scholarly journals Wavelet analysis for non-stationary, non-linear time series

2015 ◽  
Vol 2 (6) ◽  
pp. 1705-1737
Author(s):  
J. A. Schulte
Keyword(s):  
Time Series ◽  
Phase Transitions ◽  
Wavelet Analysis ◽  
Multiple Testing ◽  
Linear Time ◽  
Nonstationary Time Series ◽  
Nonlinear Interactions ◽  
Quasi Biennial Oscillation ◽  
False Discovery ◽  
Biennial Oscillation

Abstract. Methods for detecting and quantifying nonlinearities in nonstationary time series are introduced and developed. In particular, higher-order wavelet analysis was applied to an ideal time series and the Quasi-biennial Oscillation (QBO) time series. Multiple-testing problems inherent in wavelet analysis were addressed by controlling the false discovery rate. A new local autobicoherence spectrum facilitated the detection of local nonlinearities and the quantification of cycle geometry. The local autobicoherence spectrum of the QBO time series showed that the QBO time series contained a mode with a period of 28 months that was phase-coupled to a harmonic with a period of 14 months. An additional nonlinearly interacting triad was found among modes with periods of 10, 16, 26 months. Local biphase spectra determined that the nonlinear interactions were not quadratic and that the effect of the nonlinearities was to produce non-smoothly varying oscillations. The oscillations were found to be skewed so that negative QBO regimes were preferred, and also asymmetric in the sense that phase transitions between the easterly and westerly phases occurred more rapidly than those from westerly to easterly regimes.

scholarly journals Wavelet analysis for non-stationary, nonlinear time series

2016 ◽  
Vol 23 (4) ◽  
pp. 257-267 ◽  
Author(s):  
Justin A. Schulte
Keyword(s):  
Time Series ◽  
Phase Transitions ◽  
Wavelet Analysis ◽  
False Discovery Rate ◽  
Multiple Testing ◽  
Nonstationary Time Series ◽  
Nonlinear Interactions ◽  
Quasi Biennial Oscillation ◽  
False Discovery ◽  
Biennial Oscillation

Abstract. Methods for detecting and quantifying nonlinearities in nonstationary time series are introduced and developed. In particular, higher-order wavelet analysis was applied to an ideal time series and the quasi-biennial oscillation (QBO) time series. Multiple-testing problems inherent in wavelet analysis were addressed by controlling the false discovery rate. A new local autobicoherence spectrum facilitated the detection of local nonlinearities and the quantification of cycle geometry. The local autobicoherence spectrum of the QBO time series showed that the QBO time series contained a mode with a period of 28 months that was phase coupled to a harmonic with a period of 14 months. An additional nonlinearly interacting triad was found among modes with periods of 10, 16 and 26 months. Local biphase spectra determined that the nonlinear interactions were not quadratic and that the effect of the nonlinearities was to produce non-smoothly varying oscillations. The oscillations were found to be skewed so that negative QBO regimes were preferred, and also asymmetric in the sense that phase transitions between the easterly and westerly phases occurred more rapidly than those from westerly to easterly regimes.

scholarly journals Stratospheric ozone interannual variability (1995–2011) as observed by Lidar and Satellite at Mauna Loa Observatory, HI and Table Mountain Facility, CA

2012 ◽  
Vol 12 (11) ◽  
pp. 30825-30867
Author(s):  
G. Kirgis ◽  
T. Leblanc ◽  
I. S. McDermid ◽  
T. D. Walsh
Keyword(s):  
Time Series ◽  
Solar Cycle ◽  
Interannual Variability ◽  
Southern Oscillation ◽  
Stratospheric Ozone ◽  
Montreal Protocol ◽  
Quasi Biennial Oscillation ◽  
Mauna Loa ◽  
Table Mountain ◽  
Biennial Oscillation

Abstract. The Jet Propulsion Laboratory (JPL) lidars, at the Mauna Loa Observatory, Hawaii (MLO, 19.5° N, 155.6° W) and the JPL Table Mountain Facility (TMF, California, 34.5° N, 117.7° W), have been measuring vertical profiles of stratospheric ozone routinely since the early 1990's and late-1980s respectively. Interannual variability of ozone above these two sites was investigated using a multi-linear regression analysis on the deseasonalized monthly mean lidar and satellite time-series at 1 km intervals between 20 and 45 km from January 1995 to April 2011, a period of low volcanic aerosol loading. Explanatory variables representing the 11-yr solar cycle, the El Niño Southern Oscillation, the Quasi-Biennial Oscillation, the Eliassen–Palm flux, and horizontal and vertical transport were used. A new proxy, the mid-latitude ozone depleting gas index, which shows a decrease with time as an outcome of the Montreal Protocol, was introduced and compared to the more commonly used linear trend method. The analysis also compares the lidar time-series and a merged time-series obtained from the space-borne stratospheric aerosol and gas experiment II, halogen occultation experiment, and Aura-microwave limb sounder instruments. The results from both lidar and satellite measurements are consistent with recent model simulations which propose changes in tropical upwelling. Additionally, at TMF the ozone depleting gas index explains as much variance as the Quasi-Biennial Oscillation in the upper stratosphere. Over the past 17 yr a diminishing downward trend in ozone was observed before 2000 and a net increase, and sign of ozone recovery, is observed after 2005. Our results which include dynamical proxies suggest possible coupling between horizontal transport and the 11-yr solar cycle response, although a dataset spanning a period longer than one solar cycle is needed to confirm this result.

scholarly journals Variability in the speed of the Brewer–Dobson circulation as observed by Aura/MLS

2013 ◽  
Vol 13 (9) ◽  
pp. 4563-4575 ◽  
Author(s):  
T. Flury ◽  
D. L. Wu ◽  
W. G. Read
Keyword(s):  
Time Series ◽  
Interannual Variability ◽  
Lower Stratosphere ◽  
Meridional Circulation ◽  
Time Lag ◽  
Quasi Biennial Oscillation ◽  
One Year ◽  
The Tropics ◽  
Biennial Oscillation ◽  
Stratospheric Water Vapour

Abstract. We use Aura/MLS stratospheric water vapour (H2O) measurements as tracer for dynamics and infer interannual variations in the speed of the Brewer–Dobson circulation (BDC) from 2004 to 2011. We correlate one-year time series of H2O in the lower stratosphere at two subsequent pressure levels (68 hPa, ~18.8 km and 56 hPa, ~19.9 km at the Equator) and determine the time lag for best correlation. The same calculation is made on the horizontal on the 100 hPa (~16.6 km) level by correlating the H2O time series at the Equator with the ones at 40° N and 40° S. From these lag coefficients we derive the vertical and horizontal speeds of the BDC in the tropics and extra-tropics, respectively. We observe a clear interannual variability of the vertical and horizontal branch. The variability reflects signatures of the Quasi Biennial Oscillation (QBO). Our measurements confirm the QBO meridional circulation anomalies and show that the speed variations in the two branches of the BDC are out of phase and fairly well anti-correlated. Maximum ascent rates are found during the QBO easterly phase. We also find that transport of H2O towards the Northern Hemisphere (NH) is on the average two times faster than to the Southern Hemisphere (SH) with a mean speed of 1.15 m s−1 at 100 hPa. Furthermore, the speed towards the NH shows much more interannual variability with an amplitude of about 21% whilst the speed towards the SH varies by only 10%. An amplitude of 21% is also observed in the variability of the ascent rate at the Equator which is on the average 0.2 mm s−1.

The stratospheric quasi-biennial oscillation observed in the semidiurnal ground pressure data

1995 ◽  
Vol 13 (7) ◽  
pp. 740-744 ◽  
Author(s):  
H. Teitelbaum ◽  
F. Vial ◽  
P. Bauer
Keyword(s):  
Time Series ◽  
Pressure Measurements ◽  
Pressure Data ◽  
Quasi Biennial Oscillation ◽  
Ground Pressure ◽  
Trace Back ◽  
Stratospheric Balloon ◽  
Highly Correlated ◽  
Biennial Oscillation ◽  
Balloon Measurements

Abstract. Ground pressure observations made at Macao (22°N, 113°E) from 1953 to 1991 are analyzed and compared with the stratospheric quasi-biennial oscillation (QBO) data obtained during the same interval. The periods of the two phenomena and their time evolution are found to be close to each other. Furthermore, the time series of the stratospheric winds and the S2(p) QBO signature are highly correlated, thus confirming earlier analysis. On this basis, pressure measurements obtained at Batavia (now Djakarta: 6°S, 107°E) from 1870 to 1944 are used to trace back the QBO phenomenon before the advent of systematic stratospheric balloon measurements. The inferred period, which varies between 25 and 32 months, suggests that the QBO has been present in the atmosphere at least since 1870.

scholarly journals Spatiotemporal variation of the ozone QBO in MLS data by wavelet analysis

2008 ◽  
Vol 26 (12) ◽  
pp. 3719-3730 ◽  
Author(s):  
S. Fadnavis ◽  
G. Beig
Keyword(s):  
Wavelet Analysis ◽  
Vertical Structure ◽  
Meridional Circulation ◽  
Maximum Amplitude ◽  
Double Peak ◽  
Quasi Biennial Oscillation ◽  
Double Peak Structure ◽  
Peak Structure ◽  
Phase Propagation ◽  
Biennial Oscillation

Abstract. Spatiotemporal characteristics of the ozone quasi-biennial oscillation (QBO) over the tropical-subtropical stratosphere (40° S–40° N) have been examined by analyzing data from the Microwave Limb Sounder (MLS) aboard Upper Atmospheric Research Satellite (UARS) for the period 1992–1999. A combination of regression analysis and wavelet analysis combines to act as an accurate QBO filter. Wavelet analysis provides inter-annual variability of amplitude and phase of the ozone QBO in the vertical structure of tropical-subtropical stratosphere. It gives minute details of phase propagation and descend rates, which can be used as input to models. Latitude-height structure shows evidence of a secondary meridional circulation induced by the QBO as double peak structure at the equator with maximum amplitude at two pressure levels 30 hPa and 9 hPa and a node at 14 hPa. The equatorial maxima are out of phase with each other. The maximum amplitude (~1.4 ppmv) of the ozone QBO was observed near the equator at 10 hPa. Descent rate of the easterly phase is greater than westerly. The lag correlation of the ozone QBO with circulation and variation of descent rates in the vertical structure of the stratosphere are examined in detail. In the equatorial upper stratosphere ozone anomalies descent with the rate ~1.5 km/month but in tropics and subtropics (above 2 hPa) they propagate upward.

scholarly journals The role of the QBO in the inter-hemispheric coupling of summer mesospheric temperatures

2010 ◽  
Vol 10 (10) ◽  
pp. 23403-23422
Author(s):  
P. J. Espy ◽  
S. Ochoa Fernández ◽  
P. Forkman ◽  
D. Murtagh ◽  
J. Stegman
Keyword(s):  
Time Series ◽  
Planetary Wave ◽  
Wave Activity ◽  
Quasi Biennial Oscillation ◽  
Mesospheric Temperature ◽  
Stratospheric Dynamics ◽  
Time Lagged ◽  
Biennial Oscillation ◽  
Lagged Correlation

Abstract. Inter-hemispheric coupling between the polar summer mesosphere and planetary-wave activity in the extra-tropical winter stratosphere has recently been inferred using Polar Mesospheric Cloud (PMC) properties as a proxy for mesospheric temperature (Karlsson et al., 2007). Here we confirm these results using a ten-year time series of July mesospheric temperatures near 60° N derived from the hydroxyl (OH) nightglow. In addition, we show that the time/lagged correlation between these summer mesospheric temperatures and the ECMWF winter stratospheric temperatures displays a strong Quasi-Biennial Oscillation (QBO). The sign and phase of the correlation is consistent with the QBO modulation of the extra-tropical stratospheric dynamics in the Southern Hemisphere via the Holton-Tan mechanism (Holton and Tan, 1980). This lends strength to the identification of synoptic and planetary waves as the driver of the inter-hemispheric coupling, and results in a strong QBO modulation of the polar summer mesospheric temperatures.

Brain networks construction using Bayes FDR and average power function

2019 ◽  
Vol 29 (3) ◽  
pp. 866-878
Author(s):  
Piero Quatto ◽  
Nicolò Margaritella ◽  
Isa Costantini ◽  
Francesca Baglio ◽  
Massimo Garegnani ◽  
...  
Keyword(s):  
Time Series ◽  
False Discovery Rate ◽  
Correlation Coefficient ◽  
Power Function ◽  
Multiple Testing ◽  
Statistical Power ◽  
Brain Connectivity ◽  
Average Power ◽  
Statistical Error ◽  
False Discovery

Brain functional connectivity is a widely investigated topic in neuroscience. In recent years, the study of brain connectivity has been largely aided by graph theory. The link between time series recorded at multiple locations in the brain and the construction of a graph is usually an adjacency matrix. The latter converts a measure of the connectivity between two time series, typically a correlation coefficient, into a binary choice on whether the two brain locations are functionally connected or not. As a result, the choice of a threshold τ over the correlation coefficient is key. In the present work, we propose a multiple testing approach to the choice of τ that uses the Bayes false discovery rate and a new estimator of the statistical power called average power function to balance the two types of statistical error. We show that the proposed average power function estimator behaves well both in case of independence and weak dependence of the tests and it is reliable under several simulated dependence conditions. Moreover, we propose a robust method for the choice of τ using the 5% and 95% percentiles of the average power function and False Discovery Rate bootstrap distributions, respectively, to improve stability. We applied our approach to functional magnetic resonance imaging and high density electroencephalogram data.

scholarly journals Multidecadal variations of the effects of the Quasi-Biennial Oscillation on the climate system

2016 ◽  
Vol 16 (24) ◽  
pp. 15529-15543 ◽  
Author(s):  
Stefan Brönnimann ◽  
Abdul Malik ◽  
Alexander Stickler ◽  
Martin Wegmann ◽  
Christoph C. Raible ◽  
...  
Keyword(s):  
Time Series ◽  
Climate Model ◽  
Surface Air Temperature ◽  
Polar Vortex ◽  
Boreal Winter ◽  
Mean Flow ◽  
Quasi Biennial Oscillation ◽  
Large Variability ◽  
Model Simulations ◽  
Biennial Oscillation

Abstract. Effects of the Quasi-Biennial Oscillation (QBO) on tropospheric climate are not always strong or they appear only intermittently. Studying them requires long time series of both the QBO and climate variables, which has restricted previous studies to the past 30–50 years. Here we use the benefits of an existing QBO reconstruction back to 1908. We first investigate additional, newly digitized historical observations of stratospheric winds to test the reconstruction. Then we use the QBO time series to analyse atmospheric data sets (reconstructions and reanalyses) as well as the results of coupled ocean–atmosphere–chemistry climate model simulations that were forced with the reconstructed QBO. We investigate effects related to (1) tropical–extratropical interaction in the stratosphere, wave–mean flow interaction and subsequent downward propagation, and (2) interaction between deep tropical convection and stratospheric flow. We generally find weak connections, though some are statistically significant over the 100-year period and consistent with model results. Apparent multidecadal variations in the connection between the QBO and the investigated climate responses are consistent with a small effect in the presence of large variability, with one exception: the imprint on the northern polar vortex, which is seen in recent reanalysis data, is not found in the period 1908–1957. Conversely, an imprint in Berlin surface air temperature is only found in 1908–1957 but not in the recent period. Likewise, in the model simulations both links tend to appear alternatingly, suggesting a more systematic modulation due to a shift in the circulation, for example. Over the Pacific warm pool, we find increased convection during easterly QBO, mainly in boreal winter in observation-based data as well as in the model simulations, with large variability. No QBO effects were found in the Indian monsoon strength or Atlantic hurricane frequency.

scholarly journals Variability of the Brewer-Dobson circulation's meridional and vertical branch using Aura/MLS water vapor

2012 ◽  
Vol 12 (8) ◽  
pp. 21291-21320 ◽  
Author(s):  
T. Flury ◽  
D. L. Wu ◽  
W. G. Read
Keyword(s):  
Time Series ◽  
Water Vapor ◽  
Lower Stratosphere ◽  
Meridional Circulation ◽  
Time Lag ◽  
Quasi Biennial Oscillation ◽  
Stratospheric Water Vapor ◽  
One Year ◽  
The Tropics ◽  
Biennial Oscillation

Abstract. We use Aura/MLS stratospheric water vapor measurements to infer interannual variations in the speed of the Brewer-Dobson circulation (BDC) from 2004 to 2011. Stratospheric water vapor (H2O) is utilized as a tracer for dynamics and we follow its path along the vertical and meridional branch of the BDC from the tropics to mid-latitudes. We correlate one year time series of H2O in the lower stratosphere at two subsequent altitude levels (68 hPa, ~18.8 km and 56 hPa, ~19.9 km at the Equator) and determine the time lag for best correlation. The same calculation is made on the horizontal on the 100 hPa (~16.6 km) level by correlating the H2O time series at the Equator with the ones at 40° N and 40° S. From these lag coefficients we derive the vertical and horizontal speeds of the BDC in the tropics and extra-tropics respectively. We observe a clear interannual variability of the vertical and horizontal branch. The variability reflects signatures of the Quasi Biennial Oscillation (QBO). Our measurements confirm the QBO meridional circulation anomalies and show that the speed variations in the two branches of the BDC are out of phase and fairly well anti-correlated. Maximum ascent rates are found during the QBO easterly phase. We also find that the transport towards the Northern Hemisphere (NH) is on the average two times faster than to the Southern Hemisphere (SH) with a mean speed of 1.15 m s−1 at 100 hPa. Furthermore, the speed towards the NH shows much more variability with an amplitude of about 21% whilst the speed towards the SH varies by only 10%. An amplitude of 21% is also observed in the variability of the ascent rate at the Equator which is on the average 0.2 mm s−1 and hence about 5000 times slower than the meridional branch.

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