Post on 30-Jan-2016
description
Paul O’Brien and R. L. McPherron
UCLA/IGPP
tpoiii@igpp.ucla.edu
Advances in Ring Current Index Forecasting
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
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
Dst Distribution (Main Phase)
No D
ata
No D
ata
Median T
rajectory
D
st Q
- Dst/
-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
-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
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
Fit of vs 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.
0 2 4 6 8 10 122
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)
?
How to Calculate the Wrong Decay Rate
• Using a least-squares fit of Dst to Dst we can estimate
• If we do this without first binning in VBs, we observe that depends on Dst
• 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 04
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
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
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)
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
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 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.
ACE Gap
Details of Model Errors in Simulated Real-Time Mode
Model RMSE PredictionEfficiency
RMSEDst < -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
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
Summary• Dst follows a first order equation:
– dDst/dt = Q(VBs) - Dst/(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
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
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
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/
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)
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
Dst = NN(Dst,VBs,…)
Phase Space TrajectoriesSimple Decay Oscillatory Decay
*D A Dstst * * D A D B Dst st st
Dst(t)
Dst(t+t)-Dst(t)
Dst(t)
Dst(t+t)-Dst(t)Variable Decay
* *( )D A D B Dst st st 2
Dst(t)
Dst(t+t)-Dst(t)
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