ENA measurements of the ring current

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ENA measurements of the ring current

• Robert DeMajistre

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(No Transcript)
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Overview

• Motivation for ENA imaging
• Measurement mechanism
• The HENA instrument
• HENA measurements/retrievals
• Validation
• Results
• The next steps

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• 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)

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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

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ENA emission from RC
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ENA imaging
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IMAGE geometry
(geographic)
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High Energy Neutral Atom Imager
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Example HENA Image
Earth disk
Clock Angle
Magnetic field lines
Particle brightness is represented in false color
Direction to Sun
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Sample image sequence
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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

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Tuning scheme
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Tuning inputs
Simulated image from October 4, 2000
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TuningResults

• Second difference (H2) provides better
  quantitative agreement at the peak
• Markov provides better overall morphology
• In practice, we combine the two

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Results for actual image
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PreliminaryValidation
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• 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

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100-150 keV Oxygen 40-50 keV
Hydrogen March 31, 2001
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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

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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.

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Backup
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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

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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
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Remote sensing is indirect
yFXP
Forwardmodel
Inversemodel
XF-1yP
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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

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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

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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

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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

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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

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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
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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

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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

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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

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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
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s
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Intensity at s
Intensity at 0
Source at s
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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
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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

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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)

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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

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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

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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
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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?)

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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

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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)

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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

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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

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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