a. Quiescent case

Figure 4 shows x–z cross sections of the total liquid and ice hydrometeor mixing ratio through the center of the convective storm in grid 4 at various times for the quiescent environment case. At 20 min the storm is in the early stages of development with a maximum hydrometeor mixing ratio of 6 g kg⁻¹, at z = 4 km. By 30 min, explosive growth has occurred with cloud top at 16.5 km and a maximum hydrometeor mixing ratio of 13 g kg⁻¹ at z = 7 km. At 40 min, the storm is in the mature stage. Outflow at the cloud top is causing an anvil to form and precipitation is occurring at the surface. At 50 min the storm is in its decaying stage. Mixing ratios are decreasing due to hydrometeor fall out, sublimation, and evaporation. The strongest updraft occurred around 30 min at z = 11 km and the peak value was 39 m s⁻¹. Downdrafts driven by evaporation and waterloading began to develop beneath the updraft core at 40 min and reached a magnitude of 8 m s⁻¹ at 50 min. The maximum precipitation was 52 mm and occurred at the grid point at the center of the storm.

Figure 5 shows an x–z cross section of the pressure perturbation in grid 2 through the center of the storm at 30 min. Only small magnitudes of the pressure perturbation are contoured in this figure in order to illustrate the thermally induced Lamb waves. This field is not perfectly symmetrical as are the fields in Fig. 4 since grid 4 is not exactly in the center of grids 3 and 2 and because of the interpolations used in the contouring routine. The maximum amplitude of nearly 0.6 Pa occurs at the surface at x = −110 and 90 km. This circular ring of high pressure propagates away from the storm at the speed of sound. The vertical structure of the pressure and density perturbations in the compression wave are approximately the same as the theoretical solution for a Lamb wave in an isothermal atmosphere (see for instance NPb). The horizontal velocity, however, did not increase with height as much as the theoretical solution. Model sensitivity tests with prescribed heating and an isothermal atmosphere gave extremely good agreement with the theoretical solution for the pressure and density perturbations. The horizontal velocity perturbations were slightly in disagreement at upper levels. Agreement was improved by eliminating Rayleigh friction in the uppermost levels. It was felt that overall the Rayleigh friction layer was of benefit to this study and that it was important to include it.

Figure 6 shows an x–z cross section of the pressure perturbation in grid 2 through the center of the storm at 50 min. This figure illustrates the n1 gravity wave mode with a minimum pressure of −8 Pa occurring at the surface at x = −75 and 45 km. This circular ring of low pressure propagates away from the storm at a speed of ∼48 m s⁻¹. This propagation speed is quite fast because of the high tropopause. A high pressure maximum of 3 Pa occurs at z = 10 km above the surface minimum. The structure of this mode in two dimensions has been discussed by Nicholls et al. (1991b) and Pandya et al. (1993). Figure 7 shows an x–z cross section of the pressure perturbation in grid 2 through the center of the storm at 80 min. This figure illustrates the n2 gravity wave mode with a maximum surface pressure of nearly 4.5 Pa occurring at x = −75 and 45 km. As discussed by Nicholls et al. (1991b), it is characterized by a surface high, a midlevel minimum, and an upper-level high. It propagates at half the speed of the n1 mode. At this stage it is superimposed on the tail end of the n1 mode. The tail end of the n1 mode has a pronounced positive pressure perturbation at the surface and a negative perturbation aloft, which is a major difference from the two-dimensional studies by Nicholls et al. (1991a,b). Some idealized sensitivity tests with prescribed heating suggests this behavior is mainly due to the three-dimensional geometry, rather than significant forcing of an oppositely signed n1 mode caused by a change in the vertical profile of the latent heating later on in the storm life cycle. Also, as will be seen, the tail end of the n2 mode has pressure perturbations of opposite sign than the forward part of the wave. The surface high pressure associated with the n2 mode is very distinct from the surface high associated with the shallow cold pool outflow between x = −40 and x = 5 km. Slower-moving high-order gravity wave modes are also evident in this figure.

Figures 8a–d show time series of the pressure perturbation at the first grid point above the surface (z = 200 m) at various distances from the storm. The first pulse that occurs during the first few minutes in Fig. 8a, at 35 km from the storm in grid 4, is due to the prescribed 5-min heating used to initiate the storm. The shape of this compression wave is clearly similar to the two-dimensional solution shown in Fig. 2, not to the three-dimensional solution. This is evidence that the wave is a Lamb wave, which travels in the horizontal plane. This is then followed by a slight peak in pressure at 22 min, which is due to a low-frequency compression wave generated by the latent heat release in the storm. At this location this compression wave is superimposed on the gravity waves generated earlier by the prescribed heating as well as the leading edge of the n1 gravity wave mode generated by latent heat release in the storm. This makes its shape and amplitude hard to discern. Interestingly, there are small high-frequency fluctuations superimposed on the lower-frequency compression wave, which will be discussed later. The large decrease in pressure of 14.3 Pa is mainly due to the n1 gravity wave mode. This is followed by a large positive pressure pulse, which is a superposition of the tail end of the n1 mode and the forward part of the n2 gravity wave mode. Figure 8b shows a time series of the pressure perturbation at a distance of 75 km from the center of the storm. The waves have propagated into grid 3 at this location, which results in a slight distortion of the waves. The compression wave or Lamb wave generated by latent heat release is now more evident. The positive pressure perturbation is 0.6 Pa. The amplitude of the n1 negative pressure perturbation is 6.8 Pa. The following positive pressure perturbation has started to separate into two maxima. The first is the positive lobe associated with the n1 mode and the second, which can just be seen at the edge of the figure, the forward part of the n2 mode. This separation of modes will be shown in more detail for longer duration runs later. Figure 8c shows a time series of the pressure perturbation at a distance of 174 km from the storm, which is in grid 2. Significant distortion of the waves is evident due to their passage into the coarser grid. However, this figure does illustrate the negative pressure lobe of the Lamb wave, which has started to separate from the slower-moving n1 mode. Figure 8d shows a time series of the pressure perturbation at a distance of 390 km from the storm, which is in grid 1. Even more distortion of the waves has occurred. Only the Lamb waves generated by the prescribed heating and the latent heat release have reached this location.

In order to illustrate the Lamb wave close to the storm in more detail, an identical simulation was made with the standard model discussed in section 4, which does not allow the generation of thermal compression waves. The time series for this run was then subtracted from that for the fully compressible model. It was found that although extremely similar, the storm simulated with the standard model was not identical to the storm simulated with the fully compressible model. Therefore, subtracting the time series does not give the pure compression wave signal since the gravity waves do not have exactly the same amplitudes. The reason for this small difference between the two models is interesting and requires further investigation. Figures 9a and 9b show the difference pressure series between the two model runs at distances of 35 and 75 km from the storm, respectively. In Fig. 9a, the positive peak at t = 60 min appears to be due to slightly larger amplitude gravity wave modes in the fully compressible run so that the latter part of this time series needs to be treated with some caution. Nevertheless, it shows much more detail of the Lamb wave close to the storm, in particular the positive lobe and the higher-frequency oscillations, which are superimposed.

This figure can be used to determine the decay rate of the Lamb wave with the horizontal distance traveled from the source. In Fig. 9a, the amplitude of the positive peak of the Lamb wave is 1.23 Pa, which is at a distance of 35 km from the storm. Assuming a 1/(distance)^1/2 decay rate, the amplitude should be 0.84 Pa at 75 km. The simulated amplitude of 0.83 Pa seen in Fig. 9b is in very good agreement with the 1/(distance)^1/2 decay rate.

To determine the decay rate of the n1 gravity wave mode generated by the convective storm, we use Figs. 8a and 8b at distances of 35 and 75 km from the storm, respectively, and estimate the contributions to the large trough by the gravity waves produced by the prescribed heating and the Lamb wave. A simulation was run without microphysics with the standard model in order to isolate the gravity waves produced by the prescribed heating. At 35 km from the storm, the contribution to the trough from these gravity waves was found to be −0.4 Pa (not shown) and the contribution from the Lamb wave can be seen to be −1.2 Pa at t = 39 min from Fig. 9a. Subtracting these values from the trough amplitude of 14.3 Pa gives an estimate of 12.7 Pa for the amplitude of the n1 gravity wave mode, at 35 km from the storm. Assuming a more rapid 1/distance decay rate for gravity waves, then at 75 km the amplitude would be 5.9 Pa. The estimated amplitude of the simulated n1 gravity wave mode at this location, using the same procedure as before, is 5.7 Pa. Therefore, the decay rate of the gravity wave with distance traveled is much more rapid than the Lamb wave and appears to be 1/distance. The amplitude of the n1 gravity wave mode shown in Fig. 8c, which is in grid 2 at 174 km from the storm, suggests a slightly faster than 1/distance decay rate. The coarse resolution in this grid and weak model diffusion probably account for this faster than predicted decay rate. A 1/distance decay rate is the same as for the three-dimensional solution for a compression wave discussed in section 2. This is perhaps not surprising considering that gravity wave energy propagates upward, not just horizontally like it does for the Lamb wave.

Since the shape of the two-dimensional solution in Fig. 2 is similar to that generated in the numerical model by the prescribed heat source, it is of interest to calculate the idealized two-dimensional solution for the latent heating from the simulated convective storm, shown in Fig. 10. In order to do so, we make use of the fact that the pressure perturbation in a Lamb wave decays with height as exp(−z/γH), where H = RT/g is the scale height and γ = c_p/c_υ. Although we know that the maximum heating rate is actually elevated above the surface in the simulated rainstorm, we ask what the solution would be if the heating was a maximum at the surface and decayed as exp(−z/γH). Then we can consider the solution to be a vertical stack of infinitesimal layers with the solution in each layer given by the idealized two-dimensional linear solution and for a heating rate, which decays as exp(−z/γH). Then the total heating for this idealized scenario is

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where r = (x² + y²)^1/2 and ρ₀Q₀ is the heating rate per unit volume at r = 0, z = 0. Evaluating Eq. (10) gives Q₀ = Q_t/γHρ₀b²π. This is the value of Q₀ we use in Eq. (A5) to obtain the pressure perturbation at the surface for the two-dimensional idealized solution, which has the same net heating Q_t as in the simulated storm. The time series for Q_t in Fig. 10 was written out every 1.25 s, which was the model time step. Therefore, the idealized two-dimensional solution for this heating rate was determined by summing up the solutions for a series of pulses spaced 1.25 s apart, for a pulse width of 1.25 s, and for a Q₀, which varies with time as Q_t(t)/γHρ₀b²π. This solution is shown in Fig. 11 at a distance of 75 km from the source, which can be compared with the simulated compression wave in Fig. 9b. The amplitude of the positive peak is 0.77 Pa, whereas the amplitude of the simulated positive peak is 0.83 Pa. Given the assumptions used in deriving the idealized two-dimensional solution, the similarity of the amplitude and shape of the wave with the simulated Lamb wave is surprising. The similarity of the amplitudes in particular should be viewed with some caution since it has been assumed that 1) the atmosphere is isothermal;2) the heating is maximized at the surface, decreases exponentially with height, and has a horizontal variation give by Q₀b⁴/(r² + b²)²; 3) that all the energy is transferred horizontally by the Lamb waves, that is, that there is no vertical transport; and 4) that latent heating is the primary mechanism for forcing of the Lamb wave, that is, the effects of mass sources and sinks due to phase changes between water and vapor can be neglected. On the other hand, the good agreement could be indicative that the amplitude of the Lamb wave generated is fairly insensitive to the vertical structure of the heating and that only a small fraction of the energy is transferred vertically. The idealized solution shows a smaller second peak, which can also be seen in Fig. 9b. The amplitude of the negative lobe is almost as large as the positive lobe agreeing with Fig. 8d. There are small high-frequency oscillations with the same period as the simulated wave shown close to the storm in Fig. 9a, although their magnitude is quite a bit less. Comparing Figs. 10 and 11 it can be seen that the time it takes for the large positive and negative lobes to pass a location, or the period, is approximately equal to the lifetime of the convective storm. It is recognized that the term “period” is being used rather loosely here to refer to the temporal width of this nonrecurrent waveform, as is the term “frequency” when referring to the inverse of this period.

Mapes (1993) and McAnelly et al. (1997) have suggested that thermally induced gravity waves may cause uplift of environmental air that could favor the development of additional convection. For this quiescent environment case, the upward displacement at 35 km from the storm was 55 m at 1 h into the simulation. It was centered at 4–5 km above the surface. This appeared to be mainly due to the n2 mode with some additional contribution by a higher-order mode or modes. Although not a very large displacement, a number of convective cells in close proximity, or an MCS, might lead to enough uplift to initiate additional convection if the atmosphere is close to being convectively unstable.

A simulation was carried out with the standard model run out to 4 h to examine the longer-term behavior of the gravity waves. Less vertical levels were used, but the horizontal dimensions of grid 3 (grid increment 3 km) were increased to give better resolution of the gravity waves farther from the storm. Figure 12 shows the pressure perturbation series at 174 km from the storm, which is within grid 3 for this simulation. The negative lobe of the n1 mode has a minimum of −2.1 mb at 1.4 h, which is a slightly larger amplitude than for the previous simulation with the fully compressible model, which did not have such a good resolution at this location (Fig. 8c). The positive peak of the n1 mode, which passes at 1.8 h has clearly separated from the positive peak of the n2 mode, which passes at 2.75 h at this location. The n2 mode also has a negative lobe with the minimum passing at 3.2 h. In Fig. 8a, at 35 km from the storm, the positive peaks of the n1 and n2 modes coincide, passing this location at approximately 59 min, although it is difficult to say from this figure at exactly what time each mode passes. Therefore, the estimated speed of the n2 mode calculated from the times its positive peak passes 35 km (Fig. 8a) and 174 km (Fig. 12) is 139 km divided by 106 min giving 22 m s⁻¹, which is slightly less than half the speed of the n1 mode, which propagates at approximately 48 m s⁻¹. Estimating the speed of the n2 gravity wave mode from another time series written out during the long duration run, when the n2 peak was clearly visible, gave a speed of 23 m s⁻¹.

b. Vertical wind shear case

Figure 13 shows a vertical cross section of the condensate and wind vectors at 40 min for the shear case. The updraft tilts downshear with strongest velocities on the upshear side of the storm. At upper levels, the condensate is advected downstream forming an anvil. The maximum value of the condensate mixing ratio is slightly less at this time than for the quiescent case. The strongest updrafts occurred around 30 min, at z = 10 km, and the peak value was 32 m s⁻¹. This was a longer-lived storm than the quiescent case with a significant updraft at 90 min. The precipitation maximum was 75 mm. The rainfall also occurred over a larger area than for the quiescent case and the total was twice as much.

Figure 14 shows a horizontal cross section of the wind vectors and pressure perturbation 200 m above the surface at 60 min. The high pressure perturbation region >18 Pa in the center of the figure is approximately the area occupied by the cold pool outflow. The low pressure anomaly associated with the n1 gravity wave mode can be seen exiting the west, south, and north boundaries of the fine grid. It has already exited the east boundary since the mean wind in the troposphere is ∼8 m s⁻¹ toward the east. There is an asymmetry of the high pressure anomaly with fairly large values extending north and south of the storm.

Figures 15a and 15b show vertical cross sections of the pressure perturbation and temperature perturbation, respectively, at 65 min in grid 4. There is a distinctive n2 looking structure between x = −30 km and x = −45 km. This consists of warm air at upper levels with cool air beneath and the characteristic high/low/high pressure perturbations. Since the environment is near dry adiabatic between the surface and 1.5 km, the pressure perturbations associated with the gravity waves are nearly constant with height in this layer and the temperature perturbations are small. The cold pool has a temperature deficit of ∼2.5 K and is formed by evaporatively cooled air sinking and spreading out at the surface. Velocities are strong in the cold pool at this time, so nonlinear advective effects are important, whereas the gravity wave modes are much more linear in character.

Figures 16a–c show time series of the pressure perturbation 35 km to the west, 35 km to the east, and 390 km to the west of where the storm was initiated, respectively. The Lamb wave generated by latent heat release is not very evident 35 km from the storm. The n1 gravity wave mode can be clearly identified in both Figs. 16a and 16b. On the east side of the storm, the time it takes for the negative lobe of the n1 mode to pass is less, mainly because the mean westerlies cause the wave to pass this location more quickly. However, the instantaneous fields show that the n1 mode does appear to be broader and slightly weaker in amplitude east of the storm. Also, the high pressure maxima aloft is more elevated than on the west side of the storm. The high pressure peak at 83 min in Fig. 16a seems to be due to a superposition of the positive lobes of the n1, n2, and n3 modes. On the east side of the storm, the high pressure peak at 57 min appears to be due to a weak n2 structure, while the stronger peak at 75 min appears to be an n3 structure. The effects of shear on the modes, especially on the slower-moving higher-order ones, are obviously quite complicated. However, these results do show how different the waves observed at locations upshear and downshear of storms are likely to be. It can be inferred that the compression wave seen in Fig. 16c has a longer wavelength than for the quiescent case (Fig. 8d). The interval between the positive and negative peaks is 37 min, whereas for the quiescent case it is only 20 min. The magnitude of the negative peak is less than for the quiescent case. Figure 17 shows the total latent heating rate. Comparing with Fig. 10 for the quiescent case, it can be seen that the maximum occurs a bit later and is a bit larger. There is far more net heating for the shear case. As a result of the convection being long lived, the net heating does not become negative unlike the quiescent case. Figure 18 shows the idealized two-dimensional linear solution for this heating rate at 75 km from the storm. This is very similar in structure to the simulated compression wave shown in Fig. 16c. The peak value is almost the same as for the quiescent case and occurs at almost the same time. The peak value does not correlate well with the peak heating rate in Fig. 15, but leads it by about 8 min after taking into account the time taken for the wave to travel 75 km. This is a consequence of the amplitudes of the wave depending on the rate of change of the heating rate, not just its magnitude.

c. Transfer of internal and gravitational potential energies

NPa and NPb discussed how compression waves could transfer total energy in the atmosphere at the speed of sound. The total energy flux vector appearing in the total energy equation is given by E_tu + pu where E_t is the total energy ρ(c_υT + gz + u²/2), E_tu is the flux of total energy carried by the flow itself, and pu is the pressure work term [see, e.g., Gill 1982, his Eq. (4.74);NPA, their Eq. (4)], where for simplicity radiation effects and diffusion of heat and kinetic energy have been neglected. Since the energy flux vector is not simply E_tu, but includes the pressure work term pu, there is not such a simple interpretation of total energy transfer as there is, for instance, for mass transfer, where the rate of change of mass in a volume depends just on the mass fluxes ρu across the surface of the volume. Nevertheless, due to the conservative form of the total energy equation, perturbations of total energy field can be seen to move around from one region to another with total energy being conserved, as seen in the analytical and numerical model examples presented in NPa. It is in this sense that we refer to total energy transfer. This situation is by no means unique. For ordinary sound waves and internal gravity waves the wave energy flux vector is not E_wu, where E_w is the wave energy [see, e.g., Gill 1982, his Eq. (6.14.7); NPa, their Eqs. (21) and (36)]. Yet it is common to refer to wave energy as being transferred by these types of waves, with the understanding that the transfer is not due to the flux E_wu but to the wave energy flux vector.

In NPa the internal energy per unit volume E_i = ρc_υT was rewritten using the equation of state p = ρRT for a dry atmosphere as c_υp/R. Internal energy perturbations c_υp′/R from an initial internal energy c_υp₀(z)/R were considered. This perturbation form should not be confused with the perturbation energy, or wave energy, mentioned in the introduction, which involves linear approximations. It is simply the difference after subtracting the large amount of internal energy present in the initial state and does not involve any approximations [see Eq. (7) of NPa, and sections 4 and 5 of that paper for discussion of wave energy]. Looking at Fig. 1b, the two-dimensional solution for p′, at a particular location versus time for the linear compression wave model, it may not be obvious that this wave results in a net transfer of internal energy, since it has a negative lobe as well as a positive lobe. Figure 19 shows the pressure perturbation and internal energy perturbation versus distance from the source for the same wave. Since this is a cylindrical wave, the energy per unit length in an increment of radius dr is 2πrc_υp′ dr/R. The internal energy per unit area 2πrc_υp′/R, plotted in this figure, shows that the factor 2πr leads to an increase in the positive area beneath the curve and a decrease in the negative area compared to the curve for p′, which results in a net positive internal energy in the wave. For this linear model, the net energy input is exactly equal to the net internal energy. There is also some kinetic energy associated with the wave so that the total energy does not add up to exactly equal the net energy input. This small error is a result of linearizing the equations as discussed in NPa.

For the numerical convective storm simulation, the effects of moisture need to be included. Using the equation of state p = ρRT(1 + 0.61w), the internal energy perturbation to a good approximation is

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Since the resolution in the coarser grids for the three-dimensional simulation is not very good and results in a distortion of the waves, an energy analysis was also carried out for a two-dimensional simulation with a much better coarse-grid resolution (3-km grid increment). The energies were calculated from the surface to 50 km, so as not to include the upper-level Rayleigh friction layer. The gravitational potential energy perturbation per unit volume was calculated as ρ′gz. For this simulation, it was found that the sum of the perturbation internal and gravitational potential energies within the domain was 87% of the latent heat released in the domain calculated according to Eq. (9). This disagreement is mainly due to the loss of mass from the air due to phase changes from vapor to liquid and ice water. This conclusion is supported by a simulation with the mass source term S in Eq. (8) eliminated, which resulted in a very good agreement between the sum of the perturbation internal and gravitational potential energies in the domain and the latent heat release. The loss of water vapor from the air as condensation occurs, represented by a negative value of S in Eq. (8), opposes to some extent the expansion brought about by latent heat release resulting in slightly weaker amplitude Lamb waves than would otherwise occur. After the convection has almost completely dissipated and the two oppositely moving Lamb waves had separated from the slower moving gravity waves, the energies were calculated separately for the two outer regions occupied by the Lamb waves and the central region occupied by the gravity waves. Since there were still cloud remnants, there were some very small compression wave perturbations within the region occupied by gravity waves. In the Lamb wave regions, the ratio of perturbation gravitational potential energy to perturbation internal energy was 0.4. This ratio is the well-known proportion R/c_υ of gravitational to internal energy for a hydrostatic atmosphere (see, e.g., Holton 1979). The sum of these energies in the Lamb wave regions was slightly greater than the total in the domain and equal to 88% of the total latent heat release. In the region occupied by gravity waves, the net perturbation gravitational potential energy was negative. Its magnitude was ∼2% of the total latent heat release. This decrease is predominantly due to a net decrease in density in this region due to expansion of air brought about by the latent heat release. The net perturbation internal energy in this region was positive with a magnitude of ∼1% of the latent heat release. This small increase is apparently due to a reduction of the net moisture in this region brought about by precipitation, which tends to increase the first term of Eq. (11) relative to the second term. An energy analysis for the three-dimensional simulation shows similar results, although the poorer resolution in the coarser grids was probably responsible for a larger difference between the net latent heat release and the net energy perturbation. The net kinetic energy within the domain reached a maximum during the growing phase of the convective cell and was approximately 1% of the total change in internal and gravitational potential energies that had occurred. To check the three-dimensional results an idealized simulation was run with fewer vertical levels, but with better horizontal resolution in the coarse grid. Convective heat release was represented by a large magnitude prescribed heat source and the microphysical scheme was not implemented. Good energy conservation was obtained and the Lamb wave was clearly transferring internal energy and gravitational potential energy to the periphery of the domain at the speed of sound.

d. Resurgence of convection

For the longer duration quiescent case simulation, an interesting small-scale buoyancy oscillation occurred at low levels after the storm decayed. Figures 20a–c show vertical cross sections of the temperature perturbation, water vapor mixing ratio perturbation, and the x component of velocity, respectively, at 90 min. There is a warm bubble of air next to the surface caused by the downdraft air overshooting its equilibrium level. The maximum temperature anomaly in the bubble is 1.1 K. It is centered in the middle of the cold pool outflow, which at this time is only 0.7 K colder than the environment near the surface. The downdraft air was much drier than the environmental air near the surface and has resulted in a moisture deficit of approximately 3 g kg⁻¹. As the cold pool spread out at the surface, the vertical motion at the leading edge lifted up the moist environmental air that was then advected back over the cold pool. This is partly responsible for the large moisture anomaly above the warm bubble of ∼2 g kg⁻¹. This moisture anomaly also resulted from moist air, which was advected toward the storm at low levels early on and lifted up, but did not make it into the main updraft. When the downdraft formed, it brought dry air through the center of this moist region. As the downdraft weakened, horizontal and vertical advection of the moist surrounding air led to the formation of the large moisture anomaly in the region that had been occupied by the downdraft. The horizontal velocity field shows quite strong horizontal convergence within the warm bubble as the air starts to rebound. The ensuing upward motion in the moist anomaly caused a small cloud to form at 110 min. Figure 21 shows the total liquid and ice mixing ratio at 130 min, which is 40 min after the rebound started to occur. A narrow convective cell with a maximum mixing ratio of 6 g kg⁻¹ has formed. This develops into a storm similar to the first, but less intense, with approximately two-fifths of the heat release. The time lag between the peak heating rates for the two storms was 1 h and 50 min. Apparently, the moisture that had advected over the top of the first storms cold pool was a major source of convective available potential energy (CAPE) for the second storm.

It is possible that this mechanism may sometimes play a role in resurgences of convection in nature. McAnelly et al. (1997) discussed two mesoscale convective systems that exhibited an early meso-β-scale convective cycle (a maximum and subsequent minimum) followed by reintensification. In that paper, it is suggested that the n2 gravity wave mode has the effect of modifying the environment for convection and hence may play a role in the reintensification and upscale growth of convection. It is also possible that the small-scale low-level buoyancy oscillations found in this study could sometimes play a role by initiating new convection in MCSs, along with other low-level forcing mechanisms such as gust fronts, and that some of the CAPE for the reintensification may come from the moist air atop the cold pools from the earlier convection.

The first cell, which developed in the shear case was longer lived than for the quiescent case, as can be seen from comparing the latent heating rates in Figs. 10 and 17. The initial strongest cell for the quiescent case decayed almost completely because of the development of the downdraft, caused by waterloading and evaporation, which very effectively cut off the low-level updraft circulation. Due to the updraft tilt that occurred for the shear case, the downdraft formed on the downshear side of the updraft, so that the updraft circulation was maintained longer. However, as can be seen in Fig. 17, the net latent heating was reduced to near zero by 67 min. This came about because of the development of a deep cold pool at 60 min, which blocked the flow of low-level air into the updraft. Also, because some of the cold dry downdraft air, which formed the cold pool was entrained into the updraft from the downshear side. The updraft did not completely disappear, however, but managed to maintain itself by feeding on moist environmental air, which had been advected over the cold pool. Although a warm bubble formed near the surface on the downshear side when the downdraft overshot its buoyant equilibrium level, there was not a rebound producing a resurgence of convection. This occurred because the downdraft was continually maintained in this region since the storm did not completely decay. Therefore, the warm bubble was under a rain shaft and drier air from aloft was maintained over it. The storm remained weak for almost an hour, after which a moderate resurgence to a quasi-steady state occurred. This resurgence coincided with the cold pool becoming more shallow. This apparently reduced the low-level blocking of inflow and the entrainment of cold dry air near the surface into the updraft. The storm regained moderate strength by feeding on the moist air atop the cold pool. Figure 22 shows the wind vectors and water vapor perturbation 600 m above the surface at 120 min, which is the time the resurgence took place. As can be seen, the updraft is feeding on moist air, approximately 1 g kg⁻¹ moister than the environment, from all sides of the storm, except immediately downshear, which is the very dry downdraft region.

Gravity waves were produced by these resurgences of convection for both cases, but none as strong as those produced by the initial cells. It is possible that the n1 mode induced during the quasi-steady stage for the shear case may have had a role in enhancing the low-level flow of moist air atop the cold pool, contributing to the longevity of the storm. During this stage, the updraft continually built on the upshear side and was often quite vertical at low levels, whereas at upper levels it tilted downshear. The hydrometeors were then advected downstream at upper levels maintaining the anvil. In this quasi-steady stage the storm did not move with the mean flow in the troposphere, but was approximately stationary with respect to the environmental air in the lowest kilometer.