the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 15 Jan 2026
Hourly-Scale Modeling of Storm Transitions in Southern Brazil with Markov Chains
Abstract. Southern Brazil faces escalating flood risk, yet intraday storm dynamics remain under-characterized. This work presents a season-resolved, intraday Variable Length Markov Chain analysis (VLMC) of storm state transitions, using hourly precipitation from 15 INMET stations from 2007 to 2024. Storms were identified and quantified by depth, duration, and intensity, then classified into Moderate, Strong, and Very Strong states. Peak mean intensities reach 9 to 11 mm h⁻¹ in mountainous units, compared with maxima near 7 mm h⁻¹ on the coast, where mean intensities are about 3 mm h⁻¹. Storms last roughly 11 to 13 hours in the Southern Plateau and Southern Shield, and 15 to 17 hours in the Central Depression and Coastal Plain, indicating greater lowland persistence. Upward transition probabilities increase in summer, with Moderate to Strong and Strong to Very Strong reaching about 0.20 in orographic areas, while persistence of Very Strong ranges from 0.10 to 0.20 in the Southern Shield. In winter, downward transitions to Moderate exceed 0.90 across most of the domain. Chi-square diagnostics support first-order, season-specific chains with stable transition structure. These intraday, spatially resolved probabilities link geomorphology to storm persistence and provide actionable inputs for early warning, zoning, and climate risk management.
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Status: final response (author comments only)
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RC1: 'Comment on egusphere-2025-5114', Anonymous Referee #1, 31 Jan 2026
The article is well written and well structured. However, there are still some points that deserve attention in the manuscript review.Abstract: The abstract presents an excess of numerical results, which in some sections could be described in a more qualitative way, in order to avoid overloading information in a synthesis that should be concise.In addition, I recommend that the research objective be clearly separated from the methodology employed in the second sentence of the abstract.Introduction: The first and second paragraphs lack more robust justifications for the development of the study. Expand the discussion on the trends observed in precipitation extremes in the Southern Region of Brazil over the last few decades, incorporating more recent references.Furthermore, it is important to specify which main atmospheric systems are associated with these events, such as Mesoscale Convective Complexes, the South American Low-Level Jet, and frontal systems, among others. Although these aspects are explored in depth in the results, a brief mention in the Introduction would further clarify the study's physical framing.It is recommended to consider, for example, the following references:
- https://doi.org/10.1007/s00704-007-0329-x
- https://doi.org/10.1002/joc.5031
- https://doi.org/10.1002/joc.7119
- https://doi.org/10.1080/02626667.2020.1863969
- https://doi.org/10.1002/joc.7911
Reorganize the last paragraph of the Introduction to more clearly separate the motivation for the work from the specific objectives of the study.Although the research is based on hourly-scale data, this scale is not conceptually explored in the Introduction; in this context, the concept of nowcasting could be mentioned.Study Area: In Table 1, the meaning of the variable "desvest" is unclear and should be explained. In addition, the average precipitation figure needs clarification: is it an hourly average, right? Carefully review this data and detail your findings better in the text.The relationship between storm occurrence and the geomorphology of the study area could also be discussed in greater depth.Methodology: It is necessary to clarify which references supported the choice of thresholds corresponding to the 95th and 99th percentiles. In this context, the climate extremes indices proposed by ETCCDI can be mentioned, for example.Is the definition of the 5 mm threshold for characterizing storms widely adopted in the literature? How are storms with high precipitation rates in short intervals, such as 15 minutes, treated? In addition, the consideration of wind gusts could be discussed, since wind can precede precipitation and cause significant damage, operationally characterizing a storm.In line 121, it is unclear how the stations were grouped; was any clustering method used? In line 174, the stationarity of the process is assumed, but it is unclear whether it was tested or merely postulated.Results: In Figure 4, the distinction between continent and ocean does not appear.In line 207, it is worth noting that extreme events are not necessarily outliers in the physical sense; in fact, it is possible to estimate outliers within the set of extreme events.In Figure 5, it would be interesting to include the annual boxplot as well. I suggest evaluating the possibility of reorganizing the figures by precipitation intensity classes to make the comparison between seasons more efficient.The analysis regarding autumn was poorly explored. The transitional nature of this season could be better discussed, with a focus on the fact that the escalation to severe states is statistically rare during this period.In line 302, it is emphasized that not only the frontal systems themselves should be considered; Spring sometimes experiences a higher frequency of cold fronts. Therefore, it is important to highlight the role of more stable air associated with migrating anticyclones.In line 315, also mention the katabatic flow of the Andes and its interaction with the LLJ, which favors the occurrence of Mesoscale Convective Complexes in the region.Carefully review the use of abbreviations throughout the text, ensuring that all are defined on their first occurrence (for example, LLJ in lines 299 and 315).Conclusions: The conclusions are relatively weak and do not clearly demonstrate the study's scientific novelty. I recommend reducing the presentation of numerical values, which have already been extensively discussed in the results section, and emphasizing the work's original contributions and its specific practical implications more objectively.Citation: https://doi.org/10.5194/egusphere-2025-5114-RC1 -
RC2: 'Comment on egusphere-2025-5114', Alexson Caetano da Silva, 18 Feb 2026
The study investigates the sub-daily dynamics of storms in southern Brazil (Rio Grande do Sul – Drainage Area of the Lagoons, DAL), modeling transitions between storm intensity states using seasonal first-order Markov chains based on hourly precipitation data from 15 INMET stations (2007–2024).
The manuscript presents several strengths. First, the hourly scale of analysis represents a relevant contribution for the region, where most previous studies have focused on daily or monthly scales. Second, the seasonal separation of the modeling framework improves the physical consistency of the results, acknowledging the strong seasonal modulation of rainfall dynamics. In addition, the dataset is reasonably robust, comprising 15 stations and recent observations. Nevertheless, the temporal coverage (17 years) could ideally be extended to better represent long-term climatological variability. The study also offers practical applicability, providing useful insights for hydrological modeling, flood risk management, and infrastructure planning in the study region.
However, the reviewer identifies several aspects that should be strengthened before the manuscript can be considered for publication:
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Although the title refers to Variable Length Markov Chains (VLMC), the implemented framework is essentially a first-order Markov chain with seasonal segmentation. There is no comparison with second-order chains, non-homogeneous Markov models, or integration with atmospheric covariates.
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The model lacks out-of-sample validation and does not include comparisons with alternative modeling approaches, which limits the assessment of predictive skill and robustness.
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The physical discussion remains relatively superficial. The connections with the Low-Level Jet (LLJ), Mesoscale Convective Complexes (MCCs), and regional circulation patterns are predominantly qualitative and would benefit from a more quantitative analysis.
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The connection with climate change is still limited. Although CMIP6 projections are mentioned in the discussion, there is no temporal analysis of trends in transition probabilities, nor an evaluation of non-stationarity in the Markov matrices.
Therefore, prior to acceptance, the following improvements are recommended:
a) Include comparisons with Hidden Markov Models and second-order Markov chains;
b) Incorporate predictive validation (e.g., out-of-sample testing or cross-validation);
c) Test for temporal trends in the transition matrices;
d) Explore potential non-stationarity in the time series.
Overall, while the study presents relevant regional contributions, the inclusion of the above methodological and diagnostic enhancements would substantially strengthen its scientific robustness and suitability for publication in an international journal.
Citation: https://doi.org/10.5194/egusphere-2025-5114-RC2 -
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