EGU General Assembly 2020
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the Creative Commons Attribution 4.0 License.

A daily estimate of phase speed to explore the link between Arctic Amplification and Rossby waves

Jacopo Riboldi, François Lott, Fabio D'Andrea, and Gwendal RIvière
Jacopo Riboldi et al.
  • Laboratoire de Météorologie Dynamique, École Normale Supérieure, Paris, France

Rossby wave activity is intimately related to the day-to-day weather evolution over midlatitudes and to the occurrence of extreme events. Global warming trends may also affect their characteristics: for example, it has been hypothesized that Arctic warming with respect to midlatitudes, known as Arctic Amplification, may lead to a reduction in the speed of Rossby waves, to more frequent atmospheric blocking and to extreme temperature events over midlatitudes. Testing this hypothesis requires an estimate of the evolution and of the variability of phase speed in recent decades and in climate model simulations. However, measuring the phase speed of the global Rossby wave pattern is a complex task, as the midlatitude flow consists of a superposition of waves of different nature (e.g., planetary vs synoptic) across a broad range of wavenumbers and frequencies.

We propose here a framework, based on spectral analysis, to understand the variability of Rossby wave characteristics in reanalysis and their possible future changes. A novel, daily climatology of wave spectra based on gridded upper-level wind data is employed to study the evolution of Rossby wave phase speed over the Northern Hemisphere between March 1979 and November 2018. A global estimate of phase speed is obtained by doing a weighted average of the phase speed of each wave, with the associated spectral coefficients as weights.

Several insights about the drivers of phase speed variability at different time scales and their link with extreme temperature events can be gained from this diagnostic. 1) The occurrence of low phase speeds over Northern Hemisphere midlatitudes is related to a poleward displacement of blocking frequency maxima; conversely, the occurrence of high phase speed is related to blocking occurring at lower latitudes than usual. 2) Periods of low phase speed are associated with the occurrence of anomalous temperatures over Northern Hemisphere midlatitudes in winter, while this linkage is weaker during boreal summer. 3) No significant trend in phase speed has been observed during recent decades, despite the presence of Arctic Amplification. The absence of trend in phase speed is consistent with the evolution of the meridional geopotential gradient during recent decades. On the other hand, the high temporal resolution of the phase speed metric highlights the intraseasonal and interannual variability of Rossby wave propagation and points to 2009/10 as an extreme winter characterized by particularly low phase speed.

How to cite: Riboldi, J., Lott, F., D'Andrea, F., and RIvière, G.: A daily estimate of phase speed to explore the link between Arctic Amplification and Rossby waves, EGU General Assembly 2020, Online, 4–8 May 2020, EGU2020-9212,, 2020.


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displays version 1 – uploaded on 24 Apr 2020
  • AC1: Hyperlinks, Jacopo Riboldi, 24 Apr 2020

    The hyperlinks in the presentation do not work properly in preview mode, but only if the presentation is downloaded and opened. Sorry for this unexpected inconvenience.

  • CC1: Comment on EGU2020-9212, Olivia Martius, 27 Apr 2020

    Hi Jacopo

    Great results! Your composites for the high phase speeds seem to indicate a tropical influence over the Pacfic and seem to point to extratropical variablity (fewer Greenland blocks?) over the Atlantic.

    How exactly do you calculate cp?



    • AC2: Reply to Olivia: high phase speed events + clarifications about phase speed metric computation, Jacopo Riboldi, 28 Apr 2020

      Thanks a lot Olivia! We are also excited for the insights that this phase speed diagnostic is bringing.

      The results of the study, outlined in the presentation, not only suggest that high phase speed events are associated with reduced blocking activity at the end of the storm tracks, but highlight at the same time enhanced blocking occurrence at low latitudes (35-50°N). One can see a hint of that over the Pacific (see the slide about blocking), but this effect is very visible in the Atlantic too when employing the blocking diagnostic by Woolings et al. (2018), based on 500hPa geopotential anomalies rather than PV anomalies (it is harder to meet the -1.3PVU anomaly threshold at low latitudes). Maybe these low-latitude blocking can maybe accelerate the polar jet from the equatorward side: we are currently working on this hypothesis.

      About the phase speed computation, we spectrally decompose the meridional wind field in a series of (wavenumber,phase speed) harmonics, following Randel and Held (1991). The decomposition is done first along each latitude circle and then averaged. Assuming that the evolution of the flow over a given time period corresponds to the combination of these harmonics (superposition principle), a global value of phase speed can be obtained by averaging the speed of each wave while using the spectral power associated to each harmonic as a weight. For example, to simplify, let's imagine there are only two harmonics in the flow: a first one (n1=5, cp1=7m/s) with a spectral coefficient of 0.75 and a second one (n2=3, cp2=-5m/s) with a spectral coefficient of 0.5. In this very idealized setup, the global phase speed of the pattern would be

      c=[(7m/s)•0.75 + (-5m/s)•0.5]/(0.75+0.5)=2.2 m/s

      In case two waves have the exact same spectral coefficient, same wavenumbers and opposite phase speed (e.g., n1=n2=3, cp1=+5m/s, cp2=-5m/s), the result would be zero. This is also consistent with the superposition principle, as a stationary (standing) wave can be described as the interference of two equal waves, one propagating and one counterpropagating, in the same medium.

      Now, the hemishperic flow evolution is much more complex. We choose then a broad range of harmonics not to exclude a-priori any wave: in the study we do such a weighted average considering all the harmonics between n=1 and 15 and phase speed between -30m/s and +30m/s (we tried different ranges, but most of the power sits in this range and results do not change substantially). If a certain harmonic is not present at a given time, the associated low values of spectral coefficient make sure that it gets a low weight and does not impact the global phase speed value. We were satisfied to notice that this metric faithfully represents both the interannual and intraseasonal variability of midlatitude Rossby wave propagation. For instance, notice in slide 4 that the two DJF seasons with lowest seasonally averaged phase speed are 2009/10 and 1984/85, which featured a sudden stratospheric warming and particularly negative Arctic Oscillation values (and extreme cold waves over midlatitudes).