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From Research to Real-Time: Modeling and Forecasting the
Ring Current
Paul O’Brien
UCLA/IGPP
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Outline• Background
– The Ring Current
– Measuring Dst
– Pressure Correction
– The Dessler-Parker-Skopke Relation
– The Burton Equation
– Coupling Functions
– Distribution of Dst & VBs
– A variable decay parameter? (figure)
– Contaminants and the decay parameter
– Charge Exchange (O+ and H+)
– 2/86 storm w/ major O+ contribution
• Our Data Analysis– Introduction to phase space
– PDFs in phase space
– Evolution of phase-space trajectory
– Neural Network verification
– How to calculate & Q
– Q vs VBs
– vs VBs
– Calculation of pressure correction
• Derivation of a VBs relationship– Schematic vs L
– Derivation of VBs function
– Fit of vs VBs to data
• Verification– Small & large storm simulations
– Errors for small & large storms
– How to calculate the wrong – 6 comparisons from simulated real-time
• Application– Real-time Dst web page
– ACE/Kyoto system description
– Look forward
• Summary
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Meet the Ring Current• During a magnetic storm,
Southward IMF reconnects at the dayside magnetopause
• Magnetospheric convection is enhanced & hot particles are injected from the ionosphere
• Trapped radiation between L ~2-10 sets up the ring current, which can take several days to decay away
• We measure the magnetic field from this current as Dst
Day of Year
91 92 93 94 95 96 97 98 99-300
-200
-100
0
100
Dst
(n
T)
March 97 Magnetic Storm
91 92 93 94 95 96 97 98 990
5
10
VB
s (m
V/m
)
91 92 93 94 95 96 97 98 990
20
40
60
Ps
w
(nP
a)
Pressu
re Effect
Inje
ctio
nRecovery
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Measuring DstProjection of a uniform axial field onto Earth’s surface
Magnetic effects of a symmetric equatorial ring current
SymmetricRing
Current
Dipole Axis
MagneticFieldLines
AxialMagneticField
i
ii
HB
cos
i
i
i
H
B
ii
i
North
Dst BH
ii
i
ii
cos
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Pressure Correction
• Dst is contaminated by the magnetopause currents– Dynamic pressure brings these currents closer
to the Earth– The correction is usually presented as:
Dst Dst b P csw*
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Dessler-Parker-Sckopke Relation
• Dst is proportional to the total kinetic energy of the particles in the ring current
– B0 is the surface field of the Earth
– E(t) is the energy of the field in space
– Em is the quiet time energy of the field in space
Dst t
B
E t
Em
*( ) ( )
0
2
3
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The Burton Equation• If we assume the energy in the ring current is governed
by injection and decay, the dynamic equation is:
• Which becomes the Burton equation:
• Q is the injection term, is the decay time
dE t
dtU t
E t( )( )
( )
dDst
dtQ t
Dst t* *
( )( )
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Coupling Functions– Q(t) is usually assumed to be linearly related to a
Solar wind-magnetosphere coupling function– Q is provided in terms of IMF/Plasma parameters in
GSM coordinates
– VBs is the most common coupling function• The Dawn-Dusk component of the interplanetary electric
field. Bs is |Bz| for Southward Bz and 0 for Northward Bz
– Other coupling functions include • v2BTsin4(/2)
• P1/3VBs
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Distribution of Dst & VBs
• Dst is dominated by values near -20 nT
• VBs is dominated by values near 0 mV/m
• Storms make up very little of this data
-200 -150 -100 -50 0 500
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0.5
Dst (nT)
Fre
quen
cy
0 1 2 3 4 5 6 7 8 9 100
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
VBs (mV/m)
Fre
quen
cy
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A Variable Decay Parameter?
-300
-200
-100
0
-400
100
Feb 6 Feb 7 Feb 8 Feb 9 Feb 10 Feb 11
February 1986 Great StormD
st (
nT)
Total Kinetic Energy
Fast
Slow
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Contaminants and the Decay Parameter
• The decay parameter seems to vary during some storms
• Since 1975, when Burton published his equation, there have been many theories proposed to explain this variation
• One theory has the tail current moving closer to the Earth and then recovering during intense storms– The tail current may contribute up to 50 nT of Dst
– This could cause a very rapid intensification and recovery of Dst
• Often, when a new contaminant is suggested a modification of the decay parameter is required
• So far, none of these contaminant theories have been generally adopted
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Oxygen (O+) Injection
• The ring current is primarily made up of ~100keV protons (H+)
• O+ has a much shorter charge exchange lifetime than H+
• Very strong storms have very rapid recovery just after minimum Dst
• This coincides with large O+ injection
• This suggests that decay rate is a function of Dst
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Oxygen (O+) Injection Example• Near minimum Dst,
the inner part of the radiation belt is dominated by O+ ions
• The O+ ions decay away very quickly
• This suggests that the initial rapid decay of Dst is related to O+
-300
-200
-100
0
-400Feb 6 Feb 7 Feb 8 Feb 9 Feb 10 Feb 11
Dst
(nT
)
0.2
0.0
February 1986 Great Storm
Ene
rgy
Par
titio
n
0.4
0.6
0.8
1.0
H+
O+
Inner Zone
Fast
Slow
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Phase Space & the Burton Equation
Dst(t)
Dst(t+t)
Recovery
Main Phase
d Dst
dta VBs
Dst( )*
Dst t t Dst t a VBsDst
t( ) ( ) *
Dst(t)
Dst(t+t)-Dst(t)
Main Phase
Recovery
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Dst Distribution (Main Phase)
VBs moves & tilts trajectory
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Motion of Median Trajectory
As VBs is increased, distributions slide left and tilt, but linear behavior is maintained.
VBs = 0 VBs = 1 mV/m VBs = 2 mV/m
VBs = 3 mV/m VBs = 4 mV/m VBs = 5 mV/m
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Neural Network Verification• A neural
network provides good agreement in phase space
• The curvature outside the HTD area may not be real
-25 -20 -15 -10 -5 0 5 10 15-150
-100
-50
0Neural Network Phase Space
Dst
Dst
VBs = 0VBs = 1VBs = 2VBs = 3VBs = 4VBs = 5
NN Dst Stat Dst
Hig
h T
rainin
g D
ensity
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Calculating Q and
• We fit the median phase-space trajectory to a line:
• We calculate a new Q and for each VBs bin– By measuring Q & for various VBs bin sizes
around each bin center, we can project what each would be for infinitely small bins
Dst Q VBs tt
VBsDst ( )
( )
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Q is nearly linear in VBs
• The Q-VBs relationship is linear, with a cutoff below Ec
• This is essentially the result from Burton et al. (1975)
0 2 4 6 8 10 12-80
-70
-60
-50
-40
-30
-20
-10
0
10
VBs (mV/m)
Inje
ctio
n (
Q)
(nT
/h)
Injection (Q) vs VBs
Ec = 0.49
Offsets in Phase Space
Points Used in FitQ = (-4.4)(VBs-0.49)
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is nonlinear in VBs
• We want to fit this curve with an analytical function, but which one?– A polynomial will
work, but it will not be good for extrapolation
– If we have a physically justifiable function, it can be used for extrapolation
0 2 4 6 8 10 122
4
6
8
10
12
14
16
18
20
(h
ours
)
VBs (mV/m)
Decay Time () vs VBs
?
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Calculation of Pressure Correction
• So far, we have assumed that the pressure correction was not important.This is true because:
Dst Dst b P
Dst Dst
swVBs Dst
*
,
*
• But now we would like to determine the coefficients b and c.
• We can determine b by binning in [P1/2] and removing Q(VBs)
(PS Offset) - Q
Best Fit ~ (7.26) [P1/2]
-0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8-12
-10
-8
-6
-4
-2
0
2
4
6
(Phase-Space Offset) - Q vs P1/2]
(PS
Off
set)
-Q
(n
T/h
)
[P1/2] (nPa1/2/h)
• We can determine c such that Dst* decays to zero when VBs = 0
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-10 -5 0 5 10
-10
-8
-6
-4
-2
0
2
4
6
8
10
-X
-Y
Trajectories for qE0Re/muB0 = 8.00e-004
-10 -5 0 5 10
-10
-8
-6
-4
-2
0
2
4
6
8
10
-X
-Y
Trajectories for qE0Re/muB0 = 2.40e-003
The Trapping-Loss Connection Decreases
Larger VBs
• The convection electric field shrinks the convection pattern
• The Ring Current is confined to the region of higher nH, which results in shorter
• The convection electric field is related to VBs
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• The charge-exchange lifetimes are a function of L because the exosphere density drops off with altitude
• is an effective charge-exchange lifetime for the whole ring current. should therefore reflect the charge-exchange lifetime at the trapping boundary
Speculation on (VBs)• A cross-tail electric field E0
moves the stagnation point for hot plasma closer to the Earth. This is the trapping boundary (p is the shielding parameter)
• Reiff et al. 1981 showed that VBs controlled the polar-cap potential drop which is proportional to the cross-tail electric field
cos ( )
/
/
6
0
0
1m
H H
s
vn n
Hr r
L L
n e
e
e a VBs p( ' ) /1E a a VBsPC0 0 1
LW
qpR EsE
p
3
0
1/
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Fit of vs VBs• The derived
functional form can fit the data with physically reasonable parameters
• The fit is best at p=1, no shielding
• Our 4.69 is slightly larger than 1.1 from Reiff et al.0 2 4 6 8 10 12
2
4
6
8
10
12
14
16
18
20
VBs (mV/m)
(h
ours
)
Decay Time ()
from Phase-Space Slope Points Used in Fit = 2.40e9.74/(4.69+VBs)
?
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Small & Big Storms
0 50 100 150-120
-100
-80
-60
-40
-20
0
20
Dst Comparison for storm 1980-285
Dst
(n
T)
0 50 100 1500
1
2
3
4
5
6
Ec = 0.49 mV/m
VB
s m
V/m
Epoch Hours
Dst Model (1hr step) Model (multi-step)VBs
0 20 40 60 80 100 120 140 160 180-250
-200
-150
-100
-50
0
50
Dst Comparison for storm 1982-061
Dst
(n
T)
0 20 40 60 80 100 120 140 160 1800
5
10
15
VB
s m
V/m
Epoch Hours
Dst Model (1hr step) Model (multi-step)VBs
Ec = 0.49 mV/m
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Small & Big Storm Errors
• More errors are associated with large VBs than with large Dst
-50 -40 -30 -20 -10 0 10 20 30 40 50-120
-100
-80
-60
-40
-20
0
20
Dst
(nT
)
Error: Model-Dst (nT)
Dst Transitions for 1980-285
Error VBs > Ec
VBs > 5
-50 -40 -30 -20 -10 0 10 20 30 40 50-250
-200
-150
-100
-50
0
50
Dst Transitions for 1982-061
Error VBs > Ec
VBs > 5
Dst
(nT
)
Error: Model-Dst (nT)
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How to Calculate the Wrong Decay Rate
• Using a least-squares fit of Dst to Dst-Q we can estimate
• If we do this without first binning in VBs, we observe that depends on Dst
• However, if we first bin in VBs, we observe that depends much more strongly on VBs
• A weak correlation between VBs and Dst causes the apparent -Dst dependence-200 -150 -100 -50 0
4
6
8
10
12
14
16
18
20
Dst Range (nT)
for various ranges of Dst (without specification of VBs)
-200 -150 -100 -50 04
6
8
10
12
14
16
18
20
Dst Range (nT)
(h
ours
)
All VBs
VBs = 0VBs = 2
VBs = 4
for various ranges of Dst (with specification of VBs)
(h
ours
)
VBs = 0
VBs = 2
VBs = 4
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Comparisons to Other Models
308 310 312 314 316 318 320 322 324 326-200
-150
-100
-50
0
50
UT Decimal Day (1998)
nT
266 267 268 269 270 271 272 273 274 275 276-300
-250
-200
-150
-100
-50
0
50
UT Decimal Day (1998)
nT Kyoto Dst
AK2 AK1 UCB ACE Gap
AK2 is the new model, Kyoto is the target, AK1 is a strictly Burton model, and UCB has slightly modified Q and . AK2 has a skill score of 30% relative to AK1 and 40% relative to UCB for 6 months of simulated real-time data availability. These numbers are even better if only active times are used.
ACE Gap
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Details of Model Errors Model RMSE Prediction
EfficiencyRMSEDst < -50 nT
UCB 21 nT 31% 40 nTAK1 19 nT 41% 38 nTAK2 16 nT 59% 24 nT
-50 -40 -30 -20 -10 0 10 20 30 40 500
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
Error (nT)
Fra
ctio
n of
All
Poi
nts
Error Distributions For 3 Real-Time Models
UCBAK1AK2Bin Size:
5 nT
ACE availability was 91% (by hour) in 232 days
Predicting large Dst is difficult, but larger errors may be tolerated in certain applications
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Real-Time Dst On-Line With real-time
Solar wind data from ACE and near real-time magnetic measurements from Kyoto, we can provide a real-time forecast of Dst
We publish our Dst forecast on the Web every 30 minutes
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ACE/Kyoto System
• The Kyoto World Data Center provides provisional Dst estimate about 12-24 hours behind real-time
• The Space Environment Center provides real-time measurements of the solar wind from the ACE spacecraft
• We use our model to integrate from the last Kyoto data to the arrival of the last ACE measurement
• This usually amounts to a forecast of 45+ minutes
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Looking Forward
• The USGS now provides measurements of H from SJG, HON, and GUA only 15 minutes behind real-time
• If we can convert H into H in real-time, we can use a 3-station provisional Dst to start our model, and only have to integrate about an hour– We have built Neural Networks which can provide Dst
from 1, 2 or 3 H values and UT local time
• Shortening our integration period could greatly reduce the error in our forecast
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Summary• We have modified the standard model of the ring
current– We parameterized the Burton equation for Dst in terms
of VBs
– We have verified the qualitative features of our results with a neural network
• Injection and decay depend on VBs– Dst dependence is very weak or absent
• We have suggested a mechanism for the decay dependence on VBs
– Convection is brought closer to the exosphere by the cross-tail electric field
– It has not been necessary to invoke composition changes (O+)
• The new model outperforms two earlier models with comparable complexity