Time Series Analysis of Diurnal Cycles in Small-Scale Turbulence

N.H. Chan, J.B. Kadane, and T. Jiang


Two unconventional time series techniques are employed to study the diurnal effect in deep stratified layers in the upper equatorial ocean. A modified spectral approach and a modified time domain approach based on the variogram are used to handle unequally spaced data. A new criterion based on the exceedances of mixing activities is introduced to identify local nights and days adaptively. Using these techniques, diurnal cycles that cannot be explained by simple heat convection are found in deep mixed layers. Tentative ARMA models of the detrended data are entertained. Instead of fitting highly complicated models, the modified approach together with simple ARMA models provide useful tools in analyzing data sets of this nature. This paper offers a rigorous statistical method that can be used to detect diurnal effects in oceanography.

KEY WORDS AND PHRASES: ARMA, Diurnal cycles, Exdeedance, Periodogram, Time series, Unequally spaced data, Variogram, Viscous dissipation rate.