I did a lot of investigations on this
together with my students on GOCE and
Swarm missions in particular. I have CHAMP as
well, but I have not included many CHAMP results
because they are a bit older. So the contents of my
presentation: I will start with an
introduction, the satellite missions in
orbit that
I've worked on and that provide data on
the thermosphere and satellite
aerodynamics, the measurement principles
and processing algorithms that we apply,
and then space weather in the
thermosphere...and then there's a big
issue that we're currently still working
on: it's the uncertainty and satellite
aerodynamics and scale of the
thermosphere of the upper atmosphere. And
I'd like to finish with a very special
data set that we are going to release
early next year:
The GOCE reentry special data set. So this
is an animation that I made this week.
It's a bit dark, but it basically
represents the upper pressure level of a
thermosphere model. So this is a surface
of constant pressure. You cannot really
see it very clearly, but this 
surface - it moves up and down here with
the day and the night. You can see it's
contracting and expanding a little bit.
This is a sort of true scale...I tried to make
it true scale. And then on top of it you
see also temperature. You see a little bit
of brighter purple and darker purple...
that's the temperature. And this is what
the thermosphere looks like when
everything is normal and everything is
quiet. Of course, when your satellite flies through it
is a little bit higher drag on the day
side and lower on the night side
because of this...this variability. If you
have a polar satellite there's actually
a larger effect: If you're over the poles
the earth is a little bit flattened, so
you're a little bit higher up and you
have a little bit less drag than if
you're over the equator where the Earth
is a bit more bulgy. And then this is
an animation on the day when 
something happens on the Sun. It's a
geomagnetic storm. I will go into more
detail later, but you can see that the
thermosphere can also be quite violent,
so you see these waves that start at
high latitudes, and then they travel down
to lower latitudes. These waves - they
take about three hours to pass, so this
is much faster of course than in reality.
And of course when your satellite is flying
through such a storm you'll see huge
fluctuations of density, and we will see
that in the Swarm data later on as well.
So the satellites that really have
revolutionized this type of
investigation in the last 20 years...it
started with CHAMP.
So before CHAMP, we have to go back to
the late 70s / early 80s with the
"Atmosphere Explorer" / "Dynamic Explorer"
missions that provided very good data.
CHAMP was a satellite, it's called
"challenging micro satellite payloads", to
investigate magnetic fields and the
gravity field of the Earth. It's a German satellite.
GRACE ("Gravity Recovery and Climate Experiment") was a sort of successor to CHAMP in terms of the gravity field.
There were two satellites flying behind each other.
And to measure the gravity fields...
basically there's a problem... you have to
measure the acceleration of the gravity
fields, and then the acceleration due to
drag, and solar radiation pressure
that's basically a sort of nuisance to
this type of measurement. So they had
very accurate accelerometers on these satellites to measure these... what they call
non-gravitational accelerations, and drag is the largest non-gravitational acceleration
if you're low enough. So when
I started working on this, the GOCE mission
mission was already being planned and
launched, and I had colleagues in my
department working on the gravity and
the orbit determination aspects of GOCE.
Of course I got the possibility to also use
the accelerometers on GOCE for this
type of work. All of that was also important information 
for an ESA mission -
Swarm: so these are three identical
satellites that are currently still in
orbit. All the other satellites that I
showed already rentered. Swarm is probably
going to stay in orbit for a very long
time, so we can keep on doing this type
of research. There's an issue with
the accelerometers in Swarm though... they
do not work as well as on the
earlier satellites. And then there's also
GRACE Follow-On
which is very similar to GRACE - it's a sort of
updated version of the earlier GRACE - also
two satellites flying behind each other.
The latest that I have heard is that
it's going to go into science operations
early next year.
So if you look at the altitude
profile of these missions you can see
that's starting in 2000 with CHAMP, and
GRACE, and then GOCE 2009 to 2013, and
then Swarm took over. Swarm was launched,
I think, two weeks after the end of life of
GOCE. Yeah, we have a nearly continuous or actually
complete data sets, and GRACE Follow-On
is starting out here. GOCE is a very
special case because the altitude is so low.
It had an ion engine to compensate the
drag, and that allowed it to stay at
this about 250 kilometer range for a
very long time, and towards the end of
the life they took more risk and made it
go even lower... you can see here in steps
going lower. e-POP (Enhanced Polar Outflow Probe) satellite - it's in an elliptical
orbit that's been adopted by the ESA
Swarm team, and they're currently not
doing investigations on the thermosphere.
Now, solar activity is also important for drag.
The higher the solar activity the higher the drag.
The lower altitude the lower the
drag. So you have a sort of good signal
if you're in this lower right corner, and
in this upper left corner, the signal of the
drag that you can measure from the
accelerations on the satellite -
it becomes quite small. And at one point, it also becomes smaller than the radiation
pressure or even smaller than the errors
that you make in modelling the radiation
pressure. So I put the line here... I'm not exactly sure where to put this line... you can
move it up or down, or tilt it maybe a
little bit, but we definitely see that
with Swarm B a large part of the
mission is below this line, and we have
some problems getting reliable data from
it, and also for GRACE A and B when it
was flying at the very deep solar
minimum in 2008, and more recently also
Swarm A and C, as we're moving into a new
very deep solar minimum. Of course, if
you're not interested in the
thermosphere... if the thermosphere is a
nuisance to you, this very low signal
it's only a good thing of course. So... but
for me, for doing investigations, I'd like
to have a good signal. So the orbital
planes... these are all polar-orbiting
satellites.
GOCE was in dawn / dusk, nearly Sun-synchronous orbit. It was not maintained
to be Sun-synchronous, so you can see
very slight drift over the lifetime. And
you see CHAMP and GRACE, but also Swarm
does this / has this precession of the
orbit that takes a couple of months
to cover all local times. Yeah, that's
also interesting because - of course - the
upper atmosphere is very closely tied to
the Sun, so you want to make measurements
at midnight and noon as well. If you
would have only had GOCE we would
never have any measurements at midnight
and noon for example. So that's the
introduction of the satellites.
The measurement principle: so all of the satellites carry accelerometers and in
most of the satellites they work quite
well. Accelerometer is basically the
proof mass... so this is a block (this is
for the CHAMP satellite) and it's
basically a satellite within a
satellite. It's supposed to be
free-floating - just like the satellite is
free-floating in space. This block,  this
little piece of metal, is free-floating
inside this cage which here consists of
three parts. And here on the right, you
can see when all the three parts are put
together, and this little block is inside
of it. So this cage has this very
peculiar shape because they are
basically electrodes. So you can apply
voltages to each of these plates, and if
you do that in a correct way
this proof mass will be free-floating,
and of course the voltages that you have to apply
are proportional to the
accelerations that the satellite
experiences from the outside. So this
accelerometer is put in the center
of mass of the satellite, so all the
gravitational accelerations... they are
exactly the same for this mini satellite inside and the big satellite that is
surrounding it, but for example if
particles hit the outside walls of the
satellite then you get drag on the big
satellite... but of course the proof mass
is shielded from drag, so it wants to
move relative to the big satellite, and
then the electrodes have to keep it in
place, so we can then convert these
voltages to accelerations...and in the end
accelerations to drag. All of the
accelerometers have some issues on very
long timescales. So they tend to have a
sort of bias drift and you need to
correct for that, and traditionally we do
that by also estimating accelerations
from GPS, and this works basically the
same way as the GPS in your car... and we
have a little bit more sophisticated GPS
receivers on all of these satellites
that can receive dual frequencies and
record the phase of the GPS signals, and
with that we can calculate the orbit to
one or two / three centimeters, and we can
also of course then get velocity and
acceleration from that data. And in Delft (University), we have found ways to optimize this to
get the best possible acceleration
information that we then turn into drag
because if you process for the best
orbit accuracy you do not necessarily
get the best accelerations and
vice-versa.
Okay, so for Swarm this is basically the
only data that we can use for two of the
three Swarm satellites.
I already told you that the accelerometer is
not working very well... this
drift that all of these accelerometers show
on a timescale of many days... Swarm
shows these types of drifts within an
orbit! It's basically a very accurate
monitor of the temperature inside the
satellite: Basically, when the temperature
fluctuates because it's moving in and
out of the Sun the acceleration signal
also fluctuates, so there's a sensitivity
there that was not intended to be that
large. And for Swarm C, we can correct it
because there are also real thermistors on
the satellite, so we can combine the data
to correct for it. For the other two
Swarm satellites, this is not really
feasible, but we have optimized this GPS
acceleration measurement type. So I've
made this animation for GOCE to show
the different types of accelerations. So
GOCE is in a dawn / dusk orbit. Of course
you have an aerodynamic acceleration, but
the ion thrust is designed to compensate
for that. Aerodynamic acceleration also
includes components that are due to wind,
so it does not necessarily align with
the main axis of the satellite. The
ion thruster is mounted on the satellite,
so it always provides a force in the
same direction. Let me start it again. And
then we also have a radiation pressure
which is a relatively small force
especially for GOCE if you're flying
so low, and in the case of GOCE, it's also
always because of its dawn / dusk orbit
more or less orthogonal to the
aerodynamic acceleration. So you have to
model this ion thrust in the case of GOCE.
The other satellites do not have this continuous
thrust, so there you don't have to
do it, but for all satellites, we also have to
model the solar radiation pressure...
remove it from the acceleration. And then
we end up with an observation of the
modeled acceleration. And the modeled acceleration
depends on the relative velocity of the
atmosphere which is this blue arrow...
which we calculate from the orbits...and
the Earth rotates underneath the orbit
and drags that atmosphere with it.
And then of course you have to have an
input for the density, so initially you
can take a model for that. And then the
satellite aerodynamic model itself
consists of geometry model and a gas
surface interaction model. So the gas
surface interaction model basically
tells you when a particle from the
atmosphere hits surface of the satellite... how
does it leave it? Does it exchange a lot
of energy or only little bit of energy? Does it reflect in a specular way like a mirror?
Or is there a chance to bounce off in any direction?
So there are some assumptions that you have to
put in this satellite
aerodynamic model. Alright... one page full
of equations and I will not go into all
of those, but I just want to mention that
there is this "exact theory"... we know how
to predict satellite drag in the case of
diffuse reflection of gas particles on
the surface. So here's the drag
coefficient, the lift coefficient, and
basically what's important is what goes
into it. So here we have the wall
temperature of the satellites. Of course
we have the velocity... we have here the
temperature of the gas and the molecular
mass of the gas, so the composition of
the atmosphere and the temperature of
the atmosphere are also important. So
this is an "exact theory", but of course we
do not have all these inputs exactly.
We do not have a temperature sensor on
these satellites. We do not have a sensor
that detects whether we're in atomic
oxygen or atomic nitrogen or helium. So
we have to also make assumptions, and
that's why our results have some error.
You can apply these equations:
it's basically an equation for a single
panel which then generates drag and lift -
also depending on this angle, and of
course drag is much larger than lift, so
this is different in space compared to
lower in the atmosphere where you can
generate considerable lift, but in this
free molecular flow regime, lift is always
a very small fraction of the drag.
And here, I have a zoomed-in version that looks
at what the lift basically looks like, so
you could see from the equations
that it's quite a complicated set of
equations, but it's really an exact
theory, and basically from everything...
from all the data processing that we did
until now it seems to be quite exact
within the limitations of the unknown inputs
that we get. There are also simplifications
of this theory, for example if you have a
very short object... a satellite that's very
compact, you can eliminate some of the
terms in this equation on the previous page,
and then for example you get something
that looks more like... really like a cosine
here that crosses through this 90
degrees here. So this theory really works...
is really necessary if you have these
very slender satellite shapes, and
if you looked at the photos at the
beginning you saw that basically all
of these satellites are very slender
because - you know - the designers wanted to
maximize their lifetime and keep drag to
a minimum. But some of these satellites
have also been flown in different ways.
So this is the normal way that - for
example - CHAMP was flown with the boom
forward and this very slender
configuration, like an arrow, but there
were a few occasions where they turned the
satellite to its side... just to test
things not only for the aerodynamics, but
also for the magnetic field measurements. And
then you can apply basically these
equations and get different variants of
the drag coefficient based on various
input parameters. And you can see that
for a compact shape, there is limited
sensitivity to altitude for example, but
there is this parameter of energy
accommodation. This is basically how much
energy do the gas particles exchange
with the surface. And I've put in here two
fixed values, and then there's a sort of
theory that this behaves in a certain
way. I will not explain it, but then you
will get the much larger dependency. This
part is actually important: you can see
that for a compact shape, if you're
flying sideways, there's still a sort
of limited range... but if you have this
very elongated shape you become very
sensitive to all of these 
differences. The problem is that in the
past - when thermosphere models started
to be developed - people used basically a
simple theory... and that basically said
that for all the objects they could just
use something like 2.2 as drag coefficient,  and those measurements were
used in the early thermosphere models
- Jacchia models for example. Later on, when
mass spectrometer data became available,
they had to calibrate the mass
spectrometer, and it took the Jacchia
model that was based on this 2.2 (coefficient)
to calibrate the mass spectrometer the
data that went into the MSIS model - which
is still more or less the state of the
art - but as you can see here, there's
very little room to go lower than 2.2, but if you apply the theory in
different ways there is a lot of room to
get larger drag coefficients than 2.2,
so this is already an
indication that there might be a bias in
the current thermosphere models because of
the way the drag on satellites has
historically been treated. Ok, so now we
have all these ingredients for our aerodynamic model,
and we get a modeled acceleration. Of
course, we also get observed acceleration.
So this is true GOCE data... acceleration
data that we're putting in here.
The direction of the relative velocity then
gives the crosswinds, and then we can
basically
scale the acceleration. We look at the
difference in the scale of the
acceleration, the magnitude of the
acceleration to derive the density from
it. And I think in this, that's the light
yellow arrow here... you can see that it
behaves quite - you know - nervously. And this
orange arrow is based on the model which
behaves very smoothly, so now we can use
the difference between these two (modeled
and observed) accelerations to get the density
out of it, and also wind. You can see the
first step that we do is to basically
rotate the relative velocity vector. So
we add a little green vector here, so
that our modeled acceleration matches the
direction of the observed acceleration.
And that's... our first output is this
crosswind velocity, so we can basically
measure one component of the wind. The
wind of course is a 3D vector, but using
this approach we have to assume that the
in-track winds have some value either 0
or we use a model, and then we can get the
cross-track  wind  out. The reason that we
cannot get in-track wind is that if you
have a variation in in-track wind... if you
make this arrow a little bit longer... then
also the acceleration becomes a little
bit longer, but you can also see that
density basically does the same thing.
If you get higher density you get higher
acceleration. And the errors in the
density model are much larger than
basically the error in the relative
velocity that's due to the in-track wind.
And that is because basically most of this
relative velocity is the 7.8 or so
kilometers per second of the orbital
velocity, and the wind is only maybe a
few hundred meters per second on top of that.
For presentation, I will stick mostly to
the densities. So the equations that I
gave... those are for flat panels. Of course
you can build a satellite model of your
satellite by combining multiple flat
panels. There's an even better approach,
but it's much more labor-intensive. It's to
make such a 3D model of your satellite
with a lot of detail, and then you sort of 
"Monte Carlo approach", and that's basically
what a student of mine did for these
four satellites. We are now transitioning
also in the official processing of the
Swarm data to these models.
So this is a sort of portrait of the Swarm data for
the first two and a half years. On the
x-axis is the time, on the y-axis is the
angle along the orbit, so basically every
single vertical line here is one orbit
of data - starting from the ascending node,
so going over the equator, going over the
North Pole, going over the equator
southwards on the other side of the
Earth, and then going over the South Pole.
And what you can see here is that -
because the orbit precesses - we're
moving through this bulge in the thermosphere
that is close to the subsolar point.
The Sun always heats up one side
of the thermosphere, and when the orbit
is going in a day-night configuration
you get a large bulge. Actually, there's a
little bit of delay, so this is more
halfway through the afternoon, and then
of course this is in the night on the
other side of the orbit. You can see here
that the density is getting weaker
because we started at a high solar
activity, and we're moving to lower and lower 
solar activity, and if you would extend
this all the way up to 2018 it will become
very dark because we're now going through
solar minimum. Two of the Swarm satellites
are moving very close to each other.
They're a hundred and forty kilometers  flying side by
side when they're going over the equator,
and they probably cross over the pole
and they keep a separation of 10
kilometers in the along track direction
so that they don't collide over the pole.
So we can look at the GPS-derived
accelerations from Swarm A and C.
You can see that we can look at the difference
in this Swarm A and C density, and this
is basically 10 to the minus 15, while
here we have 10 to the minus 12, so
they're basically sampling the same part
of the thermosphere. But you can still
see that there's some pattern here that
if one satellite moving a little bit
further in the afternoon it gets a
little bit larger density than the other
one, and then when it's past the peak of
the afternoon density bulge, it will be
the other way around
and the other one will be a bit larger.
So this also gives us some confidence in the data. For GOCE, I made this analysis of how the data
compares to the models, so this is one year (Oct 2012 - Sept 2013) of GOCE data towards the end of its life.
That's basically when it was flying much
lower...even than in the beginning... and
solar activity was quite high. So these
are really the best conditions to get
the best possible densities from
satellites, and I made a comparison with
a lot of different models... so those of
you are working with thermosphere models
are probably familiar with "NRLMSISE", 
"Jacchia-Bowman", and "DTM" (that's a French
model), so these are three empirical
models. Then "HASDM" is an American US Air Force-
calibrated model, and we got only the
output along the GOCE trajectory. We
do not have access to the model
itself, but we have access to the model
output along the satellite track. And
then "GITM 1 and 2" and "TIE-GCM" and "UAMP" are
physics-based models. So these are very
computationally intensive models.
The movie that I showed at the beginning was
made using TIE-GCM. You can see that this
peak should be - you know - somewhere around
1 if there is no bias between the
model and the data, and you can see that
most of the GOCE observations are a
little bit lower than 1. The ratios of
the GOCE-observed over -modeled densities
are a little bit lower than 1. So
GOCE returns a little bit lower
densities. And for the physics-based models it's a bit
of a mixed bag... some of them are
providing much higher ...some much lower or much
higher densities depending on which model
you choose. And of course, how narrow this
peak is, is how well the model does.
And this HASDM model here performs the
best. JB-2008 and DTM-2013 come next, and
NRLMSISE-00 (that's the oldest of
the three empirical models) is a
little bit lower here in the middle. So
we can use this data now to evaluate how
well the models do, and of course newer
models will incorporate this data and
then you cannot do this comparison in
a fair way anymore. Okay, I will not go
into too much detail in all the applications.
We did a lot of very fun stuff looking
at coupling of the lower atmosphere with
the upper atmosphere. It was not so fun
when the big earthquake happened in
Japan which caused a huge tsunami, but
- for example - with GOCE we flew through
an acoustic wave and also a gravity wave
that was generated by the earthquake and
by the tsunami,
so we could detect in space how the atmosphere was put in motion at the ground. Those were very
spectacular results of GOCE, and
shows how sensitive these measurements
actually are. But I will spend a little
bit of time on space weather in the
thermosphere. At the beginning, I showed
this geomagnetic storm, and I think that
is pretty important if you want to
design very low flying satellites. So the
origin of space weather is of course the
Sun. And this is a famous graphic that is
used a lot to explain space weather. We
have the Earth here and the Sun over
there, and you can see that from time to
time the Sun really expels these huge
clouds of plasma,
and some of the times this plasma comes
into the neighborhood of the Earth. The
Earth has this protective bubble because
of its magnetic field. It's the
magnetosphere. But that there can be an
interaction between the magnetosphere
and the solar wind, so that's one
mechanism for putting energy from the
Sun into the upper atmosphere... into the
system of the Earth. And that's an
important aspect of space weather. But for
the upper atmosphere there's also
another aspect, and that's just the
radiation of the Sun. So the Sun also of
course emits light. We are very much used
to the visible light, but the upper atmosphere
basically protects us from this extreme
ultraviolet and x-ray radiation by
absorbing it, and this part of the
spectrum which is very weak compared to
the visible part... it contributes also to
heating of the thermosphere. So the visible part
of the spectrum of the Sun is very stable.
We do not really see an
11-year cycle when we go out and look at the Sun
at visible light, but if you look at the
ultraviolet and x-rays there's a really
strong difference between low solar
activity and high solar activity.
And there's this 11-year cycle that
basically controls that. So those are the
two mechanisms. If you now go back to
this magnetosphere, it's basically
protecting us... so why does this matter?
This is a little cartoonish movie that I
made: Basically, you have this orientation
of the magnetic field of the Earth, and
the solar wind also carries particles
with it that are charged particles, and
they carry with it... sort of frozen-in...
they call it frozen-in field lines of the
Sun's magnetic field, as this plasma
leaves the surface of the Sun. A lot of
the time, this plasma has a northward
orientation, and then you can see that it
aligns with the orientation of the
arrows at the Earth's magnetic field, and in
that case the Earth's magnetosphere
really acts as a shield. There's not much
energy exchange happening. But during
some of these really big eruptions, there
can also be a very strong negative
magnetic field. You can see this compass...
There are actually magnetometers that are
positioned outside of the magnetosphere
on the Sun-Earth line in the Lagrange point,
and when you see the compass needle
basically turning south,
you get about one hour warning time at
maximum that something is going to
interact with the
magnetosphere. And you can see here that the field line
from the interplanetary magnetic field
now connects with the Earth's magnetic
field, and these red dots are basically
particles that then can flow into the
upper atmosphere. They also can flow
outward... I do not show it here, but they
can lose some energy when they collide
with the upper atmospheric particles and
that causes the aurora... and also can
cause heating up of the upper atmosphere in
the polar regions. But this is not all!
You can see that this then also
compresses basically the field lines on
the night side, and this is even a larger
effect. And at some point you could also
see a reconnection of the field lines in
this region. So this is basically the
tail of the magnetosphere and that's a
sort of a reservoir also of charged
particles, and when field lines reconnect
there, there can be a burst of energy
that then also flows into the Earth's
atmosphere from the backside. And that
was what was happening there... Maybe I show
it one more time.
It's a very short movie... so this is the
normal configuration. And this is the
sort of geomagnetic storm, the configuration
that causes the geomagnetic storm and
you can see a lot of extra energy going
into the upper atmosphere from the day side
and the night side. And that is
causing the aurora and the heating up.
So that is also the cause of these ripples
that you see originate at the poles and
then it's heated up there, and then of
course it's like you drop a rock into a
pond... the waves have to travel outwards
to establish a new equilibrium. This is
another animation I made of the same
event: Here you can actually see the data
from this magnetometer in the Lagrange
point. It's pointing northwards. And now
it's starting to point southwards on
this morning of the 17th, so we have to
wait another day. On the left, you see the
magnetometer data from the Swarm satellite
and the density data from the Swarm satellites. And here a model of the
density. See here the Swarm data... but there
are little circles here that have
basically the same color as the model,
which means that there's a good match
between the model and the data. And now,
this magnetic storm sets off... you can see
here, it actually was in two
phases, and now it's really starting
to point southward... and you get a lot of
energy
that's being put in by these high-latitude
currents, so you can see here the
magnetometers that when there's a large
gradient in the magnetometers there are
large currents, and that means that
there's a large energy input because they are
vertical currents here. That's the same
type of thing that Nickolay was talking
about earlier. So this is the main phase
of the storm when you have very high
density spanning the entire globe.
There's actually a minimum of density
now at the poles because all the
densities that travel from the poles, both
the North Pole and the South Pole, basically
piles up at lower latitudes. So sometimes
you actually see also - like when you throw a rock into a pond - you do not
only see the waves going upwards, but
later you also see it going downwards...
a very deep minimum in density in these
regions close to the poles. This is
a sort of expert version of the same
animation where I actually plot also
a sort of timeline on the left of these
currents, but I think more interesting
is here on the right, the (air) densities. So
yellow are the observations from the
Swarm accelerometer in this case that
we corrected for all these issues that
we had. For this particular case we could
do it. And in the background in blue,
you see the model along the Swarm track, and
we both see it's sampled as Swarm passes by.
That's basically the fixed blue line, but
you also see this moving line which is
basically how the atmosphere is bubbling
in time... even when Swarm is not there.
And now we're getting closer to
the storm...well actually, you have to wait one more day.
So this is the day for the storm when
everything is more or less quiet, but you can
still see a lot of these little ripples
in the density data. You can see here...
it's now 0.6 kilogram per
cubic meter. And as the storm hits
I think we will go to 5.0, so that's
actually a factor of ten...
almost... higher densities during one part
of the storm. So now we're approaching
the storm. So this is the start of the
storm. This is the first phase. Actually,
the storm calmed down a little bit for a
few hours...and then early in the
afternoon, there was a second phase of
the storm. And here we have a peak that
goes all the way to 5.5 or
something like that, and another peak in
orbit later. So you can really see how
wild the fluctuations in the density are.
And of course, the model and the data do not
entirely agree, but that at least they
agree on the order of magnitude of these
fluctuations. For some orbits, there's a
very good agreement, but for others it's
not, and you can imagine
how dynamic this environment is... that
it's very difficult to really get a good prediction.
What we also see is
that after the storm the model predicts
much higher densities than the data
gives, so actually the real thermosphere
cools down a little bit faster than what
the model can predict. And that's a
limitation in the model, so this data is
also used to find these limitations and
then maybe to fix that in future
generations of the model. So this picture
of the wind data from GOCE... as we
increase the geomagnetic activity, that's
this "Kp" on the bottom, you can see the
the Kp increase, and then you can see the
wind pattern. Basically you get larger
winds if you get such a magnetic storm.
This is all winds over various
storms... and you can also see that the maximum
wind / backward wind basically moves closer
to the equator... moves away from the pole.
And you get - within this inner region of
the pole - you get really large
intensification of the winds as well.
Since time is running out, I want to
cover uncertainties in aerodynamic
modeling: This is going back to these
equations... there was a sensitivity to the
energy accommodation coefficient. So the way that
particles either adapt to the
temperature of the satellite wall... so the
particles have higher temperature, the
gas has a much higher temperature ...
a thermal velocity. The satellite wall has a
lower temperature. And when it (a particle) hits the wall,
the question is: Does it stick around
there a little bit and bounce around, and
then lose some of the thermal energy
before it goes away? Or does it act more
like a sort of mirror where it goes away
with the same energy as it had?
And basically, this energy accommodation
coefficient is meant to take that into
account. If it's 1.0, it basically means
that it bounces around a little bit on
the microscopic surface and then goes
away with a much lower temperature of the
wall. If it's zero, it retains all of its
own energy. And of course, that has an
effect on the drag. You can see on the
left here that if you lower the energy
accommodation, you get higher drag, so if
we take this aerodynamic model and we
plug in this lower energy accommodation
we actually get lower densities. Higher drag
from the model means lower densities.
For these panels that have some sort of
inclination, you can see that there's
also an effect on the lift.
That has a big effect on how we
calculate the winds. You can imagine that if
you have a lift or a sideways force... the more
lift you generate by basically turning
the knob on this energy accommodation
coefficient downwards, the less
acceleration can be explained by the
wind. And the winds will get lower. And
that's basically what you're seeing in
this plot which is... as a function of
magnetic latitude for different
conditions... this is for Solstice and
Equinox, but basically, for this explanation
it's not so important.
We basically see much larger winds from
our data (just the blue and the orange;
the orange is behind the blue; those are just
two different geometry models), compared
to the wind model. And the wind model is a
climatological model, so it's sort of
averaging out all of the wind data that
there is. So you would expect that to
have a lower magnitude, but still... this is
something like a factor of two or more.
And then, if we lower the energy
accommodation from 1.0 to 0.6, you can see
that we get a much better agreement. So
this is already one indication that
maybe this energy accommodation (coefficient) should be lowered. Even if you do not trust the
model... you know, maybe the model should
have predicted double the wind speed or
something like that....
I think it's also interesting that
basically the wind gets more
self-consistent. So when there are
deviations in the attitude, it's causing
different amounts of lift. And if you do
not get this lift exactly right you
misinterpret it, and you get an error in
the wind, and it only expands this
envelope of the wind that you see here.
So if you tune it to the right value you
can get much better wind data from this
processing. So you might say "okay, there's
a lower value for the wind. Perfect, let's
process all of the data with this lower
value!", but if you look at the density if
we move to a lower value... you can see
that - in reality - the density from the
current MSISE model (and the two colors
below that are again for the two
different geometry models), the
densities that we get from the data...
we basically move away from the model for
the density. So even if we move closer to
the model for the winds... by doing the
same operation, we move away for the
density. So somebody is going to be angry
at us I think...depending on what we
choose ;0). So we really have to investigate
this very thoroughly, and defend our
investigations.
This is - I think - also very interesting.
This is for the different satellites. You
also would expect - basically - if you have
very good geometry models for the
different satellites that you would also
get consistency between the different
satellite measurements. Of course, you can
split it up into various levels of solar
activity... so this is its solar minimum, and
this is its solar maximum, and this is
somewhere inbetween. And you can see that
there is the best consistency at solar
maximum.
Apparently, the models... they do not do so
well at solar minimum. So let's
concentrate on this one. And here also
you see that there's a bit better
consistency for these lower values of
the energy accommodation coefficients,
but I would not be able to tell whether
0.5, or 0.7, or 0.8 or 0.85
or something is the best value, from this
alone. This is a 3D view of the Swarm
satellites during a special maneuver.
These two satellites that were flying side
by side. This is the telemetry visualized.
And you can see that the satellites, they
are normally moving in that direction and
at some point the operators did this
test where they flip the satellites, make
satellites flip around like sideways for
periods and then even fly forwards for a
period. So this is a very basic plot
which I just made last week for this
 type of analysis. Basically, you can
get here again this is relative velocity...
that's the vector in blue. Then you have /
I have here introduced 4 different
versions for these 4 different
accommodation coefficients for the
accelerations. But I think I flipped the
labels around here... so I think this
darkest one should be 0.4, and the
lightest one should be 1.0. So I will
correct this when I deliver the slides.
I had not been able to recreate this movie
in time. But you can see here, basically,
this is the normal configuration you see
here in the blue lines. You see for these
4 different aerodynamic models on the
left and the right the two different
satellites... whether or not there's an
agreement between the density
observations. So let me get back to the
start when it was a little bit cleaner.
Here for example, you basically get these
three different levels or four different
levels of density, depending on which aerodynamic
model parameter you get. There's also a
white line here underneath, and that is
the model. So most of the time, the data
there's a little bit lower than the
model, but there are some occasions where
it's exactly overlapping, and you can
also see here that one satellite is
having a slightly different density, but
also from the accelerations we see
that this is the same. Now, when we flip to a
situation where one of the satellites
flying sideways, we have to use the y-
axis of the body-fixed frame to get to
these densities. And this is where it
gets a little bit complicated. There
you have to look at the yellow bars on the
left and the blue bars on the right, and
they have to match up. And here you
cannot really distinguish which of the
four models is better. At some points, one
of the satellites flies with its nose in
the wind, and at that point - let me see if
I can find a good moment in the movie...yeah -
for example here: so we have for Swarm A
a much lower sensitivity to this model
parameter, and for Swarm C a much higher
sensitivity. And here, you can actually
see that if you look at which of the
ones matches best... that's probably this
0.8 one, so it's the second one
from the top, both for the yellow and for
the blue. This is actually also an
indication that 0.8 is maybe a
better choice for this particular moment in time,
but you can see that things behave quite
wildly, so my student has done some
statistical analysis of these different
configurations of the two attitude
angles for the different satellites, and
then you would expect them, for the ideal
case, that's basically the ratio of Swarm
A over Swarm C density, is somewhere
within a few percent of 1, and that
happens for most cases. And then there
are these special cases, where one of the
satellites is flying with its nose in
the wind, when there's a very large sensitivity...
or very large difference in
sensitivity between Swarm A and Swarm C.
And all of these intersections, they
happen at a value somewhere between
0.8 and 0.85, so this our
latest result that also indicates that
this energy accumulation coefficient...
a good value / a better value might be
0.85. We're currently using point 0.93.
And I want to show this to end my
presentation. Here, I'm showing 4
different density models, so the
3 main empirical models (NRLMSISE-00, Jacchia-Bowman-2008, and DTM-2013), and
this is showing basically a map with (at the
subsolar point) this density bulge for
these 3 models. And "WACCM-X" is
basically a physical model that covers
the entire atmosphere, and you can see that
it's a much more detailed model. This is
the reentry of GOCE, so on the bottom
left
we have here the height of GOCE
during its last three weeks, when it ran
out of fuel. And it's going to basically
crash here. And on the bottom right you
see - basically for every orbit - a sort of
time series...
what the density from the model and
from the data looks like. And we actually
have two versions of the data here. First
I'm going to play this out,
we concentrate on the difference between
the four maps. You can actually see the
map of the earth rotating underneath, so
basically we're fixing our map on the
subsolar point here at 12 o'clock. As
the satellite gets lower, you will see
that for... especially for WACCM-X, the
nature of this variation in the map
changes. You see basically a diminishing of
this subsolar point bulge... also here for
NRLMSISE-00, and you will see a secondary
maximum pop up. And you see it much more
clearly here. And you can see: Jacchia-Bowman-2008 for example, does not represent
this at all. It's not very accurate for
this lower part of the atmosphere.
And now, we're dropping to below 200
kilometers / 250 kilometers, and that's the
end of the mission. A little bit of a zoomed-in view here on this data: We actually
have these different colors representing
the different models, and then the black
dots are the accelerometer-derived data.
There's also a gray line behind here
where we have have just used the GPS, and
you can see that they match very closely.
These black dots, they have a little
bit more of this... what looks like noise,
but I'm pretty sure that this is
actually true variations of density that
were measured along the GOCE track. And I
think these are waves basically
propagating upwards from the lower
atmosphere.
So it's basically weather from the lower
atmosphere reaching a higher atmosphere,
causing these little wiggles in the
density data. So now it gets interesting.
We are now at 200 kilometers (altitude) more or
less. Slightly below. And part of the
accelerometer became saturated at that
point, so the the instrument was not
designed to measure such large
accelerations. And you can see it basically
drop until the signal basically drops
away, but we still have here in gray these
GPS-derived accelerations... and we have
that until 6 hours before the actual
reentry, when the last full downlink of
GPS-data was provided. And that's it.
You look at the scale of the densities:
there you can see during this last phase...
now the maximum is 0.8, and here it
goes all the way up,
in the last orbits, to 150 (!) which is -
let me see what time is this? - this is
still more than an hour before the actual reentry, when the satellite was at 124 km (altitude).
At that point, we still have some confidence in our orbit
determination. So we also have wind, and
here you also can see the effect of the
saturation of the accelerometers. This may
be a bit too complicated of a plot... just to
show that we have a good agreement between
GOCE data on the left and HWM14 data
on the right. So if you want more
explanations on what this plot actually
means just talk to me. Where does all
this energy go? Because we have drag
basically slowing down the orbit, the
orbit getting lower...
of course the satellite heats up. And
this is a picture from the End of
Mission Operations Report. So the
mission operators, they also had the
telemetry (data) of the temperature of the
different components of the satellite,
and you can see, for example the battery
here, I think it's the blue one... it went
from 20 Celsius to 80 Celsius during the
last telemetry that they received. And if
you go further towards the back of the
satellite there is also an increase in
temperature... this ion propulsion
electronics unit (IPCU) also saw a rise in the
temperature, but it's much more modest.
It goes from maybe 13 to 15 degrees, so I think
this was a very interesting reentry
experiment / "almost-reentry
experiment" at the end of the GOCE
mission. You can see here that there's
continuous data until 6 hours before
reentry, and then there are a few
individual passes. I think we should be
very grateful that they scheduled these
passes... unfortunately they could not get
continuous data downlink anymore. They
used a station on Antarctica. And
actually, they hired of course a couple
of passes... they have to pay the station
to track and download the data from
GOCE, and at some point they had
predicted that GOCE would reenter in
the Indian Ocean, and they said to the
station "okay, we don't have to track it
anymore",  but in the end GOCE passed over
all of Antarctica and plunged into the
Atlantic Ocean near the Falkland Islands.
So they could have even maybe tried to
listen to GOCE during this last half
hour or so of its life... and maybe got one
more data point for this temperature
graph ;0)... that would have been really nice, 
but they thought it had already died.
Ok, so that's the end of my talk. Yeah, the
main message that I want to give away...
we talked about a lot of different things...
but I think the main message is that
computing exact aerodynamic forces and
torques on satellites, it's not a
completely solved problem yet.
Of course that's also addressed in this
project :0). There are strong indications
from the analysis of CHAMP, GOCE and Swarm
density and wind data that the energy
accommodation should be lower than
previously thought. And this has
implications for the scale of the
thermosphere, so if we apply these right
values for the wind our thermosphere
density is going to be lower than
indicated by current empirical models.
And that means that if you stick to your
same drag coefficients for your mission
analysis you're going to have longer
lifetimes,
space debris is going to last longer in
orbit... things like that, but I have to
give one warning that - for practical
purposes - mission analysis for example, it
is really important to use satellite
aerodynamic models and thermosphere
models that are consistent with each
other. So maybe, if you're still using
NRLMSISE-00 for your mission analysis, it's
better not to use this very
sophisticated aerodynamic model... pretty
elongated shapes etc.  You will get more
consistent results if you use the old
2.2 [...]. There's somewhere in between that will
maybe give you the best result. All of
this should be consistent. Currently, it's
a bit of a mess, but I hope that also the
DISCOVERER project can help! Thanks...
