Wave Packet Diagnostics for Winter TPARC
Generated by Edmund Chang, Stony Brook University
A. What are wave packets?
Several studies in the1990s have shown that mid-latitude baroclinic waves are predominantly organized in downstream developing wave packets. These wave packets propagate with group velocity much faster than the phase speed of individual troughs and ridges, thus at the leading (eastern) edge of these wave packets, new troughs and ridges tend to develop (“downstream” development since mid-latitude flows are usually eastward), and at the trailing (western) edge of these wave packets, mature troughs and ridges tend to undergo decay.
A nice example of a wave packet is shown in Chang (1993):
The figure on the left shows contours of 300 hPa geopotential height for the period 18-28 December, 1985. The successive downstream development of 5 troughs during that period (A-E), all the way from Asia across the Pacific and North America and then the Atlantic, is highlighted in the figure. The right panels show Hovmoller diagrams of the 300 hPa meridional velocity (and its square) averaged between 30 and 60 N for the entire month, with the period shown in the left panel as well as the 5 troughs highlighted. From the Hovmoller plots, the distinct difference between the phase speed (the magenta arrow on the right panel) and the group velocity (the green arrow) is clearly visible. Lee and Held (1993) showed that these wave packets are prevalent in idealized model simulations as well as in Southern Hemisphere summer, while Chang and Yu (1999) and Chang (1999) showed that these wave packets are prevalent in the mid-latitudes of both the Northern and Southern Hemisphere during both winter and summer.
B. Dynamics of wave packets
In terms of energetics, upper level baroclinic waves tend to radiate energy downstream via the ageostrophic geopotential flux, leading to energy decay of the existing mature ridge/trough system and development of a new downstream trough/ridge system. More details can be found in Orlanski and Katzfey (1991), Orlanski and Chang (1993), Chang and Orlanski (1994), and Chang (2000, 2001). In terms of potential vorticity (PV) dynamics, downstream development is due to advection of the mean PV gradient near the tropopause by the perturbation velocity of existing upstream PV perturbations (basically similar to the dynamics involved in the group propagation or dispersion of Rossby waves). More discussions on the PV aspects can be found in Nielsen-Gammon and Lefevre (1996).
C. Visualizing wave packets
One easy way of visualizing wave packets is by examining Hovmoller plots (see middle panel of Fig. 1) of upper level (usually at 300 hPa, which is close to the tropopause level at mid-latitudes) meridional velocity (N-S component, or v). The v component is chosen because previous studies have shown that v is dominated by zonal wave number 4-7 (or waves with wavelength between 4000 and 7000 km) disturbances, while geopotential height (z) or the zonal wind (u) are dominated by much larger scale and lower frequency disturbances. In the daily diagnostics, a Hovmoller diagram based on the 16 day GFS control deterministic forecast is plotted, showing v averaged between 30-60 N for the full 16 day duration.
While the Hovmoller diagram is a good summary tool, one must be careful in its interpretation, since it is computed based on a fixed latitude band (30-60 N here), while the latitude of wave packets can vary with the background flow. One refinement of the Hovmoller diagram to allow for latitude variations of the waveguide has been suggested by Martius et al. (2006a). Nevertheless, even with the refinement, it is clear that one single longitude-time plot cannot summarize everything that goes on, since the upper tropospheric wave guide is usually split into two branches over Eurasia (see Chang and Yu 1999) as well as from time to time over North America. Thus time sequences of 2-D plots showing the evolution of wave packets are useful.
To highlight wave packets in 2-D, Lee and Held (1993) suggested using a procedure called complex demodulaton. Basically, at each latitude, the meridional velocity (v) is assumed to vary as A(x)cos(kx+c(x)), where k is the carrier wavenumber, generally around 6 for mid-latitudes, and A(x) is a slowly varying (in space) envelope, and c(x) is a slowly varying phase. Using the procedure of complex demodulation (see Section 2c of Chang and Yu 1999), the envelope function A(x) can be computed. An example is shown below:
2-D maps of the envelope function computed in this manner are shown in the diagnostics. In the current implementation, the carrier wave number k is a function of latitude and calendar month. Generally speaking, k is smaller at high latitudes, and larger during the warm season. Refinements of the procedure have been suggested by Zimin et al. (2003, 2006), but I do not have time to incorporate those refinements in my computer programs.
D. Applications of wave packet diagnostics
As discussed above, previous studies have shown that these wave packets are prevalent in the mid-latitudes, thus following these wave packets allows one to follow the evolution of major mid-latitude disturbances. These wave packets have also been shown to be important in wave/zonal mean flow interactions (Chang, 2005a). Previous studies have shown that the initiation of a lot of high impact weather is associated with these wave packets (e.g. Orlanski and Sheldon 1995, Shapiro and Thorpe 2004, Martius et al 2006b, Chang 2005b). Studies have also shown that forecast errors develop and propagate like wave packets (Hakim 2005), and impacts of targeted observations also spread out like these wave packets (Szunyogh et al 2002). In winter TPARC, we have found that these wave packet diagnostics allow us to better interpret the upstream spreading of forecast sensitivity as target lead time is increased – essentially relating sensitivity based targeting to feature based targeting, with the features considered being not just individual troughs and jet streaks, but also wave packets. One can argue that the utility of medium range lead time sensitivity (Sellwood et al 2008) is ultimately tied to the group propagation aspect of atmospheric perturbations associated with these wave packets.
This material is based upon work supported by the National Science Foundation and NOAA. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author and do not necessarily reflect the views of the sponsor agencies.
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