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Empirical D-region modelling, a progress report
Pergamon
Adv. Space Res. Vol. 22, No. 6. pp. 157-166, 1998 0 1998 COSPAR. Published by Elsevier Science Ltd. All rights reserved Printed in Great Britain 0273-l 177/98 $19.00 + 0.00 PII: SO273-1177(98)00095-7
EMPIRICAL D-REGION MODELLING, A PROGRESS REPORT M. Friedrich’, and K.M. Torkar2
‘Department of Communications and Wave Propagation, Technical University Graz, Inffdgasse A-801 0 Graz, Austria 2Space Research Institute, Austrian Academy of Sciences, Inffeldgasse 12, A-801 0 Graz, Austria
12,
ABSTRACT The most reliable measurements of electron densities in the lower ionosphere are all based on rocketborne radio wave propagation experiments. The grand total of 247 such profiles yields only about 100 cases usable for the establishment of non-aurora1 electron density models, the number of usable data for the derivation of other empirical parameters such as effective electron loss rate, cluster transition height or the negative ions is even smaller. The construction of models based on limited data relies on careful screening and weighting of the inputs, while the methods chosen must reflect physically justified assumptions, and the results should be compatible with theory. Under these restrictions empirical models of D01998 COSPAR. Published by Elsevier Science Ltd. region parameters are presented and discussed. AVAILABLE
DATA
The paper reports the status of empirical D-region modelling. Models covering other regions of the ionosphere or theoretical ion-chemical approaches are not reviewed. Dedicated empirical models of the D-region were published earlier by e.g. McNAMARA (1979); also IRI covers this height region (BILITZA, 1990). However, the origin of data that entered these models can retrospectively no longer be separated into more or less appropriate measurements. A new modelling approach is made using data expected to be from suitable measurements. Due to the relatively dense background atmosphere in the D- and E-regions a sounding rocket is exposed to hydrodynamic flow, i.e. compression or rarefaction of the medium in the immediate vicinity of the rocket payload. In-situ measurements are therefore inevitably uncertain in their absolute values. Radiowave propagation experiments in which an RF wave is transmitted from the ground to the flying payload yield information on the underlying electron content completely unaffected by electrical payload charging or aerodynamic effects (THRANE, 1974). The first measurements of this kind were processed using the Appleton-Hartree (-F&sterling) magneto-ionic theory which only crudely treats collisional effects; since these early measurements were confined to altitudes above 90 km, the application of this inadequate theory has no bearing on the results. Later measurements primarily made use of the dual refractive properties of the magneto-plasma by measuring the rotation of the plane of polarisation (Faraday rotation, MECHTLY et al., 1972; BENNETT et al., 1972; JACOBSEN and FRIEDRICH, 1979) or - notably at the equator - differential absorption. For the latter in particular a more rigorous treatment of the collision frequency is essential and the formulation of the ionosphere’s refractive index after SEN and WYLLER (1960) is generally used. The further refinement of that theory by FRIEDRICH et al. (1991) is applied
M. Friedrich
758
140.
and K. M. Torkar
120-
35. VI z .eo 30_ G
110 _
s
130-
IOO90-
r
25
5 "0 t -g
15_
s-
10
-
20.
80" 70.
5.
60. 60. __ 0
Fig. I
O_ 20
Number
40
of rocket
60
data
80
100
per
kilometre
120
of
80
Fig. 2 Number
100
of rocket
120
flights
140
160
180
200
per solar activity
inter-
val.
height.
only to a few rocket flights and does not reveal significantly different results. Density profiles from probes together with radio wave propagation experiments aboard the same rocket payloads can be normalised to the propagation data. The empirical models of other D-region parameters described in the following require not only electron densities and consequently are each based on data sets smaller than the above mentioned 247 profiles of rocket-borne wave propagation data. The data usable for the prime objective described in the present paper are ti-om non-aurora1 latitudes under “normal” conditions, i e. geomagnetic latitudes >6 lo, and conditions of Winter anomaly and eclipses are excluded. Fig. 1 shows the number of data per kilometre of altitude, whereas in Fig. 2 the number of rocket flights per solar activity interval is given. NON-AURORAL
ELECTRON DENSITIES
Electron densities outside the aurora1 zones are reasonably predictable, whereas at high latitudes typical shapes of the profiles can only be given retrospectively using L’.K.the aurora1 index or K,, as parameter.
In the following the expected and predictabIe variations of electron densities are given in order of their importance. s The ion pair production rate in the atmosphere is a function of the number density of the ionisable constituent (e.g. NO in the D-region) and the local flux of ionising radiation (e.g. Lyman-a). With increasing zenith angle x the extraterrestrial ionising radiation suffers increasing absorption and vanishes beyond x = 90”. Assuming a constant recombination rate of the free electrons with ions the dependence of electron density on x is described by (cosx)~).~(CHAPMAN, 193 1). but due to the curvature of the Earth a corrected formulation (Chapman function) must be applied near grazing incidence. In the absence of direct sunlight (x > 100’) ionisation is provided by Lyman-o and -b scattered in the geocorona and thus depends but a little on the solar zenith angle (cf: STROBEL et al., 1974). whereas galactic cosmic rays and possible stellar X-rays are fully independent of solar zenith angle. The simple zenith angle dependence as quoted above is fu~he~ore complicated by the fact that the reco~~~biIlation rate in the
Empirical D-Region M~elling
lower D-region becomes tron to neutrals forming additional loss process, most vanish and thereby rate with electrons.
759
much larger at night. This is chiefly due to two processes: u) attachment of elecnegative ions is effective in the absence of photo-detacl~lnellt and constitutes an and b) the densities of atomic oxygen below a ledge situated at about 84 km alfavour the formation of cluster ions with their significantly larger recombination
Season The season is expected to impact on the ionosphere in three ways: LI) Nitric oxide is produced through ionisation in the thermosphere and transported downwards into the mesosphere. The length of the day will therefore be important both for the production of NO and the photolysis on the way to the D-region. In a first approximation the densities are larger in Winter than in Summer (“normal winter anomaly”, SCHWENTEK, 1971; SOLOMON et al., 1982). h) The neutral temperature undergoes a seasonal variation generally folIowing an annual wave, whereas at the equator there is a semi-annual component due to the fact that the longest daily insolation occurs at the equinoxes ($ CIRA-86. REES ct ul., 1990). This temperature variation obviously must have a profound influence on the highly temperature dependent reactions leading to water cluster ions with their much larger recombinatioil rates. and c) the Earth’s orbit around the Sun is slightly elliptic with the perihelion shortly after the northern hemisphere Winter solstice. Latitude The latitude dependent sunlit fraction of the day largely determines the concentration of nitric oxide, but also of other trace constituents and temperature. Charged particles, however, follow the magnetic field lines such that geomagnetic latitude provides a better description of their variation. Solar particle fluxes contribute to ionisation at night and at somewhat higher altitudes (> IO0 km) whereas cosmic rays are important below say 6.5 km; both sources increase with geomagnetic latitude. Solar Activitv Enhanced solar activity expressed either by Sun spot ilumber R, or as 10.7 cm solar radio tlux is associated with increased fluxes of Lyman-a and solar X-rays, but decreased fluxes of galactic cosmic rays. One hence expects electron densities to be positively correlated with solar activity except for the lowest part of the D-region where ionisation by cosmic rays dominates and an inverse behaviour is actually observed (MECHTLY ct ~11..1972). Model Structures The mathematical s~ucture to which we want to fit the data assumes mutual independence of each layer considered (altitude, neutral density or pressure surface) from the one above or below. The models described in the 10' 100 10'0 10" 11 following are termed FIRI-**, i.e. FaradayELECTRON DENSITY, mm3 based IRI. The choice of the complexity of Fig. 3 Electron densities of FIRIfor various solar zenith the mathematical structure by which electron angles as a function of neutral density; approximate altitude is densities are assimilated must be carefully given for guidance only (from FRIEDRICH and TORKAR, chosen: A high order of the function better 1992).
M. Friedrich and K. M. Torkar
760
assimilates the input data, but requires more data to establish the necessary constants. A low order strutture on the other hand can be established from fewer data at each altitude level and yields more realistic values for extrapoIated conditions poorly covered by data. The earliest model of this kind (FIRI-01) was published by FRIEDRICH and TORKAR ( 1992) and uses 72 non-amoral, “normal” profiles. Only the strong dependence on the solar zenith angle is taken into account for reasons explained above. The influence of the solar activity is eliminated by converting the input electron density data to an average value R, = 60 elnploying the dependence incorporated in IRI, whereas latitude and season are crudely accounted for by fitting at constant neutral density levels according to the CIRA atlnospheric modei. log/Y, = A + B ln[Ch(X)]
(I)
Onfy the parameters A and B have to be determined as a function of height (or neutral density), where A represents an electron density profile for a hypothetical overhead Sun, and B corresp{)Ilds to the exponent n in the (~0s~)~ formula. Zenith angles beyond 90” are acco~lted for by a Chapman function extended into full night (SMITH and SMITH, 1972). Fig. 3 shows the outcome of the analysis for zenith angles between 20 and 160”. FIRIapplies the Chapman function for the zenith angle dependence, a sine wave for the season and linear functions for latitude and soIar activity, respectively. It could be shown that (~1’the sixteen terms which occur when multiplying all functions with each other, many only contribute marginally even for the
FEB
AUG SEP OCT NOV
DEC
-60”
-400
00
Latitude
20”
400
60’
Fig. 4 Distribution of rocket launches in latitude and season together with some permanent rocket launching sites. Also indicated are contours of constant daily integrated insolation IL Note that there are fewer points than rockets, because on some days more than one rocket was launched.
~pi~cal
761
D-Region M~elIing
0.4
0.3
0.2
0.1
0 0
20"
40"
60"
80"
loo"
120"
140"
160"
180"
Zenithangle,ckg
Fig. 5 Distribution of rocket flights vs. integrated daily insolation C and solar zenith angle x. Note that not all combinations of zenith angle and integrated insolation are conceivable.
most extreme combination of inputs. The final function was chosen such that any seasonal variation vanishes at the equator. Strict symmetry to noon and solstice as well as equality between geographic and geomagnetic latitude is assumed. At each kilometre of height eiectron densities are thus described by: 100, =A + Wn(Chx) + Chln(Chx) + Dhsin[x(SO+d)ll82] + EFIO,,+ J’ln(ChX)F,,,7 + GXF10,7+ Hh
(2)
with the latitude h, the day number d since Winter solstice and the solar flux FlO,?.The height dependent constants A to 13 are determined from the data. Using F10,7rather than Sun spot number R, yields a marginally better fit of the data particularly below 95 km. Internally R, inputs are converted to F,,,, using the relation after THOMSON (1995). The model was presented at the 3 1” COSPAR Meeting in Birmingham 1996 (FRIEDRICH and TORKAR, 1997). FIRI-03: Changes of electron density with season and latitude are predomin~tly caused by variations of @IO]. In a simple scenario NO is produced in the recombination processes of 02+ and N2+,transported to the mesosphere and lost by photo-dissociation. It is reasonable to assume that also the densities of other relevant minor species will depend on the length of the day. The effective length of the day therefore crucially determines how much NO is actually available in the D-region. Season and latitude are here lumped into one parameter characterising the insolation C of the day in question by integrating cosx from sunrise to sunset. The result is scaled such that C = 1 refers to 24 hours of overhead Sun (x = 0”). C thus replaces season and latitude and the following relation applies: 100, = A + Bln(ChX) + eC + DCln(Chx) + EF,O,, + J’Fu,&r(Chx) + GF,&
+ HCF,O,,ln(Chx)
(3)
M. Friedrich and K. M. Torkar
762
Fig. 4 shows lines of constant C vs. season and latitude between rtr60°.Also indicated by dots are the dates of the various rocket launches which contribute data to this model. It is assumed that the ionosphere will e.g. have the same behaviour at 20” latitude in December as at 60” in August, i.e. the known seasonal and fatitudiial variation of temperature and its influence on the ion chemistry {electron loss) is ignored. In Fig. 5 the rocket flights are shown as a function of insolation of the day of the launch vs. zenith angle during the launch. Clearly more data are needed for small X and large x. Profiles obtained from FIRI- are very close to those of FIRI-02, but do allow for a semi-annual variation at the equator. However the latitudinal variation of cosmic rays and charged particles which was implicitly included in FIRI-02, is here not accounted for. In order to assess the qualities of the different models an average error factor is defined as exp~ln~~~(rocket)/~~(model~]~ of all input values. FIRI- yields a value of 1.667 in the altitude range from 70 to 120 km (i.e. the rocket values are on average larger or smaller than the model values by that factor) compared to 1.702 in the case of FIRI-02. Although this fit is only marginally better than that of FIRI-02 it is believed to provide a better description because it allows for a seasonal variation at the equator and yields more reasonable values for extrapolated conditions. The only smoothing with altitude is a running mean of the height-dependent coefficients in Eq. 3. In Fig. 6 tropical electron density profiles for noon and mi~ight are shown, respectively, as examples for widely different zenith angles. The ledge around 83 km during the day probably reflects a corresponding ledge in Ir\rO], whereas the steep rise of the density at night is most likely due to the sudden occurrence of atomic oxygen. This increase which is more pronounced in individual profiles, but occurs at slightly different altitudes, is smeared out somewhat in the model. Fig. 7 shows equatorial profiles for equinox and solstice for x = 60” and low solar activity. As expected the equinox values are slightly larger due to the larger insolation; apparently the effect of increased NO by ionisation in the E-region outweighs the larger destruction of NO by photodissociation. Radio wave absorption which originates predomin~tly in the D-region was observed by many researchers to be significantly larger in the afternoon, but no explanation was put forward (e.g. LASTOVICKA, 1977). Fig. 8 shows the average diurnal variation of the signal strength of an A3 radio path of 2.83 MHz over 500 km (TORKAR et al., 1978). This asymmetry is largest in Summer suggesting a “sluggishness” of the ionosphere which becomes more ?-?-!Y-T: : :: ; i : :: apparent when the Sun rises or sets : :: : : .j..i. faster. No hysteresis is discernible in : : :,, : : : : :; ; : Winter, but the absorption is larger for .i..+ .._: : : j :. : the comparable solar zenith angles. The : : ; :: j j lifetime of ions in the D-region is be: :: ‘?: : : :: :; I : : I : ;: lieved to be very short and can thus not :: .;__.,.1. .i? explain the observed effect. The re:; i ,: i: : : .:_..,. I_ cently available data on mesospheric .j_;. :: :: : [NO] from the experiment HALOE :: :: .&. ..:..i..;.. aboard the satellite UARS show dif:: : :: : .: ij : ferences between densities derived at ..:..:+ sunrise vs. those from sunset. This j.-+ asy~e~ amounts to the PM values Ii:: being almost one order of magnitude .:..:.i. i ;; larger than the AM densities near 80 1 iii km at the equator; at 50” latitude this Electron density, m” hysteresis vanishes. Although the absolute values of simulated electron densi* Fig. 6 Tropical midnight and noon electron density profiles usmg ties using HALOE PO] are not consisFIRI- for low solar activity (x = 0” and 180°, respectively, 2” latitent with the empirical electron densitude at solstice and F10.7= 75, May 10). :
‘: i : ;I
..,
!_I_
:
::
i f
:i +.
:
:...;.;. :.:. :1 :: .;.i. :+-q :: i.:..;.:. ii i:.: ; .;...;.;. ::: : :..,.j_
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:
i
:
;
:
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Empi~caI D-Region M~elling
763
ties of FIRI~F~ED~CH et al., 1996), it was tested if a corresponding asymmetry in the electron densities can be found in FIRI-03. Fig. 9 shows equatorial profiles for x = 60” and low solar activity using only AM and PM data, respectively. Why PO] should undergo a diurnal variation is unresolved, since its lifetime is believed to be of the order of days. In Fig. 10 the dependence on solar activity is tested. The latitude, zenith angle and season are chosen for conditions best covered by input data. One clearly sees a positive correlation at all altitudes above 65 km and - as predicted - the reverse behaviour below that height.
c
. ..
. ..
. ..
. ..
. ..
60
. .. 4
lo8
Beyond FIRI-
Electron density, me3
In contrast to FIRI-
Fig. 7 Equatorial electron densities for equinox and solstice for condi tude is completely tions of low solar activity and a zenith angle of 60”.
geomagnetic latiignored in FIRI-03.
An inclusion by e.g. linear dependence on magnetic latitude can be provided. This initially leads to 16 coefficients, but analogous to the procedure applied in FIRI-02, coefficients of combined parameters which only con~ibute very little can be omi~ed. The amount of available data only permits to sensibly determine eight coefficients.
In a further step one can - as in FIRI- - carry out the fit procedures for constant neutral densities or pressure surfaces. One thus re-introduces latitude and season without increasing the complexity of the describing function. Whether this added procedure yields a significant improvement remains to be tested. I
I
I
I
I
I
I
I
I
I
I
I
I
I
1
n-0-25
I
1
I
I
I
I
I
1
I
I
I
1
**........*,
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Fig. 8 Variation of a 2.83 MHz signal over a 502 km path as a function of solar zenith angle during a period of low solar activity. The dotted line is the average variation throughout the year. Note the large hysteresis in Summer and the high absorption in Winter (afier TORKAR et al., 1978).
M. FrIedrich and K M. Torkar
764
OTHER D-REGION PARAMETERS “‘I
i
i
i
iiiiii
i
i
i
iiiiii
i
i
i
iiiiil
Aurora1 Zone Electron Densitv
_ _
_
_I_
_
L
J_I_I_IJ
LI_
_ _
Electron density.
IK’
In the aurora1 zone the basically unpredictable influx of energetic charged particles dominates the ion pair production. Models for these conditions can only retrospectively describe the situation. There are presently two published models, one based on literally thousands of EISCAT profiles and the other on about 100 in .situ rocket data 1991; (KIRKWOOD and COLLIS, FRIEDRICH and TORKAR. 1995a. respectively). Both models separate between day and night conditions and use locally measured riometer absorption as the describing parameter. Currently work is in progress to combine the best of both models. i.e. the large number from EISCAT with the much lower density threshold oi‘ the rocket data.
Fig. 9 Equinox electron densities using AM and PM data only. The model values are for x = 40”, low solar activity and equinox at the equator at low solar activity
Cluster Ion Transition
(F,,, , = 67). The number of available measurements to establish an empirical relation where the transition from water cluster ions to molecular ones occurs. is very limited. At night the actual level 01’the chemically important ledge in atomic oxygen seems to be very variable and no obvious behaviour could be found. During the day when photo-detachment seems to be more important than [Oj a clear correlation of the transition height with temperature could be found. The formulation published by FRIEDRICH and TORKAR (1988) still holds. but the updated \,crsion should be used (FRlEDRlCH and ‘I‘ORKAR. 1995b). Negative Ions
The fraction of ions among the negatively charged species is the quantity customarily Electron density. nl-’ derived. Due to photo-detachment negative Fig. 10 Solar activity dependence of electron densities at 30” ions become negligible above about 60 km latitude and 60” solar zenith angle (Flo7 = 67/l 50. equinox). during the day, but are present in considerable amount at night below about 90 km. 10’
Empirical D-Region M~elling
765
Using a subset of the data employed in the present context, the most recent model for night time is described by FRIEDRICH and TORKAR (199%). Daytime values of the same negative ion fraction appear about 20 km lower. Effective Electron Recombination
Rate
No new data have become available and the model published by TORKAR and FRIEDRICH probably still the best attempt (daytime only),
(1988) is
CONCLUSIONS With the relatively small number of indisputable D-region electron density profiles an empirical model of the variation of electron densities as a function of insolation, solar zenith angle and solar activity was established. The fact that all altitudes are treated independently allows any shape of the protile. The average uncertainty of the prediction vs. the rocket data in the present FIRI-03 model is 1.67 compared to I .85 in FIRIand 1.70 in FIR&02. Further improvements are expected from the specific inclusion of geomagnetic Iatitude and the ~angement for constant pressure levels. Possibly the weakest point in the present treatment is the use of a Chapman function extended into full night. The model is based on “normal”, nonaurora1 electron densities; however the extrapolation to aurora1 regions provides electron density profiles representative for extremely quiet conditions. A combined EISCAT and rocket data model for auroral latitudes is currently being developed and should yield more representative values. The empirical models of other D-region parameters basically make use of the same set of rocket-based electron densities, but also require at least one other measured physical parameters. Consequently there are even fewer usable data and no new results are presently available. ACKNOWLEDGEMENTS The contributions by Messrs. R. Erlacher and R. Pilgram to the numerical computations are acknowledged. Many unpublished rocket data were made available to the authors by the experimenters. Flights with Austrian instruments were supported by grants of the Austrian Science Foundation. REFERENCES Bennett, F.D.G., J.E. Hall, and P.H.G. Dickinson, D-Region Electron Densities and Collision Frequencies from Faraday Rotation and Differential Absorption Me~urements, J. atmos. terr. P&s. 34 (8), p. 321, 1972. Bilitza, D., International Reference Ionosphere, URSI-COSPAR, Goddard Space Flight Center, Greenbelt MD 2077 1, 1990.
National Space Science Data, NASA
Chapman, S., Absorption and Dissociation or Ionising Effects of Monoc~omati~ Earth, Pro&. Roy. Sot. 43, pp. 26-45, 193 1.
Radiation on a Rotating
Friedrich, M., R. Finsterbusch, KM. Torkar, and H. Sp&ker, A Further Generalisation Wyller Magneto-Ionic Theory, A&. Space Rex 11 (lo), pp. 105-l 08, 1991.
of the Sen and
Friedrich, M., D.E. Siskind, and K.M. Torkar, HALOE Nitric Oxide Measurements in View of Ionospheric Data, Paper SA32B-05 presented at AGU Fall Meeting, San Francisco, 1996. Friedrich, M., and KM. Torkar, Empirical Transition Heights of Cluster Ions, Adv. Space Rex 8 (4), pp. 235-238,1988,
766
M. Friedrich and K. M. Torkar
Friedrich, M., and K.M. Torkar, An Empirical Model of the Nonauroral D Region, Radio Sci. 27 (6), pp. 945-953, 1992. Friedrich, M., and K.M. Torkar, Typical Behaviour of the High Latitude Lower Ionosphere, Adv. Space Rex 16 (1) pp. 73-8 1, 1995a. Friedrich, M., and K.M. Torkar, A Contribution to IRI for the D-Region, Adv. Space Rex 15 (2), pp. 161164,1995b. Friedrich, M., and K.M. Torkar, An Attempt to Parameterise Negative Ions in the Ionospheric D-Region, ESA SP-370, pp. 257-261, 1995~. Friedrich, M., and K.M. Torkar, Comparison Between a Statistical and a Theoretical Model of the D-Region, Adv. Space Rex in press, 1997. Jacobsen, T.A., and M. Friedrich, Electron Density Measurements in the Lower D-Region, J. atmos. terr. Phys. 41(12), pp. 1195-1200,1979 Kirkwood, Sheila, and P.N. Collis, The High Latitude Ionosphere Observed by EISCAT, Adv. Space Res. 11 (lo), pp. 109-l 12, 1991. LaStovicka, J., Seasonal Variation in the Asymmetry of Diurnal Variation in the Lower Ionosphere, J. atmos. terr. Phys. 39, pp. 891-894, 1977. McNamara, L.F., Statistical Model of the D-Region, Radio Sci. 14, pp. 1165-l 173, 1979. Mechtly, E.A., S.A. Bowhill, and L.G. Smith, Changes of Lower Ionosphere Electron Concentration Solar Activity, J. atmos. terr. Phys. 34, pp. 1899-1907, 1972.
with
Rees, D., J.J. Barnett, and Karin Labitzke, COSPAR International Reference Atmosphere, Part II, Adv. Space Res. 11 (1 l), 1990. Schwentek, H., Regular and Irregular Behaviour of the Winter Anomaly in the Ionospheric Absorption, J. atmos. terr. Phys. 33, pp. 1647-1650, 1971. Sen, H.K., and A.A. Wyller, On the Generalization geophys. Res. 65, pp. 3931-3950, 1960.
of the Appleton-Hartree
Magnetoionic
Formulas, J.
Smith III, F.L., and C. Smith, Numerical Evaluation of Chapman’s Grazing Incidence Integral ch(X,Q, J. geophys. Res. 79, pp. 3592-3597, 1972. Solomon, Susan, P.J. Crutzen, and R.G. Roble, Photochemical Coupling Between the Thermosphere and the Lower Atmosphere 1. Odd Nitrogen from 50 to 120 km, J. geophys. Res. 78, pp. 7206-7220, 1982. Strobel, D.F., T.R. Young, R.R. Meier, T.P. Coffey, and A.W. Ali, The Night-Time Ionosphere: E-Region and Lower F-Region, J. geophys. Res. 79, pp. 3 1771-3 178, 1974. Thomson, R., The Ten Centimetre Solar Radio Flux, IPS Radio & Space Services, Internet, http://www.ips.gov.au/, 1995. Thrane, E.V., Ionospheric Profiles up to 160 km - A Review of Techniques and Profiles, in: COSPAR Methods of Measurements and Results of Lower Ionosphere Structure, K. Rawer (ed.), pp. 3-21, Akademie, Berlin, 1974. Torkar, K.M., and M. Friedrich, Empirical Electron Recombination J. atmos. terr. Phys. 50 (8), pp. 749-761, 1988.
Coefficients in the D- and E-Region,
Torkar, K.M., M. Friedrich, W. Wallner, G. Rose, and H.U. Widdel, Preliminary Results of Absorption Measurements of a Central European A3 Path, Kleinheub. Ber. 21, pp. 155-l 61, 1978.
Adv. Space Res. Vol. 22, No. 6. pp. 157-166, 1998 0 1998 COSPAR. Published by Elsevier Science Ltd. All rights reserved Printed in Great Britain 0273-l 177/98 $19.00 + 0.00 PII: SO273-1177(98)00095-7
EMPIRICAL D-REGION MODELLING, A PROGRESS REPORT M. Friedrich’, and K.M. Torkar2
‘Department of Communications and Wave Propagation, Technical University Graz, Inffdgasse A-801 0 Graz, Austria 2Space Research Institute, Austrian Academy of Sciences, Inffeldgasse 12, A-801 0 Graz, Austria
12,
ABSTRACT The most reliable measurements of electron densities in the lower ionosphere are all based on rocketborne radio wave propagation experiments. The grand total of 247 such profiles yields only about 100 cases usable for the establishment of non-aurora1 electron density models, the number of usable data for the derivation of other empirical parameters such as effective electron loss rate, cluster transition height or the negative ions is even smaller. The construction of models based on limited data relies on careful screening and weighting of the inputs, while the methods chosen must reflect physically justified assumptions, and the results should be compatible with theory. Under these restrictions empirical models of D01998 COSPAR. Published by Elsevier Science Ltd. region parameters are presented and discussed. AVAILABLE
DATA
The paper reports the status of empirical D-region modelling. Models covering other regions of the ionosphere or theoretical ion-chemical approaches are not reviewed. Dedicated empirical models of the D-region were published earlier by e.g. McNAMARA (1979); also IRI covers this height region (BILITZA, 1990). However, the origin of data that entered these models can retrospectively no longer be separated into more or less appropriate measurements. A new modelling approach is made using data expected to be from suitable measurements. Due to the relatively dense background atmosphere in the D- and E-regions a sounding rocket is exposed to hydrodynamic flow, i.e. compression or rarefaction of the medium in the immediate vicinity of the rocket payload. In-situ measurements are therefore inevitably uncertain in their absolute values. Radiowave propagation experiments in which an RF wave is transmitted from the ground to the flying payload yield information on the underlying electron content completely unaffected by electrical payload charging or aerodynamic effects (THRANE, 1974). The first measurements of this kind were processed using the Appleton-Hartree (-F&sterling) magneto-ionic theory which only crudely treats collisional effects; since these early measurements were confined to altitudes above 90 km, the application of this inadequate theory has no bearing on the results. Later measurements primarily made use of the dual refractive properties of the magneto-plasma by measuring the rotation of the plane of polarisation (Faraday rotation, MECHTLY et al., 1972; BENNETT et al., 1972; JACOBSEN and FRIEDRICH, 1979) or - notably at the equator - differential absorption. For the latter in particular a more rigorous treatment of the collision frequency is essential and the formulation of the ionosphere’s refractive index after SEN and WYLLER (1960) is generally used. The further refinement of that theory by FRIEDRICH et al. (1991) is applied
M. Friedrich
758
140.
and K. M. Torkar
120-
35. VI z .eo 30_ G
110 _
s
130-
IOO90-
r
25
5 "0 t -g
15_
s-
10
-
20.
80" 70.
5.
60. 60. __ 0
Fig. I
O_ 20
Number
40
of rocket
60
data
80
100
per
kilometre
120
of
80
Fig. 2 Number
100
of rocket
120
flights
140
160
180
200
per solar activity
inter-
val.
height.
only to a few rocket flights and does not reveal significantly different results. Density profiles from probes together with radio wave propagation experiments aboard the same rocket payloads can be normalised to the propagation data. The empirical models of other D-region parameters described in the following require not only electron densities and consequently are each based on data sets smaller than the above mentioned 247 profiles of rocket-borne wave propagation data. The data usable for the prime objective described in the present paper are ti-om non-aurora1 latitudes under “normal” conditions, i e. geomagnetic latitudes >6 lo, and conditions of Winter anomaly and eclipses are excluded. Fig. 1 shows the number of data per kilometre of altitude, whereas in Fig. 2 the number of rocket flights per solar activity interval is given. NON-AURORAL
ELECTRON DENSITIES
Electron densities outside the aurora1 zones are reasonably predictable, whereas at high latitudes typical shapes of the profiles can only be given retrospectively using L’.K.the aurora1 index or K,, as parameter.
In the following the expected and predictabIe variations of electron densities are given in order of their importance. s The ion pair production rate in the atmosphere is a function of the number density of the ionisable constituent (e.g. NO in the D-region) and the local flux of ionising radiation (e.g. Lyman-a). With increasing zenith angle x the extraterrestrial ionising radiation suffers increasing absorption and vanishes beyond x = 90”. Assuming a constant recombination rate of the free electrons with ions the dependence of electron density on x is described by (cosx)~).~(CHAPMAN, 193 1). but due to the curvature of the Earth a corrected formulation (Chapman function) must be applied near grazing incidence. In the absence of direct sunlight (x > 100’) ionisation is provided by Lyman-o and -b scattered in the geocorona and thus depends but a little on the solar zenith angle (cf: STROBEL et al., 1974). whereas galactic cosmic rays and possible stellar X-rays are fully independent of solar zenith angle. The simple zenith angle dependence as quoted above is fu~he~ore complicated by the fact that the reco~~~biIlation rate in the
Empirical D-Region M~elling
lower D-region becomes tron to neutrals forming additional loss process, most vanish and thereby rate with electrons.
759
much larger at night. This is chiefly due to two processes: u) attachment of elecnegative ions is effective in the absence of photo-detacl~lnellt and constitutes an and b) the densities of atomic oxygen below a ledge situated at about 84 km alfavour the formation of cluster ions with their significantly larger recombination
Season The season is expected to impact on the ionosphere in three ways: LI) Nitric oxide is produced through ionisation in the thermosphere and transported downwards into the mesosphere. The length of the day will therefore be important both for the production of NO and the photolysis on the way to the D-region. In a first approximation the densities are larger in Winter than in Summer (“normal winter anomaly”, SCHWENTEK, 1971; SOLOMON et al., 1982). h) The neutral temperature undergoes a seasonal variation generally folIowing an annual wave, whereas at the equator there is a semi-annual component due to the fact that the longest daily insolation occurs at the equinoxes ($ CIRA-86. REES ct ul., 1990). This temperature variation obviously must have a profound influence on the highly temperature dependent reactions leading to water cluster ions with their much larger recombinatioil rates. and c) the Earth’s orbit around the Sun is slightly elliptic with the perihelion shortly after the northern hemisphere Winter solstice. Latitude The latitude dependent sunlit fraction of the day largely determines the concentration of nitric oxide, but also of other trace constituents and temperature. Charged particles, however, follow the magnetic field lines such that geomagnetic latitude provides a better description of their variation. Solar particle fluxes contribute to ionisation at night and at somewhat higher altitudes (> IO0 km) whereas cosmic rays are important below say 6.5 km; both sources increase with geomagnetic latitude. Solar Activitv Enhanced solar activity expressed either by Sun spot ilumber R, or as 10.7 cm solar radio tlux is associated with increased fluxes of Lyman-a and solar X-rays, but decreased fluxes of galactic cosmic rays. One hence expects electron densities to be positively correlated with solar activity except for the lowest part of the D-region where ionisation by cosmic rays dominates and an inverse behaviour is actually observed (MECHTLY ct ~11..1972). Model Structures The mathematical s~ucture to which we want to fit the data assumes mutual independence of each layer considered (altitude, neutral density or pressure surface) from the one above or below. The models described in the 10' 100 10'0 10" 11 following are termed FIRI-**, i.e. FaradayELECTRON DENSITY, mm3 based IRI. The choice of the complexity of Fig. 3 Electron densities of FIRIfor various solar zenith the mathematical structure by which electron angles as a function of neutral density; approximate altitude is densities are assimilated must be carefully given for guidance only (from FRIEDRICH and TORKAR, chosen: A high order of the function better 1992).
M. Friedrich and K. M. Torkar
760
assimilates the input data, but requires more data to establish the necessary constants. A low order strutture on the other hand can be established from fewer data at each altitude level and yields more realistic values for extrapoIated conditions poorly covered by data. The earliest model of this kind (FIRI-01) was published by FRIEDRICH and TORKAR ( 1992) and uses 72 non-amoral, “normal” profiles. Only the strong dependence on the solar zenith angle is taken into account for reasons explained above. The influence of the solar activity is eliminated by converting the input electron density data to an average value R, = 60 elnploying the dependence incorporated in IRI, whereas latitude and season are crudely accounted for by fitting at constant neutral density levels according to the CIRA atlnospheric modei. log/Y, = A + B ln[Ch(X)]
(I)
Onfy the parameters A and B have to be determined as a function of height (or neutral density), where A represents an electron density profile for a hypothetical overhead Sun, and B corresp{)Ilds to the exponent n in the (~0s~)~ formula. Zenith angles beyond 90” are acco~lted for by a Chapman function extended into full night (SMITH and SMITH, 1972). Fig. 3 shows the outcome of the analysis for zenith angles between 20 and 160”. FIRIapplies the Chapman function for the zenith angle dependence, a sine wave for the season and linear functions for latitude and soIar activity, respectively. It could be shown that (~1’the sixteen terms which occur when multiplying all functions with each other, many only contribute marginally even for the
FEB
AUG SEP OCT NOV
DEC
-60”
-400
00
Latitude
20”
400
60’
Fig. 4 Distribution of rocket launches in latitude and season together with some permanent rocket launching sites. Also indicated are contours of constant daily integrated insolation IL Note that there are fewer points than rockets, because on some days more than one rocket was launched.
~pi~cal
761
D-Region M~elIing
0.4
0.3
0.2
0.1
0 0
20"
40"
60"
80"
loo"
120"
140"
160"
180"
Zenithangle,ckg
Fig. 5 Distribution of rocket flights vs. integrated daily insolation C and solar zenith angle x. Note that not all combinations of zenith angle and integrated insolation are conceivable.
most extreme combination of inputs. The final function was chosen such that any seasonal variation vanishes at the equator. Strict symmetry to noon and solstice as well as equality between geographic and geomagnetic latitude is assumed. At each kilometre of height eiectron densities are thus described by: 100, =A + Wn(Chx) + Chln(Chx) + Dhsin[x(SO+d)ll82] + EFIO,,+ J’ln(ChX)F,,,7 + GXF10,7+ Hh
(2)
with the latitude h, the day number d since Winter solstice and the solar flux FlO,?.The height dependent constants A to 13 are determined from the data. Using F10,7rather than Sun spot number R, yields a marginally better fit of the data particularly below 95 km. Internally R, inputs are converted to F,,,, using the relation after THOMSON (1995). The model was presented at the 3 1” COSPAR Meeting in Birmingham 1996 (FRIEDRICH and TORKAR, 1997). FIRI-03: Changes of electron density with season and latitude are predomin~tly caused by variations of @IO]. In a simple scenario NO is produced in the recombination processes of 02+ and N2+,transported to the mesosphere and lost by photo-dissociation. It is reasonable to assume that also the densities of other relevant minor species will depend on the length of the day. The effective length of the day therefore crucially determines how much NO is actually available in the D-region. Season and latitude are here lumped into one parameter characterising the insolation C of the day in question by integrating cosx from sunrise to sunset. The result is scaled such that C = 1 refers to 24 hours of overhead Sun (x = 0”). C thus replaces season and latitude and the following relation applies: 100, = A + Bln(ChX) + eC + DCln(Chx) + EF,O,, + J’Fu,&r(Chx) + GF,&
+ HCF,O,,ln(Chx)
(3)
M. Friedrich and K. M. Torkar
762
Fig. 4 shows lines of constant C vs. season and latitude between rtr60°.Also indicated by dots are the dates of the various rocket launches which contribute data to this model. It is assumed that the ionosphere will e.g. have the same behaviour at 20” latitude in December as at 60” in August, i.e. the known seasonal and fatitudiial variation of temperature and its influence on the ion chemistry {electron loss) is ignored. In Fig. 5 the rocket flights are shown as a function of insolation of the day of the launch vs. zenith angle during the launch. Clearly more data are needed for small X and large x. Profiles obtained from FIRI- are very close to those of FIRI-02, but do allow for a semi-annual variation at the equator. However the latitudinal variation of cosmic rays and charged particles which was implicitly included in FIRI-02, is here not accounted for. In order to assess the qualities of the different models an average error factor is defined as exp~ln~~~(rocket)/~~(model~]~ of all input values. FIRI- yields a value of 1.667 in the altitude range from 70 to 120 km (i.e. the rocket values are on average larger or smaller than the model values by that factor) compared to 1.702 in the case of FIRI-02. Although this fit is only marginally better than that of FIRI-02 it is believed to provide a better description because it allows for a seasonal variation at the equator and yields more reasonable values for extrapolated conditions. The only smoothing with altitude is a running mean of the height-dependent coefficients in Eq. 3. In Fig. 6 tropical electron density profiles for noon and mi~ight are shown, respectively, as examples for widely different zenith angles. The ledge around 83 km during the day probably reflects a corresponding ledge in Ir\rO], whereas the steep rise of the density at night is most likely due to the sudden occurrence of atomic oxygen. This increase which is more pronounced in individual profiles, but occurs at slightly different altitudes, is smeared out somewhat in the model. Fig. 7 shows equatorial profiles for equinox and solstice for x = 60” and low solar activity. As expected the equinox values are slightly larger due to the larger insolation; apparently the effect of increased NO by ionisation in the E-region outweighs the larger destruction of NO by photodissociation. Radio wave absorption which originates predomin~tly in the D-region was observed by many researchers to be significantly larger in the afternoon, but no explanation was put forward (e.g. LASTOVICKA, 1977). Fig. 8 shows the average diurnal variation of the signal strength of an A3 radio path of 2.83 MHz over 500 km (TORKAR et al., 1978). This asymmetry is largest in Summer suggesting a “sluggishness” of the ionosphere which becomes more ?-?-!Y-T: : :: ; i : :: apparent when the Sun rises or sets : :: : : .j..i. faster. No hysteresis is discernible in : : :,, : : : : :; ; : Winter, but the absorption is larger for .i..+ .._: : : j :. : the comparable solar zenith angles. The : : ; :: j j lifetime of ions in the D-region is be: :: ‘?: : : :: :; I : : I : ;: lieved to be very short and can thus not :: .;__.,.1. .i? explain the observed effect. The re:; i ,: i: : : .:_..,. I_ cently available data on mesospheric .j_;. :: :: : [NO] from the experiment HALOE :: :: .&. ..:..i..;.. aboard the satellite UARS show dif:: : :: : .: ij : ferences between densities derived at ..:..:+ sunrise vs. those from sunset. This j.-+ asy~e~ amounts to the PM values Ii:: being almost one order of magnitude .:..:.i. i ;; larger than the AM densities near 80 1 iii km at the equator; at 50” latitude this Electron density, m” hysteresis vanishes. Although the absolute values of simulated electron densi* Fig. 6 Tropical midnight and noon electron density profiles usmg ties using HALOE PO] are not consisFIRI- for low solar activity (x = 0” and 180°, respectively, 2” latitent with the empirical electron densitude at solstice and F10.7= 75, May 10). :
‘: i : ;I
..,
!_I_
:
::
i f
:i +.
:
:...;.;. :.:. :1 :: .;.i. :+-q :: i.:..;.:. ii i:.: ; .;...;.;. ::: : :..,.j_
_.I.
:
i
:
;
:
:’
.;..i.;.
7:
.:..1. j : : ; : : .j..; :
: j
:: ji
: : _j...;.:. j ij
iii
:
:.
:
::
+i.
+.;
:.
i
Empi~caI D-Region M~elling
763
ties of FIRI~F~ED~CH et al., 1996), it was tested if a corresponding asymmetry in the electron densities can be found in FIRI-03. Fig. 9 shows equatorial profiles for x = 60” and low solar activity using only AM and PM data, respectively. Why PO] should undergo a diurnal variation is unresolved, since its lifetime is believed to be of the order of days. In Fig. 10 the dependence on solar activity is tested. The latitude, zenith angle and season are chosen for conditions best covered by input data. One clearly sees a positive correlation at all altitudes above 65 km and - as predicted - the reverse behaviour below that height.
c
. ..
. ..
. ..
. ..
. ..
60
. .. 4
lo8
Beyond FIRI-
Electron density, me3
In contrast to FIRI-
Fig. 7 Equatorial electron densities for equinox and solstice for condi tude is completely tions of low solar activity and a zenith angle of 60”.
geomagnetic latiignored in FIRI-03.
An inclusion by e.g. linear dependence on magnetic latitude can be provided. This initially leads to 16 coefficients, but analogous to the procedure applied in FIRI-02, coefficients of combined parameters which only con~ibute very little can be omi~ed. The amount of available data only permits to sensibly determine eight coefficients.
In a further step one can - as in FIRI- - carry out the fit procedures for constant neutral densities or pressure surfaces. One thus re-introduces latitude and season without increasing the complexity of the describing function. Whether this added procedure yields a significant improvement remains to be tested. I
I
I
I
I
I
I
I
I
I
I
I
I
I
1
n-0-25
I
1
I
I
I
I
I
1
I
I
I
1
**........*,
l!w
Fig. 8 Variation of a 2.83 MHz signal over a 502 km path as a function of solar zenith angle during a period of low solar activity. The dotted line is the average variation throughout the year. Note the large hysteresis in Summer and the high absorption in Winter (afier TORKAR et al., 1978).
M. FrIedrich and K M. Torkar
764
OTHER D-REGION PARAMETERS “‘I
i
i
i
iiiiii
i
i
i
iiiiii
i
i
i
iiiiil
Aurora1 Zone Electron Densitv
_ _
_
_I_
_
L
J_I_I_IJ
LI_
_ _
Electron density.
IK’
In the aurora1 zone the basically unpredictable influx of energetic charged particles dominates the ion pair production. Models for these conditions can only retrospectively describe the situation. There are presently two published models, one based on literally thousands of EISCAT profiles and the other on about 100 in .situ rocket data 1991; (KIRKWOOD and COLLIS, FRIEDRICH and TORKAR. 1995a. respectively). Both models separate between day and night conditions and use locally measured riometer absorption as the describing parameter. Currently work is in progress to combine the best of both models. i.e. the large number from EISCAT with the much lower density threshold oi‘ the rocket data.
Fig. 9 Equinox electron densities using AM and PM data only. The model values are for x = 40”, low solar activity and equinox at the equator at low solar activity
Cluster Ion Transition
(F,,, , = 67). The number of available measurements to establish an empirical relation where the transition from water cluster ions to molecular ones occurs. is very limited. At night the actual level 01’the chemically important ledge in atomic oxygen seems to be very variable and no obvious behaviour could be found. During the day when photo-detachment seems to be more important than [Oj a clear correlation of the transition height with temperature could be found. The formulation published by FRIEDRICH and TORKAR (1988) still holds. but the updated \,crsion should be used (FRlEDRlCH and ‘I‘ORKAR. 1995b). Negative Ions
The fraction of ions among the negatively charged species is the quantity customarily Electron density. nl-’ derived. Due to photo-detachment negative Fig. 10 Solar activity dependence of electron densities at 30” ions become negligible above about 60 km latitude and 60” solar zenith angle (Flo7 = 67/l 50. equinox). during the day, but are present in considerable amount at night below about 90 km. 10’
Empirical D-Region M~elling
765
Using a subset of the data employed in the present context, the most recent model for night time is described by FRIEDRICH and TORKAR (199%). Daytime values of the same negative ion fraction appear about 20 km lower. Effective Electron Recombination
Rate
No new data have become available and the model published by TORKAR and FRIEDRICH probably still the best attempt (daytime only),
(1988) is
CONCLUSIONS With the relatively small number of indisputable D-region electron density profiles an empirical model of the variation of electron densities as a function of insolation, solar zenith angle and solar activity was established. The fact that all altitudes are treated independently allows any shape of the protile. The average uncertainty of the prediction vs. the rocket data in the present FIRI-03 model is 1.67 compared to I .85 in FIRIand 1.70 in FIR&02. Further improvements are expected from the specific inclusion of geomagnetic Iatitude and the ~angement for constant pressure levels. Possibly the weakest point in the present treatment is the use of a Chapman function extended into full night. The model is based on “normal”, nonaurora1 electron densities; however the extrapolation to aurora1 regions provides electron density profiles representative for extremely quiet conditions. A combined EISCAT and rocket data model for auroral latitudes is currently being developed and should yield more representative values. The empirical models of other D-region parameters basically make use of the same set of rocket-based electron densities, but also require at least one other measured physical parameters. Consequently there are even fewer usable data and no new results are presently available. ACKNOWLEDGEMENTS The contributions by Messrs. R. Erlacher and R. Pilgram to the numerical computations are acknowledged. Many unpublished rocket data were made available to the authors by the experimenters. Flights with Austrian instruments were supported by grants of the Austrian Science Foundation. REFERENCES Bennett, F.D.G., J.E. Hall, and P.H.G. Dickinson, D-Region Electron Densities and Collision Frequencies from Faraday Rotation and Differential Absorption Me~urements, J. atmos. terr. P&s. 34 (8), p. 321, 1972. Bilitza, D., International Reference Ionosphere, URSI-COSPAR, Goddard Space Flight Center, Greenbelt MD 2077 1, 1990.
National Space Science Data, NASA
Chapman, S., Absorption and Dissociation or Ionising Effects of Monoc~omati~ Earth, Pro&. Roy. Sot. 43, pp. 26-45, 193 1.
Radiation on a Rotating
Friedrich, M., R. Finsterbusch, KM. Torkar, and H. Sp&ker, A Further Generalisation Wyller Magneto-Ionic Theory, A&. Space Rex 11 (lo), pp. 105-l 08, 1991.
of the Sen and
Friedrich, M., D.E. Siskind, and K.M. Torkar, HALOE Nitric Oxide Measurements in View of Ionospheric Data, Paper SA32B-05 presented at AGU Fall Meeting, San Francisco, 1996. Friedrich, M., and KM. Torkar, Empirical Transition Heights of Cluster Ions, Adv. Space Rex 8 (4), pp. 235-238,1988,
766
M. Friedrich and K. M. Torkar
Friedrich, M., and K.M. Torkar, An Empirical Model of the Nonauroral D Region, Radio Sci. 27 (6), pp. 945-953, 1992. Friedrich, M., and K.M. Torkar, Typical Behaviour of the High Latitude Lower Ionosphere, Adv. Space Rex 16 (1) pp. 73-8 1, 1995a. Friedrich, M., and K.M. Torkar, A Contribution to IRI for the D-Region, Adv. Space Rex 15 (2), pp. 161164,1995b. Friedrich, M., and K.M. Torkar, An Attempt to Parameterise Negative Ions in the Ionospheric D-Region, ESA SP-370, pp. 257-261, 1995~. Friedrich, M., and K.M. Torkar, Comparison Between a Statistical and a Theoretical Model of the D-Region, Adv. Space Rex in press, 1997. Jacobsen, T.A., and M. Friedrich, Electron Density Measurements in the Lower D-Region, J. atmos. terr. Phys. 41(12), pp. 1195-1200,1979 Kirkwood, Sheila, and P.N. Collis, The High Latitude Ionosphere Observed by EISCAT, Adv. Space Res. 11 (lo), pp. 109-l 12, 1991. LaStovicka, J., Seasonal Variation in the Asymmetry of Diurnal Variation in the Lower Ionosphere, J. atmos. terr. Phys. 39, pp. 891-894, 1977. McNamara, L.F., Statistical Model of the D-Region, Radio Sci. 14, pp. 1165-l 173, 1979. Mechtly, E.A., S.A. Bowhill, and L.G. Smith, Changes of Lower Ionosphere Electron Concentration Solar Activity, J. atmos. terr. Phys. 34, pp. 1899-1907, 1972.
with
Rees, D., J.J. Barnett, and Karin Labitzke, COSPAR International Reference Atmosphere, Part II, Adv. Space Res. 11 (1 l), 1990. Schwentek, H., Regular and Irregular Behaviour of the Winter Anomaly in the Ionospheric Absorption, J. atmos. terr. Phys. 33, pp. 1647-1650, 1971. Sen, H.K., and A.A. Wyller, On the Generalization geophys. Res. 65, pp. 3931-3950, 1960.
of the Appleton-Hartree
Magnetoionic
Formulas, J.
Smith III, F.L., and C. Smith, Numerical Evaluation of Chapman’s Grazing Incidence Integral ch(X,Q, J. geophys. Res. 79, pp. 3592-3597, 1972. Solomon, Susan, P.J. Crutzen, and R.G. Roble, Photochemical Coupling Between the Thermosphere and the Lower Atmosphere 1. Odd Nitrogen from 50 to 120 km, J. geophys. Res. 78, pp. 7206-7220, 1982. Strobel, D.F., T.R. Young, R.R. Meier, T.P. Coffey, and A.W. Ali, The Night-Time Ionosphere: E-Region and Lower F-Region, J. geophys. Res. 79, pp. 3 1771-3 178, 1974. Thomson, R., The Ten Centimetre Solar Radio Flux, IPS Radio & Space Services, Internet, http://www.ips.gov.au/, 1995. Thrane, E.V., Ionospheric Profiles up to 160 km - A Review of Techniques and Profiles, in: COSPAR Methods of Measurements and Results of Lower Ionosphere Structure, K. Rawer (ed.), pp. 3-21, Akademie, Berlin, 1974. Torkar, K.M., and M. Friedrich, Empirical Electron Recombination J. atmos. terr. Phys. 50 (8), pp. 749-761, 1988.
Coefficients in the D- and E-Region,
Torkar, K.M., M. Friedrich, W. Wallner, G. Rose, and H.U. Widdel, Preliminary Results of Absorption Measurements of a Central European A3 Path, Kleinheub. Ber. 21, pp. 155-l 61, 1978.