In this study, hourly precipitation data were used to identify “storms”. A storm is defined as a continuous stretch of precipitation separated by at least 6 h of zero precipitation, with a minimum total precipitation of 5 mm. This criterion for defining a storm was adopted from previous studies to ensure comparability (Lamjiri et al., 2017; Palecki et al., 2005). For each storm, the total precipitation (mm) was estimated as the sum of hourly precipitation values from the start to the end of the event. The storm duration (h) was defined as the number of hours with a minimum total precipitation of 5 mm, from the beginning to the end of the event. The average storm intensity (mm h⁻¹) is the total precipitation divided by the storm duration. Finally, the maximum storm intensity (mm h⁻¹) is the highest hourly precipitation rate observed from the beginning to the end of the event (see Fig. 3). The variables characterizing the storm, as defined above, were spatialized as an average over the study basin.

The results of the storm characterization are presented in Fig. 4. The highest precipitation amounts occur in the Southern Plateau, with average magnitudes of approximately 29 mm per event. Total precipitation shows a decrease, being greater in the Southern Plateau (north) and decreasing toward the Coastal Plain (south), with a slight increase observed in the mountainous region of the Southern Shield.

The average storm duration is shorter in the mountainous areas of the Southern Plateau and Southern Shield, ranging between 11 and 13 h, whereas the longest-lasting storms occur in the ocean-facing foothills of the Central Depression and Coastal Plain, ranging between 14 and 17 h.

Rainfall intensities are higher in the western part of the DAL and lower near the ocean. Consequently, maximum intensities are also greater in the west, particularly in the mountainous zones of the Southern Plateau and Southern Shield, where average peak values range from 9 to 10 mm h⁻¹. In contrast, precipitation intensities are lower in the Coastal Plain, with mean values of 3 mm h⁻¹ and maximum intensities averaging around 8 mm h⁻¹.

The time series modeled with Markov chains corresponds to the Maximum Storm Intensity of the storms characterized in the previous analysis. An exploratory graphical analysis was conducted to evaluate potential seasonal differences. Figure 5 presents violin plots of the data grouped by season, alongside the annual distribution for comparison.

The results highlight clear seasonal contrasts. During summer, rainfall intensities are higher in terms of magnitude (greater extreme values between 27 and 90 mm h⁻¹), higher frequency, and variability (interquartile range between 5 to 14 mm h⁻¹). In contrast, winter exhibits the lowest intensities (extreme values between 18 and 48 mm h⁻¹), with fewer extreme events and reduced variability (interquartile range between 4 to 8 mm h⁻¹) compared to the other seasons. Spring and fall display intermediate behavior between the two opposite phases, with spring showing slightly higher rainfall intensities relative to fall. Compared to seasonal violin plots, the annual distribution appears smoother and more generalized, effectively integrating seasonal differences while maintaining the influence of extreme events. This reinforces the importance of analyzing seasonal behavior separately, as aggregation may mask distinct seasonal patterns in intensity and variability.

Considering the seasonal differences highlighted in Fig. 5, four separate time series were constructed, one for each season at every station. First-order transition matrices were then derived, and the order of each chain was verified. The χ2 values and corresponding p-values of this test are presented in Table A1. Additionally, the temporal homogeneity of the Markov chains defined by season was assessed through the transition matrices, with the χ2 statistics and p-values also reported in Table A1.

The results indicate that, for each station and season analyzed, the transition matrices exhibit homogeneous behavior consistent with first-order Markov chains. The χ2 statistics and their corresponding p-values were generally not significant (p > 0.05), suggesting that transition probabilities do not vary substantially within each station and can be considered stable over time. This outcome reinforces the suitability of applying Markov chains and validates the results obtained from modeling extreme rainfall events using this approach.

In this section, the transition probabilities between rainfall intensity states are presented, grouped by season: spring (Fig. 6), summer (Fig. 7), winter (Fig. 8), and fall (Fig. 9). The interpretation of the transition maps follows this logic: the initial state corresponds to the rows, and the subsequent state to the columns. Therefore, Figs. 6b, 7b, 8b, and 9b illustrate the probability of transitioning from the Moderate state (row) to the Strong state (column). The same logic applies to all other cells and figures presented in this section.

Figure 6 shows the transition probabilities between rainfall intensity states derived from the Markov chain modeling for spring. Upward transition probabilities, like Moderate to Strong (Fig. 6b), Strong to Very Strong (Fig. 6f), Moderate to Very Strong (Fig. 6c) are relatively low, remaining below 0.2 across the entire study area. In contrast, there is a high probability of downward transitions to the Moderate state, like Strong to Moderate (Fig. 6d) and Very Strong to Moderate (Fig. 6g), with values exceeding 0.7 throughout the region and particularly pronounced in the Coastal Plain.

Probabilities of transitioning to or persisting in the Strong state remain below 0.1 (Fig. 6b, e, h), although slightly higher in the mountainous regions of the Southern Plateau and Southern Shield. In the lowland areas of the Central Depression and Coastal Plain, the probability of maintaining Strong conditions is nearly zero. The greater persistence of the Strong state in mountainous zones may be attributed to the role of topography in modulating orographic convection, which in spring has not yet reached its peak development.

Figure 7 shows the transition probabilities between rainfall intensity states for summer. The probability of maintaining a Moderate storm state ranges between 0.7 and 0.95 (Fig. 7a, d, g), indicating strong persistence. In contrast, the probability of remaining in the Strong or Very Strong states is below 0.2 (Fig. 7b, c, e, f, h, i).

Upward transitions, like Moderate to Strong (Fig. 7b), Strong to Very Strong (Fig. 7f), and Moderate to Very Strong (Fig. 7c) display higher probabilities in summer compared to the other seasons. The probability of a Moderate to Strong transition reaches up to 0.2 in the Southern Shield, while the probability of Strong to Very Strong transitions ranges from 0.025 to 0.2 across the Central Depression and Coastal Plain. Persistence of the Very Strong state can reach 0.2, particularly in the mountainous Southern Shield (Fig. 7c, f, i).

The higher rainfall intensities in the mountainous regions coincide with the peak of convection in the area, where orographic effects enhance air uplift and favor more intense storms. Conversely, in the flat areas of the Central Depression and Coastal Plain, Very Strong events dissipate more quickly. This pattern reflects the typical behavior of plains, where the absence of topographic barriers reduces the persistence of convective systems.

Figure 8 shows the transition probabilities between rainfall intensity states for winter. During this season, extreme events are less frequent, with downward transition probabilities reaching values close to 0.9 (Fig. 8a, d, g). While Upward transition probabilities, like Moderate to Strong (Fig. 8b), Strong to Very Strong (Fig. 8f), Moderate to Very Strong (Fig. 8c), remain near 0.025. The probability of transitioning from Strong to Very Strong (Fig. 8f), or of persisting in the Very Strong (Fig. 8c, f, i), is below 0.025 across the entire study area.

In contrast, downward transitions (Strong to Moderate, Very Strong to Moderate) are dominant, with probabilities exceeding 0.9 in most of the region. Unlike summer and spring, winter does not exhibit distinct spatial patterns in the behavior of extreme events, indicating a more homogeneous distribution of rainfall intensity across the study area.

Figure 9 shows the transition probabilities between rainfall intensity states for fall. Upward transition probabilities, like Moderate to Strong (Fig. 9b), Moderate to Very Strong (Fig. 9c), remain below 0.1 across the study area. Similarly, transitions between the Strong and Very Strong states (Fig. 9f, h) are generally below 0.2, with slightly higher values observed for the Strong to Very Strong transition (Fig. 9f). This behavior reflects the transitional nature of fall, during which atmospheric conditions become less favorable for the development and intensification of convective systems. As a result, the escalation toward severe states is statistically rare, and storms tend to remain within moderate or weak intensity levels. This seasonal pattern indicates a shift from the convectively active regime of summer toward the more stable conditions characteristic of winter.

The comparative analysis of rainfall regimes throughout the year reveals well-defined patterns of persistence and transition in storm events, closely linked both to seasonal dynamics and to the particularities of regional topography. In spring, there is a marked tendency for rapid returns to moderate conditions after high-intensity episodes, a phenomenon especially evident in the Coastal Plain. By contrast, in the elevated areas of the Southern Plateau and Southern Shield, the Strong state persists more frequently, suggesting a significant influence of topography in modulating orographic convection.

During summer, rainfall dynamics become more complex: upward transitions to more intense states – Moderate to Strong and Strong to Very Strong – are more frequent, particularly concentrated in the Southern Shield, where topographic conditions act as catalysts of repeated and intense convective processes. In the lowland regions, such as the Central Depression and Coastal Plain, Very Strong events tend to dissipate more quickly, consistent with the absence of orographic forcing mechanisms that sustain convective activity.

Fall, in turn, is characterized by a remarkable stability in rainfall regimes: Moderate events predominate with little variability, and transition probabilities between states remain considerably low. This regularity suggests a more predictable rainfall pattern, marked by a more uniform distribution of precipitation. In winter, downward transitions dominate, with probabilities exceeding 90 %, and sequences of extreme events are rare. This pattern is consistent with the predominance of frontal systems, which tend to generate less intense, more homogeneous, and shorter-lived rainfall.

Taken together, the findings highlight the decisive role of topography in enhancing the intensity and persistence of summer rainfall, as well as the concentration of prolonged flood risk in the lowland areas during winter. These seasonal and spatial differences are of strategic importance for hydrological modeling and for the design of risk management policies tailored to the specific characteristics of the territory.

Our findings indicate higher probabilities of upward transitions (e.g., Strong to Very Strong) during summer, consistent with synoptic studies in the region (Sanches et al., 2019; Schumacher et al., 2016; Teixeira and Prieto, 2020b), which highlight the intensification of the Low-Level Jet and moisture convergence in this season. Moreover, Sanches et al. (2019) reported a significant increase in extreme events in December and a reduction in return periods, which aligns with the elevated upward transition probabilities observed in our study (up to 0.2 in the Southern Shield).

In winter, by contrast, our analysis shows dominant downward transitions (e.g., Very Strong to Strong), suggesting that frontal systems prevailing during this season are more stable and less convective, consistent with the findings of Teixeira and Prieto (2020a, b). However, this behavior is not solely related to the frontal systems themselves but also to the presence of more stable air masses associated with migrating anticyclones following frontal passages. This mechanism favors less intense rainfall and reduces the likelihood of consecutive extreme events, in agreement with Britto et al. (2006), who documented the frequent passage of cold fronts. Our results extend this evidence by showing that such systems quickly return to moderate conditions.

The persistence of Strong and Very Strong events in mountainous areas confirms that orography modulates the rainfall regime, enhancing air uplift and storm continuity during summer. In contrast, the rapid dissipation of extremes in the Central Depression and Coastal Plain reflects the flat topography, where the absence of orographic barriers limits convective persistence. This is consistent with previous studies (Britto et al., 2006; Guedes et al., 2019; Teixeira and Prieto, 2020a) that identified persistent events associated with frontogenesis and slow-moving cyclogenesis in mountainous zones. Our results add detail by showing that these areas exhibit higher maximum intensities (9–11 mm h⁻¹) and greater persistence of Strong states, supporting the hypothesis that relief enhances both frontal and convective rainfall.

The higher upward transition probabilities observed in summer over the Southern Shield reflect mechanisms similar to those described for MCCs, where the Low-Level Jet (LLJ) and orography favor the persistence of intense rainfall. In addition, the katabatic flow from the Andes and its interaction with the LLJ enhance low-level moisture transport and convergence, creating favorable conditions for the development and maintenance of MCCs in the region (Salio et al., 2007). Ribeiro-Viana et al. (2009) reported 22 MCCs between October and December 2003, with an average duration of 18.6 h, consistent with the persistence patterns identified in our study.

Storm characterization further revealed that rainfall events in lowland areas tend to last longer, which aligns with the increase in 5 d precipitation totals (CMax5) documented by Minuzzi and Lopez (2013). This suggests that storm persistence is a key driver of seasonal rainfall accumulation. The marked geomorphological contrasts in the study area also help explain why trend analyses do not show consistent signals across all stations, as highlighted by Melo et al. (2015). Orography not only influences trend detection but also affects the occurrence of extreme indices (R95p, R99p) (Melo et al., 2015) and the ICEXT index (Extreme Rainfall Intensity), analyzed by Minuzzi and Lopez (2013).Both studies show that relief can either attenuate or intensify extreme rainfall occurrence, producing spatially contrasting responses. In this context, the spatial variability of storm transition dynamics identified in this study may also reflect differences in how local precipitation regimes respond to ongoing climate variability. Although the temporal homogeneity analysis performed in this study supports the assumption of stationary transition probabilities within the analyzed period, these results should be interpreted within the relatively short observational window

Furthermore, across southern Brazil, including Paraná, Santa Catarina, and Rio Grande do Sul, multi-model projections from CMIP6 indicate stronger precipitation extremes through mid to late century. Intensity-based indices rise, with increases in RX1day and RX5day, very-wet days (R95p), and the simple daily intensity index (SDII), alongside higher frequencies of heavy-rain days (R20mm) (Avila-Diaz et al., 2020, 2023). These projected changes suggest a potential shift in the underlying transition structure of storm dynamics, where probabilities associated with more intense states may increase over time. In this sense, while the current results support a stationary framework, future climate conditions may lead to non-stationary behavior in storm transition probabilities, reinforcing the need for extended analyses under changing climate scenarios.

The heterogeneous storm patterns driven by topography highlight the need for differentiated management strategies across physiographic units. The high persistence of rainfall in the Southern Shield indicates that this region may be an important source of runoff and sediment, suggesting the need for reforestation and soil management practices to reduce flood peaks. In the plains, where extreme events may lead to prolonged flooding, priority should be given to wetland restoration and the reinforcement of early warning systems to mitigate risks. Furthermore, Marques and Möller (2008), who studied water levels in the Lagoa dos Patos, emphasized that while storms dissipate in this ecosystem, water accumulation remains significant.

These management strategies are particularly relevant in light of evidence from previous studies pointing to an increasing trend in rainfall. In this sense, Guedes et al. (2019) reported that 50 % of the stations they analyzed showed a significant increase in annual rainfall, linked to El Niño events. Also, Berlato et al. (2007) also demonstrated a generalized increase in precipitation in Rio Grande do Sul, associated with the higher frequency of El Niño. Such findings are concerning when considered alongside projections of increased El Niño frequency and intensity (Cai et al., 2014; Chen et al., 2024). Furthermore, Melo et al. (2015) estimated increases in R95p and R99p indices and projected up to 600 mm of additional annual rainfall above the 95th percentile by the end of the century in Rio Grande do Sul. Similarly, Junges et al. (2019) found a significant increase of 6.3 mm yr⁻¹ in annual precipitation, with notable seasonal increases in spring (+2.5 mm yr⁻¹) and winter (+1.9 mm yr⁻¹).