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Improved analytical representation of electron temperature in the IRI
Adv. Space Res. Vol.4, No.1, pp.93—95, 1984 Printed in Great Britain. All rights reserved.
0273—1177/84 $0.00 + .50 Copyright © COSPAR
IMPROVED ANALYTICAL REPRESENTATION OF ELECTRON TEMPERATURE IN THE IRI D. Bilitza Albert-Ludwigs-Universitat, D-7800, Freiburg, F.R. G.
ABSTRACT In the last decade extensive measurements from incoherent scatter stations and from several satellite missions have considerably improved our knowledge of long— and short—term variations in the ionospheric electron temperature. Comparisons with IRI have revealed some shortcomings of this earlier model. It is obvious that in different altitude regions one has to concentrate the modelling efforts on different parameters. Here a model representation is proposed that will facilitate approaches (for the different altitude regions) in one analytic form. INTRODUCTION The present IRI model for the electron temperature represents the gross altitudinal, latitudinal (geomagnetic), diurnal and seasonal behavior observed in incoherent scatter and AEROS satellite measurements. With the increased data base, it should now be possible to account for more specific features. Especially the following shortcomings should be eliminated in the new edition of I RI: (i) Altitudinal variation: The constant temperature gradient above 400 km of altitude leads to an overestimation of the temperatures at high altitudes. (ii) Latitudinal variation: There appears to be a discontinuity in the IRI model at 400 geomagnetic latitude due to the incomplete functional interconnection of the typical altitude profiles. For example, at low latitudes there is a local minimum at about 300 km (Fig. Ia) and for middle latitudes there is a continuous increase (Fig. Ib). (iii) Diurnal variation: The actual variation is much more specific, especially during dawn (early morning peak near the magnetic equator) and afternoon. These features decrease with increasing altitude, (iv) Seasonal variation: The model variation seems to be too small below about 800 km, and too large above 1200 km. (v) Missing variations: The variation with solar activity should be included (IRI is based on low solar activity data). Measurements and theoretical calculations suggest distinctive different behaviors at low and middle latitudes and at low and high altitudes. The strong anti—correlation between electron density and temperature would be helpful in describing day—to—day temperature variations if measured densities were available. From the listing above it is obvious that the electron temperature is governed by different influences in different altitude regions. At high altitudes (z > 600 km) the profile shape and absolute values are determined by the heat flux downwards from the plasrnasphere. This heat flux depends on the heat capacity of the plasmaspheric magnetic field tube and on the amount of heat stored in this field tube.
93
94
D. Bilitza
I~~~~___ 1000
-
2000
3000
1/K
~~~___
1000
2000
3000
1/K Fig. I.
Variation of electron temperature with height;
(a) low latitudes, (b) middle latitudes. At low altitudes the large neutral densities, and therefore the large heat transfer from electrons to neutrals, force the electron temperature down to the neutral temperature. At intermediate heights the energy gain of the electron gas (from photoelectrons) is roughly proportional to electron density, whereas the energy losses (to the ions) are proportional to the square of electron density. Therefore, a strong anti—correlation between electron density and temperature is observed. PROPOSED MODEL FUNCTION It would be quite helpful to have an analytic function for the altitudinal variation of the electron temperature, in which the function parameters would be allowed to vary with different ionospheric parameters in different altitude regions. The best way to establish such a function goes back to an approach by Booker /1/. One divides the temperature profile in regions of constant gradient dT dz
—
=
to. 1
for
z. i—i
~ z ~ z. 1
,
1
=
I
and connects these regions analytically by Epstein—transitions
M,
Electron Temperature in the TEl
dT
Integrating from
+
h—I i=1
+
to.1+1
-to.
1 exp(—(z-z.)/d.)~
to z, one gets
Z
T (z)
=
93
=
S
T (z e
) a
+ to (z—z
) a
+
M-1 2 i=1
1+exp((z—z.)/d.) (to. 1+1
—m.)d. 1
1
ln
1
1
1 +exp((z—z~)/d.)
Ionospheric electron temperature profiles (with or without the local minimum at about 300 km) can be described by four constant gradient regions (M4). This is illustrated in Fig. I. It then remains to investigate the latitudinal and temporal variation of the ID parameters: m~, to 2, to3, to[~~ Z1~ 22, z3, d1, d2, d3. For m2, to3, 22 and d2, incorporation of the anti—correlation between density and temperature should be helpful, whereas for m1~, z3 and d3 the magnetic field geometry (L—value) has to be considered. At present, the IRE electron temperature model is adjusted so as to reach the CIRA neutral temperature at 120 km altitude. This can be guaranteed by setting Z = 120 km and Te(Za)
=
TCIRA (120 km). REFERENCES
I.
H.G. Booker, J. Atmos. Terr. Ph~. 39, 619 (1977).
0273—1177/84 $0.00 + .50 Copyright © COSPAR
IMPROVED ANALYTICAL REPRESENTATION OF ELECTRON TEMPERATURE IN THE IRI D. Bilitza Albert-Ludwigs-Universitat, D-7800, Freiburg, F.R. G.
ABSTRACT In the last decade extensive measurements from incoherent scatter stations and from several satellite missions have considerably improved our knowledge of long— and short—term variations in the ionospheric electron temperature. Comparisons with IRI have revealed some shortcomings of this earlier model. It is obvious that in different altitude regions one has to concentrate the modelling efforts on different parameters. Here a model representation is proposed that will facilitate approaches (for the different altitude regions) in one analytic form. INTRODUCTION The present IRI model for the electron temperature represents the gross altitudinal, latitudinal (geomagnetic), diurnal and seasonal behavior observed in incoherent scatter and AEROS satellite measurements. With the increased data base, it should now be possible to account for more specific features. Especially the following shortcomings should be eliminated in the new edition of I RI: (i) Altitudinal variation: The constant temperature gradient above 400 km of altitude leads to an overestimation of the temperatures at high altitudes. (ii) Latitudinal variation: There appears to be a discontinuity in the IRI model at 400 geomagnetic latitude due to the incomplete functional interconnection of the typical altitude profiles. For example, at low latitudes there is a local minimum at about 300 km (Fig. Ia) and for middle latitudes there is a continuous increase (Fig. Ib). (iii) Diurnal variation: The actual variation is much more specific, especially during dawn (early morning peak near the magnetic equator) and afternoon. These features decrease with increasing altitude, (iv) Seasonal variation: The model variation seems to be too small below about 800 km, and too large above 1200 km. (v) Missing variations: The variation with solar activity should be included (IRI is based on low solar activity data). Measurements and theoretical calculations suggest distinctive different behaviors at low and middle latitudes and at low and high altitudes. The strong anti—correlation between electron density and temperature would be helpful in describing day—to—day temperature variations if measured densities were available. From the listing above it is obvious that the electron temperature is governed by different influences in different altitude regions. At high altitudes (z > 600 km) the profile shape and absolute values are determined by the heat flux downwards from the plasrnasphere. This heat flux depends on the heat capacity of the plasmaspheric magnetic field tube and on the amount of heat stored in this field tube.
93
94
D. Bilitza
I~~~~___ 1000
-
2000
3000
1/K
~~~___
1000
2000
3000
1/K Fig. I.
Variation of electron temperature with height;
(a) low latitudes, (b) middle latitudes. At low altitudes the large neutral densities, and therefore the large heat transfer from electrons to neutrals, force the electron temperature down to the neutral temperature. At intermediate heights the energy gain of the electron gas (from photoelectrons) is roughly proportional to electron density, whereas the energy losses (to the ions) are proportional to the square of electron density. Therefore, a strong anti—correlation between electron density and temperature is observed. PROPOSED MODEL FUNCTION It would be quite helpful to have an analytic function for the altitudinal variation of the electron temperature, in which the function parameters would be allowed to vary with different ionospheric parameters in different altitude regions. The best way to establish such a function goes back to an approach by Booker /1/. One divides the temperature profile in regions of constant gradient dT dz
—
=
to. 1
for
z. i—i
~ z ~ z. 1
,
1
=
I
and connects these regions analytically by Epstein—transitions
M,
Electron Temperature in the TEl
dT
Integrating from
+
h—I i=1
+
to.1+1
-to.
1 exp(—(z-z.)/d.)~
to z, one gets
Z
T (z)
=
93
=
S
T (z e
) a
+ to (z—z
) a
+
M-1 2 i=1
1+exp((z—z.)/d.) (to. 1+1
—m.)d. 1
1
ln
1
1
1 +exp((z—z~)/d.)
Ionospheric electron temperature profiles (with or without the local minimum at about 300 km) can be described by four constant gradient regions (M4). This is illustrated in Fig. I. It then remains to investigate the latitudinal and temporal variation of the ID parameters: m~, to 2, to3, to[~~ Z1~ 22, z3, d1, d2, d3. For m2, to3, 22 and d2, incorporation of the anti—correlation between density and temperature should be helpful, whereas for m1~, z3 and d3 the magnetic field geometry (L—value) has to be considered. At present, the IRE electron temperature model is adjusted so as to reach the CIRA neutral temperature at 120 km altitude. This can be guaranteed by setting Z = 120 km and Te(Za)
=
TCIRA (120 km). REFERENCES
I.
H.G. Booker, J. Atmos. Terr. Ph~. 39, 619 (1977).