Based on the previous post on applying Dynamic Time Warping as a metric for LTE modeling of oceanic indices, it makes sense to apply the metric to the QBO model of atmospheric winds. A characteristic of QBO data is the sharp transitions of wind reversals. As described previously, DTW allows a fit to adjust the alignment between model and data without incurring a potential over-fitting penalty that a conventional correlation coefficient will often lead to.
For QBO fitting, the approach was to initially use the DTW metric to guide the optimization, and then switch to a correlation coefficient when the fitting process settled into an asymptotic regime. The objective is to continue to cross-validate the published model’s predictive power as described in Chapter 11 of Mathematical Geoenergy. The result is shown below for the post-Y2K cross-validation (assuming a 1960-2000 training interval) of the 30 hPa QBO time series.
A couple of observations can be noted. The first is that a long-range periodicity can be seen in the applied tidal forcing, revealing a 45 year repeat cycle of 19 QBO periods. One needs to study the middle panel above to pick the pattern out, but once observed it’s very evident to the eye. This value is computed by applying a side-band-aliasing modulo calculation as follows:
19 / (365.242 / 27.212 mod 1) = 45.01
where 27.212 days is the lunar Draconic cycle. At some point it may make sense to refer to this standard as the 45/19 QBO model, where 45/19 is the “quasi-biennial” period.
Secondly, note how the so-called QBO disruptions of the 2015/2016 & 2019/2020 winters are accommodated in the model extrapolation. The timing of the two disruptions in the upper panel are indicated by blue down-arrows, yet the model does not seem especially contrary to the data. It maintains the general phase across the disruption events so the “anomalous” nature reported in several papers does not seem out of the ordinary.
Consider two possibilities to further argue both for-or-against in classifying these disruptions as anomalies:
- The understanding of QBO is limited so that what seemingly is an anomaly according to the current model, ceases to become an anomaly in a more mature model of the behavior. That would be like explaining the existence of Neptune by the anomalous orbit of Uranus. In a more comprehensive model, the anomaly is now absorbed into the updated orbit.
- There are other observations, say at different altitudes, that are out of the ordinary, or that the behavior observed is actually an external transient. That would be similar to a tsunami or hurricane temporarily impacting tidal gauge measurements. In that case, the transient doesn’t impact the long term coherence of the tidal cycles.
Possible that both cases can be partly true. As for #2, consider that the QBO data evaluated above ends before 2022. The usual site for QBO data was stored at FU Berlin, and I wasn’t aware that it had been transferred to Karlsruhe Institute of Technology until after doing the model fit above. So that means that a little more than 2 years are available for further cross-validation. The extrapolation of the same fit is shown below.
The agreement maintains beyond the previous end-point, suggesting that the disruption did not interfere with the long-term phase coherency. Yet, the tidal forcing model is not close to being accepted as a consensus model either, so there was never any consideration of other QBO researchers judging the disruption in the context of the model described here. To me the disruption doesn’t appear to be any more anomalous than the poorer fit near the year 2010. That is the point of #1 — without a valid model to judge against, what is considered an anomaly?
As a further cross-validation example, the chart below uses a severely restricted training interval, spanning only the years 1960 to 1975.
From this perspective, considering the possibility of some zealous over-fitting, it becomes more difficult to judge which cross-validation regions should be considered anomalous.
Consider a separate QBO time-series corresponding to the 50 hPa altitude, trained for 1960-1975 :
Here, the anomalies at 2015/2016 and 2019/2020 are even less striking. as other regions fare worse.
Next, QBO at 70 hPa altitude
Higher in altitude QBO at 15 hPa
A potential approach is to cross-validate the set of QBO time-series collectively, which would help isolate the invariant parameters of the model.
To be presented at next month’s EGU
“Driving of the QBO by gravity waves and global-scale waves: a comparison between satellite data and reanalyses” by M. Ern https://meetingorganizer.copernicus.org/EGU24/EGU24-3929.html
“The quasi-biennial oscillation (QBO) is the dominant mode of atmospheric variability in the tropical stratosphere. It has effects on the weather and climate in the tropics and the extratropics. The QBO is a wave-driven circulation pattern of alternating easterly and westerly winds that propagate downward with time. Climate models have problems in simulating a realistic QBO because of problems in simulating the QBO wave driving in a realistic way. Both mesoscale gravity waves and global-scale tropical waves contribute to the wave driving of the QBO, but the relative contribution of the different wave types is not well known.”
My take: the driving gravity waves are synced by the lunar tidal cycle — how much more parsimony (i.e. the least complex realistic explanation) is required?
https://acp.copernicus.org/articles/24/2465/2024/
Title: “Aeolus wind lidar observations of the 2019/2020 quasi-biennial oscillation disruption with comparison to radiosondes and reanalysis”
“The QBO disruption of 2019/2020 consisted of a weakening of the westerly winds in the lower stratosphere and the development of an easterly jet around an altitude of 22 km. This study has explored a disparity in the timing of the onset of this easterly jet between Aeolus observations and ERA5 and found differences in TTL winds and Kelvin wave variance which might help to explain this.”
“Some global climate models infer an increased frequency of disruptions as a consequence of climate change (Anstey et al., 2021); however, with just two such disruptions so far, there is a limited sample size of events to study. It may be that disruptions either are part of or have become part of the natural cycle of the QBO on longer timescales.“
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The 45 year repeat period is not exact. The precise conditions do not replicate and certainly disruptions can be misidentified as part of the natural cycle that just haven’t been observed previously.
The above chart is an overfit to the 1965 to 1980 interval. To the right in yellow focus in on the regions that are supposedly anomalous according to the blue arrows.
The complement of the above using DTW
Not much differentiates apart from the LTE modulation at the bottom. The annual and impulse modifications at the top are small in comparison to the main signal >100
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