Diabatic Heat Effects on the Generation of Energy for Evolution of a SACZ Event: A Perspective from the Lorenz Energy Cycle

a. Synoptic analysis of event

The synoptic analysis results show that the anticyclonic and cyclonic circulations in the lower troposphere (indicated with H and L in Fig. 3) favor the intense airflow convergence, rising or sinking in the troposphere over SA. The anticyclonic circulation associated with the Bolivian high and upper-level cyclonic vortices near the Brazilian northeast coast at 200 hPa (Kousky and Gan 1981; Kodama 1992; Lenters and Cook 1997; Zhou and Lau 1998) is consistent with the strongest atmosphere updrafts at 500 hPa in the SACZ region and, thus, with the extreme convection observed. In addition, the anticyclonic circulations at the low levels, which show the compensation subsidence regions for the upward movement in the mainland and ocean SACZ area, contributed to the severe heat wave in southern Brazil, Uruguay, and the central Argentina region (see, for example, Blunden and Arndt 2014, p. S173).

A geopotential eddy (Φ*) analysis at 200 hPa, revealed that the different SACZ patterns observed in Fig. 3 were favored by the influence of wave train configurations established at midlatitudes (see appendix B, Fig. B1). We find that during 12–15 December, the location of the anticyclonic circulations at 850 hPa around southern Brazil, Uruguay, and Argentina (Fig. 3a) were largely influenced by the alternating positions of high and low centers from the wave train (see, for example, Fig. B1). Furthermore, this wave train favored the lowering of the height near 27°S, 38°W, which consequently led to a surface pressure drop there. This increased the extent of surface mass convergence and convection over the ocean area.

At the beginning of the period from 16 to 22 December, the wave train configuration led to the anticyclonic circulation expanding at 850 hPa on the mainland and the 200 hPa height lowering over the ocean near the SE and south of BA (see Φ* in Figs. B1b,d). This likely led to the confinement, expansion, and intensification of the convection to the north, which results in strong rains around the southern part of northeast Brazil (NEB) and the northern part of SE (Fig. 1). Finally, at the end of this period, the displacement of the anticyclonic circulation toward the southwest Atlantic Ocean, combined with the height center displacement near SE toward the mainland, forced the cyclogenesis at the surface around 28°S, 44°W. During 23–26 December, the cyclogenesis favored the low pressure extension at the surface to the south and a slight southward convection shift (Figs. B1c,e). Cyclone activity in this region seems to be a predominant characteristic of the SACZ events and has an important role in the heat flow at low levels in the ocean SACZ area due to the sea surface temperature changes (Pezzi et al. 2022). Thus, the midlatitudes wave train plays an important role in the SACZ event evolution through cyclogenesis processes in the southernmost areas.

At the end of the period of 23–26 December, the wave train configuration seems to favor anticyclonic circulation expansion on the surface over the SA central region, which led to the event decay (Fig. B1f). Thus, different wave train positioning configurations acted to favor the establishment, expansion/retraction, and decay of the SACZ event.

b. Structure of the diabatic heat rate and energy generation

The vertical structures and horizontal distribution of the diabatic heat rate (Q/C_p) and energy generation components [G(P_M) and G(P_E)] calculated by thermodynamic energy and Oort’s equations are in Figs. 4 and 5, respectively. We examine the vertical structures of the Q/C_p for each subarea (Figs. 4a–d) and discuss their effects on the energy generation terms [G(P_M) (Figs. 4a′–d′) and G(P_E) (Figs. 4a″–d″)].

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Vertical structure of the diabatic heat rate (Q/C_p), generation of zonal mean available potential energy, G(P_M), and eddy available potential energy generation, G(P_E), for each SACZ subarea. Average of (a) Q/C_p, (a′) G(P_M), and (a″) G(P_E) for 12–15 Dec; (b) Q/C_p, (b′) G(P_M), and (b″) G(P_E) for 16–22 Dec; (c) Q/C_p, (c′) G(P_M), and (c″) G(P_E) for 23–26 Dec; (d) Q/C_p, (d′) G(P_M), and (d″) G(P_E) for 12–26 Dec 2013.

Citation: Journal of the Atmospheric Sciences 80, 9; 10.1175/JAS-D-22-0245.1

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Spatial distribution of the diabatic heat rate (Q), eddy potential energy generation [G(P_E)], transient [G(P_TE)], and stationary [G(P_SE)] components. Average of (a) Q, (a′) G(P_E), (a″) G(P_TE), and (a′″) G(P_SE) for 12–15 Dec; (b) Q, (b′) G(P_E), (b″) G(P_TE), and (b′″) G(P_SE) for 16–22 Dec; (c) Q, (c′) G(P_E), (c″) G(P_TE), and (c′″) G(P_SE) for 23–26 Dec; (d) Q, (d′) G(P_E), (d″) G(P_TE), and (d′″) G(P_SE) for 12–26 Dec 2013. The units are in W m⁻².

Citation: Journal of the Atmospheric Sciences 80, 9; 10.1175/JAS-D-22-0245.1

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The diabatic heat rate (Q/C_p) generally reaches its peak in the middle troposphere (around 500 hPa, Figs. 4a–d). This suggests that most of the latent heat released during the event occurred at these levels. Our analysis revealed that the heating estimated as the residual of the thermodynamic equation was larger in subareas 2 and 3 (located in the tropics/subtropics), where the latent heat release effect in convective clouds was most pronounced. Previous research has also documented higher latent heat release in these levels and regions during the austral summer (Hantel and Baader 1978; Seo and Son 2012; Ling and Zhang 2013; van der Wiel et al. 2015a).

Analyses of the Q/C_p vertical structure in each of the five SACZ’s acting subareas show that the heating increased by a factor of 3 at middle levels in subarea 1 from the first (12–15 December) to the second period (16–22 December) and decreased to a quarter at the end of the event in subarea 5 (Figs. 4a–d). The intense airflow convergence in the SACZ area, influenced by wave train configurations established in midlatitude, provided this heating increase. As previously discussed, the wave trains favored the band convection expansion to the north and convergence enhancement near the SE and NEB coasts between 16 and 22 December (Figs. 3b and B1d). Another key finding from the Q/C_p analysis was the heating increase in the middle troposphere levels during 23–26 December in subarea 4, located slightly to the south in the subtropics (Fig. 4c). During this period, the SACZ convection moved slightly to the south, considering its most northerly position. In synoptic analysis, we found that this was influenced by transient waves passing on the south of the SACZ’s acting region, which led to the cyclone’s development near 28°S and 44°W (Fig. 3c). The cyclone, in its turn, intensified the convection over this region, supporting the findings of Grimm and Dias (1995), Ambrizzi et al. (1995), and Grimm (2019). For more information about the cyclogenesis process in SA, see Reboita et al. (2018) and de Jesus et al. (2021).

On average, the diabatic heat rate was greater during 16–22 December when the event reached its northernmost position, which we call SACZ-NP, in subareas 2 and 3 (Fig. 4). The analysis of the storm’s latent heat release structure is important to understanding the energy generation structure. Thus, now we will look at the impact of this on energy generation for the event.

The G(P_M) [G(P_E)] terms depend on the covariance of the meridional (zonal and temporal) deviations of Q and T. Therefore, G(P_M) and G(P_E) act as sources (sinks) of the respective energy terms, P_M and P_E, when this covariance is positive (negative). Figures 4a′–d′ show that the G(P_M) was greater from middle to upper troposphere levels (between 600 and 250 hPa) such as in Q structures, except for the maxima, which were in subareas 4 and 5, where the horizontal thermal gradient is larger, resulting in a strong positive correlation between Q and T. Although Q was small at low levels in subarea 5, G(P_M) exhibits some positive (negative) values at 850 hPa (975 hPa), indicating a large T deviation caused by transient processes near the surface.

For the different periods, we found that during 12–15 December, the largest G(P_M) values were found in subareas 4 and 5, and the maximum peak in subarea 5 coincides with the Q maximum there, indicating a large contribution of the Q meridional deviations in G(P_M) and on the SACZ ocean area extension. Between 16 and 22 December, we observe the subarea 3 dominance both in Q and on the generation components, and a strong reduction in subareas 4 and 5, corroborated with synoptic analysis. As discussed before, the lowering of height seen around subarea 3 improves the convection and so increases Q in this subarea. The large negative G(P_M) values observed around 250 hPa in subarea 5 during this period were favored by the strong influence of wave trains that drove a sharp change in the trends of meridional temperature deviations from negative (−0.06°K, at 1200 UTC 21 December) to positive (0.10°K, at 1200 UTC 22 December), leading to a strong negative covariance between Q and T deviations (Fig. 4b′). In the tropics and subtropics, G(P_M) was larger during this period, which is consistent with the convection expansion and the increased meridional temperature gradient in those areas. Finally, during 23–26 December, G(P_M) became large again in subarea 4, indicating strong activities related to transient wave processes in the southernmost areas. In general, Q values in subareas 1, 2, and 3 had less impact in G(P_M) mainly during 12–15 and 23–26 December, because the meridional temperature gradient in those areas was weaker.

The G(P_E) profiles also had large positive values between middle to upper levels (maxima peaks around 400 hPa), mainly when the event had been northernmost. Considerable contributions at low troposphere levels (below 850 hPa) are also observed in the tropics and subtropics (Fig. 4″), revealing the low-level heating and cumulus clouds presence in those SACZ areas. By analyzing each period, it was observed that during 12–15 December, the large G(P_E) values were found above 500 hPa in 2, 4, and 5 subareas (Fig. 4a″). On the other hand, during 16–22 December, the largest contributions were found in subarea 3 (Fig. 4b″) where the wave train favored the convection and increased the covariance between Q and T deviations. In the last period, the wave train led to increasing G(P_E) subarea 4 (Fig. 4c″). These results show the regions where the positive (negative) covariance between the zonal and temporal deviations of Q and T is larger (smaller).

It should be noted that in the tropics, the G(P_E) values had maxima peaks above 300 hPa, indicating that the potential energy is also generated in the upper troposphere–lower stratosphere region, and this can be reflecting the deep convection from large cumulonimbus clouds that throw a lot of energy over the low stratosphere.

In general, potential energy from both forms was generated at low and upper levels (below 800 hPa and above 400 hPa) in the tropics/subtropics and between 600 and 300 hPa in the southernmost subareas (3, 4, and 5) but was destroyed below 850 hPa in higher latitudes of the SACZ (subareas 4 and 5). This shows the important role played by boundary layer diabatic heating in the tropics, as happens in the Bolivian Altiplano (Fig. 3) and the diabatic heating effects from the convective disturbance in higher latitudes. These results are confirmed in its spatial structure (Fig. 5), where it is observed that on the tropics and subtropics, G(P_E) is positive in the SACZ and intertropical convergence zone (ITCZ) activity areas and near the Andes Mountains on its east side. The value of G(P_E) is also positive at high latitudes over the regions of storm tracks (Trenberth 1991; Hoskins and Hodges 2005; Graff and Lacasce 2012), where the positive covariance between temporal and zonal variations of T and Q is larger. During the final period, G(P_E) was negative in parts of the subareas 3 and 4 (Fig. 5c′), which indicates the break-event pattern. G(P_E) results also reveal that the SACZ ocean extension was mainly maintained by transient processes on 16–22 December (Figs. 5b″,b′″) and by quasi-stationary processes between 23 and 26 December (Figs. 5c″,c′″), showing the importance of those types of atmospheric processes on the energy generation for the SACZ events.

Briefly, until here we showed that the release of latent heat through diabatic heat has a significant impact on energy generation for SACZ events, and this happens mainly from middle to upper levels. Significant contributions were also observed at low levels in the tropics, subtropics, and the last subarea. The next step consists of investigating the energy cycle and analyzing how the observed patterns in the synoptic analysis are reflected in the LEC.

c. Analysis of the LEC components

In this section, we analyze all LEC components and the vertical structures of the energy components (P_M, P_E, K_M, and K_E) for the SACZ event that occurred from 12 to 26 December 2013.

Figure 6 displays the volume integral results for the energy cycle during the event in the five subareas. We also computed the LEC using a larger domain, but the differences were not significant for many LEC terms, so their results will not be shown. The analysis was based on the average of the subareas that were arranged over the SACZ location pattern and followed the convection area changes during the event (see Fig. 3). Thus, Fig. 6 refers to the averages when the event’s most convective area was in its most central position (SACZ-CP) on 12–15 December, the northernmost pattern (SACZ-NP) from 16 to 22 December, and finally when the convection was again slightly confined near SACZ-CP, which we also denote as SACZ-CP, between 23 and 26 December 2013.

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Results of the LEC model for SACZ. Average for the period of (a) 12–15 Dec, (b) 16–22 Dec, (c) 23–26 Dec, and (d) 12–26 Dec 2013 (on the left side) and for the SACZ climatology (Clim for 67 SACZ episodes, on the right side). The symbols ↗ and ↘ in (b) and (c) were used to highlight whether an increase and decrease in the variable value was observed in relation to its previous value, respectively. The units are at 10⁵ J m⁻² for energy and W m⁻² for trends, conversion rate terms, generation, and dissipation.

Citation: Journal of the Atmospheric Sciences 80, 9; 10.1175/JAS-D-22-0245.1

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According to Fig. 6, in the first period, 12–15 December, the net heat balance (heating/cooling) in low and high latitudes over the SACZ region resulted in a notably high G(P_M) of 40.21 W m⁻². The P_M is converted to P_E at an average rate of 1.79 W m⁻², through baroclinic processes. Similarly, due to the heat supply (heating/cooling between continent/ocean and clouds), P_E was generated with a mean rate of 2.23 W m⁻². The C(P_E, K_E) term reveals that P_E was the primary source of K_E, accounting for 3.47 W m⁻², which is more than 3 times the absolute value of the conversion component from K_E to K_M [C(K_E, K_M) = −1.02 W m⁻², barotropic instability]. Another notable result is found in the dissipation D(K_M) at a mean rate of 37.77 W m⁻², indicating that a significant energy rate has been transferred to aspects of the mean flow that are not represented on the data grid resolution and to other processes such as cooling and dissipative friction.

The contributions of energy transport terms in the first period were dominated by B(K_M), with −4.34 W m⁻² mean, acting as a component that reduces the K_M trends, $\partial K_M/\partial t<0$. B(P_M) is positive (with 1.99 W m⁻² mean), meaning that the heat transport at the boundaries acted as an additional source to maintain the P_M increase. However, P_M gives a lot of energy to K_M (about 40.79 W m⁻²), and this favored the P_M fall ($\partial P_M/\partial t<0$). Although the B(P_E) and B(K_E) terms are negatives as observed in B(K_M), indicating that they acted as sinks of those energy types (P_E and K_E), the trends of eddy energy terms ($\partial P_E/\partial t$ and $\partial K_E/\partial t$) are slightly positive which means that other sources of P_E [G(P_E) > 0 and C(P_M, P_E) > 0] and K_E [C(P_E, K_E) > 0 and C(K_E, K_M) < 0] performed an important role to maintain the eddies activity.

For reservoir components, we observe that during this period the temporal and horizontal temperature variation in the SACZ area resulted in P_M and P_E of 1.17 × 10⁵ and 1.23 × 10⁵ J m⁻², respectively. K_M is by far the largest reservoir component, with 10.76 × 10⁵ J m⁻² mean, showing the significant influence of the subtropical jet in the event region. The K_E is 2.72 × 10⁵ J m⁻² (more than the sum of P_M and P_E), indicating that there are significant eddy wind activities in the area.

During 12–15 December, the negative tendencies for $\partial P_M/\partial t$ and $\partial K_M/\partial t$ (−0.38 and −2.35 W m⁻²) lead to decreases the P_M and K_M in the period of 16–22 December. Similarly, the positive tendencies for the eddies $\partial P_E/\partial t$ and $\partial K_E/\partial t$ (0.02 and 0.04 W m⁻²) may explain the larger values of P_E and K_E in the second period. Despite the fact that tendencies were still positive during 16–22 December, the P_E term was slightly smaller in the last period (23–26 December). The reasons for this were the decrease in its sources [G(P_E) and C(P_M, P_E)] during the last period.

It can be seen from Fig. 6 that the kinetic energy dissipation components, D(K_M) and D(K_E), have large values, 37.77 and 3.08 W m⁻², respectively. Those terms are defined in Eqs. (3) and (4) as residuals from the balance of the tendency, the conversions, and the boundary terms. In fact, the dissipation terms are related to the scale of events that are not represented in the resolution of the data. They include not only the energy dissipated by friction and cooling but also the direct energy cascade to the smaller eddies that are not represented by the data grid (0.5° × 0.5°) used in this analysis. This large residual (dissipation) rate helps to account for the large conversion rate C(P_M, K_M) (40.79 W m⁻²) that does not affect the growth rate of K_M ($\partial K_M/\partial t\hspace{0.17em}=-2.35\mathrm{W}{\mathrm{m}}^{-2}$). This is an indication that part of that conversion can migrate to small-scale flow.

During the established period, 16–22 December, SACZ convective area expanded to the north and was extremely intense in the subareas 1, 2, and 3, resulting in a 25% increase in the K_E (3.39 × 10⁵ J m⁻²) compared to the previous period. P_E was greater than in the initial period, indicating that the continent-ocean thermal contrast was greater throughout this period. This was primarily the result of the greatest zonal temperature gradient maintained by horizontal and vertical sensible heat transport [C(P_M, P_E) > 0 and G(P_E) > 0] in the subareas 3, 4, and 5. These results were confirmed from a more detailed analysis of the P_E mean values for each subarea which were 11.25% and 38.08% higher on average in subareas 3 and 5 compared to other periods (12–15 and 23–26 December, SACZ-CP). Still, during 16–22 December, P_M was about 30% less in subarea 5 compared to the other periods, evidencing the wave train influence. According to Gutierrez et al. (2009), the thermal circulations induced by very strong baroclinic eddies are predominant in these areas, therefore acting to destabilize the atmosphere as seen in previous discussions.

The generation of P_M, G(P_M), the K_M dissipation, D(K_M), and the conversion rate from P_M to K_M, C(P_M, K_M), with mean of 19.68, 16.22, and 19.84 W m⁻², respectively, were reduced to about half of the values of the first period. This decrease was not observed in the dissipation of eddy kinetic energy, D(K_E), which grew by almost 6%, reaching 3.27 W m⁻² in this period.

In the last period, between 23 and 26 December 2013, generation terms reveal that, due to the negative correlation between heating and temperature deviation, P_M was destroyed [G(P_M)= −16.22 W m⁻²]. The G(P_E) decreased below half of its value in the initial period (with negative values in the last 18 h). This shows a break of the SACZ pattern at the finish of this period (Figs. 5 and B1f). As observed in the onset and mature stages, the barotropic conversion favored the increase of K_E in the SACZ regions by draining energy from K_M [C(K_E, K_M) < 0, barotropic instability], with a stronger rate of −1.24 W m⁻², indicating the domain of barotropic instability during this period. In addition, during this period, K_M transfers energy to P_M [C(P_M, K_M) < 0], resulting in a liquid cooling in the southernmost regions and higher energy consumption by the indirect local zonal mean circulation (Kim and Kim 2013). During the final period, the boundary flow terms acted as sources for P_M, P_E, K_M, and K_E, draining energy from out of the domain at mean rates of 0.26, 0.18, 6.03, and 0.38 W m⁻², respectively. These results, besides showing that these terms can be comparable to those found for the SAMS by Gutierrez et al. (2009), also provide evidence that sensible heat and momentum transport are important to the event evolution.

Also corroborating the weakening of the event, the dissipative term D(K_M) has a negative value (−13.47 W m⁻²), showing a reverse cascade of energy and helping to account for the conversion rate [C(P_M, K_M) = −17.11 W m⁻²] from K_M to P_M. The negative dissipation, D(K_M), can serve as an indicator of the event’s end. Further studies could examine this hypothesis in other events, along with an analysis of higher-resolution data.

The mean energy trends ($\partial P_M/\partial t,\partial P_E/\partial t,\partial K_M/\partial t,\partial K_E/\partial t$) in the final period reveal the larger positive tendencies, resulting in a positive contribution for the energy reservoir. It is interesting to observe that this SACZ event remained highly active; in fact, the energy components P_E and K_E had higher values (1.39 × 10⁵ and 3.72 × 10⁵ J m⁻²) in the last period than in the beginning. This was mainly through the flow terms that play a very important role to increase the energy terms in the final periods of 23–26 December.

On average, G(P_M) was 14.54 W m⁻², indicating a strong correlation between latent heat release and meridional temperature deviations during the event. P_M was converted to P_E at a mean rate of 1.27 W m⁻², through baroclinic processes. Similarly, due to the covariance temporal and zonal deviation between heating and temperature, P_E was generated at a rate of 1.78 W m⁻². The P_E was converted to K_E at a mean rate of 2.76 W m⁻², implying the rising (sinking) of relatively warm (cold) air in the SACZ area. A portion of K_E was dissipated by friction and turbulence at a mean rate of 3.17 W m⁻². However, the barotropic instability [C(K_E, K_M) < 0 (done at a mean of −0.91 W m⁻²)] acted throughout the event which favored the eddy jet intensification in the SACZ regions. The contributions of flow terms were dominated by B(P_M) with a 1.23 W m⁻² mean. Although the contributions of the other terms [B(P_E), B(K_M), and B(K_E)] were small on the event average (12–26 December), they present nonnegligible values.

In the reservoir components, P_M in the SACZ (0.91 × 10⁵ J m⁻² on average) tends to be smaller than the global averages found by Li et al. (2007, 2011), Marques et al. (2009), Kim and Kim (2013), and Pan et al. (2017), which is consistent with the low temperature gradient in these regions (Mendonça and Bonatti 2008a; Da Silva and Satyamurty 2013). K_M is dominant with an average of 10.21 × 10⁵ J m⁻², showing the large influence of subtropical jets during the event. The temporal and zonal deviations of winds and temperature also had great importance, resulting in P_E and K_E of 1.35 × 10⁵ and 3.28 × 10⁵ J m⁻², respectively.

The positive potential energy trends suggest a large contribution from these energy generation forms. On the other hand, the positive kinetic energy trends indicate less dissipation; that is, the intensification of the winds reflected the decrease in dissipation. Those components present a negative tendency for the zonal mean state and a positive for the eddy energies.

Although the mean trends of potential energies are positive ($\partial P_M/\partial t$ and $\partial P_E/\partial t>0$) between 16 and 26 December, some facts are indicating that the atmosphere in the SACZ area becomes less unstable, such as the destruction of P_M and P_E after 1800 UTC 25 December [G(P_M) and G(P_E) become negative], the energy consumption by the local zonal mean circulation [C(P_M, K_M) < 0] and the fall into half of C(P_E, K_E).

When looking at the climatology mean results of LEC (considering 67 events) obtained based on the subareas in Fig. 3a, we observed that the mean values of energy terms in this event were not significantly large when compared to the SACZ events climatology mean values. For instance, the mean potential energies represent only 30.94% and 25.77% of the P_M and P_E climatologies, respectively. In the kinetic energies, those were 95.79% for K_M and 76.29% for K_E. Furthermore, the C(P_M, P_E) for the event represents only 12.27% of the climatic average.

Despite these facts, some interesting aspects highlight the characteristics of this event: 1) the LEC climatology shows that the P_E is mainly maintained by the average state of the potential energy (P_M), which was not observed in the present event; 2) while dry baroclinic instability [G(P_E) < 0, C(P_M, P_E) > 0 and C(P_E, K_E) > 0] dominate in the climatology, in the present event the moist baroclinic instability [G(P_E) > 0, C(P_M, P_E) > 0, and C(P_E, K_E) > 0] dominated during almost the entire event (93.33% of the time, except for the last 24 h); 3) the results of C(K_E, K_M) suggest a most intense barotropic instability in this event compared to the climatology; and finally, 4) while the B(K_M) and B(K_E) contribute to decrease K_M and K_E on the climatic mean, in this event these transport components acted to amplify/increase K_M and K_E, which was important to keep jet activity active and the convection in the domain during the last period analyzed.

Figure 7 shows the time mean state during 12–26 December 2023 for the vertical structures of P_M, K_M, P_E, and K_E in the SACZ region. The profiles for the periods of 12–15 (SACZ-CP), 16–22 (SACZ-NP), and 23–26 December 2013 (SACZ-CP) are not shown. These results represent the zonal averages of each subarea of SACZ activity at each pressure–latitude point.

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Latitude–pressure profiles of the energy components (contours) and total mechanical energy (TME; shaded) for the acting area of the SACZ event. Average of (a) zonal mean available potential energy P_M, (b) zonal mean kinetic energy K_M, (c) eddy available potential energy P_E, and (d) eddy kinetic energy K_E. The contour range is 10–50 and 25 thereafter for P_M, 5–30, 10–50, and 25 thereafter for K_M, 2–10 and 5 afterward for P_E, and 2–20 and 5 thereafter for K_E. The units are at 10⁵ J m⁻² bar⁻¹ or 10² J m⁻² hPa⁻¹.

Citation: Journal of the Atmospheric Sciences 80, 9; 10.1175/JAS-D-22-0245.1

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In general, larger contributions of P_M were observed in the subtropics at low levels and to the south 35°S in the troposphere column. P_M centers are also observed at upper levels between 600 and 100 hPa in the tropics/subtropics (Fig. 7), reflecting the strong latent heating release at midlevels (see Fig. 4). The P_E structure exhibits the maxima in low troposphere levels at 20°S (Fig. 7c), which coincides with the regions of largest eddy potential energy generation [G(P_E), in subarea 3 (see Figs. 4 and 5)]. Large contributions of P_E are also found in higher latitudes than 35°S, where the low-level maxima are associated with growing extratropical cyclones (Li et al. 2007; Kim and Kim 2013). In the tropics, the centers are weaker and located in the lower troposphere between 2° and 5°S. These results indicate the low continental thermal gradient in the equatorial regions and land–sea contrast in subarea 3 (near the subtropics) which increases the zonal temperature gradient in this SACZ region and, thus, P_E values there.

The influences of tropospheric and stratospheric jets during the event are highlighted in the K_M and K_E pressure–latitude structures (Figs. 7b,d). The K_M maxima are located in jet stream regions at 200 hPa to the south of 32°S. It was observed that the maxima associated with jets were stronger/more intense and slightly displaced to the north during 12–15 and 23–26 December 2013. K_E is associated with jet perturbations and it is affected by K_M and P_E since synoptic cyclonic vortices are controlled by temperature disturbances (Li et al. 2007). The K_E maxima are also found at upper levels close to the subtropical jet regions. We find that during 12–15 December, K_E presents maximum center values (around 35 × 10⁵ J m⁻² bar⁻¹) when compared to 16–22 (25 × 10⁵ J m⁻² bar⁻¹), meaning more intense eddies wind activities in the first period. On average, K_E cores were located between K_M and P_E, which is interesting, since this shows the connection/influence of these two components in the structures and K_E maxima locations.

In Fig. 7, shading represents the TME mean for the periods analyzed. TME is given by the sum of four energy components, thus showing the effects of the winds (K_M and K_E) and temperature variation (P_M and P_E). These structures highlight the regions with the larger contributions of each type of energy. The contributions of potential energies are larger at low levels, where the zonal and meridional temperature gradients are large, and kinetic energies at high levels over the jet regions, highlighting the importance of these components and how they are connected to contribute to the event evolution.

The time series of the energy terms P_M, P_E, K_M, K_E, and TME (at the four synoptic times) are presented in Fig. 8. Temporal variation analysis of the LEC components is important to understanding the evolution of the dynamics and thermodynamics of the event. These indicate the changes related to the jets, cyclones, and anticyclones in the SACZ regions during the event.

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Time series of zonal mean available potential energy (P_M, in red), eddy available potential energy (P_E, in blue), zonal mean kinetic energy (K_M, in green), and eddy kinetic energy (K_E, in purple) average in the subareas 1–5 of the SACZ event between 0000 UTC 12 Dec and 1800 UTC 26 Dec 2013. The black dotted line is the time series for TME, equal to the sum of the four energy components.

Citation: Journal of the Atmospheric Sciences 80, 9; 10.1175/JAS-D-22-0245.1

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Throughout the event evolution, P_M and P_E terms varied between 0.25 and 1.60 × 10⁵ J m⁻². Both P_M and P_E had large contributions during the beginning and/or the end of each period analyzed. For instance, while P_M major values that contributed a lot to the event evolution were during 12–13, 20–21, 23–24, and 25 December after 1800 UTC, P_E contribution was mainly during 16–19 December (values directly reflected in Fig. 6). These alternations, beyond indicating warming/cooling and an increase in the temperature gradient in zonal and meridional directions during these periods, can also be seen as important to support the convective activities and episode duration. Likewise, the energy components associated with air mass movements ranged from 2.5 to 5 × 10⁵ J m⁻² for K_E and between 7.5 and 15 × 10⁵ J m⁻² for K_M. These results, as well as those already analyzed (in previous items), show that K_M predominates over other components in the SACZ regions, which is important to maintain the jet activities and consequently the convection in the most southern areas. It is interesting to note that the energy components time series plot shows strong energy growth in the initial times (between 0000 UTC 12 December and 0600 UTC 13 December, mainly on the P_M, K_M, and K_E where this is most evident). This indicates that the environment presented favorable conditions for the event’s evolution hours before its onset. Satellite image analysis corroborates this, showing a cloud band with the SACZ orientation one day before the event establishment.

The evolution of energy component results show that the most significant trends (highest in absolute values), observed in Fig. 6 during 12–15 December in P_M and K_M and from 23 to 26 December in the rest of the components, are reflecting the P_M and K_M strong drop observed from 0600 UTC 13 December and their increasing after 1200 UTC 25 December (Fig. 8). The time series analyses of the conversion terms (figures not shown) indicate that the K_M drop was a consequence of a drop in the conversion from P_M to K_M [C(P_M, K_M)]. This is also supported by successive P_M falls, observed from 0600 UTC 13 December forward. On the other hand, the trends during 23–26 December in P_E and K_E components are also related to the P_E trends growth and conversion component time series from P_M to P_E [C(P_M, P_E)] and C(P_E, K_E). In addition, the peaks observed in the power generations throughout the event evolution (figures also not shown) agree with the main peaks observed in potential energies (P_M and P_E), showing the agreement between generation terms and their respective energy components. Similarly, G(P_M) and G(P_E) terms calculated by Oort’s formulation [Eqs. (C5) and (C6)], reflect the main P_M and P_E peaks in the time series and represent well the heating effects for the event evolution. However, they present some discrepancies with the values found using the balance between input and output components of the energy reservoirs [Eqs. (1) and (2)]. On mean, G(P_E) calculated by Eq. (C6), is similar to the value obtained from Eq. (2) (1.78 and 1.98 W m⁻²), but G(P_M) had about 90% differences [that is, 14.54 W m⁻² in Eq. (1) and 0.93 W m⁻² by Eq. (C5)], which can be due to the energy generated in the small scale that are not represented on the data grid used and by large geopotential meridional deviation in higher latitudes that resulted in large C(P_M, K_M) values and consequently, on G(P_M) values.

Besides showing the large predominance and influence of jet streams to boost the generation of vortexes associated with the mass lifting (convection) over the SACZ southern region and evidence of the strong connection between LEC components, the results obtained give strong indications that atmospheric instability of the SACZ episodes can be explained with the LEC model.