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