Title: ENA measurements of the ring current
1ENA measurements of the ring current
2(No Transcript)
3Overview
- 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)
5Global 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
6ENA emission from RC
7ENA imaging
8IMAGE geometry
(geographic)
9High Energy Neutral Atom Imager
10Example HENA Image
Earth disk
Clock Angle
Magnetic field lines
Particle brightness is represented in false color
Direction to Sun
11Sample image sequence
12Retrieval 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
13Tuning scheme
14Tuning inputs
Simulated image from October 4, 2000
15TuningResults
- Second difference (H2) provides better
quantitative agreement at the peak - Markov provides better overall morphology
- In practice, we combine the two
16Results for actual image
17PreliminaryValidation
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
19100-150 keV Oxygen 40-50 keV
Hydrogen March 31, 2001
20Next steps
- TWINS
- Dual vantage point
- Earth looking
- Launches in 06 and 07
- Casini/INCA
- Currently orbiting Saturn
- Good data on both Saturn and Titan
21Conclusion
- 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.
22Backup
23Overview
- 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
24What?
- 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
25Remote sensing is indirect
yFXP
Forwardmodel
Inversemodel
XF-1yP
26Problems 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
27Example 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
28The 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
29Adding 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
30Constrained 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
31Constraints 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
32Constraints
- 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
33Metrics 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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35EOM 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
36Equation 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
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Intensity at 0
Source at s
37Instrument 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
38Approach 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
39Case 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)
40Constraint 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
41Impact 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
42Common 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
43System 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?)
44Measurement 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
45Calibration 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)
46Science 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
47Next 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
48Conclusions
- 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