities is a frequently encountered problem in stochastic analysis of hydrologic time series data. Conventional methods of spectral analysis such as those currently used in the analysis of hydrologic data have some long recognized disadvantages. The maximum entropy spectral analysis (MESA) method was developed as an alternative to conventional spectral analysis and has received considerable attention in exploratory geophysics. Several aspects of application of MESA to hydrologic time series are discussed in this paper. The performance of the MESA method is compared with the commonly used Blackman and Tukey method. MESA can be extended to obtain additional stochastic characteristics such as autocorrelation, partial autocorrelation, inverse autocorrelation, inverse partial autocorrelation, and cross spectra of time series data. Thus spectral analysis and computations related to stochastic model development may be integrated by using MESA. The simple relationship between maximum entropy and maximum likelihood spectra may be used to filter our pseudoperiodicities that occur in maximum entropy spectra estimated by using large filter orders.