Climatologies of Rossby waves and Streamers – results and perspectives
Cornelia Schwierz, Olivia Martius and Huw C. Davies
Institute for Atmospheric and Climate Science, ETH Zurich, Switzerland,
cornelia.schwierz@env.ethz.ch
The rationale of Rossby wave propagation in the extratropical atmosphere is laid out in terms of the potential
vorticity perspective. It is shown that Rossby waves are best diagnosed along their dynamical waveguide. The
usefulness of a climatology of such waves is demonstrated in a climatological study of extreme precipitation
events on the Alpine southside that are intimately related to the presence of upper-level intrusions that
constitute the manifestation of amplifying and breaking Rossby waves. Comments are made on the complexity
of the wave propagation phenomenon and the open issues regarding their predictability.
1.
Introduction
Rossby waves (RW) are an ubiquitous
feature of planetary- and synoptic-scale flow and
were first described by Rossby (1939, 1940) as
propagating wave disturbances that modify the
zonal flow. By definition RWs exist on the
underlying, instantaneous isentropic potential
vorticity (PV) gradient and their propagation
properties can be derived using the notion of the
so-called “Rossby-wave restoring mechanism” (for
a review on RW theories see Platzmann 1968).
The seat for planetary-scale RWs is provided by
the weak planetary PV-gradient (the β-gradient)
and it has been suggested, that they can for
instance emanate from a tropical wave source
(such as the ENSO heating and vorticity anomaly)
and propagate into the extra-tropics (e.g. Wallace
and Gutzler 1981). Compared to the planetary PVgradient, a significantly stronger PV-gradient exists
in the extratropics. It is localized at the tropopause
(TP) and distinctly confined in both the vertical and
horizontal direction (Fig. 1). In effect, the gradient
forms a narrow band that is co-aligned with the jet
stream at the TP break (Fig. 1) and acts as a
wave-guide for the extratropical RWs. The
supported RWs exhibit shorter, synoptic-scale
wave-lengths ~O(1000km), have different triggers
and constitute an integral part in baroclinic
development.
During their life-cycle RWs amplify to form
elongated tropospheric and stratospheric filaments
(PV streamers) as they break. The amplified waves
and streamers have a multifold influence on the
dynamics of mid-latitude flow: e.g. in their role in
surface cyclone development (Appenzeller and
Davies 1995), the formation of cut-offs and
exchange of stratospheric and tropospheric air
masses (Sprenger and Wernli 2003), the
establishment of modes of inter-annual variability
(Franzke et al. 2004), the transport of dust
aerosols (Sodemann et al. 2005) and in particular
their linkage to high-impact weather, such as
extreme precipitation (Massacand et al. 1998),
flooding (Grazzini and van der Grijn 2002) and
even a sequence of such events (Langland et al.
2002). Hence it is highly desirable to diagnose and
predict these wave signatures (cf. THORPEX
Science Plan).
Fig.1: Example of the instantaneous isentropic PVgradient (shaded, units 10-6 PVU m-1). (a) On the 320-K
isentrope, 2-PVU PV contour and wind speed (contours
50, 70, 80, 90 ms-1) overlaid. (b) South–north cross
section at 30W. Vertical coordinate: θ; PV isolines [1, 2
(bold) 3, 4, 5, 6, 8 PVU]; and 50, 70, 80, 90 ms-1 isotachs
(dashed) overlaid (reproduced from Schwierz et al.
2004).
2.
Diagnosing Rossby
refined Hovmöller diagram
waves
–
a
Traditionally the propagating RWs are
displayed by meridionally averaging a wave proxy
(e.g. meridional wind) in a band encompassing the
jet stream (~35-60° latitude) for every time step
and plotting it in a longitude-time frame (Hovmöller
1949). However as noted earlier, the actual waveguide is aligned with the jet stream which (i) is
seldom oriented strictly zonal and (ii) during RW
amplification (accompanying severe weather) does
exhibit excursions exceeding the pre-defined zonal
band (cf. Fig. 1). An indication of the isentropic
wave signature can be gleaned from Fig.2. A RW
train is present that extends from the Pacific to the
Atlantic and exhibits an amplification at~40W
associated with a developing stratospheric
streamer. It is evident, that the wave is aligned
closely with the isentropic dynamical tropopause
(PV=2 contour), which is used as a proxy for the
enhanced PV gradient at the TP break.
Consideration of Figs 2 and 3 thus prompts a
refinement of the traditional Hovmöller plot to
display the wave propagation as it occurs along the
PV-waveguide. Details of the novel methodology
and a comparison can be found in Martius et al.
(2005a). Fig. 4 shows an example of the novel
display in comparison to the traditional method.
The wave-train from Nov 2-7 is present in both
diagrams, albeit with reduced amplitude in the
traditional plot. In particular the issues pointed out
earlier (cf. Fig. 3) are visible. The peak on Nov 2 is
significantly reduced at ~50W and even seems to
be absent at ~15E (Fig. 4a), thus cancellation in
the meridional average leads to the interpretation
of a vanished wave train at that longitude, whilst
the wave continues its propagation in Fig. 4b and
even attains large amplitudes due to the significant
wave amplification.
Fig. 2: Isentropic (320K) meridional wind component
(shaded, m/s) and PV=2pvu contour (red).
Fig. 3 exemplifies some of the points raised above.
In the sector 60-40W the wave extends further
north than the pre-defined zonal band of 30-60N
such that the traditional method cannot entirely
capture the wave peak. Also, along 15E, a major
wave-breaking event is present that results in a
convoluted TP and a meridionally superposed
positive and negative wave peak, leading to partial
cancellation and hence reduced amplitudes in the
30-60N average.
Fig. 4: Traditional (left) and PV-Hovmöller (right)
diagrams for November 1991 (reproduced from Martius
et al. 2005a).
Note in passing that by using the new methodology
also Hovmöller diagrams of the PV=2 contour
length (representative of RW breaking) are
obtained and complement the RW diagnostic (for
an example, see Martius et al. 2005a).
The new Hovmöller diagnostic is extracted for the
entire ERA40 climatology and can be applied to
examine systematically wave occurrences during
particular weather situations of interest and to
study potential wave precursors. An example is
presented here for extreme precipitation cases on
the Alpine southside.
3.
Streamer climatology and heavy
precipitation events on the Alpine
southside
Fig. 3: Same as Fig. 2 for 2 Nov 1991, 12 UTC. Latitude
circles 35 and 60N and longitudes 60W, 40W and 15E
indicated (reproduced from Martius et al. 2005a).
Case studies have indicated a close
connection of stratospheric intrusions upstream of
the Alpine ridge with Alpine heavy precipitation
(HP) (Massacand et al. 1998). The mechanism
proposed includes a southerly flow component
induced by the upper-level streamer that can
penetrate to the surface and interact with the both
the Atlantic/Meditteranean water reservoir and the
Alpine ridge. In addition, the PV-streamer is
associated with vertical upward motion at its
eastern flank and reduced static stability
underneath it. Together, these factors provide a
favourable environment to trigger ororaphicallylocked HP. In Martius (2005) a climatology of
isentropic PV streamers is established
from
ERA40 data. This climatology is linked to an
observational climatology of daily precipitation over
the Alpine area for the period 1966-99. As a result,
a quantitative estimate of the linkage between
tropopause-level intrusions and HP on the Alpine
south side and its seasonal cycle is derived
(Martius et al. 2005b). The link is strongest in
autumn, where over 80% of the extreme
precipitation cases are associated with an upperlevel streamer. The spatial frequency of HP-related
streamers and the upper-level PV composite for
those cases is shown in Fig. 5.
Fig. 5: (a) Frequency [%] of isentropic streamers
associated with the most extreme 1% of precipitation at
the Alpine southside. (b) Isentropic upper-level PV
average [pvu] for the 1% strongest HP events
(reproduced from Martius et al. 2005b).
In more than 50% of the HP days a PV streamer is
present over NW France and SW England. The
structure of the frequency composite is spatially
confined and elongated and bears strong
resemblance to the prototype HP-streamer (Fig.
5a). An average of the actual PV distribution for the
1% HP events exhibits a corresponding structure
with a deep stratospheric intrusion and indications
of upstream and downstream ridges related to the
concomittant diabatic heating (Fig. 5b). In addition
it is found that in the presence of a streamer there
is a relative increase of 70% in the probability of
exceedance at all precipitation thresholds (not
shown). Hence streamers are the dominant upperlevel signature of heavy precipitation events. Since
streamers are a result of RW propagation and
breaking it is interesting from a predictability
perspective to examine potential RW precursors of
these HP events.
4.
Rossby wave precursors of heavy
precipitation events
From the ERA40 climatology of refined
Hovmöller diagrams (cf. section 2) the 5% HP
events were extracted and the Hovmöller diagrams
centered on the date when HP occurred. In this
way, composites of the wave diagrams can be
compiled, that show the RWs leading up to the HP
event, i.e. the meridional velocity signal up to
twelve days prior to it. In addition, statistical
significance tests can be undertaken in comparison
to the climatologcal data base of Hovmöller
diagrams (Monte Carlo test at 99% level).
Fig. 6 depicts the significant wave precursor
signals and their seasonal variability. Coherent
wave precursor signal exist for all seasons for lead
times from 0-2 days, but interesting seasonal
differences are found.
In winter, over the west coast of North America a
coherent wave signal can be identifed seven days
prior to the HP day. The composite precursor
signal in autumn looks similar regarding its
amplitude, phase speed and distance covered.
Note that a weakly negative signal is present over
eastern Europe, downstream of the PV streamer,
in the autumn and winter composite. In spring, the
in-situ wave signal over the eastern Atlantic and
Europe is of notable temporal persistence and first
observed at day -6 over Europe. However the
upstream extension of the precursor signal is
shorter in spring than in autumn and winter. Of all
seasons, the precursor wave is weakest in
summer, in terms of amplitude and temporal and
spatial extent. Note that the amplitude of the
autumn mean wave signal is larger than in summer
despite the fact that the former sample is
signifcantly larger (cf. caption of Fig. 6), indicating
that the autumn waves may be larger in amplitude
and/or better phase-locked. A coherent precursor
signal is present only four days prior to the HP
days in summer.
Fig. 6: Composites of RW signals for HP events, derived
from Hovmöller plots along the tropopause. (a) DJF (40
cases), (b) MAM (99), (c) JJA (128), (d) SON (177).
5.
Concluding Remarks
Several aspects of this study are of prime
interest within the context of THORPEX. (i) RWs
and RW breaking are clearly linked to high-impact
weather and extreme events, and their propagation
is also related to the development of forecast
errors (cf. Langland et al. 2002). (ii) Extratropical
RWs propate on the locally enhanced PV gradient,
whose amplitude in part determines the wave
speed and scale. (iii) The waves are preferentially
diagnosed along the band of enhance PV gradient,
in order to best capture their amplitude and
direction and also the wave train extension. (iv)
The existence of multiple wave guides (not shown)
gives rise to wave energy transfer poleward or
equatorward that can nicely be depicted and
captured in the refined Hovmöller diagrams. (v) A
climatology of these RW features provides a basis
to investigate significant wave disturbances that
trigger severe weather events, and moreover to
study the instigators of the waves themselves. (vi)
From a predictability perspective, the ingredients
involved in RW propagation are subject to large
uncertainties, in particular the strength and
representation of the PV gradient, i.e. the wave
guide (cf. Didone et al., this issue).
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