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Abstract. This work is a first statistical analysis of large scale traveling ionospheric disturbances (LSTID) in Europe using total electron content (TEC) data derived from GNSS measurements. The GNSS receiver network in Europe is dense enough to map the ionospheric perturbation TEC with high horizontal resolution. The derived perturbation TEC maps are analysed studying the effect of space weather events on the ionosphere over Europe.Equatorward propagating storm induced wave packets have been identified during several geomagnetic storms. Characteristic parameters such as velocity, wavelength and direction were estimated from the perturbation TEC maps. Showing a mean wavelength of 2000 km, a mean period of 59 min and a phase speed of 684 ms −1 in average, the perturbations are allocated to LSTID. The comparison to LSTID observed over Japan shows an equal wavelength but a considerably faster phase speed. This might be attributed to the differences in the distance to the auroral region or inclination/declination of the geomagnetic field lines.The observed correlation between the LSTID amplitudes and the Auroral Electrojet (AE) indicates that most of the wave like perturbations are exited by Joule heating. Particle precipitation effects could not be separated.

Strong ionospheric perturbations were generated by the intense geomagnetic storm on 17 March 2015. In this article, we are studying perturbations in the European‐African sector observed in the total electron content (TEC). Focal points are wavelike phenomena considered as large‐scale traveling ionospheric disturbances (LSTIDs). In the European‐African sector, the storm produced three different types of LSTIDs: (1) a concurrent TEC perturbation at all latitudes simultaneously; (2) one LSTID propagating toward the equator, having very large wave parameters (wavelength: ≈3600 km, period: ≈120 min, and speed: ≈500 m/s); and (3) several LSTIDs propagating toward the equator with typical wave parameters (wavelength: ≈2100 km, period: ≈60 min, and speed ≈600 m/s). The third type of LSTIDs is considered to be exited as most LSTIDs either due to variations in the Joule heating or variations in the Lorentz force, whereas the first two perturbation types are rather unusual in their appearance. They occurred during the partial recovery phase when the geomagnetic perturbations were minor and the interplanetary magnetic field turned northward. A westward prompt penetration electric field is considered to excite the first perturbation signature, which indicates a sudden TEC depletion. For the second LSTID type, variations in the Lorentz force because of perturbed electric fields and a minor particle precipitation effect are extracted as possible excitation mechanisms.

This paper is concerned with the construction of an iterative algorithm to solve nonlinear inverse problems with an 1 constraint. One extensively studied method to obtain a solution of such an 1 penalized problem is iterative soft-thresholding. Regrettably, such iteration schemes are computationally very intensive. A subtle alternative to iterative soft-thresholding is the projected gradient method that was quite recently proposed by Daubechies et.al. in [3]. The authors have shown that the proposed scheme is indeed numerically much thriftier. However, its current applicability is limited to linear inverse problems. In this paper we provide an extension of this approach to nonlinear problems. Adequately adapting the conditions on the (variable) thresholding parameter to the nonlinear nature, we can prove convergence in norm for this projected gradient method, with and without acceleration. A numerical verification is given in the context of nonlinear and non-ideal sensing. For this particular recovery problem we can achieve an impressive numerical performance (when comparing it to non-accelerated procedures).

[1] Although ionospheric perturbations such as traveling ionospheric disturbances have a strong impact on Global Navigation Satellite Systems (GNSS) and other space-based radio systems, the description of individual perturbations is difficult. To overcome this problem, it is suggested to use a disturbance ionosphere index (DIX) that describes the perturbation degree of the ionosphere in a less specific form as a proxy. Although such an index does not describe the exact propagation conditions at the measurement site, the estimated index number indicates the probability of a potential impact on radio systems used in communication, navigation, and remote sensing. The definition of such a DIX must take into account the following major requirements: relevance to practical needs, objective measure of ionospheric conditions, easy and reproducible computation, and availability of a reliable database. Since the total electron content has been shown in many publications to act as an outstanding parameter for quantifying the range error and also the strength of ionospheric perturbations, we propose a DIX that is based on GNSS measurements. To illustrate the use of the index, recent storms monitored in 2011 and the Halloween storm are discussed. The proposed index is a robust and objective measure of the ionospheric state, applicable to radio systems which are impacted by a highly variable perturbed ionosphere.