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ENA measurements of the ring current

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Title: ENA measurements of the ring current


1
ENA measurements of the ring current
  • Robert DeMajistre

2
(No Transcript)
3
Overview
  • Motivation for ENA imaging
  • Measurement mechanism
  • The HENA instrument
  • HENA measurements/retrievals
  • Validation
  • Results
  • The next steps

4
  • In situ measurements
  • Cluster observation of the ring current
  • Precise measurements
  • Lack of global context single trace through a
    4 dimensional structure (3 space, time)

5
Global context
  • In situ measurements often alias space and time
  • Overall morphology is difficult to deduce
  • Multiple spacecraft help
  • Statistical models are difficult to assemble
  • Combination of precise in situ measurements and
    qualitative morphology very attractive
  • ENA imaging to the rescue

6
ENA emission from RC
7
ENA imaging
8
IMAGE geometry
(geographic)
9
High Energy Neutral Atom Imager
10
Example HENA Image
Earth disk
Clock Angle
Magnetic field lines
Particle brightness is represented in false color
Direction to Sun
11
Sample image sequence
12
Retrieval Method
  • Transform spatial integral into dipole
    coordinates (L, f, m), expand pitch angle
    dependence in Legendre polynomials
  • Use 2-D linear quadrature to convert to linear
    equations
  • Use 2-D constrained least squares to solve

13
Tuning scheme
14
Tuning inputs
Simulated image from October 4, 2000
15
TuningResults
  • Second difference (H2) provides better
    quantitative agreement at the peak
  • Markov provides better overall morphology
  • In practice, we combine the two

16
Results for actual image
17
PreliminaryValidation
18
  • Selected Results
  • Ring current peak is often observed at midnight
    (or later) rather than at the classical
    position at dusk
  • Dipolarizations and depletions (observed) in
    time series clues to how substorms develop

19
100-150 keV Oxygen 40-50 keV
Hydrogen March 31, 2001
20
Next steps
  • TWINS
  • Dual vantage point
  • Earth looking
  • Launches in 06 and 07
  • Casini/INCA
  • Currently orbiting Saturn
  • Good data on both Saturn and Titan

21
Conclusion
  • ENA imaging is giving us a new view into ring
    current morphology
  • Weve improved our insight into the storm time
    behavior of the magnetosphere
  • In coordination with the in situ instruments we
    can make important quantitative statements about
    how the magnetosphere behaves.

22
Backup
23
Overview
  • Remote sensing what and why
  • Mathematical framework for inverse problems
  • Case studies
  • Nighttime electron density inferred from
    ultraviolet emission measurements (TIMED/GUVI)
  • Atmospheric composition inferred from Stellar
    Occultation Measurements (MSX/UVISI)
  • Ion intensities inferred from Energetic Neutral
    Atom (ENA) imaging (IMAGE/HENA)
  • System engineering implications

24
What?
  • Making measurements where the instrument does not
    have direct physical access to the object of
    measurement

Why?
Many problems in space science require
measurement of multiple locations nearly
simultaneously costs of sufficient in situ
measurements are prohibitive
25
Remote sensing is indirect
yFXP
Forwardmodel
Inversemodel
XF-1yP
26
Problems with using exact inverse
yFXP
XF-1yP
  • Solution may not exist
  • Only for an EOM in specific forms
  • It may not be unique many x may produce a
    single y
  • It may be poorly conditioned slightly different
    x may yield different y
  • Measurement noise is always present
  • Pose a similar problem that can be solved more
    easily

27
Example of direct retrieval
IKh
  • Simplified example similar to recombination
    problem
  • Linear problem
  • Noise added to measurement
  • Noise amplification very noticeable (poorly
    conditioned)
  • Only marginally acceptable results

28
The least squares alternative
  • Instead of exact solution, search for the values
    of x that are most consistent with the
    measurement
  • Minimize the square (epTSy-1ep) of the prediction
    error epy-F(xp) weighted by the inverse of Sy
    (the measurement covariance)
  • There are standard solutions for linear problems
    (e.g., Bevington)
  • Even moderately nonlinear problems can be solved
    iteratively

29
Adding information
  • The least squares solution is likely to be just
    as ill conditioned as is the direct solution
  • Adding measurements is not very effective
    (N-1/2)
  • Additional physical information must be
    introduced to stabilize the inversion

30
Constrained inversions
  • Minimize epTSy-1epgxTHxwhere the matrix H is
    chosen with the expectation that xTHx should be
    small. The tuning parameter g modulates the
    influence of the constraint
  • Example if we expect x to be smooth, we could
    put HD1TD1, where D1 is the first derivative
    operator

31
Constraints in perspective
  • Constraints add information to the problem
  • Can be formally equivalent to additional
    measurements
  • H and g quantify the character of these
    constraints

(y-Kx)Ts-2 (y-Kx)gxDTDx
32
Constraints
  • Constraints can dramatically reduce error
    amplification
  • They can also introduce significant systematic
    errors
  • Prediction error ALWAYS increases
  • Relying on information in addition to the actual
    measurements

33
Metrics for tuning constraints
  • Tune through simulation
  • cr2(1/Ny) epTSy-1ep does the data fit the
    model
  • g (1/Nx)(xm-xs)T Sx-1(xm-xs) does the
    retrieval match the input to the simulation
  • q(cr2 -1)2(g-1)2
  • Minimize q

34
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35
EOM for space based measurements
  • Many measurement systems can be represented by a
    common physical model
  • Though mechanisms vary, the formal similarity is
    striking
  • Two essential parts
  • Instrument equation
  • Equation of transfer

36
Equation of transfer
  • Applicable to a wide variety of information
    carries
  • Photons
  • Massive particles in tenuous media

Transmission from 0 to s
Transmission from s to s
s
ò





s
d
E
s
s
T
E
s
J
E
s
T
E
I
E
s
I
)

,
(
)

(
)

0
,
(
)

0
(
)

(
0
Intensity at s
Intensity at 0
Source at s
37
Instrument equation
  • Covers most instrument effects
  • Non-linearity neglected for now
  • Assumes instrument measures local intensity of
    information carriers

Smearing function
Background counts in channel i
Counts in channel i
38
Approach to Solution
  • Cast problem in general form
  • Replace integrals with discrete quadratures
  • Linearize the problem (if necessary)
  • Formulate constraints
  • Tune the constraints
  • Validate with independent measurements

39
Case studies
  • TIMED/GUVI electron density retrievals one
    dimensional, single color, single constituent
    retrieval (limited by SNR)
  • MSX/UVISI Stellar occultation one dimensional,
    multi-spectral, multi constituent retrieval
    (limited by SNR and size of data set)
  • IMAGE/HENA ENA imaging two dimensional
    retrieval (limited by SNR and viewing geometry)

40
Constraint Matrices
  • Boundary constraint force solution to be small
    at boundaries of L
  • Cylindrical boundary in f
  • Smoothness constraint with asymmetry parameter
  • First difference (force solution to be small)
  • Second difference (force Laplacian to be small)
  • Markov constraint force changes to be small
    over a correlation length
  • Optimize smoothness strength, g, boundary
    strength, l, and either asymmetry or correlation
    length, a need a method

41
Impact of ENA measurements
  • ENA imaging on the IMAGE spacecraft provides the
    first global view of the inner magnetosphere
  • The retrievals described here have been used to
    study global behaviors for the first time
  • Skewed peak of the ring current density towards
    midnight
  • Dipolarizations of the ring current during
    substorms
  • Growth phase dropouts choking off of the ring
    current during the growth phase

42
Common Elements of Case Studies
  • Similar inversion procedures have been
    successfully applied to disparate data sets
  • Problems and solutions are formally similar
  • Common tuning process for constraints are used
  • Suggests common solutions in measurement system
    design
  • Replace integrals with discrete quadratures
  • Linearize the problem (if necessary)
  • Formulate constraints
  • Tune the constraints
  • Cast problem in general form
  • Validate with independent measurements

In all cases, retrievals were designed after
instrument flight
43
System Engineering
  • The tools used for developing retrievals and
    tuning constraints can also be used as part of
    instrument design
  • Forward modeling of the Equation of Measurement
  • Retrieval sensitivity to instrument parameters
  • System focus on retrieval accuracy rather than
    radiometric accuracy
  • Optimize (quantitatively) instrument tradeoffs
    based on final retrieval accuracy(e.g., should I
    sacrifice some SNR for better spectral
    resolution?)

44
Measurement System Design
  • Develop coupled simulation of radiation mechanism
    and instrument early
  • Use it to help with instrument and spacecraft
    tradeoffs
  • Keep it current as project develops
  • Alternate lower fidelity models can be developed
    and compared
  • Add data system and inversion modules to be used
    with optimization of instrument
  • Use these modules to identify and exploit
    opportunities for in-flight calibration refinement

45
Calibration and data products
  • Currently, calibration emphasizes the production
    of radiances from instrument data (required by
    NASA)
  • Shift focus to characterizing full instrument
    function for use in retrievals.
  • Shift priority to lower level data products for
    retrieval team and higher level products for the
    users (calibrated radiances are almost always of
    marginal utility)

46
Science Impacts
  • Night-side ionosphere
  • New quiet time maps of the low/midlatitude
    ionosphere
  • Basis for studying the quiet time interaction of
    the thermosphere/ionosphere
  • Stellar Occultation
  • Study of ozone behavior during polar night
  • Study of molecular oxygen and ozone in the
    mesosphere/thermosphere
  • ENA
  • First global quantitative view of the inner
    magnetosphere
  • Several storm time phenomena have been observed
    and studied from a global perspective
  • Comparisons with models of the inner magnetosphere

47
Next steps
  • Night-side ionosphere
  • SSUSI an instrument similar to (but more
    sensitive than) GUVI is now in orbit, more are
    planned
  • Additional instruments are being proposed
    focusing on nighttime limb observations
  • Stellar occultation
  • Instruments to be proposed include extensions to
    IR for use at Mars
  • ENA
  • Doublestar (now flying )TWINS (near launch) to
    provide multi-position ENA measurements
  • Cassini/INCA now at Saturn, IBEX now phase B

48
Conclusions
  • Weve described a general framework for space
    based remote sensing
  • Techniques developed here have been used
    successfully across a broad range of applications
  • The products resulting from these techniques are
    being applied to significant and interesting
    problems
  • The techniques also allow for more effective
    system design of remote sensing systems
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