F1 Region Ion Composition in Svalbard During the International Polar Year 2007–2008

Ions in the F region ionosphere at 150–400 km altitude consist mainly of molecular NO+ and O2+ ${\mathrm{O}}_{2}^{+}$ , and atomic O+. Incoherent scatter (IS) radars are sensitive to the molecular‐to‐atomic ion density ratio, but its effect to the observed incoherent scatter spectra is almost identical with that of the ion temperature. It is thus very difficult to fit both the ion temperature and the fraction of O+ ions to the observed spectra. In this paper, we introduce a novel combination of Bayesian filtering, smoothness priors, and chemistry modeling to solve for F1 region O+ ion fraction from EISCAT Svalbard IS radar (75.43° corrected geomagnetic latitude) data during the international polar year (IPY) 2007–2008. We find that the fraction of O+ ions in the F1 region ionosphere is controlled by ion temperature and electron production. The median value of the molecular‐to‐atomic ion transition altitude during IPY varies from 187 km at 16–17 MLT to 208 km at 04–05 MLT. The ion temperature has maxima at 05–06 MLT and 15–16 MLT, but the transition altitude does not follow the ion temperature, because photoionization lowers the transition altitude. A daytime transition altitude maximum is observed in winter, when lack of photoionization leads to very low daytime electron densities. Both ion temperature and the molecular‐to‐atomic ion transition altitude correlate with the Polar Cap North geomagnetic index. The annual medians of the fitted transition altitudes are 14–32 km lower than those predicted by the International Reference Ionosphere.


Introduction
Typical ion composition in the F region ionosphere makes a smooth transition from molecular NO + and O + 2 below 150 km altitude to almost pure atomic O + around 350 km altitude.The ion composition is a key parameter that affects energy exchange rates between the ions and the thermospheric neutral particles, ion and neutral chemistry, and electron recombination speeds.The F region ion composition is a key unknown also in attempts to understand molecular ion upflow and outflow from the ionosphere to the magnetosphere (Takada et al., 2021).However, many aspects of the molecular-to-atomic ion transition remain unknown, because it occurs at too low altitudes for in situ satellite observations, and the ground-based incoherent scatter radar (ISR) observations cannot provide information about the ion composition without limiting assumptions about the ion or electron temperature if conventional analysis tools are used (Evans, 1967;Kelly & Wickwar, 1981).The so-called temperature ion composition ambituity (TICA) (Martínez-Ledesma & Díaz Quezada, 2019) arises from the fact that changes in ion composition and ion temperature can lead to almost identical changes in the incoherent scatter spectra.As a consequence, the ISR data do not only lack the ion composition information, but the ion composition is typically taken from a model, and the ion and electron temperatures fitted to the observed sepctra are biased whenever the true ion composition is different from the model values (Blelly et al., 2010).
Several different approaches have been proposed for solving the TICA problem.Lathuillere et al. (1983) and Lathuillere and Pibaret (1992) used coarse resolutions in time and altitude to reach such a high statistical accuracy in the observed incoherent scatter spectra that both ion temperature and composition could be fitted without any extra information.Kelly and Wickwar (1981) constrained the electron temperature in presence of ion frictional heating and the ion temperature in presence of electron precipitation to enable the ion composition fits.Bjørnå and Kirkwood (1988), Fredriksen (1990), and Aponte et al. (2007) used the incoherent scatter plasma lines to gain the necessary extra information about the electron density and electron temperature to enable the composition fits, and Häggström and Collis (1990) used tri-static electric field measurements and ion energy equation to reach the same goal.The most popular approach to overcome the TICA problem has been the full-profile analysis, in which one assumes that the plasma parameter altitude profiles are smooth, and the ion composition profile is often even assumed to follow some pre-defined shape.These methods include both full-profile solvers that actually fit the plasma parameters to the raw radar data (Cabrit & Kofman, 1997;Litvine et al., 1998), and models to make corrections to the fitted plasma parameters (Blelly et al., 2010;Shibata et al., 2000;Zettergren et al., 2010).
The techniques listed above have not made their way to routine EISCAT radar data analysis for several reasons, for example, because coarse altitude resolutions of tens of kilometers and integration times of several minutes are typically not acceptable, the plasma lines are not always detectable and their analysis is tedious, and the true fullprofile solvers require considerable computing power if one wants to include also the E region, which requires high altitude resolution, in the same analysis.A computationally light-weight solution that resembles the fullprofile analysis, and even extends the principle to an assumption of smoothness in time, was proposed by Virtanen et al. (2021).The Bayesian Filtering Module (BAFIM) is able to fit F 1 region ion compositions in relatively quiet conditions, but the authors concluded that support from a chemistry model would be needed to better capture rapid ion temperature and composition variations in active conditions.Chemistry modeling is already in use in AMISR radar data analysis (Richards et al., 2009), in which the ion composition is modeled in each range gate separately by a chemistry model called the Ion Density Calculator (IDC) (Richards, 2011;Richards et al., 2010).The same chemistry model is used also in the latest versions of the International Reference Ionosphere (Bilitza et al., 2022).
In this paper we combine the BAFIM tool (Virtanen et al., 2021) with the IDC (Richards, 2011;Richards et al., 2010) to carry out IS radar data analysis in a way that produces reliable estimates of the fraction of O + ions and ion temperature in the F region.The chemistry model is coupled with BAFIM in such a way that it guides the solver toward physically reasonable solutions, but does not force the final solution to exactly match with the chemistry model.This approach allows us to use the model also when the neutral background ionosphere is not exactly known or when the ions are not in chemical equilibrium.We apply the technique to the almost continuous 1-year EISCAT Svalbard incoherent scatter radar run conducted during the International Polar Year (IPY) from March 2007 to February 2008, and study the statistical properties of ion composition, ion temperature, and electron density at 75.43°corrected geomagnetic latitude, corresponding typically to the polar cap location.Statistical results of the F region ion composition from high-latitude radars have been previously provided only by Litvine et al. (1998), who used about 1,200 hr of data from the EISCAT Tromsø radar site in the auroral oval, and by Shibata et al. (2000) who used 528 hr of data from the same site.To our knowledge, our study is the first to provide statistics of F 1 region ion composition from a polar cap ISR.Our about 5,000 hr data set is also larger than those in the previous studies, although it was collected during only 1 year, during solar minimum conditions.
The paper is organized as follows.In Section 2 we shortly review the typical ion and neutral compositions in the E and F region ionosphere, as well as the basic ion chemical reactions and atmospheric dynamics that alter the ion composition.In Section 3 we introduce the data and the data analysis technique, and give an example of the analysis results.Statistical results from 1 year of data are presented in Section 4, the key findings are discussed in more detail in Section 5, and the final conclusions are given in Section 6.

F-Region Ion and Neutral Composition and Chemistry
Examples of typical number densities of the major ion and neutral species in the E and F regions of the ionosphere are shown in Figure 1.The ion densities are calculated with the International Reference Ionosphere (IRI) model version 2020 (Bilitza et al., 2022), and the neutral densities with the Naval Research Laboratory Mass Spectrometer and Incoherent Scatter radar (NRLMSISE-00) model (Picone et al., 2002).The model values are calculated for geographic coordinates of the EISCAT Svalbar radar (78.15°N, 16.02°E) for 01 April 2007 10:00 UTC.The figure shows that, in this case, the molecular NO + and O + 2 form almost 100% of the ion density in the E and lower F regions up to 180 km altitude.A smooth transition from the molecular ions to atomic O + takes place between 180 and 270 km altitudes, and the ion gas is almost 100% O + above 270 km.The molecular-to-atomic ion transition altitude z 50 , where total number density of the molecular ions NO + + O + 2 ) is equal to the atomic O + ion density, is shown as a horizontal dashed line at 215 km altitude.The ion composition reflects altitude variations in the neutral composition, in which the molecular N 2 and the atomic O are the dominant species below and above 230 km altitude, respectively.The altitudes given above are only illustrative, because the densities undergo both diurnal and seasonal variations, and are affected by solar activity.
Ions are produced by solar EUV and soft X ray radiation, impact ionization by precipitating particles, and in chemical reactions.They are lost via recombination and rearrangement reactions.The molecular NO + and O + 2 ions are lost mainly via dissociative recombination in the reactions.
Where α 1 and α 2 are the reaction rates of the reactions Equations 1 and 2, correspondingly.As recombination of atomic O + is very slow, the atomic O + ions are lost mainly via rearrangement with neutral N 2 and O 2 in the reactions.O where k 1 and k 2 are the corresponding reaction rates.The molecular NO + and O + 2 ions produced in the rearrangement reactions Equations 3 and 4 are subsequently lost via the dissociative recombination reactions Equations 1 and 2. The reaction rates depend on electron and ion temperatures and energy states of the particles involved, but the dissociative recombination rates α i are roughly of the order of 10 13 m 3 s 1 , and the charge transfer rates k i of the order of 10 17 -10 18 m 3 s 1 .For details of the ion chemical reactions and their reaction rates, we refer to Richards (2011).
The ion composition may undergo rapid variations during ion frictional heating and particle precipitation events.The ion heating speeds up the loss of atomic O + and the production of molecular NO + in the rearrangement reaction Equation 3 between O + and N 2 , because the reaction rate k 1 is approximately proportional to square of the ion temperature in high temperatures (Kelly & Wickwar, 1981), k 1 = 7.0 ⋅ 10 19 (T i / 1000) 2.12 when T i > 1000K (Richards, 2011).The heating may also drive thermal expansion of the neutral atmosphere, which increases the neutral N 2 and O 2 densities in the F region and thus speeds up the production of molecular NO + and O + 2 in the rearrangement reactions Equations 3 and 4. On the other hand, the molecular NO + and O + 2 ions undergo dissociative recombination with the free electrons (reactions Equations 1 and 2).The net effect is that ion frictional heating tends to increase the fraction of molecular ions out of the total ion content, but to decrease the total ion (electron) number density.These effects are discussed in detail by Zettergren and Semeter (2012) and Zettergren et al. (2014).Electron production, either by photoionization or by particle precipitation, increases the total ion density and the fraction of the atomic O + ions, because the higher electron density speeds up the dissociative recombination reactions Equations 1 and 2 but does not affect the rearrangement reactions Equations 3 and 4 (Kelly & Wickwar, 1981).The above suggests that the neutral composition, the ion production rate and the ion temperature are the key factors that control the ion composition.

Data and Data Analysis
We use a novel combination of advanced inverse mathematics and chemistry modeling to solve for the electron density N e , electron temperature T e , ion temperature T i , line-of-sight bulk plasma velocity V i , and the fraction of atomic O + ions out of the total ion content p from one year of EISCAT Svalbard radar data, collected during the IPY 2007-2008.This section describes the data and the analysis technique.

ESR IPY Data
From March 2007 until February 2008 the EISCAT Scientific Association operated the EISCAT Svalbard radar (ESR) almost continuously in the same operation mode, as opposed to the usual campaign-based operations with a variety of observation modes.The so-called ipy-mode used the field-aligned 42 m antenna and produced samples of the incoherent scatter autocorrelation function with 6 s time resolution.The experiment covers altitudes from the D region up to 509 km altitude and uses alternating codes (Lehtinen & Häggström, 1987) with 30 μs bit length.The data are sampled with 15 μs sampling steps, which leads to 4.5 km range resolution at "full" (multiples of 30 μs) ACF lags and to 2.25 km resolution at the fractional (15, 45, 75, … μs) lags (Huuskonen et al., 1996).We call these data "the IPY data".
EISCAT has conducted plasma parameter fits to the IPY data using the Grand Unified Incoherent Scatter Design and Analysis Package (GUISDAP) (Lehtinen & Huuskonen, 1996) and these data are available in the Madrigal data base.The fitted parameters are N e , T e , T i , and V i .The fraction of O + ions p is taken from the IRI model in the standard GUISDAP analysis.It is well known that the IRI ion compositions are inaccurate in the F 1 region, which leads to artifacts in ion and electron temperatures in the standard GUISDAP fits (Blelly et al., 2010;Virtanen et al., 2021).
The IPY data were collected at the very end of solar cycle 23 close to the sunspot minimum.The median Kp index during the IPY year was 1+, hence the period was mostly geomagnetically quiet.The largest value of the Kp index recorded during the whole year was 6-, which was reached in only two three-hour periods in May 24 and August 6, and there were only 21 3-hr intervals with Kp ≥ 5.The ESR typically observes the polar cap/cusp ionosphere (Fujiwara et al., 2012), but it may observe also the ionospheric footprint of the closed field lines that connect to the plasma sheet (i.e., the auroral oval), or the different boundary layers in between these regions (Ogawa et al., 2003).

Ion Composition Fits and the Bayesian Filtering Module
In ISR plasma parameter fits, one finds such a combination of plasma parameters that a theoretical autocorrelation function of the incoherent scatter signal, as calculated with the selected parameters, matches with the measurements.In the most general form of the incoherent scatter theory, the theoretical autocorrelation function is a function of the number density, temperature, bulk velocity, and ion-neutral collision frequency of each ion species, the corresponding parameters of the electrons, and the magnetic field (Kudeki & Milla, 2011).Simplifying assumptions are needed in practice, because the measurements do not contain sufficient information for estimating all these parameters.The typical assumptions are that all ion species are in the same temperature and drift with the same velocity, and that the ion composition and collision frequencies are equal to model values calculated for example, with IRI and MSIS.The magnetic field effects are negligible if the radar beam is not very close to perpendicular to the magnetic field.These assumptions lead to the classical four-parameter fit of N e , T e , T i , and V i .The four-parameter fit is typically used in "gated" F region incoherent scatter analysis, in which one divides the radar beam into discrete intervals called range gates, and fits plasma parameters to the measured autocorrelation function data separately at each gate.
The Bayesian Filtering Module (BAFIM) (Virtanen et al., 2021) is an extension module to the standard EISCAT data analysis tool GUISDAP (Lehtinen & Huuskonen, 1996).BAFIM adds properties of full-profile analysis (Holt et al., 1992;Lehtinen et al., 1996), in which one fits plasma parameters along the whole radar beam at once, to the originally gated analysis tool, and extends the idea of full-profile analysis also to time dimension.When analyzing EISCAT radar data with combined BAFIM and GUISDAP, one assumes that the plasma parameter profiles are smooth in both altitude and time.These assumptions are justified when the radar beam is field-aligned and the analysis proceeds with reasonably short steps in time.The full-profile analysis alone is known to enable ion composition fits (Cabrit & Kofman, 1997;Litvine et al., 1998), and the BAFIM implementation effectively allows one to select resolutions of each plasma parameter separately (Virtanen et al., 2021).One can thus use coarse resolutions for the ion composition and thus improve its accuracy, but still solve the other parameters with better resolutions.
When combined with high range resolution, the original idea of full-profile analysis leads to a large inverse problem, whose solution is computationally heavy.In the BAFIM implementation the actual fit is performed at each altitude separately, and the smoothness assumptions are added by means of Bayesian filtering (Särkkä, 2010, for example) and correlation priors (Roininen et al., 2011).This approach keeps the analysis computationally light-weight.The BAFIM analysis proceeds as a sequence of prediction and update steps.In the prediction step, one produces a prior model of the plasma parameters for the current time step.The prediction is based on the fit results from the previous time step.In the update step, one runs the normal GUISDAP fit of plasma parameters using the prediction as a prior.The smoothness assumptions are built in the prediction step, in which one smooths the plasma parameter profiles in altitude and controls how much the parameters are allowed to change between subsequent time steps.For details of the BAFIM implementation, see Virtanen et al. (2021).
While Virtanen et al. (2021) demonstrated the F 1 region ion composition fits with BAFIM, it was also noted that the tool is not well suited for rapid ion temperature and composition variations.This limits also its use in analysis of large data sets, because such data unavoidably contain also measurements from active conditions.The authors suggested that ion chemistry modeling could be added to the analysis to improve its performance in presence of rapid temperature variations.We note that these issues are related to the F region ion temperature variations and the TICA in particular, and the tool has been successfully used for high-resolution E region analysis in presence of rapid electron density and temperature variations (Tesfaw et al., 2022).

Ion Composition Fits With BAFIM and IDC
The Ion Density Calculator (IDC) (Richards, 2011;Richards et al., 2010) is a chemistry model that calculates densities of NO + , O + 2 , N + , N + 2 , and O + ions.The model assumes that all of the ions except O + are in chemical equilibrium, and iteratively finds such an ion composition that the total number density of all ion species matches with a known electron density.In our case the electron density is measured with the radar.The model is based on the chemistry of the Field Line Interhemispheric Plasma (FLIP) ionosphere model (Richards, 2002) and it is included in the latest versions of the IRI (Bilitza et al., 2022).
The IDC model was originally developed for photoionization, but the model works also in presence of auroral particle precipitation, because the additional ion production is implicit in the measured electron density (Richards et al., 2010).Strong ion convection and the produced increase in ion temperature affect the chemical reaction rates and may thus become an issue in modeling (Richards et al., 2010).However, as is explained below, we have coupled the IDC in our analysis tools in such a way that the true temperatures are always used in the model, which guarantees that correct reaction rates are used also when the ions are heated.
We have created an upgraded version of BAFIM that is coupled with the IDC to improve the ion composition fits.We use this tool to fit five plasma parameters, N e , T i , T r = T e /T i , V i , and p, to the IPY data.The upgraded BAFIM has two key differences to the original implementation of Virtanen et al. (2021).First, there is an additional upgrade step with the IDC after the GUISDAP fit, and second, the plasma parameters considered as final fit results are those produced by smoothing in altitude.
In the IDC step we have plasma parameters x = (N e ,T i ,T r ,V i ,p) T and their covariance matrix P from the GUISDAP fit.We then look for an updated set of parameters x′ = N′ e ,T′ i ,T′ r ,V′ i ,p′) T that minimize the cost function Here p IDC is the fraction of O + ions as calculated with the IDC with N′ e , T′ e = T′ r T′ i , and T′ i as inputs.The two terms in Equation 5 are penalties for deviations from the GUISDAP fit result and the IDC prediction, respectively.The standard deviation σ IDC is selected by the user and it controls how tightly the updated parameters x′ are bound to the IDC model predictions.With large σ IDC the model has no effect, and with very small σ IDC p′ is forced to match with the IDC prediction.We have used σ IDC = 0.1 in this paper.We emphasize that we do not force the compositions to match with the IDC prediction, but due to the first term in Equation 5 the solution is reasonably close to the GUISDAP fit and the smoothness assumptions of BAFIM are still in place.The final fit results are plasma parameters x″ and their covariance matrix P″ produced by smoothing in altitude by correlation priors, as explained in (Virtanen et al., 2021).The chemistry modeling together with some technical improvements to control of the correlation lengths allow us to use considerably longer time steps than those used by Virtanen et al. (2021) and Tesfaw et al. (2022).
The iterative fit with the cost function Equation 5 also guarantees that the ion and electron temperatures we input to IDC are based on measurements, and that the fitted combination of plasma parameters is reasonable from the chemistry point-of-view.This approach allows us to avoid the issues with temperature dependent reaction rates mentioned by Richards et al. (2010).We might still suffer from biases caused by the neutral atmosphere model (NRLMSISE-00), which naturally does not reproduce thermal expansion of the atmosphre due to short-lived heating events.However, errors in the neutral background tend to produce non-physical bends in the plasma parameter profiles, and this effect is thus minimized by the requirement that the profiles must be smooth in altitude.
We have analyzed the whole IPY data with 60 s time resolution using the combination of BAFIM and IDC in GUISDAP.Details of the BAFIM settings used in the analysis and how the input parameters scale with time resolution are give in Appendix A. An example of the fit results and a comparison with fit results from standard GUISDAP are shown in Figure 2, which contains results from 01 April 2007 03-06 UTC.The figure shows five plasma parameters, N e , T e , T i , p, and V i as function of time and altitude.The left panels show the new analysis results with BAFIM and IDC, while the right panels show results from the standard GUISDAP fit.The electron density profiles (top panels) show several clear electron precipitation events with significant ionization down to the E region.The precipitation also heats the electron gas, producing electron temperature enhancements above 150 km altitude (second row).The ion temperature profiles (third row) show a group of strong ion frictional heating events that enhance T i above 2000 K between 04:30 and 05:30 UTC.Weaker ion heating is seen both before and after the strongest events.
The fourth row of Figure 2 shows the fraction of O + ions p and the molecular-to-atomic transition altitude z 50 (black lines).With BAFIM and IDC (left) this is a fit result, while with the standard GUISDAP (right) p and z 50 are IRI model values.The fitted O + fraction has the largest fluctuations at 04:30-06:00 UTC, when both electron precipitation and ion frictional heating take place.The frictional heating tends to increase z 50 , which is rapidly lowered by electron precipitation between the heating events.These variations are naturally missing from the model values used in the standard GUISDAP fit.The ion composition affects also the ion and electron temperatures, whose overall characteristics are similar in the two fit results, but there are clear differences in their absolute values.
The bottom row shows the line-of-sight plasma velocities, including ion upflows in connection to the energy input by electron precipitation and ion frictional heating.The velocities show similar features in the two analysis results, but the smoothness constraints in the analysis with BAFIM and IDC reduce noise and make real variations in V i better visible.

Statistical Results
In this section we present statistical results derived from the IPY data.We concentrate on three key parameters that characterize the F region ion composition variations and their drivers.The parameters are the molecular-toatomic ion transition altitude z 50 , ion temperature at 200 km altitude T i , and electron density at 200 km altitude N e .The 200 km altitude was selected, because it is close to the average z 50 .We show also comparisons to model values calculated with the International Reference Ionosphere version 2020 (Bilitza et al., 2022).

Overview of Transition Altitudes During the Whole Year
Figure 3 shows z 50 , T i and N e as function of day of year and magnetic local time (MLT).The MLT has several alternative definitions and it depends on the selected magnetic coordinate system (Laundal & Richmond, 2017).We use the altitude adjusted corrected geomagnetic coordinates (Shepherd, 2014) and calculate the MLT as magnetic longitude difference between the ESR site and a sub-solar point at 700 km altitude.With the ESR coordinates this definition leads to MLT = UTC + 2.5 hr on average, which we use for the UTC to MLT conversion.As the IPY started in March, days 1-60 are from year 2008, while the rest are from 2007.The figure shows also contours of the solar zenith angle (SZA) overlaid in each panel.
The transition altitudes in the first panel of Figure 3 show a clear diurnal variation, with largest z 50 typically observed between magnetic midnight and 10 MLT.The transition altitudes are generally lower during daytime than at night, and the morning maxima are lower during summer than during winter.Ion temperature at 200 km altitude (the second panel of Figure 3) shows also a clear diurnal variation with maxima in the same 00-10 MLT sector with the transition altitude.However, T i has another local maximum at 14-17 MLT.Main characteristics of N e (third panel) follow the solar zenith angle contours, indicating that the F 1 region electron density is controlled by photoionization.The daytime and summer maxima in N e match with the minima in z 50 (first panel).One should notice that Sun is visible at 200 km altitude when SZA <105°, which means that the F region is always sunlit from March to October and for several hours close to local noon at mid-winter.

MLT Variations in Transition Altitude
The MLT variations of z 50 , T i and N e are shown in more detail in Figure 4, which shows median values together with 10%, 25%, 75% and 90% percentiles in 1-hr MLT bins, as calculated from the whole year of IPY data.The corresponding median values calculated from IRI model predictions are shown as red lines.The transition altitude in the first panel of Figure 4 shows a clear diurnal variation with a maximum median value 208 km at 04-05 MLT and a minimum value 187 km at 16-17 MLT.The IRI prediction shows qualitatively similar night maximum and daytime minimum, but their locations are shifted by about 3 hours toward earlier MLTs, and the values are up to 32 km larger than our results.Width of the z 50 distributions, calculated as difference of the 90% and 10% percentiles, has a maximum of 45 km at 07-08 MLT and a mimimum of 20 km at 19-20 MLT.
The MLT variations of T i are shown in the second panel of Figure 4.While T i shows clear diurnal variations, these variations are substantially different from the z 50 variations.The ion temperature has two maxima, 920 K at 05-06 MLT and 870 K at 15-16 MLT in the median values.The 75% and 90% percentiles have their maxima closer to noon than the median values, at 07-08 MLT in the morning side and 14-15 MLT in the afternoon.The ion temperature is very variable in the morning side, and width of the T i distribution reaches 760 K at 07-08 MLT.
Given that the ion temperature affects the ion composition via the temperature-dependent reaction rates, one might find the large difference between the diurnal variations of median T i and z 50 surprising.The IRI prediction does not show significant diurnal variations in T i .
An explanation to the different behaviors of z 50 and T i is given by the electron density, shown in the bottom panel of Figure 4.The electron density is strongly controlled by solar EUV radiation and thus has a dayside maximum after MLT noon and a minimum at 02-03 MLT.In the T i maximum at 15-16 MLT, the high electron density keeps the fraction of molecular ions and thus also z 50 low, because the dissociative recombination of NO + and O + 2 is fast when N e is large.Although the increased ion temperature speeds up the rearrangement of atomic O + into molecular NO + , the molecular ions are lost so rapidly that their fraction of the total ion content cannot become large.In the morning hours the electron density is increasing and the z 50 maximum at 04-05 MLT is before the T i maximum at 05-06 MLT, because N e is lower at 04-05 MLT than an hour later.The IRI prediction of N e is generally lower than our measurement and maximizes earlier, 12-13 MLT.Underestimation of F 1 region N e by previous versions of IRI in Svalbard has been reported by (Bjoland et al., 2016).One can also see that the IRI z 50 is controlled by the IRI N e variations, which may be expected as the IRI T i is almost constant.

Solar Zenith Angle Dependence of the Transition Altitude
While one may reasonably assume that the MLT variations in ion temperature are mainly due to the varying location of the radar with respect to the plasma convection cells, the variations in electron density are largely due to variations in solar illumination.It is thus illustrative to study the variations also as function of solar zenith angle, as shown in Figure 5.The data points from before and after local noon are shown separately, because there is a clear asymmetry between the morning and evening sides.
The electron densities in the third panel of Figure 5 show a clear SZA dependence as expected, and the narrow distributions indicate that the density is primarily controlled by the solar radiation.In the morning side, the densities are almost constant for 125°-100°zenith angles, and they increase monotonically with decreasing zenith angle for zenith angles 100°-55°.In the evening side the electron densities are generally larger than in the morning side, and the densities still decrease also at zenith angles larger than 100°.This might be due to the long lifetime of the O + ions and plasma transport from the dayside.The zenith angle dependence of N e continues to angles larger than 90°, because the solar radiation can still reach the atmosphere due to curvature of the Earth.With 100°zenith angle the incoming radiation has passed through the ionosphere at 100 km altitude, which is enough for majority of the ionizing radiation to be absorbed.
The ion temperatures in the second panel of Figure 5 do not show strong SZA dependence, but they are more variable in the morning side than in the evening side, and have interesting small maxima at the 90-100°zenith angles.The transition altitude z 50 in the first panel of Figure 5 shows clear variations with SZA, with smallest and largest values at smallest and largest zenith angles, correspondingly.The z 50 variations match well with those of the electron density, large electron densities corresponding to low z 50 , superimposed with some effects from the relatively stable ion temperature.Like T i , also z 50 shows interesting local maxima close to sunset at 95-100°z enith angles.The mechanism that causes the local z 50 maxima remains unclear, but could be related to atmospheric dynamics or transient ion chemistry effects at the Solar terminator.

Seasonal Variations
Figure 6 shows median values of z 50 , T i and N e as function of MLT, but separately for winter, equinoxes, and summer.The seasons are centered on solstices and equinoxes, and each data point belongs to the season whose center is closest to it.The spring and autumn data are merged to form one equinox data set because they behave similarly.With this division the whole winter has SZA ≥95°and the whole summer has SZA ≤85°, but the equinox data set has twice as much data points as the winter and summer ones.We note that we have only 1 year of IPY data and the results thus reflect the variations typical for a deep solar minimum year.
The figure shows that the morning side maxima of z 50 and T i are both at 07-08 MLT on summer.The maxima are at the same time, because the electron density increases very smoothly with MLT during summer mornings.The overall high N e in summer also favors the atomic ions, and the maximum z 50 in summer is only 203 km.The evening side T i maximum at 16-17 MLT does not create a maximum in transition altitude because the electron densities are high at this time.During equinoxes, the morning side T i maximum moves to 05-06 MLT and the z 50 maximum of 215 km occurs one hour earlier, 04-05 MLT.The MLT difference is probably due to a large gradient in N e , which favors large fractions of molecular ions at earlier MLTs when the electron density is lower.The evening side maximum in T i coincides with large N e also during equinoxes, which keeps z 50 low despite the ion heating.
The winter data in Figure 6 are quite different from summer and equinoxes.The transition altitude has a morning side maximum at 02-03 MLT, separated by two hours from the T i maximum at 00-01 MLT, but still in a region with relatively high T i .A distinct feature of the winter data is a daytime maximum in z 50 and a corresponding minimum in N e .The winter time electron densities are very low in general, and the density has two maxima at 07-08 and 17-18, because photoionization is practically non-existent and the F region density is created mainly by soft precipitation.The daytime maximum in z 50 is caused by the N e minimum.This phenomenon will be discussed in more detail in Section 5.1.

Correlation With Geomagnetic Activity
As ion temperature is a key parameter that affects the ion composition, one may reasonably assume that the ion composition should correlate with the level of geomagnetic activity via increased ion frictional heating.Figure 7 shows distributions of fitted transition altitudes (top), ion temperatures at 200 km altitude (middle), and electron densities at 200 km altitude (bottom) as function of the Polar Cap North (PCN) index (Troshichev et al., 2006).The PCN index is a measure of the solar wind merging electric field and it estimates the polar cap magnetic activity generated by the solar wind magnetosphere interaction.The data are divided into four equally sized blocks according to the solar local time (SLT = MLT 1.5 hr).The data in each panel are binned in PCN and either z 50 , T i , or N e .The bin widths are 0.2 mV/m for PCN, 5 km for z 50 , 100 K for T i , and 10 10 m 3 for N e .The color-coded quantity is the sum of data points in each bin divided by the total number of data points, that is, the probability of a randomly chosen point to belong to a particular bin.
The results show that both z 50 and T i increase with increasing PCN when PCN is positive.The strongest response occurs 03-09 SLT and the effect weakens toward the evening, the weakest response being observed 15-21 SLT.The strongest response to PCN in both z 50 and T i is located in the same local time sector with the generally highest ion temperatures (Figure 4).This is expected, because the T i maximum suggests that plasma convection leads to strongest ion frictional heating in this sector.The response is weaker in the 09-15 SLT bin, where the electron density is high, and in the 15-21 SLT bin, where the electron density is higher than in the morning side and the ion temperatures are lower in general.The electron densities do not show clear PCN dependence.

Effects of N e and T i in the F 1 Region Ion Composition
Variations in the molecular-to-atomic ion transition altitude were connected to variations in electron density and ion temperature in Section 4. It is thus illustrative to study in more detail how the F 1 region ion composition responds to changes in N e and T i .The left panel of Figure 8 shows a model calculation of the fraction of O + ions as function of ion temperature and electron density.Electron and ion temperatures are assumed to be equal, and the neutral background atmosphere is taken from the NRLMSISE-00 model for 21 March 2007 a 05:00 UTC at 200 km altitude.The results demonstrate how high electron densities and low ion temperatures favor atomic O + ions, while low densities and high ion temperatures favor the molecular ions, as discussed in the earlier sections.The fraction of O + ions is also strongly dependent on N e when T i < 1000 K. Similar model calculations show that the differences between the measured N e and the IRI prediction in Figure 4 can shift the modeled z 50 by tens of kilometers, and could thus explain the differences between the observed z 50 and the IRI prediction shown in Figure 4. Regarding the winter daytime maximum in z 50 , the figure shows that the fraction of O + ions is always low when the electron density is of the order of 10 10 m 3 .Distribution of the fitted O + fractions at 200 km altitude during the whole IPY year are shown on the right in Figure 8.The figure is in good qualitative agreement with the model calculations on the left, which correspond to only one particular instant of time and neutral background atmosphere.The measurements do not cover all combinations of T i and N e , because solar radiation will necessarily heat the ionosphere so that combinations of high N e and extremely low T i are impossible, while high T i speeds up the recombination and thus prevents the combinations of high T i and high N e .

Diurnal Variations of Transition Altitude and Ion Temperature
The Joule heating pattern in the auroral oval is known to have maxima in the dawn side and in the dusk side, due to convection electric fields (Cai et al., 2016, and references therein).However, the ESR is typically in the polar cap, and Cai et al. (2016) found only the afternoon Joule heating maximum around 15 MLT from ESR measurements.The Joule heating pattern observed by Cai et al. (2016) thus cannot directly explain our observations of z 50 , which peaks in the morning side, and T i , which has two maxima.
A key difference between our results and the Joule heating studies is that the ion temperature is proportional to kinetic energy per particle, while the Joule heating rates are expressed as power per unit volume.The same Joule heating rate may thus lead to different ion temperatures, depending on the ion (electron) density.In our data the morning side ion temperature maximum at 05-07 MLT (Figure 4) is actually larger than the afternoon maximum at 15-16 MLT, but N e is considerably lower around the morning side maximum.The morning side T i maximum may thus be generated with considerably smaller heating power per unit volume than the afternoon maximum.This is demonstrated in Figure 9, which shows the product T i N e as function of MLT.The product is proportional to the kinetic energy per unit volume and can thus be compared with Joule heating rates.The median values of T i N e do not have a morning side maximum, because the T i maximum is smoothed out by the lower N e .The product has maximum at 15-16 MLT, which is exactly the MLT bin where Cai et al. (2016) found the afternoon hot spot in Joule heating.
The afternoon hot spot in Joule heating does not create a z 50 maximum in summer and equinoxes (see Figure 6), because ion production by photoionization keeps the electron density high, which favors the atomic ions.An exception is winter, when there is no photoionization and z 50 is clearly elevated close to the afternoon maximum in T i , as one can see from Figure 6.However, the day-side maximum in z 50 does not coincide with the afternoon maximum in T i even at winter, because the very low electron density between 10 and 11 MLT creates the z 50 maximum there.
The morning side maximum in Joule heating creates both T i and z 50 maxima in all seasons, as illustrated in Figure 6.This is because the electron densities are generally lower before 8 MLT than 13-16 MLT.The effect of electron density is still visible also in the morning side maximum, where the transition altitudes are clearly lower in summer than during other seasons, because the electron densities in the 00-08 MLT sector are much higher in summer than at other times of the year.

Limitations of the Analysis Method and Potential Future Work
The BAFIM analysis assumes that the plasma parameters vary smoothly in both time and range (altitude).Incorrect use of such assumptions could obviously lead to incorrect analysis results if sharp gradients were present in the ionosphere.In BAFIM the smoothness is expressed in terms of probabilities, and also relatively sharp gradients may be produced if the measurements give strong enough evidence about their existence.For example, relatively sharp temporal gradients are seen in all plasma parameters in Figure 2. The assumption of smoothness in range is well justified in field-aligned observations, because the high ion and electron mobilities along the field-line prevent generation of large gradients.The gradients tend to be larger in the E and lower F regions than above, which we take into account by means of using shorter correlation lengths in these regions (Virtanen et al., 2021).We thus believe that the smoothness assumptions do not significantly bias the results from field-aligned observations, but the method may not be applicable to other beam directions in its present form.However, prior models very similar to those used in BAFIM are used for 4-dimensional (three spatial dimensions plus time) ionospheric tomography (Norberg et al., 2023).These techniques could possibly be generalized to volumetric plasma parameter fits with the multi-beam EISCAT3D radar (McCrea et al., 2015).
The IDC assumes chemical equilibrium of all other ion species except O + , and takes the neutral background atmosphere from the empirical NRLMSISE-00 model.These assumptions may affect the chemistry modeling in active conditions, in which the chemistry may not have time to reach equilibrium, and energy input from the magnetosphere may lead to thermal expansion of the neutral atmosphere.The way we have coupled BAFIM and IDC reduces these effects to the smallest possible level, because IDC is used merely to guide the solver toward a physically reasonable solution, and the smoothness assumptions in BAFIM efficiently suppress artifacts created by inaccurate chemistry modeling.For example, the chemistry modeling could overestimate the fraction of molecular ions in very short-lived frictional heating events, during which the ionosphere is not in chemical equilibrium.However, the overestimation would lead to unrealistic local ion temperature maxima, which would be suppressed by the smoothness assumptions.Comparing the plasma parameter profiles before and after applying the smoothness constraints in altitude, we find that the median change in z 50 from the smoothness constraints is 6.5 km downwards, and the 25% and 75% percentiles are 9.5 and 3.3 km, correspondingly.This indicates that the NRLMSISE-00 model may lead to overestimation of molecular ion content on average, but the effect is smaller than the variability seen in Figure 4. the altitude resolution, and the process noise variances scale with the time step duration to adjust for different time resolutions.
One remaining effect that was not considered by Virtanen et al. (2021) is that the correlations in time introduced by the Bayesian filtering propagate information about smoothness in altitude in between adjacent time steps.The smoothing in altitude was thus stronger than one could expect based on the correlation lengths alone.The effect becomes clearly visible when one moves from the approximately 5 s time resolution of (Virtanen et al., 2021) to the 60 s resolution used in this paper.To accommodate for this effect, we multiply the length scales s h i by square root of the time step duration Δt.The length scales are thus given in units s 1/2 and the final correlation length is the product s h i Δt 1/ 2 H.The parameters used in the BAFIM analysis presented in this paper are listed in Table A1.

Figure 1 .
Figure 1.Neutral and charged particle density profiles in Svalbard on 1 April 2007 at 10:00 UTC, calculated with the NRLMSISE-00 and IRI-2020 models, respectively.The horizontal dashed line shows the molecular-to-atomic ion transition altitude z 50 .

Figure 2 .
Figure 2.An example of plasma parameter fit results using BAFIM and IDC with GUISDAP (left) and results using the standard GUISDAP (right) from April 2007.From top to bottom, the panels are electron number density, electron temperature, ion temperature, O + ion fraction, and line-of-sight plasma velocity (positive away from the radar).The black line in the fourth panel is the molecular-to-atomic transition altitude z 50 .The solar local time (SLT) is 1 hour ahead UTC, and the magnetic local time (MLT) is 2.5 hr ahead UTC.

Figure 3 .
Figure 3. Molecular-to-atomic ion transition altitude (left), ion temperature at 200 km altitude (middle), and electron density at 200 km altitude (right) as function of day of year and magnetic local time.The white areas are missing data due to radar operations in other than the standard IPY mode, or due to technical issues with the radar.Solar zenith angles are shown as contour lines.At 200 km altitude Sun is behind Earth at zenith angles larger than 105°.The solar local time is 1.5 hr behind MLT.

Figure 4 .
Figure 4. MLT variations of molecular-to-atomic ion transition altitude (top), ion temperature at 200 km altitude (middle) and electron density at 200 km altitude (bottom).The black lines show the median values, the dark blue areas are between 25% and 75% percentiles, and the light blue areas are between 10% and 90% percentiles.The red lines show medians of IRI-2020 model values.

Figure 5 .
Figure 5. Solar zenith angle variations in the same format as in Figure 4, for morning and evening sides separately.

Figure 7 .
Figure 7. Distribution of fit results as function of the PCN index and the molecular to atomic transition altitudes (top row), the PCN index and ion temperature at 200 km altitude (middle row), and the PCN index and electron density at 200 km altitude (bottom row).Each column of panels corresponds to a SLT bin shown on the top.Notice the logarithmic color scale for probability.

Figure 8 .
Figure 8. Left: Model results of O + ion fraction at 200 km altitude as function of T i and N e .The composition is calculated with the IDC model using neutral background atmosphere from NRLMSISE-00 for Svalbard on 21 March 2007 at 05 UTC.Right: Measured O + ion fraction at 200 km altitude as function of T i and N e .The medians are calculated from 1 year of ESR data.Only bins that contain at least 100 data points are shown.

Figure
Figure MLT variations of the product T i N e (at 200 km).The black line is the median over the whole year, and the shaded areas show the 10%, 25%, 75%, and 90% percentiles.
Note: N e , T i , T r , and V i are fitted at all altitudes above h min .The constants s h and s t are scaling factors that control smoothness of the solutions in range and time, respectively, as explained in the text.