Original paper
POP-analysis and sampling interval
Egger, Joseph
Meteorologische Zeitschrift Vol. 10 No. 4 (2001), p. 351 - 355
published: Oct 15, 2001
DOI: 10.1127/0941-2948/2001/0010-0351
Open Access (paper may be downloaded free of charge)
Abstract
The POP-analysis applies a regressive model of first order with time step Dt to the data of a multivariate process. In many cases, Dt is the sampling interval of these data. Main frequencies, principal oscillation patterns (POPs) and forcing intensities are determined this way. These results of the POP-analysis depend, of course, on Dt. On the other hand, one is mainly interested in the true frequencies of the process investigated. A damped linear oscillator of frequency ω and damping rate ε with white noise forcing is chosen to study the sensitivity of POP-results to the choice of Dt. Such a process is ideally suited for a POP-analysis. The deviation of the POP-frequencies from the true frequency of the oscillator is caused exclusively by the choice of a finite time step Dt. The analytic solution to this problem shows that the POP-analysis underestimates the damping rate if ε > |ω|. Large overestimates occur for ω2 Dt » ε. Frequencies are almost always underestimated but the deviations are small except for εDt ≥ 0.2, and/or for oscillations with periods T0 ≤ 8Dt. Forcing intensities are captured quite well unless εDt > 0.2 and/or ωDt |ω| ist. Große Überschätzungen treten bei ω2 Dt » ε ein. Die Frequenzen werden so gut wie immer unterschätzt aber die Abweichungen sind klein, es sei denn εDt > 0.2 oder es gelte für Perioden der Schwingungen T0 0.2 und/oder ωDt < 0.6. Diese Ergebnisse werden verallgemeinert. Es wird gezeigt, dass die Fehlerabschätzungen für Frequenzen und Dämpfungsraten wie sie für ein zweidimensionales Modell hergeleitet werden auch bei POP-Analysen in höheren Dimensionen gültig sind.