Analysis of the dynamics and complexity of rainfalland streamflowtime series in Ceará, Brazil: integrating chaos theory, information theory, machine learningand stochastic approaches

Abstract

Situations that are initially simple and easy to understand in detail can become complicated due to the presence of chaos. Employing a new combination of methods linear systems, chaos theory and information theory, the paradigm is challenged deterministic/stochastic conventionally used in the dynamics of hydrological variables. The aim is to provide a more robust understanding of the complexity and chaos underlying these phenomena and improve the predictability of these time series. the first phase of the research focused on the detection of deterministic chaos using non-linear methods and of chaos theory. The results revealed that more than 70% of the time series of rainfall and 80% of the flows showed signs of chaos in monthly timescales, using the correlation dimension. However, the detection of chaotic series decreased as the time scales increased. The evaluation of the highest exponent of Lyapunov indicated a stronger presence of chaos in flows than in rainfall, suggesting that rainy seasons with deterministic chaos have longer predictability periods than their counterparts of flows. These findings have crucial implications for resource management. water resources and the development of integrated plans, especially considering the limitations inherent in long-term flow forecasts. The second analysis used methods from theory of information, specifically the multiscale entropy (MSE), to deepen the understanding of the complexity of time series. The MSE analysis indicated that the flows exhibit lower entropy (greater predictability) on smaller timescales, which means less complexity. Notably, a distinct decrease in complexity was observed in half of the precipitation stations, while two discharge stations in the southeast region showed an increase in entropy, suggesting greater complexity in these time series specific. These findings highlight the importance of understanding hydrological dynamics, because the complexity of these series varies both spatially and temporally. Specifically, the part northwest of the state, which is considered more complex in terms of rainfall and flow.A complexity and chaotic behavior observed in the hydrological regime of Ceará play a vital role in water resources. Taking advantage of the detection results of the chaos, the third phase of the study used 20 precipitation time series that showed chaos deterministic as input data for machine learning models. The results showed that the Support Vector Machine and Random Forest models stood out in forecasting, however, each model was adapted to unique rainfall patterns in different locations. The successful performance of these models demonstrates the potential of methods data-driven forecasting of rainfall dynamics without the need for information extensive physics. The final phase of the study applied a multi-model framework, incorporating six forecasting models, to predict short-term and long-term average annual flow. The models hybrids outperformed independent models, suggesting the effectiveness of this method to improve the accuracy of long-term forecasts. However, the study recognizes the limitation of excluding exogenous variables that can influence the flow, such as rainfall and climate indices. In In conclusion, this doctoral thesis offers a comprehensive examination of the complexities inherent to time series of precipitation and flow, in addition to providing an innovative methodology for detect, analyze and predict these series using nonlinear methods, chaos theory and theory of information. The research findings have significant potential to improve the reliability of hydrological forecasts and improve water management strategies. water resources.