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X-621-72-235
THEORETICAL
MODEL FOR
THE LATITUDE
DEPENDENCE
OF
THE
THERMOSPHERIC
ANNUAL
AND
SEMIANNUAL
VARIATIONS
by
H.
G.
Mayr
Thermosphere
and
Exosphere
Branch
Goddard
Space
Flight
Center
Greenbelt,
Maryland
and
H.
Volland
Astronomical
Institutes
University
of
Bonn
Bonn,
W.
Germany
June
1972
Goddard
Space
Flight
Center
Greenbelt,
Maryland
PRECEDING
PAGE
BLANK
NOT
FLMID
CONTENTS
Page
ABSTRACT
.........................................
-v
1.
INTRODUCTION
..... ...................................
1
2.THEORY
.
.......................................
2
3.
INPUT PARAMETERS
...
............................
8
4.
ANNUAL
VARIATIONS
...............................
12
5.
SEMIANNUAL
VARIATION
....................
.........
17
6.
CONCLUSION
. ..
.....................
..............
21
ACKNOWLEDGEMENT
...................................
22
REFERENCES
. . . .
.............................
22
ILLUSTRATIONS
Figure
Page
1
Schematic
diagram
for
the
physical
processes
that
influence
the
temperature
and
composition
of
the
thermosphere
.........
3
2
Schematic
picture
for
the
latitude
dependence
of
the
annual
com-
ponent
of
the
various
physical
parameters
with
the
important
processes
emphasized
in
circles
........... .........
12
3
Relative amplitudes
for
the
O-,
He-,
and
N2-concentrations,
the
mass
density
p
and
the
gas
temperature
Tg
in
the
annual
com-
ponent.
The
values
are
valid for
the
summer
pole
and
are
the
coefficients
of
the
spherical
function
P
1
(0)
=
cos
0
(8
=
polar
distance)
which
describes
the
latitude
dependence.
Positive
signs
indicate
positive,
maximum
values;
negative
signs
indi-
cate
negative,
minimum
values
in
the
northern
summer
hemi-
sphere.
Solid
lines
are
taken
from
the
N
2
-O-model
which
describes correctly
the
energetics
and
thus
the
gas
temperature.
Dashed
lines
stem
from
the
He-model
which
is energetically
un-
realistic
corresponding
to
the
assumption
of
diffusive
equilibrium
iii
ILLUSTRATIONS-(continued)
Figure
Page
3
for
the
major
constituents
N
2
and
O
up
to
500
km.
Note
the
(cont.)
large
difference
between
the
"diffusive
equilibrium"
solution
and
the
"diffusion"
solution
for
the
gas
temperature
Tg
as
well
as
the
small
and
nearly
height
independent
amplitude
of
the
mass density
P
..............................
13
4
Amplitudes
from
the
thermospheric
wind
field
in
the
annual
component
of
the
N
2
-O-model.
The
maximum
vertical
veloci-
ties,
W,
are
directed
upward
and
are
shown
for
the
summer
pole,
the
maximum
meridional
velocities,
U,
blowing
toward
the
winter
hemisphere
are
shown
at
the
equator,
and
in the
northern
hemisphere
the
zonal
winds,
V,
are
eastward
in
winter
and
westward
in
summer
with
their
maximum
ampli-
tudes
at
45
°
latitude.
Dashed
lines
are
for
the
O-component,
solid
lines
are
for
the
N
2
-component.
Note
that
the
difference
between both
constituents
is
particularly
large
for
W,
but
is
also
not
negligible
for
U
...........................
16
5
The
N2-O-model
shown
for
different
eddy
diffusion
coefficients.
Note
that
all
parameters are
affected
including
Tg
.........
18
6
Relative
amplitudes
for
the
physical
parameters
of
density
and
temperature
of
the
semiannual
variations.
The
values
are
valid
for
the
poles
and
are
the
coefficients
of
the
spherical
harmonic
P
2
(0).
Positive
signs
indicate
at
the
poles
maximum
and
minimum
values during
equinox and
solstice,
respectively.
Negative
signs
indicate
the
opposite.
The
N
2
-0-model
and
the
He-model
are
differentiated
with
solid
and
dashed
lines, respectively.
Note
the
large
difference
between "diffusive
equilibrium?'
solution
(dashed
line)
and
"diffusion"
solution
(solid
line)
for
Tg, and
the
height
independent
and
very
small
amplitude
of
the
mass
density
p . . 20
iv
THEORETICAL
MODEL
FOR
THE
LATITUDE
DEPENDENCE
OF
THE
THERMOSPHERIC
ANNUAL
AND
SEMIANNUAL
VARIATIONS
by
H.
G.
Mayr
Thermosphere
and
Exosphere
Branch
Goddard
Space
Flight
Center
Greenbelt,
Maryland
and
H.
Volland
Astronomical
Institutes
University
of
Bonn
Bonn,
W.
Germany
ABSTRACT
A
three
dimensional
model
for
the
annual
and
semiannual
variations
of
the
thermosphere
is
presented
in
whichenergy
and
diffusive
mass
transport
associ-
ated
with the
global
circulation
are
considered
in
a
self
consistent
form.
It
is
shown
that
these
processes
play
a
major
role
in the
thermosphere
dynamics
and
thus account
for
a
number
of
temperature
and
composition
phenomena
such
as
(a)
The
helium
and
oxygen
bulges
in
the
winter hemispheres
at
lower
alti-
tudes,
(b)
The
relatively
large
temperature
variations
(-
26%)
in
the
annual
com-
ponent
exceeding
by
a
factor
of
three
those
inferred
from
the
satellite
drag
data
and
which
would
be
much
too
large
for
a
thermosphere
in
dif-
fusive
equilibrium,
(c)
The
7%-variation
of
the
exospheric
temperature
at
the
poles
in
the
semiannual
component
associated
there
with
a
significant
depletion
of
oxygen and
helium
during
the
equinox,'
(d)
The
nearly
height
independent
and
relatively small
amplitude
in
the
total
mass
density
which
is
responsible
for
the
fact
that
the
latitude
dependence
of
the
semiannual effect
has
so
far
eluded
observations
from
the
satellite
drag
data.
v