[ Detected peaks vary from current range of lunation period. Subject to further analysis.]
Spectral power density of northern hemisphere sea ice extent.
NOAA sea ice extent data was used from 1988 onwards. This subset was used due to platform changes. Earlier data had fewer orbits per day, some notable breaks in coverage and was obviously not homogeneous with the period used.
The data are provided with daily dates. These were converted to floating point Julian day format for processing. To avoid loss of resolution and precision in the FFT processing, the data were high-pass filtered with a 260 day Lanczos filter to concentrate on the sub-annual signal.
Several different taper functions ( including no taper ) were used to determine whether the results may be caused or distorted by the taper windowing operation.
It was also found that removing the auto-regression by analysing the first difference of the daily data( rate of change ) gave more consistent results.
This detailed segment of the spectrum shows peaks near the synodic lunar month ( the visible lunar phases ). Annotated values are approximate cursor values. Calculated values were determined at higher resolution.
Due to the varying angular velocity of the Earth’s orbit this period, defined by Earth-moon-sun alignment is somewhat variable throughout the year.
The range of the synodic lunar period or “lunation” is approximately 29.27 to 29.83 days*, the long term average being 29.53059 days.
The two extreme values, which occur at perihelion and aphelion portions of the Earth’s orbit, are clearly present. The latter in the form a spectral triplet. The two extremes are more clearly present since they occur for longer than fast changing periods in between. The relative strength of the 29.9 day triple around January and shorter 29.2 day peak around July shows when synodic cycle ( visible lunar phase ) has it’s strongest effect. The combined power in the 29.92 day triplet is about three times greater than 29.2 day peak.
Best estimation of peak values:
29.926 * 11555.992 = 31.64 years; triplet asymmetry: 0.002 %
The triplet is highly symmetrical in both frequency interval and side-lobe amplitude, strongly supporting the interpretation of this being an amplutude modulated signal. The combined power of the three peaks of the triplet makes it significantly stronger than the surrounding noise floor.
Since the side peaks have a frequency separation of only 0.5%, the derived period of the modulation frequency can have considerable uncertainty. An uncertainty of +/-0.01 in each peak would produce an uncertainty of +/-13% in the longer period.
The data autocorrelation fn was calculated +/- 20.5 years and two different taper functions and no taper function produced essentially the same result, so the long term modulation would seem to be real and not an artefact of the processing, ie. there is a long term variation in the amplitude of the synodic lunar cycle on Arctic ice cover. In view of the length of the dataset ( 23.8 years after filtering ), this is not evidence that it is a repetitive cyclic change.
The anomalistic lunar cycle is also present:
The magnitude of these periodicities shown in a broader context. The major peaks are harmonics of the annual cycle 365.25/5; 365.25/6, 365.25/7, etc. ::
* J. Meeus, ‘Les durees extremes de la lunaison’, l’Astronomie (Societe Astronomique de France), Vol. 102, pages 288 – 289 (July – August 1988).