As expected, the control run shows characteristics comparable to the Southern Hemi- sphere: Since no zonally asymmetric surface forcing is applied, we find a lack of quasi- stationary waves. This forcing structure yields a very strong polar vortex exhibiting mean winds around 100 ms−1 at its core (Figure 4-7a), with a standard deviation of 5 ms−1. Figure 4-2a shows a representative excerpt from the control run for zonal mean zonal wind u at 60◦S and 10 hPa (below the jet core). The location for the time series of zonal mean zonal wind was chosen according to the WMO definition of sudden warmings, where a necessary condition for a major sudden warming is defined by a wind reversal at 60◦ latitude and at a pressure level of 10 hPa.
The corresponding vertical EP flux is shown in Figure 4-2b, depicting latitudinally integrated vertical EP flux at 96 hPa given by R2070◦◦SS Fza cos ϕ dϕ, where Fz is given
by
Fz = ρ0f a cos(ϕ)
v0θ0
∂θ/∂z, (4.1)
where ρ0 is density as a function of pressure, f is the Coriolis parameter, a is the
Earth’s radius, ϕ is latitude, v0θ0 is the heat flux and ∂θ/∂z is the vertical gradient in
potential temperature. This is the quasi-geostrophic spherical definition of the ver- tical EP flux approximated according to the dominant terms of Equation (1.9). The
EP flux time series is shown at a height of 96 hPa, corresponding to a height where the synoptic tropospheric influence becomes negligible and where the amplitudes of the small wave numbers begin to grow as they propagate into the stratosphere, i.e. the wave flux able to propagate past 96 hPa tends to directly interact with the strato- spheric flow.
The time series of the EP flux entering the stratosphere looks noisy (Figure 4- 2b). Stratospheric variability is therefore significantly reduced as compared to the real atmosphere with only small bursts of wave activity, which are not able to induce sudden warmings over the entire run.
200 400 600 800 1000 1200 1400 1600 1800 2000 0
50 100
a) zonal mean zonal wind
days m/s 200 400 600 800 1000 1200 1400 1600 1800 2000 0 2 4 6x 10
11 b) Fz flux (wave−1 & wave−2)
days
kg*m/s
2
Figure 4-2: Control run: a) Representative part of the time series of zonal mean zonal wind at 60◦S and 10 hPa in ms−1. b) Latitudinally integrated vertical component of the EP flux as described in the text for the sum of wave-1 and wave-2 at 96 hPa for the same time period, integrated between 20◦ and 70◦S as given by Equation (4.1).
Both mechanisms described in the introduction to this chapter (the generation of traveling waves by baroclinic instability to long waves as well as by nonlinear inter- actions among synoptic-scale eddies) are possible candidates for causing the observed traveling waves.
the stratosphere, the control run is compared to two runs where synoptic-scale waves are suppressed. One run suppresses all waves except for a mean flow and wave-2, while the other run allows for a mean flow and both wave-1 and wave-2. Section 2.2.3 provides the mean states of these runs.
The different tropospheric mean states between the described runs dominantly influence the way and magnitude at which tropospheric traveling waves are gener- ated. Comparing Figures 2-3 to Figures 2-6 and 2-5 indicates that the maximum tropospheric wind speeds at the tropospheric jet are shifted equatorward in the trun- cated runs by several degrees in latitude, and tropospheric westerlies reach further into the tropics in the upper troposphere in the truncated runs. The tropospheric jet is stronger in magnitude in the truncated runs, and all runs show the possibility of a weaker secondary jet centered around 20◦ latitude. The stratospheric vortex is considerably stronger in the control run, which is due to the increased upward plan- etary wave flux in the truncated runs as will be discussed in the next section. The stratospheric vortex is more confined to poleward of 30◦ latitude, while the truncated runs exhibit westerlies further into the tropics.
Suppressing synoptic-scale eddies by a severe spectral truncation not only changes the mean state of the troposphere, but it also yields an increase in planetary wave flux into the stratosphere along with a significant increase in stratospheric variability (Figures 4-3a and 4-4a). In particular, large amplitude warmings occur intermittently associated with large excursions in the EP fluxes (Figures 4-3b and 4-4b). These sudden warmings occur at a similar magnitude and frequency as in the topography run (compare to Chapter 2) for the run truncated to wave-2, but slightly less frequent and weaker in the run truncated to wave-1 and wave-2.
In order to verify that the atmospheric mean states indeed exhibit traveling waves, zonal phase speed spectra for wave-2 for all runs are shown in Figure 4-5. Due to the lack of a surface forcing, there is no forcing of quasi-stationary wave components with phase speeds close to zero. Both traveling wave numbers 1 (not shown) and 2 are present (except of course for the run truncated to wave-2).
200 400 600 800 1000 1200 1400 1600 1800 2000 0
50 100
a) zonal mean zonal wind
days m/s 200 400 600 800 1000 1200 1400 1600 1800 2000 0 2 4 6x 10
11 b) Fz flux (wave−1 & wave−2)
days
kg*m/s
2
Figure 4-3: Same as Figure 4-2 but for the run truncated to wave-1 and wave-2.
200 400 600 800 1000 1200 1400 1600 1800 2000 0
50 100
a) zonal mean zonal wind
days m/s 200 400 600 800 1000 1200 1400 1600 1800 2000 0 2 4 6x 10
11 b) Fz flux (wave−1 & wave−2)
days
kg*m/s
2
spersed with episodes of slower propagation in either direction (Figure 4-5). Wave-2 exhibits maximum eastward phase speeds on the order of 10 - 20 ms−1 for both trun- cated runs, while in the control run, there is broad variability with a less distinct peak at slower eastward phase speeds. The traveling waves are more dominant for the truncated runs, especially for the run truncated to wave-2. A comparison to the real atmosphere can be obtained by e.g. considering the power spectra of the Southern Hemisphere sea level pressure field computed in Mechoso and Hartmann (1982).
As the waves originate in the troposphere, the differing tropospheric mean states and variability between the control and the truncated runs are dominantly responsible for the difference in wave generation. Figure 4-6 shows the growth rate σ as given by
σ = f0 N ∂u ∂z (4.2)
as a measure of the growth rate of the most unstable mode in the model atmosphere, proportional to the Eady growth rate for the most unstable mode, where N2 = gθ ∂θ∂z is the Brunt-V¨ais¨ala frequency as a measure of atmospheric stability. The derivatives are evaluated in the lower troposphere between the model levels at 514 hPa and 925 hPa. Figure 4-6 indicates that the most unstable modes exist around the region of the tropospheric jets for all model runs, and the growth rates dominate at the location of their respective jets over the respective other model runs (compare to Figures 2-3, 2-5 and 2-6 for the model mean wind distribution). The mean state of the truncated runs exhibits a secondary peak around 60◦latitude, indicating the possibility for wave growth at high latitudes, while for the control run, wave growth maximizes around 45◦ latitude and falls off strongly poleward of the tropospheric jet. In general, the growth rate increases for the suppression of synoptic-scale eddies.