Inertia gravity waves associated with deep convection observed during the summers of 2005 and 2007 in Korea

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1 JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 116,, doi: /2011jd015684, 2011 Inertia gravity waves associated with deep convection observed during the summers of 2005 and 2007 in Korea Mi Ok Ki 1 and Hye Yeong Chun 1 Received 23 January 2011; revised 13 June 2011; accepted 17 June 2011; published 27 August [1] Characteristics of inertia gravity waves associated with convection are investigated in the lower stratosphere using high resolution radiosonde data observed from 18 June to 15 July of 2005 and 2007 in Korea. Three dimensional ray tracing model and reanalysis data are used to investigate the propagation and the sources of the observed waves. The observed waves associated with convections are discriminated based on the existence of convections when and where the rays reach the average height range of convective clouds. Waves observed in 2005 and 2007 show similar spectral characteristics, but wave energy in 2007 is significantly larger than in The observed waves propagate from three source regions: the northeastern, southeastern, and western regions around Korea. They show preferential propagation directions based on their sources, and convections from the western region generate larger amplitude gravity waves than the other two regions. The spectral characteristics of the observed waves are determined largely by those of the convective forcing, along with the wave propagation condition associated with background wind and stability. The significantly larger mean wave energy in 2007 occurs because more observed waves originate from the western region of Korea in 2007 than in 2005 where convective forcing is much larger than in the other source regions. Citation: Ki, M.-O., and H.-Y. Chun (2011), Inertia gravity waves associated with deep convection observed during the summers of 2005 and 2007 in Korea, J. Geophys. Res., 116,, doi: /2011jd Introduction [2] Atmospheric gravity waves transport momentum and energy from the troposphere where they are mostly generated to the middle atmosphere where they are dissipated through diffusion, wave breaking, and critical level filtering processes. The large scale circulation in the middle atmosphere cannot be explained without considering momentum forcing by gravity waves [Lindzen, 1981; Holton, 1983; Garcia and Solomon, 1985]. [3] Many observational studies on gravity waves have been conducted using various observational techniques such as radar [Sato, 1994; Venkat Ratnam et al., 2008], satellite [Wu and Waters, 1996; Tsuda et al., 2000], radiosonde [Kitamura and Hirota, 1989; Tsuda et al., 1994; Vincent and Alexander, 2000], and rocketsonde [Hirota, 1984]. Among these, radiosonde data can be a good resource to study atmospheric gravity waves in the troposphere and lower stratosphere, which can provide wind and temperature data simultaneously with extensive temporal and geographical coverages, mostly in the Northern Hemisphere, and the high vertical resolution in lower altitudes. Several observational studies using radiosonde [e.g., Karoly et al., 1996; Vincent and Alexander, 2000; Wang et al., 2005; Chun et al., 1 Department of Atmospheric Sciences, Yonsei University, Seoul, South Korea. Copyright 2011 by the American Geophysical Union /11/2011JD ; Chun et al., 2007a] revealed that the dominant gravity waves observed by radiosonde have an intrinsic frequency of (2 3)f, a vertical wavelength of 2 5 km, and a horizontal wavelength of km. They are typically low frequency gravity waves. [4] Atmospheric gravity waves are generated mainly by tropospheric sources such as the jet stream, cumulus convection, and mountains [Fritts and Alexander, 2003, and references therein]. Among various tropospheric sources, cumulus convection is believed to be the major source for nonstationary gravity waves. Although many studies have paid attention to the tropical regions [e.g., Vincent and Alexander, 2000; Karoly et al., 2003; Tsuda et al., 2004], cumulus convection is also important as a gravity wave source in the extratropical regions, especially during summertime [e.g., Gong and Geller, 2010]. Recently, several observational and numerical studies [e.g., Sato, 1993; Kim et al., 2005; Chun et al., 2007a] were conducted to study gravity waves induced by convection in the extratropical regions. Chun et al. [2007a] reported that the observed inertia gravity waves associated with convection have an average intrinsic frequency of 3.55f, horizontal wavelength of 551 km, and vertical wavelength of 5.19 km during an observation period on August 2002, when Typhoon Rusa passed over the Korean peninsula. The mean observed horizontal and vertical wavelengths for Typhoon Rusa are consistent with the numerical modeling results of km and 3 11 km, respectively [Kim et al., 2005]. [5] Gravity waves observed by radiosonde and their relationship with convective sources have been investigated 1of16

2 Figure 1. Geographical locations of the radiosonde observation stations in Korea. by Tsuda et al. [1994], Vincent and Alexander [2000], Karoly et al. [2003], and Chun et al. [2007a]. The first three studies were conducted in the tropical region, and they correlated gravity wave energy in the lower stratosphere and convective source at the same location and time. However, Chun et al. [2007a] correlated the observed waves and their sources using a ray tracing calculation, noting that the relationship between gravity waves and their sources must be included when considering spatial and temporal propagation of gravity waves. This has particular importance for radiosonde studies because radiosondes observe mainly low frequency waves that can propagate from their source regions for long horizontal distances and durations. [6] In this study, characteristics of inertia gravity waves in the lower stratosphere and their relationship with convective sources are investigated using high resolution radiosonde data observed during the summers of 2005 and 2007 in Korea. The wave source relationship is examined based on three dimensional wave propagation using a raytracing model. In particular, the differences in the spectral characteristics, wave energy, and propagation properties of the gravity waves observed between 2005 and 2007 are investigated and associated with those in the convective sources. The wave analysis methods used in the present study are basically similar to those of Chun et al. [2007a]. However, much more careful processes are made in the selection of appropriate soundings for calculations of wave characteristics and of three dimensional ray traces to avoid any uncertainties in the methods. In addition, to understand the differences in the properties of the gravity waves observed between 2005 and 2007, detailed analyses of convective sources in the two years are made in the present study. 2. Data and Analysis Method [7] The radiosonde data collected during the Korea Enhanced Observing Program (KEOP) from 18 June to 15 July of 2005 and 2007 are used in this study. Radiosondes are observed at four stations in Korea as shown in Figure 1: Osan (37.10 N, E), Heuksando (34.68 N, E), Gosan (33.28 N, E), and Haenam (34.55 N, E). The balloons were launched four times per day at each observation station, except at Haenam, where observation was made eight times per day during a few severe events in Temperature and wind were recorded every 1 5 s, which corresponds to a height resolution of 5 30 m based on the average ascending speed of the balloons ( 5 ms 1 ). The observed soundings are equally interpolated into 50 m intervals, with smoothing from a 500 m moving average to remove noiselike fluctuations. By applying 500 m moving average, perturbations with vertical wavelengths less than 1 km are reduced significantly in their powers, although with no significant influence in the perturbations at the dominant vertical wavelengths ( 2 6 km) (not shown). [8] Because this study investigates gravity waves in the lower stratosphere, a height range of z =17 30 km is defined as the analysis segment (13 km depth). Thus, only soundings that ascended at least to 30 km can be used for the present study. The lower limit of the analysis segment is above the tropopause (z = km) over the Korean peninsula in summer [Chun and Song, 2001] and is chosen to avoid the influences of abrupt changes in temperature near the tro- 2of16

3 popause [Vincent and Alexander, 2000]. The upper limit of the analysis segment is chosen to contain components with long vertical wavelengths while, simultaneously, using as many soundings as possible for statistically meaningful results. Among 342 (430) soundings observed in 2005 (2007), 237 (211) soundings are used in the present study. [9] The perturbations of temperature and wind are obtained by subtracting the basic state profiles from the observed profiles. The basic state profiles in the analysis segment are defined as the third order polynomial using the least squares method [Vincent et al., 1997]. To make sure the observed perturbations are, in fact, inertia gravity waves, we quantitatively determine whether the observed perturbations satisfy the polarization relationship by using the degree of polarization (dp) [Eckermann, 1996]. For most soundings, dp is larger than 0.5 with an average value of 0.68 (0.71) in 2005 (2007). Observed perturbations with dp larger than 0.5 are considered as coherent inertia gravity waves and are the only ones used in the following analyses. Two hundred three (200) cases having dp larger than 0.5 are used in 2005 (2007). [10] The characteristics of observed waves are estimated from each observed sounding. The intrinsic frequency (^!)of the observed waves is obtained from the axial ratio of the hodograph of horizontal wind perturbations using Stokes parameters [Vincent et al., 1997] considering the transverseshear effect [Hines, 1989]. In the present study, we only analyze wave parameters for the soundings that satisfy the condition of 1.1f < ^! <10f [Vincent and Alexander, 2000; Yamamori and Sato, 2006], and thus 191 (189) soundings are used for the following analysis in 2005 (2007). The upper limit of the criterion is imposed, because the intrinsic frequency greater than 10f is less reliably determined considering the accuracy of horizontal wind detected by radiosonde as discussed by Vincent and Alexander [2000]. The vertical wave number (m) of the observed waves is calculated from the observed zonal and meridional wind perturbations, and the horizontal wave number (k h ) is obtained from the dispersion relationship of inertia gravity waves for a given m and ^!. Details on the estimation of wave parameters are in Appendix A. [11] To analyze sources of the observed waves, a threedimensional ray tracing model developed by Chun et al. [2007a] is used. Details on the ray tracing equations are described in Appendix B. The basic state wind, stability, and scale height required for ray tracing calculations are obtained from the European Centre for Medium Range Weather Forecasting (ECMWF) 6 hourly reanalysis data ERA interim [Simmons et al., 2007] with in longitude and latitude and 37 layers between 1000 and 1 hpa. During the ray tracing calculation, the data are spatially interpolated for each ray position. Temporal variations of the basic state wind, stability, and scale height are ignored during the calculation, and thus in the present study w is assumed to be constant while following rays. [12] The backward time integration is started at z = 23.5 km above each observation station with initial wave parameters. The starting altitude of z = 23.5 km is the center of the stratospheric analysis layer (z = km). The initial values for wave parameters (k*, l*, ^!*) are the estimated values from the observed soundings. Here, k* and l* are obtained from k h as k* =k h cos and l* =k h sin. Note that m is obtained from the dispersion relationship with given k, l, and ^!, not only for the initial step but also for each time step during the backward time integration. At the initial time step, m obtained from the dispersion relationship is consistent with that from the observed sounding. The time interval of backward integration is chosen as 100 s because the results using a time interval less than 100 s are basically the same as those with a 100 s interval. Four termination conditions are imposed for backward time integration: (1) m 2 0, (2) the ray meets the critical level (^! = f or vertical wavelength l z < 100 m), (3) the ray reaches the ground, and (4) the integration time exceeds 60 h. [13] Because radiosonde soundings might contain observational errors, wave parameters estimated from the observed soundings have inherent uncertainty. Since the back trajectories calculated by the backward time integration are generally sensitive to the initial values of rays, a sensitivity test is performed to evaluate the impact of possible errors in each initial value of the wave parameters (k*, l*, ^!*). Following Ki and Chun [2010], for each sounding we create a set of 125 rays containing all possible combinations of initial wave parameters (k 0, l 0, ^! 0 ), calculated by adding arbitrary errors of ±5% and ±10% to k*, l*, and ^!*: k 0 ¼ k* 0:05k* n; ðn ¼ 0; 1; 2Þ ð1þ l 0 ¼ l* 0:05l* n; ðn ¼ 0; 1; 2Þ ð2þ ^! 0 ¼ ^!* 0:05^!* n; ðn ¼ 0; 1; 2Þ: ð3þ [14] The initial vertical wave number m 0 is calculated using the dispersion relationship of inertia gravity waves with given k 0, l 0, and ^! 0. Therefore, for each set of wave parameters (k*, l*, ^!*), 125 rays with slightly different wave numbers and frequencies are launched at the same time and the same position. Then, the convergence cases of the observed waves are selected as follows: From the termination position of the ray having the initial wave parameters (k*, l*, ^!*), more than 70% of 125 rays are terminated (1) within a certain horizontal area (radius R = 3 in degree of longitude and latitude) and (2) within a certain vertical range (z = ±2 km). If a case satisfies these two convergence criteria, the case is used to investigate the wave source based on the ray tracing approach in the present study. Among 191 (189) observed soundings used for the ray tracing calculation, 81 (64) cases are satisfied by the convergence criteria in 2005 (2007). [15] There are also some uncertainties related to the initial position of the ray tracing calculation. First, there are uncertainties in the initial horizontal position of the raytracing calculation. Since balloons can drift horizontally by the background wind, observed horizontal position of waves in the lower stratosphere can be different from the radiosonde station at the ground. However, the balloon drift is less significant in summer than in winter near the Korean peninsula, because the jet strength is much weaker in summer. Second, there are uncertainties in the initial altitude of the ray tracing calculation. Although we launch rays at z = 23.5 km, center altitude of the wave analysis layer, 3of16

4 Figure 2. Back trajectories of the observed waves in (a) 2005 and (b) The boxes indicate domains considered as the main wave source areas. wave can be launched any height between 17 and 30 km with the same initial wave parameters. When we changed the initial launching altitudes in the range of ±2 km from z = 23.5 km, the obtained trajectories are found to be somewhat different from those launched at z = 23.5 km. Thus, some cautions might be required to conduct the raytracing calculation with initial launching position as well as initial wave parameters. 3. Results 3.1. Observed Inertia Gravity Waves Associated With Deep Convection [16] The observed waves in the present study can be generated by various sources in the troposphere. Mountains that reach up to 30 km can hardly be a source of gravity waves in this study because of critical level filtering, considering that the prevailing wind near Korea is westerly in the troposphere and easterly in the stratosphere during summer season. Cumulus convection can be an important source of gravity waves in summer near the Korean peninsula where convective clouds frequently occur along fronts associated with monsoon circulation and following typhoons. Jet stream and fronts can be other sources of gravity waves near the Korean peninsula. To evaluate upper tropospheric jet front system as a source of gravity waves near the Korean peninsula, the residual of the nonlinear balanced equation (DNBE) at 200 hpa is calculated using the ECMWF ERAinterim data following Zhang [2004]. During the period in both 2005 and 2007, the regions of DNBE larger than a threshold value of s 2 [Zhang, 2004] exist around the Korean peninsula where the horizontal wind speed exceeds 50 m s 1 at 200 hpa. However, considering that the groundbased phase speed of the gravity waves associated with the upper level jet front systems is 3 30 m s 1, as shown in the previous numerical modeling studies [e.g., Zhang, 2004; Plougonven and Snyder, 2007] and observational studies [e.g., Sato and Yoshiki, 2008], the gravity waves associated with the upper level jet front systems are mostly filtered out before they reach to the stratosphere under the summertime prevailing wind in the East Asia. Thus, it is less likely that the jet front system is a main source of observed gravity waves in the present study. [17] To determine the convective waves, the existence of convective sources is identified using equivalent blackbody brightness temperature (T BR ) data during the ray tracing calculation only using the convergence cases determined in section 2. The T BR data are measured by the Multifunctional Transport Satellite 1R (MTSAT 1R) at IR1 channel ( mm) with a horizontal resolution of 4 km 4 km at the nadir point and a temporal resolution of 1 h around the Korean peninsula over 110 E 145 E and 20 N 50 N. Geostationary Operational Environmental Satellite 9 (GOES 9) IR1 channel ( mm) measurements with a horizontal resolution of 4 km 4 km at nadir point are alternatively used when MTSAT 1R was not available during some periods in In the present study, we consider only deep convective clouds as possible convective sources of the observed gravity waves, because they are likely to generate gravity waves that can propagate up to 30 km. Since the average height range of deep convective clouds near Korea is z =6 13 km [Chun et al., 2007a], the time and horizontal location of each ray are checked when it reaches the height range of z =6 13 km. If the T BR within the 16 km 16 km horizontal domain from the horizontal location of the ray at a certain time is less than the temperature of the standard atmosphere [Holton, 1992], the observed wave is considered as the wave related to convective sources. Among 81 (64) cases that passed the convergence criteria, 29 (23) cases are classified as convective waves in 2005 (2007). [18] Figure 2 shows the back trajectories of the observed convective waves from each observation station in the summers of 2005 and During the observation periods of 2005 and 2007, the waves originate from similar regions around the Korean peninsula. The majority of the observed waves propagate from the regions located to the east and southeast of the Korean peninsula (boxes A and B in Figure 2, respectively). Some of the observed waves in 2007 originate from the west of the Korean peninsula (box C in Figure 2), while only one case in 2005 originates from that region. 4of16

5 Table 1. Averages and Standard Deviations of ^!/f, Vertical Wavelength (l z ), and Horizontal Wavelength (l h ) for the Observed Waves in 2005 and 2007 Year ^!/f l z (km) l h (km) ± ± ± ± ± ± Given that around the Korean peninsula during the observation period the prevailing tropospheric (stratospheric) wind is westerly (easterly), the waves generated by the convective sources to the east of the Korean peninsula can be detected easily in the stratosphere, as discussed by Chun et al. [2007a]. However, waves generated by the sources to the west of the Korean peninsula can be observed only if they have eastward intrinsic phase speeds large enough to overcome the easterly prevailing wind in the stratosphere. For both 2005 and 2007, the three possible source regions (domains A, B, and C) are determined based on the back trajectories of the observed waves, as indicated in Figure 2. If the back trajectory of each wave terminates in a certain domain, the wave is classified into the cases that originate from that domain. The waves that terminate within 3 in degree of longitude and latitude from a certain domain are also classified into the cases that originate from that domain to consider uncertainty of termination position of rays. Thirteen (13), 14 (4), and 1 (3) cases for 2005 (2007) are selected as the cases that originate from domains A, B, and C, respectively. [19] The intrinsic frequency, vertical wavelength, and horizontal wavelength of convective observed waves in 2005 and 2007 are similar to each other. The intrinsic frequency and vertical wavelength of the observed waves are mainly (1 4)f and 2 6 km, respectively. The horizontal wavelength of the observed waves ranges from 200 to 800 km. The average values of intrinsic frequency, vertical wavelength, and horizontal wavelength are 2.77f (2.61f ), 3.47 (3.44) km, and (560.53) km for 2005 (2007), as indicated in Table 1 (with their standard deviations). The intrinsic frequency and vertical wavelength of the present study are somewhat smaller than, while the horizontal wavelength is similar to, data observed during 20 August to 5 September 2002 in Korea, as reported by Chun et al. [2007a] (intrinsic frequency 3.55f, vertical wavelength 5.19 km, and horizontal wavelength 551 km). [20] During the observation period of Chun et al. [2007a], Typhoon Rusa influenced the regions around the Korean peninsula. Considering that wave source and propagation conditions (i.e., impact of background wind and stability) are the two major factors that determine the characteristics of gravity waves [Chun et al., 2007b], the differences in the characteristics of waves between Chun et al. [2007a] and the present study might be due to different convective sources as well as background states. The background wind and stability around the Korean peninsula during the observation periods in 2005 and 2007 are not largely different from each other, while they are somewhat different (not shown) compared with those in the summer of 2002 about which Chun et al. [2007a] reported. In 2002, the North Pacific subtropical high, which can largely determine the circulation pattern around the Korean peninsula during the summer, progressed greatly northward, and consequently the jet stream existed poleward than in 2005 and It is noted that the observation period in the present study corresponds to the East Asia summer monsoon season in Korea called Changma, and the background flows around the Korean peninsula during this period differ each year according to the interannual variabilities in the location and strength of the North Pacific subtropical high and associated variabilities in the fronts/jet streams. Another source of difference may stem from the higher vertical resolution data used in the present study. Chun et al. [2007a] used radiosonde data with vertical resolution of 700 m, much coarser than the data used in this study. Thus, even though both studies use the same analysis depth, the higher vertical resolution of the present study allows smaller vertical wavelength components than that obtained by Chun et al. [2007a], as discussed by Ki and Chun [2010]. [21] Characteristics of the inertia gravity waves in the present study are comparable to those observed by MU radar at Shigaraki in Japan (35 N, 136 E) during the passage of Typhoon Kelly (1987) reported by Sato [1993]. For two cases of the observed inertia gravity waves in Sato [1993], the horizontal wavelengths (300 and 600 km), vertical wavelengths (2.7 and 6.0 km), and intrinsic periods (9 and 8 h, which are corresponding to intrinsic frequencies as 2.32f and 2.61f ) were reported, and they are in the range of the observed wave parameters in the present study. [22] We examine the features of inertia gravity waves with respect to their possible source regions. Figure 3 shows the scatterplots of ^!/f, vertical wavelength, and horizontal wavelength of the observed waves that originate from domains A, B, and C in 2005 and The characteristics of waves from different regions are not largely different from each other. Figures 4 and 5 show the vertical profiles of horizontal wave number, vertical wave number, background wind projected to the horizontal wave number vector (V proj = ~V ( ~ k h / ~ k h )), and square of buoyancy frequency following the rays of the observed waves in domains A, B, and C, for 2005 and 2007, respectively. The horizontal wave numbers almost do not change following rays, implying that the horizontal wave numbers of the waves can be predominantly determined by their source. However, the vertical wave numbers of the observed waves change significantly during their propagation. If it is assumed that a 2 is negligibly small, m 2 can be obtained by m 2 =(k 2 + l 2 )(N 2 ^! 2 )/(^! 2 f 2 ) following the dispersion relationship of inertia gravity waves. Because the intrinsic frequency is determined mainly by V proj, the vertical wave number is determined by V proj and the buoyancy frequency for a given horizontal wave number, since the change of the Coriolis parameter is relatively small when compared with other parameters. The vertical wave numbers of the observed waves have a minimum at z =12 13 km with the small stability and the large magnitude of negative V proj, and then they increase with height due to the increasing stability and the decreasing magnitude of negative V proj in the stratosphere. [23] Figure 6 shows the intrinsic and ground based phase velocities estimated from the observed soundings in the lower stratosphere for 2005 and Details on the method to estimate the phase velocity and group velocity of observed 5of16

6 Figure 3. Scatterplots of (top) ^!/f, (middle) vertical wavelength, and (bottom) horizontal wavelength for the observed waves that originate from (a) domain A, (b) domain B, and (c) domain C as shown in Figure 2. The crosses and open circles in the scatterplots indicate cases for 2005 and 2007, respectively. The abscissas indicate the number of cases that originate from each domain. waves are in Appendix A. The intrinsic phase speed of the observed waves is generally m s 1 for both 2005 and From their source regions, the ground based phase velocities of the observed waves show preferential directions. The observed waves propagate mainly southwestward from domain A, located in the northeastern region, and northwestward and northeastward from domain B, located in the southeastern region of the Korean peninsula. From domain C, located in the western region of the Korean peninsula, the observed waves propagate mainly northeastward. This implies that the preferential propagation direction of the observed waves in this study is determined primarily by the location of source regions under the easterly background wind in the stratosphere. [24] To examine wave activity in the lower stratosphere, wave energy is also estimated for each sounding. Details on the estimation of kinetic, potential, and total wave energies are in Appendix A. Unlike similar spectral characteristics of the observed waves, the wave energies in 2005 and 2007 are largely different from each other. The average kinetic, potential, and total wave energies per unit mass are 2.24 (3.04) J kg 1, 1.35 (2.15) J kg 1, and 3.59 (5.19) J kg 1 in 2005 (2007), respectively (Table 2), and the averages of wave energies in 2005 (2007) are smaller than (comparable to) those of the observed waves (E k 3 4 Jkg 1, E p 2J kg 1, and E t 5 6 Jkg 1 ) in June and July 1998 at Pohang, Korea, reported by Chun et al. [2006]. The averages of wave energies in 2007 are significantly larger than those in 2005 at the 95% confidence level. Because the stability and background wind in 2007 are not significantly different from those in 2005, the larger wave energy in 2007 results from the larger amplitude of the observed waves. [25] Figure 7 shows the scatterplots of kinetic, potential, and total energies of the observed waves that originate from domains A, B, and C in 2005 and Distinctively, the observed waves from domain C show considerably larger wave energy compared with those from the other two domains during Among 20 cases for 2007, four cases have a total wave energy larger than one standard deviation from mean total wave energy, and two cases among them propagate from domain C. When the cases from domain C are excluded from 2007, the average kinetic and potential energies in 2007 are not significantly larger than those in 2005 at the 95% confidence level. Thus, it seems that the waves from domain C result in larger average wave energy in Given that the features of gravity waves are primarily determined by their sources and propagation conditions [Song et al., 2003; Chun et al., 2007b], and that the background wind and stability that determine the wave propagation condition are similar in 2005 and 2007, differences in the wave energies between 2005 and 2007 can be related to their convective sources. Thus, in sections 3.2 and 3.3 we will examine the characteristics of convective sources during the observation periods of 2005 and 2007, and their relationship with the observed waves. [26] We estimate the vertical fluxes of the zonal and meridional momentum of the convective gravity waves. Details on the estimation of the gravity wave momentum flux using the radiosonde data can be found in Appendix A. For the zonal momentum flux, the average values of eastward and westward momentum fluxes are (0.02) m 2 s 2 and ( 0.004) m 2 s 2 in 2005 (2007), respectively. This implies that the eastward momentum flux in 2007 is 1 order of magnitude larger than that in 2005, 6of16

7 Figure 4. Profiles of (a) horizontal wave number, (b) vertical wave number, (c) horizontal wind, and (d) square of buoyancy frequency following the rays of observed waves that originate from (top) domain A, (middle) domain B, and (bottom) domain C for although with a similar magnitude of the westward momentum fluxes in 2005 and For the meridional momentum flux, the average values of northward and southward momentum fluxes are (0.02) m 2 s 2 and ( 0.002) m 2 s 2 in 2005 (2007), respectively. Compared with the previous result in Korea by Chun et al. [2006] that calculated the total (sum of eastward and westward momentum) zonal momentum flux in 1998, the total zonal momentum fluxes in the present study are slightly smaller in 2005 with different sign ( m 2 s 2 ), but much larger in 2007 (0.016 m 2 s 2 ) than Chun et al. s [2006] June (0.002 m 2 s 2 ) and July (0.007 m 2 s 2 ) means. [27] In order to understand the differences in the momentum fluxes between 2005 and 2007, we show in Figure 8 the zonal and meridional momentum fluxes estimated from observed waves originated from domains A, B, and C, respectively. Note that y axes in domain C are different from those in domains A and B. In domain A, the 7of16

8 Figure 5. Same as in Figure 4 except for zonal and meridional momentum fluxes of 2005 and 2007 are generally similar to each other. In domain B, there are only four cases in 2007 and it is rather difficult to compare the two years. It is interesting that the meridional momentum flux is significantly larger than the zonal momentum flux in domain B, especially in 2005, and it is likely due to the convective sources including typhoons that moved northward from the southeastern and southwestern seas. In domain C, the magnitudes of the eastward and northward momentum fluxes in 2007 are considerably larger, especially one case with very large meridional momentum flux, than those in other domains, resulting in the larger averages in the eastward and northward momentum fluxes of However, the difference of the momentum fluxes between 2007 and 2005 in domain C are statistically less significant, considering only three (one) cases belonging to domain C in 2007 (2005) Convective Source [28] In the present study, cumulus convection is investigated using T BR in the region over 110 E 145 E and 20 N 50 N around the Korean peninsula with a resolution of 8of16

9 Figure 6. Distributions of intrinsic phase velocity of the observed waves for (a) 2005 and (b) 2007 and ground based phase velocity of the observed waves for (c) 2005 and (d) Dots with different colors denote the cases that originate from different domains. The cases originating from domain A, domain B, and domain C are as shown in longitude and latitude. In this study, deep convection is considered as the wave source which generates gravity waves that can propagate in the stratosphere. To estimate the existence of deep cumulus convection, the deep convective activity (DCA) index is used, following Chun et al. [2007a]: 8 < 245 T BR ; if T BR < 245 K DCA ¼ : ð4þ : 0 ; otherwise [29] Figure 9 shows the average patterns of DCA during the observation periods of 2005 and Because the observation periods occur during the East Asian monsoon season, strong convection activity associated with fronts stretches from eastern China into Korea and Japan. Compared with 2005, the convective activity of 2007 is much stronger in the southern part of Japan along the track of Typhoon Man Yi, which passed through the region during July The main source regions of the observed waves as determined by back trajectories (domains A, B, and C) correspond well to the regions of strong convection activity for both 2005 and During the observation period, DCA in domain A is smaller compared with that in B and C. Generally, the convection developed in eastern China moves northeastward along the boundary of the North Pacific subtropical high. When propagating northeastward, the convection passes over the western sea of Korea or southern Japan, and sometimes it is enhanced over those regions. Then it gradually dissipates in northeastern Japan. This explains why convective activity in domain A is weaker than in domains B and C. Table 2. Averages and Standard Deviations of Kinetic (E k ), Potential (E p ), and Total (E t ) Wave Energies per Unit Mass for the Observed Waves in 2005 and 2007 Year E k (J kg 1 ) E p (J kg 1 ) E t (J kg 1 ) ± ± ± ± ± ± of16

10 Figure 7. Scatterplots of (top) kinetic energy, (middle) potential energy, and (bottom) total energy of wave per unit mass for the observed waves that originate from (a) domain A, (b) domain B, and (c) domain C as shown in Figure 2. The crosses and open circles in the scatterplots indicate cases for 2005 and 2007, respectively. The abscissas indicate the number of cases that originate from each domain. [30] To examine the characteristics of convective forcing, the power spectral density (PSD) of DCA with respect to ground based phase speed and horizontal propagation direction is obtained. To do this, the three dimensional PSD of DCA with respect to k, l, and w [PSD(k, l, w)] is calculated in domains A, B, and C. Then the PSD with respect to ground based horizontal phase speed (c) and propagation direction (8) is constructed from k, l, and w comprising each component pffiffiffiffiffiffiffiffiffiffiffiffiffiffi of PSD(k, l, w). Here, cpand ffiffiffiffiffiffiffiffiffiffiffiffiffiffi 8 are calculated by c = w/ k 2 þ l 2 and 8 = cos 1 (k/ k 2 þ l 2 ), respectively, and 8 is the angle measured counterclockwise from the east. Details are given by Kim et al. [2009]. [31] Figure 10 shows the PSDs of DCA with respect to c and 8 in domains A, B, and C. The radius of dotted circle describes the ground based horizontal phase speed, and the angle indicates the propagation direction measured counter- Figure 8. Scatterplots of (top) zonal and (bottom) meridional momentum fluxes per unit mass averaged in the lower stratosphere for the observed waves that originated from (a) domain A, (b) domain B, and (c) domain C as shown in Figure 2. The crosses and open circles in the scatterplots indicate cases for 2005 and 2007, respectively. The abscissas indicate the number of cases that originated from each domain. 10 of 16

11 Figure 9. Averaged deep convective activity (DCA) during 18 June to 15 July of (a) 2005 and (b) The boxes indicate the same regions as in Figure 2. clockwise from the east. The white regions inside the black contour are the wave prohibition regions where more than 80% of the spectral components composing each point do not satisfy the vertical propagation condition of inertia gravity waves [ f 2 < ^! 2 < ^! c 2, where ^! c is the frequency when m 2 = 0 in (10)] between z = 17 and 30 km. To calculate both ^! and ^! c, the horizontal wind and temperature averaged in each domain are used to estimate the background wind and stability. In all domains, the convective forcing shows large power in most directions, but the largest power generally occurs in the eastward direction because of the directional movement of the convective system in the troposphere. The convective forcing that propagates in the direction of is largely filtered, and it is mainly due to critical level filtering by the basic state wind in the lower stratosphere. For 2007, considerable power shows in the north northwestward direction ( ) in domain B, and it is much larger than that for The magnitude of convective forcing in domain C is the largest among the three domains for both 2005 and [32] In order to examine possible generation mechanisms of convective gravity waves, we estimated the mean wind relative to the convection following the method proposed by Kuester et al. [2008]. We found that the dominant moving direction and speed of convections are northeastward ( 40 from east) and 0 10 m s 1 in all domains in both 2005 and When we assume the top of convection at 13 km, the mean horizontal wind at 13 km is east southeastward in all domains with a speed of 25 m s 1 and 18 m s 1 in domains A and C, respectively, and 4 ms 1 in domain B in both 2005 and Thus, the mean wind relative to the convection is southeastward larger than 10 m s 1 in domains A and C, while it is less than 10 m s 1 in domain B. This implies that the obstacle effect can be a possible generation mechanism of convective gravity waves in domain A and C, while it is less clear in domain B. Detailed analyses on the generation mechanisms of the observed convective gravity waves remain to be done for future research Relationship Between Convective Source and Observed Waves [33] Convective forcing in domains A, B, and C can generate waves that propagate in all directions from each source region, although convective forcing moving in the northeastward and southeastward directions is prominent. However, the ground based phase velocities of the waves observed in the lower stratosphere have preferential propagation directions from their source regions, as shown in Figure 6. Therefore, the forcing on the propagation directions of the observed waves is believed to explain the relationship between convective source and the observed waves. [34] To examine the relationship between the convective sources and observed waves, we first calculated a threedimensional PSD(k, l, w) of DCA using the two dimensional time series of DCA(x, y, t). Then, using the dispersion relation of the three dimensional waves, with the vertically averaged wind and stability between z = 17 and 30 km, we obtain PSD(k, l, w, m) of DCA. The reason to calculate m for the convective forcing based on the dispersion relationship of inertia gravity waves is to know the forcing components that could generate three dimensional gravity waves. Finally, we calculate one dimensional PSDs with respect to the ground based frequency, horizontal wave number, and vertical wave number. The spectral power at each bin, for example, the vertical wave number, m 0 represents the integration of PSD over the area where m 0 dm < m < m 0 + dm with dm = km 1, and the obtained power spectrum is normalized so that its integral in dm is equal to the integral of PSD(k, l, w) indkdldw. [35] Figure 11 shows the PSDs in area preserving forms with respect to the ground based period, horizontal wavelength, and vertical wavelength that are averaged in the 11 of 16

12 Figure 10. Power spectral density (PSDs) of DCA with respect to horizontal phase speed and propagation direction that obtained in domains A, B, and C indicated with boxes in Figure 2 for (left) 2005 and (right) Dotted rings indicate phase speed of 20, 40, and 60 m s 1. The white regions inside the black contour indicate wave prohibition regions where more than 80% of the wave components composing each point do not satisfy the vertical propagation condition of inertia gravity waves. 12 of 16

13 Figure 11. PSDs of DCA in domains A, B, and C along the propagation directions of the observed waves with respect to ground based period, horizontal wavelength, and vertical wavelength for (a) 2005 and (b) The gray lines are multiplied by a factor of 2 for comparison. The dots in each plot indicate average (top) ground based period, (middle) horizontal wavelength, and (bottom) vertical wavelength of observed waves from domains A (gray), B (light gray), and C (black) for 2005 (Figure 11a) and 2007 (Figure 11b) with their range shown as a bar. selected propagation directions in each domain for both 2005 and 2007: , , and 0 90 in domains A, B, and C, respectively. These propagation directions are selected based on the dominant propagation directions of the observed gravity waves in the stratosphere as shown in Figure 6, rather than the dominant propagation directions of the convective forcing shown in Figure 10. The idea behind this approach is that the convective forcing represented by PSD(k, l, w) of DCA can generate gravity waves that reach to the stratosphere with the same spectral components, unless those components are filtered out below the stratosphere by several wave dissipation processes. Therefore, the forcing components that generate gravity waves that survived in the stratosphere are the ones that we are interested in. For better comparison, the spectrum in domain A is multiplied by a factor of 2 because of its small magnitude. The dots in Figure 11 indicate the average ground based period, horizontal wavelength, and vertical wavelength of the observed waves from each domain, and the bar indicates the range of each parameter. [36] Several interesting features are shown in Figure 11. First, the characteristics of the observed waves are generally consistent with the spectral characteristics of convective forcing, although in a confined spectral range in each domain where major forcing exists. The waves observed by radiosondes in this study are mainly low frequency inertia gravity waves (1 4)f with horizontal wavelengths longer than 400 km and the vertical wavelengths ranging from 2 to 4 km. Second, the spectral shapes of the convective forcing in each domain are generally similar in 2005 and 2007, except that the magnitude of convective forcing in domain B for 2007 is larger than that for Third, the forcing components in all domains show large power in periods smaller than 10 h for both 2005 and Although convective forcing shows 13 of 16

14 a wide spectrum in the horizontal wavelengths, dominant power exists at the horizontal wavelengths of km. The forcing shows large power at the vertical wavelengths of 1 10 km, with spectral peaks at 4 6 km. Fourth, the magnitude of the convective forcing in domain C is much larger than that in the other domains for both 2005 and Although the waves from domain C in 2005 might have large wave energy, the average wave energy in 2005 is much less than that in 2007, likely because only one wave originated from domain C in The observed waves from domain C in 2007 have larger wave energy compared to those from the other domains, and they are the ones that contribute to the significantly large average wave energy in [37] Because radiosonde captures mainly the low frequency inertia gravity waves with a horizontal wavelength of km and a vertical wavelength of 2 5km[Karoly et al., 1996; Vincent and Alexander, 2000; Chun et al., 2007a], observation of only a confined spectral range of the waves induced by convective sources might be expected. Thus, the discrepancy of spectral characteristics between convective forcing and observed waves can be explained as caused by observational constraints. Also, the present analysis method to derive a single vertical wavelength from each observed radiosonde sounding has an inherent limitation because the observed waves in radiosonde are generally formed by the superposition of multiple monochromatic waves [Chun et al., 2007a]. If there is more than one primary peak in the vertical wavelength spectrum of the observed waves, the vertical wavelength estimated by equation (A1) might represent the average of the vertical wavelengths in the spectrum, which may cause the discrepancy between the forcing spectrum and the observed wave spectrum. Even so, despite some limitations of the current methodology, the characteristics of the observed waves are well represented by those of the convective forcing. This demonstrates that the spectral characteristics of the forcing and the vertical propagation condition of gravity waves can determine the observed features of gravity waves in the stratosphere, as pointed out by Song et al. [2003] and Chun et al. [2007b]. 4. Summary and Conclusions [38] Using high resolution radiosonde data, characteristics of inertia gravity waves associated with convections are investigated in the lower stratosphere during 18 June to 15 July of 2005 and 2007 in Korea. To examine the sources and propagation properties of the observed waves, a threedimensional ray tracing model is used. The convective gravity waves are determined based on the existence of deep convections during a ray tracing calculation using initial parameters estimated from radiosonde soundings. When the rays of the observed waves propagate downward, passing through the deep convection region in the height range of 6 13 km, the observed waves are considered as convective gravity waves. The observed waves show similar characteristics between 2005 and The average intrinsic frequency, vertical wavelength, and horizontal wavelength of the observed waves are 2.77f (2.61f), 3.47 (3.44) km, and (560.53) km for 2005 (2007), respectively. On the other hand, the observed waves in 2007 show significantly larger wave energy than those in The average kinetic, potential, and total wave energies per unit mass are 2.24 (3.04) J kg 1, 1.35 (2.15) J kg 1, and 3.59 (5.19) J kg 1 in 2005 (2007), respectively. [39] The observed waves in 2005 and 2007 originate from the same general regions around the Korean peninsula. They propagate mainly from the northeastern, southeastern, and western regions around the Korean peninsula with preferential propagation directions opposite the direction to their source regions. The observed waves are classified into three groups based on their source regions in the above three regions around the Korean peninsula. Among 28 (20) observed waves, 13 (13), 14 (4), and 1 (3) cases for 2005 (2007) are considered as the cases that originate from the northeastern, southeastern, and western regions around the Korean peninsula, respectively. To understand the relationship between the observed waves and the convective sources in the three source regions, we compare the spectral characteristics of the observed waves and the convective forcings in the directions of major wave propagation in the stratosphere in each domain. The spectral characteristics of the observed waves are generally represented by those of the convective forcings in their source regions. [40] Wave characteristics between 2005 and 2007 are compared in conjunction with yearly variation of convective sources and wave propagation conditions through the background wind and stability. It is found that the observed waves in the lower stratosphere in 2005 and 2007 are similar to each other in many aspects, except for the significantly larger wave energy in 2007 than in There are two possible reasons for the similar characteristics of the observed waves in 2005 and First, the convective forcing in possible source regions shows similar spectral characteristics between 2005 and 2007, although their magnitude is somewhat different. Thus, the similar characteristics of the observed waves can result from the similar spectral characteristics of convective forcings in their source regions. Second, because only a confined spectral range of the gravity waves can be captured by radiosondes, the similar characteristics of the observed waves between 2005 and 2007 can be influenced by the observational window of the radiosonde. The significantly larger mean wave energy in 2007 (compared to 2005) results from the larger number of waves in 2007 (three waves compared to one wave in 2005) from the western region on the Korean peninsula, where convective forcings are much larger than in other source regions. [41] It is noteworthy that the convective gravity waves revealed in the present radiosonde observations are relatively low frequency components among the wide range spectrum of the convective gravity waves observable in the atmosphere. Nevertheless, the current information can be useful to validate recent high resolution general circulation models (GCMs) that explicitly resolve gravity waves and to develop convective gravity wave parameterization used in GCMs. Considering that there is not much observational evidence of the convective gravity waves in the midlatitudes, the current results also can be used as a valuable information to advance our understanding of the generation and propagation of convective gravity waves. Appendix A: Wave Analysis [42] The mean horizontal propagation direction (8) of gravity waves is determined by 8 = tan 1 (y/x) using 14 of 16