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    The flight (a) route and (b) altitude (gray line) with vertical acceleration (m s−2; black line) as a function of time from 0956 (at Jeju) to 1115 (at Osaka) UTC 2 Sep 2007, derived from the DFDR with a 1-s interval. The location (33.679°N, 131.264°E) and time (1034 UTC) of the turbulence encounter are depicted as a black aircraft in (a) and a labeled arrow in (b), respectively.

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    (a) Vertical acceleration (solid line), wind speed (dashed line), and wind direction (dotted line) and (b) TKE (dotted line) and flight level (solid line) as a function of time from 1033:10 to 1036:10 UTC 2 Sep 2007, derived from the DFDR. The vertical lines contain the start (89 s) and end (109 s) times of the turbulence event.

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    Brightness temperature (shading) obtained from the MTSAT 4-km data at (a) 0733, (b) 0833, (c) 0933, and (d) 1033 UTC and sea level pressure (white contours) derived from the NCEP–NCAR reanalysis data with 1° × 1° horizontal grid spacing at 0600 UTC 2 Sep 2007 over South Korea and western Japan. Contour intervals in all plots are 4 hPa, and the location of the turbulence encounter is depicted as an asterisk in all plots.

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    Time series for the minimum BT (solid line) within the inner boxes shown in Fig. 3, calculated using the MTSAT data with 20–30-min time intervals. Note that lower (higher) values of the minimum BTs are in the upper (lower) portion of the y axis. The vertical dashed line indicates the time of the turbulence encounter by the aircraft.

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    Horizontal locations of (a) the first three domains (domain 1 with Δx = 30 km, domain 2 with Δx = 10 km, and domain 3 with Δx = 3.3 km) superimposed on the terrain height (m) of domain 1 and (b) the last four domains (domain 3, domain 4 with Δx = 1.1 km, domain 5 with Δx = 0.37 km, and domain 6 with Δx = 0.12 km) superimposed on the terrain height (m) of domain 3. The contour intervals in (a) and (b) are 300 and 200 m, respectively. Locations of the turbulence encounter and the radiosonde station at Fukuoka are depicted in (b) as an asterisk within domain 6 and a dot within a circle in domain 4, respectively.

  • View in gallery

    (a) Geopotential height (contours) superimposed on horizontal wind speed (shading; reference vector is 30 m s−1) and direction (vector orientation) at 300 hPa and (b) SLP (contours) at 1200 UTC 2 Sep 2007, obtained from RDAPS 30-km analysis data provided by (left) KMA and (right) WRF model output of domain 1. Contour intervals in (a) and (b) are 60 gpm and 4 hPa, respectively. The location of the turbulence encounter is depicted as an asterisk in all plots, just down and to the right of the center of each panel.

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    Skew T–logp diagram (solid line is temperature and dashed line is dewpoint) obtained from the observed (black lines) and the simulated (gray lines) soundings at Fukuoka at 0600 UTC 2 Sep 2007. Simulated (rightmost profile) and observed (leftmost profile) wind speeds and directions at each level are shown on the right side of the diagram with full (10 m s−1) and half (5 m s−1) barbs. Isotherms in 10°C intervals are denoted as slantwise thin lines.

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    (a) Composite image obtained from the MTSAT at 1033 UTC and (b) column-maximum radar reflectivity (shading) and sea level pressure (contours), derived using the simulated result in domain 2 at 1030 UTC 2 Sep 2007. Location of the turbulence encounter is depicted as an asterisk in (b).

  • View in gallery

    Simulated SGS TKE (>0.1 m2 s−2; shading) with total cloud mixing ratio (>0.1 g kg−1; contours) in domain 4 at z = 11.2 km at (a) 0800, (b) 0830, (c) 0900, (d) 0930, (e) 1000, and (f) 1030 UTC 2 Sep 2007. The location of the turbulence encounter and the flight route of the aircraft around the event time are depicted as the asterisk in (a)–(f) and the dots in (f), respectively. The inner boxes mark the region of deep convection.

  • View in gallery

    Time series of the maximum vertical velocity (solid line) within the inner boxes shown in Fig. 9, calculated using the model outputs of domain 4 with 1.1-km horizontal grid spacing and 10-min time intervals. The vertical dashed line indicates the time (1034 UTC) of the turbulence encounter.

  • View in gallery

    Vertical cross sections of total cloud mixing ratio >0.05 (light shading) and >0.1 (dark shading) g kg−1 with potential temperature (contours) taken along the diagonal solid line in Fig. 9f at (a) 0800, (b) 0830, (c) 0900, (d) 0930, (e) 1000, and (f) 1030 UTC 2 Sep 2007. Contour intervals in all plots are 2 K. The location of the turbulence encounter projected on the cross sections is depicted as an asterisk in all plots.

  • View in gallery

    SGS TKE (shading) with total cloud mixing ratio (0.05, 0.1, and 1 g kg−1; thick lines) and potential temperature (contours) in the inner boxes in Fig. 11 at (a) 0800, (b) 0830, (c) 0900, (d) 0930, (e) 1000, and (f) 1030 UTC 2 Sep 2007. Contour intervals in all plots are 2 K except in (e) and (f), which are 1 K. The arrows in (b) are described in the text. The asterisk in (e) and (f) indicates the location of the turbulence encounter.

  • View in gallery

    (a) SGS TKE (shading), total cloud mixing ratio (0.03, 0.1, and 1 g kg−1; solid contours), and horizontal wind vectors at z = 11.2 km in domain 5. Vertical cross sections of (b) horizontal wind speed (shading), (c) ∂u/∂z (shading), and (d) SGS TKE (shading) along the blue line in (a), using the model results in domain 6 at 1014 UTC 2 Sep 2007. Blue and black contours in (b) and (c) are y vorticity (s−1) and total cloud mixing ratio (0.03 and 0.1 g kg−1), respectively. In (d), the blue contour is zero N2 at 1014 UTC, and the black and red lines show the total cloud mixing ratio of 0.03 g kg−1 and the isentrope of 346 K at 1012 (dashed) and 1014 (solid) UTC, respectively. Negative values in (b)–(d) are stippled. The turbulence location in all plots is indicated by an asterisk.

  • View in gallery

    Vertical cross sections of (left) SGS TKE (shading) with total cloud mixing ratio (0.03 and 0.1 g kg−1; blue lines) and potential temperature (black contours) and (right) the Richardson number (shading) with zero N2 (thick line) and VWS (contours) along the blue line in Fig. 13a at (a),(b) 1014, (c),(d) 1024, and (e),(f) 1034 UTC 2 Sep 2007, calculated using the model results of domain 6. Contour intervals in left and right panels are 2 K and 0.01 s−1, respectively. The turbulence location projected in the cross section is depicted as an asterisk in all plots.

  • View in gallery

    As in the left panels of Fig. 14, but showing the resolved TKE (shading), as defined in the text, at (a) 1014, (b) 1024, and (c) 1034 UTC.

  • View in gallery

    (a)–(c) As in the left panel of Fig. 14, but taken at (a) 0956, (b) 1000, and (c) 1004 UTC. (d) Same as Fig. 14a. (e) The temporal evolution (tx cross section) of vertical velocity (m s−1) at z = 12.5 km in (a)–(d) with vertically averaged SGS TKE (shading) between z = 12.7 and 13.3 km. The y axis is the time from 0930 UTC, when the gravity waves begin to appear. (f) The vertical profile of zonal-mean horizontal wind speed U in (b). Slant lines in (e) and the vertical line in (f) represent a phase speed of 3.2 m s−1, and the horizontal line in (f) is z = 13.6 km.

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A Numerical Simulation of Convectively Induced Turbulence above Deep Convection

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  • 1 Department of Atmospheric Sciences, Yonsei University, Seoul, South Korea
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Abstract

At 1034 UTC 2 September 2007, a commercial aircraft flying from Jeju, South Korea, to Osaka, Japan, at an altitude of approximately 11.2 km encountered severe turbulence above deep convection. To investigate the characteristics and generation mechanism of this event, the real atmosphere is simulated using the Weather Research and Forecasting model with six nested domains, the finest of which is a horizontal grid spacing of 120 m. The model reproduces well the observed large-scale flows and the location and timing of the turbulence along the evolving deep convection. Three hours before the incident, isolated deep convection with two overshooting tops develops in a warm area ahead of the cold front in the southwestern region of the turbulence. As the deep convection moves with the dominant southwesterly flow toward the incident region, its thickness shrinks significantly because of weakening of upward motions inside the convection. Twenty minutes before the incident, the dissipating convection disturbs the southwesterly flow at the incident altitude, enhancing local vertical wind shear above the dissipating convection. The leading edge of the cloud stretches toward the lee side because of shear-induced y vorticity, finally overturning. This activates turbulence and vertical mixing at the cloud boundary through convective instability in the entrainment process. While the dissipating convection, its thickness still shrinking, continues to move toward the observed turbulence region, the turbulence generated at the cloud interface is advected by the dominant southwesterly flow, emerging about 1–2 km above the dissipating convection and intersecting the aircraft’s flight route at the incident time.

Corresponding author address: Prof. Hye-Yeong Chun, Dept. of Atmospheric Sciences, Yonsei University, 262 Seongsanno, Seodaemun-ku, Seoul 120-749, South Korea. E-mail: chunhy@yonsei.ac.kr

Abstract

At 1034 UTC 2 September 2007, a commercial aircraft flying from Jeju, South Korea, to Osaka, Japan, at an altitude of approximately 11.2 km encountered severe turbulence above deep convection. To investigate the characteristics and generation mechanism of this event, the real atmosphere is simulated using the Weather Research and Forecasting model with six nested domains, the finest of which is a horizontal grid spacing of 120 m. The model reproduces well the observed large-scale flows and the location and timing of the turbulence along the evolving deep convection. Three hours before the incident, isolated deep convection with two overshooting tops develops in a warm area ahead of the cold front in the southwestern region of the turbulence. As the deep convection moves with the dominant southwesterly flow toward the incident region, its thickness shrinks significantly because of weakening of upward motions inside the convection. Twenty minutes before the incident, the dissipating convection disturbs the southwesterly flow at the incident altitude, enhancing local vertical wind shear above the dissipating convection. The leading edge of the cloud stretches toward the lee side because of shear-induced y vorticity, finally overturning. This activates turbulence and vertical mixing at the cloud boundary through convective instability in the entrainment process. While the dissipating convection, its thickness still shrinking, continues to move toward the observed turbulence region, the turbulence generated at the cloud interface is advected by the dominant southwesterly flow, emerging about 1–2 km above the dissipating convection and intersecting the aircraft’s flight route at the incident time.

Corresponding author address: Prof. Hye-Yeong Chun, Dept. of Atmospheric Sciences, Yonsei University, 262 Seongsanno, Seodaemun-ku, Seoul 120-749, South Korea. E-mail: chunhy@yonsei.ac.kr

1. Introduction

Deep convection in the atmosphere is one of the important sources for generating small-scale turbulent eddies (roughly 50–1000-m horizontal size) that can affect commercial aircraft. According to Kaplan et al. (2005), 86% of the severe turbulence events that caused human or structural damage in the United States from 1990 to 1996 occurred less than 100 km from the observed convective clouds. In the climatological behavior of upper-level turbulence (>20 000 ft; 1 ft ≈ 0.305 m) as recorded in pilot reports, approximately 20% of the turbulence over the United States (Wolff and Sharman 2008) and 11% of the turbulence over South Korea (Kim and Chun 2011) are related to deep convection, as identified by lightning-flash data.

Convectively induced turbulence (CIT) is generally classified into one of two categories, depending on its location: in-cloud CIT and out-of-cloud CIT (Lester 1994). In-cloud CIT occurs in cloud boundaries because of strong variations in vertical velocity within the convective updraft. Although it is difficult to predict exactly the initiation and generation of individual convective cells using operational numerical weather prediction (NWP) models with ~10-km horizontal grid spacing, pilots may easily avoid possible encounters with in-cloud CIT by detecting cloud boundaries visually and by observing onboard radar echoes. On the other hand, it is more difficult to identify the presence (generation, propagation, and dissipation) of out-of-cloud CIT, because it usually occurs in cloud-free or clear-air weather conditions.

As observational techniques and computational capacity have developed, several studies to understand out-of-cloud CIT have been conducted. Luce et al. (2010) used very high frequency middle-and-upper-atmosphere radar and lidar to observe clear-air turbulence underneath cirrus clouds ahead of an accompanying warm front. Lenz et al. (2009) and Bedka et al. (2010) showed that convectively induced transverse bands and overshooting tops, detected by brightness temperatures (BTs) through the infrared (IR) window channel of geostationary satellites with horizontal resolution of ~1 km, correlate highly with in situ turbulence data observed by commercial aircraft.

The spatial and temporal resolution of current observations still are not fine enough to understand the microscale phenomenon of out-of-cloud CIT. One feasible way to overcome this limitation is to investigate observed cases by using a high-resolution numerical model to simulate the entire evolving three-dimensional structure of a specific instance of turbulence, along with its surrounding atmospheric conditions such as convection and large-scale flows. To do this, it is essential to simulate simultaneously the entire evolution of atmospheric flows at multiscales, ranging from large-scale forcing to small-scale out-of-cloud CIT that may directly affect an aircraft.

Several studies have been done using high-resolution numerical models to investigate the generation mechanisms of out-of-cloud CIT. In Lane et al. (2003), the Dickinson turbulence event that occurs above developing convection was simulated in two- and three-dimensional numerical simulations with seven nested domains that reasonably reproduced not only the large-scale flow but also the out-of-cloud CIT. Lane et al. classified the generation mechanism for out-of-cloud CIT into two categories: 1) convective and shearing instabilities above the developing convection that are caused by convectively induced strong flow deformation and 2) subsequent breakdown of the convectively induced gravity waves after the initial overshooting tops. Given that in a two-dimensional framework the background zonal wind above the convection decreases with height (i.e., a negative wind shear condition), the wave propagating to the westward (i.e., in the downshear direction) can break down when it approaches its critical level at which the phase speed is equal to the background zonal wind, which finally leads to out-of-cloud CIT farther above the convection. Lane and Sharman (2008) extended the Lane et al. (2003) results to examine the effect of changing wind shear and static stability on gravity wave breaking above deep convection. Using a series of two- and three-dimensional ideal simulations, they showed that the altitude of the out-of-cloud CIT above the deep convection depends on the strength of the vertical wind shear (VWS) and the atmospheric stability above the deep convection. They suggested that additional sensitivity tests for directional wind shear and cloud properties, as well as other real-case simulations under various conditions, are still necessary to investigate the unexpected nature of out-of-cloud CIT.

Because of the potential severity of CIT, the Federal Aviation Administration (FAA) recommends in its avoidance guidance that an aircraft flying over a developing and/or mature thunderstorm should avoid cloud top by at least 1000 ft vertically for every 5 m s−1 of cloud-top wind speed (FAA 2012). Commercial airlines in South Korea have similar guidelines to avoid CIT. For example, a commercial aircraft should climb to at least 5000 ft above cloud top when it passes over well-organized deep convection (J.-S. Shin 2008, personal communication). It is still unclear whether such guidance allows an aircraft to avoid out-of-cloud CIT in all cases.

A particularly severe turbulence event occurred en route from Jeju, South Korea, to Osaka, Japan, at 1034 UTC 2 September 2007 near convection and eventually caused six in-flight injuries. Unlike the case of the Dickinson turbulence that occurred above developing convection (Lane et al. 2003), this case likely occurred above dissipating convection. The objective of this study is to document the detailed evolution of the observed turbulence near deep convection and to investigate the generation mechanism of the turbulence with numerical simulations. The Advanced Research Weather Research and Forecasting (ARW-WRF; Skamarock et al. 2008) model with six nested domains is used to simulate simultaneously multiple atmospheric conditions that range from large-scale flow to subsequent turbulence generation. Section 2 describes the investigation of the turbulence encounter, and section 3 gives the experimental design of the ARW-WRF model. Section 4 compares the model results with available observations. Details of the convective evolution and the turbulence generation mechanism are investigated in section 5 using the high-resolution simulation results. A summary and discussion are given in the last section.

2. Investigation of the turbulence encounter

On 2 September 2007, a commercial passenger aircraft (Airbus A300) en route from Jeju to Osaka encountered severe turbulence near Fukuoka, Japan, at 33.68°N, 131.26°E (Fig. 1a). Figure 1b shows the flight altitude (ft) and vertical acceleration (g = 9.8 m s−2) as a function of the flight time from 0956 to 1115 UTC, obtained from the digital flight data recorder (DFDR). To examine more precisely the turbulent features in the DFDR around the incident time (1034:40 UTC), we show in Fig. 2 the time series of the vertical acceleration, wind speed, wind direction, turbulent kinetic energy (TKE), and flight level for 3 min from 1033:10 to 1036:10 UTC. The DFDR data are recorded every 1 s for the vertical acceleration and 4 s for the winds, and the winds are linearly interpolated to 1 s. In Fig. 2b, TKE [=(u2 + υ2)/2] is calculated by the wind perturbations that are defined by subtracting the background velocities that are averaged over 8 s (from 4 s before to 4 s after each time). Because the speed of the aircraft was 260 m s−1 during the period, horizontal scales of the turbulent motion retain less than 2 km (i.e., aircraft-scale turbulence) (Sharman et al. 2012; Lane et al. 2012).

Fig. 1.
Fig. 1.

The flight (a) route and (b) altitude (gray line) with vertical acceleration (m s−2; black line) as a function of time from 0956 (at Jeju) to 1115 (at Osaka) UTC 2 Sep 2007, derived from the DFDR with a 1-s interval. The location (33.679°N, 131.264°E) and time (1034 UTC) of the turbulence encounter are depicted as a black aircraft in (a) and a labeled arrow in (b), respectively.

Citation: Journal of Applied Meteorology and Climatology 51, 6; 10.1175/JAMC-D-11-0140.1

Fig. 2.
Fig. 2.

(a) Vertical acceleration (solid line), wind speed (dashed line), and wind direction (dotted line) and (b) TKE (dotted line) and flight level (solid line) as a function of time from 1033:10 to 1036:10 UTC 2 Sep 2007, derived from the DFDR. The vertical lines contain the start (89 s) and end (109 s) times of the turbulence event.

Citation: Journal of Applied Meteorology and Climatology 51, 6; 10.1175/JAMC-D-11-0140.1

After the aircraft departed from Jeju at 0956 UTC, it ascended to its cruising altitude of 35 000 ft (Fig. 1b). Near 1034 UTC (Fig. 2a), it suddenly experienced two patches of strong variations in vertical acceleration, that is, 2.26g (between +1.92g and −0.34g) around 89 s and 0.97g (between +1.55g and +0.57g) around 105 s. This is consistent with two strong peaks in the wind speed and direction. The variations of 2.26g and 0.97g correspond to extreme and moderate–severe intensities of turbulence as given by the standard turbulence criteria of the International Civil Aviation Organization (Schwartz 1996) and FAA (Lane et al. 2012). This event lasts for about 30 s (about 8 km in horizontal distance, shown as two vertical lines). During this event, the aircraft experienced strong bumpiness three times, shown as steep changes of the flight level (solid) in Fig. 2b. After that, the pilots changed their cruising altitude to escape this turbulent flow (Fig. 2b), and then the vertical acceleration and wind speed and direction become smoother (Fig. 2a). The TKE averaged during this event (30 s) is 6.23 m2 s−2. In section 5c, this value will be compared with the simulated turbulence. Note that we cannot extract the cube root of the eddy dissipation rate (ε1/3; Cornman et al. 1995, 2004) because of the lack of additional information on the aircraft state (mass, inertial vertical velocity, etc.).

The reported cruising altitude of 35 000 ft at the incident time corresponds to an actual height of z = 11.2 km, computed by converting the pressure (241.7 hPa), as measured by the onboard barometer, to height using the standard atmospheric assumption (e.g., Lane et al. 2003; Kim and Chun 2010). After this incident, in which four passengers and two flight attendants suffered major or minor injuries, the aircraft changed its cruising altitude to 30 000 ft and eventually landed at Osaka at 1115 UTC. According to the pilots’ statements, the impending turbulence gave no warning signs such as visually detectable deep convection or well-organized onboard radar echoes surrounding the aircraft (J.-S. Shin and I.-G. Kim 2008, personal communications).

To determine the existence of deep convection along the large-scale flow before the incident time, the evolution of BT around the turbulence location is examined at four different times (Fig. 3). Data in Fig. 3 come from the IR channel of the Multifunctional Transport Satellite (MTSAT) with 4-km-horizontal-resolution data. Figure 3 also shows sea level pressure (SLP) at 0600 UTC, derived from the 6-hourly National Centers for Environmental Prediction–National Center for Atmospheric Research (NCEP–NCAR) reanalysis data with 1° × 1° horizontal grid spacing (Derber et al. 1991). As can be seen from the SLP at 0600 UTC, a low pressure system with the minimum SLP of 1001.28 hPa was located over the East Sea, and a cold front was elongated to the southwest into the Korea Strait. Ahead of this front, isolated deep convection appeared on the southwestern side of the turbulence location at 0730 UTC, about 3 h before the turbulence encounter (Fig. 3a). Under these synoptic circumstances, the prefrontal trough on the warm-air side of the cold front provided the conditions necessary to develop the convection. As the convection moved northeastward, carried by the dominant southwesterlies, it continued to develop until 0830 UTC (Fig. 3b). The convection then began diffusing and spreading horizontally (Fig. 3c) until 1030 UTC (Fig. 3d), demonstrating that the deep convection analyzed in this study was in the dissipating stage near the turbulence incident time and location.

Fig. 3.
Fig. 3.

Brightness temperature (shading) obtained from the MTSAT 4-km data at (a) 0733, (b) 0833, (c) 0933, and (d) 1033 UTC and sea level pressure (white contours) derived from the NCEP–NCAR reanalysis data with 1° × 1° horizontal grid spacing at 0600 UTC 2 Sep 2007 over South Korea and western Japan. Contour intervals in all plots are 4 hPa, and the location of the turbulence encounter is depicted as an asterisk in all plots.

Citation: Journal of Applied Meteorology and Climatology 51, 6; 10.1175/JAMC-D-11-0140.1

To examine the evolution of the convection’s intensity quantitatively, the time series of the minimum BTs found within the inner boxes (shown in Fig. 3) is depicted in Fig. 4, using the MTSAT data with 20–30-min time intervals. Note that lower (higher) values of the minimum BTs are in the upper (lower) part of the y axis. As shown in Fig. 4, there are two peaks in minimum BT, one at 0810 UTC (218.07 K) and the other at 0850 UTC (216.91 K), indicating that the deep convection was in the developing and/or mature stage until 0900 UTC and further implying that the height of the cloud top increased abruptly because of the two overshooting tops within the deep convection. After 0900 UTC, the minimum BTs increased significantly to 224.65 K at 1000 UTC. In the horizontal and vertical distributions of the radar reflectivity near the encounter region at 1030 UTC in Japan, echo structure of the convection represents a single-cell convection (A. Kudo 2011, personal communication), indicating that the deep convection investigated in this study was a single-cell-type convection. This also strongly suggests that the turbulence encounter at 1034 UTC 2 September 2007 was related to this deep convection while in the dissipating stage. In such conditions, it is likely that pilots near the dissipating convection would have had difficulty in detecting any indication of severe turbulence. In summary, the violent turbulence occurred for 30 s, corresponding to 8 km of horizontal coverage near Fukuoka around 1034 UTC 2 September 2007, when the eastward-cruising aircraft at 35 000 ft (z = 11.2 km) passes through northeastward-moving convection.

Fig. 4.
Fig. 4.

Time series for the minimum BT (solid line) within the inner boxes shown in Fig. 3, calculated using the MTSAT data with 20–30-min time intervals. Note that lower (higher) values of the minimum BTs are in the upper (lower) portion of the y axis. The vertical dashed line indicates the time of the turbulence encounter by the aircraft.

Citation: Journal of Applied Meteorology and Climatology 51, 6; 10.1175/JAMC-D-11-0140.1

3. Experiment design of the model

The high-resolution numerical model used in this study is the ARW-WRF model, version 3.1, which was developed by NCAR and released in April of 2009. This model is governed by nonhydrostatic and fully compressible prognostic equations on a grid structure of the Arakawa-C type. Detailed configurations of this model can be found in Skamarock et al. (2008). The ARW-WRF model has been used successfully for NWP and research. This model also has been used for studies on aviation turbulence (e.g., Feltz et al. 2009; Trier and Sharman 2009; Trier et al. 2010; Kim and Chun 2010).

Figure 5 shows the locations of the six nested domains considered in this study, with horizontal grid spacings of 30, 10, 3.3, 1.1, 0.37, and 0.12 km in domains 1, 2, 3, 4, 5, and 6, respectively. The locations of all domains are chosen to encompass the region of the turbulence encounter, as shown in Fig. 5b. To facilitate direct comparison of large-scale atmospheric conditions, domain 1 has the same horizontal grid spacing (Δx = 30 km) and extent (5730 km × 5130 km) as the analysis data from the Regional Data Assimilation and Prediction System (RDAPS) of the Korean Meteorological Administration (KMA). Model top is 20 hPa (about z = 27 km) with 113 vertical sigma layers. Vertical grid spacing in all domains decreases from 300 m at the planetary boundary layer (PBL) top (about z = 2 km) to 100 m at z = 9 km, and then it increases linearly from 100 m at z = 13 km to 500 m at the model top. Between z = 9 and 13 km and below the PBL top, constant vertical grid spacings of about 100 m and 50 m, respectively, are used. In all domains, a sponge layer with Rayleigh damping is applied in the uppermost 5 km to prevent artificial reflections from the rigid upper boundary, and lateral boundary layers are specified with 5 relaxation grid points. For initial and boundary conditions, the 6-hourly NCEP global final (FNL) reanalysis data with 1° × 1° horizontal grid spacing are used. The model was integrated for 18 h (0000–1800 UTC 2 September 2007) in domains 1 and 2 and for 9 h (0600–1500 UTC 2 September 2007) in domains 3, 4, 5, and 6. To simulate several scales of atmospheric flows simultaneously, two-way nesting interactions are conducted among domains 1–6 for 9 h (0600–1500 UTC 2 September 2007) and between domains 1 and 2 for 18 h (0000–1800 UTC 2 September 2007).

Fig. 5.
Fig. 5.

Horizontal locations of (a) the first three domains (domain 1 with Δx = 30 km, domain 2 with Δx = 10 km, and domain 3 with Δx = 3.3 km) superimposed on the terrain height (m) of domain 1 and (b) the last four domains (domain 3, domain 4 with Δx = 1.1 km, domain 5 with Δx = 0.37 km, and domain 6 with Δx = 0.12 km) superimposed on the terrain height (m) of domain 3. The contour intervals in (a) and (b) are 300 and 200 m, respectively. Locations of the turbulence encounter and the radiosonde station at Fukuoka are depicted in (b) as an asterisk within domain 6 and a dot within a circle in domain 4, respectively.

Citation: Journal of Applied Meteorology and Climatology 51, 6; 10.1175/JAMC-D-11-0140.1

The physical parameterizations used in this study include the cloud microphysics scheme by Hong and Lim (2006), the land surface scheme by Chen and Dudhia (2001), the shortwave radiation scheme by Dudhia (1989), the longwave radiation scheme by Mlawer et al. (1997), and the Mellor–Yamada–Janjić (MYJ) PBL scheme by Janjić (2002). The cumulus parameterization scheme by Kain (2004) is used only in domains 1 and 2. Note that the MYJ PBL scheme selected in this study takes into account the vertical mixing not only in the PBL but also in the free atmosphere by predicting subgrid-scale (SGS) TKE. In the selected PBL scheme, the nonzero SGS TKE is generated when the gradient Richardson number Rig is smaller than the critical value (0.505; Janjić 2002). Here,
eq1
where U and V are the grid-scale zonal and meridional wind components, respectively; θυ is the virtual potential temperature; and . Horizontal mixing is calculated using the Smagorinsky first-order closure scheme (Skamarock et al. 2008).

4. Comparison between the observations and model results

In this section, the large-scale features and deep convection simulated in the model are compared with those in the available observations, such as the RDAPS analysis data, radiosonde sounding data, and MTSAT imagery, to examine how the model reproduces the real atmosphere in the present case.

First, synoptic-scale flows assimilated in the 30-km RDAPS domain (Fig. 6, left) are compared with those simulated in the 30-km WRF model domain (domain 1; Fig. 6, right) at 1200 UTC 2 September 2007. Note that 1200 UTC is the closest time among the 12-hourly RDAPS analysis data to the incident time (1034 UTC). At the 300-hPa level (Fig. 6a), a highly curved upper-level trough with a jet stream of 48–50 m s−1 is located over the Korean Peninsula. The trough moves eastward toward the incident region following the prevailing westerly wind and the southwesterly jet. This trough and southerly jet along the boundary of the northwestern Pacific Ocean high are converging near the turbulence location. At the surface (Fig. 6b), a low pressure system, with a minimum SLP of 1001 hPa, is located over the East Sea, and its cold front is elongated to the Korea Strait. The low pressure system is being strengthened as the upper-level trough approaches the surface frontal system. Figure 6 shows that the large-scale flow surrounding the turbulence region is fairly well reproduced in the WRF 30-km model domain.

Fig. 6.
Fig. 6.

(a) Geopotential height (contours) superimposed on horizontal wind speed (shading; reference vector is 30 m s−1) and direction (vector orientation) at 300 hPa and (b) SLP (contours) at 1200 UTC 2 Sep 2007, obtained from RDAPS 30-km analysis data provided by (left) KMA and (right) WRF model output of domain 1. Contour intervals in (a) and (b) are 60 gpm and 4 hPa, respectively. The location of the turbulence encounter is depicted as an asterisk in all plots, just down and to the right of the center of each panel.

Citation: Journal of Applied Meteorology and Climatology 51, 6; 10.1175/JAMC-D-11-0140.1

Some noticeable discrepancies exist in Fig. 6b between the simulation and RDAPS: 1) the SLP pattern at the western edge of the WRF 30-km domain (over the Tibetan plateau region near 30°–35°N, 100°–105°E) is less clear in the simulation and 2) the ninth typhoon, Typhoon Fitow, centered near 28°N, 149°E in the southeastern part of the domain, is less intense in the simulation than in the observations. The reduced typhoon intensity may be caused by the absence of a tropical-cyclone bogus scheme during the model initialization process. These differences notwithstanding, upper-level large-scale flows (Fig. 6a) and SLP (Fig. 6b) near the turbulence region (shown as an asterisk in Fig. 6) seem not to be affected significantly by either the air flows over the Tibetan Plateau or the Typhoon Fitow. Because the realistic simulation of the SLP over the Tibetan Plateau and/or the Typhoon Fitow is not the main purpose of this study, it is concluded that the larger-scale simulation in the area of the turbulence is sufficient for the purposes of this study.

Fukuoka, shown as a dot surrounded by a circle in Fig. 5b, is the closest radiosonde station to the turbulence location, although the horizontal distance between Fukuoka and the turbulence location is about 40 km. Figure 7 compares data from soundings taken at Fukuoka at 0300 UTC with simulation results in domain 1, expressed as a conventional skew T–logp diagram. There exist 0300 and 1200 UTC soundings at Fukuoka on 2 September 2007 near the time of the observed turbulence (1034 UTC), and the sounding prior to the event is examined in Fig. 7 in consideration that Fukuoka is located upstream of the incident. Note that the observed and simulated wind barbs are also shown in the right side of Fig. 7. In the thermodynamic profile, a shallow inversion layer appears in the lower troposphere at z = 1 km, the location of the lifting condensation level (LCL). The convective available potential energy (CAPE) on the basis of the observed data is about 1568 J kg−1, sufficient to provide favorable conditions for well-developed convection. The tropopause height, defined as the lowest level at which the lapse rate is less than 2°C km−1 for a layer thicker than 2 km (World Meteorological Organization 1957), is located near z = 13.4 km. In the wind profile, a southwesterly flow dominates the entire troposphere and horizontal wind speed increases with height to z = 8 km, where the maximum wind speed is 17–20 m s−1. Above z = 8 km, wind speed continually decreases to z = 16 km. The model captures the vertical features of the observed sounding fairly well, although with some discrepancies: 1) local fluctuations in the observed profile of the dewpoint temperature are not simulated accurately, 2) the simulated LCL (924-hPa level) is a little lower than the observed one (908-hPa level) because of the slightly larger PBL moisture (and thus higher relative humidity) in the simulation and as a result 3) the CAPE in the simulation (1907 J kg−1) is a little greater than is observed (1568 J kg−1), and 4) the simulated maximum wind speed at z = 8 km (17 m s−1) is slightly lower than the observed one (20 m s−1), especially for the southerly wind.

Fig. 7.
Fig. 7.

Skew T–logp diagram (solid line is temperature and dashed line is dewpoint) obtained from the observed (black lines) and the simulated (gray lines) soundings at Fukuoka at 0600 UTC 2 Sep 2007. Simulated (rightmost profile) and observed (leftmost profile) wind speeds and directions at each level are shown on the right side of the diagram with full (10 m s−1) and half (5 m s−1) barbs. Isotherms in 10°C intervals are denoted as slantwise thin lines.

Citation: Journal of Applied Meteorology and Climatology 51, 6; 10.1175/JAMC-D-11-0140.1

Figure 8 compares the simulated deep convection with the observations at 1030 UTC 2 September 2007. Figure 8a shows the composite image of the MTSAT focused on the turbulence region, and Fig. 8b shows the column-maximum radar reflectivity (shading) and the SLP (contours) simulated in domain 2 (Δx = 10 km). At this time, simulated clouds align along the surface cold front that extends from the East Sea to the East China Sea through the Korea Strait (Fig. 8b), consistent with the observed clouds shown in Fig. 8a. Ahead of this front, convection with less widespread decibel reflectivity (dBZ) than the wide band along the front appears near the turbulence location in domain 2 (Fig. 8b), which is also similar to the observations (Fig. 8a). Although some local discrepancies in the convective structures are found in Fig. 8, the model results are in good agreement with the observations for the timing, location, and detailed structure of the simulated deep convection, as well as for the large-scale features surrounding the incident region. Therefore, the detailed evolution of the deep convection and the generation mechanism of the turbulence will be examined in the next section using the higher-resolution domains of the nested model.

Fig. 8.
Fig. 8.

(a) Composite image obtained from the MTSAT at 1033 UTC and (b) column-maximum radar reflectivity (shading) and sea level pressure (contours), derived using the simulated result in domain 2 at 1030 UTC 2 Sep 2007. Location of the turbulence encounter is depicted as an asterisk in (b).

Citation: Journal of Applied Meteorology and Climatology 51, 6; 10.1175/JAMC-D-11-0140.1

5. Model results

a. Evolution of the targeted deep convection

Figure 9 shows the horizontal evolution of the simulated nonzero SGS TKE (shading) and cloud boundary (contours) in domain 4 (Δx = 1.1 km) at z = 11.2 km (the altitude of the turbulence encounter) for 2.5 h, from 0800 to 1030 UTC. For 1 h, from 0800 to 0900 UTC, the deep convection (inner boxes in Fig. 9) is in the developing stage. During this time, the convection develops as a large mass of cloud in the troposphere, with three individual convective cells. At 0830 UTC, the first updraft of the convection reaches above z = 11.2 km, penetrating the tropopause (Fig. 9b). At 0900 UTC, two more updrafts penetrate above z = 11.2 km (Fig. 9c), while the first updraft has begun to spread out because of the divergent flows at the cloud top (Figs. 9b,c). After 0900 UTC, the highly dense cloudy masses near the individual convective cells diffuse significantly, suggesting that the targeted deep convection has mostly dissipated by 1030 UTC (Figs. 9d–f). During this period, nonzero SGS TKE outside the cloud boundary begins to appear at z = 11.2 km (Figs. 9d–f), intersecting the flight route of the aircraft (Figs. 9e,f). At 1030 UTC, the simulated turbulence location is highly consistent with the actual location of the turbulence encounter (Fig. 9f).

Fig. 9.
Fig. 9.

Simulated SGS TKE (>0.1 m2 s−2; shading) with total cloud mixing ratio (>0.1 g kg−1; contours) in domain 4 at z = 11.2 km at (a) 0800, (b) 0830, (c) 0900, (d) 0930, (e) 1000, and (f) 1030 UTC 2 Sep 2007. The location of the turbulence encounter and the flight route of the aircraft around the event time are depicted as the asterisk in (a)–(f) and the dots in (f), respectively. The inner boxes mark the region of deep convection.

Citation: Journal of Applied Meteorology and Climatology 51, 6; 10.1175/JAMC-D-11-0140.1

To examine the quantitative intensity of the simulated deep convection, the time series of maximum vertical velocities within the inner boxes of Fig. 9 is shown in Fig. 10, using the model results in domain 4 with 10-min time intervals. According to this time series, the first peak of 33.13 m s−1 occurs at 0820 UTC, corresponding to the convective cell shown in Fig. 9b. The second peak of 33.1 m s−1 at 0850 UTC is due to the subsequent two cells shown in Fig. 9c. After 0850 UTC, the maximum vertical velocity decreases considerably to 2.14 m s−1 by 1030 UTC (Fig. 10), implying that the targeted deep convection is in the dissipating stage at the incident time. The evolution of the maximum vertical velocity shown in Fig. 10, with two peaks in the developing stage and a significant decrease in the dissipating stage, correlates well with the time series for the observed minimum BT shown in Fig. 4. These correlations support the conclusion that the model aptly simulates the evolution of the observed deep convection.

Fig. 10.
Fig. 10.

Time series of the maximum vertical velocity (solid line) within the inner boxes shown in Fig. 9, calculated using the model outputs of domain 4 with 1.1-km horizontal grid spacing and 10-min time intervals. The vertical dashed line indicates the time (1034 UTC) of the turbulence encounter.

Citation: Journal of Applied Meteorology and Climatology 51, 6; 10.1175/JAMC-D-11-0140.1

b. Vertical evolution of the targeted deep convection

Figure 11 shows vertical cross sections of the total cloud mixing ratio of greater than 0.05 and 0.1 g kg−1 (light and dark shading, respectively) and the potential temperature (contours) at selected times, taken along the diagonal solid line shown in Fig. 9f, which is parallel to the direction of motion of the targeted deep convection. Figure 12 zooms in on the corresponding inner boxes in Fig. 11, showing vertical cross sections of the cloud boundary (thick contours), potential temperature (contours), and SGS TKE greater (shading).

Fig. 11.
Fig. 11.

Vertical cross sections of total cloud mixing ratio >0.05 (light shading) and >0.1 (dark shading) g kg−1 with potential temperature (contours) taken along the diagonal solid line in Fig. 9f at (a) 0800, (b) 0830, (c) 0900, (d) 0930, (e) 1000, and (f) 1030 UTC 2 Sep 2007. Contour intervals in all plots are 2 K. The location of the turbulence encounter projected on the cross sections is depicted as an asterisk in all plots.

Citation: Journal of Applied Meteorology and Climatology 51, 6; 10.1175/JAMC-D-11-0140.1

Fig. 12.
Fig. 12.

SGS TKE (shading) with total cloud mixing ratio (0.05, 0.1, and 1 g kg−1; thick lines) and potential temperature (contours) in the inner boxes in Fig. 11 at (a) 0800, (b) 0830, (c) 0900, (d) 0930, (e) 1000, and (f) 1030 UTC 2 Sep 2007. Contour intervals in all plots are 2 K except in (e) and (f), which are 1 K. The arrows in (b) are described in the text. The asterisk in (e) and (f) indicates the location of the turbulence encounter.

Citation: Journal of Applied Meteorology and Climatology 51, 6; 10.1175/JAMC-D-11-0140.1

At 0800 UTC (Fig. 11a), the initial updraft of the convective cell is developing and deepening to about z = 8 km. In the enlarged cross section at the cloud-top region (Fig. 12a), sloped and overturning isentropes, due to the cooling from convective updrafts, are evident near the cloud top. Vertical motion within the cloud is upward, and the flow out of the cloud is stable and smooth, with no evidence of instability. At 0830 UTC (Fig. 11b), this updraft penetrates the tropopause, located at about z = 13.4 km (see Fig. 7), and the cloud top reaches up to about z = 14.4 km. Because of this overshooting, gravity waves are generated and propagate upward to the stratosphere. Near the cloud top (Fig. 12b), the cloud boundary begins to overturn vertically with consequent vertical mixing, as shown by the nonzero SGS TKE near x = 30–34 km and z = 13.5–14 km (right arrow). Given that negative vertical velocity exists locally in this region (not shown), the vertical mixing is likely related to the entrainment process, in which unsaturated environmental air near the cloud top penetrates downward through the cloud boundary to mix with saturated cloudy air, which eventually leads to the dilution of the convective cloud top (e.g., Squires 1958; Klaassen and Clark 1985). Once this occurs, motion on the cloud top is no longer stable, as shown by some isentropes on the cloud top that are vertically overturned near z = 13.5–14 km at x = 10–15 km and x = 30–35 km as indicated by arrows in Fig. 12b. By 0900 UTC (Fig. 11c), the cloud top of the first updraft significantly decreases to about z = 12 km while the second updraft (behind the first one) also penetrates the tropopause and then deepens to about z = 13.6 km. These two overshooting tops in the developing stage are consistent with the two peaks in the time series of the maximum vertical velocity described in Fig. 10.

In Fig. 12c, out-of-cloud CIT (identified by the overturning of isentropes with nonzero SGS TKE) is located about 1 km above the first convective cell, near z = 13–13.4 km and x = 42–48 km while cloud thickness for both the first and second convective cells shrinks significantly (Fig. 11d) as the magnitude of upward motion decreases rapidly in the dissipating stage (Fig. 10). Because the convection during this period moves horizontally at about 11 m s−1 (80 km in 2 h) and the zonal-mean wind at 1000 UTC (Fig. 16f, which will be described below) decreases with height from 11 m s−1 at z = 9 km to 6 m s−1 at z = 11 km, the upstream regions (i.e., the left side) form the lee side of both convective turrets. For this reason, the dissipating convection cells tilt in the downshear direction (i.e., to the left) during the dissipating stage (Figs. 11d–f). In Fig. 12d, isentropes are relatively less compressed on the lee side of the first updraft, near z = 10.5–11.5 km and x = 55 km. This indicates strong cloud-induced flow deformation and causes nonzero SGS TKE due to local shear instabilities (0 < Ri < 1) outside the cloud boundary. At 1000 UTC (Fig. 11e), the two cloud cells continue moving toward the turbulence-encounter region and become more tilted in the downshear direction, with concurrent significant shrinking of their thicknesses. In Fig. 12e, localized shear instabilities with nonzero SGS TKE also appear on the lee side of the second convective cell, near z = 11.5–12 km and x = 50–57 km, consistent with previous studies about aircraft hazards on the lee side of the convection (e.g., Pantley and Lester 1990; Bedard and Cunningham 1991). By 1030 UTC (Fig. 11f), the entire cloud mass of the targeted deep convection has mostly disappeared. Simulated nonzero SGS TKE outside the cloud still appears 1–2 km above the dissipating cloud, near z = 11–11.4 km and x = 86–96 km (Fig. 12f). At the incident time (1034 UTC), the location of the simulated nonzero SGS TKE closely coincides with the location of the turbulence encounter (indicated by the asterisk).

c. Generation mechanism of the turbulence encounter

The previous section shows that the nonzero SGS TKE outside the cloud is likely related to two types of instabilities: 1) convective instability due to the entrainment of environmental air into the cloud and 2) localized shear instability due to the cloud-induced flow deformation on the lee side of the convection. According to previous studies, upward motion in the convective cell and downward motion in the environment cause buoyancy gradients across the cloud interface that result in the production of y vorticity according to the 2D vorticity equation [∂η/∂t ∝ −∂B/∂x, where η (=∂u/∂z − ∂w/∂x) and B are the y vorticity and buoyancy, respectively] (e.g., Klaassen and Clark 1985; Grabowski and Clark 1991). When positive (negative) shear exists, convective cells or cumulus turrets tilt and stretch in the downshear (upshear) direction because of the shear-induced y vorticity. Positive feedback between the production of y vorticity and buoyancy gradients across the cloud interface leads to overturning and vertical mixing at the cloud boundary through convective instability in the entrainment of environmental air into the cloud (e.g., Klaassen and Clark 1985; Grabowski and Clark 1991, 1993). With these factors in mind, the generation mechanism of the out-of-cloud CIT shown in Fig. 12f is examined in this section.

The simulated turbulence that passes through the incident region 1–2 km above the dissipating convection (Fig. 12f) is generated initially near the cloud boundary approximately 20 min before the incident time. To understand the excitation of the simulated turbulence, Fig. 13a shows the SGS TKE (shading), total cloud mixing ratio (contours), and horizontal wind vectors at z = 11.2 km, calculated using the model results in domain 5 (Δx = 0.37 km) at 1014 UTC. Derived using the model results in domain 6 (Δx = 0.12 km) at 1014 UTC, vertical cross sections of horizontal wind speed (m s−1), ∂u/∂z (s−1), and SGS TKE (m2 s−2), taken along the blue line depicted in Fig. 13a, are shown in Figs. 13b–d, respectively. Blue and black contours in Figs. 13b and c are y vorticity (η; s−1) and total cloud mixing ratio (0.03 and 0.1 g kg−1), respectively. In Fig. 13d, zero N2 (s−2) is depicted as a blue contour (near x = 4 km and z = 11.2 km), and the total cloud mixing ratio of 0.3 g kg−1 and the isentrope of 346 K at 1012 (dashed) and 1014 (solid) UTC are shown as black and red lines, respectively.

Fig. 13.
Fig. 13.

(a) SGS TKE (shading), total cloud mixing ratio (0.03, 0.1, and 1 g kg−1; solid contours), and horizontal wind vectors at z = 11.2 km in domain 5. Vertical cross sections of (b) horizontal wind speed (shading), (c) ∂u/∂z (shading), and (d) SGS TKE (shading) along the blue line in (a), using the model results in domain 6 at 1014 UTC 2 Sep 2007. Blue and black contours in (b) and (c) are y vorticity (s−1) and total cloud mixing ratio (0.03 and 0.1 g kg−1), respectively. In (d), the blue contour is zero N2 at 1014 UTC, and the black and red lines show the total cloud mixing ratio of 0.03 g kg−1 and the isentrope of 346 K at 1012 (dashed) and 1014 (solid) UTC, respectively. Negative values in (b)–(d) are stippled. The turbulence location in all plots is indicated by an asterisk.

Citation: Journal of Applied Meteorology and Climatology 51, 6; 10.1175/JAMC-D-11-0140.1

At 1014 UTC (Fig. 13a), a dominant southwesterly flow at the incident altitude is horizontally perturbed and distorted not only in the cloud but also on the lee side of the convection when it passes through the dissipating convection. At this time, nonzero SGS TKE appears at the leading edge of the dissipating cloud, which is the focus of the current study (Fig. 13a). Because of the horizontal disturbances in the cloud and on its lee side, the magnitude of the horizontal wind speed in the layer from z = 10 to 11.2 km is relatively smaller than the speed in the layers slightly above (z = 11.2–11.8 km) and below (z = 10 km) (Fig. 13b). Therefore, VWS above the dissipating convection is locally intensified in a layer from z = 11 to 11.6 km and from x = 1 to 7 km, causing positive y vorticity. In this region, the negative value of ∂w/∂x induced by the positive and negative vertical velocities in and out of the dissipating convection generates additional positive y vorticity, although the magnitude of ∂w/∂x is much smaller than ∂u/∂z in this area, because the maximum vertical velocity of the dissipating convection at this time is small (see Fig. 10). Thus, the positive y vorticity is nearly identical to the shear component of the y vorticity (∂u/∂z; Fig. 13c). In Figs. 13b and 13c, the leading edge of the cloud boundary begins to deform near z = 10.6–11.6 km and x = 4 km because of the shear-induced y vorticity in this region (Fig. 13d). This cloud deformation is more pronounced at 1014 UTC than at 1012 UTC, which results in overturning of isentropes (red contours) near the cloud interface at z = 11.2 km and x = 2–7 km (Fig. 13d). This finally activates turbulence and vertical mixing through convective instability in the entrainment of environmental air into the cloud across the cloud boundary (Fig. 13d). The generation mechanism for the turbulence at the leading edge of the dissipating convection elucidated in the current study is consistent with cloud interfacial instability (e.g., Klaassen and Clark 1985; Grabowski and Clark 1991, 1993).

To examine the evolution of the simulated turbulence, Fig. 14a (1014 UTC) shows the vertical cross section of nonzero SGS TKE (shading), isentropes (contours), and the cloud boundary (blue thick contour). Figure 14b (1024 UTC) shows the Richardson number (shading), VWS (contours), and zero Brunt–Väisälä frequency (thick contour). Figures 14c and 14d show the same data but at 1024 UTC, and Figs. 14e and 14f show the results for 1034 UTC. Figure 14 is taken along the blue line shown in Fig. 13a and uses model results from domain 6 (Δx = 0.12 km). Note that the vertical ranges in Fig. 13 and Fig. 14 are slightly different, although they are taken across the same horizontal distance.

Fig. 14.
Fig. 14.

Vertical cross sections of (left) SGS TKE (shading) with total cloud mixing ratio (0.03 and 0.1 g kg−1; blue lines) and potential temperature (black contours) and (right) the Richardson number (shading) with zero N2 (thick line) and VWS (contours) along the blue line in Fig. 13a at (a),(b) 1014, (c),(d) 1024, and (e),(f) 1034 UTC 2 Sep 2007, calculated using the model results of domain 6. Contour intervals in left and right panels are 2 K and 0.01 s−1, respectively. The turbulence location projected in the cross section is depicted as an asterisk in all plots.

Citation: Journal of Applied Meteorology and Climatology 51, 6; 10.1175/JAMC-D-11-0140.1

For 20 min, from 1014 to 1034 UTC (Figs. 14a,c,e), the local flow condition that can generate nonzero SGS TKE near the cloud interface moves along the dominant southwesterly flow while the thickness of the dissipating convection shrinks continuously as the convection moves toward the observed turbulence encounter (shown as an asterisk). The turbulence caused by convective instability, near z = 11.2 km and x = 5–14 km, becomes wider and stronger at 1024 UTC (Figs. 14c,d) than at 1014 UTC (Figs. 14a,b) and finally comes out of the highly deformed cloud boundary in this region (Fig. 14c). By 1034 UTC, this turbulent region has continued to move horizontally, finally being located about 1–2 km above the dissipating convection. This dissipating convection intersects the location of the observed turbulence (Figs. 14e,f). With the assumption that the simulated results produced in this study are realistic, the severe turbulence encounter near Fukuoka at 1034 UTC 2 September 2007 was due to this out-of-cloud CIT.

The simulated SGS TKE values (~0.18 m2 s−2) are much smaller than the observation (Fig. 2b), however. This is likely due to the fact that in fine-resolution domains many of the small-scale turbulent eddies that can directly affect the aircraft (horizontal scales of less than ~2 km) can be explicitly resolved rather than having to be parameterized. Note that the smallest horizontal scales (~6Δx) resolvable in domains 5 and 6 are 2.2 and 0.7 km, respectively. To examine this possibility, the “resolved” TKE {=[(u′)2 + (υ′)2 + w2]/2} is calculated using the model results in domain 6. Here, the wind perturbations are defined by subtracting the background velocities that are obtained by taking a moving average of each velocity component over 16 × 16 grid points. Figure 15 shows the resolved TKE (shading) with cloud mixing ratio (black) and potential temperature (blue) along the blue line in Fig. 13a at different times. When compared with the SGS TKE shown in the left panels of Fig. 14, the areas of the resolved TKE in Fig. 15 are much broader, and the magnitude of the resolved TKE near the observed turbulence encounter is higher than 5 m2 s−2, with two peaks of 9.1 and 7.2 m2 s−2. Together with the SGS TKE, the total TKE is consistent with the observed TKE value, with two violent patches of variation pattern. This very close agreement between simulation and observation strongly suggests that the aviation industry should also consider turbulence above dissipating convection as an important inducer of CIT, even though only one case was examined in this study. Note that air traffic near the incident region in Japan around the time of the turbulence encounter presented here (±30 min of 1030 UTC 2 September 2007) was not so dense that other aircraft could encounter any turbulence near the dissipating convection (A. Kudo 2011, personal communication).

Fig. 15.
Fig. 15.

As in the left panels of Fig. 14, but showing the resolved TKE (shading), as defined in the text, at (a) 1014, (b) 1024, and (c) 1034 UTC.

Citation: Journal of Applied Meteorology and Climatology 51, 6; 10.1175/JAMC-D-11-0140.1

Current turbulence-avoidance guidelines state that an aircraft flying over convection should avoid the cloud top by at least 1000 ft vertically for every 5 m s−1 of the cloud-top wind speed (FAA 2012). Because the wind speed at the cloud-top altitude (z = 10 km) was approximately 10 m s−1 (Fig. 16f) at 1034 UTC, an aircraft following this guideline would need to move at least 2000 ft (about 0.7 km) above the cloud top. Even if the aircraft had followed this guideline in the situation investigated in this paper, it still would not have gained sufficient clearance of the turbulence, because the out-of-cloud CIT is located about 1–2 km (3200–6400 ft) above the dissipating convection. Therefore, the deficiencies of the current turbulence-avoidance guideline, highlighted by Lane and Sharman (2008), should be reconsidered not only for the developing stage of deep convection but also for the dissipating stage.

Fig. 16.
Fig. 16.

(a)–(c) As in the left panel of Fig. 14, but taken at (a) 0956, (b) 1000, and (c) 1004 UTC. (d) Same as Fig. 14a. (e) The temporal evolution (tx cross section) of vertical velocity (m s−1) at z = 12.5 km in (a)–(d) with vertically averaged SGS TKE (shading) between z = 12.7 and 13.3 km. The y axis is the time from 0930 UTC, when the gravity waves begin to appear. (f) The vertical profile of zonal-mean horizontal wind speed U in (b). Slant lines in (e) and the vertical line in (f) represent a phase speed of 3.2 m s−1, and the horizontal line in (f) is z = 13.6 km.

Citation: Journal of Applied Meteorology and Climatology 51, 6; 10.1175/JAMC-D-11-0140.1

d. Subsequent breaking of the convectively induced gravity wave

This section describes the generation mechanism of the subsequent gravity wave breaking near z = 13 km and x = 12–20 km (Fig. 14a). To elucidate the evolution of the gravity waves and their breaking, Figs. 16a–c show vertical cross sections with the same parameters as the left panels of Fig. 14, except taken at three earlier times. Figure 16d is the same as Fig. 14a, and Fig. 16e shows the space–time (xt) cross section of the vertical velocity (contour) at z = 12.5 km and the vertically averaged SGS TKE (shading) between z = 12.7 and 13.3 km in Figs. 16a–d. Figure 16f shows the vertical profile of the zonal-mean horizontal wind speed at 1000 UTC along the blue line in Fig. 13a. Note that the y axis in Fig. 16e is the time (min) since 0930 UTC. At 0956 UTC (Fig. 16a), phase lines of the gravity waves in z = 12.5–13.5 km and x = 0–10 km are tilted in the negative x direction, indicating upward propagation of gravity waves through the tropopause at z = 13.4 km and into the lower stratosphere. The waves with small horizontal wavelength (<10 km) are initially generated by the first updraft near z = 10–12 km and x = 60–70 km at 0930 UTC, as shown in Fig. 12d. One wave starts to break down at 1000 UTC with nonzero SGS TKE at z = 13.3 km and x = 8 km (Fig. 16b). Once breaking begins to appear, it extends farther downstream, following the motion of the dissipating convection (Figs. 16c,d). The out-of-cloud CIT eventually is located about 2 km farther aloft (up to z = 13 km) above the dissipating convection of Fig. 14.

A vertically propagating gravity wave induced by deep convection can be a source of out-of-cloud CIT in the following ways. First, wave amplitude increases with height because of decreasing air density, which finally results in wave steepening and subsequent breaking at higher altitudes (Lindzen 1981). Second, an increase in atmospheric stability N near the tropopause can reduce the vertical wavelength λz of the wave according to the dispersion relationship for the two-dimensional internal gravity waves (λz ≈ |cU|/N, where c and U are the phase speed and background wind speed, respectively), which increases the potential for breaking (VanZandt and Fritts 1989). In a similar manner, vertically propagating waves will break or dissipate when they approach their critical level zc at which the background wind speed is equal to the horizontal phase speed of the wave [U(zc) = c]. As can be seen in Fig. 16e, the horizontal wavelength and phase speed of the waves are about 6–7 km and 3.2 m s−1 (tilted lines in Fig. 16e), respectively. Given the background wind condition shown in Fig. 16f, a wave with phase speed of 3.2 m s−1 meets its critical level at z = 13.6 km, depicted as a horizontal solid line in Fig. 16f, and it can break down at this time. The generation mechanism for convectively induced gravity wave breaking described in this study is consistent with Lane et al. (2003) and Lane and Sharman (2008), although the current study is focused primarily on the dissipating convection.

6. Summary and discussion

At 1034 UTC 2 September 2007, a commercial aircraft flying at its cruising altitude of 35 000 ft near Fukuoka and en route from Jeju to Osaka suddenly encountered a severe turbulence event (lasting about 30 s), which caused six in-flight injuries. After landing, the pilots stated that there were no prewarning signals, such as developing thunderstorms or well-organized onboard radar echoes, around the incident location and time. In observations, however, deep convection ahead of the cold front developed in the southwestern region of the incident at 3 h before the turbulence time. As this deep convection was advected with the dominant southwesterly wind toward the turbulence location, it entered into the dissipating stage, with a significant decrease of maximum BTs. The convection eventually passed through the turbulence location at the incident time, suggesting that the severe turbulence examined in this study is likely related to the dissipating convection.

We investigate the generation mechanism of the observed turbulence event using a high-resolution numerical simulation. In this study, the WRF model, with six nested-grid refinements (with the smallest grid spacing of 120 m), is used to reproduce the multiscale atmospheric environments surrounding the turbulence. We find that the numerical simulations capture reasonably well the observed large-scale flows and out-of-cloud CIT along the dissipating convection.

In the developing stage of the deep convection, an initial updraft penetrates the tropopause and then subsequent updrafts appear behind the initial updraft. As the deep convection moves toward the turbulence location, the thickness of the convection shrinks significantly because of the rapid decrease of upward motion in the convection. In the dissipating stage, the dominant southwesterly flow at the aircraft’s cruising altitude passes through the dissipating convection and then is disturbed significantly not only in the cloud but also on the lee side of the convection at 20 min before the incident time. This intensifies the local VWS on the lee side, which results in the production of positive y vorticity. According to the 2D vorticity equation, positive feedback between the production of y vorticity and horizontal buoyancy gradients across the cloud boundary finally activates overturning and vertical mixing through convective instability at the cloud boundary in the entrainment of unsaturated environmental air into the cloud. While the dissipating convection with shrinking thickness continues to move toward the observed turbulence region, the atmospheric conditions that generate turbulence at the cloud interface move along the dominant southwesterly flow and come out of the convection, eventually being located 1–2 km above the dissipating convection and passing through the observed turbulence region at the incident time. Meanwhile, vertically propagating convective gravity waves with a phase speed of 3.2 m s−1 subsequently break down as they approach their critical level. In this situation, the out-of-cloud CIT is located farther aloft, about 2 km above the dissipating convection. Even though only one case study is conducted here, the currently used turbulence-avoidance guidance (FAA 2012) should be reconsidered not only for the developing and/or mature stage of the deep convection but also for the dissipating stage of the deep convection.

The results in this study are based on a single numerical simulation and hence could depend highly on the fidelity of the model initial and boundary conditions and physical parameterization assumptions. We could not perform systematic sensitivity tests for the factors that can influence the results, except for some sensitivity tests for the horizontal grid spacing and PBL schemes (not shown). For given physical parameterization schemes, timing and location of the simulated turbulence with a horizontal resolution of higher than 3.3 km do not significantly differ from each other. The result with the Yonsei University (YSU; Hong et al. 2006) PBL scheme is somewhat different from that with the MYJ scheme used in this experiment: the simulated turbulence region near the dissipating convection with the YSU scheme is more spread out and disconnected from the observation than it is with the MYJ scheme. This is likely due to the different cloud properties in the two experiments associated with different moisture flux in the PBL, which results in higher CAPE (2323 J kg−1) with the YSU scheme than with the MYJ scheme (1907 J kg−1) as compared with the observation (1568 J kg−1) at Fukuoka (Fig. 7).

As computer capacity relevant to NWP models has increased rapidly in recent history, the grid resolution of the operational NWP models has increased. Locally focused high-resolution numerical modeling has successfully predicted observed turbulence cases, not only for complex mountains (e.g., Clark et al. 2000; Lane et al. 2009; Kim and Chun 2010) but also for convective systems [e.g., Lane et al. (2003), Trier and Sharman (2009), and the study presented here]. Thus, SGS TKE produced from NWP models can be used to forecast aviation turbulence directly, and these results can be compared with a currently used turbulence forecasting system [e.g., Graphical Turbulence Guidance (GTG); Sharman et al. 2006], although the ability of the model to do this will depend on how well it can predict the convection, which varies from case to case. Considering that the forecasting performance of the GTG during the summertime over eastern Asia is relatively lower than in other seasons (Kim et al. 2011), the parameterized SGS TKE directly derived from an operational NWP model with higher grid resolution could help to improve turbulence forecasts, at least when related to convective systems associated with large-scale flows over eastern Asia.

Acknowledgments

This work was funded by the KMA Research and Development Program under Grant CATER 2012-2011.

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