A short-term ionospheric forecasting empirical regional model (IFERM) has been developed to predict the state of the critical frequency of the F2 layer (foF2) under different geomagnetic conditions. IFERM is based on 13 short term ionospheric forecasting empirical local models (IFELM) developed to predict foF2 at 13 ionospheric observatories scattered around the European area. The forecasting procedures were developed by taking into account, hourly measurements of foF2, hourly quiet-time reference values of foF2 (foF2_QT), and the hourly time-weighted accumulation series derived from the geomagnetic planetary index ap, (ap(τ)), for each observatory. Under the assumption that the ionospheric disturbance index ln(foF2/foF2_QT) is correlated to the integrated geomagnetic disturbance index ap(τ), a set of statistically significant regression coefficients were established for each observatory, over 12 months, over 24 h, and under 3 different ranges of geomagnetic activity. This data was then used as input to compute short-term ionospheric forecasting of foF2 at the 13 local stations under consideration. The empirical storm-time ionospheric correction model (STORM) was used to predict foF2 in two different ways: scaling both the hourly median prediction provided by IRI (STORM_foF2_MED,IRI model), and the foF2_QT values (STORM_foF2_QT model) from each local station. The comparison between the performance of STORM_foF2_MED,IRI, STORM_foF2_QT, IFELM, and the foF2_QT values, was made on the basis of root mean square deviation (r.m.s.) for a large number of periods characterized by moderate, disturbed, and very disturbed geomagnetic activity. The results showed that the 13 IFELM perform much better than STORM_foF2,sub>MED,IRI and STORM_foF2_QT especially in the eastern part of the European area during the summer months (May, June, July, and August) and equinoctial months (March, April, September, and October) under disturbed and very disturbed geomagnetic conditions, respectively. The performance of IFELM is also very good in the western and central part of the Europe during the summer months under disturbed geomagnetic conditions. STORM_foF2_MED,IRI performs particularly well in central Europe during the equinoctial months under moderate geomagnetic conditions and during the summer months under very disturbed geomagnetic conditions. The forecasting maps generated by IFERM on the basis of the results provided by the 13 IFELM, show very large areas located at middle-high and high latitudes where the foF2 predictions quite faithfully match the foF2 measurements, and consequently IFERM can be used for generating short-term forecasting maps of foF2 (up to 3 h ahead) over the European area.

This paper focuses on a detailed comparison, based on the F2-layer peak characteristics foF2 and hmF2, between the International Reference Ionosphere (IRI), which is a climatological empirical model of the terrestrial ionosphere, and the IRI Real-Time Assimilative Mapping (IRTAM) procedure, which is a real-time version of IRI based on data assimilation from a global network of ionosondes. To perform such a comparison, two different kinds of datasets have been considered: (1) foF2 and hmF2 as recorded by 40 ground-based ionosondes spread all over the world from 2000 to 2019; (2) foF2 and hmF2 from space-based COSMIC/FORMOSAT-3 radio occultation measurements recorded from 2006 to 2018. The aim of the paper is to understand whether and how much IRTAM improves IRI foF2 and hmF2 outputs for different locations and under different diurnal, seasonal, solar and magnetic activity conditions. The main outcomes of the study are: (1) when ionosonde observations are considered for validation, IRTAM significantly improves the IRI foF2 modeling both in accuracy and precision, while a slight improvement in the IRI hmF2 modeling is observed for specific locations and conditions; (2) when COSMIC observations are considered for validation, no noticeable improvement is observed from the IRTAM side for both foF2 and hmF2. Indeed, IRTAM can improve the IRI foF2 description only nearby the assimilated ionosonde locations, while the IRI hmF2 description is always more accurate and precise than IRTAM one.

A new analytical formula for H₀, one of the three parameters (H₀, g, and r) on which the NeQuick model is based to describe the altitude profile of the electron density above the F2-layer peak height hmF2, has recently been proposed. This new analytical representation of H₀, called H_0,corr, relies on numerical grids based on two different types of datasets. On one side, electron density observations by the Swarm satellites over Europe from December 2013 to September 2018, and on the other side, IRI UP (International Reference Ionosphere UPdate) maps over Europe of the critical frequency of the ordinary mode of propagation associated with the F2 layer, foF2, and hmF2, at 15 min cadence for the same period. The new NeQuick topside representation based on H_0,corr, hereafter referred to as NeQuick-corr, improved the original NeQuick topside representation. This work updates the numerical grids of H_0,corr by extending the underlying Swarm and IRI UP datasets until December 2021, thus allowing coverage of low solar activity levels, as well. Moreover, concerning Swarm, besides the original dataset, the calibrated one is considered, and corresponding grids of H_0,corr calculated. At the same time, the role of g is investigated, by considering values different from the reference one, equal to 0.125, currently adopted. To understand what are the best H_0,corr grids to be considered for the NeQuick-corr topside representation, vertical total electron content data for low, middle, and high latitudes, recorded from five low-Earth-orbit satellite missions (COSMIC/FORMOSAT-3, GRACE, METOP, TerraSAR-X, and Swarm) have been analyzed. The updated H_0,corr grids based on the original Swarm dataset with a value for g = 0.15, and the updated H_0,corr grids based on the calibrated Swarm dataset with a value for g = 0.14, are those for which the best results are obtained. The results show that the performance of the different NeQuick-corr models is reliable also for low latitudes, even though these are outside the spatial domain for which the H_0,corr grids were obtained, and are dependent on solar activity.

The ionospheric equivalent slab thickness ( $\tau $τ ) is a parameter characterizing both the distribution of the plasma in the ionosphere and the shape of the corresponding vertical electron density profile. It is calculated as the ratio of the vertical total electron content (vTEC) to the ionospheric F2-layer electron density maximum (NmF2). Since its definition dated back in the 60s, a lot of information on the behavior of $\tau $τ for different helio-geophysical conditions has been cumulated and the connection with several plasma properties has been also demonstrated. The beginning of the Global Positioning System (GPS) era in the 90s had a strong effect on the studies about $\tau $τ because GPS signals allow to obtain the vTEC up to about 20000 km of altitude. Recently, $\tau $τ has also found application in many data-assimilation methodologies, especially for the improvement of empirical ionospheric models based on near real-time data. All of these topics are reviewed and discussed in this paper based on the literature published in the last sixty years.Moreover, to highlight and summarize the main global climatological features of $\tau $τ , in this work we selected thirty-two ionospheric stations globally distributed and co-located with ground-based Global Navigation Satellite System (GNSS) receivers, for the last two solar cycles. This allowed to collect a dataset of NmF2 and vTEC that represents the largest and most complete ever analyzed for studies concerning $\tau $τ , which gave the chance to deeply investigate its spatial, diurnal, seasonal, and solar activity variations. The corresponding results are presented and discussed in the light of the existing literature.