As a first attempt to understand the impact of typhoon-generated gravity waves (TGWs) on typhoon development, Typhoon Saomai (2006) is simulated and effects of TGWs on background flows are examined by considering momentum flux. The momentum flux of TGWs and its vertical divergence/convergence are larger during the developing stage than during the mature and decaying stages of the typhoon. In the developing and mature (decaying) stages of the typhoon, TGWs act to decrease (increase) vertical wind shear, which is known to inhibit a typhoon's intensification. Thus, TGWs can help a typhoon intensify when the typhoon develops. Upper-level divergence increases notably before a typhoon enters both rapidly-developing and mature stages. A significant portion of upper-level divergence is found to be due to TGWs.
 The typhoon, as a strong convective system, is a significant source of gravity waves. Since typhoon-generated gravity waves (TGWs) were observed in the mesosphere and thermosphere [Hung et al., 1990], they have been investigated by MU radar [e.g., Sato, 1993] and rawinsonde [Chun et al., 2007] observations. Recently, numerical modeling has been performed to study TGWs [Kim et al., 2005; Kim and Chun, 2010; Kuester et al., 2008]. Previous studies of TGWs have focused on the characteristics of TGWs and their influence on the background flow, in particular in the stratosphere. The typhoon itself has been considered as a gravity wave source, but to date there have been no studies of the feedback from TGWs to the typhoon.
 Numerical-modeling studies have shown that TGWs deposit significant momentum into the upper troposphere and lower stratosphere. This momentum deposition can modify the background wind. Therefore, TGWs are expected to affect typhoon dynamics, because the environmental flow around a typhoon is a major factor determining the typhoon's evolutionary processes, along with a typhoon's internal dynamics and energy from the ocean. Especially, the vertical wind shear is known to have a negative influence on a typhoon's intensification [e.g., Gray, 1968; DeMaria, 1996]. Many observational [e.g., Black et al., 2002] and numerical [e.g., Jones, 1995; Wong and Chan, 2004] studies have shown that the vertical wind shear affects a typhoon's intensity and movement and causes an asymmetry in the convective activity.
 Figuring out typhoon-TGW interaction would improve our understanding of typhoon dynamics. In this study, we first attempt to investigate the impact of TGWs on their source. Since TGWs can modify upper-level background flow and vertical wind shear, we focus on the influence of TGWs on the background conditions that affect typhoon development. For this, we simulate Typhoon Saomai (2006) and examine the background-flow changes induced by TGWs by calculating the momentum flux of TGWs and its vertical divergence. Then we investigate their possible influences on typhoon development by considering the environmental conditions, including the vertical wind shear and divergence field.
2. Typhoon and Numerical Simulations
 Typhoon Saomai, which formed in the western Pacific on 4 August 2006 as a tropical depression, became a strong typhoon on 7 August. The typhoon moved northwestward and made landfall on the southeastern coast of China on 10 August. According the Japan Meteorological Agency (JMA), the lowest minimum sea-level pressure was ∼925 hPa. We focus on the period 12 UTC 7–18 UTC 10 August 2006, covering the developing through the decaying stages of the typhoon.
 All results in this study are based on three-dimensional simulations performed by Kim and Chun  using the Advanced Research Weather Research and Forecasting (WRF-ARW) modeling system version 2.2 [Skamarock et al., 2005]. Three domains with horizontal grid spacings of 27 km (D1), 9 km (D2), and 3 km (D3) were nested (two-way interaction), and the innermost domain (D3) was designed to move following the typhoon center. The area covered by D3 was 1188 km × 1188 km. The vertical dimension used 77 levels, from the surface to 5 hPa (z = ∼35 km), with a damping layer at the uppermost 5 km. European Center for Medium-Range Weather Forecasts (ECMWF) analysis data (0.25° × 0.25°) were used for the initial and boundary conditions, and the Geophysical Fluid Dynamics Laboratory (GFDL)-type bogussing scheme [Kwon et al., 2002] was used to initialize the typhoon. Cloud physical processes used the WRF Single-Moment 6-class microphysics scheme [Hong and Lim, 2006] (in all domains) and the cumulus parameterization scheme by Kain and Fritsch  (in D1 and D2). In D1 and D2, the model was integrated for 36 (P1: 00 UTC 7–12 UTC 8 August 2006) and 60 (P2: 06 UTC 8–18 UTC 10 August 2006) hours. In D3, in which all analyses are performed, 24-hour (12 UTC 7–12 UTC 8) and 54-hour (12 UTC 8–18 UTC 10) integrations were conducted in P1 and P2, respectively. Details of the simulations are given by Kim and Chun .
 Typhoon Saomai was simulated reasonably well in terms of the track and intensity [see Kim and Chun, 2010, Figure 1]. The simulated typhoon track was similar to the JMA best track, but shifted slightly southward at the end of the P2 simulation. The typhoon intensity was weaker than the JMA value, but the trend of an intensity variation was reproduced well. The analysis period is separated into four parts based on the typhoon's intensity variation: Slow-developing (P1: 12 UTC 7–12 UTC 8), rapid-developing (P2-1: 18 UTC 8–12 UTC 9), mature (P2-2: 12 UTC 9–06 UTC 10), and decaying (P2-3: 06 UTC 10–18 UTC 10) stages.
3.1. Momentum Flux
 The simulated TGWs are given by Kim and Chun [2010, Figure 2]. Their dominant horizontal wavelengths and frequencies are 20–100 km and 0.3–2 hours, respectively. For detailed characteristics of waves, see Kim and Chun . We calculate the vertical flux of horizontal momentum (momentum flux) outside the convective region associated with the typhoon to examine the effects of TGWs on mean flows. To focus on upper tropospheric gravity waves, we perform the analyses at z = 12–17 km. Lower boundary is determined based on the average cloud-top height of z ∼ 12 km in the present simulations. Variables for calculating momentum flux are saved at 10 minute intervals. First, we obtain the three-dimensional spectrum of the momentum flux with respect to zonal wavenumber, meridional wavenumber, and frequency. Then, we extract the wave components that satisfy the frequency of inertia-gravity waves (f2 < 2 < N2, where f is the Coriolis parameter, is the intrinsic frequency, and N is the Brunt-Väisälä frequency). The filtering of waves by this criterion mainly occurs at the critical level (2 = f2) and for waves with the intrinsic frequency less than f. At grid points where deep convection develops, especially in the eyewall regions, cloud often reaches z ∼ 15–17 km. In order to exclude the momentum flux due to convection and focus on gravity-wave momentum flux, we omit the momentum flux inside the cloud region at which any of the mixing ratios of cloud water, rain water, graupel, ice, and snow exceeds 0.1 g/kg.
Figure 1 shows the domain-averaged zonal and meridional momentum fluxes. The momentum flux varies with time and height. For some regions, momentum flux magnitude increases with height, because the waves induced by lower cloud meet the waves generated by higher cloud. The momentum flux is relatively large in the developing stage of the typhoon with a maximum zonal value of 0.021 N m−2 near z = 13 km and 04 UTC 8 and minimum zonal value of −0.042 N m−2 near z = 13 km and 13 UTC 7. The meridional momentum flux in the developing stage shows its maximum of 0.023 N m−2 near z = 14 km and 14 UTC 7 and minimum of −0.021 N m−2 near z = 12 km and 03 UTC 8. In P2-1, when the typhoon intensifies rapidly, meridional momentum flux (0.014 N m−2 at z ∼ 14.5 km and 19 UTC 8) is relatively large compared with the zonal one. The momentum flux is also significant in the beginning of P2-2 and P2-3 when the typhoon intensity begins to increase and decrease, respectively. Although the present simulations represent essential features of the typhoon, some convective features, especially near the eyewall, cannot be fully resolvable. Influences of unresolved small-scale and high-frequency waves on the momentum flux budget may not be negligible, and they can be understood by higher-resolution simulations.
3.2. Gravity-Wave Forcing
 From the vertical divergence/convergence of the momentum flux, we calculate the zonal and meridional gravity-wave forcing (wave-induced mean wind tendency) (Figure 2). Gravity-wave forcings are relatively strong in the developing stages, and also large at the beginning of a typhoon's mature stage (12 UTC 9), especially in the zonal direction (0.15 m s−1/hr). The zonal forcing is generally positive (negative) below (above) z ∼ 15 km except for some regions in P1, likely due to the background wind structure. In the analyses region, the easterly wind decreases (increases) with height below (above) z ∼ 15 km as shown by Kim and Chun [2010, Figure 4]. Therefore, waves propagating eastward relative to the background wind with positive momentum flux can meet the critical level below z ∼ 15 km. On the other hand, waves propagating westward relative to the background wind with negative momentum flux can reach above z ∼ 15 km without being filtered and a large portion of them may be filtered at the critical level above z ∼ 15 km.
 We estimated 2-hourly background wind using gravity-wave forcing (not shown). Wind component at t is estimated by the sum of that at t-2 hrs and wind changes by gravity-wave forcing averaged during 2 hours from t-2 hrs (t = t−2 hrs + GW × 2 hrs, where is the background wind and GW is the gravity-wave forcing averaged between t-2 hrs and t.). From the estimated wind, we can understand how gravity-wave forcing would change the background wind. The estimated wind is somewhat different from an actually simulated wind since the background wind tendency is determined not only by gravity-wave forcing but also by various terms such as the pressure gradient force, Coriolis force, advection, and diffusion. Nevertheless, the estimated wind explains well the simulated wind variation. The estimated wind is used to examine the impact of TGWs on the vertical wind shear, which will be shown in the next section.
3.3. Vertical Wind Shear and Upper-Level Divergence
Figure 3 shows the vertical wind shear, a critical environmental factor that inhibits a typhoon's intensification [e.g., Gray, 1968; DeMaria, 1996; Wong and Chan, 2004]. This study diagnoses TGWs' effects on vertical wind shear using the estimated wind from gravity-wave forcing. In typhoon studies, vertical wind shear is usually defined as the magnitude of a wind-vector difference between 850 hPa and 200 hPa. Since wave activity is calculated in the height coordinate that begins from z = 3 km in this study, we define the vertical wind shear as the magnitude of a domain-averaged horizontal wind-vector difference between z = 3 km (∼700 hPa) and z = 12.5 km (∼200 hPa). Under this definition, wind shear is slightly (∼1–1.5 m s−1) smaller than that between 850 hPa and 200 hPa in the present simulations.
 The simulated wind shear (solid line) is 0.5–7.6 m s−1. This is less than the value of 11.9 m s−1 calculated by Baik and Paek  in the corresponding latitudes (15°N–25°N) for the western North Pacific tropical cyclones. The wind shear decreases with time in the developing stage, and shows its minimum value at 10 UTC 9, just before the typhoon enters the mature stage. The shear is ∼4–5 m s−1 in the mature stage, and increases with time in the decaying stage. The negative influences of vertical wind shear on typhoon intensification shown in previous studies are also found in the present simulations. A lag-correlation coefficient between the wind shear and the typhoon intensity is −0.8 (−0.71) at a 1-hour lag in the P1 (P2) simulation.
 The dashed line in Figure 3 shows the vertical wind shear after 2 hours estimated from the gravity-wave forcing. This indicates the value that the wind shear is expected to have after 2 hours if the background wind is determined by gravity wave effect alone during 2 hours. Since the gravity-wave forcing is significant above z ∼ 12 km, the effects of TGWs on the shear are mostly from the upper-level wind change by TGWs. In the P1 simulation, gravity-wave forcing tends to increase (decrease) the shear during the first (latter) half of the simulation. In the P2 simulation, we can clearly see that gravity-wave forcing plays a role to decrease the shear in the developing and mature stages but increases the shear in the decaying stage of the typhoon. Since the background wind tendency is determined not solely by gravity-wave forcing, the wind shear after 2 hours in the simulation is different from that indicated by dashed line. Nevertheless, from Figure 3 we can estimate the gravity wave effects on the background wind shear and find that TGWs can contribute to a favorable condition for a typhoon's intensification (weakening) in the developing and mature (decaying) stages.
 Vertical wind shear direction is southwestward (southeastward) in the developing (mature and decaying) stages (not shown). The relation between the vertical wind shear and the simulated precipitation [Kim and Chun, 2010, Figure 2] is consistent with the observational study by Black et al.  who showed that precipitation associated with a typhoon is stronger in the left side of the downshear direction. TGWs do not significantly affect wind shear direction, as the sign of the gravity wave effect on the background wind shear is the same for both zonal and meridional directions. TGWs are found to shift the downshear direction slightly anticlockwise (azimuthal angle less than 10°), at least in the present case.
Figures 4a and 4c show the horizontal divergence calculated by simulated wind perturbations. Convergence associated with a typhoon vortex exists below z ∼ 14 km. There is a divergence above z ∼ 14 km, becoming large near z = 15–16 km. The upper-level divergence is largest around 18 UTC 8, about 6 hours before the typhoon begins to intensify rapidly, and then slightly decreases between 00 UTC and 06 UTC 9. It increases again after 00 UTC 9 and reaches the second largest value near 9–11 UTC 9. At this time the typhoon is still intensifying, and the typhoon intensity reaches its maximum value (mature-stage intensity) 2–3 hours after that. This upper-level divergence is positively correlated with the typhoon intensity, with a correlation coefficient of 0.75 (P1) and 0.65 (P2).
 The change of the upper-level divergence with typhoon evolution is also related to gravity-wave activity. Figures 4b and 4d show the divergence due exclusively to gravity wave components. The wave-induced divergence is relatively large above z ∼ 14 km, at which the total divergence is strong, and shows larger values in the developing and mature stages than in the decaying stage of the typhoon. The wave-induced divergence shows alternate positive and negative signs, and this varies with a period of ∼18 hours. Also, we calculated the departure of the total divergence at z = 14–17 km from its time-averaged value, and found that it also varies with a period of 18 hours (not shown). We can see the correlation between the total divergence and wave-induced divergence. When the upper-level divergence decreases (increases) with time, wave-induced divergence shows a negative (positive) sign. We found that about 50% of the upper-level divergence change is explained by TGWs, although it varies depending on the typhoon's evolution and location.
4. Summary and Conclusions
 Studies on TGWs have focused on waves' characteristics and influence mainly on the stratospheric flow so far. From modeling studies that showed significant momentum deposition in the upper troposphere and lower stratosphere by TGWs [e.g., Kim et al., 2005], it was expected that TGWs affect the typhoon development by modifying the background flow. This study examined first the impact of gravity waves generated by Typhoon Saomai on typhoon development. We investigated how TGWs modify the background flow by calculating the momentum flux of TGWs using WRF-ARW simulations. The vertical divergence of the momentum flux is relatively larger in the developing stage than in the mature and decaying stages of the typhoon. As a result, background-wind tendencies induced by TGWs are different depending on the stage of a typhoon's evolution.
 We calculated how TGWs can change the vertical wind shear, one of the inhibiting factors in a typhoon's intensification. The results show that TGWs act to decrease (increase) the vertical wind shear in the developing and mature (decaying) stages of the typhoon. This means that TGWs can contribute to favorable wind shear conditions for the developing and mature stages. On the other hand, TGWs can help a typhoon decay once typhoon intensity begins to decrease. Horizontal divergence is relatively large at z = 14–17 km and varies depending on the typhoon's evolution. Upper-level divergence, which is positively correlated with the typhoon intensity, is found to be related significantly to the gravity-wave activity.
 Based on the previous studies about effects of environmental conditions on typhoons, this study estimated how the change of the background condition by TGWs can affect the typhoon development. To understand influences of the background-flow change by TGWs on the typhoon dynamics in detail, we need more studies. Ensemble numerical simulations in various background conditions induced by TGWs would be a good way to understand the interaction between TGWs and typhoon. Finally, given that momentum forcing exerted above the cloud can induce the lower-level divergence or convergence [Kim and Chun, 2007], the effects of TGWs on the lower tropospheric environmental condition will be investigated in future studies.
 This study was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (20100000308).