1. Gravity Wave Analysis of Four Years of High Vertical Resolution U.S. Radiosonde Data Ling Wang and Marvin A. Geller Institute for Terrestrial and Planetary Atmospheres State Univ. of New York at Stony Brook

2. Overview Data and Method Data and Method Morphology of gravity wave (GW) energies derived from the data Morphology of gravity wave (GW) energies derived from the data Latitudinal distributions of some important GW parameters including wavelengths, intrinsic frequencies and propagation directions Latitudinal distributions of some important GW parameters including wavelengths, intrinsic frequencies and propagation directions Results of some ray-tracing experiments Results of some ray-tracing experiments Summary and Conclusions Summary and Conclusions

3. Data and Method Rawinsonde 6-second data Rawinsonde 6-second data From NOAA National Climatic Data Center (CDC) From NOAA National Climatic Data Center (CDC) Both temperature and horizontal wind are available. Both temperature and horizontal wind are available. In general, data are available twice daily at 0000 and 1200 UTC, from Jan. 1998 to Dec. 2001 (year 2002 data will also be available soon). In general, data are available twice daily at 0000 and 1200 UTC, from Jan. 1998 to Dec. 2001 (year 2002 data will also be available soon). Vertical resolution ~30 m for temperature, and ~150 m for wind Vertical resolution ~30 m for temperature, and ~150 m for wind

4. Location map of U.S. high vertical resolution radiosonde stations (95 in total). In general data are available twice daily (0 and 12 UTC) from Jan 1998 to Dec 2001.

5. The method follows closely Allen and Vincent (1995) and Vincent et al. (1997) The method follows closely Allen and Vincent (1995) and Vincent et al. (1997) Tropospheric segment (2-8.9 km, except in Alaska where 2-7.4 km is used) Tropospheric segment (2-8.9 km, except in Alaska where 2-7.4 km is used) Lower stratospheric segment (18-24.9 km) Lower stratospheric segment (18-24.9 km) For each individual segment, gravity wave perturbation is evaluated from : For each individual segment, gravity wave perturbation is evaluated from : where the mean profiles are estimated from the second order polynomial fit. Method

6. Total gravity wave energy density : Total gravity wave energy density : The vertical propagation direction is derived from wind perturbation hodograph using rotary-spectral technique. The vertical propagation direction is derived from wind perturbation hodograph using rotary-spectral technique. The horizontal propagation direction is derived from the major axis of the perturbation velocity ellipse (using the Stokes-parameters technique) and the sign of. The horizontal propagation direction is derived from the major axis of the perturbation velocity ellipse (using the Stokes-parameters technique) and the sign of. The intrinsic frequency can be estimated from the axial ratio of the wind perturbation hodograph. The intrinsic frequency can be estimated from the axial ratio of the wind perturbation hodograph.

7. The most dominant vertical wavelength is simply estimated from the energy-weighted mean vertical wavelength. The most dominant vertical wavelength is simply estimated from the energy-weighted mean vertical wavelength. The characteristic horizontal wavelength is derived from the gravity wave dispersion relation. The characteristic horizontal wavelength is derived from the gravity wave dispersion relation. The zonal momentum flux is determined by: The zonal momentum flux is determined by:

8. GROGRAT – three-dimensional Gravity-wave Regional Or Global RAy Tracer (Marks and Eckermann,1995) GROGRAT – three-dimensional Gravity-wave Regional Or Global RAy Tracer (Marks and Eckermann,1995) It uses a nonhydrostatic dispersion relation and the WKB approximation. It uses a nonhydrostatic dispersion relation and the WKB approximation. Wave saturation amplitude is determined from a slantwise dynamic instability criterion. Wave saturation amplitude is determined from a slantwise dynamic instability criterion. Both turbulent damping, and radiative damping (Zhu, 1993) are included. Both turbulent damping, and radiative damping (Zhu, 1993) are included. A ray-tracing model

9. Horizontal wind and temperature profiles (red lines) observed over Ponape Island (158.2ºE, 7ºN) on Jan. 28, 1998 at 12 UTC. The mean profiles which are estimated by the second order polynomial fits (blue lines) are also shown. Wave-like structures can be clearly seen in the sounding. Lower Stratosphere 18-24.9 km Troposphere 2-8.9 km

10. Monthly and zonal mean total gravity wave energy density Et (J/kg) in the lower stratosphere (upper panel) and troposphere (lower panel) during 1998-2001  In the lower stratosphere, Et decreases poleward, and is stronger in winter than summer.  In the troposphere, Et is also stronger in winter than summer, but it maximizes at mid-latitudes.

11. Troposphere: clear gravity wave energy maxima exist over the Rocky Mountains Contoured maps of four-year (1998-2001) averaged seasonal mean GW energy Et over the continuous U.S. in the troposphere

12. Contoured maps of four-year (1998-2001) averaged seasonal mean Et over the continuous U.S. in the lower stratosphere Lower Stratosphere: the principal gravity wave energy maxima are seen mostly in the south and east U.S.

13. Contours of monthly mean U, and time series of monthly mean Et (solid lines) in the lower stratosphere for four adjacent stations in the U.S. ??? similar background wind, geographically close, but very different GW activity in the lower stratosphere

14. Contoured maps of the ratios of four-year (1998-2001) averaged seasonal mean Et in the lower stratosphere to that in the troposphere Over most of the U.S., the ratios of lower stratospheric to tropospheric energy densities are around 1 or less.

15. Contoured maps of MAM seasonal mean Et in the troposphere during 1998-2001 Tropospheric GW energies exhibit considerable interannual variation.

16. Contoured maps of MAM seasonal mean Et in the lower stratosphere during 1998-2001 Lower stratospheric GW energies also exhibit considerable interannual variation.

17. Left panels: MAM seasonal mean Et in the lower stratosphere during 1998-2001 Right panels: the corresponding zonal wind at 200 hPa (from NCEP reanalysis) Suggestion of ENSO influence on gravity wave interannual variation in the south and east U.S. in the lower stratosphere

18. Upper: month-latitude contour of monthly mean energy density Et in the lower stratosphere lower: month-height contour of monthly mean zonal wind averaged over 130º-170º E at 7.5ºN Strongest GW activities occur during the descent of the QBO westerly phase, except for the winter of 1997-98.

19. The twice-daily time series of tropospheric total energy density (black lines) vs. that of the lower stratosphere (red lines) over Norman, OK (35.2ºN, 97.5ºW) during 1998 The twice-daily time series of tropospheric gravity wave energies is virtually uncorrelated with that of the lower stratosphere. Corr < 0.15, below the 95% confidence level

20. The simulation of 12-hourly time series of tropospheric (red line) and lower stratospheric (black line) Et (normalized) using ray-tracing. The source is set to be constant but it is intermittent. Intermittency can even cause the anti-correlation between lower stratospheric and tropospheric GW energy time series.

21. Four-year averaged fraction of upward propagation GW for each of the stations in the troposphere (red dots) and lower stratosphere (black dots). Also shown are the latitudinal binned curves. Indication that some waves might be generated in the upper troposphere and/or tropospheric reflections of GW are occurring

22. Four-year averaged intrinsic frequency for each of the stations in the troposphere (red dots) and lower stratosphere (black dots). Also shown are the latitudinal binned curves.

23. Four-year averaged intrinsic frequency divided by the Coriolis parameter for each of the stations in the troposphere (red dots) and lower stratosphere (black dots). Also shown are the latitudinal binned curves.

24. Four-year averaged vertical wavelength for each of the stations in the troposphere (red dots) and lower stratosphere (black dots). Also shown are the latitudinal binned curves. This is consistent with the latitudinal distribution of total energy density.

25. Four-year averaged total energy density for each of the stations in the troposphere (red dots) and lower stratosphere (black dots). Also shown are the latitudinal binned curves.

26. Schematic showing vertical wavenumber power spectra of GW perturbations with variances of E1 and E2, respectively in energy-conserved form. Stronger GW variance corresponds to longer energy- weighted mean vertical wavelength, and vice versa.

27. Four-year averaged horizontal wavelength for each of the stations in the troposphere (red dots) and lower stratosphere (black dots). Also shown are the latitudinal binned curves. a

28. is also roughly constant Vertical wavelength does not vary too much (due to observational considerations) and  k ~ f and horizontal wavelength decreases with latitude. Lower stratospheric horizontal wavelength is longer because the Brunt- Vasalla frequency is larger there. As is demonstrated below, the latitudinal distribution of horizontal wavelength is a straightforward result of gravity wave dispersion relation.

29. Four-year averaged horizontal propagation direction for each of the stations in the troposphere (red dots) and lower stratosphere (black dots). Also shown are the latitudinal binned curves.

30. GROGRAT ray-tracing experiments A group of radiosonde stations (21 in total) are selected to perform the experiments similar to those of Alexander and Vincent (2000), but with much wider choices of model parameters. A group of radiosonde stations (21 in total) are selected to perform the experiments similar to those of Alexander and Vincent (2000), but with much wider choices of model parameters. For each of the stations, monthly mean time series of Et and zonal momentum flux in the lower stratosphere during Jan. 1998-Dec. 2001 are simulated, and are compared to the observations. For each of the stations, monthly mean time series of Et and zonal momentum flux in the lower stratosphere during Jan. 1998-Dec. 2001 are simulated, and are compared to the observations. The quality of the fit is determined by the linear correlation and regression (correlation coefficient, slope and intercept) between the modeled and observed Et and zonal momentum flux. The quality of the fit is determined by the linear correlation and regression (correlation coefficient, slope and intercept) between the modeled and observed Et and zonal momentum flux.

31. The background fields are taken from monthly mean NCEP reanalysis data interpolated to the location of the selected stations. The background fields are taken from monthly mean NCEP reanalysis data interpolated to the location of the selected stations. The gravity wave source is specified as a spectrum of momentum flux versus phase speed. The gravity wave source is specified as a spectrum of momentum flux versus phase speed. Each ray is assigned the same horizontal wavelength, although that wavelength is allowed to vary from case to case. Each ray is assigned the same horizontal wavelength, although that wavelength is allowed to vary from case to case. Only vertical wave propagation is considered in the current experiments. Only vertical wave propagation is considered in the current experiments.

32. Location map of the selected stations where GROGRAT ray-tracing experiments are performed. The stations where relatively good fits can be obtained are circled.

33. (1) (3) (4) (5) (2) Bm and Cw are parameters to be specified. Note that spectrum shapes (1)-(4) are taken from Alexander and Vincent (2000). Five types of source spectrum shapes:

34. Examples of the five model source spectrum shapes described by equations (1) (black line), (2) (red line), (3) (blue line), (4) (green line), and (5) (orange line). This is for the case of u0=10 m/s, Cw=6 m/s, and Bm=0.03 m2/s2 Spectrum shapes (1) and (4) are anisotropic, whereas spectrum shapes (2), (3), and (5) are isotropic.

35. Table of parameters used in the experiments ParameterValues Source spectral shape equations (1), (2), (3), (4), (5) (0.01, 0.1, 0.03, 1, 5, 10, 15, 20, 100) m/s Horizontal wavelength (10, 50, 100, 300, 600, 1000, 1500, 2000, 3000, 4000) km (0.03, 0.1, 0.3, 1, 5, 10, 20) m2/s2 Source altitude (1.5, 8.75, 11.75, 14.75, 17.75) km

36. Observed (red lines) and modeled (black lines) monthly time series of the lower stratospheric energy density Et (left column) and zonal momentum flux (middle column) for four stations. The right column is the total momentum flux at the source. Examples of good fits Corr.ge. 0.5 Intercept.le. 20% Slope € [0.8, 1.2]

37. Configuration of the good fits St. Paul Island, AK Riverton, WY Wilmingtion, OH Koror/Palau Island Source spectral shape equation (1) 10101010 Horizontal wavelength 60060010001500 0.030.030.030.03 Source altitude 17.7517.7511.7517.75

38. Relatively good fits can be obtained from 10 of the 21 stations. Relatively good fits can be obtained from 10 of the 21 stations. One necessary condition to get relatively good fits for both Et and momentum flux is that the time series of the total momentum flux at the source level must resemble that of the observed momentum flux in the lower stratosphere. One necessary condition to get relatively good fits for both Et and momentum flux is that the time series of the total momentum flux at the source level must resemble that of the observed momentum flux in the lower stratosphere. Another necessary condition is that the observed time series of wave energy density and zonal momentum flux have to be significantly correlated. Another necessary condition is that the observed time series of wave energy density and zonal momentum flux have to be significantly correlated. The above two conditions alone are not sufficient to produce a good fit, however. The above two conditions alone are not sufficient to produce a good fit, however. For all of the stations, only anisotropic source spectra (mostly shape 1, sometimes shape 4) can produce relatively good fit in both Et and momentum flux, indicating that the observed anisotropy of GW propagation direction in the lower stratosphere is most likely caused by the anisotropy of the source, at least for these well fitted stations. For all of the stations, only anisotropic source spectra (mostly shape 1, sometimes shape 4) can produce relatively good fit in both Et and momentum flux, indicating that the observed anisotropy of GW propagation direction in the lower stratosphere is most likely caused by the anisotropy of the source, at least for these well fitted stations. The effect of background wind filtering cannot be neglected completely. The effect of background wind filtering cannot be neglected completely. Some conclusions of the experiments

39. Fritts and VanZandt (1993) 3-D gravity wave power spectrum model “ t ” can be estimated from the spectral slope at high wavenumbers from temperature soundings, whereas “ p ” can be determined from Typically, (t, p)=(3, 5/3)

40. “t” differs considerably from its typical value : 3 Contours of zonal and monthly mean vertical wavenumber spectral index “t” in the lower stratosphere and troposphere

41. Contours of zonal and monthly mean frequency spectral index “p” in the lower stratosphere and troposphere “p” differs considerably from its typical value : 5/3

42. Summary and Conclusions Lower stratospheric gravity wave energies decrease poleward and are stronger in (Northern Hemisphere) winter than summer. Lower stratospheric gravity wave energies decrease poleward and are stronger in (Northern Hemisphere) winter than summer. Tropospheric gravity wave energies are also stronger in winter than summer, but they maximize at middle latitudes (35˚-40˚N) (new result). Tropospheric gravity wave energies are also stronger in winter than summer, but they maximize at middle latitudes (35˚-40˚N) (new result). In the troposphere, gravity wave energy maxima exist over the Rocky Mountains (consistent with previous works). In the lower stratosphere the energy maxima are mostly in the southeastern U.S. (new result). In the troposphere, gravity wave energy maxima exist over the Rocky Mountains (consistent with previous works). In the lower stratosphere the energy maxima are mostly in the southeastern U.S. (new result). QBO and ENSO effects appear to account for much of the observed interannual variability in lower stratospheric gravity wave energies, but this should become clearer with a longer period of analysis. QBO and ENSO effects appear to account for much of the observed interannual variability in lower stratospheric gravity wave energies, but this should become clearer with a longer period of analysis. The time series of tropospheric and lower stratospheric gravity wave energies are virtually uncorrelated with each other (new result). The time series of tropospheric and lower stratospheric gravity wave energies are virtually uncorrelated with each other (new result).

43. Over most of the U.S., the ratios of lower stratospheric to tropospheric energy densities are ~ 1 or less (new result). Over most of the U.S., the ratios of lower stratospheric to tropospheric energy densities are ~ 1 or less (new result). Approximately 50% of the tropospheric gravity waves show upward energy propagation, whereas there is about 75% upward propagation in the lower stratosphere. Approximately 50% of the tropospheric gravity waves show upward energy propagation, whereas there is about 75% upward propagation in the lower stratosphere. Important wave parameters such as wavelengths, and intrinsic frequencies display distinctive latitudinal patterns (new result). Important wave parameters such as wavelengths, and intrinsic frequencies display distinctive latitudinal patterns (new result). In the lower stratosphere, gravity waves generally propagate eastward south of 25˚N and westward north of 25˚N. This is shown to be caused most likely by the anisotropy of the gravity wave source spectrum, although the effect of background wind filtering cannot be excluded completely. In the lower stratosphere, gravity waves generally propagate eastward south of 25˚N and westward north of 25˚N. This is shown to be caused most likely by the anisotropy of the gravity wave source spectrum, although the effect of background wind filtering cannot be excluded completely. Gravity wave frequency spectral index “p”, and vertical wavenumber spectral index “t” deviate from their typical values considerably, and show some seasonal and latitudinal patterns (new result). Gravity wave frequency spectral index “p”, and vertical wavenumber spectral index “t” deviate from their typical values considerably, and show some seasonal and latitudinal patterns (new result).

44. Examples of zonal wind soundings in the lower stratospheric segment for both Norman, OK and Nashville, TN during Dec. 2000-Jan. 2001. Each sounding is displaced by 40 m/s.

45. The cases for two more western tropical Pacific stations

46. Contours of monthly mean U, and time series of monthly mean Et (thick lines) and zonal momentum flux (thin lines) in the lower stratosphere for Yap Island and Koror/Palau Island

47. Propagation time (days) versus latitude for different intrinsic frequencies. The propagation time is the time it would take a wave of a given frequency and a vertical wavelength of 2.5 km to travel vertically through a 7-km-deep layer in the lower stratosphere.

48. Maps of angular distribution of GW horizontal propagation directions observed in the lower stratosphere and troposphere over the western tropical Pacific during June 1998 and 1999 Indication of wind filtering effect as the cause of the anisotropy of the lower stratospheric GW propagation Propagation direction in L.S. Propagation direction in T. Zonal wind direction in T.