PHYSICAL REVIEW E 100, 012217 (2019) Recurrence quantification analysis with wavelet denoising and the characterization of magnetic flux emergence regions in solar photosphere B. M. F. Reis, * J. M. Rodríguez Gómez, T. S. N. Pinto, T. R. C. Stekel, L. A. Magrini, O. Mendes, L. E. A. Vieira, A. Dal Lago, and J. R. Cecatto National Institute for Space Research, São José dos Campos, São Paulo 12227-010, Brazil E. E. N. Macau National Institute for Space Research, São José dos Campos, São Paulo 12227-010, Brazil and Federal University of São Paulo, São José dos Campos, São Paulo 12247-014, Brazil J. Palacios Leibniz-Institut für Sonnenphysik (KIS), Freiburg im Breisgau, 79104, Germany M. O. Domingues † National Institute for Space Research, São José dos Campos, São Paulo 12227-010, Brazil (Received 15 December 2017; published 29 July 2019) Solar systems complexity, multiscale, and nonlinearity are governed by numerous and continuous changes where the sun magnetic fields can successfully represent many of these phenomena. Thus, nonlinear tools to study these challenging systems are required. The dynamic system recurrence approach has been successfully used to deal with this kind challenge in many scientific areas, objectively improving the recognition of state changes, randomness, and degrees of complexity that are not easily identified by traditional techniques. In this work we introduce the use of these techniques in photospheric magnetogram series. We employ a combination of recurrence quantification analysis with a preprocessing denoising wavelet analysis to characterize the complexity of the magnetic flux emergence in the solar photosphere. In particular, with the developed approach, we identify regions of evolving magnetic flux and where they present a large degree of complexity, i.e., where predictability is low, intermittence is high, and low organization is present. DOI: 10.1103/PhysRevE.100.012217 I. INTRODUCTION Recurrence plot (RP) is considered to be one of the most efficient methods to deal with nonlinear and nonstationary time series [1,2]. It allows us to properly characterize the underlying system, following its changes over time [2,3]. As RP extracts the invariant properties of the system, it can be used to understand the relationship between interactive systems. The main tool to analyze an RP is the recurrence quantifi- cation analysis (RQA), which was introduced by Zbilut and Webber [4] and is very effective to properly characterize the system dynamics and even to keep track of changes in the dyn- amics over time. However, it may be very sensitive to the presence of noise [5]. Additive noise or inbound noise may disturb the data series so that real recurrences are washed up, and so RQA presents numerical artifacts in many cases to pointing wrong results. To deal with this problem, we introduce a new preprocessing approach, based on the wavelet formalism for denoising. This new approach takes advantage * barbara.reis@inpe.br † margarete.domingues@inpe.br of the well-known denoising ability based on the amplitude and local regularity detection of the wavelet coefficients [6–8]. To verify our methodology we apply it to the character- ization of the solar magnetic field. The solar magnetic field presents a variety of phenomena in different time and spatial scales. The magnetic field is important to describe the solar activity and complex dynamics of the solar atmosphere. The dynamics in the solar photosphere from small-scale flux emer- gence to active regions shows signs of the complex behavior of magnetic fields below the surface. The characterization of magnetic flux emergence can give some ideas about the physical mechanisms that are respon- sible for solar atmospheric phenomena. The relationship be- tween the flux emergence regions and active regions has been widely studied; however, due to its complexity, many questions are still open [9]. The complex behavior of the solar atmosphere, such as the interaction of emerging flux with preexisting magnetic fields can lead to the creation of current sheets and magnetic reconnection in these regions [10]. Additionally, events from the smallest scales of the solar magnetism, such as small-scale magnetic flux intensification, coalescence, or splitting of small magnetic elements—such as bright points [11]—are fundamental to understand the surface dynamics. 2470-0045/2019/100(1)/012217(8) 012217-1 ©2019 American Physical Society