Maybe they should consider possible causes beyond the atmosphere, for instance the orbital relationship with Venus? It has an 8 year cycle with Earth.
To tell you honestly, after the initial excitement, I was quite dissapointed with what was done in the study.
Not only did they not check any potential (cosmic or solar system) cause beyond Earth's immediate surroundings, but they also removed any presumed "external excitation source" and just focused on assumed Earth's internal motion.
The pretreatments of the ΔLOD and PM time series are shown in the Methods. Figure
1 shows the ΔLOD and PM records used. For the periodic signals present in the PM and ΔLOD, the consensus is that they are excited by the Earth’s internal or external sources through the conversion of angular momentum
21. Hence, we need to rule out the influence of external excitation sources before determining that a target signal is from the Earth’s internal motion. There are three external excitation sources of the PM and ΔLOD changes, the atmospheric, oceanic, and hydrological effects. Of these, the first two effects are the two main external excitation sources
21,
22,
23; although hydrological effects will also excite the Earth’s rotation changes, previous studies have proven that the hydrological effects have no significant contribution to the target 5.5–10 yr period band
13,
23 and different hydrological models have clear deviations
13,
24. Hence, similar to previous studies
13,
22, we only consider the atmospheric and oceanic effects.
Pretreatment described in Methods part of the paper revealed that they 'tweaked' the datasets (using a model) to extract only those periodicity signals they were initially interested in.
Datasets and preprocessing
The PM observations were obtained from the EOPC01 dataset (1861/01-1889/12 with 0.1 yr sampling and 1900/01–2019/12 with 0.05 yr sampling); the ΔLOD record was combined with a long-term dataset
56 (1623/06-2008/06 with 1 yr sampling from IERS; EOPC01) and the EOPC04 ΔLOD record
57 (1962/01–2019/12 with 1-day sampling); the AAM (1949/01–2019/12, sampling at 6 h) record was from the Special Bureau for the Atmosphere
58,
59,
60. The AAM was calculated from NCEP/NCAR reanalyses archived on pressure surfaces, and the inverted barometer (IB) pressure term was chosen as the mass term. The OAM record was obtained from the Special Bureau for the Oceans’ datasets: ECCO_50 yr
61 (1949/01–2003/01, sampling at 10 days) and ECCO_kf080i
62 (1993/01–2020/3, sampling at 1 day). Those datasets are shown in Supplementary Fig.
1.
To standardize the sampling intervals of the records, we down-sampled all records to 1 yr, and to avoid aliasing effects in this down-sampling process, a low-pass filter (with a cut-off frequency fc = 0.5 cpy) was used prior to down-sampling.
Note that although the theoretical amplitudes of the 8.85 yr and 9.3 yr zonal tides are quite small (only ~2 μs for the 9.3 yr tide and <1 μs for the 8.85 yr tide) and far less than the background noise level of the ΔLOD time series, they were removed from this ΔLOD record based on a given model63 to avoid the effects of some well-known signals on the target ~8 yr period band. The
dΔLOD/d
t was obtained by a classical discrete numerical derivation algorithm, i.e.,
dΔLOD(
ti)/d
t = [ΔLOD(
ti+1) − ΔLOD(
ti)]/Δ
t.
Then, in Supplementary Information where they described "The execution of the stabilized AR-z spectrum", it's written that the Monte Carlo method was introduced to further suppress the error estimation.
In addition, when comparing the LOD data yearly averages curve in Fig. 1c with the same plot in Supplementary Fig. 1c, they evidently don't match, with the plot in the actual paper body most likely being the 'wrong' one, because the similar plot to Suppl. Fig. 1c is found in Extended Data Fig. 7 to the first 'multidecadal' study.
And that's not taking into account the plots already shown in this thread where it's obvious that, looking at the yearly averages, the Earth wasn't spinning faster in early 2000s than it was in 2020 (check the red line in
this plot for example) as the Fig. 1c in the paper indicated.
After seeing all that, I kinda lost further interest to go into more detailed reading of the rest of the paper, and decided to wait for cca 40 more days until complete 62 years of LOD daily data (1962-01-01 - 2023-12-31) would be available online to conduct more thourough Fourier analysis, using possibly a 'sliding time interval' to check for potential time evolution of signal positions, i.e. quasi-periodicities that might change in time as described in the paper below.
Besides, from preliminary analysis of LOD daily data shown in this thread, most dominant periodicity signals were at 1 year and less, except the one of cca 20+ years which in fact might correspond to full solar magnetic field cycle that takes cca 22 years to make a complete round (N pole come back to its 'initial' position, for example).
One 'good' thing that came out of this study though, or at least an interesting one for me, is that it provided LOD yearly averages for period before 1962, where it showed that the Earth was spinning at least as fast, if not even faster, around 1930s as it was last year. FWIW.
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& 
& all the non-binary 'facepalm' emojis Scottie might give us
