Local empirical model of ionospheric plasma density derived from Digisonde measurements at Irkutsk

Abstract

Ionogram data from routine ionospheric observations in Irkutsk, Russia using a DPS-4 Digisonde sounder were hand-scaled for the 6-year period from December 2002 to December 2008 to derive a local empirical model of the electron density distribution in the bottomside ionosphere that provides a comprehensive description of the diurnal, seasonal, and solar activity variations of the major ionospheric characteristics. The paper describes the technique for building the local empirical model and the results of comparing its diurnal, seasonal, and solar activity specifications with the standard IRI-2007 climatological model for the same period of time, and retrospective observational data from the Millstone Hill incoherent scatter radar (1976–2002) and a collocated Digisonde (1989–1990, 1998–2004). Reasoning for the observed differences between the three datasets is then provided in terms of background physical phenomena. Primary focus of the paper is the behavior of three F₂ layer characteristics: the F₂ peak density (N_mF₂), the peak height (h_mF₂) and the bottomside thickness (B₀).

1. Introduction

The DPS-4 Digisonde (Reinisch et al., 1997) was installed at Irkutsk, Russia (52.3N, 104.3E) in November, 2002. All Digisonde ionogram data have been manually scaled using an interactive ionogram scaling software, SAO Explorer (Reinisch et al., 2004; Khmyrov et al., 2008). The electron density profiles (EDP) were inverted from all suitable ionogram traces using the NHPC method (Reinisch and Huang, 1983). In addition to the EDP itself, NHPC provides two standard IRI parameters for the EDP representation, the bottomside thickness B₀ and the shape parameter B₁ using the Reinisch and Huang (1998) technique. In order to validate the quality of the observational data, the ionospheric F region parameters measured with the DPS-4 were compared to available data from a co-located chirpionosonde (Brynko et al., 1988) and the Irkutsk incoherent scatter radar (Shpynev, 2004); this comparison revealed no systematic discrepancies between the data from the different instruments for quiet geomagnetic conditions (Ratovsky et al., 2005).

Six years of the hand-scaled ionospheric characteristics from December 2002 to December 2008 were used to build a local empirical model of ionospheric electron density (LEMI) for Irkutsk. The Irkutsk LEMI model complements monthly-median climatological ionospheric specifications provided by global models like the IRI-2007 (Bilitza and Reinisch, 2008) by accounting for the regional specifics of the ionospheric plasma distribution that elude detailed reproduction in a global model. Study of the comprehensive patterns of the diurnal, seasonal, and solar activity variations of ionospheric characteristics provided by LEMI makes our model a useful tool for understanding the physical mechanisms of these variations.

The following sections compare the LEMI diurnal, seasonal, and solar activity behavior with the IRI-2007 (Bilitza and Reinisch, 2008) prediction and with long-term observational data from the Millstone Hill (42.6N, 288.5E) incoherent scatter radar (1976–2002), the co-located ionosonde (1989–1990, 1998–2004) (Lei et al., 2004, 2005), and other instruments. Comparison of LEMI with data from a different mid-latitude location allowed us to identify the longitudinal differences in the local ionospheric specifications. We then discuss observed differences in the context of background physical phenomena. For the purpose of such comparison, we selected three F₂ layer parameters: the F₂ peak density (N_mF₂), the peak height (h_mF₂), and the bottom-side thickness (B₀) and used the latest IRI-2007 model version (Bilitza and Reinisch, 2008) with the following options: URSI maps for N_mF₂, CCIR maps for h_mF₂, and the Gulyaeva option for B₀.

2. LEMI Construction Technique

The source data for the empirical model representation are the ionospheric characteristics obtained by the Irkutsk Digisonde operating at a 15-minute cadence. Each measured characteristic P is considered as a function of local time (LT), day of year (D) and year (Y), i.e., P (LT, D, Y). In order to represent the regular part of the observed P (LT, D, Y) behavior that we expect to be associated with climatological specifics of the diurnal, seasonal, and long-term solar activity variations, we used the 27-day sliding window median P_med (LT, D, Y) for each combination of LT, D, and Y in the sets {P (LT, D–13, Y), ⋯, P (LT, D+13, Y}. As shown in numerous data analysis applications, use of the median filtering instead of a classic averaging preserves strong gradients in the source data while suppressing the short-term variability with periods below the filter length (27 days in our case). No data (including high magnetic activity conditions) were removed from the median calculations.

As a unit of annual variations we selected the month (M) equal to T/12, where T = 365.25 days is the solar year (YS). The solar year YS starts from the winter solstice of leap year (December 21). The month continuously varies from 0 to 12, the month = 0 corresponds to the beginning of YS. Since the same days of different years do not correspond exactly to equal month values, we transformed P_med (LT, D, Y) to P_med (LT, M, Y_S) at equal month steps using simple linear interpolation. Hereinafter, we use traditional month names, implying that the zero month is December, the 1st month is January, the 2nd is February, and so on. The beginnings of December and June correspond to the winter and summer solstices and the beginnings of March and September refer to the spring and autumn equinoxes.

Calculated P_med (LT, D, Y) are then converted into a P_med (LT, M, YS) representation suitable for describing the annual variations, where Y_S is the solar year, and the month M is equal to T/12, where T = 365.25 days of Y_S. The solar year YS starts from the winter solstice of a leap year (December 21). The month continuously varies from 0 to 12, with the 0th month corresponding to the beginning of YS. Since the same days of different years do not correspond exactly to equal month values, we had to transform P_med (LT, D, Y) to P_med (LT, M, Y_S) at equal one-month steps using a simple linear interpolation. In the rest of our manuscript, we use conventional month names, implying that the 0th month is December, the 1st month is January, etc. In this presentation, December begins on the winter solstice, June begins on the summer solstice, and March and September begin on the spring and autumn equinoxes.

The 27-day running medians were used as an input for LEMI. The main assumption is that the P_med (LT, M, YS) can be approximated by a linear function of a suitable solar activity index. As a solar activity proxy we selected the 10.7 cm solar radio flux (F_10.7) whose daily values are available from WDC-A in Boulder, Colorado (ftp://ftp.ngdc.noaa.gov/STP/SOLAR_DATA) in solar flux units s.f.u. (1 s.f.u. = 10⁻²² Wm⁻² Hz⁻¹). Dependence of P_med on Y_s is therefore replaced by a linear function on F_10.7, so that P_med (LT, M, F_10.7) is used for further derivations, with the source values of F_10.7 linearly interpolated to appropriately obtain the solar radio flux values for any given M and Y_S. Under assumption of its linear dependence on F_10.7, each model characteristic can be presented in the slope-intercept form:

(1)

where P₀ is the intercept value of the characteristic P_med for the low solar activity of F_10.70 = 70 s.f.u. and P_D is the slope value, dP_med/dF_10.7, describing how sensitive the characteristic P is to changes in the solar activity. For convenience of the presentation the P_D values are calculated per increment of s.f.u., and in the remainder of this manuscript they are expressed in the units of (characteristic unit / 100 s.f.u.).

The model parameters P₀ (LT, M) and P_D (LT, M) can be obtained by the linear regression of P_med (LT, M, F_10.7)on F_10.7. The quality of the linear fit turns out to be dependent on the amount of averaging applied to the daily F_10.7 values. We tested different sliding window averaging periods for F_10.7 (from 27 days to 1 year) in order to minimize the linear regression RMS error. For most of the available P_med data, the 1 year period gave the best fit, with exception of December daytime, for which the 27 day period was optimal. Generally, median data are not well correlated with the solar activity intra year variations (from 27 days to 1 year) with the exception of December daytime. This fact is in agreement with our previous studies (Ratovsky et al., 2009) where the difference between the observed /_o F₂ medians and IRI prediction was found to be poorly correlated with the F_10.7 intra year variations. Finally, we selected the 1-year running mean of daily F_10.7 as a solar activity proxy input for LEMI.

Once P₀ (LT, M) and P_D (LT, M) sets are available for discrete values of LT (15 minute increments) and M (0 to 11), the next step is to interpolate them over LT and M so that P₀ and P_D can be obtained for any given local time and month. We used a cardinal B-spline approximation (Schoenberg, 1969) to represent P₀ and P_D sets continuously, calculating the spline coefficients with a fixed month step ΔM = 1 and various local time steps ΔLT ranging from 0.25 to 1 hour to select the optimal time resolution of the approximation. Figure 1 shows the relative root mean square differences ΔN_mF₂ between 15-minute time step medians of N_mF₂ and the LEMI values with ΔLT resolution of 0.5 and 1.0 hour. The ΔN_mF₂ values are obtained by averaging the differences over all the years of observations for each month. Observed differences are due to the F_10.7 linear regression error and inaccuracy of the B-spline approximation. We found that ΔN_mF₂ values observed for different local time resolutions ΔLT are very similar except for the morning time interval around 7–8 LT in December. Such similarity is typical for all winter months, and for this reason we used 0.5-hour local time step for all B-spline approximations. Table 1 summaries the important steps required for the construction of the LEMI model.

Fig. 1

Relative root mean square deviations (ΔN_mF₂) between 15-minute time step medians of N_mF₂ and the values calculated with the LEMI under local steps equal to 0.5 hour (dashed line) and 1 hour (circles).

Table 1 Construction of the LEMI model.

In order to compare LEMI results with the IRI empirical model we calculated P₀ and P_D coefficients using IRI predicted values as the source data and following steps 2–4 of the technique. The comparisons are presented in following sections

3. Results and Discussion

3.1 N_mF₂ morphology

The LEMI diurnal-seasonal behavior of N_mF₂ for low solar activity (F_10.7 = 70 s.f.u.) as a function of local time LT and month M is shown in Fig. 2(a). The high and low values are depicted by the solid and dashed contours, respectively. The daytime seasonal variations show two local maxima: in March (∼4·10⁵ cm⁻³) and October (∼5·10⁵ cm⁻³) and two local minima: in January (∼3.1·10⁵ cm⁻³) and July (∼2.7·10⁵ cm⁻³). The nighttime N_mF₂ is largest in June and smallest in January, with intermediate values between these months. Maximum N_mF₂ during the late evening hours (20–22 LT) occurs in May, one month earlier than during the nighttime.

Fig. 2

Diurnal-seasonal variations of N_mF₂ in [10⁵ cm⁻³] under low solar activity for LEMI (a) and IRI (b). The high and low values are depicted by the solid and dashed contours, respectively.

The Irkutsk daytime seasonal pattern of N_mF₂ differs from the Millstone Hill pattern (Lei et al., 2005) where daytime N_mF₂ is largest in the winter and smallest in the summer, with intermediate values at equinoxes. This difference has been reproduced by the Coupled Thermosphere-Ionosphere-Plasmasphere model (Zou et al., 2000) and explained by the dependence of the winter down welling zone latitude on the geomagnetic longitude (Rishbeth et al., 2000a) that makes a “far-from-the-pole” station (Irkutsk) different from a “near-the-pole” station (Millstone Hill) during the same season.

We can distinguish three types of N_mF₂ diurnal behavior under low solar activity. The winter-like (October– February) pattern is characterized by the main maximum near noon, the local post midnight maximum (2–2:30 LT), and two local minima in the evening (18:30–21 LT) and in the morning (6–7 LT). Typical summer (May–July) behavior is characterized by the main evening maximum (∼21 LT), the main morning minimum (∼3 LT), the local prenoon maximum LT), and the local afternoon minimum (15 LT in May and 17 LT in June, July). Typical equinox (March, September) pattern is characterized by only one maximum near noon and one minimum in the morning (∼5 LT).

The IRI prediction (Fig. 2(b)) of the N_mF₂ diurnal-seasonal behavior under low solar activity reproduces the LEMI pattern reasonably well, though IRI systematically underestimates both the maxima and minima of N_mF₂ obtained with LEMI.

The study of the P_D slope as a function of LT and M provides insight into how the ionospheric diurnal-seasonal pattern changes with increasing solar activity. Figure 3(a) shows the LEMI diurnal-seasonal behavior of the in [10⁵ cm⁻³/100 s.f.u.] units. The daytime N_mF₂ (11–13 LT) is most sensitive to solar activity near the winter solstice (N_mF_2D ∼ 14 10⁵ cm⁻³/100 s.f.u.) and least sensitive near the summer solstice (N_mF_2D ∼3–3.6 10⁵ cm⁻³/100 s.f.u.), with intermediate values at equinoxes (9–10.5 10⁵ cm⁻³/100 s.f.u. in March and 7–8.5 10⁵ cm⁻³/100 s.f.u. in September). Thus, with increasing solar activity the daytime N_mF₂ peak moves from March and October towards the winter solstice. This peculiar behavior agrees with the ionospheric maps developed by Torr and Torr (1973) that, for high solar activity, reproduce larger values of winter critical frequency f_oF₂ than the summer and equinox f_oF₂ for all considered midlatitude stations. The Irkutsk LEMI daytime seasonal pattern of the N_mF_2D agrees with both Millstone Hill (Lei et al., 2005) and the IRI patterns (Fig. 3(b)).

Fig. 3

Diurnal-seasonal variations of the slope of the linear dependence on F_10.7, N_mF_2D in [10⁵ cm⁻³/100 s.f.u.] for LEMI (a) and IRI (b). The high and low values are depicted by the solid and dashed contours, respectively.

According to LEMI (Fig. 3(a)), the summer (May–July) diurnal behavior of N_mF₂ is characterized by the highest sensitivity to solar activity during the evening hours (N_mF_2D∼ 19–20 LT, 4–5 10⁵ cm⁻³/100 s.f.u.), the lowest sensitivity during the morning (N_mF_2D ∼ 3:30 LT, ∼1.5 10⁵ cm⁻³/100 s.f.u.), and monotonic increase from morning to evening. Such LEMI behavior means that the prenoon N_mF₂ maximum that we observed in the summer diurnal pattern for low F_10.7 disappears with increasing solar activity. As for the IRI prediction (Fig. 3(b)), the diurnal maximum of the summer N_mF_2D is seen at prenoon and noon hours, rather than in the evening, which makes the evening and prenoon maxima of N_mF₂ comparable to each other with increasing solar activity. This disagreement between the IRI-predicted and the observed summer diurnal behavior of f_oF₂ was discussed previously by Ratovsky et al. (2009). The Irkutsk summer diurnal behavior of the slope differs from the Millstone Hill behavior (Lei et al., 2005), where the summer N_mF_2DD varies only weakly during the day (2–3 10⁵ cm⁻³/100 s.f.u.).

Figure 3(a) also demonstrates that there is an area of extremely weak dependence of N_mF₂ on solar activity (N_mF_2D < 0.5 10⁵ cm⁻³/100 s.f.u.) in the postmidnight hours. This means that the enhancement of postmidnight N_mF₂ gets weaker with increasing solar activity, which agrees with the studies of Mikhailov et al. (2000). The authors explained this phenomenon by suggesting that the nighttime recombination rate increases faster than the nighttime influx from the plasmasphere with increasing solar activity.

Ratovsky et al. (2009) observed that the solar activity dependence of the diurnal f_oF₂ minimum at Irkutsk is much weaker than the IRI prediction. This disagreement manifests itself in the difference between the postmidnight N_mF_2D obtained with LEMI and IRI. According to IRI, the average postmidnight (0–3 LT) N_mF_2D varies from 1.1 to 3.5 10⁵ cm⁻³/100 s.f.u. (from December to June), whereas the LEMI values are 0.4 and 2.5 10⁵ cm⁻³/100 s.f.u. for December and June, respectively. The Millstone Hill (Lei et al., 2005) average postmidnight summer is close to the LEMI value, whereas the winter is close to the IRI prediction for Irkutsk. Possibly, the balance between the recombination rate and the plasmasphere influx, and hence the postmidnight depends on the geographic location. In support of this explanation, modeling by Zou et al. (2000) showed that the December midnight ratio N_mF₂ (F10.7 = 180)/N_mF₂ (F_10.7 = 100) is the smallest at “far-from-the-pole” longitudes.

3.2 h_mF₂ morphology

Figure 4(a) shows the LEMI diurnal-seasonal behavior of the F₂ peak height h_mF₂ under low solar activity (F_10.7 = 70 s.f.u.). The high (nighttime) and low (daytime) values are depicted by the solid and dashed contours, respectively. The average daytime (10–14 LT) seasonal variations show an annual pattern with the December minimum (209 km) and the April–May maximum (228 km). The average nighttime (22–02 LT) seasonal variations also show an annual pattern with the June–July minimum (282 km) and the November maximum (294 km). Both daytime and nighttime seasonal patterns of LEMI are somewhat different from the IRI model (Fig. 4(b)) that predicts a semiannual pattern both for average daytime (10–14 LT) and nighttime (22–02 LT) h_mF₂. The daytime h_mF₂ has local maxima in March (243 km) and September (240 km), and local minima in July (210 km) and January (218 km). The nighttime h_mF₂ has local maxima in March (324 km) and October (313 km), and local minima in July (292 km) and December (302 km).

Fig. 4

Diurnal-seasonal variations of h_mF₂ in [km] under low solar activity for LEMI (a) and IRI (b). The high and low values are depicted by the solid and dashed contours, respectively.

Figure 5(a) shows diurnal-seasonal dependence of h_mF₂ on solar activity by plotting values in units of [km/100 s.f.u.]. The peak height of the ionosphere is most sensitive to the solar activity in the postmidnight hours. Another area of strong dependence (h_mF_2D > 60) is seen in the afternoon hours in October and from March to August. The area of weak dependence of h_mF₂ on solar activity (h_mF_2D < 50) is seen in the prenoon hours for all months except October and in the late evening hours for all months except June and July.

Fig. 5

Diurnal-seasonal variations of the slope of the linear dependence on F_10.7, in [km/100 s.f.u.] for LEMI (a) and IRI (b). The high and low values are depicted by the solid and dashed contours, respectively.

The pattern of the LEMI diurnal-seasonal behavior of h_mF_2D is different from both the IRI prediction (Fig. 5(b)) and the Millstone Hill data (Lei et al., 2005). IRI predicts that the h_mF_2D is approximately proportional to the solar zenith angle, so that highest sensitivity to increasing solar activity level is seen in the daytime hours (∼6–15 LT) for the summer and equinox months. At Millstone Hill (Lei et al., 2005) remains below 56 km/100 s.f.u., with higher values during daytime than at night, a diurnal peak at around 1300–1400 LT in all seasons, and a weaker dependence in winter than in other seasons.

Table 2 Daytime and nighttime annual mean of h_mF₂ (F_10.7 = 140) in [km] and h_mF_2D in [km/100 s.f.u.] for different stations. The station coordinates are shown in parentheses. Dip is the magnetic field dip angle of the station.

We compared the LEMI daytime (10–14 LT) and nighttime (22–02 LT) annual mean of with values observed at midlatitude stations (Rishbeth et al., 2000b). Table 1 demonstrates the daytime and nighttime annual mean of h_mF_2D and h_mF₂ (F_10.7 = 140 s.f.u.). Except for Irkutsk and Millstone Hill, the observational data are taken from the paper of Rishbeth et al. (2000b). The Irkutsk h_mF₂ (F_10.7 = 140) was calculated using expression (1) and LEMI values of h_mF₂₀ and . Using the same technique, we calculated Millstone Hill h_mF₂ (F_10.7 = 140) using the data of Lei et al. (2005). One can see from Table 2 that h_mF₂ is most sensitive to solar activity for the “far-from-the-pole” stations (Port Stanley, Wakkanai, Irkutsk) and this sensitivity is not correlated to the magnetic field dip angle.

3.3 B₀ morphology

The LEMI diurnal-seasonal behavior of the bottomside thickness B₀ under low solar activity (F_10.7 = 70 s.f.u.) is shown in Fig. 6(a). The high and low values are depicted by the solid and dashed contours, respectively.

Fig. 6

Diurnal-seasonal variations of B₀ in [km] under low solar activity for LEMI (a) and IRI (b). The high and low values are depicted by the solid and dashed contours, respectively.

Diurnal behavior of B₀ during winter and equinox (from September to March) is characterized by so called morning and evening collapses (Lei et al., 2004) when B₀ is minimal. The local times of the collapses (8:45–6:00 and 15:15–18:00 LT) are close to the times of sunrise and sunset at zero altitude. The B₀ at the minima increases from 47–48 km at the winter solstice to 57–63 km at the spring and autumn equinoxes. In November–January the midnight B₀ (70–75 km) exceeds the noon one (56–59 km), in March and September the noon B₀ (84 km) exceeds the midnight one (66–69 km), and in October and February the noon and midnight B₀ values (64–68 km) are comparable. So, in winter and equinox months the diurnal-seasonal pattern of B₀ is close to being symmetric about noon as well as the winter solstice. The summer-like (April–August) diurnal behavior is characterized by the only one maximum near noon (12:30–12:45 LT) and one minimum in the late evening hours (21:15–21:45 LT, B₀ = ∼60 km). Maximum diurnal B₀ values rise from 99 km in April to 137 km in July and after that decrease to 116 km in August. The average daytime (10–14 LT) seasonal variations of B₀ show an annual pattern with the December minimum (56 km) and the July maximum (133 km). The average nighttime (22–02 LT) seasonal variations also show an annual pattern with the May minimum (63 km) and the November maximum (75 km).

In general, diurnal-seasonal pattern of B₀ is close to that at Millstone Hill (Lei et al., 2004). There are differences in the nighttime behavior. At Millstone Hill the winter noon and midnight values are close together, and the nighttime B₀ does not show an evident seasonal effect.

The LEMI diurnal-seasonal behavior of B₀ is somewhat different from the IRI prediction (Fig. 6(b)). IRI predicts a well-pronounced morning maximum (dominant for the winter months), which is not observed in the LEMI pattern. The IRI’s evening collapse occurs later in the evening hours (18–21 LT) in comparison to LEMI. Both models give comparable daytime seasonal patterns of B₀, though IRI overestimates the winter B₀ and underestimates the summer B₀. Compared to LEMI, the IRI predicts an opposite nighttime seasonal behavior with the December minimum (68 km) and the June maximum (92 km).

The LEMI diurnal-seasonal behavior of the B₀ sensitivity to increasing solar activity level, , is shown in Fig. 7(a). No clear diurnal-seasonal pattern of can be seen. In contrast to LEMI, IRI gives a clear pattern of B_0D (Fig. 7(b)). Similar to h_mD IRI preducts greater dependence of B₀ on solar activity ( > 60 km/100 s.f.u.) in the daytime hours (∼6–15 LT) from March to September.

Fig. 7

Diurnal-seasonal variations of the slope of the linear dependence on F_10.7, in [km/100 s.f.u.] for LEMI (a) and IRI (b). The high and low values are depicted by the solid and dashed contours, respectively.

Millstone Hill data (Lei et al., 2004) suggest that increase of solar activity level from low (F_10.7 = 90 s.f.u.) to high (F_10.7 = 180 s.f.u.) results in increase of B₀ by about 30% during the night and by about 20% during the day, except for the morning collapse periods in equinox and winter when B₀ increases by less than 10%. In order to compare these observations with LEMI, we had to regroup and average our data to match Lei et al. (2004) technique of binning data into three seasons, namely summer (May–August), winter (November–February), and equinox (March, April, September and October). We averaged the LEMI and IRI mean nighttime (22–02 LT) and mean daytime (10–14 LT) values of over the three seasons. Using available Millstone Hill observations of B₀ under low (F₁₀₇ = 90 s.f.u.) and high (F₁₀₇ = 180 s.f.u.) solar activity (Lei et al., 2004), we obtained estimates of . Table 3 shows the final results. For the nighttime, the IRI does not show any seasonal variations; whereas both the Irkutsk LEMI and Millstone Hill summer B_0D noticeably exceeds the winter one and the equinox B_0D is close to the winter one. In all presented cases, the summer daytime exceeds the winter one, but the IRI summer daytime noticeably overestimates both the Irkutsk LEMI and Millstone Hill ones.

Table 3 Mean nighttime (22–02 LT) and mean daytime (10–14 LT) values of B_0D in [km/100 s.f.u.] averaged over the three seasons.

4. Conclusion

Data from routine ionospheric observations at Irkutsk, Russia using a DPS-4 Digisonde sounder were used to derive a local empirical model of the electron density that provides a comprehensive description of the diurnal, seasonal, and solar activity variations of the major ionospheric characteristics. We have compared the local model patterns with the IRI-2007 prediction (Bilitza and Reinisch, 2008) and the retrospective data from long-term mid-latitude measurements by the Millstone Hill incoherent scatter radar and the collocated Digisonde (Lei et al., 2004, 2005).

The comparison revealed both similarities and differences between Irkutsk and Millstone Hill diurnal, seasonal and solar activity variations. The observed disagreements can in part be explained by the different location of the instruments at “far-from-the-pole” and “near-the-pole” longitudes. The observed strong dependence of the nighttime h_mF₂ on the level of solar activity is found to be in agreement with the observations at “far-from-the-pole” sites reported by Rishbeth et al. (2000b). Many of the local Irkutsk model features, such as the diurnal-seasonal pattern of N_mF₂ under low solar activity and the slope of the daytime N_mF₂ dependence on F_10.7, are reasonably well reproduced by the IRI prediction, although there are differences.

In winter and equinox months the diurnal-seasonal pattern of B₀ under low solar activity is found to be nearly symmetric about noon as well as the winter solstice. This feature will be useful for empirical modeling. The local model does not give a clear diurnal-seasonal pattern of the slope of B₀ dependence on F_10.7, but season averages of the daytime and nighttime B₀ do agree with available Millstone Hill observations.