#### 3.1. Temperature-Colored Satellite Image

[15] Figure 4 shows a GOES satellite image of eastern North America at 0432 UT on 30 October 2007. Wallops Island is shown as a red star. This image is dominated by TS Noel centered near 73°W and 22°N. Noel started as a tropical depression on 28 October at 0 UT, was upgraded to a TS on 28 October at 1200 UT, and was further upgraded to a hurricane on 02 November at 0 UT. When upgraded to a hurricane, Noel was located at 77°W and 26°N. By 0 UT on 03 November, it began to dissipate as it reached the cold water off the eastern coast of North America at 72°W and 32°N. It subsequently moved NEwards up the east coast of North America, and dissipated by 06 November at 0600 UT near 50°W and 64.2°N.

[16] Figure 4 is colored by temperature. This is important, because it allows for identification of the plumes and clusters undergoing convective overshoot. From balloon soundings and the National Centers for Environmental Prediction (NCEP) reanalysis data, we estimate a tropopause temperature of ∼ −79°C at *z*_{trop} = 15.0 ± 0.5 km. Localized cold temperatures on the anvils imply convective overshoot, because a parcel of air which moves adiabatically through the tropopause and into the stratosphere has a colder temperature than the surrounding air. Therefore, the plum and red colors in Figure 4 (which denote fluids colder than −80°C) are indicative of regions where convective overshoot occurred. We see that convective overshoot occurred near and SE of the center of TS Noel. Additionally, there is a single plume undergoing convective overshoot in the Carribbean Sea just east of the Yucatan Peninsula.

[17] The band of white clouds noticeable between Noel and the east coast of the United States is an area of weak convection and high cirrus clouds. These cloud tops were much warmer than the tropopause (white regions denote temperatures of > −55°C); therefore, they were located well below the tropopause. Note that Bermuda (65°W and 32°N) was reporting towering cumulous at the time, which is convection that has not grown into thunderstorms which reach the tropopause. Figure 5a shows a balloon sounding at Bermuda taken at 00 UT on 30 October 2007, which is a higher resolution depiction of the atmospheric stability occurring in this area. Bermuda was somewhat south of a cold front, which provided mechanical lift to low level air parcels. An air parcel rises along a moist adiabat (parallel to the green line), and has buoyancy until reaching a temperature equal to the observed temperature (red line), which occurs at *z* ∼ 9.3 km. Above this altitude, momentum carries the parcel a few hundred meters until it cools and sinks below this altitude. Then it warms and rises, etc. The parcel thus oscillates around this equilibrium level. At this latitude, the tropopause is ∼12.5–13 km. Therefore, it is unlikely that the weak convection occurring in these white bands of clouds excited any high-frequency GWs, because the convection never reached the tropopause.

[18] Figures 5b and 5c show the zonal and meridional winds from this balloon sounding. We see that there is a strong zonal shear at this location. This wind shear could have generated GWs if unstable to the Kelvin-Helmholtz instability [*Fritts*, 1982]. These GWs would have had phase speeds comparable to the mean wind, ∼20–30 m/s, and horizontal wavelengths of a few to tens of km (*Fritts and Alexander*, 2003). Because only GWs with *c*_{H} > 100 m/s can propagate to the bottomside of the F layer (V07), and the observed waves have *c*_{H} ≥ 140 m/s and *λ*_{H} > 100 km (see section 4.2), it is quite unlikely that any of the TIDDBIT waves were generated by an unstable tropospheric shear.

#### 3.3. Propagation of Primary GWs

[20] We first calculate the GW spectra excited from the 15 convective objects shown in Figure 6. Examples of GW spectra from plumes and clusters are shown by *Vadas et al.* [2009a]. Next, we position each GW spectrum at the location of the convective object (at 0432 UT and *z* = *z*_{trop}), and ray trace the GWs into the stratosphere, mesosphere, and thermosphere. Figure 7 shows horizontal slices of the reconstructed GW neutral density perturbations, *ρ*′/, from *z* = 100 to 220 km and from 0530 to 0630 UT. The times were chosen to show the evolution of the GW packet which contributes significantly to the creation of the thermospheric body force. The maximum amplitude for each image varies, and is as large as 30%. These GWs are saturated. Without the inclusion of wave saturation, the GW amplitudes would have been (unrealistically) 5–20 times larger; these values are much larger than in VL09 because (1) there are 15 convective objects here as opposed to a single convective plume, which greatly increases the wave amplitudes in regions of constructive interference, (2) most of the convective objects are clusters here, thereby increasing the GW amplitudes by a factor of ∼2–3, and (3) the plume updraft velocities here are twice as large as in VL09, thereby doubling the GW amplitudes. These 3 effects yield GW amplitudes that are at least 8–12 times larger than in VL09 if wave saturation is not included. The maximum density perturbations of the primary GWs in VL09 was 10–15%. In hindsight, it was not necessary to include wave saturation in VL09, because nearly all of the primary GWs were unsaturated prior to dissipating from kinematic viscosity and thermal diffusivity.

[21] There are several important features in Figure 7. First, constructive and destructive interference of waves from different clusters and plumes is quite apparent. Second, the GWs at *z* ≥ 180 km have *λ*_{H} > 100 km. This agrees with GW dissipative theory (V07). Third, the waves that survive to *z* ∼ 205 km are propagating N, NW, NE, and Eward, but are not propagating S and SWward. This is because the winds are SWward at *z* ∼ 150 km (see Figure 2). Finally, although the GWs appear as ∼180–270° concentric rings at *z* ≤ 160 km, they appear instead as partial “arcs” at *z* ≥ 175 km because of dissipative filtering.

[22] Figure 8 shows horizontal slices of *ρ*′/ at *z* = 140 km from 0520 to 0700 UT. At early times, very large *λ*_{H} GWs are apparent. At later times, smaller *λ*_{H} GWs reach this altitude, since they have smaller vertical group velocities but similar periods. Figures 9a–9c shows *ρ*′/ at *z* = 140 km for the most energetic cluster, the three most energetic clusters, and all 15 of the clusters and plumes. Although the most energetic cluster is visible in all panels of Figure 9, the other clusters and plumes contribute significantly in Figures 9b and 9c, creating complex interference patterns in Figure 9c. Note that the maximum amplitudes in Figures 9a–9c are similar because the waves are saturated (to different extents) in each panel.

#### 3.4. Dissipation of Primary GWs and Creation of Horizontal Body Forces

[23] GWs transport momentum. Thus, when they break or dissipate in the atmosphere, they create horizontal body forces [*Hines*, 1972; *Vadas and Fritts*, 2004, 2006]. We now calculate the mesospheric and thermospheric body forces created from the breaking and dissipation of the primary GWs (e.g., Figure 7). The zonal and meridional components of the body force are

respectively [*Andrews et al.*, 1987]. Here, *u*, *v*, and *w* are the zonal, meridional, and vertical velocity perturbations of the GW, and overlines denote averages over 1–2 wave periods and wavelengths.

[24] Figure 10 shows the zonal and meridional components of the body forces at the latitudes where they are maximum. The meridional component is somewhat larger than the zonal component, and has a maximum value of *F*_{y} ∼ 0.85 m s^{−2} (Nward) at 73.5°W, 24.4°N and *z* = 112 km. The zonal component maximizes at a somewhat higher altitude, *z* = 136 km, with a value of *F*_{x} ∼ 0.60 m s^{−2} (Eward) at 71.7°W and 21.7°N. These accelerations are consistent with previous results from a single convective plume (VL09). However, the thermospheric body force is lower here by ∼50–70 km because of wave saturation. Note that there is significant forcing up to *z* ∼ 190–200 km. The altitude of the body force maximum moves upwards in time.

[25] Both the zonal and meridional body force components excite secondary GWs [e.g., *Vadas and Fritts*, 2001]. We now focus only on the meridional body force component because (1) its amplitude is somewhat larger than the zonal component's amplitude, and (2) Nward-propagating secondary GWs at Wallops Island would be primarily created from the meridional component of the force, because horizontal body forces do not excite significant secondary GWs perpendicular to their direction of action. Figure 11 shows horizontal slices of *F*_{y} as a function of time. The contour levels in the first row (near the mesopause) are 10 times smaller than in rows 2–5. The mesospheric body forces (at *z* ≃ 90 km) are located north of the deep convective clusters, but end abruptly at 26–27°N. On the other hand, although *F*_{y} is maximum in the thermosphere at 24.4°N, there are significant large-amplitude thermospheric body forces up to ∼33°N, especially for late times at *z* = 160 to 180 km. Thus, the horizontal regions covered by the mesospheric and thermospheric body forces are quite different. This occurs because different waves (with different *λ*_{H} and *c*_{H}) contribute at each altitude and location. In particular, the waves which contribute most strongly to the mesospheric body force have *λ*_{H} ∼ 20–30 km (and small *c*_{H}), whereas the waves which contribute most strongly to the thermospheric body force have 40 < *λ*_{H} < 150 km (and larger *c*_{H}) (VL09). We now investigate why the breaking/dissipating GWs propagate to ∼35°N at *z* ∼ 160–180 km, but propagate only as far north as ∼27°N at *z* ∼ 90 km.

[26] A Boussinesq GW in a windless, isothermal atmosphere propagates at the angle *α* with respect to the vertical via [*Kundu*, 1990]

where *τ*_{b} = 2*π*/*N* is the buoyancy period. Therefore, smaller period waves propagate closer to the vertical than larger period waves. When a GW propagates vertically by Δ*z*, it also propagates horizontally, Δ*x*_{H}, during the same time by

where *c*_{g,H} = ∂*ω*_{Ir}/∂*k*_{H} and *c*_{g,z} = ∂*ω*_{Ir}/∂*m* are the horizontal and vertical group velocities, respectively, and Δ*t* is the time taken to propagate Δ*z* and Δ*x*_{H}. Since *c*_{g,H}/*c*_{g,z} ∼ *m*/*k*_{H} ∼ *τ*_{r}/*τ*_{b} from equation (1), equation (8) becomes

Equation (9) shows the well-known result that GWs with larger periods travel further horizontally than GWs with smaller periods while propagating the same vertical distance Δ*z* [e.g., *Hines*, 1967; *Richmond*, 1978; *Waldock and Jones*, 1987; V07].

[27] For a GW to propagate from 23°N to at least 27°N from the tropopause to *z* = 90 km, it needs to have a period of *τ*_{r} ≥ 32 min from equation (9), where Δ*z* ∼ 90–15 = 75 km and *τ*_{b} ∼ 5.5 min. Since the meridional component of the phase speed is

those Nward GWs having *λ*_{y} ≤ 30 km will have phase speeds of *c*_{y} ≤ 15 m/s. Because the model winds are *V* ∼ 10–15 m/s at *z* ∼ 70–80 km, all of those GWs with *λ*_{y} ∼ 20–30 km and *τ*_{r} ≥ 32 min are removed by critical level filtering. Waves with shorter periods have larger *c*_{y} = *ω*_{r}/*l* (thereby avoiding critical levels), and reach *z* ≃ 90 km south of 27°N, where they break and contribute to the mesospheric body force. On the other hand, a medium-scale Nward GW with *λ*_{y} ∼ 100 km can propagate from 23°N to 33°N from the tropopause to *z* = 160 km with a period of *τ*_{r} ≃ 45 min from equation (9), where we have taken *τ*_{b} ∼ 6 min. From equation (10), those Nward GWs having *λ*_{y} ∼ 100 km and *τ*_{r} ≃ 45 min have phase speeds of *c*_{y} ≃ 40 m/s. Thus, these latter GWs escape critical level filtering in the lower atmosphere. Once in the thermosphere, these GWs avoid critical level filtering because the winds are generally Sward or slightly Nward (see Figure 3); eventually, they dissipate. Therefore, it is the larger phase speeds of the GWs which dissipate at *z* ∼ 160 km as compared to those which dissipate at *z* ∼ 90 km that leads to the thermospheric body forces extending much further north than the mesospheric body forces in Figure 11.

[28] We note from Figure 11 that the spatial inhomogeneities of the thermospheric body forces, ∼100–150 km, are much smaller-scale than that calculated previously from a single plume [*Vadas and Fritts*, 2006, hereafter VF06; VL09]; this occurs because of constructive and destructive interference created by the GWs from the 15 convective objects. For *z* > 140 km, each image is different from the previous image, implying thermospheric body force durations of ≤15 min. These spatial inhomogeneities and temporal intermittencies imply excited secondary GWs from the thermospheric body forces with *λ*_{H} ∼ 100–400 km and *τ*_{Ir} = 2*π*/*ω*_{Ir} ∼ 10–20 min.

[29] Although we calculated the response from a single satellite image, because the storm was fairly uniform in time and slow-moving, it is likely that the spatial variability of the body forces during this 6-hr period can be approximated as averages in time of Figure 11. The temporal variability is still ≤15 min, because of the variability of the exact plume and cluster locations and times.

[30] Summarizing, the approximate region occupied by the mesospheric body forces at *z* = 90 km is 69–78°W and 20–26°N, and the approximate region occupied by the thermospheric body forces is *z* = 110–190 km, 62–80°W and 20–33°N. Portions of these regions will excite secondary GWs at various times. We choose *z* = 90 km and *z* = 140 km as the average mesospheric and thermospheric body force excitation altitudes, respectively, for purposes of reverse ray tracing the TIDDBIT waves in section 5.