Ionosphere Research and its
applications
1. Methods ionosphere model identification.
Ionosphere physical phenomenon is very
complicated. Therefore ionosphere models are heuristic and are created by
experimental data by interpolation.
1.1 Identification by table.
There are a set of different tables those contains experimental data. These tables looks like:
|
L |
B, Gs |
Density of protons |
|||||||||
|
0.1 |
0.4 |
1.0 |
4.0 |
10.0 |
30.0 |
50.0 |
100.0 |
200.0 |
400.0 |
||
|
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
10 |
11 |
12 |
|
1.20 |
0.18035 |
2.50E+03 |
2.50E+03 |
2.46E+03 |
2.40E+03 |
2.30E+03 |
2.30E+03 |
2.00E+03 |
1.40E+03 |
7.00E+02 |
1.40E+02 |
|
0.19000 |
1.20E+03 |
1.20E+03 |
1.12E+03 |
1.07E+03 |
1.03E+03 |
9.60E+02 |
9.49E+02 |
7.00E+02 |
3.70E+02 |
7.00E+01 |
|
|
0.20000 |
4.00E+02 |
3.79E+02 |
3.67E+02 |
3.56E+02 |
3.44E+02 |
3.27E+02 |
3.10E+02 |
2.40E+02 |
1.40E+02 |
2.20E+01 |
|
|
0.20500 |
2.05E+02 |
1.91E+02 |
1.82E+02 |
1.74E+02 |
1.70E+02 |
1.63E+02 |
1.48E+02 |
1.26E+02 |
7.71E+01 |
1.16E+01 |
|
|
0.21000 |
1.00E+02 |
8.98E+01 |
8.69E+01 |
7.84E+01 |
7.28E+01 |
6.58E+01 |
5.93E+01 |
4.50E+01 |
2.80E+01 |
4.70E+00 |
|
|
0.21500 |
4.20E+01 |
3.57E+01 |
3.29E+01 |
2.69E+01 |
2.42E+01 |
1.85E+01 |
1.62E+01 |
1.02E+01 |
2.50E+00 |
5.37E-01 |
|
|
0.22000 |
1.00E+01 |
8.00E+00 |
7.15E+00 |
5.46E+00 |
4.58E+00 |
3.00E+00 |
2.00E+00 |
8.63E-01 |
1.60E-01 |
1.00E-01 |
|
|
0.22400 |
1.00E+00 |
1.00E+00 |
8.04E-01 |
2.00E-01 |
1.00E-01 |
1.00E-01 |
1.00E-01 |
1.00E-01 |
1.00E-01 |
1.00E-01 |
|
|
1.30
|
0.14185 |
3.48E+04 |
3.44E+04 |
3.40E+04 |
3.10E+04 |
2.67E+04 |
1.60E+04 |
1.30E+04 |
7.82E+03 |
2.97E+03 |
4.99E+02 |
|
0.16000 |
1.62E+04 |
1.58E+04 |
1.54E+04 |
1.46E+04 |
1.29E+04 |
9.00E+03 |
7.30E+03 |
4.40E+03 |
1.67E+03 |
2.57E+02 |
|
|
0.18000 |
6.61E+03 |
6.52E+03 |
6.43E+03 |
6.04E+03 |
5.47E+03 |
4.10E+03 |
3.35E+03 |
2.14E+03 |
8.06E+02 |
1.15E+02 |
|
|
0.20000 |
1.72E+03 |
1.77E+03 |
1.74E+03 |
1.60E+03 |
1.50E+03 |
1.20E+03 |
1.02E+03 |
7.82E+02 |
2.97E+02 |
3.69E+01 |
|
|
0.20500 |
1.15E+03 |
1.09E+03 |
1.13E+03 |
9.69E+02 |
9.89E+02 |
8.04E+02 |
6.65E+02 |
5.02E+02 |
2.12E+02 |
2.47E+01 |
|
|
0.21000 |
5.65E+02 |
5.37E+02 |
6.14E+02 |
5.32E+02 |
5.20E+02 |
4.04E+02 |
3.39E+02 |
2.60E+02 |
1.19E+02 |
1.31E+01 |
|
|
0.21500 |
1.91E+02 |
1.94E+02 |
2.03E+02 |
2.04E+02 |
1.82E+02 |
1.45E+02 |
1.36E+02 |
9.64E+01 |
6.17E+01 |
5.50E+00 |
|
|
0.22000 |
3.48E+01 |
3.44E+01 |
3.40E+01 |
3.10E+01 |
3.01E+01 |
2.67E+01 |
2.45E+01 |
2.25E+01 |
1.67E+01 |
1.58E+00 |
|
|
0.22500 |
2.90E+00 |
1.00E+00 |
1.00E+00 |
9.62E-01 |
9.49E-01 |
9.06E-01 |
8.75E-01 |
8.49E-01 |
7.69E-01 |
2.83E-01 |
|
|
0.22800 |
6.20E-01 |
1.00E-01 |
1.00E-01 |
1.00E-01 |
1.00E-01 |
1.00E-01 |
1.00E-01 |
1.00E-01 |
1.00E-01 |
1.00E-01 |
|
|
1.40 |
0.11358 |
1.40E+05 |
1.40E+05 |
1.40E+05 |
1.20E+05 |
7.89E+04 |
3.60E+04 |
2.50E+04 |
1.40E+04 |
4.58E+03 |
7.00E+02 |
|
0.12000 |
1.10E+05 |
1.10E+05 |
1.00E+05 |
9.49E+04 |
6.58E+04 |
3.10E+04 |
2.20E+04 |
1.20E+04 |
4.00E+03 |
5.89E+02 |
|
|
0.14000 |
5.30E+04 |
4.80E+04 |
4.30E+04 |
3.79E+04 |
3.10E+04 |
1.70E+04 |
1.30E+04 |
7.50E+03 |
2.40E+03 |
3.50E+02 |
|
|
0.16000 |
2.59E+04 |
2.20E+04 |
2.18E+04 |
1.86E+04 |
1.60E+04 |
1.00E+04 |
8.00E+03 |
4.70E+03 |
1.40E+03 |
2.10E+02 |
|
|
0.18000 |
9.69E+03 |
9.10E+03 |
8.30E+03 |
8.00E+03 |
7.20E+03 |
5.40E+03 |
4.20E+03 |
2.50E+03 |
8.30E+02 |
1.10E+02 |
|
|
0.20000 |
3.00E+03 |
3.00E+03 |
3.00E+03 |
2.70E+03 |
2.59E+03 |
2.20E+03 |
2.00E+03 |
1.00E+03 |
3.79E+02 |
3.79E+01 |
|
|
0.20500 |
2.04E+03 |
2.12E+03 |
2.16E+03 |
1.79E+03 |
1.83E+03 |
1.56E+03 |
1.43E+03 |
7.08E+02 |
3.03E+02 |
2.46E+01 |
|
|
0.21000 |
1.24E+03 |
1.33E+03 |
1.36E+03 |
1.12E+03 |
1.15E+03 |
9.42E+02 |
9.12E+02 |
4.45E+02 |
2.19E+02 |
1.32E+01 |
|
|
0.21500 |
7.30E+02 |
7.80E+02 |
7.95E+02 |
6.59E+02 |
6.76E+02 |
5.51E+02 |
5.07E+02 |
2.69E+02 |
1.36E+02 |
6.40E+00 |
|
|
0.22000 |
4.00E+02 |
4.00E+02 |
4.00E+02 |
3.75E+02 |
3.30E+02 |
2.80E+02 |
2.49E+02 |
1.50E+02 |
6.00E+01 |
2.59E+00 |
|
|
0.22500 |
1.96E+02 |
1.72E+02 |
1.67E+02 |
1.86E+02 |
1.31E+02 |
9.60E+01 |
9.71E+01 |
7.31E+01 |
1.39E+01 |
8.89E-01 |
|
|
0.23000 |
8.22E+01 |
6.47E+01 |
6.07E+01 |
8.02E+01 |
4.32E+01 |
3.08E+01 |
2.75E+01 |
2.81E+01 |
2.94E+00 |
3.41E-01 |
|
|
0.23600 |
2.07E+01 |
1.57E+01 |
1.43E+01 |
1.74E+01 |
9.02E+00 |
6.64E+00 |
4.99E+00 |
5.25E+00 |
5.45E-01 |
1.47E-01 |
|
|
0.24000 |
3.50E+00 |
3.00E+00 |
2.70E+00 |
2.00E+00 |
1.60E+00 |
1.00E+00 |
8.42E-01 |
5.32E-01 |
1.60E-01 |
1.00E-01 |
|
|
0.24300 |
1.00E+00 |
1.00E+00 |
9.04E-01 |
4.02E-01 |
1.00E-01 |
1.00E-01 |
1.00E-01 |
1.00E-01 |
1.00E-01 |
1.00E-01 |
|
|
1.50
|
0.09234 |
5.31E+05 |
5.20E+05 |
5.00E+05 |
3.78E+05 |
1.97E+05 |
3.77E+04 |
2.37E+04 |
1.33E+04 |
4.34E+03 |
5.65E+02 |
|
0.10000 |
3.46E+05 |
3.37E+05 |
3.26E+05 |
2.48E+05 |
1.30E+05 |
3.11E+04 |
2.04E+04 |
1.15E+04 |
3.76E+03 |
4.84E+02 |
|
|
0.12000 |
1.29E+05 |
1.27E+05 |
1.23E+05 |
9.49E+04 |
5.31E+04 |
1.99E+04 |
1.45E+04 |
8.28E+03 |
2.70E+03 |
3.42E+02 |
We need approximation of these models
by interpolation law. This task is solved by usage of nonlinear regression. Nonlinear
regression in statistics is the problem of fitting a model.
to multidimensional x,y data, where f is a nonlinear function of x, with regression
parameter θ.
Nonlinear regression operates with
selections. This software implements two methods of manipulation with
selections. The first method loads selection iteratively, i.e., step by step.
The second one loads selection at once.
The architecture of nonlinear
regression software that uses iterative regression is presented in the
following scheme:
Let us describe the components of this
scheme. The iterator provides data-in selections x and y. The y
is the Left part of fitting the equations. The Transformation
corresponds to the nonlinear function f, and generates the Left part
of the fitting model. The Processor coordinates all the actions and
corrects the Regression parameters. Let us consider an example of approximation
of particles' density by following function:
where B, E are
induction and energy and a, b, c, d, f,
d are coefficients those we should define. Following picture shows as
this problem is solved by our technology.
Let us desribe elements of this picture. The SQL element performs an SQL query to database. It looks like:
The Function element
contains approximation function.
Right part of the window shows that
variable x is linked to parameter B of end y is
linked to patameter Energy of Selection. The Processor
solves task of regression.
1.2 Visualization of results.
Scientific results requires visualization. Our technology enables us different kinds of 3D and 2D visualization. For example 3D visualization of obtained function looks like:
The 2D grayscale visualizaion is
presented on the following picture:
Light places correspond to maximal values of function. Another kind of 2D visualization is rainbow one. It is presented at the following picture:
Red color correspond to maximal vaues
and violet correspond to minimal ones.
1.3 Identification with motion model.
Let us consider following situation.
We have a spacecraft. Its initial condition are known. We have measurements of
parameters of ionosphere and we wish to define regression dependence of
ionosphere parameter from Earth's magnetic field and height. The task is
decomposed by two steps.
1.3.1 Step 1. Simulation.
During this step we shall obtain time dependencies of magnetic induction and height of time. Following picture present scheme of simulation
We have Earth and Earth's magnetic
field. Model of the field is rigidly linked to Earth's reference frame. However
we should simulate magnetic field near spacecraft. So we install virtual sensor
of the field at spacecraft. Our technology performs this operations by the
following way:
This picture contains Motion
model of spacecraft. This model is used for positioning of Spacecraft's
frame. The F1 link means that 6D position of Spacecraft's
frame is considered relatively Eearth's frame. The L
2 link means that Magnetic Field is considered
relatively Eearth's frame. Link L 3 means that virtual Sensor
is installed at Spacecraft's frame. The Output
calculates module of magnetic field by the following formula:
We can notice that this formula
calculates square of vector product of induction vector by itself. During this
step we've calculated dependences of magnetic field module on time.
1.3.2 Information processing.
Now we already have dependences of
magnetic field, and height. Processing of this data is presented in the
following picture:
So the Height, B
and Experimental data components contains data of spacecraft's
height, magnetic induction and ionospheric experimental data. The term Regression
formula does not requires comments.
2. Example of the complicated model
application.
Models of ionosphere are used for determination of damage by high energy particles. To define this damage we should have comprehensive motion model of spacecraft. Quantatively this model is presented at following picure:
Currents of its equipment interacts
with Earth's magnetic field. Spacecraft has a photovoltaic that is an
elastic vibrations body. It is used a flywheel for angular stabilization of the
spacecraft. Now let us construct this situation:
Let us describe components of this
picture. The 3D motion model is a motion model of spacecraft
as material point. It is used in 6D motion model of Spacecraft Body.
The models of Photovoltaic and Flywheel are
connected to model of Spacecraft Body. The 
link
means mechanical connection. The parameters of Spacecraft Body
are used in Spacecraft frame. The virtual Sensor
is used for determination of parameters of Magnetic Field and Damage
field near spacecraft. The Damage field is the field
of ionosphere particles. Parameters of fields those are defined by Sensor
are used in Transformation. Transformation
calculates damage effect and control laws of Spacecraft Body
and Flywheel.