Use of singular spectral analysis to reconstruct average monthly flow time series with complex behavior

Emprego da análise espectral singular para a reconstrução de séries temporais de vazões médias mensais com comportamento complexo

Abstract

Time series analysis is a useful tool for many practical water resource management applications, such as planning and anticipating conflict around water use. These analyses are also necessary for the use, design and operation of hydrotechnical works and for the protection of aquatic ecosystems. Basically, his review focuses on classic models such as Box and Jenkins. However, restrictive assumptions about data and residuals make its use difficult. As an alternative, non-parametric approaches are interesting due to their application versatility. One of the techniques that has been widely used in the analysis of flow time series is Singular Spectral Analysis (SSA). However, its application is concentrated as a pre-processor or in hybrid approaches and, because of this, many studies focus only on the model to be improved, leaving gaps in the process understanding that underlie the SSA. Within this context, and because of this, the objective of this study is to present the SSA technique in detail, through an application to a time series of monthly average flows with complex behavior (Jucu River, located in Southeast Brazil), in order to overcome gaps associated to a rigorous understanding of the procedures that make up the SSA. The Sequential SSA technique was used to decompose signal and noise components. The reconstructed series preserved the dynamics of the observed series, suggesting a strong influence of the signal component (trend and seasonality) on its behavior. It’s expected that the technique can be used with greater fluidity by specialists and contribute to the management of water resources.

Keywords:
decomposition; reconstruction; singular spectrum analysis