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    Locations of the three nested domains.

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    Synoptic situation for the Australian region at (a) 1800 UTC 10 Mar 2006, (b) 0600 UTC 11 Mar 2006, and (c) 1800 UTC 11 Mar 2006 (adapted from the Bureau of Meteorology MSLP analysis).

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    MODIS Terra satellite image of the Great Australian Bight at 1015 CST 11 Mar 2006. The arrow highlights the kink in the cloud lines.

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    Divergence (shaded, s−1) and horizontal wind vectors (scale 10 m s−1 below each panel) at σ = 0.97 (altitude = 250 m) at (a) 1030 CST in domain 3 (481 × 481 grid points, wind vectors plotted every 20 grid points) and (b) 1730 CST 11 Mar 2006 in domain 2 (241 × 241 grid points, wind vectors plotted every 15 grid points). Wind vectors represent the wind relative to the convergence lines.

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    Vertical cross section of virtual potential temperature and horizontal wind relative to the disturbances (vectors, scale = 10 m s−1) at (a) 0930, (b) 1330, and (c) 1830 CST 11 Mar 2006. Wind vectors plotted every 20 grid points.

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    A close-up of Fig. 5b showing the waves. Virtual potential temperature (thick lines), horizontal wind relative to the waves (vectors), and vertical velocity (positive values in solid lines and negative values in dotted lines) are plotted. Wind vectors are plotted at every second grid point.

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    Vertical profiles of (a) virtual potential temperature and (b) horizontal wind component parallel to the plain of the cross section 20 km ahead (solid line) and behind (dashed line) the waves at 0930 CST 11 Mar 2006.

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    Traces of surface pressure (hPa), virtual potential temperature (K), mixing ratio (g kg−1), and diagonal wind component (m s−1) at (a) 0930 and (b) 1330 CST 11 Mar 2006.

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    Vertical profile of μ2 as defined in Eq. (10).

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    Synoptic situation for the Australian region at (a) 1200 UTC 30 Dec 2007, (b) 0000 UTC 31 Dec 2007, and (c) 1200 UTC 31 Dec 2007 (adapted from the Bureau of Meteorology MSLP analysis).

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    (a) MODIS Terra satellite image at 1015 CST and (b) MODIS Aqua satellite image at 1510 CST 31 Dec 2007.

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    Divergence (shaded, s−1) and horizontal wind vectors (scale 10 m s−1) at σ = 0.97 (altitude = 250 m) at 1030 CST 31 Dec 2007 in domain 3 (466 × 466 grid points, wind vectors plotted every 20 grid points).

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    Vertical cross section of virtual potential temperature and horizontal wind relative to the disturbances (vectors, scale = 10 m s−1) at (a) 0330, (b) 0630, and (c) 1830 CST 31 Dec 2007. Wind vectors plotted every 20 grid points.

  • View in gallery

    A close-up of Fig. 13b showing the waves. Virtual potential temperature (thick lines), horizontal wind relative to the disturbances (vectors), and vertical velocity (positive values in solid lines and negative values in dotted lines) are plotted. Wind vectors are plotted every second grid point. Note that the isolines for the vertical velocity are not equidistant, with the innermost isoline at the leading wave denoting 2.5 m s−1.

  • View in gallery

    Vertical profile of (a) virtual potential temperature and (b) horizontal wind component parallel to the plain of the cross section 20 km ahead (solid line) and behind (dashed line) the waves at 0330 CST 31 Dec 2007.

  • View in gallery

    Traces of surface pressure (hPa), virtual potential temperature (K), mixing ratio (g kg−1), and diagonal wind component (m s−1) at (a) 0330 and (b) 0630 CST 31 Dec 2007.

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    Synoptic situation for the Australian region (a) 0000 UTC 31 Mar 2005, (b) 1200 UTC 31 Mar 2005, (c) 0000 UTC 1 Apr 2005, and (d) 1200 UTC 1 Apr 2005 (adapted from the Bureau of Meteorology MSLP analysis).

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    MODIS Terra satellite image of the Great Australian Bight at 0915 CST 1 Apr 2005.

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    Divergence (shaded, s−1) and horizontal wind vectors (scale 10 m s−1) at σ = 0.97 (altitude = 250 m) at (a) 0030 and (b) 0730 CST 1 Apr 2007 in domain 3 (466 × 466 grid points, wind vectors plotted every 20 grid points).

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    Vertical cross section of virtual potential temperature (shaded), horizontal wind relative to the disturbances (vectors, scale = 10 m s−1), and vertical velocity (contour lines, nonequidistant interval) at (a) 2330 CST 31 Mar 2005, (b) 0330 CST 1 Apr 2005, and (c) 0730 CST 1 Apr 2005. Wind vectors are plotted every 15 grid points.

  • View in gallery

    A close-up of Fig. 20 showing the waves. Virtual potential temperature (K) (thick lines), horizontal wind relative to the waves (m s−1) (vectors), and vertical velocity (positive values in solid lines and negative values in dotted lines) are plotted. Wind vectors are plotted every second grid point. Note that the isolines for the vertical velocity are not equidistant, with the innermost isoline at the leading wave denoting 1.5 m s−1.

  • View in gallery

    Vertical profile of (a) virtual potential temperature (K) and (b) horizontal wind component (m s−1) parallel to the plain of the cross section 20 km ahead (solid line) and behind (dashed line) the waves at 2330 CST 31 Mar 2005. (c),(d) As in (a),(b), but at 0730 CST 1 Apr 2005.

  • View in gallery

    Traces of surface pressure (hPa), virtual potential temperature (K), mixing ratio (g kg−1), and diagonal wind component (m s−1) at (a) 2330 CST 31 Mar 2005 and (b) 0330 CST 1 Apr 2005.

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Nonlinear Waves ahead of Fronts in the Great Australian Bight

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  • 1 Meteorological Institute, University of Munich, Munich, Germany
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Abstract

This study investigates nonlinear waves ahead of cold fronts in the Great Australian Bight, south of the Australian continent. These waves often form a series of roll clouds on their crests analogous to the “morning glory,” which is observed around the Gulf of Carpentaria in northeastern Australia. High-resolution visible satellite imagery from NASA’s polar-orbiting Aqua and Terra satellites between 23 October 2004 and 29 February 2008 is used to determine how frequently these cloud lines occur ahead of cold fronts. A total of 14 cases are identified with the most cases occurring in summer and none occurring in winter. The authors hypothesize that the summer maximum is due to a combination of lower cloud amounts associated with summertime cold fronts, and a stronger maritime stable layer, which is produced as hot continental air, is advected offshore.

Three cloud line events are modeled using the fifth-generation Pennsylvania State University–National Center for Atmospheric Research (PSU–NCAR) Mesoscale Model (MM5, version 3.6). In each case the low-level divergence field reveals convergence lines, which coincide with the cloud lines as identified on the satellite images. In two cases vertical cross sections of virtual potential temperature and horizontal and vertical velocity through the disturbances show a cold front advancing into a stratified environment leading to wave production at the leading edge of the cold air mass. Modeled maximal upward velocities range between 0.8 and 2.5 m s−1. Surface pressure jumps of about 1 hPa associated with the propagating waves occur in each case, which coincides with that predicted by simple bore theory. In two cases the front moves at supercritical speed (i.e., the frontal speed is larger than the speed of the fastest mode of small-amplitude long waves). In the third case the front does not propagate and the nonlinear waves produced become stationary as well.

Corresponding author address: Christoph Schmidt, Meteorological Institute, University of Munich, Theresienstr. 37, 80333 Munich, Germany. Email: schmidt@meteo.physik.uni-muenchen.de

Abstract

This study investigates nonlinear waves ahead of cold fronts in the Great Australian Bight, south of the Australian continent. These waves often form a series of roll clouds on their crests analogous to the “morning glory,” which is observed around the Gulf of Carpentaria in northeastern Australia. High-resolution visible satellite imagery from NASA’s polar-orbiting Aqua and Terra satellites between 23 October 2004 and 29 February 2008 is used to determine how frequently these cloud lines occur ahead of cold fronts. A total of 14 cases are identified with the most cases occurring in summer and none occurring in winter. The authors hypothesize that the summer maximum is due to a combination of lower cloud amounts associated with summertime cold fronts, and a stronger maritime stable layer, which is produced as hot continental air, is advected offshore.

Three cloud line events are modeled using the fifth-generation Pennsylvania State University–National Center for Atmospheric Research (PSU–NCAR) Mesoscale Model (MM5, version 3.6). In each case the low-level divergence field reveals convergence lines, which coincide with the cloud lines as identified on the satellite images. In two cases vertical cross sections of virtual potential temperature and horizontal and vertical velocity through the disturbances show a cold front advancing into a stratified environment leading to wave production at the leading edge of the cold air mass. Modeled maximal upward velocities range between 0.8 and 2.5 m s−1. Surface pressure jumps of about 1 hPa associated with the propagating waves occur in each case, which coincides with that predicted by simple bore theory. In two cases the front moves at supercritical speed (i.e., the frontal speed is larger than the speed of the fastest mode of small-amplitude long waves). In the third case the front does not propagate and the nonlinear waves produced become stationary as well.

Corresponding author address: Christoph Schmidt, Meteorological Institute, University of Munich, Theresienstr. 37, 80333 Munich, Germany. Email: schmidt@meteo.physik.uni-muenchen.de

1. Introduction

Low-level cloud lines associated with nonlinear wave phenomena (i.e., undular bores and solitary waves) have been observed ahead of cold fronts worldwide (Drake 1984; Clarke 1986; Clarke 1998; Demoz et al. 2005). When upper-level cloud is absent, such cloud lines are seen frequently in satellite images when the cold front propagates into an environment where the mid- and upper levels are dry. A similar situation is typical for fronts propagating southward through Texas (Demoz et al. 2005) and for fronts propagating over the Great Australian Bight, south of the Australian continent. In the latter case, dry air from the continent is advected southward ahead of the front by the mid- and upper-level winds (Wilson and Stern 1985).

Clarke (1986) presented seven cases of atmospheric undular bores observed over the waters south of Australia between 1969 and 1985. An undular bore is a hydraulic jump occurring at the interface between two atmospheric layers with waves at its leading edge (Simpson 1997). Two cases from Clarke (1986) were shown to be produced from thunderstorm outflows, while the remaining five cases were associated with an approaching cold front. Clarke (1986, p. 74) notes that, as a cold front encounters the stably stratified marine inversion, it may “produce a bore, which in time may become undular, and eventually decay to a train of solitary waves.” Clarke (1986) also indicated the possibility that the cold front itself can transform into an undular bore. The development of a nocturnal stable layer over land may allow the waves to propagate onshore, as in the case of the solitary wave train observed at Melbourne, Australia, on 6 January 1984 (Physick 1986). These waves were shown to develop in a prefrontal trough ahead of the cold front itself, and were located about 300 km ahead of the front. A recent study by Hartung et al. (2010) investigates the evolution of an undular bore generated by a cold front over the southern plains of the United States using both observational data and the Weather Research and Forecasting Model (WRF). Their numerical simulation confirmed both the existence of the observed wave packet and a prefrontal environment conducive to the formation of these waves.

Because of the sporadic occurrence of cloud lines ahead of cold fronts, detailed observations of them have not been made. In fact, it is unclear how often such cloud lines are observed over southern Australia. For this reason a small climatology of their occurrence based on high-resolution visible satellite images for the Australian region from October 2004 to February 2008 is presented here.

Similar cloud lines have been observed over Cape York Peninsula and the Gulf of Carpentaria in northeastern Australia, and are referred to as morning glories (see Smith 1988; Christie 1992; Reeder and Smith 1998 for reviews). In these cases, the clouds form in the crests of nonlinear internal waves that propagate on a low-level stable layer, and occur frequently in the late dry season (September–mid-November). Owing to their regularity, a number of field experiments have been conducted around the Gulf of Carpentaria to examine their formation (e.g., Clarke et al. 1981; Smith et al. 1982, 1986, 2006; Smith and Morton 1984; Smith and Page 1985; Menhofer et al. 1997a,b; Thomsen and Smith 2006). Occasionally, in this region, morning glories propagating from the south have been observed ahead of subtropical cold fronts over land (e.g., Smith et al. 1995; Deslandes et al. 1999; Reeder et al. 2000; Thomsen et al. 2009). High-resolution numerical modeling studies using both idealized models (Goler and Reeder 2004) and the fifth-generation Pennsylvania State University–National Center for Atmospheric Research (PSU–NCAR) Mesoscale Model (MM5; Thomsen and Smith 2006) have been successful in simulating the morning glory. A further aim of this work is to use MM5 to examine the generation of the cloud lines ahead of cold fronts within the Great Australian Bight region.

Low-level nonlinear internal wave disturbances, such as the morning glory, have been shown by Christie and Muirhead (1983) to pose a serious hazard to aircrafts during take-off and landing, because of the associated intense transient horizontal and vertical wind shear zones near the surface. As clouds are not always present with morning glory disturbances, (i.e., they may occur as clear-air disturbances), aircraft may encounter them without being warned by approaching roll clouds. In cases where the wave amplitude is relatively large, nonlinear waves may lift air above the level of free convection and trigger deep convection and thunderstorms if the environment is conditionally unstable (Smith et al. 1982). A further problem concerning nonlinear internal wave disturbances ahead of cold fronts is the associated change in wind speed and direction with the passage of the waves. This is particularly important in southeastern Australia in summer when forecasts of wind changes are often crucial in deciding strategies to combat wildfires (Smith et al. 1982). Thus, further study into these cloud lines ahead of cold fronts is warranted.

Hartung et al. (2010) provides a comprehensive description of gravity currents, undular bores, and solitary waves, and so only a brief discussion will be given here to describe the features addressed in this study. A gravity current or density current is a quasi-horizontal flow generated by a horizontal density difference. The gravity current possesses a low-level feeder flow, where the low-level air within the gravity current flows toward the leading edge, thus possessing a velocity greater than the speed of advance of the gravity current. Examples of gravity currents in the atmosphere include cold-air outflows from thunderstorms, and sea-breeze fronts. A midlatitude cold front with precipitating clouds may produce a gravity current due to evaporative cooling. However, dry nonprecipitating cold fronts may transform themselves to a structure resembling that of a gravity current with a low-level feeder flow immediately behind the front. This process is called “cross-frontal collapse” and the front itself “self-sharpening.” This behavior of some cold fronts has been investigated by Smith and Reeder (1988).

A similar phenomenon of mass transport is the bore, which is a hydraulic jump with a sudden increase of fluid depth. A bore is called internal if it is formed at the interface between two fluids of air of different density. Internal bores may develop waves at this interface [i.e., become undular, when the ratio h1/h0 < 2 (Simpson 1997), where h1 and h0 are the heights of the lower fluid layer behind and ahead of the jump, respectively]. For h1/h0 > 2, the leading edge of the bore becomes turbulent (Simpson 1997). Nonlinear waves investigated in this study are the example par excellence of atmospheric internal undular bores. Internal bores in the atmosphere are often generated by a gravity current propagating into a stratified layer of air with the first wave of the bore developing around the head of the gravity current. As both gravity currents and bores are associated with the transfer of mass, it is often difficult to distinguish both phenomena from each other. However, within a bore the flow relative to the disturbance is negative, meaning that the bore propagates at a speed faster than the normal component of the wind immediately behind (Clarke 1986). For a gravity current, as described above, the relative flow is positive.

One last nonlinear feature addressed here is the solitary wave, where a transfer of energy occurs instead of mass as for gravity currents and bores. A solitary wave is a single symmetrical hump that propagates at a uniform speed without changing its form. Nonlinear waves in the atmosphere being clearly undular bores in their early stage may eventually evolve into a series of amplitude-ordered solitary waves (Christie 1992).

An analysis of borelike characteristics in the numerical results presented herein will be performed using simple bore theory as applied in Clarke (1983, 1986). Hydraulic bore theory shows that the speed of a bore is given by
i1520-0493-138-9-3474-e1
where c0 is the speed of the fastest mode of small-amplitude long waves, also termed the critical velocity, and u is the normal velocity of the fluid ahead of the bore. The upstream Froude number F can in turn be expressed as a function of the normalized lifting at the bore, δh/h, where h is the depth of the undisturbed low-level stratified layer:
i1520-0493-138-9-3474-e2
In the case of a deep neutral layer underlain by a shallow stable layer, and uniform motion u, c0 is given by
i1520-0493-138-9-3474-e3
where m = 1, g is gravity, and
i1520-0493-138-9-3474-e4
is a measure of density excess in the lower layer. The virtual potential temperature in the nearly neutral upper layer is given by θu and that in the lower layer by θl. One problem with this theory is the assumption of a uniform velocity in the vertical ahead of the bore. However, this problem will be addressed as in Clarke (1986) and explained later [see section 4a(3)].
In the case where θl(z) increases linearly from the surface to θu at z = h, c0 is given by
i1520-0493-138-9-3474-e5
where N is the Brunt–Väisälä frequency in the lower layer. Equation (5) is equivalent to Eq. (3), when The value of m depends on the profile of θ within the boundary layer; however, m = 0.90 will be assumed here (Clarke 1983).
The magnitude of the pressure jump δp can be estimated by
i1520-0493-138-9-3474-e6
where ρ is air density and δθυ represents an average deficit in virtual potential temperature in the lower layer relative to the upper one, which can be expressed as
i1520-0493-138-9-3474-e7
Hence,
i1520-0493-138-9-3474-e8
The simple bore theory described here focuses primarily on the influence of the thermal stratification G in forming the waveguide. The influence of curvature on the waveguide, as shown by Crook (1988) to be important for wave propagation, is initially not considered here through the assumption of a uniform ambient wind in Eq. (3). To account for the effect of wind curvature, linear wave theory akin to Menhofer et al. (1997a) is applied to investigate its effect on the waveguide, albeit the waves considered here are intrinsically nonlinear.
The vertical velocity profile w(z) of a two-dimensional sinusoidal wave with a horizontal wavelength 2π/k and a vertical wavelength 2π/μ is governed by the following equation:
i1520-0493-138-9-3474-e9
where
i1520-0493-138-9-3474-e10
N is the Brunt–Väisälä frequency, u(z) is the ambient wind component normal to the waves, and c is the horizontal phase speed. The parameter l2(z) is the Scorer parameter. The upward propagation of waves is restricted when μ2 > 0 at low levels and μ2 < 0 at higher levels (Scorer 1949). In the absence of curvature in the wind profile, a nearly neutral stratification (N = 0) above a stably stratified surface layer would be favorable for wave energy to be confined to the lower atmosphere. However, in general, the curvature of the wind profile is not negligible.

The present paper investigates the formation of cloud lines ahead of cold fronts, and is structured as follows. Section 2 presents a climatology of low-level nonlinear wave events over the Great Australian Bight based on high-resolution visible satellite images from October 2004 to February 2008. The MM5 model, which is used to simulate three cases, is described in section 3, and the results are presented in section 4. The conclusions are drawn in section 5.

2. Nonlinear wave climatology

Cold fronts crossing over the Great Australian Bight region (30°–38°S, 126°–141°E) are identified on the mean sea level pressure (MSLP) analyses prepared by the Australian Bureau of Meteorology. The charts are available 4 times a day at 0000, 0600, 1200, and 1800 UTC. Visible satellite imagery (250-m resolution) from the Moderate Resolution Imaging Spectroradiometer (MODIS) on board the National Aeronautics and Space Administration (NASA) Aqua and Terra polar-orbiting satellites are used to detect cloud lines ahead of cold fronts. During their orbits, Terra passes over southern Australia at 2345 UTC (0915–1015 CST), and Aqua passes over at 0440 UTC (1410–1510 CST), thus giving two images of the area of interest each day. [Central Standard Time (CST) for South Australia is CST = UTC + 9.5 h in winter and 10.5 h in summer.] MODIS satellite images for the region are available from 23 October 2004, and so a time period until 29 February 2008 is chosen here.

In general the cloud lines could be seen easily in the relatively cloud-free area ahead of the cold front. Often, more than 10 individual cloud lines could be identified, with 1 case exhibiting over 25 lines. In some cases it was clear that the leading cloud line was smooth whereas successive lines were ragged in structure, reflecting their relatively turbulent nature (Reeder et al. 1995). Often the cloud lines blended into almost invisible lines, which could just be discerned on the image. In other cases, where the cloud lines were only partially covered by upper- and midlevel clouds, it was usually clear that the cloud lines were at low levels.

A total of 12 cases were identified during the entire time period, with another 2 cases classified as uncertain. Three particular cases were visible on the satellite images as middle level cloud lines, which appeared broader and more ragged in outline compared to the low-level cloud lines. Such midlevel cloud lines have been observed to accompany low-level morning glories over northeastern Australia and are believed to be nonlinear wave disturbances that propagate on elevated inversions in the midtroposphere (Christie 1992). The case on 26 January 2006 suggests this connection between the low- and midlevel cloud lines, where the satellite image from the morning shows five low-level cloud lines, while the afternoon image 5 h later shows midlevel cloud lines farther to the east.

For the two uncertain cases, both in January 2008, low-level cloud lines are evident, but are located about 500 km from the analyzed cold front, and thus may not be directly associated with it. However, the cloud lines on both days do coincide with a prefrontal trough. Hanstrum et al. (1990) have shown that frontogenesis may occur rapidly in the prefrontal trough, generally at the expense of the approaching midlatitude cold front, and this may have happened in these two cases. For this reason, these two cases have been included in the climatology.

During the period of investigation, 256 cold fronts passed the region of interest. The total number of cloud line events observed per year and season is shown in Table 1. The summer season refers to December of the previous year together with January and February of the present year (e.g., summer 2005 comprises December 2004 and January and February 2005). The number of seasons during the time period 23 October 2004–29 February 2008 is given in brackets on the x axis. The 3.43 spring seasons are from the time period beginning on 23 October 2004. The largest number of cold front passages occurred in winter, and the least occur in summer. During summer, 13.7% of the cold fronts were accompanied by cloud lines.

During the analyzed period, nonlinear wave events occurred predominantly in summer with an average of two events per year. An average of one event per season occurred in autumn and spring. No cloud lines were identified in winter. Because of the short time period used and the relatively few observed events, these interseasonal differences cannot be regarded as being statistically significant. As the climatology is based on visible satellite images obtained only twice per day, the frequency may be an underestimate. Furthermore, upper-level clouds may have blocked the view on low-level cloud lines, particularly in winter where cloud associated with the front was more extensive owing to the parent low being farther north, closer to the Australian continent. In addition, the amplitude of the waves may be too small to produce cloud, and such disturbances would not be detectable in the satellite images. However, the average number of two cloud line events per summer agrees with the anemometer records during the early 1980s from Aspendale near Melbourne, which showed oscillatory wind behavior occurring at least twice per summer. Physick (1986) suggests that these wind signatures can be attributed to the passage of low-level nonlinear waves associated with fronts. However, Schultz (2005) does highlight mechanisms other than prefrontal bores, which may also lead to prefrontal wind shifts.

Although not statistically significant, the relatively high frequency of cloud lines observed during summer compared with other seasons may also be related to the maritime stable layer that is expected to be stronger in summer than in other seasons. Ahead of a cold front the northerly low-level flow originates from Finland and advects the continental air offshore (Wilson and Stern 1985). During summer, inland temperatures can exceed 40°C while water temperatures of the Southern Ocean within 500 km of the coast are about 20°C. As this hot continental air is advected offshore, a strong stably stratified internal boundary layer is formed over sea (Garratt 1987; Garratt and Ryan 1989). In winter, inland temperatures are typically no more than about 20°C while the water temperatures are around 15°C. This stronger stable layer in summer would be expected to lead to larger wave speeds, allowing the waves to propagate ahead of the cold front. For the reasons given above, we speculate that our results here might be proven with statistical significance at a later stage when a larger dataset is available.

3. Numerical model

Three cases of cloud lines over the Great Australian Bight are chosen for a numerical simulation using MM5, version 3.6 (Dudhia 1993; Grell et al. 1995). A detailed description of the model is given by Grell et al. (1995). MM5 is a limited-area, nonhydrostatic, terrain-following sigma-coordinate model, which can be used to simulate mesoscale and regional-scale atmospheric circulation.

The model consists of 23 σ levels with higher resolution near the surface. The model levels below 4 km are at heights of approximately 80, 150, 250, 500, 800, 1150, 1600, 2100, 2600, 3200, and 3800 m. The numerical simulations are performed using three nested domains at different resolutions. The outermost domain has 160 × 160 grid points with a horizontal grid spacing of 9 km, the middle domain has 241 × 241 grid points with a horizontal grid spacing of 3 km, and the innermost domain has 466 × 466 grid points for the simulations in April 2005 and December 2007. For the March 2006 case the innermost domain has 481 × 481 grid points in order to capture a kink in the northern part of the convergence lines (see section 4a). The horizontal grid spacing of the innermost domain is 1 km for all three cases. The time step for the model integration was set to 27 s for the coarsest domain, 9 s for the middle domain, and 3 s for the innermost domain. The orientation of the three nested domains for the 11 March 2006 case study is shown in Fig. 1. For the two other case studies presented here, the positions of the second and third domain were adjusted slightly according to the position of the front in question. Terrain land use and topography are taken from the U.S. Geological Survey dataset included in MM5 using a 30′ resolution for the outermost domain, a 10′ resolution for the middle domain, and a 5′ resolution for the innermost domain.

The Grell scheme is used for the cumulus parameterization (Grell 1993) and the simple ice scheme by Dudhia is used as an explicit scheme for moisture (Dudhia 1989). The Medium-Range Forecast scheme is used for the boundary layer, and the cloud radiation scheme includes a representation of longwave and shortwave interactions with explicit cloud and clear air, and provides surface radiation fluxes. Initial and boundary conditions are specified from the European Centre for Medium Range Weather Forecasts (ECMWF) analysis data with a horizontal resolution of 0.25°.

4. Results

a. 11 March 2006

1) The synoptic situation

As morning glories are confined to the lowest few kilometers of the atmosphere, the large-scale environment conducive to their genesis can be described adequately by the mean sea level pressure analyses. Figure 2 shows the synoptic situation for the Australian region at 12-hourly intervals from 1800 UTC 10 March to 1800 UTC 11 March. A low pressure system is embedded between two broad anticyclones over the Indian Ocean and the Tasman Sea, both centered at about 40°S, which is similar for all cases presented herein. The center of the low lies south of 50°S. The low intensifies with the central pressure dropping from 984 hPa at 1800 UTC 10 March to 954 hPa 24 h later. The associated cold front at 1800 UTC 10 March extends northward over the southern coastline of Western Australia. From 0600 UTC 11 March, the cold front is analyzed south of the Australian continent.

2) Satellite imagery

The high-resolution visible satellite image at 1015 CST 11 March 2006 (Fig. 3) shows a series of at least five cloud lines extending from the lower edge of the image northward to the vicinity of the Australian coastline (beyond the upper edge of the image). Clouds associated with the approaching cold front are visible in the lower-left quadrant of the image. The series of cloud lines in Fig. 3 exhibits a prominent kink, highlighted by the arrow on the image. In the subsequent high-resolution image approximately 5 h later (not shown), only remnants of the cloud lines were discernible.

3) Numerical simulation

The simulation is initialized at 0430 CST 11 March and run for 24 h. The orientation of the three nested domains is shown in Fig. 1. The third model domain resolves a series of low-level convergence lines that develop and propagate to the northeast during the model run. These lines are visible in the divergence field calculated at an altitude of 250 m and presented in Fig. 4a. Such convergence lines have been shown previously to be indicators of nonlinear waves in the atmosphere (e.g., Thomsen and Smith 2006). The position and orientation of the convergence lines at 1030 CST (see Fig. 4a) agree with the cloud lines in the Terra image at about the same time (see Fig. 3).

The divergence field plotted for domain 2 in Fig. 4b shows a kink1 in the convergence lines comparable to that of the cloud lines of the satellite image (Fig. 3). The wind vectors shown in Fig. 4b represent the wind relative to the convergence lines whose translation speed in the direction normal to the lines is about 11 m s−1 in a direction toward the northeast. Along the convergence lines north of 34°S, the opposing wind is greater than that along the lines farther south. As a result, the northeastward propagation of the northern part of the convergence lines is slowed relative to the southern part, thus producing the kink in the convergence lines. It is noticeable also that because of the stronger opposing wind along the northern part of the lines, the values of convergence are larger than that farther to the south.

Figure 5 shows a vertical cross section of virtual potential temperature and the horizontal wind field relative to the disturbances along the diagonal from the lower-left to the upper-right corner of the innermost domain. The horizontal wind component represents the calculated wind component parallel to this diagonal. The x axis of each panel in Fig. 5 represents the distance in km from the lower-left corner of the domain. As the convergence lines are oriented approximately in a northwest–southeast direction, it is assumed here that they propagate approximately northeast, although one cannot say this with certainty as there is no point of reference on the lines that can be followed. This assumption is also used for the following two cases.

At 0930 CST 11 March (Fig. 5a) the isentropes exhibit a jump at x = 200 km with a vertical velocity over 0.2 m s−1 (not shown). This situation is typical of the genesis stage of an undular bore (Goler and Reeder 2004). Based on the abrupt change in wind speed, the leading edge of the cold front is located about 230 km to the southwest of the bore (not shown). This location of the front is confirmed by plotting the vertical component of vorticity near the surface (not shown). This plot resembles that of divergence (Figs. 4a,b), where enhanced negative vorticity marks the positions of both the convergence lines and the cold front about 200 km behind. However, in the following two cases a cold front could not be inferred from the vorticity field. At 1330 CST (Fig. 5b) five waves are visible, as determined by the undulations in the contours of virtual potential temperature, a close-up of which is presented in Fig. 6. The updraft is strongest at the leading edge of the waves with a velocity of 0.8 m s−1. The maximum vertical displacement due to the waves is about 700 m as determined from the displacement of the uppermost isentrope below the mixed layer (310-K isentrope). The wavelength is about 10 km. The waves mark an abrupt change in the wind speed of 10 m s−1 from ahead of the waves to behind them. The number of waves visible in the numerical simulation at the mature stage matches the number of waves observed in the satellite image, although the time of the mature stage does not correspond to that in the satellite image. By 1830 CST (Fig. 5c) the undular bore is at its decaying stage as its amplitude is lower than at 1330 CST. Within this time period, the depth of the stable layer ahead of the bore, which serves as a waveguide, also decreases.

Clarke (1986) discussed that a cold front can transform into a undular bore. Figure 5 suggests that this transformation may have occurred at the leading edge of the cold front. To confirm that this feature has borelike characteristics, simple bore theory is applied as in Clarke (1983, 1986). The quantity G in Eq. (4), representing the degree of stratification of the lower layer, is evaluated using the virtual potential temperature profile 20 km ahead of the bore at the genesis stage (0930 CST), given in Fig. 7a. For this and subsequent cases, the parameters of the disturbance will be based on the genesis stage. Figure 7a shows that cooling occurred following the passage of the waves. The assumption of an absence of strong curvature of the flow is valid within the stable layer where an average value for u is calculated as done in Clarke (1986). Above the stable layer the wind profile does exhibit curvature; however, as mentioned previously, the analysis here is concerned primarily with the thermodynamic properties of the stable layer in providing a suitable waveguide.

The upper boundary of the low-level stable layer is not obvious (Fig. 7a); however, its depth is estimated to be 1200 ± 100 m corresponding with a small kink at about θl(h) = 307.5 K. The potential temperature of the near-neutral layer is taken as θu = 311 ± 1 K. The virtual potential temperature at the ground is 296 ± 1 K. Approximating θl(z) as a linear function and using the values for the virtual potential temperature at the lower and upper boundary of the stable layer, Eq. (4) gives G = 19.0 ± 0.9 m s−1. Using the average value for u of −9.0 ± 1.0 m s−1 in the lower layer (see Fig. 7b), Eq. (3) gives c0 = 8.1 ± 1.3 m s−1.

To calculate the Froude number F, the normalized lifting δh/h is estimated from the change in elevation of the 308-K isentrope in Fig. 5a, which represents the lifting at the top of the stable layer h. With δh = 500 ± 100 m, a Froude number is calculated as F = 1.31 ± 0.06, which encompasses the Froude number of Fu = 1.26 given by Binnie and Orkney (1955) below which the excess energy can be radiated away by a smooth wave train increasing in length with time (Clarke 1983). Equation (1) gives the speed of the bore as cb = 13.3 ± 2.5 m s−1, which is consistent with that observed from Fig. 5 of about 12.8 m s−1.

Figures 8a,b show the surface pressure, virtual potential temperature, mixing ratio, and diagonal wind component at the genesis and mature stage corresponding with Figs. 5a,b. A pressure jump of 1.0 ± 0.1 hPa is associated with the bore and is in an environment where the pressure decreases from northeast to southwest. Using Eq. (8) with the values calculated earlier give a pressure jump of δp = 1.5 ± 0.5 hPa, which agrees with that modeled (Fig. 8a). The surface pressure remains elevated immediately behind the bore and decreases at the same rate to the southwest as ahead of the bore. This signature can also be seen in the surface wind trace. At the genesis stage (Fig. 8a), the surface traces of virtual potential temperature and mixing ratio do not indicate this disturbance. At the mature stage (Fig. 8b), all four traces show the waves. The temperature drop and the second wind change 200 km behind the waves highlight the leading edge of the advancing cold front.

As noted earlier, the position of the cold front is estimated to be where the wind speed abruptly changes some 200 km behind the undular bore (see, e.g., Fig. 8). The speed of the front from 0930 to 1330 CST is calculated as cf = 10.4 ± 0.7 m s−1. As cf > c0, the front moves at supercritical speed. Laboratory experiments by Wood and Simpson (1984) along with numerical simulations by Haase and Smith (1989) showed that for a gravity current entering a stable layer in a supercritical regime, a bore develops at the leading edge and moves at the same speed as the gravity current. Two or more waves may also form and thus the gravity current takes on the appearance of an undular bore. As discussed in Smith and Reeder (1988) and Clarke (1986), a cold front can behave locally as a gravity current (i.e., the wind speed u immediately behind the front being larger than the speed of the front). By the sequence described above, a cold front that resembles a gravity current and moving at supercritical speed into a stratified environment may transform into an undular bore at the leading edge. As can be seen in Fig. 5b, the cold front in this case does not have features of a gravity current as the relative flow (ucf) is negative at all levels. However, although the front did not resemble a gravity current, bore formation at the leading edge was possible.

The waveguide characteristics, based on the wind profiles shown in Fig. 7, can be investigated using linear wave theory akin to Menhofer et al. (1997a), albeit the waves considered here are intrinsically nonlinear. Figure 9 shows the vertical profile of μ2 20 km ahead of the waves at the genesis stage. Below 2 km, μ2 is mainly positive, consistent with a propagating wave. Above 2 km to an altitude of 4 km μ2 is negative. In accordance to the theory described above, this profile shows that the atmospheric environment was favorable for wave development at low levels. It should be highlighted here that, as the calculation of μ2 involves the second derivative with height of the ambient wind from the model data [Eq. (10)], the fine details shown in Fig. 9 may not be accurate. For two following cases examined, the basic structure of the vertical profile of μ2 is similar and will not be shown. A critical level, whereby the wind and the bore phase speed are identical, was not observed in any of the three cases examined.

b. 31 December 2007

1) The synoptic situation

The synoptic situation at 12-hourly intervals from 1200 UTC 30 December 2007 to 1200 UTC 31 December is presented in Fig. 10, and shows some similarities to the March 2006 case. Broad anticyclones in the Indian Ocean (centered along about 35°S) and in the Tasman Sea (centered at about 45°S) are prominent features. A low pressure system south of 55°S (off the chart) moves eastward during the 24 h, along with its associated cold front that extends northward to just south of Australia. A trough line extending from a continental heat low over West Australia to the col between the two anticyclones over the south Australian waters becomes migratory as the cold front passes south of the continent. The passage of the cold front is followed by the anticyclone from in the Indian Ocean forming a ridge over the Great Australian Bight.

2) Satellite imagery

Both high-resolution visible satellite images from 31 December, presented in Fig. 11, show a series of long cloud lines, with at least 25 visible. The first eight are quite smooth, with successive cloud lines appearing more ragged. Cloud bands typical for a cold front are absent. When compared with the MSLP chart at 0000 UTC 31 December (Fig. 10b), the cloud lines appear to coincide with the prefrontal trough.

3) Numerical simulation

The MM5 simulation is initialized at 1030 CST 30 December and run for 36 h. The divergence field at 1030 CST 31 December from domain 3 is presented in Fig. 12. Long low-level convergence lines are evident whose positions coincide with the cloud lines shown in Fig. 11. To the north and east of the convergence lines, the low-level wind has speeds greater than 10 m s−1, while far to the south and west of the lines, the wind is southerly, turning cyclonically to become northwesterlies some 100 km behind the lines. A comparison of the wind field with the synoptic situation (see Fig. 10b) reveals that the convergence lines lie in the col between the two broad anticyclones.

Vertical cross sections showing virtual potential temperature and the horizontal wind component in this cross section at 0330, 0630, and 1830 CST 31 December are presented in Fig. 13. A cold front at x = 135 km in Fig. 13a is visible as an abrupt jump in the isentropes, with a vertical velocity in excess of 0.8 m s−1 (not shown). Three hours later (Fig. 13b), the potential temperature contours display wavelike undulations. A close-up of the waves is shown in Fig. 14, where five waves are discernible, which is fewer than observed in the satellite image. The largest vertical velocity (>2.5 m s−1) is at the leading edge of the waves. The maximum vertical displacement due to the waves is about 700 m, and the wavelength is about 6 km. At low levels (below 0.5 km) the horizontal wind component ahead of the waves is toward the disturbance with speeds greater than 10 m s−1. By 1830 CST (Fig. 13c), the stable layer depth ahead of the waves along with the wave amplitude has decreased.

The virtual potential temperature and the environmental wind profile 20 km ahead of the waves, shown in Figs. 15a,b, will be used to calculate the critical velocity, as performed for the March 2006 case. The stably stratified layer has a well-defined upper boundary compared with the March 2006 case, and its depth is h = 800 ± 100 m. With θl(h) = 308 ± 1 K, θl(0) = 293 ± 1 K, and a value of 310 ± 1 K for the virtual potential temperature in the near-neutral layer, gives G = 15.5 ± 2.3 m s−1. An average value of −9.0 ± 1.0 m s−1 is determined for the environmental wind ahead of the waves, when calculating the critical velocity c0 using Eq. (3). Strictly, Eq. (3) applies only in the absence of strong curvature in the wind profile. This prerequisite fails (see Fig. 15b) and thus the calculated value for c0 = 5.0 ± 2.3 m s−1 should be regarded with some caution. However, as mentioned in the introduction, the simple bore theory applied herein is used to determine primarily the influence of the stratification on the waveguide.

The lifting δh evaluated at the top of the stable layer (see Fig. 13a) at 0330 CST for the genesis stage is estimated to be about 300 ± 100 m. Equation (2) gives a Froude number of 1.28 ± 0.09, which encompasses the value 1.26, below which, according to Binnie and Orkney (1955), a smooth wave train can be expected. Figure 16 shows the surface pressure, virtual potential temperature, mixing ratio, and diagonal wind component at the genesis and mature stages corresponding with Figs. 13a,b. In Fig. 13a an abrupt pressure jump of 1.0 ± 0.1 hPa marks the beginning of the disturbance and front as judged by the steady pressure rise behind the leading edge marking the progressively colder air. This pressure jump is accompanied by a temperature decrease and rapid increase in the wind speed in the direction of the disturbance. The calculated value for the pressure jump at 0330 CST [Eq. (8)] is 0.9 ± 0.4 hPa, which encompasses the value observed in the model. Figure 16b shows an abrupt pressure jump of 1.7 ± 0.1 hPa marking the leading edge of the waves, with fluctuations in surface pressure discernible. The other surface traces shown in Fig. 16 also show fluctuations with the passage of the waves leading to either elevated or lowered values behind the disturbance. From Figs. 13b and 16 it is clear that the nonlinear waves and the cold front coincide. The theoretical speed of the bore as calculated from Eq. (1) gives cb = 8.9 ± 3.5 m s−1, which encompasses the observed values of 7.4 m s−1 in the early stage of development (Fig. 13a) and 9.0 m s−1 later on (Fig. 13b).

Between 0330 and 0630 CST the surface front moved at a speed of cf = 7.1 m s−1. As cf > c0, the cold front moved at a supercritical speed into an environment conducive to undular bore formation (see Figs. 13 and 14). An answer to the question whether the front behaved as a gravity current, thereby transforming its leading edge into an undular bore, or whether it propagated by means of development as a result of cross-frontal circulations associated with frontal-scale baroclinic processes (Smith and Reeder 1988) cannot be adequately given. The wind vectors representing the relative wind speed ucf in Fig. 14 show that immediately behind the surface front the relative wind speed is close to zero. The error in calculating both the diagonal wind component u and the speed of the front, cf , is comparatively large, and thus it cannot be conclusively inferred that the front behaved as a gravity current.

c. 31 March–1 April 2005

1) The synoptic situation

As in the two previous cases, anticyclones over the Indian Ocean and the Tasman Sea are centered along a latitude of about 35°S (see Fig. 17). On the MSLP chart at 1200 UTC 31 March, a midlatitude low pressure system is centered south of 50°S. The midlatitude cold front extending northwestwards merges with a warm front associated with a weak low over southern West Australia. During the next 24 h the midlatitude low intensifies and moves southeastward while the warm front weakens and is no longer analyzed on the chart at 0000 UTC 1 April. Another feature that can be seen on the MSLP analyses is a northwest–southeast-oriented trough line through a second weak low pressure center over West Australia. The absence of an analyzed cold front over the Great Australian Bight at latitudes where the cloud lines were observed sets this case apart from the other two examined earlier.

2) Satellite imagery

At least 15 low-level cloud lines are discernible on the image from the Terra satellite on 1 April (see Fig. 18). These are partly covered by a broad upper-level cloud band. Both the cloud lines and the cloud band have a west-northwest–east-southeast orientation. The corresponding synoptic situation is shown in Fig. 17c at 0000 UTC 1 April. A trough line is oriented northwest–southeast over the Great Australian Bight and thus does not exactly coincide with the position of the cloud lines. Whether the cold front or trough produced the cloud lines is unclear. The lack of surface observations over the southern ocean makes it impossible to determine whether the feature on the MSLP chart is indeed a trough or actually a front.

3) Numerical simulation

The simulation is initialized at 0930 CST 31 March and run for 36 h. The divergence fields at a height of 250 m at 0030 and 0730 CST 1 April for domain 3 are shown in Fig. 19. Convergence lines are evident, which remain fixed in location although their orientation and strength changes during the 7-h period. A strong northerly airflow is present ahead and through the convergence lines, while in the lower-left quadrant of the domain, the wind is predominantly from the southeast.

The vertical cross section of virtual potential temperature and the horizontal wind field is shown in Fig. 20 at 2330 CST 31 March and 0330 and 0730 CST 1 April. The tilted isentropes indicate cold air in the left half of the domain. Over the 8 h, the cold air does not propagate forward owing to the opposing wind with speeds of over 10 m s−1. Figure 20a shows two waves at the leading edge of the cold air with vertical velocity of over 0.5 m s−1 (not shown). Four hours later (Fig. 20b) three waves are evident, a close-up of which is shown in Fig. 21. A vertical velocity in excess of 1.0 m s−1 occurs at the front of the leading wave. The maximum vertical displacement associated with the waves is about 600 m. The numerical simulation was not able to resolve the number of waves observed in the satellite image. At 0730 CST (Fig. 20c), the number of waves has increased, but their amplitude has decreased as compared with those at 0330 CST (Fig. 20b). The decrease in amplitude may be coupled with the increase in the stable layer depth from 0330 to 0730 CST (Fig. 22c), whereby the wave energy becomes distributed over a larger volume of fluid (Haase and Smith 1989).

Figure 22a shows the virtual potential temperature profile 20 km ahead and behind the waves at 2330 CST 31 March. Applying simple bore theory, the critical velocity c0 is calculated using the profile ahead of the waves (Fig. 22a). The stable layer depth is h = 800 ± 100 m, and the virtual potential temperatures at the ground and the top of the stratified layer are 293 ± 1 K and 308 ± 1 K, respectively. For the near-neutral layer above, a mean value of 310 ± 1 K is used. Using an average value of the environmental wind speed in the low-level stable layer of −13.0 ± 1 m s−1 gives G = 15.5 ± 0.3 m s−1, whereby the critical velocity is c0 = 1.0 ± 2.3 m s−1. As the front is almost stationary, it is not possible to classify the flow as being definitively sub- or supercritical. Furthermore, as the wind profile does exhibit curvature (Fig. 22b), the calculation of c0 from Eq. (3) may not be strictly valid.

According to the isentropes at 2330 CST 31 March in Fig. 20a the lifting δh at the leading wave is estimated to be 350 ± 100 m. Hence, the Froude number [Eq. (2)] is 1.34 ± 0.14, which is slightly greater than the values for the Froude number in the previous cases. Figure 23 shows the surface pressure, virtual potential temperature, mixing ratio, and diagonal wind component at the genesis and mature stages corresponding to Figs. 20a,b. A pressure jump of just over 1 hPa marks the leading edge of the waves, with fluctuations in pressure visible. About 100 km behind the waves, the pressure increases, which is indicative of the colder air. All four surface traces presented in Figs. 23a,b exhibit fluctuations coinciding with the passage of the waves. Using Eq. (8), the calculated pressure jump at 2330 CST 31 March gives a pressure jump of 1.3 ± 0.6 hPa, which encompasses the observed value of 0.8 ± 0.1 hPa (Fig. 23a).

5. Conclusions

Nonlinear waves associated with fronts in the Great Australian Bight have been examined. Provided that there is sufficient moisture at low levels and the amplitude of the waves are large enough, the nonlinear waves become visible as a series of long roll clouds resembling the morning glory of the Gulf of Carpentaria region.

A climatology of cloud lines ahead of fronts in the Great Australian Bight has been produced. Using high-resolution visible satellite images available twice a day from the Moderate Resolution Imaging Spectrometers (MODIS) on board NASA’s Aqua and Terra satellites, it was found that during the period 23 October until 29 February 2008 the cloud lines were more frequent in the summer months, with an average of two cloud lines observed. The preference for summer is hypothesized to be due to a stronger maritime stable layer produced as hot continental air is advected offshore, and to the lower cloud amounts associated with the cold fronts. On average, during autumn and spring, one cloud line per season could be identified, with none observed in winter. However, because of the small sample size, these results are not statistically significant. A similar study at a later stage when more satellite images are available might therefore be advisable to support the hypothesis presented here. As clouds are not always associated with these disturbances, the numbers of nonlinear wave occurrence associated with fronts presented herein should be regarded as a lower bound.

Three cloud line cases were chosen for numerical simulations using MM5. In each case the model was able to reproduce the observed waves, although the number of waves resolved, especially in the second and third cases, was fewer than observed in the satellite images. The divergence field at low levels revealed convergence lines that coincided with the cloud lines as identified on the satellite images. Vertical cross sections of virtual potential temperature and vertical velocity showed that in the cases of 11 March 2006 and 31 December 2007 a cold front propagated into a stratified environment leading to wave production at the leading edge of the advancing cold air mass. Modeled maximum upward velocities in the case of March 2006 were 0.8 m s−1, whereas in the simulation of the case in December 2007, the vertical velocity exceeded 2.5 m s−1. In the case in March 2006, the two-dimensional wind field parallel to the cross section showed that behind the surface front, the flow relative to the front was negative confirming the borelike character of the waves. The relative flow behind the cold front of 31 December 2007 was close to zero. As errors in the calculation of the relative flow behind the surface front are too large, it cannot be ascertained whether the surface front behaved like a gravity current and thereby generated the waves ahead of it.

Simple bore theory was applied to both cases of March 2006 and December 2007. The calculations revealed that both fronts moved at supercritical speed (i.e., the frontal speed was larger than the speed of the fastest mode of small-amplitude long waves, which in turn is dependent on the thermodynamic profile of the invaded medium). The theoretical values for the surface pressure jump at the leading waves matched the values from the simulations.

The case of 1 April 2005 was unlike those of March 2006 and December 2007. Long smooth low-level cloud lines were clearly discernible on the Terra satellite image, although the synoptic situation was unusual in that the cold front was stationary. The horizontal low-level divergence field revealed stationary convergence lines within the region ahead of the front. The vertical cross section of virtual potential temperature and vertical velocity showed that waves were produced at the leading edge of the stationary cold air mass with vertical velocity exceeding 1 m s−1. As the calculated value of 1.0 m s−1 for the critical velocity approximately matched the speed of the front, it was not possible to determine whether the front was moving at sub- or supercritical speeds. The pressure jump at the leading edge calculated using simple bore theory agreed with the modeled value.

The simple bore theory used here did not include the profile curvature in forming the waveguide, and for simplicity a uniform wind was used by averaging the observed wind within the stable layer. Despite this limitation, the calculations based on this theory produced phase speeds and pressure jumps for the bores, which matched those observed. To consider the effect of the wind profile on the waveguide characteristics, a separate analysis using the Scorer parameter showed that the environment for each case was conducive to wave propagation (plots only shown for the first case). The decay of the waves for March 2006 and December 2007 cases was due to a reduction in the depth of the stable layer due to the advection of continental air over the water. However, for the April 2005 case, the decay of the waves was due to a combination of the stable layer becoming colder and deeper, thereby reducing the wave amplitude, and due to the front not following the waves.

Future work would be to obtain high-time-resolution surface observations around the coast of South Australia to produce a better climatology. There are a number of coastal stations in South Australia, and the 30-min data that were available were inadequate to detect these disturbances. Further work would involve investigating the role of troughs in producing nonlinear waves to clarify the question of whether a front intruding into a stratified environment is in fact essential for nonlinear wave formation.

Acknowledgments

We would like to thank the Bureau of Meteorology, Melbourne, for providing the MSLP charts, and the MODIS Rapid Response Project at NASA/GSFC for the satellite images used in this paper. We are especially grateful to Roger Smith and Michael Reeder for their insightful comments.

REFERENCES

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Fig. 1.
Fig. 1.

Locations of the three nested domains.

Citation: Monthly Weather Review 138, 9; 10.1175/2010MWR3232.1

Fig. 2.
Fig. 2.

Synoptic situation for the Australian region at (a) 1800 UTC 10 Mar 2006, (b) 0600 UTC 11 Mar 2006, and (c) 1800 UTC 11 Mar 2006 (adapted from the Bureau of Meteorology MSLP analysis).

Citation: Monthly Weather Review 138, 9; 10.1175/2010MWR3232.1

Fig. 3.
Fig. 3.

MODIS Terra satellite image of the Great Australian Bight at 1015 CST 11 Mar 2006. The arrow highlights the kink in the cloud lines.

Citation: Monthly Weather Review 138, 9; 10.1175/2010MWR3232.1

Fig. 4.
Fig. 4.

Divergence (shaded, s−1) and horizontal wind vectors (scale 10 m s−1 below each panel) at σ = 0.97 (altitude = 250 m) at (a) 1030 CST in domain 3 (481 × 481 grid points, wind vectors plotted every 20 grid points) and (b) 1730 CST 11 Mar 2006 in domain 2 (241 × 241 grid points, wind vectors plotted every 15 grid points). Wind vectors represent the wind relative to the convergence lines.

Citation: Monthly Weather Review 138, 9; 10.1175/2010MWR3232.1

Fig. 5.
Fig. 5.

Vertical cross section of virtual potential temperature and horizontal wind relative to the disturbances (vectors, scale = 10 m s−1) at (a) 0930, (b) 1330, and (c) 1830 CST 11 Mar 2006. Wind vectors plotted every 20 grid points.

Citation: Monthly Weather Review 138, 9; 10.1175/2010MWR3232.1

Fig. 6.
Fig. 6.

A close-up of Fig. 5b showing the waves. Virtual potential temperature (thick lines), horizontal wind relative to the waves (vectors), and vertical velocity (positive values in solid lines and negative values in dotted lines) are plotted. Wind vectors are plotted at every second grid point.

Citation: Monthly Weather Review 138, 9; 10.1175/2010MWR3232.1

Fig. 7.
Fig. 7.

Vertical profiles of (a) virtual potential temperature and (b) horizontal wind component parallel to the plain of the cross section 20 km ahead (solid line) and behind (dashed line) the waves at 0930 CST 11 Mar 2006.

Citation: Monthly Weather Review 138, 9; 10.1175/2010MWR3232.1

Fig. 8.
Fig. 8.

Traces of surface pressure (hPa), virtual potential temperature (K), mixing ratio (g kg−1), and diagonal wind component (m s−1) at (a) 0930 and (b) 1330 CST 11 Mar 2006.

Citation: Monthly Weather Review 138, 9; 10.1175/2010MWR3232.1

Fig. 9.
Fig. 9.

Vertical profile of μ2 as defined in Eq. (10).

Citation: Monthly Weather Review 138, 9; 10.1175/2010MWR3232.1

Fig. 10.
Fig. 10.

Synoptic situation for the Australian region at (a) 1200 UTC 30 Dec 2007, (b) 0000 UTC 31 Dec 2007, and (c) 1200 UTC 31 Dec 2007 (adapted from the Bureau of Meteorology MSLP analysis).

Citation: Monthly Weather Review 138, 9; 10.1175/2010MWR3232.1

Fig. 11.
Fig. 11.

(a) MODIS Terra satellite image at 1015 CST and (b) MODIS Aqua satellite image at 1510 CST 31 Dec 2007.

Citation: Monthly Weather Review 138, 9; 10.1175/2010MWR3232.1

Fig. 12.
Fig. 12.

Divergence (shaded, s−1) and horizontal wind vectors (scale 10 m s−1) at σ = 0.97 (altitude = 250 m) at 1030 CST 31 Dec 2007 in domain 3 (466 × 466 grid points, wind vectors plotted every 20 grid points).

Citation: Monthly Weather Review 138, 9; 10.1175/2010MWR3232.1

Fig. 13.
Fig. 13.

Vertical cross section of virtual potential temperature and horizontal wind relative to the disturbances (vectors, scale = 10 m s−1) at (a) 0330, (b) 0630, and (c) 1830 CST 31 Dec 2007. Wind vectors plotted every 20 grid points.

Citation: Monthly Weather Review 138, 9; 10.1175/2010MWR3232.1

Fig. 14.
Fig. 14.

A close-up of Fig. 13b showing the waves. Virtual potential temperature (thick lines), horizontal wind relative to the disturbances (vectors), and vertical velocity (positive values in solid lines and negative values in dotted lines) are plotted. Wind vectors are plotted every second grid point. Note that the isolines for the vertical velocity are not equidistant, with the innermost isoline at the leading wave denoting 2.5 m s−1.

Citation: Monthly Weather Review 138, 9; 10.1175/2010MWR3232.1

Fig. 15.
Fig. 15.

Vertical profile of (a) virtual potential temperature and (b) horizontal wind component parallel to the plain of the cross section 20 km ahead (solid line) and behind (dashed line) the waves at 0330 CST 31 Dec 2007.

Citation: Monthly Weather Review 138, 9; 10.1175/2010MWR3232.1

Fig. 16.
Fig. 16.

Traces of surface pressure (hPa), virtual potential temperature (K), mixing ratio (g kg−1), and diagonal wind component (m s−1) at (a) 0330 and (b) 0630 CST 31 Dec 2007.

Citation: Monthly Weather Review 138, 9; 10.1175/2010MWR3232.1

Fig. 17.
Fig. 17.

Synoptic situation for the Australian region (a) 0000 UTC 31 Mar 2005, (b) 1200 UTC 31 Mar 2005, (c) 0000 UTC 1 Apr 2005, and (d) 1200 UTC 1 Apr 2005 (adapted from the Bureau of Meteorology MSLP analysis).

Citation: Monthly Weather Review 138, 9; 10.1175/2010MWR3232.1

Fig. 18.
Fig. 18.

MODIS Terra satellite image of the Great Australian Bight at 0915 CST 1 Apr 2005.

Citation: Monthly Weather Review 138, 9; 10.1175/2010MWR3232.1

Fig. 19.
Fig. 19.

Divergence (shaded, s−1) and horizontal wind vectors (scale 10 m s−1) at σ = 0.97 (altitude = 250 m) at (a) 0030 and (b) 0730 CST 1 Apr 2007 in domain 3 (466 × 466 grid points, wind vectors plotted every 20 grid points).

Citation: Monthly Weather Review 138, 9; 10.1175/2010MWR3232.1

Fig. 20.
Fig. 20.

Vertical cross section of virtual potential temperature (shaded), horizontal wind relative to the disturbances (vectors, scale = 10 m s−1), and vertical velocity (contour lines, nonequidistant interval) at (a) 2330 CST 31 Mar 2005, (b) 0330 CST 1 Apr 2005, and (c) 0730 CST 1 Apr 2005. Wind vectors are plotted every 15 grid points.

Citation: Monthly Weather Review 138, 9; 10.1175/2010MWR3232.1

Fig. 21.
Fig. 21.

A close-up of Fig. 20 showing the waves. Virtual potential temperature (K) (thick lines), horizontal wind relative to the waves (m s−1) (vectors), and vertical velocity (positive values in solid lines and negative values in dotted lines) are plotted. Wind vectors are plotted every second grid point. Note that the isolines for the vertical velocity are not equidistant, with the innermost isoline at the leading wave denoting 1.5 m s−1.

Citation: Monthly Weather Review 138, 9; 10.1175/2010MWR3232.1

Fig. 22.
Fig. 22.

Vertical profile of (a) virtual potential temperature (K) and (b) horizontal wind component (m s−1) parallel to the plain of the cross section 20 km ahead (solid line) and behind (dashed line) the waves at 2330 CST 31 Mar 2005. (c),(d) As in (a),(b), but at 0730 CST 1 Apr 2005.

Citation: Monthly Weather Review 138, 9; 10.1175/2010MWR3232.1

Fig. 23.
Fig. 23.

Traces of surface pressure (hPa), virtual potential temperature (K), mixing ratio (g kg−1), and diagonal wind component (m s−1) at (a) 2330 CST 31 Mar 2005 and (b) 0330 CST 1 Apr 2005.

Citation: Monthly Weather Review 138, 9; 10.1175/2010MWR3232.1

Table 1.

Seasonal distribution of nonlinear waves. The number of seasons during the time period 23 Oct 2004–29 Feb 2008 is given in parentheses.

Table 1.

1

The position of the kink lies just to the north of domain 3.

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