When do finite sample effects significantly affect entropy estimates ?

An expression is proposed for determining the error caused on entropy estimates by finite sample effects. This expression is based on the Ansatz that the ranked distribution of probabilities tends to follow an empirical Zipf law.Comment: 10 pages, 2 figure

A method for filling gaps in solar irradiance and in solar proxy data

Data gaps are ubiquitous in spectral irradiance data, and yet, little effort has been put into finding robust methods for filling them. We introduce a data-adaptive and nonparametric method that allows us to fill data gaps in multi-wavelength or in multichannel records. This method, which is based on the iterative singular value decomposition, uses the coherency between simultaneous measurements at different wavelengths (or between different proxies) to fill the missing data in a self-consistent way. The interpolation is improved by handling different time scales separately. Two major assets of this method are its simplicity, with few tuneable parameters, and its robustness. Two examples of missing data are given: one from solar EUV observations, and one from solar proxy data. The method is also appropriate for building a composite out of partly overlapping records.Comment: to appear in Astronomy & Astrophysics (2011

Non-Gaussian statistics in space plasma turbulence, fractal properties and pitfalls

Magnetic field fluctuations in the vicinity of the Earth's bow shock have been investigated with the aim to characterize the intermittent behaviour of strong plasma turbulence. The observed small-scale intermittency may be the signature of a multifractal process but a deeper inspection reveals caveats in such an interpretation. Several effects, including the anisotropy of the wavefield, the violation of the Taylor hypothesis and the occasional occurrence of coherent wave packets, strongly affect the higher order statistical properties. After correcting these effects, a more Gaussian and scale-invariant wavefield is recovered.Comment: 13 pages (including 13 postscript figures), to appear in Nonlinear Processes in Geophysic

Determination of the most pertinent EUV proxy for use in thermosphere modeling

Two major issues in the specification of the thermospheric density are the definition of proper solar inputs and the empirical modeling of thermosphere response to solar and to geomagnetic forcings. This specification is crucial for the tracking of low Earth orbiting satellites. Here we address both issues by using 14 years of daily density measurements made by the Stella satellite at 813 km altitude and by carrying out a multiscale statistical analysis of various solar inputs. First, we find that the spectrally integrated solar emission between 26-34 nm offers the best overall performance in the density reconstruction. Second, we introduce linear parametric transfer function models to describe the dynamic response of the density to the solar and geomagnetic forcings. These transfer function models lead to a major error reduction and in addition open new perspectives in the physical interpretation of the thermospheric dynamics

Extracting individual contributions from their mixture: a blind source separation approach, with examples from space and laboratory plasmas

Multipoint or multichannel observations in plasmas can frequently be modelled as an instantaneous mixture of contributions (waves, emissions, ...) of different origins. Recovering the individual sources from their mixture then becomes one of the key objectives. However, unless the underlying mixing processes are well known, these situations lead to heavily underdetermined problems. Blind source separation aims at disentangling such mixtures with the least possible prior information on the sources and their mixing processes. Several powerful approaches have recently been developed, which can often provide new or deeper insight into the underlying physics. This tutorial paper briefly discusses some possible applications of blind source separation to the field of plasma physics, in which this concept is still barely known. Two examples are given. The first one shows how concurrent processes in the dynamical response of the electron temperature in a tokamak can be separated. The second example deals with solar spectral imaging in the Extreme UV and shows how empirical temperature maps can be built.Comment: expanded version of an article to appear in Contributions to Plasma Physics (2010

Synoptic solar radio observations as proxies for upper atmosphere modelling

The specification of the upper atmosphere strongly relies on solar proxies that can properly reproduce the solar energetic input in the UV. Whilst the microwave flux at 10.7 cm (also called F10.7 index) has been routinely used as a solar proxy, we show that the radio flux at other wavelengths provides valuable complementary information that enhances their value for upper atmospheric modelling. We merged daily observations from various observatories into a single homogeneous data set of fluxes at wavelengths of 30, 15, 10.7, 8 and 3.2 cm, spanning from 1957 to today. Using blind source separation (BSS), we show that their rotational modulation contains three contributions, which can be interpreted in terms of thermal bremsstrahlung and gyro-resonance emissions. The latter account for 90% of the rotational variability in the F10.7 index. Most solar proxies, such as the MgII index, are remarkably well reconstructed by simple linear combination of radio fluxes at various wavelengths. The flux at 30 cm stands out as an excellent proxy and is better suited than the F10.7 index for the modelling the thermosphere-ionosphere system, most probably because it receives a stronger contribution from thermal bremsstrahlung. This better performance is illustrated here through comparison between the observed thermospheric density, and reconstructions by the Drag Temperature Model.Comment: 13 page