Numerical Simulations of Two Trapped Mountain Lee Waves Downstream of Oahu

MAY 2017 L I A N D C H E N 1305

LIYE LI AND YI-LENG CHEN Department of Atmospheric Sciences, School of Ocean and Earth Science and Technology, University of HawaiʻiatManoa, Honolulu, Hawaii

(Manuscript received 28 November 2015, in ﬁnal form 31 January 2017) Downloaded from http://journals.ametsoc.org/jamc/article-pdf/56/5/1305/3594081/jamc-d-15-0341_1.pdf by guest on 16 October 2020

ABSTRACT

Two trapped lee-wave events dominated by the transverse mode downstream of the island of Oahu in Hawaii— 27 January 2010 and 24 January 2003—are simulated using the Weather Research Forecasting (WRF) Model with a horizontal grid size of 1 km in conjunction with the analyses of soundings, weather maps, and satellite images. The common factors for the occurrences of these transverse trapped mountain-wave events are 1) Froude number [Fr = U/(Nh)] . 1, where U is the upstream speed of the cross-barrier flow, N is stability, and h is the mountain height; 2) insufficient convective available potential energy for the air parcel to become positively buoyant after being lifted to the top of the stable trade wind inversion layer; and 3) increasing cross-barrier wind speed with respect to height through the stable inversion layer, satisfying Scorer’s criteria between the inversion layer and the layer aloft. Within the inversion layer, where the Scorer parameter has a maximum, the wave amplitudes are the greatest. The two trapped mountain waves in winter occurred under strong prefrontal stably stratified southwesterly flow. On the other islands in Hawaii, where the mountaintops are below the base of the inversion, transverse trapped lee waves can occur under similar large-scale settings if the mountain height is lower than U/N. The high-spatial-and-temporal-resolution WRF Model successfully simulates the onset, development, and dissipation of these two events. Sensitivity tests for the 27 January 2010 case are performed with reduced relative humidity (RH). With a lower RH and less-significant latent heating, trapped lee waves have smaller amplitudes and shorter wavelengths.

1. Introduction textbooks on lee-wave theory (Atkinson 1981; Gill 1982; Durran 1986, 2003; Baines 1995; Wurtele et al. 1996; In a stably stratified atmosphere, the vertical dis- Smith 2002; Lin 2007; and others). placement of an air parcel by terrain can trigger gravity Using a two-layer model, Scorer (1949) showed that if waves (or buoyancy waves) propagating downstream of the lower layer is slower and/or more stable, resonant mountain ridges or hills (Scorer 1949; Queney et al. trapped lee waves may exist. In the original 2D lee-wave 1960; Gossard and Hooke 1975; Smith 1979). Large- theory (Scorer 1949), the focus is on transverse trapped amplitude mountain waves can produce very strong lee waves that are perpendicular to the low-level flow downslope winds on the leeside slope (Peltier and Clark direction. One of the most prominent features of moun- 1979; Klemp and Lilly 1975, 1978; Smith 1985; Durran tain waves occurs when stably stratified air moves over a 1986; Colman and Dierking 1992; Colle and Mass 1998; long mountain ridge, which triggers long transverse res- and others). In contrast to other types of mountain onant trapped waves in the lower troposphere of the lee waves, trapped lee waves propagate horizontally (Scorer side. For flow over isolated hills, in addition to transverse 1949; Sawyer 1962; Gjevik and Marthinsen 1978; Simard trapped lee waves, diverging waves that propagate later- and Peltier 1982; Sharman and Wurtele 1983; Vosper ally could also exist (Sawyer 1962; Gjevik and Marthinsen and Mobbs 1996; Sachsperger et al. 2015; and others). In 1978; Sharman and Wurtele 1983; Smith 2002; Lin 2007). recent years, there have been extensive reviews and When the mountain width is much smaller than 100 km (e.g., the island of Oahu), with a Rossby number School of Ocean and Earth Science and Technology Contribu- much greater than 1, the rotational effect of airflow is tion Number 9886. negligible. The basic wave structure is determined by the size and shape of the mountain and vertical profiles of Corresponding author: Dr. Yi-Leng Chen, [email protected] temperature, wind speed, and moisture of the impinging

DOI: 10.1175/JAMC-D-15-0341.1 Ó 2017 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses). 1306 JOURNAL OF APPLIED METEOROLOGY AND CLIMATOLOGY VOLUME 56

ﬂow (Scorer 1949; Smith 2002; Durran 2003; Lin 2007). Satellite R Series (GOES-R) Advanced Baseline Im- Lee waves have been observed in both the troposphere ager visible images with a 0.5-km resolution are useful and stratosphere (Nicholls 1973) and can sometimes be to capture these types of events during the daytime. At detected by cloud formations such as lenticular clouds or night, the GOES-R shortwave IR images (or fog ragged rotor clouds. In other cases, without enough product) with a horizontal grid ;2 km every 5 min can moisture, lee waves may generate regions of clear-air be used to monitor the lee-wave clouds. If not enough turbulence. With or without trapped lee-wave clouds, moisture is present, however, low-level trapped lee these lee-wave events can pose a potential hazard to waves could occur as clear-sky turbulences. Therefore, aviation (Doyle and Durran 2002). monitoring and predicting trapped mountain lee-wave Lee waves or mountain waves have been observed by events requires a combination of satellite observations satellites (Gjevik and Marthinsen 1978), aircraft (Caccia and high-resolution mesoscale numerical modeling

et al. 1997; Lilly 1978), radars or lidars (Ralph and Neiman with a horizontal grid on the order of 1 km. To our Downloaded from http://journals.ametsoc.org/jamc/article-pdf/56/5/1305/3594081/jamc-d-15-0341_1.pdf by guest on 16 October 2020 1997; Reeder et al. 1999; Vachon et al. 1994), and constant- knowledge, this is the first modeling study in Hawaii to level balloons over the Sierra Nevada (Holmboe and successfully reproduce the observed resonant trapped Klieforth 1957), Rocky Mountains (Klemp and Lilly 1975), lee waves in high-resolution models. Based on obser- Appalachians (Lindsay 1962), and Pennines of England vational data and model results, we discuss the phys- (Aanensen 1965). For a given mountain ridge, the occur- ical process responsible for the occurrences of this rence of lee waves depends primarily on two atmospheric type of event in Hawaii. Our study would be useful for characteristics: static stability and winds. The airflow forecasters because it shows that with proper model should have a large wind component perpendicular to the configuration, the high-resolution model is a valuable ridge that is maintained through a considerable depth of tool that can provide numerical guidance in real-time the atmosphere under a stably stratified atmosphere operational settings. These resonant trapped lee (Atkinson 1981). Note that the maximum amplitude of lee waves are a significant aviation hazard for tour oper- waves is usually in or near the layer of maximum static ations in Hawaii, especially for small aircraft or heli- stability (Starr and Browning 1972). In the third intensive copters flying over the coastal waters and over the observation period of the momentum budget over the islands. Pyrenees (PYREX) around the Pyrenean chain during Most of the previous theoretical studies of trapped lee October and November 1990, lee waves were found to be waves are based on an idealized flow over idealized hills far from stationary during their lifetime related to changes or ridges. In this study, the synoptic conditions for two in the environment (Caccia et al. 1997). trapped lee-wave events downstream of Oahu in Hawaii Under low-level east-northeast trade winds and upper- are delineated (section 4). In section 5,wewillinvestigate level westerlies, mountain waves with strong leeside the possibility of simulating the evolution of these events winds do occur in Hawaii for mountains or ridges with using high spatial and temporal 3D models using real is- tops below the trade wind inversion (Yang et al. 2008; land terrain and initialized by large-scale analyses from Van Nguyen et al. 2010; Carlis et al. 2010). During global models. High-spatial-and-temporal-resolution re- 14–15 February 2001, a wintertime downslope windstorm sults from the Weather Research and Forecasting (WRF) occurred over Oahu after the passage of a surface cold Model with full model physics are used to diagnose the 2 front under strong (.12 m s 1) low-level prevailing evolution of both events, including the onset and ending. northeast winds. For that case, the main large-scale con- From high temporal model output, changes in upstream ditions for the development of downslope windstorms conditions throughout the entire life cycle, such as the were 1) the presence of a critical level below the 400-hPa vertical wind and thermodynamic profiles including the level; and 2) strong cross-barrier flow with wind speed inversion layer, will be examined in relation to the tem- decreasing with respect to height through the postfrontal poral variations of trapped lee waves. Most theoretical inversion (Zhang et al. 2005b). For the downslope studies do not include the effects of latent heat release. In windstorms, an inversion above the ridge top with strong section 6, the feedback effects of latent heat release on cross-barrier winds (U)withFr.1[Fr=U/(Nh), where h trapped lee waves over Oahu are studied using model is the depth of the lower layer, and N is the Brunt–Väisälä sensitivity tests. An overall discussion of trapped lee- frequency] is present (Zhang et al. 2005b). wave occurrences in Hawaii is given in section 7.Inad- Trapped lee waves are observed during both the winter dition, we compare the large-scale conditions between and summer months over Hawaii (e.g., Burroughs and the trapped lee-wave and downslope wind events to Larson 1979). Forecasting the occurrence of low-level outline the different crucial factors that determine the trapped lee waves over Hawaii is challenging yet cru- occurrences of these two wave types. A summary and cial. The Geostationary Operational Environmental implications for forecasting are given in section 8. MAY 2017 L I A N D C H E N 1307

2. Background a. The local island terrain of Oahu and climatology The island of Oahu has two narrow, nearly parallel mountain ranges, the Koolau Mountain Range and the Waianae Mountain Range, with peaks of 944 and 1227 m, respectively (Fig. 1a), which are well below the typical base of the trade wind inversion (;2km)(Neiburger et al. 1961; Bingaman 2005; Cao et al. 2007). Both mountain ridges are oriented in the northwest-to-southeast direction. In summer, the subtropical high is well developed

with the mean maximum sea level pressure center located Downloaded from http://journals.ametsoc.org/jamc/article-pdf/56/5/1305/3594081/jamc-d-15-0341_1.pdf by guest on 16 October 2020 around 388N, 1508W and the pressure ridge well north of the Hawaiian Island chain. Throughout the year, the northeast trade winds have a maximum chance of occurrence(93%)duringAugust(Schroeder 1993). In winter, the subtropical high pressure cell lies farther southeast than its summer location, with the center locatedaround328N, 1308W. The ridge axis of the subtropical high (SH) extends westward from the center to just north of the Hawaiian Island chain (Juvik et al. 1998; Schroeder 1993). Bingaman (2005) identified the base of the trade wind inversion layer (or the top of the marine boundary layer) with a discontinuity in the vertical gradient of the potential temperature and a rapid decrease in relative humidity (RH) from soundings collected at two sounding sites in Hawaii (Fig. 1b). She also identified the top of the inversion layer as the height where the temperature lapse rate returns to approximately the typical value of the lapse rate in the environment. Within the trade wind inversion layer, the temperature decrease with respect to height is FIG. 1. (a) Terrain contours (m) over the island of Oahu for the slower than both within the marine boundary and aloft, high-resolution (1 km) island-scale domain with locations for dot 1 (21.358N, 158.58W) and dot 2 (21.158N, 158.48W). Line 1 is from which is close to the standard atmospheric lapse rate 21.48N, 158.358Wto21.858N, 157.48W. Line 2 is from 21.28N, 21 (26.5 K km ). Bingaman defines the inversion strength 158.38Wto21.758N, 157.38W. (b) The two-way nested domains used as DT 5 Ttop 2 Tstandard,whereTstandard 5 Tbase 1 in this study; d01 is the entire blue area. The grid sizes for the three domains are 9, 3, and 1 km, respectively. g(Ztop 2 Zbase)andg is the lapse rate for a standard atmosphere of 26.58C, and Ttop and Tbase are the temper- atures at the top and base of the inversion layer, Hawaiian Island region (Winning et al. 2017). The mini- respectively. The medium thickness of the stable trade mum vertical gradient of the GPSRO refractivity occurs wind inversion layer determined by Lihue, Hawaii, at the base of the inversion layer (Ao et al. 2012; Xie et al. soundings from June 1999 through June 2004 has a sea- 2012). Climatologically, the trade wind inversion base sonal maximum about 670 m in June and seasonal mini- determined from sounding data collected at the wind- mum of about 380 m in winter months, with a typical ward side of steep mountains (e.g., Hilo, Hawaii, and strength of 4–6 K (Bingaman 2005).Thebaseofthetrade Lihue) (Fig. 1b) is slightly higher (ca. 100–200 m) than wind inversion at Lihue is lowest (;1620 m) in January that determined by GPSRO data over the open ocean and highest in October (;2100 m) with a secondary because of orographic lifting on the windward side maximum in April (;2000 m). Recently, the global posi- (Winning et al. 2017). tioning system (GPS) radio occultation (RO) 2007–12 Since 2004, we performed daily high-resolution experi- refractivity data obtained from Constellation Observing mental forecasts over the Hawaiian Islands with a grid size System for Meteorology, Ionosphere, and Climate as small as 1.5 km for Oahu. Forecasters use our results for (COSMIC) were used to estimate the spatial distribution their daily weather forecasts. It is our experience that of the height of the marine boundary layer over the trapped lee-wave events do not occur very often in Hawaii. 1308 JOURNAL OF APPLIED METEOROLOGY AND CLIMATOLOGY VOLUME 56

When they do occur, it is mainly under the prefrontal and the wavelength of the first mode is given by southwesterly flow regime prior to the arrival of a cold front (or a shear line). The summer case reported by Burroughs cot(mH) 52l/m, (5) and Larson (1979) is an unusual one. On average, there are where up to nine frontal passages over Hawaii per year (Worthley 1967). Prior to the arrival of a cold front, the east-northeast m 5 (L2 2 k2)1/2 and l 5 (k2 2 L2)1/2 . (6) trade wind flow is interrupted. Low-level winds frequently l u shift to southeasterlies first and then turn to southwesterlies Based on Scorer’s idealized two-layer model, Durran before the arrival of the cold front. In the prefrontal (2003) applied the Boussinesq approximation to line- atmosphere, the southwesterly flow frequently brings arize internal gravity wave equations and obtained a in warm, moist, unstable air from the tropics, which single equation for the vertical velocity w for a 2D leads to heavy precipitation (e.g., Tu and Chen 2011; frame work Downloaded from http://journals.ametsoc.org/jamc/article-pdf/56/5/1305/3594081/jamc-d-15-0341_1.pdf by guest on 16 October 2020 Jayawardena et al. 2012). For these two observed trapped lee-wave events downstream of Oahu in ›2w ›2w 1 1 L2w 5 0, (7) winter, the vertical wind profiles, stability, and large- ›z2 ›x2 scale settings will be examined. with the following dispersion relationship: b. Linear theoretical framework of trapped lee waves d2w~ For a ‘‘small amplitude’’ mountain (h , U/N,whereh i 1 2 2 2 ~ 5 5 2 (L k )wi 0, i 1, 2, (8) is mountain height, U is cross-barrier wind speed, and N is dz the Brunt–Väisälä frequency) (or Fr . 1), linear theory where w~i is the amplitude of the ith Fourier component is a good approximation for airflow past a mountain of w and barrier (Scorer 1949; Queney 1948; Smith 1989; Durran 1986, 2003). Because Oahu is dominated by two narrow L2 2 k2 5 m2 , (9) mountain ridges, and the observed resonant trapped lee waves are dominated by the transverse mode, the linear where m is the vertical wavenumber. For L2 , k2, there theory based on the 2D assumption provides the basic is no real solution for m, and waves propagating upward theoretical framework for both cases. from the lower layer are evanescent aloft. When L2 . k2, Based on a two-layer model, Scorer (1949) shows that m2 is positive, and a wave can propagate vertically. Thus, for a small amplitude mountain with Earth’s rotation if the lower layer is slower and more stable than above, ignored, the Scorer parameter L2 is a key parameter for waves propagating upward may be reflected downward the study of lee waves, where and bounce between the surface and the stable layer and trapped lee waves may exist. N 2 1 d 2U Trapped lee waves could also occur in the presence of a L2 5 2 . (1) U 2 U dz2 temperature inversion through adjustment to pressure gradients generated by the deflection of the discontinuity From Eq. (1), L2 is determined by wind speed (U), (Vosper 2004; Teixeira et al. 2013; Sachsperger et al. static stability (N), and vertical wind shear. Using a two- 2015; and others). Waves trapped at the inversion are layer model, lee waves could occur if essentially the same as those propagating at an interface between two fluids with a density discontinuity (Gill 2 2 2 . 2 2 1982). Because the thickness of the inversion layer over Ll Lu p /(4H ) and (2) Hawaii is not small (Bingaman 2005), it may not be de- 2 . 2 . 2 Ll k Lu , (3) sirable to represent the trade wind inversion as an interface with a temperature discontinuity. where Ll and Lu are the Scorer parameters in the lower and upper layers, respectively; k is the horizontal wavenumber related to mountain width; and H is the 3. Data and method depth of the lower layer (Scorer 1949; Durran 2003). A more generalized criterion for the resonant waves of the a. Synoptic data nth mode (Lin 2007) is given by In this study, 1-km-resolution visible (VIS) images from the Geostationary Operational Environmental 1 p 2 2 p 2 (2n 1) $ 2 2 2 $ (2n 1) Satellites-10 (GOES-10) are used to describe the lee- (Ll Lu) , (4) 2H 2H wave clouds and their evolution. The NCEP Climate MAY 2017 L I A N D C H E N 1309 Downloaded from http://journals.ametsoc.org/jamc/article-pdf/56/5/1305/3594081/jamc-d-15-0341_1.pdf by guest on 16 October 2020

FIG. 3. Surface pressure patterns (hPa) for the 26–27 Jan 2010 trapped lee-wave case: (a) 1800 UTC 26 Jan, and (b) 0000 and (c) 0600 UTC 27 Jan 2010. The red plus sign is the location of the island of Oahu. One pennant, full barb, and half barb represent 10, 2 FIG. 2. GOES-West visible satellite imagery for the 26–27 Jan 2, and 1 m s 1, respectively. 2010 trapped lee-wave case: (a) 1800 and (b) 2345 UTC 26 Jan, and (c) 0245 UTC 27 Jan 2010. delineate the wind proﬁles and vertical atmosphere stratiﬁcation. Forecast System Reanalysis (CFSR) data (Saha et al. b. Model description 2010) every 6 h with a 0.5830.58 gridareusedtodepict the synoptic weather patterns. The Lihue soundings For the Hawaiian Island chain, previous studies sim- from the University of Wyoming archive are used to ulated island circulations under different trade wind 1310 JOURNAL OF APPLIED METEOROLOGY AND CLIMATOLOGY VOLUME 56 Downloaded from http://journals.ametsoc.org/jamc/article-pdf/56/5/1305/3594081/jamc-d-15-0341_1.pdf by guest on 16 October 2020

FIG. 4. Lihue’s soundings and wind proﬁles: (a) 1200 UTC 26 Jan, and (b) 0000 and (c) 1200 UTC 27 Jan 2010. One pennant, full barb, and half barb represent 25, 5, and 2 2.5 m s 1, respectively. (From the sounding data ar- chived at the University of Wyoming.)

regimes (Zhang et al. 2005a; Yang et al. 2005; Yang and addition, the Noah land surface model (Chen and Dudhia Chen 2008; Van Nguyen et al. 2010; Carlis et al. 2010). 2001), with vegetation cover and soil properties compiled For these studies, the first 12 h of the model runs are by Zhang et al. (2005a), is used. Soil moisture and soil considered as the model spinup period. After spinup, the temperature are spun up for 2 months prior to the simu- orographic influences on the airflow are well repre- lation period with the soil moisture and soil temperature sented in the high-resolution nested domains. updated daily from the 24-h forecast of the model run of The WRF Model, version 3.5, is used to simulate these the previous day (Yang et al. 2005). two trapped lee-wave events downstream of Oahu in TheCFSR6-hourlydatawithahorizontalgridof winter (24 January 2003 and 27 January 2010). The Betts– 0.5830.58 are used to initialize the model. The mod- Miller–Janjic´ cumulus parameterization (Janjic´ 2000, eling strategy consists of three two-way nesting do- 1994), Yonsei University planetary boundary layer mains with horizontal grid spacing of 9, 3, and 1 km, scheme (Hong et al. 2006), new Eta microphysics (Roger respectively (Fig. 1b). The 1-km domain covers the et al. 2001), and Rapid Radiative Transfer Model radia- entire island of Oahu. There are 38 vertical levels tion scheme (Iacono et al. 2008) are employed. In from the surface to the 100-hPa level, with smaller MAY 2017 L I A N D C H E N 1311 Downloaded from http://journals.ametsoc.org/jamc/article-pdf/56/5/1305/3594081/jamc-d-15-0341_1.pdf by guest on 16 October 2020

FIG.5.GOES-10 VIS satellite imageries for the 24–25 Jan 2003 trapped mountain lee-wave case: (a) 0252, (b) 1752, and (c) 2215 UTC 24 Jan, and (d) 0252 UTC 25 Jan 2003. increments at the lower levels and the trade wind in- axis to the southeast of the island of Oahu, the low-level versionlayerthanabove(Chen and Feng 2001). winds over the island were weak southerlies (Fig. 4a). At 1800 UTC 26 January, the midlatitude cyclone was 4. Synoptic settings for two trapped lee-wave present to the northwest of the Hawaiian Islands, with a events downstream of the island of Oahu cold front extending in the northeast–southwest direction (Fig. 3a). From 1800 UTC 26 January to 0000 UTC a. Case of 26–27 January 2010 (TRAP1) 27 January 2010, a cold front moved toward the island On 27 January 2010, a wintertime trapped lee-wave of Oahu, and the subtropical high retreated eastward event occurred downstream of the island of Oahu. At (Figs. 3a,b). Concurrently, the wind direction shifted 1800 UTC 26 January 2010, trapped lee-wave clouds were from southerlies to southwesterlies (Fig. 4b), and the observed to the northeast of the Koolau Mountain Range approaching cold front lifted the base of the inversion (Fig. 2a) and became more organized after 2345 UTC layer from z 5 1.5 km to above z 5 2km (Fig. 4b). 26 January 2010 (Fig. 2b). These waves are dominated by During this period, well-developed traverse trapped lee- the transverse mode (Smith 2002). The maximum wave clouds were observed (Fig. 2c). After the cold wavelengths were around 12 km at 0245 UTC 27 Janu- front passed the island of Oahu (Fig. 3c), the low-level ary 2010 (Fig. 2c). Based on satellite VIS images, this winds turned to northwesterlies, parallel to the moun- trapped lee-wave case can be divided into three phases: tain ridges. The trapped lee-wave clouds quickly dissi- 1) developing (1800–2300 UTC 26 January); 2) mature pated because of the change in wind direction. In the (0000–0400 UTC 27 January); and 3) decaying (0500– meantime, the postfrontal inversion base was around 1200 UTC 27 January). z 5 3km(Fig. 4c). From 1200 UTC 26 January (Fig. 4a) Before this trapped lee-wave event, with a southward to 1200 UTC 27 January (Fig. 4c), convective available 2 shift of the subtropical high (Fig. 3a), the inversion base potential energy (CAPE) was less than 5 J kg 1, and the determined from the Lihue sounding (Fig. 4a) was at surface air parcel was negatively buoyant after being z 5 1.5 km, which is slightly lower than its typical height lifted to the top of the trade wind inversion. This is in in January (;1.6 km) (Bingaman 2005). With the ridge contrast to the conditionally unstable atmosphere under 1312 JOURNAL OF APPLIED METEOROLOGY AND CLIMATOLOGY VOLUME 56

(1800–2100 UTC 24 January 2003); 2) mature (2100– 2300 UTC 24 January 2003); and 3) decaying (2300 UTC 24 January–0500 UTC 25 January 2003). At 1752 UTC 24 January 2003 (Fig. 5b), the trapped lee-wave clouds became visible to the northeast of the island of Oahu. At 2200 UTC 24 January 2003, well-deﬁned trapped lee- wave clouds extended more than 200 km downstream under the southwesterly winds. These waves are dominated by the transverse mode. The synoptic conditions favorable for the trapped lee-wave clouds included the approaching cold front and retreating subtropical high.

Before this event, orographic clouds over the mountains Downloaded from http://journals.ametsoc.org/jamc/article-pdf/56/5/1305/3594081/jamc-d-15-0341_1.pdf by guest on 16 October 2020 were observed (Fig. 5a). At 0000 UTC 24 January 2003 (Fig. 6a), the subtropical high was to the east of the Hawaiian Islands with the ridge axis to the south of Oahu as a midlatitude cyclone moved to the north of the Hawaiian Islands (Fig. 6a). From 0000 to 1800 UTC 24 January 2003, Oahu was in the prefrontal region (Fig. 6b). Meanwhile, the ridge axis of the subtropical high extended westward with increasing central pressure from .1020 hPa to .1025 hPa. As a result, the pressure gradient between high and low pressure systems in- creased, and the prefrontal southwesterly flow strength- ened (Fig. 6b). In addition to low-level winds, the approaching cold front also influenced the vertical wind profile and inversion height. During 1200 UTC 23 January– 0000 UTC 24 January 2003, the atmosphere was stably stratified with the base of the inversion layer at z 5 1.5 km (Figs. 7a,b). As the cold front moved closer, the base of the inversion layer was lifted to 2 km at 1200 UTC 24 January 2003 (Fig. 7c). After the passage of the cold front over the island of Oahu around 1200 UTC 25 January 2003 (Fig. 6c), the inversion was still present (Fig. 7d). However, as the low-level winds shifted from prefrontal southwesterlies to postfrontal northeasterlies, the trapped lee-wave event dissipated. The CAPE from 1200 UTC 23 January (Fig. 7a) to 1200 UTC 25 January 2 (Fig. 7d) was less than 70 J kg 1. Similar to TRAP1, the surface air parcel was negatively buoyant after being lifted to the top of trade wind inversion. FIG.6.AsinFig. 3, but for (a) 0000 and (b) 1800 UTC 24 Jan, and (c) 1200 UTC 25 Jan 2003. 5. Model simulations of two trapped lee-wave events the prefrontal southwesterly flow regime for heavy- a. Case of 26–27 January 2010 (TRAP1) rainfall cases (Jayawardena et al. 2012; Tu and Chen 2011; and others). 1) WAVE EVOLUTION b. Case of 24–25 January 2003 (TRAP2) The evolution of the vertical motion at the 850-hPa During 23–24 January 2003, another trapped lee-wave level at different stages of the trapped lee-wave event for case was observed by GOES-10 VIS satellite images the 26–27 January 2010 case (Fig. 8) is in agreement with (Fig. 5). This trapped lee-wave event is classified into satellite observations (Fig. 2). The base of the inversion three stages based on satellite observations: 1) developing layer for this case is above z 5 2km with moisture MAY 2017 L I A N D C H E N 1313 Downloaded from http://journals.ametsoc.org/jamc/article-pdf/56/5/1305/3594081/jamc-d-15-0341_1.pdf by guest on 16 October 2020

FIG.7.AsinFig. 4, but for (a) 1200 UTC 23 Jan, (b) 0000 and (c) 1200 UTC 24 Jan, and (d) 1200 UTC 25 Jan 2003. confined underneath (Fig. 4b). Thus, the 850-hPa level is Mountains (Figs. 8b,c), consistent with the satellite- within the marine boundary layer. observed lenticular clouds (Fig. 2b). At the mature Before the event, airflow on the northeastern lee side stage, the simulated trapped lee waves are more orga- of the Koolau Mountains is dominated by descending nized and extend farther downstream (Fig. 8c). The 2 airflow (Fig. 8a). In the developing stage around maximum vertical motion reaches 1.5 m s 1. The simu- 1800 UTC 26 January 2010 (Fig. 8b), waves are simulated wavelength at the 850-hPa level in the mature lated between the Waianae and the Koolau Mountains stage is around 12 km (Fig. 8c), in agreement with the and extend to the northeast of Oahu. The simulated satellite images (Fig. 2b). During the decaying stage oscillations in the vertical motion are divided into two (Fig. 8d), the simulated lee waves disappear without branches: one to the north caused by the resonance of vertical motion oscillations off the leeside coast of Oahu. waves triggered by the Waianae and Koolau Mountains; The moisture distributions (shading) and isentropic the other to the south solely caused by the Koolau contour along line 1 (Fig. 1a) during this event (Fig. 9) 1314 JOURNAL OF APPLIED METEOROLOGY AND CLIMATOLOGY VOLUME 56 Downloaded from http://journals.ametsoc.org/jamc/article-pdf/56/5/1305/3594081/jamc-d-15-0341_1.pdf by guest on 16 October 2020

21 FIG. 8. Simulated vertical motion (m s ) at the 850-hPa level for the trapped lee-wave case of 26–27 Jan 2010: (a) 1200 and (b) 1800 UTC 26 Jan, and (c) 0000 and (d) 1200 UTC 27 Jan 2010. indicate that before this trapped lee-wave event of upstream flow at dot 1 in Fig. 1a are shown in Fig. 10, (Fig. 9a), simulated moisture is confined below z 5 1.5 km including winds, U/N, and L2 (U is the cross-barrier wind and leeside oscillations exist in the dry stable layer speed along line 1, and N is the Brunt–Väisälä frequency above z 5 2 km. In the developing stage (Fig. 9b), the calculated on the basis of unsaturated air). The up- simulated low-level oscillations below the inversion are stream conditions at dot 1 and dot 2 (not plotted) are evident, and RH greater than 90% is present over the similar except for slight differences due to location be- upslope region of the Waianae Range. In the mature cause the cold front passed the island of Oahu from the stage (Fig. 9c), the gravity waves between the surface northwest to the southeast. and the inversion (approximately depicted by the 308-K Figure 10a shows that the prefrontal southwesterly potential temperature contour line) are well developed. flow upstream between z 5 1 and 2 km increases from 2 2 From the developing (Fig. 9b) to the mature stage 8ms 1 at 1800 UTC to over 10 m s 1 at 0300 UTC. From (Fig. 9c), the simulated RH below the inversion in- 2200 UTC 26 January to 0400 UTC 27 January, the wind creases. The wave amplitude is the greatest around the speed increases with respect to height through the in- 308-K potential temperature contour line, correspond- version (ca. 1.5–2.5 km). After 0600 UTC 27 January ing to the inversion base. During the decaying phase, the 2010, however, the simulated low-level cross-barrier southwesterly flow shifts to northeasterlies, and buoy- flow decreases significantly and shifts to a westerly di- ancy oscillations dissipate without trapped lee waves rection, ending the trapped lee-wave event. (Fig. 9d). Section 5a(2) will discuss the close relationship In Fig. 10b, U/N increases from 0.7 to 1.0 km during between the evolution of the trapped lee waves and the development stage, indicating that Fr is greater than changes in upstream conditions. 1 after 2200 UTC. With Fr . 1, the low-level airflow can move over the mountain ridges. From 0000 to 0600 UTC 2) UPSTREAM CONDITIONS 27 January 2010, for the inversion layer between z 5 1.5 2 The temporal changes of synoptic conditions affect and 2.5 km, L2 . 1.4 km 2, and L2 decreases to less than 2 the airflow passing the mountain ridges. The time series 0.8 km 2 above z 5 3km(Fig. 10c). The difference in L2 MAY 2017 L I A N D C H E N 1315 Downloaded from http://journals.ametsoc.org/jamc/article-pdf/56/5/1305/3594081/jamc-d-15-0341_1.pdf by guest on 16 October 2020

FIG. 9. The vertical cross sections of potential temperature (K; contours) and relative humidity (%; shading) along line 1 (Fig. 1) during the different phases of the 27 Jan 2010 trapped lee-wave case. The white dashed line outlines the area with RH . 90% where clouds are very likely to occur. between the inversion layer and above the 3-km level is coast. The RH (%) along the vertical cross section 2 2 0.6 km 2. With H 5 2.5 km, p2/(4H2) is around 0.4 km 2, (Fig. 12a) indicates an extremely dry layer between 2 2 2. 2 2 5 satisfying Ll Lu p /(4H ). Thus, the decrease in the z 1.5 and 3.5 km above the inversion layer, which is Scorer parameter is large enough for trapped lee-wave consistent with the Lihue sounding at 0000 UTC (Fig. 7b). development. During the trapped lee-wave event, os- In the early stage (Figs. 11a and 12a), trapped lee waves cillations are most significant within the inversion layer are simulated but without lee-wave clouds (Fig. 5a). between z 5 1.5 and 2.5 km (Fig. 9). From 0300 to 1800 UTC 24 January 2003, the cold front moved closer toward the island of Oahu from the b. Case of 24–25 January 2003 (TRAP2) northwest. The strengthening prefrontal southwesterly winds led to an increase in the wavelengths from ;12 to 1) WAVE EVOLUTION ;18 km with larger vertical motions (Figs. 11a,b). In During the early stage of TRAP2, satellite images at the meantime, the maximum vertical motion increases 2 0300 UTC 24 January 2003 show clear skies with limited from 1 to greater than 1.5 m s 1. Trapped lee-wave clouds over the mountains and in the lee side (Figs. 5a,b), clouds are evident in the satellite images (Fig. 5b). The whereas the model results suggest that oscillations in simulated vertical motions at the 850-hPa level vertical motion are already present (Fig. 11a). The ab- (Fig. 11c) and the potential temperature contours sence of lee-wave clouds during the early stage is related (Fig. 12c) all indicate the presence of trapped lee to insufficient moisture at that time (Fig. 12a). waves. Trapped lee-wave clouds are likely to occur After 0300 UTC 24 January 2003, the vertical motion associated with the rising motions from the wave at the 850-hPa level (Fig. 11a) and the potential tem- troughstocrestswithhighRH(.90%) (Fig. 12b). perature contours (Fig. 12a) all suggest significant lee- At 0300 UTC 25 January 2003, the cold front passed side oscillations, extending to the northeastern leeside Oahu. As a result, low-level winds turned from 1316 JOURNAL OF APPLIED METEOROLOGY AND CLIMATOLOGY VOLUME 56

2 (1.5 km) increases from 12 to more than 20 m s 1 (Fig. 13a). With stronger winds than TRAP1, the observed and simulated wavelengths during the mature stage (;18 km) of TRAP2 are longer than TRAP1 (Table 1). The simulated horizontal wind speeds from the surface to the inversion base increase with respect to height through the inversion. The wind directions are almost perpendicular to the mountain ridges. After the passage of the cold front at 0300 UTC 25 January 2003, the simulated winds turn to westerlies and weaken. Without a strong cross-barrier wind component, the

trapped lee waves dissipate. Downloaded from http://journals.ametsoc.org/jamc/article-pdf/56/5/1305/3594081/jamc-d-15-0341_1.pdf by guest on 16 October 2020 The maximum upstream wind speeds during the TRAP2 case are almost twice that during TRAP1 (Figs. 10a and 13a). The calculated U/N is over 1.5 km during the trapped lee-wave development, much higher than the mountain heights of 0.9–1.2 km, and satisfies the Fr . 1 condition (Fig. 13b). From the vertical profile of the Scorer parameter, it is apparent that the most favorable period for trapped lee-wave development is between 0600 to 1800 UTC, consistent with the simulated vertical motions (Fig. 11). The Scorer parameter 2 L2 decreases from 1.2 to 0.4 km 2 from z 5 2to3km (Fig. 13c). The difference in the Scorer parameter be- 2 tween the inversion layer and aloft is 0.8 km 2, which is 2 larger than p2/(4H2)(;0.6 km 2). Thus, the decrease in L2 with respect to height above the ridge top is large enough for trapped lee-wave development. In summary, the 3D wave structures of TRAP1 and TRAP2 are well simulated in the high-resolution (1 km) WRF Model. Analysis of wave structure and upstream airflow in this section indicates that the crucial features necessary for the trapped lee-wave development in wintertime are 1) a strong stably stratified (with very little CAPE or no CAPE) prefrontal cross-barrier wind component related to the approaching cold front with Fr . 1; and 2) decreasing L2 related to the vertical FIG. 10. Time series of upstream airflow at location dot 1 in Fig. 1 gradient of the wind shear and the stability profile for the 26–27 Jan 2010 case. (a) Upstream U component (contours; 21 through the inversion with the difference between the ms ) and horizontal wind vectors. One pennant, full barb, and 2 2 2 half barb represent 25, 5, and 2.5 m s 1, respectively. (b) The inversion layer and above larger than p /(4H ). The 2 quantity U/N, where U (m s 1) is cross-barrier wind speed and maximum amplitude occurs near the inversion layer just 2 2 N (s 1) is static stability. (c) Scorer parameter (L2;km 2). below the inversion base. With sufficient moisture, trapped lee-wave clouds may occur in the rising branch southwesterlies to westerlies and then northeasterlies. of oscillation in the marine boundary layer. With the change in the prevailing wind direction, the simulated oscillations in the lee side dissipate (Figs. 11d 6. Impact of latent heat release and 12d). For most theoretical studies on airflow over idealized 2) UPSTREAM CONDITIONS mountain ridges, the effects of latent heat release are not For the TRAP2 case on 25 January 2003, low-level considered (e.g., Scorer 1949; Smith 2002). Neverthe- 2 winds are light southwesterlies (ca. 6–8 m s 1) before the less, the effects of latent heat release on the airflow and cold front approaches. After 0600 UTC 24 January 2003, wavelengths, as well as wave amplitudes, cannot be ig- the simulated upstream airflow at the stable layer nored (Ogura 1963; Takeda 1971). With latent heating, MAY 2017 L I A N D C H E N 1317 Downloaded from http://journals.ametsoc.org/jamc/article-pdf/56/5/1305/3594081/jamc-d-15-0341_1.pdf by guest on 16 October 2020

21 FIG. 11. Simulated vertical motion (m s ) at the 850-hPa level for the 24–25 Jan 2003 trapped lee-wave case: (a) 0300, (b) 1800, and (c) 2200 UTC 24 Jan, and (d) 0300 UTC 25 Jan 2003. the buoyancy restoring force is weaker (Durran and control run, high RH (.90%) is simulated on the Klemp 1982a). When the atmosphere is saturated, the western windward coastal waters and slopes as well as effective Brunt–Väisälä frequency (Nm) is smaller than from the wave troughs to crests downstream. With suf- the dry Brunt–Väisälä frequency (Durran and Klemp ficient lifting, orographic clouds are likely to occur in 1982a; Lalas and Einaudi 1974; Dudis 1972; Hobbs et al. these areas. In the RH80 run (Figs. 14c,d), RH greater 1973). In reality, the wave response is more complicated than 90% is only simulated in the upslope region and than that predicted by simply replacing the dry stability over the mountains. The RH30 run is a dry case without with an equivalent moist stability in the saturated layer latent heat release. (Durran and Klemp 1982a). The feedback effect of latent heat release also If the upstream flow is relatively moist but cloud free, modifies the isentropic surface and stability. With la- condensation and evaporation could occur in the wave tent heating, stability is reduced with larger wave am- crests, and the unsaturated trough is similar to the dry plitudes (Fig. 14). The maximum wave amplitude in case (Durran and Klemp 1982b). The waves develop RH30 is only two-thirds that of the control run broad flat crests and narrow troughs, producing the (Figs. 14a,b,e,f). Aside from wave amplitude, wave- distinctive asymmetry in the vertical velocity field, and length also varies depending on the amount of latent the overall horizontal wavelength is much longer for the heating release. With reduced stability caused by latent dry waves. In saturated gravity waves, nonlinear effects heating, wavelengths are longer. In the control run, the act to increase the buoyancy restoring force in the wave wavelengths at z 5 2 km are about 2 times that in the crests beyond that predicted by linear theory, while RH30 simulation (Figs. 14a,b,e,f). decreasing it in the troughs (Durran and Klemp 1982b). A simple way to estimate the wavelength without the To compare the wave structures with different effects of latent heating is given by amounts of latent heat release, two model sensitive tests are performed for the TRAP1 case with RH reduced to 2pU 2pU l 5 5 , (10) 80% (RH80) and 30% (RH30) of the original values in N [g(G2g)/T]1/2 the initial and outer boundary conditions. Figure 14 shows the distributions of RH and potential tempera- where T is the temperature (K), G is the dry adiabatic ture along the cross section shown in Fig. 1a. In the lapse rate, and g is the environmental lapse rate. It is 1318 JOURNAL OF APPLIED METEOROLOGY AND CLIMATOLOGY VOLUME 56 Downloaded from http://journals.ametsoc.org/jamc/article-pdf/56/5/1305/3594081/jamc-d-15-0341_1.pdf by guest on 16 October 2020

FIG. 12. As in Fig. 9, but for the 24–25 Jan 2003 trapped lee-wave case: (a) 0300, (b) 1800, and (c) 2200 UTC 24 Jan, and (d) 0300 UTC 25 Jan 2003. apparent that wavelengths become longer with in- 1988; Rasmussen et al. 1989; Yang et al. 2008; Chen and creasing cross-barrier wind speed and shorter with a Feng 2001) with counterrotating vortices in the leeside higher N in the inversion layer. Table 1 shows the cal- wake zone (Smith and Grubisic´ 1993; Schär and Smith culated wavelengths from Eq. (11) and the observed 1993). Thus, traverse trapped lee waves do not occur in (Figs. 2c and 5c) and simulated wavelengths at the the lower troposphere over the Big Island. For Haleakala, 850-hPa level (Figs. 8c and 11c) during the mature stage Maui, with highest peaks over 3 km, the situation is of these two wintertime trapped lee-wave events. Cal- similar to the Big Island. For the west Maui mountains, culations of wavelengths from Eq. (5) given by Lin the highest peaks are around 1.7 km. The mountain (2007) are within similar wavelength ranges. Neverthe- height on Kauai is about 1.6 km, and the highest peaks less, results using Eq. (5) are sensitive to the choice of H. on east Molokai are around 1.5 km. For steep mountains Without considering the influence of latent heat release with ridges or tops below the trade wind inversion (e.g., on wavelength, Eq. (10) underestimates the wavelengths western Maui, Kauai, or Molokai), when the low-level by about 40%–55% (Table 1). With latent heating, sta- winds are strong enough with Fr . 1, transverse trapped bility decreases, which results in longer wavelengths lee waves could occur on the lee side of these islands (Atkinson 1981) and larger wave amplitudes. under similar large-scale settings. For 3D hills, divergent trapped lee waves may be present with Fr , 1. During TRAP1, the maximum wind speed is less than 7. Discussion 2 12 m s 1 (Fig. 10a), and the maximum calculated U/N is The highest mountain heights on the Big Island (the about 1.2 km (Fig. 10b). For Lanai (z 5 1km) and the island of Hawaii) are more than 4 km, which is well above northeastern arm of the mountain ridges over Kauai the base of the trade wind inversion. The low-level airflow (0.4 km) with Fr . 1, transverse trapped lee-wave clouds are is deflected around the island instead of moving over the evident on the lee sides (Figs. 15a,b). For east Molokai with mountain peaks (Leopold 1949; Smolarkiewicz et al. the highest peaks z . 1.5 km (Fr , 1), in addition to trapped MAY 2017 L I A N D C H E N 1319

TABLE 1. Observed wavelengths from satellite images, simulated wavelengths, and calculated wavelengths using Eq. (10) for TRAP1 and TRAP2.

TRAP1 TRAP2 Time 0300 UTC 2200 UTC 27 Jan 2010 24 Jan 2003 Observed wavelength (km) ;12 ;18 Simulated wavelength (km) ;12 ;18 Calculated wavelength (km) ;6 ;10

The ridge tops of Oahu are low enough such that the

Fr of the prefrontal southwesterlies could be greater Downloaded from http://journals.ametsoc.org/jamc/article-pdf/56/5/1305/3594081/jamc-d-15-0341_1.pdf by guest on 16 October 2020 than 1 but high enough to lift the air in the marine boundary layer to reach saturation with lee waves downstream. Thus, with sufficient moisture, trapped lee-wave clouds are more likely to occur in the prefrontal stably stratified southwesterly flow for Oahu as compared with the other islands. Furthermore, with steep leeside slopes, Oahu is effective in generating trapped lee-wave clouds under prefrontal southwesterly flow based on the literature (Smith 1977; Lilly and Klemp 1979). A prefrontal strong stably stratified (no CAPE or low CAPE) southwesterly flow with increasing wind speed through the inversion is the favorable large-scale setting for trapped lee-wave events. The downslope wind events occurred under different large-scale settings (Zhang et al. 2005b) as compared with trapped lee-wave events. In winter, the postfrontal stably stratified breezy northeasterly trade wind flow regime is favorable for the development of downslope windstorms. For downslope windstorms, a strong migratory high pressure moves to the northeast of the Hawaiian Islands following the passage of the cold front and merges with the semi- permanent subtropical high. This results in windy conditions across the state of Hawaii. The low-level FIG. 13. As in Fig. 10, but for the 24–25 Jan 2003 case. prevailing flow is strong easterlies/northeasterlies with strong westerlies aloft. Aside from strong low-level lee waves on the lee side of west Molokai (z 5 0.4 km), winds and a critical layer, the existence of the post- diverging trapped lee-wave clouds or ship waves (Sharman frontal inversion is critical (Zhang et al. 2005b). and Wurtele 1983) were observed as low-level airflow is deflected by the hills over east Molokai (Fig. 15b). 8. Summary During TRAP2, trapped lee-wave clouds were observed on the leeward side of western Maui, Molokai, The island of Oahu has two narrow nearly parallel Lanai, and Kauai (Figs. 15c,d). During the mature stage, mountain ranges, the Koolau Mountain Range and the 2 the cross-barrier wind speed is as strong as 20 m s 1 Waianae Mountain Range, with peaks of 944 and (Fig. 13a) and the calculated U/N of upstream flow was 1227 m, respectively (Fig. 1a), which are well below the greater than 1.5 km (Fig. 13b). The Fr of the upstream typical base of the stable inversion layer (,2 km) above flow toward Kauai, Lanai, Molokai, and western Maui the marine boundary layer. In winter, transverse trap- was, therefore, greater than 1. With sufficient moisture, ped lee waves can occur over Oahu under a strong as the air parcel in the marine boundary layer is lifted prefrontal stably stratified southwesterly flow with over the terrain, water vapor could condense from wave upper-level westerlies aloft. The conditions favorable troughs to crests to form clouds in the lee. for the occurrence of traverse trapped lee waves are 1320 JOURNAL OF APPLIED METEOROLOGY AND CLIMATOLOGY VOLUME 56 Downloaded from http://journals.ametsoc.org/jamc/article-pdf/56/5/1305/3594081/jamc-d-15-0341_1.pdf by guest on 16 October 2020

FIG. 14. As in Fig. 9, but for (a),(b) control run, (c),(d) RH80, and (e),(f) RH30 simulations. In the latter two runs, the RH is reduced to 80% and 30% relative to the control run, respectively. The locations of the two vertical cross sections are shown in Fig. 1a.

1) strong low-level winds with Fr . 1 impinging on the transverse trapped lee-wave clouds under the prefrontal mountain ridges; 2) insufficient CAPE for the surface stably stratified (with no CAPE or small CAPE) air parcel to become positively buoyant after being southwesterly flow in winter as compared with the other lifted to the top of the trade wind inversion; and 3) islands in the Hawaiian Island chain. Nevertheless, the increasing wind speed with respect to height through prefrontal atmosphere is frequently conditionally un- the stable inversion layer above the ridge tops satisfy- stable as the warm, moist tropical air is adverted ing Scorer’s criteria. At the inversion base, the Scorer northward by the southwesterly flow. Thus, it is more parameter L2 has a maximum, and wave amplitudes likely for heavy showers to occur in the warm sector of a there are the greatest. wintertime cold front (or wind shear line) rather than For trapped lee-wave clouds to form, the air in the trapped lee waves, unless the flow is stably stratified. marine boundary layer needs to have sufficient moisture The evolution of upstream flow influences the wave to become saturated by orographic lifting and rising structure, amplitude, and wavelength. As a cold front motions between the wave troughs and crests. With its approaches with increasing stably stratified strong cross- narrow ridges with heights around z 5 0.9–1.2 km and barrier flow, wavelengths are longer and trapped lee steep lee slopes, Oahu is most likely to generate waves extend farther downstream. After the upstream MAY 2017 L I A N D C H E N 1321 Downloaded from http://journals.ametsoc.org/jamc/article-pdf/56/5/1305/3594081/jamc-d-15-0341_1.pdf by guest on 16 October 2020

FIG. 15. Trapped lee waves over the other Hawaiian Islands. The trapped lee-wave clouds to the (a) northeast of Kauai at 2215 UTC and (b) lee side of Molokai at 1900 UTC for the 26 Jan 2010 trapped wave event (TRAP1). The trapped lee-wave clouds observed to the northeast of (c) Kauai at 0145 UTC and (d) Molokai and western Maui at 2045 UTC for the 24 Jan 2003 trapped lee-wave event (TRAP2). airflow weakens with a decrease in Fr, the wavelength cross-barrier wind speed and stability, trade wind in- shortens. With wind direction shifts or Fr , 1, transverse version height, and Fr to assess the likelihood of the trapped lee waves dissipate. Using model sensitivity occurrence of trapped lee-wave events on the lee side of tests and comparing observations with calculations, it is islands with tops below the inversion. The movement of evident that latent heat release will reduce stability, the cold front can also be determined by the model amplify the trapped lee waves, and widen the wave output. Nevertheless, Lihue soundings are available crests, producing longer wavelengths as compared with only every 12 h, and trapped lee-wave events typically studies that do not consider the effects of latent heating. only last 12–18 h. The 12-hourly soundings are marginal The results from this study improve our basic un- in resolving the temporal resolution of the vertical derstanding of the occurrences and evolution of trapped structure of the atmosphere to assess the timing of the lee-wave events over Hawaii. During the winter, if the initiation and duration of these events. In this regard, surface map or the 850-hPa-level chart shows a cold high-resolution models with hourly output would pro- front approaching the Hawaiian Island chain from the vide additional valuable information in advance. northwest, trapped lee waves could possibly occur in the northeastern lee side of the major Hawaiian Islands, Acknowledgments. This study was funded by the particularly Oahu, with tops or ridges below the trade National Science Foundation under Grant AGS- wind inversion if the prefrontal atmosphere is stably 1142558, NOAA under Cooperative Agreement stratified. The 850-hPa charts as well as the Lihue NA11NOS0120039, and COMET/UCAR under Part- soundings could be used to estimate the prefrontal wind ners Project Z15-20551. We also thank the University speed of the southwesterly flow, vertical profiles of of Hawai‘i/Maui High Performance Computing Center 1322 JOURNAL OF APPLIED METEOROLOGY AND CLIMATOLOGY VOLUME 56

(UH/MHPCC) for providing part of the computing re- ——, 2003: Lee waves and mountain waves. Encyclopedia of Atmo- sources, Feng Hsiao for his assistance, and May Izumi for spheric Sciences,J.R.Holton,J.Pyle,andJ.A.Curry,Eds., editing the text. Elsevier Science Ltd., 1161–1169. [Available online at http://www. atmos.washington.edu/2010Q1/536/2003AP_lee_waves.pdf.] ——, and J. B. Klemp, 1982a: On the effects of moisture on the REFERENCES Brunt–Väisälä frequency. J. Atmos. Sci., 39, 2152–2158, doi:10.1175/1520-0469(1982)039,2152:OTEOMO.2.0.CO;2. Aanensen, C. J. M., 1965: Gales in Yorkshire in February 1962. ——, and ——, 1982b: The effects of moisture on trapped moun- Geophys. Mem., 14, 1–44. tain lee waves. J. Atmos. Sci., 39, 2490–2506, doi:10.1175/ Ao, C. O., D. E. Waliser, S. K. Chan, J.-L. Li, B. Tian, F. Xie, and 1520-0469(1982)039,2490:TEOMOT.2.0.CO;2. A. J. Mannucci, 2012: Planetary boundary layer heights from Gill, A. E., 1982: Atmosphere–Ocean Dynamics. 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