A Study of Meteorological Time Series. Part 2: Nonstationarity

摘要

Lack of stationarity is induced in meteorological time series in many ways. The obliquity of the ecliptic is presumably the prime cause of the seasonal cycle in the mean. This seasonal cycle is, however, not uniformly repetitive. The interannual variability of the seasonal cycle is investigated, as an estimation problem. In addition to the seasonal cycle in the mean, there are oscillations of long period, for which no unique cause can be specified. In short time series, these long period oscillations also cause the mean to be a function of time, and thus produce nonstationarity. If spectral analysis or stochastic modeling is to be performed, it is necessary to subtract these trend like features as well as the seasonal cycle. Stationarizing the statistical expectation, however, does not even yield wide sense stationarity. Many meteorological variables display, depending on location, a nonstationarity in the variance; they may also have nonstationarity of covariance. Either one of these characteristics immediately turns the spectrum into a function of time, in addition to its naturally being a function of frequency. It is shown that the zero lag cross covariances of atmospheric variables are also nonstationary. Thus, for instance, the meridional transports of sensible heat and zonal momentum, due to the high frequency weather components, are functions of the calendar day. Hence the cross spectra due to the weather must be calculated with extreme care.