the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 30 Jan 2026
The six-year cycle in atmospheric angular momentum: robustness, zonal-wind structure, and implications for Earth rotation
Abstract. Variability near a 6-yr period has been reported in the length of day, motions within the Earth’s fluid core, several climatic parameters, and atmospheric angular momentum. Here we demonstrate the robustness of a quasi-6-yr oscillation in atmospheric angular momentum using several independent atmospheric reanalysis products over 1980–2020. This signal is highly significant, consistent across datasets, and accounts for up to about 25 % of atmospheric angular momentum variance at interannual time scales. Its expression in the atmospheric zonal wind circulation exhibits a coherent vertical structure throughout the troposphere, with maximum amplitudes near the tropopause in the tropical belt. In addition, the 6-yr oscillation in zonal winds is in phase across from southern to northern latitudes. This structure distinguishes the 6-yr signal from the annual cycle and from ENSO-related variability, and points to a large-scale, organized component of the atmospheric circulation, consistent with alternating phases of weaker and stronger atmospheric super-rotation relative to the solid Earth. While the origin of the length-of-day 6-yr cycle is relatively well established and attributed to exchange of angular momentum from the core to the mantle, the process underlying the 6-yr variability in the zonal wind circulation remains to be elucidated.
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Status: open (until 07 May 2026)
- RC1: 'Comment on egusphere-2026-82', Anonymous Referee #1, 09 Apr 2026 reply
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Pfeffer et al discuss the evidence for 6 year oscillations in the atmospheric angular momentum, winds and length of day. The topic is of interest to readers of ESD and is an area where significant questions remain so the manuscript is very appropriate for this journal. The 6 year variability shown in this study is intriguing, not least because it appears in atmospheric winds and is negatively correlated with length of day data (assuming I have understood the paper correctly). This is very different to interannual variability in LOD and AAM in general suggests that there must be a third entity to complete angular momentum conservation and this is suggested to be the fluid outer core of the Earth. The paper does various filtering and compares to ENSO variability - an obvious possible culprit given its known connections to length of day. However, I have two main criticisms. Some of the satistical analyses and figures are not very convincing and very similar versions of some of the results have been published elsewhere (e.g. Cazaneve et al 2025, Pfeffer et al 2023). I therefore recommend major revision after the arguments are strengthened and it is made clear what is really novel here.
MAJOR POINTS:
A) A number of papers have been published in recent years that show diagnostics of the 6 year variability. For example Cazaneve et al 2025 and Pfeffer et al 2023. These previous papers already show some of the results presented here. For example, that the 6 year variations in LOD appear to be anticorrelated with the atmopsheric angular momentum (Fig.6) and the results in Fig.8 on solid Earth dynamics are similar to previously published results. I think there is a need to establish what is novel and to focus on that.
B) The authors use an ENSO index that depends on a range of indicators and this could be somewhat circular when later comparing against the atmospheric winds etc. To check that this is not the case they should recalculate Fig.4 and Fig.5 using the more commonly used Nino3.4 index - does it give the same results?
C) There is significant amplitude change with time in Fig.2 and along with the preselection of 6 year variations using the filter and the fact earlier periods show less sign of 6 year cycles (L232), this all makes me worried that the apparent 6 year cycles you get here are really a produce of one short time interval when single variability events such as the El Nino of 1997/98 happen to alias onto 6 year variations. Can you show that doing a seperate analysis of the first and second half of the record in Fig.1 and 2 and omitting the large El Nino of 1997-1998 gives similar spectra and that Fig.5 looks the same in both halves of the record? I think this is important if the claims are to be convincing.
D) Fig.3, L406. This is not very convincing of a stable cycle as the latitude varies greatly and could easily be generated by aliasing of variations onto the 6 year filter timescale. Similarly, Fig.4 suggests the 6y cycles occur on the edge of, or near to ENSO variations, which could be an indication of variability in the ENSO cycle that happens to project onto 6y periods. Can you first regress out any ENSO variability from the data using the Nino3.4 index or similar and then reproduce this figure as a second panel?
E) L52, L480: I think the authors need to better acknowledge here that it is quite plausible that the 6y cycles could originate in the surface climate and drive the LOD and fluid core variability. After all it is very unlikely that the atmosphere would produce detectable responses in 0.1ms/24h changes in rotation rate whereas the climate system contains much chaotic internal variability on multiyear timescales.
MINOR POINTS:
Fig.1: Is it pure coincidence that the 2 peaks contain the frequencies that differ by a factir of two? Is it possible these are related, or even harmonics?
Fig.1: Are the winds area weighted before averaging? It is important to do that but I did not see it in the description. Also, are the winds deseasonalised to remove the annual cycle first or not?
L138: better to say 'could be related to the solar cycle'. A reference to Abarca Del Rio et al., J. Geodyn., 2003 is also appropriate here.
Please can you add a plot of the full, unfiltered data to Fig.2? If the 6y oscillation is 25% of the variance it should be visible to the eye.
L347: please be claer about what you mean by 'is corrected for AAM' here
L401: Vertical coherence is seen in many other atmospheric variations
Fig.3 shows signs of poleward propagation and the hemispheric symmetry mentioned on L426 is very similar to Scaife et al, Nat. Geosci., 2022 so I think some discussion is needed here.
L403,417: This is an interesting point. Can you emphasize this is very different to what is seen for the total interannual variability of the AAM and LOD?
Fig.8: are the core flow models shown in Fig.6 empirical in nature, if so, are some of these statements circular?