# Towards a Real-Time Description of the Ionosphere:
## 2 IRI and IRTAM Models: A Brief Recall
### Real-Time IRI and the IRTAM Method  
In recent years, different data-assimilation techniques have been applied with the intention of improving the IRI output. The aim is to move from the climatological representation provided by the standard IRI model to a description of the ionospheric weather conditions based on the ingestion of real-time measurements. [PERSON] et al. [45] used worldwide ionosonde data from 1986 to 1989 to obtain equivalent \(IG\) indices. [PERSON] et al. [46], [PERSON] et al. [47], [PERSON] et al. [48], and [PERSON] and [PERSON] [49] used Global Navigation Satellite System data to determine \(R_{12}\) and \(IG_{12}\) equivalent indices. Recently, [PERSON] et al. [14; 50; 51] proposed a new data-assimilation method, based on ionosonde data, to update the IRI model in the European region through the calculation of an effective \(IG_{12}\); their procedure has been recently updated by assimilating also vTEC values [52]. [PERSON] et al. [11; 12] and [PERSON] et al. [15] assimilating ionosonde F2-layer peak parameter measurements first determined an effective sunspot number which is used by the Simplified Ionospheric Regional Model [16], and then applied an interpolation technique to assimilate into IRI the full electron density profile recorded by ionosondes. The assimilation can be carried out as a post-processing activity, without requiring a real-time analysis; however, in recent years, big steps forward have been taken towards a real-time IRI, performing a real-time assimilation. With regard to this, very good results have been achieved by [PERSON] et al. [17; 18], who proposed the IRTAM method ([[http://giro.uml.edu/RTAM](http://giro.uml.edu/RTAM)]([http://giro.uml.edu/RTAM](http://giro.uml.edu/RTAM)), accessed on 30 July 2021). IRTAM assimilates real-time _fo_F2, _hm_F2, \(B_{0}\), and \(B_{1}\) measurements from the worldwide network of Digisonde stations (the Global Ionospheric Radio Observatory--GIRO) and uses the URSI procedure [31] to represent the difference between data and model and update the 988 coefficients of the corresponding harmonic expansion for the specific time of the assimilation. As a final step, IRTAM generates near real-time maps of _fo_F2, _hm_F2, \(B_{0}\), and \(B_{1}\) every 15 min. IRTAM uses the URSI procedure [31] to describe both _fo_F2 and _hm_F2; however, while for _fo_F2 this is exactly that of IRI, for _hm_F2 this was specifically implemented for IRTAM according to the work of [PERSON] et al. [53], and differs from any IRI _hm_F2 formulation. The [PERSON] et al. [53] procedure uses the URSI one to directly map the _hm_F2 values, that are those modeled by the [PERSON] et al. [41] formulation using the \(M(3000)\)F2 values provided by the URSI mapping procedure. Practically, this process is nothing else than a simple _hm_F2 re-mapping, with the purpose to standardize the formalism between _fo_F2 and _hm_F2. By virtue of this, the IRTAM _hm_F2 modeled values cannot be considered as a direct updating of the IRI _hm_F2 values. Moreover, in this paper, IRI _hm_F2 values are those output by the [PERSON] et al. [44] default option, whose formulation differs from the IRTAM one and is also based on different datasets. On the contrary, the IRTAM _fo_F2 modeled values are a direct update of the IRI _fo_F2 values, because both models rely on the same formalism. IRTAM is a four-dimensional data assimilation method because it does not merely assimilate the current data from the GIRO Digisonde network at the time of assimilation but takes into account also the prior 24 h history of the ionosphere at the assimilated station. This approach has the advantage of increasing the robustness of IRTAM by smoothing out data jitter, outliers, and low-confidence values through the diurnal Fourier analysis [17; 18]. Moreover, this approach is really suited to IRI because the time and spatial variations are strictly connected through the 988 coefficients [14]. The IRTAM data-assimilation algorithm is named NECTAR (Non-linear Error Compensation Technique for Associative Restoration, [18]).