Abstract
The complexity of hydrological data requires an understanding of its spatiotemporal evolution for effective modeling and prediction. In this study, the underlying spatiotemporal, chaotic, and nonlinear dynamics of rainfall and streamflow data at different timescales in Ceará were assessed by applying chaos theory concepts. This assessment included phase space reconstruction (PSR), correlation dimension, the largest Lyapunov exponent (LLE), nonlinear methods such as recurrence plots, and recurrence quantification analysis techniques. The results indicated that as the timescale increased, the required dimension for PSR decreased for most stations, indicating a shift in the dynamics of the variables. The presence of chaos was confirmed in 78% of the rainfall stations at a monthly timescale by the correlation dimension and positive values of LLE. For streamflow, 73% of monthly data showed indications of chaos using both methods. Values of LLE ranged from 0.02 to 0.24 and − 0.32 to 3.4 for monthly data of rainfall and streamflow, respectively. Most methods showed that the northwestern area of Ceará exhibited higher complexity. Furthermore, the extent of data complexity varied temporally, with the monthly timescale being more complex than the annual timescale. The study revealed that long-term predictions for streamflow may be ineffective for water resources in the region. The results suggested a potential for rainfall predictions up to six years in advance. These findings have implications for developing an integrated water management plan in the region and provide insight into how hydrological variables evolve over time and space.
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Data availability
Data was retrieved from the Brazilian National Water Agency (ANA) at http://www.snirh.gov.br/hidroweb/.
Code availability
The calculations and figures were made using the R software.
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Acknowledgements
This study was financed in part by the Conselho Nacional de Desenvolvimento Científico e Tecnológico - Brasil (CNPq), the Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - Brasil (CAPES), and the Fundação Cearense de Apoio ao Desenvolvimento Científico e Tecnológico (FUNCAP).
Funding
This study was financed in part by the Conselho Nacional de Desenvolvimento Científico e Tecnológico - Brasil (CNPq), the Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - Brasil (CAPES), and the Fundação Cearense de Apoio ao Desenvolvimento Científico e Tecnológico (FUNCAP).
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Conceptualization, FdAdSF and LZRR; Methodology, LZRR and FdAdSF; Validation, LZRR, FdAdSF; Formal analysis, LZRR, FdAdSF; Investigation, LZRR; Resources, FdAdSF; Writing—original draft preparation, LZRR; Writing—review & editing, LZRR, FdAdSF; Supervision, FdAdSF; Funding acquisition, FdAdSF.
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Rolim, L.Z.R., de Souza Filho, F.A. Exploring spatiotemporal chaos in hydrological data: evidence from Ceará, Brazil. Stoch Environ Res Risk Assess 37, 4513–4537 (2023). https://doi.org/10.1007/s00477-023-02501-5
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DOI: https://doi.org/10.1007/s00477-023-02501-5