3.1 Classical cold fronts

A classical cold front is identified in the synoptic charts when there are:

Fig. 1 Synoptic fields at 12:00 UTC on July 12, 2010 showing the features of a classical cold front. (a) Surface synoptic chart showing sea-level pressure (hPa, black line), thickness between 1000-500 hPa (dashed lines), the fronts position (cold front in blue, warm front in red and occluded front in purple) and surface data from synoptic weather stations plotted in conventional model. (b) Synoptic chart at 250 hPa showing geopotential height in tens of meters (white lines), streamlines (light blue lines), isotachs (kts, green shaded), upper level jets stream position and upper-data from synoptic weather stations plotted in conventional model. (c) Brightness temperature (ºC) from GOES-13 (data from the CPTEC, INPE). 

3.2 Subtropical fronts

In synoptic charts, a subtropical front presents the following features:

A weak horizontal temperature gradient at surface or weak horizontal 1000-500 hPa thickness gradient (Fig. 2). In other words, the distance between the isolines is higher than that shown in Figure 1a.

Weak or nonexistent horizontal dew point temperature gradient at surface (Fig. 2).

Gradual wind shift in the cyclonic sense (Fig. 2).

Subtropical jet stream (250 hPa) or polar jet coupled with subtropical jet, but far from the front at surface (Fig. 3a).

Cloudiness and precipitation behind of the subtropical front (Fig. 3b) similar to a cold front (Fig. 1c).

Fig. 2 Synoptic chart at 00:00 UTC on May 19, 2013 showing the features of a typical subtropical front. Sea level pressure (hPa) is represented with continuous black lines and 1000-500 hPa thickness (black dashed lines). Synoptic symbols plotted in conventional model are also shown in the figure. The zoom emphasizes that the values in the synoptic chart have weak dew point temperature gradient (see orange boxes, for example). 

Fig. 3 Synoptic fields at 00:00 Z on May 19, 2013 showing the features of a typical subtropical front. (a) Synoptic chart at 250 hPa showing the geopotential height in tens of meters (white lines), streamlines (light blue lines), isotachs (kts; green shaded), upper level jets stream position with the subtropical jet indicated by the red color and the and upper-level data from synoptic weather stations plotted in conventional model. (b) Brightness temperature (ºC) from GOES-13 (data from CPTEC, INPE). 

3.3 Baroclinic troughs

A baroclinic trough has the following features in the synoptic charts:

Fig. 4 Synoptic chart at 00:00 UTC on March 5, 2016. Sea level pressure (hPa) is represented with continuous black lines and 1000-500hPa thickness in black dashed lines. Synop symbols plotted in conventional model are also shown in the figure. 

Fig. 5 Synoptic fields at 00:00 UTC on March 5, 2016. (a) Synoptic chart at 250 hPa showing the geopotential height in tens of meters (white lines), streamlines (light blue lines), upper level jets stream position and upper data from synoptic weather stations plotted in conventional model. (b) Brightness temperature (ºC) from GOES-13 (from CPTEC, INPE). 

In summary, the main differences between classical cold fronts and baroclinic troughs over the Southern Hemisphere can be observed in Figure 6 (adapted from ^{Sanders, 2005}). Classical cold fronts are associated with more intense horizontal temperature gradient over their cold side than baroclinic troughs. Moreover, clouds and precipitation also occur on the cold side of the frontal systems while in baroclinic troughs it occurs on the warm side of these systems. As mentioned in ^{Sanders (2005)}, most of the weather forecasters confuse baroclinic troughs with classical cold fronts because in both there are cloudiness bands. Table I summarizes the principal differences between the three types of surface baroclinic zones.

Fig. 6 (a) Schematic sketches of a real cold front and (b) a baroclinic trough for the Southern Hemisphere. Adapted from ^{Sanders (2005}). 

3.4 Methods

After the identification of the different baroclinic systems with the criteria presented, the total number of classical cold fronts, subtropical fronts and baroclinic troughs passing by the eight cities along the Brazilian coast from 2010 to 2016 were computed. Furthermore, the monthly and seasonal averages (summer from December to February; autumn from March to May; winter from June to August, and spring from September to November) of these systems were determined.

From the eight studied cities, three (São Paulo, Rio de Janeiro and Vitória) have well defined dry (from May to September) and wet (from October to April) seasons (^{Kousky, 1988}; ^{Reboita et al., 2010}; ^{Marengo et al., 2012}). Hence, for these cities we also computed the total number of systems for dry and wet periods from 2010 to 2016.

In order to estimate the percentage of precipitation associated with each kind of system in the region with a well-defined dry and wet period, São Paulo was the city chosen for this analysis. For this reason, the same methodology by ^{Silva et al. (2014)}, ^{de Jesus et al. (2016)} and ^{Andrade (2017)} was applied, i.e., the precipitation from a classical cold front is one that occurs in the period between a day before (pre-frontal rain) and a day after (post-frontal rain) the passage of the cold front. The same method was applied for the precipitation associated with subtropical fronts and baroclinic troughs.

4.1 Mean annual frequency

The annual mean and the total number of classical cold fronts, subtropical fronts and baroclinic troughs for each city are shown in Figure 7. The frequency of classical cold fronts decreases from the south to the northeast coast of Brazil, while the frequency of subtropical fronts increases in this direction. On the other hand, baroclinic troughs are more frequent along southeastern Brazil (20º-15º S). The highest annual mean of classical cold fronts is registered in Porto Alegre (48 systems/year), of subtropical fronts in Vitória (~6 systems/year) and of baroclinic troughs is São Paulo and Rio de Janeiro (11 systems/year).

Fig. 7 Annual mean and total of classical cold fronts, subtropical fronts and baroclinic troughs by city in the period 2010-2016. The initial part of the arrows indicates the cities location. The frequency of the systems is shown in color boxes. The first line in each box indicates the total number of systems while the second one, the annual mean. 

4.2 Monthly and seasonal frequency

Figure 8 shows the monthly and seasonal frequency of classical cold fronts, subtropical fronts and baroclinic troughs for each city. Cold fronts are more frequent in winter followed by spring in all the cities studied (Fig. 8a, d). This result is associated with the position of the polar jet during the year. In the austral winter (summer), this jet reaches the most northerly (southerly) position and, consequently, the classical cold fronts follow it. Due to this seasonal pattern, cold fronts reach more frequently Brazil in winter. The findings here agree partly with other works about cold fronts in Brazil, such as ^{Cavalcanti and Kousky (2009)} and ^{Foss et al. (2017)}. These works, in general, used an automatic method based on the change of the wind direction from north to south quadrant to identify cold fronts. This criterion together with changes in air temperature and pressure are not enough to classify cold fronts as classical ones. Other systems can be included in the statistics, like a trough, which is also associated with change in the wind direction, but it does not have a strong horizontal temperature gradient at surface. For this reason, those works show higher frequency of cold fronts in spring in southeastern Brazil. We emphasize that to guarantee the presence of a classical cold front it is necessary to analyze the synoptic charts.

Fig. 8 Monthly and seasonal mean (2010-2016) of classical cold fronts, subtropical fronts and baroclinic troughs in the eight studied cities. 

Regarding subtropical fronts, these systems are more frequent in spring, except in Porto Alegre, where this kind of front essentially does not occur (Fig. 8b, e). The seasonality of subtropical fronts may be related with the presence of the Bolivian High during spring. This high has an associated ridge, which intensifies and amplifies towards the South Atlantic Ocean due to the strong pre-frontal warm advection caused by the frontal systems coming from the south of the continent. Consequently, by conservation of absolute vorticity, the upper level trough that is ahead of the ridge also intensifies and amplifies over the Atlantic Ocean (^{Kousky and Gan, 1981}). During this atmospheric configuration, some classical cold fronts can advance to lower latitudes, mainly over the ocean, becoming subtropical fronts.

Baroclinic troughs occur preferentially in spring and summer and are less frequent in winter (Fig. 8c, f). Most of these surface systems are associated with the displacement of a trough in the middle troposphere that moves mainly from west to east. In general, the surface troughs are coupled with the subtropical jet stream in upper levels that, when interacting with a humid and warm air mass, organize a band of cloudiness. In this situation, the latent heat released by condensation can contribute to develop a low-pressure system in the surface, i.e., a cyclogenetic process (^{Evans and Braun, 2012}; ^{Gozzo et al., 2014}). Most of these systems are weak extratropical cyclones, but in some cases, they can be subtropical cyclones (which are more frequent during the rainy season of Brazil [^{Gozzo et al., 2014}]).

4.3 Dry and rainy season in southeastern Brazil

Since Brazil has a large territory, it experiences different climate regimes (^{Reboita et al., 2010}). In the southeastern region, the most populated of the country, a rainy season from October to April and a dry season from May to September (^{Kousky, 1988}; ^{Reboita et al., 2010}; ^{Marengo et al., 2012}) predominate. Due to this feature, we also identified the frequency of baroclinic zones in the dry and wet periods (2010-2016) in São Paulo, Rio de Janeiro and Vitória (Fig. 9), which are cities located in southeastern Brazil as shown in Figure 7.

Fig. 9 Total number (2010-2016) of classical cold fronts, subtropical fronts and baroclinic troughs in the rainy (October-April) and dry (May-September) seasons from 2010 to 2016, in three cities in southeastern Brazil. 

The highest number of classical cold fronts occur during the dry season for all three cities in the southeast of Brazil: 104 systems in São Paulo, 77 in Rio de Janeiro and 53 in Vitória (Fig. 9a). Indeed, the dry period occurs concomitantly with the austral winter and it contributes to an environment favorable to the cold fronts occurrence. The frequency of subtropical fronts is slightly higher during the dry season than in the rainy season (Fig. 9b); this small difference can be associated with the influence of September, inside the dry season, and October, inside the rainy season, which are months with great frequency of subtropical fronts (Fig. 8b). During the dry season, the number of subtropical fronts detected was 15 in São Paulo, 18 in Rio de Janeiro and 21 in Vitória (Fig. 9b). Baroclinic troughs show an opposite behavior to classical cold fronts, meaning that these systems are more frequent during the rainy season. From 2010 to 2016, during the rainy season, 61, 47, and 43 baroclinic troughs were observed in São Paulo, Rio de Janeiro and Vitória, respectively (Fig. 9c). According to the CPTEC-INPE forecasters experience, the number of troughs during the rainy season is large and they are associated with the occurrence of the SACZ.

The percentage of precipitation associated with each of the three systems in relation to the total precipitation of the rainy and dry seasons was computed for São Paulo city (Fig. 10). According to Figure 9, during the rainy season in São Paulo there are more cold fronts and baroclinic troughs than subtropical fronts. This result impacts directly on precipitation, since these two baroclinic zones amount to 36.2% of precipitation. The contribution of subtropical fronts to precipitation during the rainy season is only 1.6% (Fig. 10). During the dry season, the number of classical cold fronts in São Paulo is higher than the other two baroclinic systems (Fig. 9). However, precipitation in this period is associated mainly with baroclinic troughs, 45.6% of the total (Fig. 10). A possible explanation of this behavior can be related to the combination of baroclinic troughs with higher temperatures observed over the southeastern region of Brazil during the end of the dry season (August and September). In this time of the year, convection becomes more frequent over São Paulo city and this factor can be responsible for more rain than that produced by cold fronts during the beginning of the dry season (May, June and July). At the beginning of the dry season, air masses are very dry in the southeastern region of Brazil, and the transients cannot produce significant volumes of rain. In Figure 10, the “other systems” classification refers to the instability produced by the combination of high temperatures and the presence of a humid air mass and by the passage of cyclonic disturbances in the middle troposphere.

Fig. 10 Percentage of precipitation (%) associated with classical cold fronts, subtropical fronts, baroclinic troughs and other systems during the dry and rainy seasons (2010-2016) in São Paulo city. 

In a more global analysis, during the rainy season almost 40% of the precipitation is associated with the three baroclinic systems while in the dry season this number increases to 60% (Fig. 10). This result agrees with other studies such as the one by ^{Silva et al. (2014)}, who established a climatology of cold fronts for a city in southeastern Brazil using the changes in wind direction to identify the systems. As mentioned before, this criterion does not allow the separation of subtropical fronts and baroclinic troughs from classical cold fronts. For this reason, the total precipitation associated with cold fronts in those studies is similar to the sum of precipitation provided here by classical cold fronts, subtropical fronts and baroclinic troughs.