Stochastic Analysis of Periodic Hydrologic Process

The harmonization of a stochastic process allows the Fourier-Stieltje's integral to represent a nonstationary stochastic process of the periodically correlated type. Therefore, the periodic runoff and precipitation processes can be represented by the Fourier series with random coefficients. The first order periodicity is explained by the periodicity of the first moment of the hydrologic variable. The periodicity in the covariance is explained by the harmonization of the stochastic component. While generating hydrologic records for the design of water resources systems, it is often assumed that the standardized hydrologic series or the residual series, after subtraction of the periodic and trend components, are stationary. Based on the Fourier series representation of the periodic process, a test for stationarity is developed. Observed monthly runoff and precipitation records are tested for stationarity as raw and transformed series.