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Register a new userEnhanced Wavelet Analysis of Solar Magnetic Activity with Comparison to Global Temperature and the Central England Temperature Record
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Added by
Robert W. Johnson Jr
Publication date
2009
fields
Physics
and research's language is
English
Authors
Robert W. Johnson
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The continuous wavelet transform may be enhanced by deconvolution with the wavelet response function. After correcting for the cone-of-influence, the power spectral density of the solar magnetic record as given by the derectified yearly sunspot number is calculated, revealing a spectrum of odd harmonics of the fundamental Hale cycle, and the integrated instant power is compared to a reconstruction of global temperature in a normalized scatter plot displaying a positive correlation after the turn of the twentieth century. Comparison of the spectrum with that obtained from the Central England Temperature record suggests that some features are shared while others are not, and the scatter plot again indicates a possible correlation.
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The variation with time from 1956-2002 of the globally averaged rate of ionization produced by cosmic rays in the atmosphere is deduced and shown to have a cyclic component of period roughly twice the 11 year solar cycle period. Long term variations in the global average surface temperature as a function of time since 1956 are found to have a similar cyclic component. The cyclic variations are also observed in the solar irradiance and in the mean daily sun spot number. The cyclic variation in the cosmic ray rate is observed to be delayed by 2-4 years relative to the temperature, the solar irradiance and daily sun spot variations suggesting that the origin of the correlation is more likely to be direct solar activity than cosmic rays. Assuming that the correlation is caused by such solar activity, we deduce that the maximum recent increase in the mean surface temperature of the Earth which can be ascribed to this activity is $lesssim14%$ of the observed global warming.
Long-term geomagnetic activity presented by the aa index has been used to show that the heliospheric magnetic field has more than doubled during the last 100 years. However, serious concern has been raised on the long-term consistency of the aa index and on the centennial rise of the solar magnetic field. Here we reanalyze geomagnetic activity during the last 100 years by calculating the recently suggested IHV (Inter-Hour Variability) index as a measure of local geomagnetic activity for seven stations. We find that local geomagnetic activity at all stations follows the same qualitative long-term pattern: an increase from early 1900s to 1960, a dramatic dropout in 1960s and a (mostly weaker) increase thereafter. Moreover, at all stations, the activity at the end of the 20th century has a higher average level than at the beginning of the century. This agrees with the result based on the aa index that global geomagnetic activity, and thereby, the open solar magnetic field has indeed increased during the last 100 years. However, quantitatively, the estimated centennial increase varies greatly from one station to another. We find that the relative increase is higher at the high-latitude stations and lower at the low and mid-latitude stations. These differences may indicate that the fraction of solar wind disturbances leading to only moderate geomagnetic activity has increased during the studied time interval. We also show that the IHV index needs to be corrected for the long-term change of the daily curve, and calculate the corrected IHV values. Most dramatically, we find the centennial increase in global geomagnetic activity was considerably smaller, only about one half of that depicted by the aa index.
Textures in images can often be well modeled using self-similar processes while they may at the same time display anisotropy. The present contribution thus aims at studying jointly selfsimilarity and anisotropy by focusing on a specific classical class of Gaussian anisotropic selfsimilar processes. It will first be shown that accurate joint estimates of the anisotropy and selfsimilarity parameters are performed by replacing the standard 2D-discrete wavelet transform by the hyperbolic wavelet transform, which permits the use of different dilation factors along the horizontal and vertical axis. Defining anisotropy requires a reference direction that needs not a priori match the horizontal and vertical axes according to which the images are digitized, this discrepancy defines a rotation angle. Second, we show that this rotation angle can be jointly estimated. Third, a non parametric bootstrap based procedure is described, that provides confidence interval in addition to the estimates themselves and enables to construct an isotropy test procedure, that can be applied to a single texture image. Fourth, the robustness and versatility of the proposed analysis is illustrated by being applied to a large variety of different isotropic and anisotropic self-similar fields. As an illustration, we show that a true anisotropy built-in self-similarity can be disentangled from an isotropic self-similarity to which an anisotropic trend has been superimposed.
A tetra of sets which elements are time series of interbeats has been obtained from the databank Physionet-MIT-BIH, corresponding to the following failures at the humans heart: Obstructive Sleep Apnea, Congestive Heart Failure, and Atrial Fibrillation. Those times series has been analyzed statistically using an already known technique based on the Wavelet and Hilbert Transforms. That technique has been applied to the time series of interbeats for 87 patients, in order to find out the dynamics of the heart. The size of the times series varies around 7 to 24 h. while the kind of wavelet selected for this study has been any one of: Daubechies, Biortoghonal, and Gaussian. The analysis has been done for the complet set of scales ranging from: 1-128 heartbeats. Choosing the Biorthogonal wavelet: bior3.1, it is observed: (a) That the time series hasnt to be cutted in shorter periods, with the purpose to obtain the collapsing of the data, (b) An analytical, universal behavior of the data, for the first and second diseases, but not for the third.
We propose a 2D generalization to the $M$-band case of the dual-tree decomposition structure (initially proposed by N. Kingsbury and further investigated by I. Selesnick) based on a Hilbert pair of wavelets. We particularly address (textit{i}) the construction of the dual basis and (textit{ii}) the resulting directional analysis. We also revisit the necessary pre-processing stage in the $M$-band case. While several reconstructions are possible because of the redundancy of the representation, we propose a new optimal signal reconstruction technique, which minimizes potential estimation errors. The effectiveness of the proposed $M$-band decomposition is demonstrated via denoising comparisons on several image types (natural, texture, seismics), with various $M$-band wavelets and thresholding strategies. Significant improvements in terms of both overall noise reduction and direction preservation are observed.
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