Based on the data of 17 mid-latitude ionospheric stations for 1958–1988, the study analyzes seasonal features of the F2 layer peak concentration (NmF2) at different longitudes with enhanced (48 > ap(τ) > 27) geomagnetic activity, where ap(τ) is the weighted average (with a characteristic time of 14 h) ap-index of this activity. As the characteristics of the NmF2 variability, the standard deviation σ of NmF2 fluctuations relative to quiet level and the average shift of these fluctuations xave during daytime (1100–1300 LT) and nighttime (2300–0100 LT) were used. It was found that at all analyzed stations, the dispersion σ2 for enhanced geomagnetic activity is greater than for quiet conditions, and, other things being equal, it is maximum in winter at night. For enhanced geomagnetic activity in all seasons, the difference in xave values between the analyzed stations is quite large. One of the reasons for this difference is associated with the dependence of xave on geomagnetic latitudes. To select these latitudes, approximations of the geomagnetic field with tilted dipole (TD), eccentric dipole (ED), or with corrected geomagnetic (CGM) coordinates were used. It was found that the xave dependence on the ED latitude is more accurate in comparison to the xave dependence on the TD latitude or CGM latitude during all seasons at night, and during equinoxes and winter, in the daytime. In summer, in the daytime hours, the xave dependences on ED latitude and CGM latitude are comparable in accuracy, and they are more accurate compared to the xave dependence on TD latitude. Consequently, ED latitudes are optimal for taking into account the effects of storms in the F2 layer peak concentration at mid-latitudes during all seasons. This conclusion has apparently been made for the first time.

Based on the global empirical model of the F2 layer critical frequency median (Satellite and Digisonde Data Model of the F2 layer, SDMF2), an analysis was made of the properties of diurnal variations in the annual asymmetry in the concentration of the F2 layer maximum NmF2 at different values of the solar activity index F. The AI index, which characterizes the relative difference in NmF2 averaged over all longitudes and latitudes between January and July at a given local time, was used as a parameter of this asymmetry. It was found that the diurnal variations of the AI index are dominated by a semidiurnal mode with maxima in the daytime and at night. The daytime maximum of the AI index is almost independent of the level of solar activity. The nighttime AI maximum decreases with increasing solar activity. For low solar activity, the daytime and nighttime AI maxima almost coincide in amplitude when AI = 16—17%. The difference in the solar radio flux between January and July due to the ellipticity of the Earth’s orbit relative to the Sun makes a significant contribution to the AI index at all hours of the day. On average, it is 3—4% and can reach 5% with low solar activity at night. The difference in the AI index for low and high activity according to the IRI model (with URSI and, especially, CCIR coefficients) is overestimated relative to the SDMF2 model at almost all hours of the day, apparently due to the limited number of experimental data when obtaining the CCIR and URSI coefficients especially over the oceans

The article presents the first results of identifying trends in annual average ionospheric indices ΔIG12 and ΔT12, which are obtained after excluding from IG12 and T12 the dependence of these indices on solar activity indices. In this case, solar activity indices are F10 and F30—solar radio emission fluxes at 10.7 and 30 cm. It was found that for the interval of 1957–2023, all analyzed linear trends are negative, i.e., quantities ΔIG12 and ΔT12 decrease over time, and these trends are significant. In absolute value, they are maximum for ΔIG12, taking into account the IG12 dependence on F1012, and minimum for ΔT12, taking into account the T12 dependence on F3012. Account for the nonlinearity of trends shows that, e.g., after 2010, they intensified. Relations are presented that make it possible, based on data from trends of the ionospheric indices (ΔIG12 or ΔT12), to judge the nature of the Δ foF2 trend over a specific point. For this, using the IRI model for foF2, a coefficient was obtained that gives the relationship between the trends of the ionospheric index and Δ foF2 over this point. Comparison with experimental data at mid-latitudes revealed that trends of the ionospheric indices make it possible to correctly determine the sign of the Δ foF2 trend and the general tendency for this trend change, but the calculated value of the trend over a specific point may differ markedly from the experimental data.

Based on data from mid-latitude ionospheric stations at close corrected geomagnetic latitudes, the properties of the variability in the F2 layer peak density (NmF2) at different longitudes were analyzed during increased (48 > ap(τ) > 27) and high (ap(τ) > 48) geomagnetic activity, where ap(τ) is the weighted average ap-index of this activity. The standard deviation σ of Nm fluctuations with respect to the quiet level and the average shift of these fluctuations xave were used as characteristics of this variability. It was found that at all analyzed stations, the variance σ 2 for increased geomagnetic activity is greater than for quiet conditions but hardly differs from σ 2 for high geomagnetic activity. For all analyzed cases, the average shift xave < 0, and for high geomagnetic activity, the absolute value of xave is greater than for increased geomagnetic activity. The difference in xave values between the analyzed stations is quite large. One reason for this difference may be related to the dependence of xave on geomagnetic latitudes. Approximations of the geomagnetic field by the tilted dipole (TD), eccentric dipole (ED), or using corrected geomagnetic (CGM) coordinates were used to select these latitudes. It was found that the dependence of xave on ED latitude is more accurate than the dependence of xave on TD latitude and, moreover, the dependence of xave on CGM latitude. Therefore, ED latitudes, and not CGM latitudes, are optimal for accounting for storm effects on the F2 layer peak density at mid-latitudes. This conclusion has apparently been obtained for the first time.

An aeronomic and dynamic correction of the GTEC median global model of the total electron content for disturbed conditions ( Ap ≥ 15 nT) is proposed. The GTEC global median model is developed for quiet conditions ( Ap < 15 nT) as a function of the geographic coordinates, universal time UT, day of the year, and solar activity level (the solar radio emission flux F 10.7). The model is based on a spherical harmonic analysis of the GIM-TEC Global Ionospheric Maps (1996–2019) provided by the Jet Propulsion Laboratory (NASA). The proposed GDMTEC global dynamic model (Global Dynamic Model of TEC) consists of the GTEC median model updated with several dynamic and aeronomic corrections related to formation of the main ionospheric trough, position of the auroral ionization maximum and changes of the thermospheric temperature and composition. The advantage of the proposed corrections of the median model is the independence of forecast of the data in real time from assimilation of the current observational data. Testing of the model for disturbed conditions shows an improvement of the forecast compared to the IRI-Plas ionospheric reference model.

Based on the medians of the F 2-layer maximum electron concentration NmF 2 for two ionospheric stations, Boulder and Hobart, in 1963–2013, an analysis of the dependence of the annual asymmetry local index R at noon on solar activity has been performed, where the R index is the January/July ratio of the summary NmF2 concentration for this pair of stations. Solar activity indices averaged over 81 days are used: Fobs is the solar radio emission flux at a wavelength of 10.7 cm measured by ground-based radio telescopes and Fadj is the value of Fobs reduced to a fixed distance from the Sun of one astronomical unit. It is found that the regression equations that manifest the NmF2 medians dependence on Fobs make it possible to obtain the annual asymmetry index R for a fixed value of Fobs with allowance for a substitution of Fobs by cFobs in these regression equations, the c coefficient is equal to 1.03 and 0.97 for January and July, respectively. The c = 1 case corresponds to neglecting the annual asymmetry in the Fobs index due to the ellipticity of the Earth’s orbit. For the c = 1 version, the R index increases with a solar activity increase from 1.2 under low activity up to almost 1.4 under high activity. An additional allowance for the annual asymmetry in Fobs leads to an increase in the R index by approximately 0.1 almost independently of the solar activity level. Apparently, this conclusion is being drawn for the first time. The Fadj index also makes it possible to obtain a correct estimate of the R index, because the annual asymmetry in the solar radiation flux is indirectly taken into account via the experimental values of NmF 2.

The properties of the variability of the maximum density of the F 2-layer Nm at different levels of solar and geomagnetic activity have been analyzed based on hourly data of the Almaty station (43.2° N, 104° E) for 1958–1988. The standard deviation σ(x) of the fluctuations of Nm relative to the quiet level (x = (Nm/Nm0 – 1) × 100,

The properties of the variability of the maximum density of the F2-layer Nm at different levels ofsolar and geomagnetic activity have been analyzed based on hourly data of the Almaty station (43.2° N, 104° E)for 1958–1988. The standard deviation σ(x) of the fluctuations of Nm relative to the quiet level(x = (Nm/Nm0 – 1) × 100, %) and the average shift of these fluctuations xave are used to characterize thisvariability. In this path, an empirical model of the F2-layer maximum density Nm0 for low geomagnetic activityhas been created. It has been found that the variability of Nm depends weakly on the level of solar activity.The dependence of the variability of Nm on geomagnetic activity is one of the main ones, along with thedependences of this variability on time of day and season. In general, the variance σ2(x) is smaller for quietconditions than for periods of high geomagnetic activity. However, during periods of high geomagnetic activity,a further increase in geomagnetic activity does not lead to an increase in the variance σ2(x). The saturationin the increase in the variance σ2(x) against the background of a continuing increase in geomagnetic activityand the absence of this saturation for the average shift xave seems to be a stable property of the variability ofthe mid-latitude ionosphere during periods of geomagnetic storms. This conclusion is based on an additionalanalysis of ionospheric variability according to data from the Irkutsk and Yamagawa stations, which arelocated about 10 degrees north and south of Almaty station, respectively.

— The index P = ( F 1 + F 81 )/2 is the optimal solar activity index for the critical frequency of the E layer, foE , where F 1 and F 81 are the flux of radio emission from the Sun at a wavelength of 10.7 cm on a given day and the 81-day average value of this flux centered on a given day. Therefore, to calculate F 81 on a given day, knowledge of F 1 is needed not only on this and previous days, but also 40 days in advance. Instead of index F 81 , in problems on short-term forecasting of this index, it is possible to use F (27, 81), the weighted average solar activity index with a characteristic time of 27 days for the current and previous 80 days. Therefore, to calculate F (27, 81), knowledge of F 1 on this and previous days suffices. This paper presents the first estimates of the effectiveness of such a replacement for foE . For this, changes in the accuracy of calculating foE were analyzed when index P is replaced by P * = ( F 1 + F (27, 81))/2 in empirical models constructed from foE data of ionospheric stations in the daytime at middle and subauroral latitudes for 1959–1995. It turns out that the P and P * indices are almost equivalent for calculating foE based on the empirical models constructed at these latitudes: the difference in the coefficients of variation for foE does not exceed 0.3% in each season at different solar cycle phases. Therefore, P * can be recommended for use in short-term foE forecasting problems, since it is based on indices F 1 for the current and previous days, as opposed to index P , which requires a forecast 40 days in advance to calculate F 1 .

The F1 and F81 indices, the value of the solar-emission flux at a wavelength of 10.7 cm on a given day, and the value of the flux averaged over 81 days and centered to the given day are used in many models of the extreme ultraviolet radiation of the Sun, ionosphere, and thermosphere as a characteristic of solar activity (as an input parameter). It is difficult to use the F81 index in problems of short-term forecasting of the aforementioned parameters with these models, because a forecast of F1 40 days in advance is needed to calculate F81. The paper presents the results of a search for a solar-activity index F(T, N) to replace F81 in these problems, where F(T, N) is a cumulative (weighted mean with a characteristic time T in days) index of that activity calculated based on F1 data over the given day and N previous days. The search is based on the determination of optimal parameters T and N from the condition of the minimum of the standard deviation of the F(T, N) index from F81 at relatively low values of N. It is found that the F(27, 81) index with parameters T = 27 and N = 3T is the effective solar-activity index sought as a replacement for F81 in the aforementioned problems. The F(27, 81) index is applicable under any solar-activity level and at any solar-cycle phase. For example, the standard deviation of the F(27, 81)/F81 ratio is insignificant (is equal approximately to 5%) for both relatively high (1954–1996) and low (1996–2020) solar-activity cycles. The average deviation (shift) of the F(27, 81) index from F81 could be ignored in many cases. For example, the shift does not exceed 2 (in units of F1 measurements) by the absolute value overall for both the growth and declining solar-cycle phases within the 1954–1996 interval.

Based on the analysis of data from subauroral ionospheric stations during daytime hours with low geomagnetic activity, it was found that the index P = 0.5( F 1 + F 81 ) is the optimal solar activity index for the daily values of the E -layer critical frequency foE , where F 1 and F 81 are the solar radio flux at a wavelength of 10.7 cm on a given day and the average of this flux over 81 days. The standard deviations σ of the foE dependence on P are at their maximum for winter. The σ value in this season for the Salekhard and Lycksele stations, which are located at the Arctic Circle and near it, is significantly greater than for the Leningrad station. Substituting the P index into the IPG, IRI, or NeQuick models allows these models to be used for the calculation of daily foE values. Based on the preliminary analysis, it was found that the NeQuick model is more accurate than the IPG and IRI models for winter and equinoxes. For summer, these models have approximately the same accuracy with a slight advantage of the IPG model. For the Salekhard and Lycksele stations in winter at foE < 2 MHz, even the NeQuick model underestimates the foE values by approximately 0.2 MHz on average. The search for the causes of this property of the ionosphere requires special consideration.

An analysis of the relationship between the monthly mean ionospheric indices IG and T and the indices of solar (F107) and geomagnetic (Ap) activity based on the massif of these data within 1954–2020 interval is presented. F107 and Ap are the monthly mean flux of the solar radio emission at a wavelength of 10.7 cm and the planetary index of geomagnetic activity Ap, respectively. It is found that the index F = (F1070 + F107–1)/2 provides a higher correlation to the ionospheric indices than the indices F107 over the given (F1070) or previous (F107–1) months. The IG and T dependencies on F in the form of a second-degree polynomials make it possible to reproduce 96% of variations in IG and 98% of variations in T for the analyzed time interval. That is the reason that the additional contribution of Ap into IG and T is weak. Nevertheless, the contribution of Ap into T and IG depends on the time of the year: it is not significant for January and is significant for July. This property of the annual anomaly in the ionospheric parameters by the IG index, apparently, is discovered for the first time. In all considered cases, an increase in Ap leads to a decrease in T and IG, that is, to a mean (global) decrease in the median of the F2-layer maximum concentration and, under equal other conditions, such a decrease is more significant in July than in January. The properties of the dependencies of the IG and T indices on F and Ap are in many aspects similar, but the accuracy of these dependencies is higher for T than for IG.

An analysis of the relation of the monthly mean ionospheric T index to the solar (F107) and geomagnetic (Ap) activity indices is presented based on a dataset of these indices for 1954–2020. F107 and Ap are the monthly mean flux of the solar radio emission at a wavelength of 10.7 cm and the planetary Ap-index of geomagnetic activity, respectively. It is found that the effective index F = (F1070 + F107–1)/2 provides a high correlation between the ionospheric and solar indices; F1070 and F107–1 are the F107 indices over the given and previous months. The dependence of T on F in the form of a second-degree polynomial makes it possible to reproduce 95–98% of variations in T over the analyzed time interval. Thus, the additional contribution of Ap to T is insignificant. Nevertheless, the contribution of Ap to T depends on the time of year: it is insignificant in January and significant in July. This revealed property of the annual anomaly in ionospheric parameters is conserved also for the contribution of the аa index of geomagnetic activity to the ionospheric T index. In all considered cases, an increase in Ap or aa leads to a decrease in the ionospheric T index, i.e., a mean (global) decrease in the median of the concentration in the F2-layer maximum. Under the same other conditions, such decrease is more significant for July than for January.

The properties of the annual asymmetry in the electron density of the F2-layer maximum NmF2 at noon are analyzed based on the global empirical model of the F2-layer critical frequency median (SDMF2 model). As a characteristic of this asymmetry, we used the R index, i.e., the January/July ratio of the total (at a given and geomagnetically conjugate points) NmF2 density at noon averaged over all longitudes. It was found that the R index decreases with increasing solar activity at low geomagnetic latitudes (Φ < 31°–33°). At higher latitudes, the R index increases with an increase in solar activity. During low solar activity, the main R maximum is located at latitude Φ = 22°–24°. During high solar activity, this R maximum is located at Φ = 64°–66°. At latitude Φ = 22°–24° in the Northern and Southern hemispheres, the longitudinal average NmF2 density in January is higher than that in July for any level of solar activity. At Φ = 64°–66°, an increase in R with increasing solar activity is mainly caused by a January increase in NmF2 in the Northern Hemisphere. The global (average over all latitudes) R index increases with increasing solar activity. Additional analysis showed that the global R index decreases with increasing solar activity in the IRI model both with URSI option and, even more so, with CCIR option. This appears to be due to the limited amount of experimental data on the obtainment of the CCIR and URSI coefficients, especially over the oceans.

Analysis of the features of the form of low solar cycles 23 and 24 for the solar-activity indices (F is the solar radio flux at a wavelength of 10.7 cm, Rz and Ri are the relative numbers of sunspots, old and new versions) and the ionospheric index of this activity T. For this, the analyzed indices are reduced to the Rz scale and smoothed (with a 24-month Gaussian filter) values of these indices are considered. It was found that the cycle forms were preserved for cycles 23 and 24 and previous solar cycles by index Rz, i.e., a definite connection was made between the cycle amplitude and the time of the onset of the cycle maximum. The same relationship was observed for the Ri index, except for cycle 23, in which the observed cycle maximum occurred 7 months later than the expected time based on previous cycles. For indices F and T, the cycle shapes also persisted up to cycle 22, but the observed cycle maxima in cycles 23 and 24 occurred almost a year later than expected, which is one of the properties of the new regime of prolonged low solar activity. In this mode, the connection between the Ri and F indices is broken, which leads to different cycle forms for these indices.

A new foE model for the auroral region is constructed; the model is based on an analysis of the models of auroral electron precipitations, the boundaries of the discrete and diffusive aurora, the main ionospheric trough, and measurements of the E-layer critical frequency foE. The model is an analytical model. It consists of solar (foE(sol)) and auroral (foE(avr)) components. The solar component of the model does not depend of geomagnetic activity. It depends on solar activity via the F index, which is determined by the solar radio emission flux at a wavelength of 10.7 cm over the previous day and three solar rotations. The auroral component of the model does not depend of solar activity. It depends on geomagnetic activity via the effective Kp* index, which takes into account the prehistory of changes in this activity. The model indirectly takes into account the dependence of the relative contribution of foE(sol) and foE(avr) to the total foE value on the difference in the heights of the maxima of these model components via the addition of a coefficient. The model qualitatively takes into account the effect of the winter anomaly in foE(avr) via the addition of a function. It is found that the errors of the new foE model in the auroral region at the nighttime hours are much lower than those in the international IRI model (with the STORM-E option) for both moderate and high geomagnetic activity. For example, the comparison with data from ionospheric stations shows that the IRI model underestimates foE in these conditions by approximately a factor of 2 on average. The average shift in foE relative to the experimental data in the new model does not exceed 20%.