1. Dynamical Constraints on the Gravity Wave Source Spectrum Used in a Parameterization of Gravity Wave Forcing David Ortland NorthWest Research Associates Bellevue, WA Code and data generously provided by : X. Zhu, M. J. Alexander, A.K. Smith, R. Garcia, C. McLandress

2. A Method for tuning the source spectra in the Alexander-Dunkerton GW parameterization What constraints are required on the structure of the GW source spectra in order to reproduce realistic winds in the MLT of a GCM or mechanistic model? Primarily concerned with obtaining qualitatively correct jet structure: tilt, magnitude and altitude where reversal occurs January monthly means:

3. Alexander-Dunkerton GW parameterization based on the Lindzen saturation criterion, in this example, effective horizontal wavelength = 1000 km, intermittency  =.04

4. This is a 1 st order differential equation that is easily integrated to find c(z), given initial condition c 0 =c(z 0 ); The source spectrum F(c) is obtained from the definition of c(z): Main Idea: The relationship between X and c(z) can be inverted

5. Diagnose the required GW forcing Given all other model forcing: Radiative and chemical heating/cooling; (X. Zhu radiation code; O 3, O 2, O, CO 2, H 2 O distributions from A.K.Smith) Molecular and eddy diffusion; (estimates from C. McLandress) Ion drag; Planetary wave forcing; Solve for GW forcing term in the zonal momentum equation required to maintain the model at given climatological zonal wind values. Disclaimer Results will be sensitive to the radiative forcing scheme

6. CIRA Jan winds and the GW force required to maintain them in a mechanistic model PW forcing Forced by GW in high phase speed tail of spectrum Forced by GW with mid-range phase speed artifact

7. Solution at 50 S: Illustrate dependence on various parameter choices Spectral shape at the tail end is not sensitive to these choices Smal l  leads to large phase speed tail Different choices for c 0 approach the same solution in the tail Smaller horiz. wl. leads to steeper slope at small c Integration started at Z 0 =80 km

8. GW source spectra obtained via inversion The spectral amplitude and shape are latitude-dependent Parameters and Initial conditions: horiz wl=1000km  =.1 z 0 = 82 km, S Hem = 40 km, N Hem c 0 (z 0 )=5+max(u(z)) for 12 km<z<z 0 width of the spectral segment is proportional to the wind shear Flat spectrum

9. Need two GW source types in the Southern Hemispere Convective Background noise Diagnosed Background Convective

10. Northern Hemisphere wave forcing Inversion at 60N starting at 40 km produces reasonable results with a single intermittency=.1, but there still may be two components to the spectrum. Breaks above 85 km PW forcing GW forcing

11. Mechanistic model results: momentum forcing components zonally symmetric primitive equations, includes radiative heating code, diffusion, ion drag, AD GW parametrization

12. Mechanistic model zonal winds: PW and high altitude GW forcing only

13. Model zonal winds, all forcing included

14. Response to low phase speed GW forcing: equatorward tilt of jet contours for GW forcing

15. How sensitive are results to spectral shape? Impose analytic form for the GW spectrum: F(c) = A / (c – u(z 0 )) 2 Latitude dependent amplitude A is derived from the inverted spectrum Use additional GW spectra for low lat S Hem and high lat N Hem Strong shears develop

16. Summary One may employ general source spectral shapes in the Alexander- Dunkerton scheme, and a analytical technique has been developed that solves for the spectrum that produces a given forcing profile; A good reproduction of climatological winds is obtained in a zonally symmetric model employing the AD scheme with a source spectrum that depends on latitude; Success of the simulation also depended on using multiple source types, especially a ‘convective’ source at low summer latitudes, so that the required forcing profile could be reproduced over a large altitude range; The equatorward tilt of the winter jet results from strong GW forcing in the lower mesosphere at high winter latitudes; Unsatisfactory results are obtained in an attempt to use the same spectral shape at all latitudes for the ‘background’ GW spectrum.