1. EQUATORIAL WAVES part 2: Vertical Propagation & the QBO

2. Equatorial waves… Summary from last week: Equatorial  -plane (  analysis valid only near equator) General case: discrete solutions from Tells us that there are three waves per n-value (n>0): –Westward-propagating (fast) gravity wave –Eastward-propagating (fast) gravity wave –Westward-propagating (slow) Rossby wave

3. Equatorial waves… Also, n=0  Rossby-Gravity (RG) wave: –Westward-propagating –« fast » at large scales –Slower at synoptic scales Also, n=-1  Kelvin wave: –Eastward-propagating –Slower at largest scales –Faster at smaller scales

4. Equatorial waves… Next – let’s consider the possibility of vertical propagation into the stratosphere. Remember gravity wave analysis in Cht 7… Shallow water analysis  shallow water waves (as in Cht 11 for equatorial waves) For atmospheric (real) gravity waves, we needed to look at a more complete set of equations (section 7.4.1) We can use this same (more complicated) approach to look at the vertical propagation of equatorial waves – especially Kelvin and RG waves (see 12.5)

5. Equatorial waves… The linearized equations on an equatorial  -plane in z*- coordinates and when full z-dependence is allowed are given by Eqs (12.29-12.32). We next assume: The m-part is new – m is the vertical wavenumber As usual, for propagation, we require conditions such that the solution is of the form exp(  imz), as opposed to exp(  mz).

6. Equatorial waves… JRH then shows the following: R-G waves: The westward-moving mode has structure in Fig. 12.13 Note that u’>0 where w’>0 and u’<0 where w’<0 so that the correlation This means there is an upward flux of westerly momentum

7. Equatorial waves… Kelvin waves: The eastward-moving mode has structure in Fig. 12.12 Note again, Upward flux of westerly momentum But … see JRH top of p.438… Net result is that RG waves produce an upward flux of easterly momentum

8. Equatorial waves…observations Both RG & Kelvin waves are observed in the troposphere & stratosphere Fig 12.14  Kelvin waves –Period  12 days –Vertical wavelength  10-12 km –Typically zonal wave 1

9. Equatorial waves…observations RG waves –Zonal wavenumber 4 –Period  4-5 days –Vertical wavelength  6-12 km Both wave types are generated by large-scale heating patterns

10. The QBO Quasi-biennial oscillation Observations…

11. The QBO Observed latitudinal extent…

12. The QBO Impact on zonally averaged flow… April 1993 (left) and 1994 (right)

13. The QBO Explanation… Driven by vertically-propagating RG and Kelvin waves –and by vertically-propagating gravity waves How? Imagine a Kelvin wave propagating eastward and upward. If the background wind is easterly, the quantity is relatively large. This allows the wave to keep propagating vertically without attenuation by e.g., radiative damping (remember that the wave also has a temperature perturbation with it – Fig. 12.13)

14. The QBO Imagine the same a Kelvin wave propagating eastward and upward. Suppose the background wind is now westerly and increasing with height. Thus as height increases the quantity becomes small. This means that the wave is moving slowly relative to the background flow. So now, the the wave becomes subject to strong attenuation by e.g., radiative damping. The wave is damped at some altitude (z c, say) as it is propagating vertically (i.e., further upward propagation is blocked).

15. The QBO At this altitude (z c ), the wave deposits its momentum into the mean flow –For comparison, imagine a wave carrying « heat » and depositing that « heat » into the background as it dissipates. –The result would be that the background is heated up! For the Kelvin wave, its eastward momentum is deposited into the flow, and thus drives the flow eastward. This westerly acceleration results in the region of stronger westerlies descending.

16. The QBO The next Kelvin wave coming up would then dissipate at a slightly lower elevation, and thus drive westerlies down further. By this mechanism, the westerlies can descend, thereby destroying the easterlies! This how one phase of the QBO works. In the opposite phase, the RG wave drives the easterlies down.

17. The QBO Blue line = RG wave – damped low in atmosphere Red line = Kelvin wave – can propagate higher until its speed is close to the background flow speed. Then it also dissipates. The opposite situation – roughly 12 months later. Now, the RG waves (blue) propagates higher and dissipates, thus driving the easterlies downward (not via a single wave – a series of waves over time!)

18. The QBO-the full cycle

19. The QBO This explanation was put forth and accepted in the 1990’s. Later it was shown that the RG & Kelvin waves alone are not enough to drive the observed QBO. Vertically-propagating gravity waves are also needed. Readings (short): 1.http://ugamp.nerc.ac.uk/hot/ajh/qbo.htm - good overview of obs. and mechanisms (plots taken from here!)http://ugamp.nerc.ac.uk/hot/ajh/qbo.htm 2.http://www-arctic.nipr.ac.jp/members/kaoru/Doc/QBO/index.html - discussion of the necessity of gravity waves in driving the QBOhttp://www-arctic.nipr.ac.jp/members/kaoru/Doc/QBO/index.html