Data used

Three types of data are used in this article: (1) foF2 values measured at Dakar station. This station operated from 1950 to December 1996. Our study covers the period from 1976 to 1995, that is, solar cycles 21 and 22. (2) Zurich sunspot number (Rz) for the influence of solar cycle phases and (3) Mayaud (1971, 1972, 1973, 1980)geomagnetic index, aa for geomagnetic activity impacts. For this study, foF2 diurnal variations are analyzed by considering solar cycle phases impacts.

For comparison with IRI model values we use IRI-2016 version that can be run through the website https://ccmc.gsfc.nasa.gov/modelweb/models/iri2016_vitmo.php.

Geomagnetic activity determination

Based on the strong correlation between geomagnetic index aa and solar wind velocity established by Svalgaard (1977), it is well-known, according to Legrand and Simon , Ouattara and Amory-Mazaudier (2009), Ouattara and Zerbo (2011), Zerbo et al. (2012), that disturbed activities are characterized by  and are classified into three groups: (1) recurrent activity due to solar high wind stream and Corotating interaction Region (CIRs). (2) shock activity due to Coronal Mass Ejections (CMEs) and magnetic clouds and (3) fluctuating activity, consequences of solar heliosheet fluctuation.

To better study the impact of quiet geomagnetic activity on the season; very quiet days are not selected according to the reference limit previously defined by Zerbo et al. (2011)and Gnabahou and Ouattara (2012)but rather with the objective of selecting the quietest days of the considered month. Indeed, for a given month, Mayaud (1980)specifies that the quietest days are obtained by taking  . But here, our quietest days per month are determined by taking the five days with the lowest aa. Daily aa values are obtained from the following website: http://isgi.unistra.fr/data_download.php.

Solar cycle phases determination

Solar cycle phases are determined by using the criteria given by Ouattara (2009), Ouattara and Amory-Mazaudier (2009), Zerbo et al. (2011)and Gnabahou and Ouattara (2012): (1) minimum phase:  , where Rz is the yearly average Zürich Sunspot number; (2) ascending phase:  and Rz greater than the previous year’s value; (3) maximum phase:  [for small solar cycles (solar cycles with Sunspot number maximum (Rz max) less than 100), the maximum phase is obtained by considering ; and (4) descending phase:   and Rz less than the previous year’s values. Based on this criterion of splitting the solar phases of both SC 21 and SC 22 concerned by the study, and in order to obtain a good  distribution  of  the  data  of the study according to solar activity, the first years of each solar phase were considered representative of the solar phase. The retained days per solar cycle phases over selected months are mentioned in Table 1.

Data analysis methods

This article aims to study foF2 hourly variations over solar cycle phases. To appreciate IRI model predictions, we will compare foF2 values from the URSI and CCIR subroutines of IRI-2016 model with those of Dakar station measured data. For this we will use error bars in the graphs given by the following equation:

where V is the variance defined by  with  mean value and N the total number of observations for a particular dataset.

The two types of analyses will be carried out: (1) comparison between foF2 profiles and the five standard profiles established by Faynot and Vila (1979)for African equatorial ionization anomaly (EIA) region and (2) quantitative analysis based on comparison between foF2 observed data profiles with those of both IRI-2016 subroutines.

The five standard profiles established by Faynot and Vila are linked to the nature, the strength or the absence of electric currents in the E layer of ionosphere (Dunford, 1967; Acharya et al., 2010, 2011; Vassal, 1982a, b); these are: "Noon bite out" or “B” profile characterized by a double peak (morning and evening) with a trough around midday; "Reversed" or “R” profile characterized by a single peak at evening; "Morning pic" or “M” profile characterized by a single maximum at morning; "Plateau" or “P” profile characterized by an ionization plateau during daytime and "Dome profile" or “D” profile characterized by a single maximum around noon. These five profiles express respectively signature of a high electrojet, an important afternoon conter-electrojet, moderate electrojet, a weak electrojet and absence of electrojet (Vassal, 1982a, b). Comparison of foF2 measured data with those of both IRI-2016 subroutines will be done by determining relative deviation of foF2 defined by:

where  are respectively model and experimental foF2 values. σfoF2 is the relative deviation with the following appreciation:

  model overestimates the experimental foF2 value;  model underestimates the experimental foF2 value;  model predictions are suitable.

Figure 1 shows foF2 diurnal time variation in left column and relative deviation percentage  in right column for minimum (panel “a”), increasing (panel “b”), maximum (panel “c”) and decreasing (panel “d”) phases of our both solar cycles. Observed data from Dakar station are represented by solid line while IRI-2016 predictions profiles are in dotted (for URSI) and in dash lines (for CCIR).

Therefore, at solar minimum, CCIR underestimates experimental data more than URSI, while URSI overestimates more than CCIR. Nevertheless, we note  a more suitable prediction of the model by day than by night. Indeed, σfoF2's curves present values within  ±10% from  0500  to  1900 LT for both subroutines, except from 0600 to 0800 LT for URSI and from 0600 to 0900 LT for CCIR.

During increasing phase (see panel "b"), all profiles are type "R". Experimental data afternoon peak is observed at 1700 LT, simultaneously with that of CCIR and one hour after that of URSI. σfoF2 curves show that both model’s subroutines overestimate experimental data by night (2000 to 0500 LT), except from 0100 to 0200 LT for CCIR and around 0400 LT for URSI. Furthermore, model underestimates measured data in the morning from 0600 to 0900 LT for CCIR and from 0600 to 0800 LT for URSI. Negative peaks are observed at 0700 LT for URSI (-17.8%) and for CCIR (-32.7%) and positive peaks at 2300 LT for URSI (+44.6%) and for CCIR (+49%).Therefore, during ascending phase, CCIR underestimates and overestimates the observed data more than URSI. Nevertheless, one notices a suitable prediction of the model by day than by night. Indeed, σfoF2 curves present values within ±10% in the morning (0500-0600 LT) and from 0900 to 2000 LT for CCIR; and throughout the day (0800-2000 LT) and from 0100 to 0200 LT, 0300 to 0400 LT and 0500 to 0600 LT for URSI.

Solar maximum (see panel "c"), experimental data curve presents a "B" profile with a late trough around 1400 LT while the model curves present "R" profiles. Experimental data afternoon peak is observed at 1700 LT, simultaneously with that of CCIR and two hours after that of URSI. Thus, experimental data profile shows a high electrojet (signature of the vertical drift E×B) presence while model predictions profiles indicate an intense counter electrojet presence. We deduce that IRI-2016 does not reproduce the upward vertical drift E×B at solar maximum. σfoF2 curves show that model's both subroutines overestimate the experimental data by night for CCIR (1900-2300 LT and 0200-0600 LT) and for URSI (2000-2300 LT); and also, before sunrise (0400-0600 LT) and in the afternoon (14-1600 LT) for URSI. Positive peaks are observed at 2200 LT for URSI (+ 52.9) and CCIR (+66.7%). The negative peak of URSI (-19.9%) is observed at 0100 LT and that of CCIR (-7.4%) is observed at 0700 LT. Therefore, at solar maximum, experimental data are more overestimated by CCIR while they are more underestimated by URSI. Nevertheless, one notices a suitable prediction of the model by day than by night. Indeed, σfoF2 curves present values within ±10% from 0200 to 1300 LT (except around 0500 LT) and from 1600 to 2000 LT for URSI and during the night (2300-0200 LT) and all the day (0600-2000 LT) for CCIR.

During decreasing phase (see panel "d") model curves present "R" profiles while experimental data curve presents a "B" profile with a trough around local noon and an afternoon peak higher than that of the morning and very close to those of the model. Experimental data afternoon peak is observed at 1700 LT, simultaneously with that of CCIR, and one hour after that of URSI. Experimental  data   profile   indicates   a   high  electrojet  (signature of the upward vertical drift  E x B) presence associated with an intense counter-electrojet. Only the latter is indicated by model's curves. Thus, IRI-2016 model does not reproduce the upward vertical drift E x B during decreasing phase. σfoF2 curves show that both subroutines overestimate the experimental data during night for CCIR (2000-0500 LT, except around 0200 LT) and for URSI (2000-0500 LT, except after 0100 to 0300 LT). This overestimation is also observed in the morning (0600-0800 LT) for CCIR. Positive peaks are observed at 2300 LT for URSI (+ 36%) and CCIR (+ 44.1%). URSI's negative peak (-5.8%) is observed at 1000 LT and the one of CCIR (-12.2%) is observed at 0700 LT. Therefore, during decreasing phase, CCIR underestimates and overestimates the experimental data more than URSI. Nevertheless, one can note an appropriate prediction of the model by day than by night. Indeed, σfoF2 curves present values within ±10% at night (0100 to 0300 LT) and throughout the day (0400-2000 LT) for URSI and around 0200LT, at dawn (0500- 0600 LT) and all the daytime (0800-2000 LT) for CCIR.

Generally, we observe that experimental data afternoon peak appears simultaneously with that of CCIR subroutine and one hour after that of URSI during all phases of both solar cycles. Also, IRI-2016 model does not reproduce the upward vertical drift E×B when it appears. This result is the same as that found by Ouattara (2013)and Ouattara and Nanema (2014) by comparing the IRI-2007's and the IRI-2012's predictions respectively with Ouagadougou experimental data. But, Guibula et al. (2019)showed, by comparing IRI-2012's predictions with Korhogo experimental data, that URSI well presents the E×B drift during increasing and decreasing solar phases while CCIR does not reproduce it whatever the solar phase. On the other hand, at Dakar station, located on the crest of the equatorial zone, we observe that URSI does not reproduce it.

Quantitative analysis of both subroutines predictions proves that predictions are better by day than by night (precisely before 1900 LT at solar minimum and before 2000 LT for the other solar phases). Time interval during which model predictions are suitable is greater for URSI than for CCIR, except at solar maximum. Model predictions are better for URSI than for CCIR like as been already demonstrated by Guibula et al. (2019)at Korhogo Station. These results prove not only the importance to include the electrodynamic mechanisms of the Equatorial Ionization Anomaly region F2 layer in the IRI model's configuration parameters, but also taking into account the singularity of the equatorial region crest. Indeed, the upward drift being the equatorial zone characteristic phenomenon, it goes without saying that the IRI model, parameterized with characteristic phenomena in particular in the mid-latitude zone, cannot reproduce the E × B drift as well as possible. In addition, it is well known that at night, the predominant recombination processes in the F2 layer contribute to the drop in electron density; on other hand in high latitude regions this electron loss is compensated by the electron precipitation phenomena in the auroral zone. These high latitude regions electrodynamic phenomena could explain IRI-2016's poor prediction by night in equatorial zone.

This study shows that IRI-2016 model gives a good prediction of foF2 variation at Dakar Station, especially during day time. Model's peaks match those of observed foF2 data. In addition, model's subroutines do not express the signature of E×B when it appears. They show intense counter-electrojet at the place of high electrojet. Predictions are better during the minimum and ascending solar phases and they are poor during the maximum and decreasing solar phases. We suggest the integration of electrodynamic phenomena characteristic of low latitudes (E × B drift or electrojet, recombination processes, etc.) in the IRI model configuration parameters to improve its accuracy.

The authors have not declared any conflict of interests.

The authors thank Brest Telecom of Bretagne for providing Dakar ionosonde data. Many thanks to ISGI data center for providing data center. They alse thank Dr. Dieter Bilitza and the IRI-2016 web master for permitting model access and model run.