From Research to Real-Time: Modeling and Forecasting the

Ring Current

Paul O’Brien

UCLA/IGPP

tpoiii@igpp.ucla.edu

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

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

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

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*

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

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* *

( )( )

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

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

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

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

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

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

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

Dst Distribution (Main Phase)

VBs moves & tilts trajectory

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

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

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 ( )

( )

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)

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

?

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

-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

• 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/

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)

?

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)

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

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

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

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

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

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

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