Transcript From Research to Real-Time: Modeling and Forecasting the

Advances in Ring Current Index Forecasting
Paul O’Brien and R. L. McPherron
UCLA/IGPP
[email protected]
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
March 97 Magnetic Storm
Recovery
0
-200
-300
91
92
93
92
92
94
95
93
94
93
94
10
VBs (mV/m)
Injection
-100
96
97
98
99
95
96
97
98
99
95
96
97
98
99
5
0
91
Pressure Effect
Dst (nT)
100
60
Psw
(nPa)
40
20
0
91
Day of Year
• 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
DDst Distribution (Main Phase)
The Trapping-Loss Connection
Trajectories for qE0Re/muB0 = 8.00e-004
10
10
8
8
6
6
4
4
2
2
-Y
-Y
Trajectories for qE0Re/muB0 = 2.40e-003
0
0
-2
-2
-4
-4
-6
-6
-8
-8
-10
-10
-10
-5
0
-X
5
• 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
10
-10
-5
0
-X
5
10
Fit of t vs VBs
Decay Time (t)
20
t from Phase-Space Slope
Points Used in Fit
t = 2.40e9.74/(4.69+VBs)
18
16
t (hours)
14
12
10
8
?
6
4
2
0
2
4
6
VBs (mV/m)
8
10
12
• 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.
How to Calculate the
Wrong Decay Rate
20
20
All VBs
VBs = 0
VBs = 2
VBs = 4
18
16
VBs = 0
18
16
14
t (hours)
t (hours)
t for various ranges of Dst
(with specification of VBs)
t for various ranges of Dst
(without specification of VBs)
12
14
VBs = 2
12
10
10
VBs = 4
8
8
6
6
4
-200
-150
-100
-50
Dst Range (nT)
0
4
-200
-150
-100
-50
Dst Range (nT)
0
• Using a leastsquares 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
Small & Big Storms
Dst Comparison for storm 1980-285
50
Dst
Model (1hr step)
Model (multi-step)
VBs
0
50
100
150
Dst (nT)
0
Dst (nT)
20
0
-20
-40
-60
-80
-100
-120
Dst Comparison for storm 1982-061
-50
-100
-150
-200
-250
0
VBs mV/m
VBs mV/m
5
4
3
2
0
0
20
40
60
80
100
120
140
160
180
15
6
1
Dst
Model (1hr step)
Model (multi-step)
VBs
10
5
Ec = 0.49 mV/m
50
100
Epoch Hours
Ec = 0.49 mV/m
150
0
0
20
40
60
80
100
Epoch Hours
120
140
160
180
Small & Big Storm Errors
Dst Transitions for 1982-061
Dst Transitions for 1980-285
20
50
0
0
-40
-60
Dst (nT)
Dst (nT)
-20
Error
VBs > Ec
VBs > 5
-50
-100
Error
VBs > Ec
VBs > 5
-150
-80
-200
-100
-120
-50 -40 -30 -20 -10
0
10
20
30
Error: Model-Dst (nT)
40
50
-250
-50 -40 -30 -20 -10
0
10
20
30
40
Error: Model-Dst (nT)
• More errors are associated with large VBs than with
large Dst
50
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
50
50
ACE Gap
0
0
-50
-100
-150
-200
Kyoto Dst
AK2
AK1
UCB
ACE Gap
nT
nT
-50
-100
-150
-250
-300
266 267 268 269 270 271 272 273 274 275 276
UT Decimal Day (1998)
-200
308
310
312
314
316
318 320
322
324
UT Decimal Day (1998)
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.
326
Details of Model Errors in Simulated Real-Time Mode
Model
RMSE
Prediction
Efficiency
RMSE
Dst < -50 nT
UCB
AK1
AK2
21 nT
19 nT
16 nT
31%
41%
59%
40 nT
38 nT
24 nT
ACE availability
was 91% (by hour)
in 232 days
Error Distributions For 3 Real-Time Models
0.16
Predicting large Dst
is difficult, but
larger errors may be
tolerated in certain
applications
Fraction of All Points
0.14
0.12
UCB
AK1
AK2
Bin Size:
5 nT
0.1
0.08
0.06
0.04
0.02
0
-50
-40
-30
-20
-10
0
10
Error (nT)
20
30
40
50
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/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 realtime 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 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
Motion of Median Trajectory
VBs = 0
VBs = 3 mV/m
VBs = 1 mV/m
VBs = 4 mV/m
VBs = 2 mV/m
VBs = 5 mV/m
As VBs is increased, distributions slide left and tilt, but linear
behavior is maintained.
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)
 3W 
Ls  

qpR
E
E 0

1/ p
• Reiff et al. 1981 showed that VBs
controlled the polar-cap potential
drop which is proportional to the
cross-tail electric field
E0   PC  a0  a1VBs
The charge-exchange lifetimes are a
function of L because the exosphere
density drops off with altitude
t 
cos6 ( m )
vn H

1
nH
nH  e  r / r0
t  eL
s
/ L0
t is an effective charge-exchange
lifetime for the whole ring current. t
should therefore reflect the chargeexchange lifetime at the trapping
boundary
 ( a ' VBs ) 1/ p
t e
Q is nearly linear in VBs
Injection (Q) vs VBs
10
0
Injection (Q) (nT/h)
-10
-20
-30
-40
-50
Offsets in Phase Space
Points Used in Fit
Q = (-4.4)(VBs-0.49)
-60
Ec = 0.49
-70
-80
0
2
4
6
VBs (mV/m)
8
10
12
• The Q-VBs
relationship is
linear, with a
cutoff below Ec
• This is
essentially the
result from
Burton et al.
(1975)
Neural Network Verification
DDst = NN(Dst,VBs,…)
Neural Network Phase Space
0
Dst
-50
NN Dst
Stat Dst
VBs = 0
VBs = 1
VBs = 2
VBs = 3
VBs = 4
VBs = 5
-100
-150
-25
-20
-15
-10
-5
DDst
0
5
10
15
• A neural
network
provides good
agreement in
phase space
• The curvature
outside the HTD
area may not be
real
Phase Space Trajectories
Simple Decay
Oscillatory Decay
 st   A * Dst
D
st   A * Dst  B * D st
D
Dst(t)
Dst(t)
Variable Decay
Dst(t+dt)-Dst(t)
Dst(t)
Dst(t+dt)-Dst(t)
2

Dst   A * Dst  B *( Dst )
Dst(t+dt)-Dst(t)
Calculation of Pressure
Correction
(Phase-Space Offset) - Q vs D[P1/2]
6
(PS Offset) -Q (nT/h)
4
2
0
• So far, we have assumed that
the pressure correction was
not important.This is true
because:
DDst  DDst *  b D Psw
-2
-4
-6
(PS Offset) - Q
-8
Best Fit ~ (7.26) D[P1/2]
-10
-12
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
D[P1/2] (nPa1/2/h)
We can determine c such that Dst* decays to
zero when VBs = 0
VBs , Dst
 DDst  DDst *
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)