G. V. Givishvili and L. N. Leshchenko
Institute of Terrestrial Magnetism, Ionosphere, and Radio Wave Propagation, Troitsk, Russia
Givishvili and Leshchenko [[2001] were the first to try to reveal seasonal features of the temperature long-term trends at the height of the E -layer maximum h_{m}E on the basis of the electron concentration and/or the critical frequency f_{o}E measurements. However, the annual variations of the molecular oxygen concentration [O_{2}], the principal ionized constituent at E -layer heights, have been taken into account by Givishvili and Leshchenko [[2001] only indirectly, using the concentration ratio of the atomic oxygen O and molecular nitrogen N _{2}. The aim of this study is to consider more accurately factors determining the seasonal behavior of the electron production and loss rates in order to be able to analyze the fine structure of the seasonal variations of the long-term trends in the lower thermosphere temperature derived from n_{e} or f_{o}E measurements.
The critical frequency f_{o}E is related to n_{e} by
(1) |
The equilibrium electron concentration n_{e} in the E region only slightly depends on diffusion processes, thermospheric winds, and electric fields. Therefore the formulae is correct there:
(2) |
where q_{m} is the ionization rate in the layer maximum and a_{D} is the effective recombination coefficient. The values of q_{m} and a_{D} both depend on T. This fact makes it possible to determine reliably values of T at the height of the E -layer maximum h_{m}E using the measurements of f_{o}E if the q_{m} and a_{D} dependencies on T are known.
The ionization of the E region is provided mainly by the solar radiation in the l = 97.7 nm and (Lyman- b ) 102.6 nm lines interacting with oxygen molecules. This two channels provide formation of 75-85% of all charged particles. An additional source of ion formation at heights of 100-120 km is related to the solar X rays interacting with oxygen molecules and also nitrogen molecules and oxygen atoms. Thus about 80-90% of the ionization rate q depend on the O_{2} content in the lower thermosphere. Therefore q is determined by the Chapman equation [Chapman, 1931]:
(3) |
where s_{i} and s_{l} are the cross sections of ionization and absorption for an O_{2} molecule, respectively, c is the solar zenith angle, J_{l} is the radiation flux at the wavelengths 102.6, 97.7, and 1-8 nm. The photoionization cross-sections are 10^{-18}, 2.5 10^{-18}, and (0.2-3.6) 10^{-18} for 102.6 nm, 97.7 nm, and 1-8 nm, respectively. The absorption cross-sections are 1.5 10^{-18}, 4.0 10^{-18}, and (0.2-0.9) 10^{-18} for the same wavelengths, respectively [Samson and Cairns, 1964; Watanabe and Hinteregger, 1962]. All s_{l} and s_{i} are constant and do not influence seasonal and long-term changes of the ionization rate. Therefore, to simplify the process of q (O_{2} ) calculations, we accept below generalized values s_{i} = 1.82 10^{-18} cm ^{2} and s_{l} = 2.34 10^{-18} cm ^{2} taking into account the weighted input of the above-indicated solar radiation ranges into the ionization rate.
In the layer maximum where the dq( O_{2}^{+})/dh = 0 condition [Chapman, 1931] is fulfilled we have
(4) |
Equation (4) is not convenient for calculations of T because of two reasons. First, one has to have all the information on absolute values and seasonal variations of [O_{2}]. However different authors [Alcayde et al., 1974; Mayr et al., 1976; Scialmon, 1974] give significantly different information. Second, to know the seasonal variations of the height where the dq(O_{2}^{+})/dh = 0 condition is fulfilled, that is, to which height the derived temperature corresponds, one has to perform additional calculations to reconstruct the q(h) vertical profile using formula (3).
So we rewrite formula (3) in the form
(5) |
Here H( O_{2}) = kT/mg is the scale height for O_{2}, k is the Boltzmann constant, m is the molecular weight of O_{2}, and g is the gravity acceleration. Substituting numerical values of k, m, g, s_{1}, and s_{2} into formula (5), we obtain
(6) |
Now there is no need to know the absolute values of [O_{2}]. According to Ivanov-Kholodny and Firsov [1974] the flux of the radiation ionizing O_{2} is
where F_{10.7} is the solar activity index.
The loss of free electrons in the daytime quiet E region occurs in their dissociative recombination with NO^{+} and O_{2}^{+} ions with the rate constants [Mehr and Biondi, 1969]:
(7) |
and
(8) |
Since at the considered heights n_{e} = [ NO^{+}] + [ O_{2}^{+}] and a ( NO^{+}) 2a ( O_{2}^{+}), the total loss rate is determined by
(9) |
where
Finally, we have
(10) |
Two ways to calculate the temperature from the f_{o}E data are considered. In the first, formula (4) is taken into account, the second is based on formula (6). Substituting these two formulae and formulae (1) and (10) into equation (2), we have
(11) |
and
(12) |
Figure 1 |
Figure 2 |
To specify the character of the seasonal variations of q_{m} and h_{m}E and also to estimate the influence of the seasonal variations of the Q parameter on the temperature evaluation, we use formula (12). Following IRI we presume that h_{m}E = 110 km all over the year. The results of the calculations for the four stations indicated above are shown in Figure 1 as T(12) values. One can see that in this case the deviations between T(12) and T( M) are relatively small in summer but are considerable in equinox periods. The important thing is that a semiannual component which is absent in the annual variations of T( M) is visually seen in the seasonal behavior of T(12).
Figure 3 |
Figure 4 |
Givishvili and Leshchenko [[2001] introduced into formula (12) a parameter g which took into account the [O_{2}] seasonal variations according to the data of the rocket measurements of the [O]/[N_{2}] ratio at a height of 130 km [Antonova and Katyushina, 1976]. In other words, T was calculated using
(13) |
The evaluation of g from the data on the [O]/[N_{2}] ratio made it possible to estimate the annual T variations at h_{m}E rather approximately. More explicit description of the relative seasonal variations of [O_{2}] at height of the E -layer maximum provides the MSIS model, if one determines the g parameter in another way: as a ratio g = [ O_{2}]_{i}/[ O_{2}]_{J}, where J stands for January and i = 1-12 corresponds to the month number. Thus g is characterized by the relative changes of [O_{2}] at about 110 km relative the values in January.
Figure 5 |
One can easily see that the discrepancy between T(13) and the model values of the temperature T( M) is in this case maximum in summer months when the discrepancy reaches 100-200 K. In winter months the difference between T(13) and T( M) is small. This indicates to the fact that in winter h_{m}E is actually close to 110 km. In summer months it should decent down to the altitudes where [O_{2}] is considerably higher than at 110 km, as has been suggested earlier. This conclusion agrees with empirical models of the midlatitude ionosphere [Fatkullin et al., 1981; Givishvili and Fligel', 1971; Robinson, 1960]. According to these models the noon values of h_{m}E vary during the year from the maximum winter values equal to 108-112 km to the minimum summer values of about 104-108 km. The incoherent scatter measurements conducted in Kharkov (50^{o} N) in 1978-1983 also indicate to a lowering of h_{m}E from winter to summer [Ivanov-Kholodny et al., 1998]. To check the conclusion on variability of the h_{m}E and to estimate its changes during the year, we calculated g ( M)
(14) |
Figure 6 |
Figure 7 |
Figure 8 |
Thus, we have now all the necessary information for calculation of the temperature at the heights of the E -layer maximum on the basis of the data on f_{o}E, including the data on the changes of both this very height (the h_{m}( M) parameter) and the O_{2} concentration at this height, i.e., the g_{m}( M) parameter.
As for the IRI model, it is worth mentioning that the reliability of the data on the electron concentration (frequency f_{o}E ) in it arises no doubts. Evidently, the same is not true for the seasonal variations of both the maximum height and ion composition of the E layer. The calculations performed show that the h_{m}E height should vary over the year. However, the assumption on the absence of annual variations of the [NO^{+}] and [O_{2}^{+}] generally speaking may not correspond to the reality. Nevertheless, some corrections to the accepted here algorithms of temperature calculations would be reasonable to insert only after statistically reliable data on the parameter Q seasonal behavior are obtained.
The analysis presented above makes in possible to make the following conclusions:
1. The method to evaluate the lower thermosphere temperature from the ionospheric vertical sounding data is specified. A parameter g is introduced which takes into account the seasonal variations of the O_{2} concentration at altitudes of the E -layer maximum. This parameter makes it possible to reproduce the annual variation of the lower thermosphere temperature at middle latitudes ( j = 42^{o}-62 ^{o} N) on the basis of the critical frequency f_{o}E measurements.
2. The assumption on the constancy of the E -layer maximum height made in the IRI model, does not fit the reality. There is ground to believe that h_{m}E = 110 km only in winter. During the rest of the year it is slightly lower. The amplitude of the seasonal variations of h_{m}E depends on latitude, increasing from 1.6 to 4.3 km in the latitudinal band 42^{o}-62^{o} N.
3. The data on the seasonal variations of the ion composition at E -layer heights presented in the IRI are doubtful. To specify the character of the annual behavior of the [NO^{+}]/[O_{2}^{+}] ratio, additional experimental studies are needed.
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