1. Advances in Ring Current Index Forecasting
Paul O’Brien and R. L. McPherron
UCLA/IGPP
Outline
Introduction and Review
Data Analysis
Linear Phase-Space Trajectory
Decay Depends on VBs
Physical Interpretation
Position of Convection Boundary
Real-Time Model
Implementation
Evaluation
Conclusions

2. 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
March 97 Magnetic Storm
100
Recovery
Dst (nT)
-100
-200
Injection
-300 91 92 93 94 95 96 97 98 99 10
Pressure Effect
VBs (mV/m) 5 91 92 93 94 95 96 97 98 99 60 40
Psw (nPa) 20 91 92 93 94 95 96 97 98 99
Day of Year

3. DDst Distribution (Main Phase)
No Data
DDst  Q - Dst/t
Median Trajectory
No Data

4. The Trapping-Loss Connection
The convection electric field shrinks the convection pattern
The Ring Current is confined to the region of higher nH, which results in shorter t
The convection electric field is related to VBs
t Decreases
Larger VBs

5. Fit of t vs VBs 2 4 6 8 10 12 14 16 18 20
VBs (mV/m)
t (hours)
Decay Time (t)
t from Phase-Space Slope
Points Used in Fit
t = 2.40e9.74/(4.69+VBs)
The derived functional form can fit the data with physically reasonable parameters
Our 4.69 is slightly larger than 1.1 from Reiff et al. ?

6. How to Calculate the Wrong Decay Rate
Using a least-squares fit of DDst to Dst we can estimate t
If we do this without first binning in VBs, we observe that t depends on Dst
If we first bin in VBs, we observe that t depends much more strongly on VBs
A weak correlation between VBs and Dst causes the apparent t-Dst dependence
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-50 4 6 8 10 12 14 16 18 20
Dst Range (nT)
t for various ranges of Dst
(without specification of VBs)
t (hours)
All VBs
VBs = 0
VBs = 2
VBs = 4
(with specification of VBs)

7. Small & Big Storms Dst Comparison for storm 1980-28550
100
150
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-80
-60
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-20 20
Dst Comparison for storm
Dst (nT) 1 2 3 4 5 6
Ec = 0.49 mV/m
VBs mV/m
Epoch Hours
Dst
Model (1hr step)
Model (multi-step)
VBs 20 40 60 80
100
120
140
160
180
-250
-200
-150
-100
-50 50
Dst Comparison for storm
Dst (nT) 5 10 15
VBs mV/m
Epoch Hours
Dst
Model (1hr step)
Model (multi-step)
VBs
Ec = 0.49 mV/m

8. Small & Big Storm Errors
-50
-40
-30
-20
-10 10 20 30 40 50
-120
-100
-80
-60
Dst (nT)
Error: Model-Dst (nT)
Dst Transitions for
Error
VBs > Ec
VBs > 5
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-40
-30
-20
-10 10 20 30 40 50
-250
-200
-150
-100
Dst Transitions for
Error
VBs > Ec
VBs > 5
Dst (nT)
Error: Model-Dst (nT)
More errors are associated with large VBs than with large Dst

9. ACE/Kyoto System
The Kyoto World Data Center provides provisional Dst estimate about 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

10. Comparisons to Other Models
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-300
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-50 50
UT Decimal Day (1998) nT
Kyoto Dst
AK2
AK1
UCB
ACE Gap
308
310
312
314
316
318
320
322
324
326
-200
-150
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-50 50
UT Decimal Day (1998) nT
ACE Gap
AK2 is the new model, Kyoto is the target, AK1 is a strictly Burton model, and UCB has slightly modified injection and decay. 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.

11. Details of Model Errors in Simulated Real-Time Mode
ACE availability was 91% (by hour) in 232 days
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-40
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-20
-10 10 20 30 40 50
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
Error (nT)
Fraction of All Points
Error Distributions For 3 Real-Time Models
UCB
AK1
AK2
Bin Size:
5 nT
Predicting large Dst is difficult, but larger errors may be tolerated in certain applications

12. 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

13. Summary Dst follows a first order equation:
dDst/dt = Q(VBs) - Dst/t(VBs)
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
The model performs well in real-time relative to two other models
Poorest performance for large VBs

14. 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 DH 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 DH values and UT local time
Shortening our integration period could greatly reduce the error in our forecast

15. Motion of Median Trajectory
VBs = 0
VBs = 1 mV/m
VBs = 2 mV/m
VBs = 3 mV/m
VBs = 4 mV/m
VBs = 5 mV/m
As VBs is increased, distributions slide left and tilt, but linear behavior is maintained.

16. Speculation on t(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 showed that VBs controlled the polar-cap potential drop which is proportional to the cross-tail electric field
The charge-exchange lifetimes are a function of L because the exosphere density drops off with altitude
t is an effective charge-exchange lifetime for the whole ring current. t should therefore reflect the charge-exchange lifetime at the trapping boundary

17. 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) 2 4 6 8 10 12
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-10
VBs (mV/m)
Injection (Q) (nT/h)
Injection (Q) vs VBs
Ec = 0.49
Offsets in Phase Space
Points Used in Fit
Q = (-4.4)(VBs-0.49)

18. Neural Network Verification
DDst = NN(Dst,VBs,…)
A neural network provides good agreement in phase space
The curvature outside the HTD area may not be real
Neural Network Phase Space
High Training Density
-50
Dst
VBs = 0
VBs = 1
VBs = 2
VBs = 3
VBs = 4
VBs = 5
NN Dst
Stat Dst
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-15
-10 -5 5 10 15
DDst

19. Phase Space Trajectories
Simple Decay
Oscillatory Decay
Dst(t)
Dst(t)
Dst(t+dt)-Dst(t)
Variable Decay
Dst(t+dt)-Dst(t)
Dst(t)
Dst(t+dt)-Dst(t)

20. Calculation of Pressure Correction
-0.6
-0.4
-0.2
0.2
0.4
0.6
0.8
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(Phase-Space Offset) - Q vs D[P1/2]
(PS Offset) -Q (nT/h)
D[P1/2] (nPa1/2/h)
So far, we have assumed that the pressure correction was not important.This is true because:
(PS Offset) - Q
Best Fit ~ (7.26) D[P1/2]
But now we would like to determine the coefficients b and c.
We can determine b by binning in D[P1/2] and removing Q(VBs)
We can determine c such that Dst* decays to zero when VBs = 0