Spectral analysis is one of the most important tools of atmospheric physics. Patterns can be extracted from measurement series with the help of spectral analysis and used as a complement to their interpolation or extrapolation. A possible application area is the analysis of atmospheric waves. Waves are harmonic spatial and temporal processes whose physical characteristics are primarily dependent on their repetition frequency and wavelength. Time series analysis is thus essential for investigating dynamic atmospheric processes, which is why various types of spectral analysis (such as wavelet analysis, harmonics analysis, maximum entropy methods) are carried out at DLR-DFD.
Time series can be classified into two different groups: deterministic and stochastic. In deterministic sequences the temporal or spatial progression is governed by an analytic formula, whereas stochastic sequences are random. For the latter, any time series thus represents only one of many possible realizations, a situation which precludes forecasts. But for deterministic processes, which can be described by a mathematical equation which ascertains a value or the outcome of a process on the basis of earlier values, forecasting is in principle possible. Both classes can be further subdivided: deterministic processes can be either periodic or nonperiodic; random processes can be stationary (i.e., temporally or spatially constant) or nonstationary.
In geophysics, deterministic and stationary random processes play a particularly large role because they can be more easily managed. For many known analytic techniques (e.g., fast Fourier Transform, maximum entropy methods) a repetition frequency or stationarity is assumed as a simplification, although in most geophysical processes this is the case only as an approximation and for limited time intervals. This gives a first indication of the complexity of time series analysis.
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