the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Robust poleward jet shifts in idealised baroclinic-wave life-cycle experiments with noisy initial conditions
- 1Meteorological Institute Munich, Ludwig-Maximilians-University, Munich, Germany
- anow at: Institute for Atmospheric and Climate Science, ETH Zurich, Zurich, Switzerland
- 1Meteorological Institute Munich, Ludwig-Maximilians-University, Munich, Germany
- anow at: Institute for Atmospheric and Climate Science, ETH Zurich, Zurich, Switzerland
Abstract. Idealised baroclinic-wave life-cycle experiments are a widely used tool to study fundamental characteristics of mid-latitude baroclinic instability. A typical life-cycle evolves from an initialised baroclinically unstable jet through an exponential growth phase of a particular unstable wave mode, followed by wave breaking during the mature phase, and wave-mean flow interaction driving a jet shift during the decay phase. Many authors distinguish between life-cycles with predominantly anticyclonic (LC1) and cyclonic (LC2) wave breaking and the transition between the two flavours is typically controlled via the strength of cyclonic meridional wind shear in the initial conditions. While baroclinic wave growth has traditionally been triggered via a specified initial perturbation with fixed zonal wave number, this study extends the concept of baroclinic-wave life-cycles by analysing the influence of random initial perturbations without any preferred zonal dependency on the life-cycle evolution. We find that the growth phase shows a robust LC1-LC2 distinction as a function of initialised meridional shear, while a preference for LC1-like characteristics is observed during the decay phase for all life-cycles with non-monochromatic initial perturbations. In particular, the persistent cut-off cyclones that typically form for LC2 initialisations are found to eventually become unstable – the earlier during the life-cycle the stronger the initial noise perturbations. All non-monochromatic life-cycles result in a poleward jet shift in their final state, regardless of the strength of the initial shear. Consistently, anticyclonic wave breaking tends to be predominant during the mature and decay phases, even for LC2 initialisations. Equatorward jet shifts associated with cyclonic wave breaking still exist, although purely as a transient interim state. We show that wave-wave interactions resulting from the initialised random wave spectrum play an important role during all phases of the life-cycle.
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Felix Jäger et al.
Status: final response (author comments only)
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RC1: 'Comment on wcd-2022-30', Dennis Hartmann, 18 Jun 2022
This paper is an interesting contribution to the literature on the impact of baroclinic shear on baroclinic lifecycles. Rather than using a single wavenumber to initialize the experiments, the authors add varying degrees of spatial white noise to the initial state. In cases of weak noise longer wavelengths grow via wave-wave interactions, (2,4,6) in the case of a base wavenumber of 6. These longer wavelengths are able to propagate toward the equator and lead to net poleward momentum flux in the case with large cyclonic barotropic shear (LC2) case as well as the LC1 case without the added cyclonic barotropic shear (LC1). If a high level of noise is added, shorter wavelengths, which are presumably more linearly unstable than wave 6, also develop early in the simulation and appear to break poleward in both the LC1 and LC2 cases. This leads to a situation where an initial stage of poleward wave breaking always occurs, but is always followed by equatorward wave propagation and breaking as the energy cascades to longer wavelengths that can propagate across the barotropic shear to the tropics. This leads one to conclude that equatorward wave propagation, poleward momentum flux, and poleward jet propagation must be a dominant feature of the general circulation, as is required by the global angular momentum balance.
Figure 3 , panels c and g are chosen at a particular time when wavenumber 4 dominates the image of PV. This misled me into thinking that wave 4 was growing by linear instability, which is not the thesis of the paper. Looking at Fig. 6 it is more obvious that this particular time is special. It would be good to note at this point that wave 2 is also evident in Fig. 3g or make some other comments to say that the dominance of wave 4 at this time is just transitory.
This is an interesting contribution and is fairly clearly written, with some exceptions that are noted below on a line-by-line and figure basis.
Comments on text:
Line 99: ‘gradually’
115: Not sure what is meant by the initial phrase “Consistent with the energetics of the systems, “
117: Would a linear analysis of the zonal mean state at this time reveal that the most unstable wavenumber is 4? Is the energy of wave 4 coming from the mean state or WMF interactions?
Fig. 3 in both cases, wavenumber 4 emerges as dominant around day 22-24. Why? It would be good at this point to say that you have picked out a particular time when wave 4 was dominant, and also point out that wavenumber 2 can also be seen at this time in panels C and G. The choice of time makes it look like it is mostly linear growth of wave 4, which is not consistent with the nonlinear theory that is actually the thesis of the paper.
135: Is that because wavenumber 4 (and 2) can propagate toward the equator, while wavenumber 6 cannot in the LC2 state?
138: On first reading, I did not quite get the physical reason for the emergence of wavenumber 4, which seems to be key. I don’t see any reason for a state consisting of wavenumber 0 and 6 to create wavenumber 4 through nonlinear exchange, but if I look back at Fig. 3 panel G, I can see some wavenumber 2. It might help to point that out. Wavenumber 4 can propagate toward the equator and produce an LC1 outcome in the end.
174: If the wave breaking event creates a spectrum of wavenumbers, why is the initial noise so important to the evolution of the flow after the first wave-breaking phase?
Fig. 6 The legend “ Specified wave 4” Is unclear. The other experiment was Specified wave 6, but it was allowed to evolve nonlinearly, whereas the curves for 4 and 3 seem to be extrapolations of their infinitesimal linear growth rates.
Fig. 6 If it is nonlinear wave exchange responsible for the growth of 2 and 4, why is their growth rate independent of the amplitude of wave 6? Their growth looks exponential, like they were linearly unstable.
194: Did you mean to say, “In contrast to experiments with weak noise,” As it is, it confused me. So in a case with white noise initialization, shorter wavelengths grow faster and tend to exhibit LC2 initial evolution, until the larger scales develop, which are able to propagate toward the equator, ending in a poleward jet shift and a more LC1-like final state.
265: One might imagine a region of parameter space where the baroclinic growth of shorter wavelengths would be fast compared to the cascade to longer wavelengths in which the cyclonic state could be maintained by the poleward breaking of these shorter waves. It might also be possible that the shorter waves contribute their energy to a stationary wave, such as in the blocking ridge situation.
Clearly for the general circulation to work, the dominant direction of eddy propagation and breaking must be toward the equator to satisfy the angular momentum balance.
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AC1: 'Reply on RC1', Philip Rupp, 20 Sep 2022
The comment was uploaded in the form of a supplement: https://wcd.copernicus.org/preprints/wcd-2022-30/wcd-2022-30-AC1-supplement.pdf
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AC1: 'Reply on RC1', Philip Rupp, 20 Sep 2022
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RC2: 'Reviewer comment on wcd-2022-30', Anonymous Referee #2, 08 Aug 2022
Eddy life cycle experiments have been used as a framework for understanding eddy-mean flow interactions in the midlatitude atmosphere for decades, as highlighted by the references provided by the authors and a recent review (Maher et al. 2019). In this study, the authors show that the sensitivity of the final jet state to the initial jet state may partly be an artifact of the idealized nature of traditional eddy life cycle experiments. When a single wavenumber is forced, wave breaking is very sensitive to meridional shear: with low shear, waves break anticyclonically, shifting the jet poleward (LC1), while with higher shear, waves tend to break cyclonically, shifting the jet equatorward (LC2).
The authors consider variations on these single wave, or monochromatic, experiments by adding noise of varying levels to excite all wavenumbers. They show that even in the limit of very weak noise, the the final state of LC1 and LC2 lifecycles are quite similar due to secondary wave breaking that occurs after the initial anticyclonic or cyclonic breaking event. The net change is primarily to LC2 cycle, where the second breaking event is anticyclonic, shifting the jet back poleward. Thus the shear has a large impact on the initial wave breaking event, but less so on the final state.
I think these are interesting results which merit publication after the authors consider the following minor revisions. It is remarkable that we are still learning about lifecycle experiments after almost half a century!
General comment
Throughout much of the paper I was concerned about how the results depend on the initial noise. This is to say, with a different realization of the noise, could the evolution of the lifecycle be materially different? This concern was partially addressed by results from 3 member ensembles (in the discussion surrounding Figure 7), but even here, it’s not possible to gauge the variance across the ensemble. I take it that the lifecycles proceed more or less the same way as long as their is some noise in the relevant wave numbers (waves 1-10 or so); even if the most important wavenumber for the secondary breaking event (wave 4) was weakly forced by the noise, nonlinear transfer of energy would invigorate it. But it would be good to establish this early in the paper.
To be constructive, would it be possible to show a few additional experiments (initiated with different noise) in Figure 2. (And possibly Figure 4, which shows the final jet states for the same integrations.) I hope that additional solid lines for the \eta=10^-3 experiments would not overly crowd the figure. If all the low noise experiments look exactly the same, the authors could just state this in the text and alleviate my concern from the start.
Another option would be an additional figure showing that the evolution of key quantities (momentum fluxes, EKE, etc.) follow very similar trajectories for different initializations of noise for all levels of \eta. (Perhaps the variation in noise matter more when \eta is large?) The key is to establish that the difference between lifecycles with different noise realizations is small compared to the difference between the experiments with noise and the monochromatic experiments.
Minor comments by wavenumber12-3. I found this line to be a bit awkward. Consider “… for LC2 initialisations are found to become unstable eventually, with the onset of instability coming sooner for larger noise perturbations.”
28 “flavours, or paradigms, of”
Paragraph at 66: As the noise is the major contribution of the manuscript, it might be nice to explain the gist of it in the text. For instance, you could say that the perturbations are white in space, equally exciting all wavenumbers (on average). Perhaps this could be done at line 77 where the amplitude of the noise is introduced.
74 along the same lines, could you briefly characterize the meaning of parameter \hat{U_s} in the text, referring to the equation number in the appendix.
77 Appendix
90. It was around here that I started worrying whether the realization of the initial noise mattered to the lifecycle. If it does not, a sentence here could put the reader at ease. This could also be discussed in the figure caption.
107 This is just a comment about style, but I find that footnotes almost over emphasize the point, as the reader breaks off the text to get to it. Consider just putting this material in the main text.
138. Could you describe this noise induced wave breaking as a secondary instability? The flow is presumably now stable to wave 6 perturbations, but not others?
142-145. This line seemed to come too early in the text. Please shift it back after Figure 5a is introduced and the result has been established.
167-7. Is this really similar to quasi-linear non-normal growth? That process is rather distinct from nonlinear wave interactions. Please provide more evidence to support this statement.
174. Is “upscale energy cascade” an appropriate way to describe this? Consider “upscale energy transfer” as the flow does not appear to be fully turbulent.
213. What is “In general” meant to signify here. Is this is reference to the fact that different realizations of noise can lead to different behavior? Or does it refer to difference that occur with variations in the shear parameter \hat{U}_s or other qualities of the initial jet state.
218. Same for “typically”.
222 Could you clarify what is meant by “overall net-poleward jet shift periods.” The tendency of anticyclonic breaking to shift the jet poleward should be reflected in the mean state.
232-4 The meaning of this sentence was a bit obscure to me. Do the authors mean that the remarkably sensitivity of monochromatic experiments to \hat{U}_s, which justified the LC1 vs LC2 paradigms, may not be justified with noise? That is, there aren’t really two kinds of wave cycles, but rather a continuum?
236 and 263. Again, consider “upscale energy transfer”
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AC2: 'Reply on RC2', Philip Rupp, 20 Sep 2022
The comment was uploaded in the form of a supplement: https://wcd.copernicus.org/preprints/wcd-2022-30/wcd-2022-30-AC2-supplement.pdf
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AC2: 'Reply on RC2', Philip Rupp, 20 Sep 2022
Felix Jäger et al.
Video supplement
Assets to Jäger et al.: Robust poleward jet shifts in idealised baroclinic-wave life-cycle experiments with noisy initial conditions Felix Jäger, Philip Rupp and Thomas Birner https://doi.org/10.5282/ubm/data.301
Felix Jäger et al.
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