Circumglobal Rossby wave patterns during boreal winter highlighted by space–time spectral analysis

Riboldi, Jacopo; Rousi, Efi; D'Andrea, Fabio; Rivière, Gwendal; Lott, François

doi:https://doi.org/10.5194/wcd-3-449-2022

Articles | Volume 3, issue 2

https://doi.org/10.5194/wcd-3-449-2022

© Author(s) 2022. This work is distributed under
the Creative Commons Attribution 4.0 License.

https://doi.org/10.5194/wcd-3-449-2022

© Author(s) 2022. This work is distributed under
the Creative Commons Attribution 4.0 License.

Articles | Volume 3, issue 2

Research article

|

08 Apr 2022

Research article |

| 08 Apr 2022

Circumglobal Rossby wave patterns during boreal winter highlighted by space–time spectral analysis

Jacopo Riboldi, Efi Rousi, Fabio D'Andrea, Gwendal Rivière, and François Lott

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Final revised paper (published on 08 Apr 2022)
Supplement to the final revised paper
Preprint (discussion started on 21 Sep 2021)
Supplement to the preprint

Interactive discussion

Status: closed

RC1:
'Comment on wcd-2021-59', Anonymous Referee #1, 22 Oct 2021
General Comments:

This study explores the boreal winter midlatitude circulation features that emerge from the daily variability modes of the upper-tropospheric zonal wavenumber - phase speed spectrum. The authors focus on the origin and evolution of hemispheric-scale Rossby wave patterns that may characterize the first two modes and test hypotheses regarding the role of tropical convection, jet stream location, and low-level baroclinicity. The analyses are novel and valuable outcomes can be drawn from them. I have a few concerns regarding the basic rationale and scope of this study and some parts of the text require technical clarifications. I recommend a major revision of this manuscript and I hope that the specific remarks listed below will be helpful in this regard.

Specific Comments:

The main goal of this study is to investigate the origin and propagation of CRWPs. In some parts of the introduction and the conclusions, it appears that another objective is to showcase the potential of the two-dimensional spectral analysis on the upper-tropospheric circulation. In the end, I am left wondering what is the exact scope of this study and what should be the take-home message for the readers. Perhaps, my confusion lies in the fact that the introduction (lines 14-67) touches on many themes and not all of them are directly relevant to the analyses. Could the authors clarify in the text the research questions adressed in this study and the respective conclusions?

Following up on the previous comment, if the motivation of the study is to investigate and better understand CRWPs, then I find the employed methodology rather indirect. Instead of constructing daily n-Cp Fourier spectra of the midlatitudes, doing an EOF analysis on these spectra, and focusing on periods when the PC of the leading modes is large hoping that the composite patterns will exhibit long-lived and/or circumglobal wave patterns, why not directly diagnose CRWP events in the wind field by simply requiring that the RWP amplitude (section 2.2.2) is large enough in a large area for e.g. 5 consecutive days? The second option would result in composite maps that are easier to interpret and actually contain the wave patterns of interest. With the employed methodology, not all the observed CRWP events are necessarily included in the top PCs of EOF1 and EOF2, while these two leading modes may also contain days with no CRWPs, thus "contaminating" the lag-composite analyses with flow configurations beyond the authors' interest.

Given that the wavenumber-frequency spectra are based on the spectral coefficients (discrete Fourier Transform), writing down their equation would perhaps be more relevant than eq.1 (inverse discrete Fourier Transform). In addition, something seems to be off with the notation in eq.1. Since this is basically a 2D inverse DFT, I would expect the arguments of the spectral coefficient to be [n,j] rather than [n,ω_j] (thus matching the two summation indices), the exponents to be like: exp[i2π(λ*n/N_L + t*j/N_T)], and ω_j to be equal to -2πj/N_T.

Is the methodology of constructing the wavenumber - phase speed spectra exactly the same as the one presented in Riboldi et al. (2019)? If so, this might be a useful remark for some readers. In any case, some things are not clearly described in the text. I am not sure what is the mathematical formulation behind the phrases: "smoothed 10 times in frequency using a three-point window" (line 103) and "The periodogram is interpolated along lines of constant phase speed" (line 104)? All the results are based on these steps, so it would greatly help the reader if they are described clearly with minimal jargon.

Why do the days of top 15% PC1/PC2 (that is, up to 30% of all winter days) are included in the CRWP1/CRWP2 lists of events? Doesn't this result in too many events, given that the first 2 EOFs only explain 22.5% of the total variance? In this regard, it is perhaps no surprise that some days are found in both the CRWP1 and CRWP2 events (e.g. 16-24 January 1987, 25-26 December 2014) and that the typical duration of the events (as reported in the Supplement) is much larger that what the evolution in Fig.5 suggests. I presume that taking the top 5% or 10% PC days in each case would produce lists of less events but more indicative(?) of the respective EOF modes. Can the authors elaborate on their rationale behind the choice of this threshold and comment on the sensitivity of the results to its exact value?

There are some causal statements in the text that - although they appear plausible at first sight - they cannot really be justified by the presented analyses. For example, in lines 267-268 it is stated that, according to Fig.6a, the strong convection is the source of negative vorticity anomaly at upper-levels a few thousand kilometers to the east. Looking at pentad-mean composites doesn't really allow such a statement and the fact that there is a synoptic-scale negative height anomaly in the area (Fig.6a) and at times an active MJO does not correspond to OLR anomalies (line 298) makes me even more hesistant to draw "causal chains" here. Similarly, line 327 reads that the North Atlantic anticyclone development is preceded by anomalously strong meridional heat fluxes over N. America (Fig.9). The problem here is that the significant patterns are rather weak/small and the plotting (contouring choice) may obscure the real sequence of events. Maybe adding the complete series of daily-mean lag composites in the Supplement would shed light on such aspects.

Technical Corrections:

The abstract ends rather abruptly. It would be worth and nice to add a sentence with the take-home messages of this study.

Line 14: "Most of the weather systems ... have their dynamical origin ..."

Line 16: "... form and track across those regions ..."

Line 18: "... displacements of the jet ..."

Line 20: "... substantially across seasons and years (Grise et al. ..."

Lines 36-37: Is this really "another" circulation pattern? The phenomena mentioned in lines 32-35 may also feature the zonal propagation of RWPs.

Lines 37-38: The readers should clearly visualize in their minds what exactly are the CRWPs that this study focuses on. The sentence "CRWPs can occur if the large-scale flow configuration is conducive to the zonal propagation of RWPs over long distances" explains when do CRWPs occur; not what they are. So, how do they look like in e.g. a snapshot of the upper-tropospheric wind field? Or is this a concept attached to longer-term means?

Lines 58-60: In these lines the benefit of the spectral analysis is briefly mentioned. Can the authors elaborate a bit more on which frameworks make "a-priori assumptions about the existence of a background flow"? Listing a couple of specific examples upon which the new framework can make a difference would better communicate the significance of this study.

Line 78: What is meant by "rapid module"?

Line 89: Do the authors mean "... the annual cycle of meridional wind..."?

Line 105: The phase speed spectra should also be a function of time, right?

Line 110: Which coordinate change is meant here?

Lines 119-120: What is meant by "averaging over different latitudes"? The approach where spectra of different latitudes are averaged, or the approach where wind anomalies are averaged over different latitudes?

Line 121: Why is a spectrum attributed to every single day? The temporal resolution is 6-hourly, so I would expect 4 global estimates S(n,cp) per day. Is there a daily averaging step that I missed?

Fig.1: Shouldn't the units be [(m/s)^2/Δc]?

Line 205: The monopole structure in EOF1 (Fig.2a) suggests variability in the amplitude of Rossby waves (with no apparent shift in wavenumber and phase speed) as shown in Fig.4a,b. Is that what the authors also imply by "enhancement of such harmonics"?

Line 214: "... wavenumber co-vary with an ..."

Line 257: "Interestingly, both PC1 and PC2 events are ..."

Lines 281-283: The procedure to assess the stat. significance of MJO amplitudes is not clear to me. Can the authors reformulate this sentence?

Figs.4,5,6,9,10: The colorbar labels are particularly small and hard to read. I guess a 50% (or more, for Fig.5) increase in the font would suffice.

Figs.4,5: Do the black contours depict 250hPa PV as in Fig. 10?

Fig.6: In lines 384-385 the authors hypothesize an equatorward shift of the jet for PC2 events. Adding contours for negative zonal wind anomalies might help evaluate this hypothesis.

Lines 308-309: The term "release of baroclinicity" doesn't sound very meaningful. Besides, should the authors briefly describe the Ambaum and Novak (2014) hypothesis, given that big part of this work (section 4.2) is about to test it? Finally, this hypothesis doesn't really talk about a "hemispheric-scale discharge of baroclinicity" as implied in lines 337-338; it focuses on the N. Atlantic storm track.

Lines 310, 315: Why is a 7-day averaging employed here instead of a 5-day one as before? Why is stat. significance assessed based on the 95th percentile instead of the 90th one as before? This inconsistency is somewhat disconcerting and hinders the comparison of Figs. 6 and 9. The maps in these 2 figures could also have the same projection for consistency.

Lines 388-390: Why would there be a problem conducting this spectral analysis in the summer season? Weaker storm tracks may also experience distinct modes of variability. Is there a technical issue I miss?
Citation: https://doi.org/10.5194/wcd-2021-59-RC1
- AC2: 'Reply on RC1', Jacopo Riboldi, 11 Jan 2022
  
  Please see the attached PDF.
  
  Citation: https://doi.org/10.5194/wcd-2021-59-AC2
RC2:
'Comment on wcd-2021-59', Anonymous Referee #2, 22 Oct 2021

This work aims to asses the main observed modes of variability and origins of Rossby wave packets (RWP) in the northern hemisphere winter.

It uses a spectral decomposition method of the upper-level circulation at each latitude to retrieve the most dominant modes of variability in the space of zonal wave number and phase speed. The first two modes are found to be associated with RWPs, and so these are used for further analysis to identify regressions with diagnostics of blocking, large-scale patterns and wave propagation.

The authors also investigate the possible origins of the wavetrains characterizing both modes. They find a likely link between the first mode and tropical convection and the MJO, and elucidate that the second mode is related to extratropical origins, though this link is less clear. They point out other interesting features, such as that both modes exhibit higher synoptic eddy activity and subtropical jet extension that allows the hemispheric wave propagation, which allow a more complete picture of how these modes come about.

The paper is clearly written and conclusions well argued. The results contribute significantly to the field of eddy-mean flow interaction and teleconnections in the northern hemisphere.

I only have minor comments after which I recommend it for publication.

General minor points:

- what is the sensitivity to the windows chosen for the spectral decomposition, and same for the thresholds chosen to isolate PC extremes?

- As I understand it, the authors use the EOFs of the spectral decomposition as the basis for their composites and regressions, because they want to analyse regimes based on the different wavenumbers/phase speeds, groups of which we know have different characteristics (e.g., planetary waves vs synoptioc waves). I like that the analysis is based on reducing dimensionality for physical reasons, but I wonder whether some of the composites, e.g. Fig. 9, would yield a less noisy time series if the v*T* and baroclinicity were directly related to the RWP? It seems that especially Fig. 8(d-f) yield consistent patterns, but with the spread being so large, the authors conclude that these consistent changes in baroclinicity are not significant. â¨At least comment outlining the disadvantages of this technique would be useful.

- the Figure labels could be enlargedâ¨.

Specific clarifications

- L20: between one year or the other - you mean inter-annually?

- The next three points aim to differentiate between the two types of mechanisms more clearly:

    - L22: single storm track (internal mechanism)…between the two (hemispheric mechanisms [or something like that])

    - L23: AN internal mechanism

    - L27: [new line] On the other hand… storm tracks (hemispheric mechanism)

- L89: please state how the smoothing was performed

- Eq. 5: it may be worth adding a comment that vT is proportional to the vertical E-vector component and will also be investigated.

- L104: "interpolated along lines of constant phase speed” What exactly do you mean?

- L186: it may be worth including Orlanski (1998) as a reference here, for the interpretation of the horizontal E vectors (https://journals.ametsoc.org/view/journals/atsc/55/16/1520-0469_1998_055_2577_pdost_2.0.co_2.xml)

- Fig. 4: I couldn’t see any green arrows

Citation: https://doi.org/10.5194/wcd-2021-59-RC2
- AC3: 'Reply on RC2', Jacopo Riboldi, 11 Jan 2022
  
  Please see the attached PDF.
  
  Citation: https://doi.org/10.5194/wcd-2021-59-AC3
RC3:
'Comment on wcd-2021-59', Anonymous Referee #3, 15 Nov 2021

The comment was uploaded in the form of a supplement: https://wcd.copernicus.org/preprints/wcd-2021-59/wcd-2021-59-RC3-supplement.pdf

Citation: https://doi.org/10.5194/wcd-2021-59-RC3
- AC4: 'Reply on RC3', Jacopo Riboldi, 11 Jan 2022
  
  Please see the attached PDF.
  
  Citation: https://doi.org/10.5194/wcd-2021-59-AC4
EC1:
'Comment on wcd-2021-59', Nili Harnik, 24 Nov 2021

I would like to add another comment to those raised by the reviewers:
The authors discuss in their introduction, among other things the Circumglobal Teleconnection Patterns (CTP) of Branstator (2002), as well as quasi resonant modes, both of which are stationary circumglobal wave trains. In the context of extreme events the stationarity is often a major factor in increasing the impact on a given location. In addition, the CTPs are diagnosed using monthly mean wind anomalies (Branstator et al, 2002), but it has been shown that on daily time scales they are comprised of localized wave packets with a near-zero phase speed but non zero group speed so that when averaging over a whole month they yield a stationary circumbglobal wave anomaly (c.f. Harnik et al, 2016 and some references therien).
On the other hand, the analysis (by construction) finds non-stationary waves with slow, but non zero phase speeds. While the phase speeds found are slow, on the order of 5m/sec. this means a propagation of around 3000 km in a week, which is much more than is found for the CTPs (see Harnik et al, 2016). Given this, is it possible that the main patterns found are not the CTPs defined by Branstator nor the waves studies in the quasi-resonance papers, but rather they are slow eastward propagating, zonally elongated wave trains?
Harnik, N., G. Messori, R. Caballero, and S. B. Feldstein (2016), The Circumglobal North American wave pattern and its relation to cold events in eastern North America, Geophys. Res. Lett., 43, 11,015–11,023, doi:10.1002/2016GL070760.

Citation: https://doi.org/10.5194/wcd-2021-59-EC1
- AC1:
  'Reply on EC1', Jacopo Riboldi, 10 Jan 2022
  Reply to Editor’s comment (https://doi.org/10.5194/wcd-2021-59-EC1)
  First of all, we would like to thank the editor for the comment and for the interest shown in the study. The comment inspired two thoughts, which will result in consequent modifications of the manuscript:
  We do not think that excluding the c_p=0m/s line would substantially affect the results, as even stationary features such as atmospheric blocking often exhibit a slow eastward or westward propagation, especially in winter when the background flow is particularly strong. The fact that periodograms are computed over a broad range of latitudes before averaging can attenuate the loss of information due to wind anomalies that happen to be moving with c_p< 1m/s on selected latitude circles (we describe in the newly added Supplementary text S2 why this is the case). Also, it is possible for waves with non-zero phase speed to still yield a circumglobal wave-like anomaly in the monthly mean: an example are recurring Rossby wave patterns (which propagate, but tend to occur at fixed longitudes; Roethlisberger et al. 2019). Instantaneous but strong wave-shaped anomalies occurring over a few days in a month can also be highlighted by the monthly mean. However, the absence of an explicit treatment of stationary waves is definitely a limitation of the employed methodology and we will comment on that in detail in a new Discussion section, added during the revision.
  
  More in general, the degree of zonal propagation of Circumglobal Rossby Wave Patterns (CRWPs) is difficult to quantify and the literature does not provide many hints in this regard. Branstator (2002), for instance, did not explicitly comment on the stationarity or propagation of their wave pattern, which is retrieved from an EOF analysis of monthly mean fields. Watanabe (2004) based their conclusions on low-pass filtered wind anomalies to remove transient disturbances although they pointed out the presence of rapid transient in the daily fields (“Propagation of wave packets, but not the wave itself, on the Asian jet is quite evident in the daily anomalies, indicating that the Rossby wave argument appears relevant for individual NAO events as well, although the anomalies are not stationary anymore”, from the same paper). The work by Feldstein and Dayan (2008) and Harnik et al. (2016) did not quantify explicitly the phase speed of the wave patterns thereby identified. Their observation of near-zero phase speed was actually derived from the visual inspection of lagged composites computed by averaging over several events. However, the compositing procedure can implicitly act as a low-pass filter for the transients and small scales, making difficult to ascertain the full range of phase speeds involved. The final section of Fragkoulidis et al. (2018) features an extended discussion of the problems that temporal and spatial averaging can originate when trying to diagnose CRWPs and circumglobal waveguides. On the other hand, the spectral approach adopted in the paper does not involve any filtering and allows to obtain a global fingerprint of the slowly- as well as of the rapidly-propagating harmonics involved in each wave pattern. This methodological difference can explain, at least partly, the not-so-slow phase speeds involved in CRWP1 and CRWP2 events. A discussion of these methodological issues and a broader comparison of the results will be added to the revised manuscript to clarify analogies and differences of the identified CRWPs with others discussed in previous studies.
  
  Bibliography
  Feldstein, S.B. and Dayan, U. (2008), Circumglobal teleconnections and wave packets associated with Israeli winter precipitation. Q.J.R. Meteorol. Soc., 134: 455-467. https://doi.org/10.1002/qj.225
  Fragkoulidis, G., Wirth, V., Bossmann, P. and Fink, A.H. (2018), Linking Northern Hemisphere temperature extremes to Rossby wave packets. Q.J.R. Meteorol. Soc., 144: 553-566. https://doi.org/10.1002/qj.3228
  Harnik, N., Messori, G., Caballero, R., and Feldstein, S. B. (2016), “The Circumglobal North American wave pattern and its relation to cold events in eastern North America”, Geophys. Res. Lett., 43, 11,015– 11,023, doi:10.1002/2016GL070760.
  Röthlisberger, M. Frossard, L., Bosart, L.F., Keyser, D., and Martius, O., " Recurrent Synoptic-Scale Rossby Wave Patterns and Their Effect on the Persistence of Cold and Hot Spells", J. Climate 32 (2019): 3207-3226, https://doi.org/10.1175/JCLI-D-18-0664.1
  Watanabe, M. (2004). Asian Jet Waveguide and a Downstream Extension of the North Atlantic Oscillation, J. Climate, 17, 4674-4691 https://doi.org/10.1175/JCLI-3228.1
  White, R. H., Kornhuber, K., Martius, O., and Wirth, V (2021), From Atmospheric Waves to Heatwaves: A Waveguide Perspective for Understanding and Predicting Concurrent, Persistent and Extreme Extratropical Weather, Bull. Amer. Meteor. Soc., pp. 1–35, https://doi.org/10.1175/BAMS-D-21-0170.1
  Wirth, V. (2020), Waveguidability of idealized midlatitude jets and the limitations of ray tracing theory, Weather Clim. Dynam., 1, 111–125, https://doi.org/10.5194/wcd-1-111-2020
  
  Citation: https://doi.org/10.5194/wcd-2021-59-AC1

Peer review completion

AR: Author's response | RR: Referee report | ED: Editor decision | EF: Editorial file upload

AR by Jacopo Riboldi on behalf of the Authors (10 Feb 2022) Author's response Author's tracked changes Manuscript

ED: Referee Nomination & Report Request started (19 Feb 2022) by Nili Harnik

RR by Anonymous Referee #2 (25 Feb 2022)

RR by Anonymous Referee #3 (27 Feb 2022)

RR by Anonymous Referee #1 (06 Mar 2022)

ED: Publish subject to technical corrections (08 Mar 2022) by Nili Harnik

AR by Jacopo Riboldi on behalf of the Authors (09 Mar 2022) Manuscript

Short summary

A revisited space and time spectral decomposition allows us to determine which harmonics dominate the upper-tropospheric flow evolution over a given time period as well as their propagation. This approach is used to identify Rossby wave patterns with a circumglobal extent, affecting weather evolution over different Northern Hemisphere regions. The results cast light on the processes originating and supporting these wave patterns, advocating at the same time for the usefulness of the technique.