arXiv subjects

Cleber Souza Corrêa

Publications and source records attributed to Cleber Souza Corrêa.

5 recordsLinked to original sources

arXiv2026

The Extended Alpha Group Dynamic Mapping

This paper investigates the qualitative behavior of a system of ordinary differential equations (ODEs) defined by a matrix operator derived from the algebraic structure of the Alpha Group. The system depends on a rotational parameter that continuously deforms the underlying geometry of the phase space. Using a fourth-order Runge-Kutta numerical scheme, we analyze the evolution of trajectories and identify the presence of critical parameter values at which the system undergoes qualitative transitions. In particular, we observe the emergence of critical dynamical regions associated with changes in the interaction between dynamically defined subspaces. As the rotation parameter varies from $0$ to $π/2$, the system transitions from a regime with Euclidean-type geometric behavior to a non-Euclidean configuration induced by the Alpha Group structure. These transitions correspond to changes in stability and global phase space organization, including the formation of invariant structures and attractor-like behavior at infinity. The results suggest that the underlying matrix operator acts as a generator of structured transformations governing the system dynamics. This work provides a computational and qualitative framework for studying parameter-dependent dynamical systems with evolving geometric structure.

math.DG↗

arXiv2026

Statistical Analysis of Spatial and Temporal Variability of Maximum Precipitation Events on the Rio Grande do Sul

A statistical analysis of precipitation at Rio Grande do Sul State was presented in this article. The aim of this work was to identify spatial and temporal patterns of maximum precipitation, which was achieved by fitting a theoretical variogram in maximum annual rainfalls and their times of occurrence. In the literature, it was found that this pattern occurs according to phenomena typical from middle latitude, such as low and high level jets, and interactions between them. Some years ago, the relationship between maximum annual rainfalls and synoptic predominant configurations was found. Therefore, this work sought to understand the climatic characteristics that are important in Aerospace and Aeronautics, as extreme weather can cause numerous consequences in these activities. The use and validation of this proposed method would make possible its application in other regions of interest in the Brazilian aerospace. Understanding these climatological features of the atmospheric circulation dynamics, and analyzing maximum annual rainfall would allow a more efficient and appropriate climate trend forecast and its application in aerospace activities.

stat.AP↗

arXiv2026

Comparing an Ensemble Kalman Filter to a 4DVAR Data Assimilation System in Chaotic Dynamics

In this paper, the Ensemble Kalman Filter is compared with a 4DVAR Data Assimilation System in chaotic dynamics. The Lorenz model is chosen for its simplicity in structure and its dynamical similarities with primitive equation models, such as modern numerical weather forecasting. It was examined whether the Ensemble Kalman Filter and 4DVAR are effective in tracking the control for 10%, 20%, and 40% of error in the initial conditions. With 10% of noise, the trajectories of both methods are almost perfect. With 20% of noise, the differences between the simulated trajectories and the observations, as well as the true trajectories, are rather small for the Ensemble Kalman Filter but almost perfect for 4DVAR. However, the differences become increasingly significant at the later part of the integration period for the Ensemble Kalman Filter, due to the chaotic behavior of the system. For the case with 40% error in the initial conditions, neither the Ensemble Kalman Filter nor 4DVAR could track the control with only three observations ingested. To evaluate a more realistic assimilation application, an experiment was created in which the Ensemble Kalman Filter ingested a single observation at the 180th time step in the X, Y, and Z Lorenz variables, and only in the X variable. The results show a perfect fit of 4DVAR and the control during a complete integration period, but the Ensemble Kalman Filter shows disagreement after the 80th time step. On the other hand, a considerable disagreement between the Ensemble Kalman Filter trajectories and the control is observed, as well as a total failure of 4DVAR. Better results were obtained for the case in which observations cover all the components of the model vector.

nlin.CD↗

arXiv2026

Multidecadal Cycles Study in the Climate Indexes Series Using Wavelet Analysis in North/Northeast Brazil

This study investigates the climatic index time series over the most recent 80 years, using monthly mean values from the Pacific Decadal Oscillation Index (PDO), Southern Oscillation Index (SOI), and monthly solar activity represented by sunspot numbers (MS), obtained from the National Weather Service Climate Prediction Center and the World Data Center SILSO, Royal Observatory of Belgium, Brussels. The statistical software R was used with the \texttt{WaveletComp} package to generate Morlet wavelet power spectra, and bivariate cross-wavelet analysis using the \texttt{biwavelet} package. The results show predominant cycles with variability scales of 32, 64, 128, and 256 months, corresponding approximately to 2.66, 5.33, 10.66, and 21.33 years. These frequencies are observed in the period from January 1933 to September 2016, totaling 993 months (82.75 years), characterizing decadal and multidecadal variability. These multidecadal cycles (of the order of 10.66 and 21.33 years) suggest a possible association with solar activity variability and climate variability in the ocean-atmosphere system. Rainfall data from January 1951 to September 2017 were analyzed for Belém, São Luiz, Fortaleza, Natal, and Fernando de Noronha, forming a north to northeast Brazilian transect. These series show similarity with the decadal and multidecadal cycles observed in the SOI, PDO, and sunspot series.

physics.ao-ph↗

arXiv2026

Multidecadal Cycles of the Climatic Index: Sunspots that Affect North and Northeast of Brazil

Using the 1951--2017 historical series of the Atlantic Meridional Mode (AMM) index and the monthly number of sunspots, it was possible to observe a significant association between them. The use of wavelet and cross-wavelet analysis showed the presence of multidecadal cycles pronounced in eleven years, as well as cycles of 2.66 and 5.33 years. The AMM index showed, in the Sea Surface Temperature (SST) component, the presence of a weak signal of 21.33 years. The influence and association of sunspot variability on surface temperature in Northern and Northeastern regions of Brazil were investigated. Using a non-parametric statistical correlation test, the historical series of surface temperature anomalies in five locations (Belém, São Luiz, Fortaleza, Fernando de Noronha, and Natal) were compared with the monthly solar-series anomalies. The temperature series used were the minimum monthly average, the monthly average, and maximum monthly average temperatures, with their respective anomalies in relation to the mean. However, among all the series (except for São Luiz), the analyzed minimum temperature anomalies showed a negative correlation with sunspots. As a preliminary result, the analyzed climatic indices present an apparent degree of memory associated with the variability of sunspot activity.

physics.ao-ph↗