Detecting and Classifying Events in Noisy Time Series

AbstractTime series are characterized by a myriad of different shapes and structures. A number of events that appear in atmospheric time series result from as yet unidentified physical mechanisms. This is particularly the case for stable boundary layers, where the usual statistical turbulence approaches do not work well and increasing evidence relates the bulk of their dynamics to generally unknown individual events.This study explores the possibility of extracting and classifying events from time series without previous knowledge of their generating mechanisms. The goal is to group large numbers of events in a useful way that will open a pathway for the detailed study of their characteristics, and help to gain understanding of events with previously unknown origin. A two-step method is developed that extracts events from background fluctuations and groups dynamically similar events into clusters. The method is tested on artificial time series with different levels of complexity and on atmospheric turbule...

[1]  F. Ramos,et al.  Analysis of phase coherence in fully developed atmospheric turbulence: Amazon forest canopy , 2008 .

[2]  Thomas Foken,et al.  Detection of long-term coherent exchange over spruce forest using wavelet analysis , 2005 .

[3]  G. Box,et al.  Distribution of Residual Autocorrelations in Autoregressive-Integrated Moving Average Time Series Models , 1970 .

[4]  Graham J. Williams.  Data Mining with Rattle and R: The Art of Excavating Data for Knowledge Discovery , 2011 .

[5]  Yuanling Zhang,et al.  Detecting Signals from Data with Noise: Theory and Applications , 2013 .

[6]  Eamonn J. Keogh,et al.  Clustering of time-series subsequences is meaningless: implications for previous and future research , 2004, Knowledge and Information Systems.

[7]  Mario Hrastinski,et al.  Wind Regimes Associated with a Mountain Gap at the Northeastern Adriatic Coast , 2013 .

[8]  P. Alfredsson,et al.  Techniques for the Eduction of Coherent Structures from Flow Measurements in the Atmospheric Boundary Layer , 2012, Boundary-Layer Meteorology.

[9]  James M. Wilczak,et al.  Large-Scale Eddies in the Unstably Stratified Atmospheric Surface Layer. Part I: Velocity and Temperature Structure , 1984 .

[10]  Jielun Sun,et al.  Determining Wave–Turbulence Interactions in the Stable Boundary Layer , 2014 .

[11]  A. Holtslag,et al.  Stable Atmospheric Boundary Layers and Diurnal Cycles: Challenges for Weather and Climate Models , 2013 .

[12]  Xiaozhe Wang,et al.  Characteristic-Based Clustering for Time Series Data , 2006, Data Mining and Knowledge Discovery.

[13]  Tak-Chung Fu,et al.  Pattern discovery from stock time series using self-organizing maps , 2016 .

[14]  P. Perron,et al.  Trends and random walks in macroeconomic time series : Further evidence from a new approach , 1988 .

[15]  Larry Mahrt,et al.  Surface Wind Direction Variability , 2011 .

[16]  Rudolf O. Weber,et al.  Automated Classification Scheme for Wind Fields , 1995 .

[17]  S. Larsen,et al.  The Nature, Theory, and Modeling of Atmospheric Planetary Boundary Layers , 2011 .

[18]  R. Snyder,et al.  Structure Function Analysis of Two-Scale Scalar Ramps. Part II: Ramp Characteristics and Surface Renewal Flux Estimation , 2012, Boundary-Layer Meteorology.

[19]  R. Snyder,et al.  Structure Function Analysis of Two-Scale Scalar Ramps. Part I: Theory and Modelling , 2012, Boundary-Layer Meteorology.

[20]  David F. Hendry,et al.  Co-Integration, Error Correction, and the Econometric Analysis of Non-Stationary Data , 1993, Advanced texts in econometrics.

[21]  E. Macau,et al.  Searching chaos and coherent structures in the atmospheric turbulence above the Amazon forest , 2008, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[22]  F. Meixner,et al.  Analysis of Low-Frequency Turbulence Above Tall Vegetation Using a Doppler Sodar , 2006 .

[23]  Jielun Sun,et al.  Turbulence Regimes and Turbulence Intermittency in the Stable Boundary Layer during CASES-99 , 2012 .

[24]  R Core Team,et al.  R: A language and environment for statistical computing. , 2014 .

[25]  Jielun Sun,et al.  Turbulence statistics of a Kelvin-Helmholtz billow event observed in the night-time boundary layer during the Cooperative Atmosphere-Surface Exchange Study field program , 2001 .

[26]  F. Guarnieri,et al.  Comparisons between two wavelet functions in extracting coherent structures from solar wind time series , 2009 .

[27]  Vladimir E. Zakharov,et al.  Nonlinear Coherent Phenomena in Continuous Media , 2000 .

[28]  T. Foken,et al.  Organised Motion in a Tall Spruce Canopy: Temporal Scales, Structure Spacing and Terrain Effects , 2007 .

[29]  L. Mahrt,et al.  Is geometry more universal than physics in atmospheric boundary layer flow , 2012 .

[30]  Alexander Gluhovsky,et al.  On the Analysis of Atmospheric and Climatic Time Series , 2007 .

[31]  Leonard A. Smith,et al.  Distinguishing between low-dimensional dynamics and randomness in measured time series , 1992 .

[32]  Michael Ghil,et al.  ADVANCED SPECTRAL METHODS FOR CLIMATIC TIME SERIES , 2002 .

[33]  Joan Cuxart,et al.  CASES-99: a comprehensive investigation of the stable nocturnal boundary layer , 2002 .

[34]  Fei Hu,et al.  Coherent Structures Detected in Atmospheric Boundary-layer Turbulence using Wavelet transforms at Huaihe River Basin, China , 2003 .

[35]  C. W. Atta,et al.  Temperature Ramps in the Atmospheric Surface Layer. , 1979 .

[36]  Tracking Hurricanes , 1966 .

[37]  Jorg M. Hacker,et al.  The composite shape and structure of coherent eddies in the convective boundary layer , 1992 .

[38]  C. Jakob,et al.  Objective Classification of Tropical Mesoscale Convective Systems , 2009 .

[39]  T. A. Black,et al.  Coherent eddies and temperature structure functions for three contrasting surfaces. Part II: Renewal model for sensible heat flux , 1997 .

[40]  Ruey S. Tsay,et al.  Analysis of Financial Time Series , 2005 .

[41]  Serge Collineau,et al.  Detection of turbulent coherent motions in a forest canopy part II: Time-scales and conditional averages , 1993 .

[42]  Eamonn J. Keogh,et al.  On the Need for Time Series Data Mining Benchmarks: A Survey and Empirical Demonstration , 2002, Data Mining and Knowledge Discovery.

[43]  Christophe Pietras,et al.  Long-term study of coherent structures in the atmospheric surface layer , 2007 .

[44]  Douglas A. Smith,et al.  Coherent structure detection using wavelet analysis in long time-series , 2000 .

[45]  Ruey S. Tsay,et al.  Analysis of Financial Time Series: Tsay/Analysis of Financial Time Series , 2005 .

[46]  H. Storch,et al.  Statistical Analysis in Climate Research , 2000 .