Empirical model of O+-H+ transition height based ontopside sounder data

Adv. Space Research, 2004






Empirical model of O+-H+ transition height based on topside sounder data




P. Marinov1, I. Kutiev2, and S. Watanabe3


1Central Laboratory for Parallel Processing, Bulgarian Academy of
Sciences, Sofia, Bulgaria
2Geophysical Institute, Bulgarian Academy of Sciences, Sofia, Bulgaria
3Graduate School of Science, Hokkaido University, Sapporo, Japan





ABSTRACT



A new model of the O+-H+ transition height (denoted as THM) is
developed, based on vertical electron density profiles from topside
ionosondes. The model provides the transition height (TH) as a function of
month of the year, local time, geomagnetic latitude, longitude and solar
flux F107. To define TH, the O+ scale height is approximated by the lowest
gradient in the measured profile and the O+ profile is reconstructed. TH is
taken at the height where O+ density becomes half of total electron
density. The model data base contains 170,033 TH values, sufficiently
sampling all parameter's ranges. THM describes the transition height by a
multivariable polynomial consisted with Chebishev's and trigonometric base
functions, which is fitted to the data in the 5-dimensional space. The
model results are compared with other available models. The comparison
shows that THM predictions agree in general with those of the other models,
but THM variations along latitude, longitude and local time have larger
amplitudes.







INTRODUCTION



The height at which O+ and H+ densities are equal is an important
characteristic of the ionospheric structure. This height is considered as
the boundary dividing the O+ dominated ionosphere from H+ (or light ions)
dominated plasmasphere. Several models has been developed to help various
aeronomical studies and ionospheric applications, all of them based on
satellite data. Titheridge, 1976 has extracted the transition height (TH)
by fitting the topside electron density profiles from Alouette-1 sounder
with theoretical models. Using 60,000 profiles measured between 1962 and
1968, he obtained transition height variations in various seasons and
levels of solar activity. Miyazaki (1979) has constructed simple model of
TH, based on TAIYO satellite data. Kutiev et al. (1984) used 1400 direct
encounters of TH from OGO 6 (1969-1970) to obtain a formula, representing
TH within ±50( dip latitude and all longitude for 20 hours and 02 hours
local time. Kutiev et al., 1994 further developed the previous model by
including data from Intercosmos-2 and limited portions of Alouette-1 and
ISS b satellite data. This model (further denoted as K94), represented TH
in 5 dimensions: sunspot number, month of the year, local time, dipole
latitude and longitude. It was based on a generalized multivariable
polynomial, containing a system of linearly independent functions.


The present model (further denoted as THM) is based of the vertical
density profiles, inferred by the topside sounders on Alouette-1, 2 and 3
and ISIS-1 and 2 satellites. It uses similar mathematical approach as in
Kutiev et al. (1994). The input parameters are local time, month of the
year, geomagnetic latitude (glat), solar flux F10.7 and longitude (long).
The gradient and transition height are extracted from each individual
profile and accumulated in 6-dimensional bins, defined by input parameters.
Then the data are fitted with a multivariable polynomial, containing a set
of base function in order to obtain the respective coefficients.






DATA


The database, archived at the National Space Science Data Center
(NSSDC), Greenbelt, MA, includes 176,622 topside electron density (Ne)
profiles from the Alouette-1a, -1b, -1c and -2 and ISIS-1 and -2 topside
sounders, covering the period 1962-1979. A detailed description of the
database is given by Bilitza (2001). All available Ne profiles were
downloaded from NSSDC, Greenbelt, MA
(ftp://nssdcftp.gsfc.nasa.gov/spacecraft_data) and processed to form the
model database.


TH DEFINITION


The O+ plasma scale height is defined as the lowest gradient of the
measured Ne profiles. The transition height is defined as the height at
which the extrapolated to higher altitudes lowest Ne gradient yields a
density which is one half of the measured Ne. We, therefore, neglect the
presence of He+ ions. Figure 1 illustrates the above definition. Measured
Ne (red crosses) are plotted in natural logarithmic scale and O+ scale
height (green line) is obtained as a regression line over the points, at
which the gradients does not exceed the lowest by 30%. The transition
height (yellow line) marks the altitude at which the logarithm of O+
density ln(n(O+)) = ln(Ne) - ln(2). The regression assures more stable
result and avoids the uncertainties invoked by the data scatter or gaps.


The constant Ne gradient assumed in this definition implies a constant
plasma temperature in O+ dominated topside ionosphere. It is well known
that in this region both, the electron and ion temperatures increase with
altitude, so the O+ scale height also increases. Simple theoretical
considerations assure that the transition height should not change
considerably when plasma temperature varies, although the density changes.
The regression, taken over several Ne values, actually represents a scale
height with an average plasma temperature in the respective altitude range.
Indeed, IRI temperature model shows that between 400 km and 700 km both ion
(Ti) and electron (Te) temperatures do not change more than 30% under all
conditions. So, the O+ scale height obtained by the regression contains the
30% increase of plasma temperatures. From the other hand, at heights around
the transition, the increased plasma temperature increases also the H+
scale height with the same proportion as that of O+ (with opposite sign).
Therefore, near the transition height both ion densities increase, but the
altitude where they become equal does not change.




MATHEMATICAL FORMULATION


The coefficient matrix CFN is a solution of the problem for LSQ-
approximation of the given data points (x(k); f(k)), x(k)=(x1(k), x2(k),
x3(k), x4(k), x5(k)), i.e. CFN minimizes the functional:



(1)


where F(CFN,x) = F(x) is an element of the LSQ-approximation.
We define the function F(x1,x2,x3,x4,x5) within the intervals [ai,bi],
[ci,di], i=1,…,5; base-functions and coefficients as follows:


(2)


where



,


are elements of coefficient matrix with a size ;
Base-functions are .
For the base-function we use:
Algebraic functions:
Tchebishev's functions: T0(s)=1, T1(s)=s,…, Tk(s)=2sTk-1(s) –
Tk-2(s), for k=2,3, …,
i.e.
Tk(s)=cos(k arccos(s));
Trigonometric functions: 1, sin(s), cos(s), …, sin(ks),
cos(ks), …;


The number of nodes N, data [a,b] and model [c,d] ranges, and the type
of the base functions for each model parameter are summarized in the table
below.


"parameter"N "[a, b] "[c, d] "Base functions"
"month "5 "[0,12) "[0,2π) "Trigonometric "
"local "5 "[0,24) "[0,2π) "Trigonometric "
"time " " " " "
"glat "7 "[-90,90] "[-1,1] "Tchebishev's "
"sf "3 "[50,250] "[-1,1] "Tchebishev's "
"long "5 "[0,360) "[0,2π) "Trigonometric "







MODEL RESULTS


Figure 2 shows the total distribution of TH values along altitude (left
histogram) and longitude (right histogram), extracted from 170,033 measured
profiles. The altitude distribution of input TH (red line) is confined
within the range of 400 km and 1200 km, which is physically reasonable. The
model prediction (blue line) reproduces well the input values and even
narrows the range towards the most likely values of 700 km. The right
histogram shows that the largest amount of data is obtained from the
American sector. The other longitudes sectors possess an average 5%, or
about 8500 in each 10(-wide bin. The local time coverage is quite uniform.
We consider that the spatial and local time coverage is statistically
reliable.


Figure 3 shows the latitude variation of THM values for 00 and 12 hours
local time in December and June at 100( and 280( East longitude. At these
longitudes displacement of the magnetic from the geographic equator is
largest and longitude differences of TH there are thought to be largest.
Left panels show TH at F107=200 and the right panels show TH at F107=100.
In all panels TH exhibits a relative maximum around equator and minimums at
both midlatitudes, with that of winter side being the deeper. TH increases
again towards higher latitudes. Longitude differences are generally larger
at night. The largest longitude difference is seen the winter side at 00 LT
in June for high solar activity (F107=200).


Figure 4 shows diurnal variations provided by THM (thick line) at
geomagnetic latitudes 0(, and 30( for June (red) and December (blue) and
F107=100 and 150. Longitude is 100(E. Model predictions of IRI (crosses and
diamonds) and those of K94 (dashed lines) are also shown in the respective
panels. Local time variation of THM in December (blue line) exhibits a
large maximum around 18 hours and a minimum around 04 hours, both at
equator and 30(. Solar flux F107 changes amplitudes only, not the shape.
Summer variations of THM are less pronounced at equator, but at 30( THM
shows a well defined increase around noon and midnight hours. Both IRI and
K94 show diurnal variations with a maximum at noon and symmetrical decrease
towards midnight. IRI and K94 predict slight seasonal differences at 30(,
but not at the equator.


Comparison made in Figure 4 reveals that, in general, THM predictions
are of the same magnitude as those of IRI and K94, which means that TH is
not underestimated due to the definition assumptions. K94 model shows
rather smoothed TH variations, result of the assumptions used to compensate
the insufficient data base. The same is obviously the case with IRI
predictions. The data base used by THM allows revealing a rather
complicated spatial and temporal behavior of the transition height. Figure
5 shows contour plots of TH distribution in glat/long coordinate frame at
noon and midnight in June and December, with F107=150. These 2D plots
complement the TH behavior shown in Figure 3. TH surface is rather patchy.
December noon plot at F107=100 (upper right) shows a deep trough of TH
around 60(, confirmed also in Figure 3. It is surprising to see the
midlatitudes minimum so poleward at all longitudes. The poleward increase
of TH is known to collocate with the main ionospheric trough in electron
density, where the polar wind decreases H+ density in F region. The same
winter minimum, however, at F107=200 is seen (left panels of Fig.3) below
60(. The extremely poleward winter minimums of TH at the low F107 values,
seen on the right panels of Figure 3, might be artefact, a result of the
fitting along F107 axis. The variability of the extracted TH values is
quite high: the standard deviation of model from the measured values (model
error) is 28%, which is around 200 km. It can be expected that such a
scatter will result in unreliable fitting along some parameter axes, as
F107 in this case. It also has to be noted that the spatial interpolation
procedure, used to draw the contour plots, can distort to a certain extent
the real data distribution, so the plots shown here provide a qualitative
picture rather than a detailed structure of TH. Figure 3 provides more
accurately the TH behavior.


CONCLUSIONS


The present model of the upper transition height (THM) is constructed as
a function of month, local time, geomagnetic latitude, geographic longitude
and solar flux F107. It is based on statistically sufficient data and
provides a detailed spatial structure and time variation of the transition
height (TH). Comparison with IRI and Kutiev et al. (1994) models shows that
there is a general agreement on the range of TH variations. The present
model provides diurnal, seasonal and spatial variations with larger
amplitudes than the other models do. The large number of coefficients for
equation (2) does not allow showing them on a table for individual usage.


ACKNOWLEDGEMENTS: Database for the present study is compiled from the
topside sounders electron density profiles downloaded from NSSDC,
Greenbelt, MA. This work was performed under NATO Grant EST.CLG.979784.


REFERENCES


Bilitza, D, International Reference Ionosphere (IRI)–Task Force
Activity Report 2000, IRI News, 8, 1/2, 8-15, June 2001.
Kutiev, I., P. Marinov, K. Serafimov, An approximation of the
height of the O+-H+ transition level for use in IRI, Adv. Space Res., 4,
1, 1984, 119.
Kutiev I., S. Stankov, P. Marinov, Analytical expression of O+-H+ ion
transition surface for use in IRI, Adv. Space Res., 14, 12, 1994, 135.
Miyazaki, S., Ion transition height distribution obtained with Taiyo,
J. Geomagn. Geoeletr., 31, S95, 1979.
Titheridge, J.E., Ion transition heights from topside electron
density profiles, Planet. Space Sci., 24, 3, 229-246, 1976.















FIGURE CAPTION


Fig. 1 Transition height definition. O+ profile (green line) is determined
by lowest gradient in the measured profile (red crosses). The X-axis
shows the natural logarithm of Ne.

Fig. 2 Left panel: altitude distribution of extracted TH (red) and model
TH (blue). Right panel: longitude distribution of TH in 10(-wide bins.

Fig. 3 Model TH versus geomagnetic latitude for F107=200 (left panels) and
F107=100 (right panels). Blue lines represent TH at 100( longitude and
red lines the same for 280( longitude. Local time and months are shown
in panels.

Fig. 4 TH versus local time for F107=100, 150 and geomagnetic latitude
(glat) = 0( and 30(. Red lines show TH in June and blue lines in
December. Dashed lines represent K94 model, while crosses and diamonds
mark IRI model.

Fig. 5 Contour plots of TH in glat/longitude. Parameters are specified
above each panel. Color scale is shown on the right.



















Fig. 1



Fig. 2





Fig. 3





Fig. 4













Fig. 5