# Towards a Real-Time Description of the Ionosphere:
## 2 IRI and IRTAM Models: A Brief Recall  
### Iri  
IRI is a project started in 1968 by the Committee on Space Research (COSPAR) and the International Union of Radio Science (URSI) with the aim to develop an international standard for the terrestrial ionosphere. In April 2014, IRI became the official International Standardization Organization (ISO) standard for the ionosphere [20]. The IRI model is empirical, based on ground and space data, and provides monthly medians of the electron density, electron temperature, ion temperature, and ion composition in the altitude range of 60 km to 2000 km [19]. Additionally, it provides the vertical total electron content (vTEC) from the lower boundary to a user-specified upper boundary. Other IRI outputs include the vertical ion drift near the magnetic equator, the F1-layer and spread-F occurrence probability, and the representation of auroral boundaries. The F2-layer peak plasma frequency _f_oF2, and the corresponding maximum electron density _Nm_F2, are two of the most important parameters when modeling the ionosphere and are related by the formula _Nm_F2 = 1.24 \(\times\) 10\({}^{10}\)(_o_F2)\({}^{2}\), where _Nm_F2 and _fo_F2 are, respectively, expressed in m\({}^{-3}\) and MHz. Both parameters are very important for a reliable characterization of the ionosphere for both scientific and applicative purposes [2; 30]. IRI proposes two options for modeling them: the model recommended by the Consultative Committee on International Radio (CCIR) of the International Telecommunication Union (ITU) and the model developed by a special URSI working group [31]. Both models use the same mathematical functions but are based on different datasets of ionosonde data and different methods to fill data gaps, especially over the ocean areas. The CCIR model is recommended mainly for land regions, while URSI is recommended when the region under investigation includes large ocean areas. Specifically, both models are based on a procedure of numerical mapping proposed by [PERSON] and [PERSON] [32; 33; 34], which is based on a Fourier time series describing the diurnal variation of monthly medians of _fo_F2 observed at each of the ionosonde stations considered to develop the model (about 150 in total). Legendre special functions (see [35] for further details) are then used to represent the variation of the Fourier coefficients with geographic coordinates and modify, the modified dip coordinate introduced by [PERSON] [36] to better describe the magnetic field dependence of ionospheric parameters. As driver index both models use the 12-month running mean (_IG_12) of the ionosonde-based Ionospheric Global (_IG_) index introduced by [PERSON] et al. [37]. To describe the global daily behavior of _fo_F2, both CCIR and URSI models require 988 coefficients because the diurnal trend is described through a 6 th order Fourier time series, then 13 time coefficients, and each time coefficient undergoes a harmonic spatial expansion to the 9 th order, then 76 spatial coefficients. This reasoning is valid for a specific month. The seasonal variability is added by sorting data as a function of the month of the year; then, 12 datasets of 988 coefficients are obtained. Finally, the solar activity variation is described by calculating these coefficients for two levels of solar activity, _IG_12 = 0 for low solar activity and _IG_12 = 100 for high solar activity, and then performing a linear interpolation between them (see [14] for further details). Since the IRI-2001 version, the _fo_F2 modeling is also accompanied by a storm option developed by [PERSON] et al. [38] and [PERSON] et al. [39; 40] to represent the ionosphere under magnetically disturbed conditions. It is based on the 33 h prior history of the _a_p magnetic index and gives reliable results, especially at mid latitudes. Concerning the _lnm_F2 modeling, IRI proposes three options. The first one has been developed by [PERSON] et al.