1. Introduction
The morning glory is a dramatic low-level roll cloud or series of roll clouds that occur in the early hours of the morning around the southern part of the Gulf of Carpentaria in northern Australia (see Fig. 1 for locations mentioned in text). Their passage overhead is usually accompanied by a sudden wind squall, with speeds comparable to the propagation speed of the morning glory (10–15 m s−1), and a pressure jump of the order of 1–2 hPa. Although morning glories form at all times of the year, they are far more frequent during the dry season months of September to mid-November, the average during this period being about one every 2 days. The roll clouds are typically 1 or 2 km in width, 1 km deep, and may extend in length for 100 km or more, with cloud bases often no more than 100 or 200 m high. However, the presence of cloud depends on the amount of moisture in the atmosphere; insufficient moisture for cloud formation leads to the morning glory propagating as a clear-air disturbance. In line with the common usage, such a clear-air disturbance will also be referred to as a morning glory.
As observed from the southern shores of the Gulf of Carpentaria, morning glories propagate from three different directions. The more commonly observed northeasterly morning glory is that which propagates from Cape York Peninsula toward the southwest. Such disturbances are commonly observed when the geostrophic flow has an easterly component over Cape York Peninsula. Due to the regularity with which it forms, the northeasterly morning glory has received the most attention in the literature. Southerly and southeasterly morning glories propagate from the south and southeast, respectively, and are observed less frequently than their northeasterly counterpart. Of all the morning glories recorded in the Burketown area, a little over half are northeasterly, one-third are southerly, while the remainder are southeasterly. (See Smith 1988, Christie 1992, and Reeder and Smith 1998 for reviews.) The northeasterly morning glory is the focus of the work presented here.
Surface micropressure records during the passage of morning glories show that their structure is not steady and varies considerably from case to case. There are times when the morning glory disturbances are clearly undular bores (see, e.g., Menhofer et al. 1997), while at other times they take the form of a localized family of discrete amplitude-ordered solitary waves (see, e.g., Christie 1992).
A number of mechanisms have been proposed for the generation of northeasterly morning glories. The earliest idea, due to Clarke et al. (1981), was that the east-coast sea breeze of the previous day excites a disturbance when it meets the low-level nocturnal jet or maritime inversion over the gulf and surrounding region. Another idea proposed was that the collision of the east- and west-coast sea breezes forms a bore that subsequently evolves into a series of amplitude-ordered solitary waves (e.g., Clarke 1984; Noonan and Smith 1986). Recently, Porter and Smyth (2002) have modeled the morning glory as a two-layer flow over topography and have suggested that the disturbance forms through the resonant interaction of the west-coast sea breeze and the topography. The central aim of the present study is to clarify the mechanism by which morning glories are generated, through a series of very high resolution numerical modeling experiments.
Previous numerical modeling studies of the morning glory can be divided into two groups. The first group of studies explicitly model the development and subsequent collision of the east- and west-coast sea breezes. Studies in this group include Clarke (1984), Noonan and Smith (1986, 1987), and Smith and Noonan (1998). Numerical experiments of this kind have produced broad-scale propagating convergence lines rather than realistic morning glory wave disturbances as the models employed have been hydrostatic and have had relatively coarse resolution (∼10 km). Nonetheless, these studies have provided great insight into the large-scale processes affecting the the formation of the morning glory. The present study also models the development of two opposing sea breezes, but at much higher resolution than previous studies, and examines the generation of realistic morning glory disturbances.
The second group treats the east-coast sea breeze as an idealized gravity current and models the disturbances that develop as the gravity current encounters an imposed stable layer. Studies of this type include those by Crook and Miller (1985), Crook (1986, 1988), Haase and Smith (1991), and Skyllingstad (1991). However, when there is an environmental flow present, there are important differences between idealized gravity currents produced by an imposed source of cold air and sea breezes produced by differential heating between the land and sea. For example, when a gravity current, produced by a cold pool stationary relative to the ground, is opposed by a uniform environmental flow, the depth of the gravity current increases (e.g., Liu and Moncrieff 1996). Conversely, sea breezes are shallow when an opposing environmental flow is imposed (e.g., Goler 2004 and numerical experiments described herein).
Both Clarke (1984) and Noonan and Smith (1986) conducted experiments that included the orography of Cape York Peninsula and compared them to the case of a flat peninsula. Noonan and Smith found that with orography included, the sea breezes meet earlier and farther inland from the west coast. In contrast, Clarke did not find such a change when orography was included. This study examines the sea breeze changes when orography is included and seeks to determine whether or not this affects the formation of the morning glory.
The paper is structured as follows. Section 2 describes the numerical model, and the boundary and initial conditions. Section 3 presents the results of the numerical experiments and examines the conditions under which the morning glory develops. Section 4 considers the effect of orography on the morning glory. Finally, some conclusions are drawn in section 5.
2. The model
The numerical model used in the present study was originally described in detail by Clark (1977). The model is nonhydrostatic, anelastic, and the finite difference approximations are second order in both space and time. The model includes a parameterization of subgrid-scale mixing (Lilly 1962; Smagorinsky 1963), but in its current configuration neglects, for simplicity, moist processes and the Coriolis effect. An idealized representation of orography is used in one model experiment.
To help focus on the fundamental dynamics of the morning glory, all the model calculations presented here are two-dimensional. In these calculations the horizontal grid spacing is 200 m, and there are 60 unevenly spaced levels in the vertical, with the lowest level at 2 m and the highest level at 15 km. Figure 2 shows the variation of the vertical grid spacing Δz with height z. The uppermost 4 km (10 levels) of the domain incorporates a Rayleigh friction absorber. For all but one of the experiments, the model domain is 640 km wide, with a strip of land 440 km wide located between two 100-km-wide bodies of water. The other experiment is 400 km wide with a 200-km-wide land mass. The aerodynamic roughness length of the land is specified as z0 = 0.1 m. Using values of z0 an order of magnitude greater or smaller does not significantly change the results of the experiments. The temperature of both bodies of water on either side of the peninsula is held constant at 300 K.
The model is initialized at sunrise using a November mean 0900 local standard time (LST) sounding taken from Willis Island (see Fig. 3), which is located approximately 450 km east of Cape York Peninsula (see Fig. 1). A uniform easterly flow is specified, which is 5 m s−1 in most cases. The land is heated during the day according to a cosine profile with a maximum surface heat flux of 550 W m−2 at noon. During the night, the surface cools at a constant rate of 40 W m−2. These values were based on the measurements of the surface energy budget over Cape York Peninsula by Tapper (1988).
3. Generation of the morning glory
a. Control experiment
As the land is heated, sea breeze circulations develop on the eastern and western sides of the peninsula during the morning and early afternoon. The leading edges of these sea breezes tend to be poorly defined as the convective eddies mix the cooler air advected onshore by the sea breeze with warmer air over the land. As the convection weakens in the late afternoon, the sea breezes sharpen and advance farther inland. The dynamics of sea breeze frontogenesis has been investigated recently by Goler (2004).
Figure 4 is a plot of potential temperature showing the two sea breezes at 2100 LST. Darker shading represents cooler potential temperatures. The sea breeze on the east coast is nearly 3 times deeper than the west-coast sea breeze because the easterly advects a deep layer of cool maritime air onshore. This cooler air within the sea breeze accelerates toward the leading edge after sunset, producing a deep stably stratified layer of air over the eastern side of the peninsula. Conversely, on the western side of the peninsula, cool maritime air is advected onshore only in the shallow lower branch of the sea breeze circulation. Moreover, the horizontal and vertical temperature gradients associated with the east-coast sea breeze are much smaller than the west-coast sea breeze. In fact, the surface air within 50 km of the leading edge of the east-coast sea breeze is warmer than the surface air anywhere in the west-coast sea breeze.
The asymmetry between the two sea breezes can be explained by considering the sea breezes without an environmental flow. In this case, the sea breezes will be symmetric, both with a surface onshore flow component and an upper offshore flow component. When an easterly environmental flow is added, the west-coast sea breeze will have a reduced onshore flow and a larger component of offshore flow. As a result, the west-coast sea breeze will not propagate as far inland. For the east-coast sea breeze, the onshore flow component will be increased and the upper offshore flow component reduced. This means that the east-coast sea breeze will propagate farther inland. Since the sea surface temperatures in the model are identical on both sides of the peninsula, the temperature difference of the air between the warmest part of the peninsula and the coast will be the same. Consequently, the horizontal temperature gradient of the west-coast sea breeze will be greater than that of the east-coast sea breeze.
Figure 4 shows large spatial variability of potential temperature in the upper portions of each sea breeze due to the remnant convective eddies generated during the day. These fluctuations are smaller in the lower part of each sea breeze as the stability of the cooler air near the surface suppresses the vertical motions, and also because of the effect of the lower boundary condition.
Figure 5 shows the potential temperature (shaded), and the relative velocity at half-hour intervals from 2200 to 0000 LST. In Figs. 5a–5c, the velocity is calculated in a frame of reference moving with the east-coast sea breeze, whereas in Figs. 5d and 5e, the velocity is calculated relative to the morning glory. These plots follow the east-coast sea breeze as it propagates to the west and encounters the west-coast sea breeze.
Figure 5a shows the east-coast sea breeze at 2200 LST, prior to meeting the west-coast sea breeze at 2210 LST at x = 214 km. Figures 5b and 5c for 2230 and 2300 LST, respectively, show the east-coast sea breeze over the cooler west-coast sea breeze. The east-coast sea breeze rides over the top of the west-coast sea breeze as the air within the leading 50 km of the east-coast sea breeze is warmer than the west-coast sea breeze. Figure 5 and video images of model output show that the two air masses do not collide violently. Instead, it appears that the east-coast sea breeze is forced to rise over the top of the west-coast sea breeze as its leading edge is more buoyant.
As the east-coast sea breeze overrides the west-coast sea breeze, eddies generated behind the leading edge of the east-coast sea breeze produce a series of waves on the west-coast sea breeze. These can be seen in Fig. 5c between x = 183 km and x = 195 km. The wave that forms the eventual morning glory begins to take shape at around 2255 LST and is located at x = 183.5 km at 2300 LST in Fig. 5c. At this time this wave is propagating to the west at 9.2 m s−1 while the speed of the east-coast sea breeze1 is 10.8 m s−1. The waves to the east of this leading crest propagate at speeds of around 8.3 m s−1.
The leading wave continues to grow reaching an amplitude of 0.8 km by 2330 LST, as shown in Fig. 5d. During this time its speed increases to 10.8 m s−1, and hence the wave is stationary with respect to the east-coast sea breeze. By 0000 LST, it is the only wave of significant amplitude, as shown in Fig. 5e. This wave exhibits a recirculation zone that is centered at x = 142.5 km, z = 0.6 km.
Figure 6a shows the disturbance at 0100 LST just after it has crossed the west coast with a speed of 12.1 m s−1. The disturbance has a prominent leading crest and a second crest embedded in the cooler air associated with the east-coast sea breeze. Figure 6b shows the surface pressure trace. There is a clear pressure jump of 0.9 hPa associated with the leading wave, and a local fall in the pressure at around x = 98.5 km, a feature that indicates a closed circulation in large amplitude waves (Brown and Christie 1994). The ratio of wave amplitude to stable layer depth is a/h ≈ 4.7.
Figure 6a shows that this closed circulation contains air that is cooler than air at the surface in its vicinity; the stable layer over the water being slightly warmer due to the absence of nocturnal cooling. This is an unstable situation in the presence of no flow. Examining plots at early times when the wave was developing (e.g., see Fig. 5e) shows that the temperature of the air in the recirculating region was the same as the air within the west-coast sea breeze. This indicates that the wave has transported this cooler air from over the land. As the morning glory propagates farther westward over the water, the air within it warms due to the warmer stable layer. Consequently, the surface pressure jump decreases to 0.7 hPa, although the morning glory still retains its structure until it reaches the edge of the model domain at 0330 LST.
b. No nocturnal surface cooling
As discussed above, the morning glory propagates on the stable layer created by the west-coast sea breeze. The following two experiments examine how the generation is affected by changes to this stable layer. This is done by repeating the control experiment without nocturnal surface radiative cooling in this section, and doubling the nocturnal surface cooling in the following section. In both cases, the change in pressure across the leading edge of the east-coast sea breeze, before it meets the west-coast sea breeze, is identical to that in the control experiment at that same time. This means that the major difference between the experiments is the stability of the west-coast sea breeze.
Figure 7 shows the numerical solution at 0100 LST, which is 170 min after the two sea breezes meet. Relatively small amplitude disturbances are generated (e.g., at x = 117, 120, 125 km). However, the key point to note is that the waves do not amplify, and this numerical experiment does not culminate in a morning glory even though the west-coast sea breeze provides a layer of cold air on which waves propagate. These waves propagate to the west at 5.8 m s−1 (compared with 8.3 m s−1 in the control experiment), whereas the east-coast sea breeze propagates at 9.2 m s−1.
c. Double nocturnal cooling
In this experiment the morning glory develops in a similar way to the control experiment. The waves generated as the east-coast sea breeze overrides the west-coast sea breeze propagate westward at 9.2 m s−1, while the east-coast sea breeze moves at 10.4 m s−1. Figure 8 shows the morning glory at 0100 LST with four prominent wave crests. These waves propagate at a speed of 13.0 m s−1.
d. Increased environmental flow
The results from the previous two experiments suggest that the growth of the morning glory requires the waves generated by the east-coast sea breeze to propagate at a speed similar to the east-coast sea breeze itself. We further examine the relationship between the speed of the sea breeze and the speed of the waves it forces by rerunning the control experiment with an easterly flow of 10.0 m s−1. Increasing the environmental flow increases the depth of the east-coast sea breeze by increasing the onshore advection of cold air. The greater depth increases the speed of the sea breeze relative to the environmental flow. Conversely, an increased environmental flow decreases the depth and speed of the west-coast sea breeze. The decreased depth also decreases the speed of the waves that propagate on the stable layer. Figure 9 shows the east- and west-coast sea breezes at 2000 LST.
The sea breezes meet at 2050 LST, 20 km inland from the west coast. Waves develop as the east-coast sea breeze overrides the west-coast sea breeze. These waves propagate westward into the maritime boundary layer over the water, the static stability of which is smaller than the west-coast sea breeze over land. Consequently, these waves decelerate as they enter the maritime boundary layer. Waves produced on the west-coast sea breeze propagate at around 7 m s−1, while on the maritime boundary layer, the waves have speeds about 5 m s−1. These speeds are small compared that of the east-coast sea breeze, which is 15.3 m s−1. The waves that are generated are very short lived, lasting around 20 min, and none grow in amplitude to form a morning glory.
e. Reduced environmental flow
In the previous numerical experiment and the experiment without nocturnal surface cooling, the east-coast sea breeze traveled considerably faster than the waves generated on the west-coast sea breeze as it undercut its east-coast counterpart. Neither numerical experiment produced a morning glory. The next numerical experiment considers the case of the control experiment rerun with a reduced easterly flow of 2.5 m s−1.
Figure 10 shows the sea breezes over the peninsula at 2100 LST. The leading edges of the two sea breezes are east of their respective positions in the control run (Fig. 4). The sea breezes meet at 2208 LST, which is comparable to the control run despite the initial meeting point being a farther 50 km inland from the west coast. The initial wave disturbance develops within the first 15 min of the east-coast sea breeze meeting the west-coast sea breeze, which compares with 30 min for the control run. The east-coast sea breeze is colder in this experiment than in the control experiment. This difference between the two experiments is due to the leading edge of the east-coast sea breeze being relatively closer to the source of cold air over the water. As a result, the cooler east-coast sea breeze is less buoyant and so a greater “collision” occurs with the west-coast sea breeze, generating a larger initial disturbance.
A morning glory develops in the same way as in the control experiment with waves after the interaction growing in amplitude as they move with the same speed of the east-coast sea breeze. The waves initially propagate westward at 8.6 m s−1, while the east-coast sea breeze moves westward at 10.0 m s−1. These values are nearly identical to those in the control experiment, even though the environmental flow has been reduced to 2.5 m s−1. The effect of this reduction in environmental flow is observed in the east-coast sea breeze at sunset where it has a speed of 7.8 m s−1, which compares to 10.0 m s−1 for the control experiment for the same time. After sunset as the sea breeze advances inland, cooler air within the sea breeze accelerates toward the leading edge. This increases the horizontal temperature gradient across the front and results in an acceleration of the sea breeze. Such frontogenesis has been observed for gravity currents in laboratory experiments by Simpson and Linden (1989), and investigated numerically by Goler (2004).
The factor controlling the speed of the sea breeze after sunset is the rate of surface heating during the day because this affects the temperature difference between the air masses over the land and the water. Rerunning the control experiment with the daytime surface heating reduced by half to a peak of 275 W m−2 produces an east-coast sea breeze that propagates westward at a speed of 8.3 m s−1 at sunset. The speed of the east-coast sea breeze increases to 9.2 m s−1 by the time it meets the west-coast sea breeze at 0030 LST. A morning glory is produced with a maximum of three waves.
Figure 11 shows the morning glory at 0100 LST that results with an environmental easterly flow of 2.5 m s−1. There are three crests present compared with two in the control experiment for the same time.
The next numerical experiment discussed is one in which there is no environmental flow. Figure 12a shows the isentropes and velocity vectors in the frame of reference fixed to the ground from the model run at 2210 LST. The two sea breezes that develop have elevated heads, each of which is about 1 km deep. They are a little asymmetric as the width of the peninsula is 440 km and the diurnal cycle on the eastern is advanced of that on the western side. Seven minutes later, the two sea breezes collide, forcing cold air to rise up to 2 km (Fig. 12b). The collision generates an eastward- and a westward-propagating solitary wave with amplitudes of about 1200 m. A bore, the leading edge of which subsequently separates into a series of solitary waves, follows the initial disturbance. The generation of these waves appears to be similar to waves generated from finite amplitude disturbances discussed in Christie (1989). The westward-propagating solitary wave at 0000 LST is shown in Fig. 12c, which is around 1.75 h after the collision. At this time the initial solitary wave is located at x = 282 km, and solitary waves have formed at the leading edge of the bore, located at x = 291 km. This separation continues, and some 4 h after the sea breeze collision there are around 11 westward- (and eastward-) propagating wave crests. The amplitude of the waves is around one-third of those in the control run.
The key difference between this numerical experiment, in which there is no environmental flow, and the control run is that the east- and west-coast sea breezes collide violently. A large-amplitude disturbance is generated quickly as cold air is thrust upward, and this disturbance propagates away as a solitary wave followed by a bore. By contrast, in the control experiment the sea breezes do not collide violently, as the east-coast sea breeze is much more buoyant than its west-coast cousin, and the waves grow to large amplitude more slowly in the hour after the sea breezes meet.
f. Northern Cape York Peninsula
Morning glories are not observed over the northern, narrower part of Cape York Peninsula. The reason for this is examined now through a numerical experiment with a land mass of width 200 km representing the northern peninsula at a latitude through Weipa (see Fig. 1). All other model parameters used in the control experiment are kept the same.
The two sea breezes meet at 1740 LST, by which time the west-coast sea breeze has penetrated 40 km inland. Figure 13 shows the two sea breezes at 1700 LST. The meeting occurs prior to nocturnal cooling taking effect, and so the stable layer created by the west-coast sea breeze is similar to that produced in the experiment without nocturnal cooling. As the east-coast sea breeze overrides the west-coast sea breeze, waves are produced, but remain small amplitude. These waves propagate westward at a speed of 5.0 m s−1 compared to the speed of the east-coast sea breeze of 8.8 m s−1. No morning glory is produced.
The failure to generate a morning glory may be because the stable layer is unable to support large-amplitude waves. Alternatively, it could be due to the east-coast sea breeze being too weak. In this case the pressure difference across the leading edge of the east-coast sea breeze is 0.25 hPa, which compares with 0.5 hPa for the control experiment. To investigate the effect of the stable layer, the thin peninsula experiment is rerun with enhanced cooling over the water to increase the stability of the maritime inversion and resemble that of the west-coast sea breeze in the control experiment. In this case it is found that the waves do grow in amplitude, reaching a peak of 1.0 km. This wave amplitude is smaller than the control experiment as the pressure difference across the leading edge of the east-coast sea breeze is smaller than in the control experiment.
g. Morning glory development
In each of the experiments discussed above, which are initialized with an easterly flow, the east-coast sea breeze is deeper and warmer than the west-coast sea breeze. As the cooler, shallower west-coast air is advected onshore and undercuts the east-coast sea breeze, waves are generated that propagate on the stable layer behind the west-coast sea breeze front. These waves grow in amplitude to form the morning glory whenever these waves have initial speeds similar to the speed of the east-coast sea breeze. The results from each experiment are summarized in Table 1. This table lists c the speed of the waves created immediately after the east-coast sea breeze rides over the west-coast sea breeze, and ce the speed of the east-coast sea breeze. The table also indicates whether or not a morning glory develops, and if so, how many waves are present at 0100 LST. The numerical experiments summarized in Table 1 show that a morning glory forms when the speed of the waves and the east-coast sea breeze is sufficiently close (within ≈2.5 m s−1), suggesting that the wave amplifies through the resonant interaction between the waves and the east-coast sea breeze.
Among other things, Table 1 lists the Froude number Fr = c/ce for each case. A morning glory develops in those model calculations considered when Fr ≥ 0.77, which indicates that the speeds of the waves and the east-coast sea breeze must be similar. Conversely, no morning glory forms in those experiments in which the Froude number does not exceed 0.63. The Froude number may be less than one and the wave still amplify because the speed of the wave increases with increasing amplitude, and as the wave grows, its speed matches that of the east-coast sea breeze more closely. Haase and Smith (1989) found that for gravity currents propagating into a stable layer, the gravity current head becomes detached from the feeder flow and forms a solitary-type wave2 when Fr ≳ 0.7.
The Froude number in the numerical experiment without an environmental flow is one since the wave and the elevated cold pool, produced from the collision, are generated at the same time and travel outward at the same rate. Nonetheless, in this case, the large-amplitude waves are not generated by a resonant interaction, but instead are generated through the collision of the two sea breezes.
Table 1 also lists the number of waves produced at 0100 LST for each experiment that developed a morning glory. It varies from two in the control experiment to five in the double nocturnal cooling experiment. Rerunning the control experiment with an extreme surface cooling rate 3 times normal (120 W m−2) gives Fr = 0.94, and produces a morning glory with seven waves at 0100 LST. Thus, as the stability of the west-coast sea breeze increases, the number of waves produced also increases. Haase and Smith (1989) have shown that for gravity currents propagating into stable layers, the number of waves increases with increasing stability and as the depth of the stable layer increases. In the experiment initialized with a 2.5 m s−1 easterly environmental flow, three waves were produced. This increase in number can be explained in part by the increased stability of the west-coast sea breeze and in part by the increased strength of the east-coast sea breeze, which has a pressure 0.1 hPa greater than for the control experiment at a comparable time. Whitham (1974) has shown that the number of waves produced from an initial disturbance increases with increasing amplitude of the disturbance.
Within the framework of the numerical model there are two mechanisms that increase the speed of wave propagation on the west-coast sea breeze, thereby bringing the waves and the east-coast sea breeze closer to resonance. First, increasing the stability of the west-coast sea breeze increases the speed of the waves that propagate on it. Second, increasing the amplitude of the east-coast sea breeze increases the amplitude of the initial waves generated, which in turn produces faster propagating waves. The closer the system is to resonance, the faster the waves will amplify. As the amplitude and the phase speed increase, a morning glory wave develops and propagates ahead of the east-coast sea breeze. The east-coast sea breeze then forces the next wave in the sequence, which in turn amplifies and propagates ahead of the forcing. Once the waves have propagated ahead of the east-coast sea breeze, they can no longer grow because the resonance interaction does not occur.
Crook (1988) has shown that a neutral layer above the stable layer, or a jet in the stable layer that opposes the wave motion, can result in small values of l2. Figure 14a shows values of l2 shaded for the control experiment at 2300 LST (the 303-K contour is plotted here for reference). Black shading denotes l2 < 0, and white shading represents l2 > 4 × 10−5 m−2, or horizontal wavelengths less than 1 km, which is a typical width of the waves shown in Fig. 5c. The phase speed of the waves that propagate on the stable layer produced by the west-coast sea breeze is c = −8.3 m s−1. There exists a broad but disjoint layer in which the Scorer parameter is negative just above the stable layer within the east-coast sea breeze. Ahead of the east-coast sea breeze, a thin layer in which the Scorer parameter is negative exists at a height of around 1 km. Although this layer may not influence the initial wave growth, such a layer is present at later times (not shown) when the morning glory has propagated ahead of the east-coast sea breeze. Throughout most of the region plotted in Fig. 14a, small-amplitude disturbances with horizontal wavelengths larger than 1 km are prevented from propagating vertically. There are only small regions in which wave energy can propagate upward (the white shaded areas). There is some evidence in the model experiments of upward-propagating waves with amplitudes of around 100 m, above the morning glory, on and above the inversion layer centered at a height of 2.8 km. For example, such waves are evident in Fig. 15, which is similar to Fig. 6, but instead shows potential temperature contoured without shading in a region extending to a height of 6 km. There are crests at x = 102 km and x = 107 km, both at a height of 2.8 km. Above this layer the waves tilt westward with height, indicating vertical wave propagation.
In all experiments, including those that do not produce a morning glory, the location of the regions in which l2 < 0, and Ri < 0.25, and the location of the critical level are very similar to Fig. 14 (the control experiment). Consequently, the existence of wave trapping regions in the atmosphere is not a sufficient condition for the development of morning glory disturbances. The most important factor is the stability of the west-coast sea breeze and its capacity to support waves with sufficiently high phase speeds.
4. The role of orography in generating the morning glory
The calculations discussed so far have taken the lower boundary to be flat even though a shallow mountain range with peaks of about 500 m run along the eastern side of Cape York Peninsula. We now investigate the role played by orography in generating the morning glory.
Clarke (1984) and Noonan and Smith (1986) included the orography of Cape York Peninsula in their modeling experiments. Clarke found that orography had little effect on both the sea breezes and the resulting bore, whereas Noonan and Smith found that the east-coast sea breeze was advanced by approximately half an hour when orography was included in their calculation. The numerical experiments conducted by Clarke and Noonan and Smith did not explicitly produce morning glory waves as they employed the hydrostatic approximation and used relatively coarse horizontal resolutions. For these reasons the effect of orography on the morning glory is not wholly clear.
a. Control run with orography
The idealized orographic profile over the peninsula used in the calculations reported here has a peak height of 500 m, 40 km inland from the east coast, and is plotted in Fig. 16. This figure also shows the two sea breezes over the peninsula which meet at 2100 LST. Compared to the control experiment, the east-coast sea breeze is 25 km farther inland, and the west-coast sea breeze is 35 km farther inland. They meet 23 km farther inland from the west coast, and 70 min earlier than in the control experiment. This difference in position is due to a greater acceleration of the sea breezes after sunset. The east-coast sea breeze has an average speed of −13.3 m s−1, which compares to −10.3 m s−1 in the control experiment. The west-coast sea breeze has an average speed of 6.9 m s−1 compared with 4.0 m s−1 in the control experiment. The east-coast sea breeze travels more quickly as the cold air flows down the mountain slope. The west-coast sea breeze also propagates more quickly as the temperature difference (0.8 K) between the sea breeze and the mixed layer is larger. The calculations with topography performed by Noonan and Smith (1986) have shown similar accelerations of the sea breezes.
The morning glory evolves in the same way as described in control experiment. Since the sea breezes meet earlier, the morning glory develops earlier. Figure 17 shows the morning glory at 0100 LST. It looks very similar to that produced in the control experiment presented in Fig. 6, suggesting that orography does not change the mechanism through which the morning glory is generated. On the basis of these numerical experiments it seems unlikely that the morning glory forms through the resonant interaction of the west-coast sea breeze and orography as suggested by Porter and Smyth (2002).
5. Conclusions
The high-resolution numerical experiments reported here have, for the first time, explicitly modeled the generation of the morning glory through the interaction of two sea breezes. The numerical calculations showed a marked asymmetry between the two sea breezes in an easterly flow. The east-coast (upstream) sea breeze was significantly deeper than the west-coast (downstream) sea breeze, which is opposite to that in idealized gravity current experiments (see Goler 2004). The leading 50 km of the east-coast sea breeze was warmer than the west-coast sea breeze as it was farther from the water, the source of cold air, and was highly modified by surface heating. This meant that the west-coast sea breeze undercut the east-coast sea breeze. As the east-coast sea breeze propagated over the west-coast sea breeze, waves were generated on the stable layer created by the west-coast sea breeze.
These waves amplified when their phase speed was close to the speed of the east-coast sea breeze (i.e., when Fr ≳ 0.7). In the control experiment, these waves grew in amplitude from approximately 200 m to 1.5 km over the course of about an hour to form the morning glory. The waves did not amplify when their phase speed was significantly less than the speed of the east-coast sea breeze (i.e., when Fr ≲ 0.7). This mismatch in the speeds occurred when the easterly flow was increased and, consequently, the east-coast sea breeze moved too fast, or when the static stability of the west-coast sea breeze was sufficiently small and hence the phase speed of the waves that propagated on it too slow. This latter point was shown to be the reason why the morning glory is not observed over the northern part of the peninsula; the narrower peninsula means that the sea breezes meet around sunset when the stability of the west-coast sea breeze has not been increased by nocturnal surface cooling. When the stability of the west-coast sea breeze was increased artificially, the waves grew in amplitude generating a morning glory. However, the waves were not as large in amplitude as in the control experiment because the leading edge of the east-coast sea breeze was more diffuse since the sea breezes met earlier.
As the waves on the surface of the stable layer formed by the west-coast sea breeze amplified only when their phase speed approximately matched the speed of the east-coast sea breeze, we have described the process as a resonant interaction between the wave and the sea breeze. The Froude number Fr may be less than unity (i.e., here Fr ≳ 0.7), and the waves still grow because their phase speed increases with increasing amplitude. As the waves amplified and accelerated, their phase speed more closely matched that of the east-coast sea breeze.
The control experiment produced a morning glory with two prominent waves at 0100 LST, while the experiment with double the surface cooling rate, which increased the stability of the west-coast sea breeze, produced a morning glory with five waves. This showed that the stability of the west-coast sea breeze affects the number of waves produced. It was shown also that the number of waves in the morning glory increased as Fr → 1. Satellite imagery has shown morning glories with as many as 20 cloud lines at sunrise (Reeder et al. 1995). In all cases investigated here, the waves stopped developing once they entered the maritime stable layer. In these experiments, surface fluxes over the water have been neglected, and so the maritime stable layer was created solely by the advection of warmer land-based air over the water. Presumably, the omission of these surface fluxes led to a weaker maritime inversion, which slowed the propagation speed of the waves.
In a numerical experiment in which there was no environmental flow, the east- and west-coast sea breezes were, for the most part, symmetrical. For this reason neither sea breeze was buoyant relative to the other, and consequently they collided forcefully. Eastward- and westward-propagating solitary waves were generated quickly from the collision. Eastward- and westward-propagating bores were created also, the leading edges of which subsequently separated into a series of solitary waves. In this case, resonance did not appear to play a role in the generation of the morning glory.
The inclusion of an idealized orographic profile representative of Cape York Peninsula made little difference to the generation of the morning glory. It did, however, result in the sea breezes meeting over an hour earlier than without orography, in agreement with Noonan and Smith (1986).
Acknowledgments
We are very grateful to Terry Clark (National Center for Atmospheric Research) for providing the model code. We would also like to thank Simon Clarke (Monash University) and Roger Smith (University of Munich) for their insightful comments. Figure 1 was produced with Online Map Creation (see online at http://www.aquarius.geomar.de/omc/omc_intro.html).
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Map of northern Australia showing Cape York Peninsula and the Gulf of Carpentaria where the morning glories are observed. The black lines near Burketown show the orientation of the northeasterly morning glory, which propagates to the southwest
Citation: Journal of the Atmospheric Sciences 61, 12; 10.1175/1520-0469(2004)061<1360:TGOTMG>2.0.CO;2
Variation of vertical grid spacing Δz with height z. The lowest model level is at z = 2 m
Citation: Journal of the Atmospheric Sciences 61, 12; 10.1175/1520-0469(2004)061<1360:TGOTMG>2.0.CO;2
Vertical profile of potential temperature for the Nov mean 0900 LST aerological sounding from Willis Island, which is located to the east of Cape York Peninsula
Citation: Journal of the Atmospheric Sciences 61, 12; 10.1175/1520-0469(2004)061<1360:TGOTMG>2.0.CO;2
Control experiment. Potential temperature, shaded in 1-K increments, showing the two sea breezes at 2100 LST, with a 40-km gap between the plots. The peninsula is located from x = 100 km to x = 540 km. The model is initialized with a 5 m s−1 easterly environmental flow
Citation: Journal of the Atmospheric Sciences 61, 12; 10.1175/1520-0469(2004)061<1360:TGOTMG>2.0.CO;2
Control experiment. (a)–(c) The east-coast sea breeze meeting the west-coast sea breeze. The velocity vectors are plotted relative to the east-coast sea breeze. For clarity they are only shown at every second horizontal grid point, and at every second vertical grid point below a height of 200 m. (d), (e) The velocity vectors are plotted relative to the speed of the wave crest
Citation: Journal of the Atmospheric Sciences 61, 12; 10.1175/1520-0469(2004)061<1360:TGOTMG>2.0.CO;2
(Continued)
Citation: Journal of the Atmospheric Sciences 61, 12; 10.1175/1520-0469(2004)061<1360:TGOTMG>2.0.CO;2
(a) Morning glory as it is crossing the west coast from land to water. (b) The surface pressure
Citation: Journal of the Atmospheric Sciences 61, 12; 10.1175/1520-0469(2004)061<1360:TGOTMG>2.0.CO;2
As in Fig. 6, but without nocturnal surface cooling
Citation: Journal of the Atmospheric Sciences 61, 12; 10.1175/1520-0469(2004)061<1360:TGOTMG>2.0.CO;2
As in Fig. 6, but with the nocturnal surface cooling doubled to 80 W m−2
Citation: Journal of the Atmospheric Sciences 61, 12; 10.1175/1520-0469(2004)061<1360:TGOTMG>2.0.CO;2
Increased environmental flow experiment. Potential temperature, shaded in 1-K increments, showing the two sea breezes at 2000 LST, with a 10-km gap between the plots. The peninsula is located from x = 100 km to x = 540 km
Citation: Journal of the Atmospheric Sciences 61, 12; 10.1175/1520-0469(2004)061<1360:TGOTMG>2.0.CO;2
As in Fig. 4, but with the model initialized with an easterly flow of 2.5 m s−1
Citation: Journal of the Atmospheric Sciences 61, 12; 10.1175/1520-0469(2004)061<1360:TGOTMG>2.0.CO;2
As in Fig. 6, but with an initial easterly flow of 2.5 m s−1
Citation: Journal of the Atmospheric Sciences 61, 12; 10.1175/1520-0469(2004)061<1360:TGOTMG>2.0.CO;2
Experiment with no environmental flow. (top) The sea breezes at 2210 LST, 7 min prior to meeting. (middle) The elevation of cold air by the collision of the sea breezes. (bottom) Westward-propagating waves 1.75 h after the collision
Citation: Journal of the Atmospheric Sciences 61, 12; 10.1175/1520-0469(2004)061<1360:TGOTMG>2.0.CO;2
Potential temperature shaded in 1-K increments showing the two sea breezes at 1700 LST. Only the westernmost 100 km of the peninsula is shown
Citation: Journal of the Atmospheric Sciences 61, 12; 10.1175/1520-0469(2004)061<1360:TGOTMG>2.0.CO;2
Control experiment at 2300 LST showing values of (a) Scorer parameter l2 and (b) Richardson number Ri with gray shading denoting Ri < 0.25. For reference, the 303-K isentrope is included as the thick line. The dashed contour marks the 8.3 m s−1 easterly isotach, which is the phase speed of the waves on the stable layer
Citation: Journal of the Atmospheric Sciences 61, 12; 10.1175/1520-0469(2004)061<1360:TGOTMG>2.0.CO;2
Similar to Fig. 6, but with potential temperature contoured without shading, and with the plot extending to a height of 6 km
Citation: Journal of the Atmospheric Sciences 61, 12; 10.1175/1520-0469(2004)061<1360:TGOTMG>2.0.CO;2
Plot of potential temperature showing the two sea breezes at 2100 LST over the entire peninsula
Citation: Journal of the Atmospheric Sciences 61, 12; 10.1175/1520-0469(2004)061<1360:TGOTMG>2.0.CO;2
Morning glory at 0100 LST with orography. The result is similar to the morning glory that develops without orography (see Fig. 6)
Citation: Journal of the Atmospheric Sciences 61, 12; 10.1175/1520-0469(2004)061<1360:TGOTMG>2.0.CO;2
Table comparing the phase speeds c of the initial waves produced with ce, the speed of the east-coast sea breeze. All velocities are westward in m s−1 . The success or failure of the experiment to produce a morning glory is also indicated, as well as the number of prominent crests that were present at 0100 LST, and the Froude number FR = c/ce
The reference point used to determine the position of the east-coast sea breeze is the location of the maximum updraft at the leading edge.
Haase and Smith use the symbol μ for what we define as Fr. In their paper the Froude number is defined as the ratio of the mean inflow speed of cold air and the densimetric speed of the gravity current.
