ENA measurements of the ring current
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ENA measurements of the ring current
Robert DeMajistre
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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
-6 -4 -2 0 2 4 6
-6
-4
-2
0
2
4
6
106
105
104
103
102
Earth Radii
dsnjj IONENA
t
ionii ddtEjtEAdEdtC0 0
2
0
sin),,,(),,,(
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IMAGE geometry
(geographic)
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High Energy Neutral Atom Imager
CHARGED PARTICLE SWEEPING COLLIMATOR
PRE-AMPS
HV SUPPLIES
2-D IMAGING, STOP MCP
COINCIDENCE MCP
1-D IMAGING, START MCP
ENACHARGED PARTICLE
+ - --
--
---
-
-
+ ++
+
++
+
+
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Example HENA Image
ClockAngle
Earth disk
Direction to Sun
Magnetic field linesParticle brightness is
represented in false color
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Sample image sequence
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Retrieval Method
• Transform spatial integral into dipole coordinates (L, , ), 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
Jion 0
C0
Jion KJion
gr gf
1)
2)
3)
4) 4)
5)
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Tuning inputs
Simulated Image
-45-30-150153045
60
45
30
15
0
-15
-30
-45
-60
12
18
00
06
0.000
1.500
3.000
12
18
00
06
2 2
22
4 4
44
6 6
66
8 8
88
10 10
1010
0.0
7.5e+05
1.5e+06
Test Ion Distribution
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
0.500
0.50
0
0.833
0.833
12
18
00
06
2
4
6
8
10
0.0
7.5e+05
1.5e+06
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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 HydrogenMarch 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
• We’ve 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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• 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
Overview
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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
Object of the Measurement
Radiation Mechanism
Transmission Medium
Mesurement System
Measured ValuesMeasurement
Inversion
y=F[X;P]
X=F-1[y;P]
e-e-
e- e- e-
O+ O+
O+
e-
O+
e-
O+ DN
Forwardmodel
Inversemodel
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Problems with using exact inverse
• 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
y=F[X;P] X=F-1[y;P]
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Example of direct retrieval
-200 0 200 400 600 800 1000 12000
20
40
60
80
100
120
Simulated Measurement (counts)
c)
• Simplified example – similar to recombination problem
• Linear problem
•Noise added to measurement
• Noise amplification very noticeable (poorly conditioned)
• Only marginally acceptable results
I=K
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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 (pTSy
-1p) of the prediction error p=y-F(x;p) 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
0 1x10 2x100
20
40
60
80
100
120
5 5
VER (photons/cm -3/s/sr)
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Constrained inversions• Minimize
pTSy
-1p+xTHxwhere the matrix H is chosen with the expectation that xTHx should be small. The tuning parameter modulates the influence of the constraint
• Example – if we expect x to be smooth, we could put H=D1
TD1, 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 quantify the character of these constraints
(y-Kx)T(y-Kx)+xDTDx
232
221
23
23332321313
22
23232221212
21
23132121111
)0(
)0(
/)(
/)(
/)(
xx
xx
xkxkxky
xkxkxky
xkxkxky
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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
VER (photons/cm -3/s/sr)0 1x10 2x105 5
0
20
40
60
80
100
120
c)
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Metrics for tuning constraints
• Tune through simulation
• r2=(1/Ny) p
TSy-1p – 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=(r2 -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
Object of the Measurement
Radiation Mechanism
Transmission Medium
Mesurement System
Measured ValuesMeasurement
Inversion
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Equation of transfer
• Applicable to a wide variety of information carries:– Photons– Massive particles in
tenuous media
Intensity at s Intensity at 0
Transmission from 0 to s
Source at s’
Transmission from s’ to s
s
sdEssTEsJEsTEIEsI0
);,();();0,();0();(
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Instrument equation
• Covers most instrument effects• Non-linearity neglected for now• Assumes instrument measures local
intensity of information carriers
Counts in channel i
Smearing function
Background counts in channel i
t E
biiiii CEtIEtEtAddEdtC
),,(),,;,,(
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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
t E
biiiii CEtIEtEtAddEdtC
),,(),,;,,(
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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 • 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, , boundary strength, , and either asymmetry or correlation length, – 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• We’ve 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