Advances in Ring Current Index Forecasting Paul O’Brien and R. L. McPherron UCLA/IGPP tpoiii@igpp.ucla.edu 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 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

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

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

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. ?

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 -200 -150 -100 -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)

Small & Big Storms Dst Comparison for storm 1980-285 50 100 150 -120 -100 -80 -60 -40 -20 20 Dst Comparison for storm 1980-285 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 1982-061 Dst (nT) 5 10 15 VBs mV/m Epoch Hours Dst Model (1hr step) Model (multi-step) VBs Ec = 0.49 mV/m

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 1980-285 Error VBs > Ec VBs > 5 -50 -40 -30 -20 -10 10 20 30 40 50 -250 -200 -150 -100 Dst Transitions for 1982-061 Error VBs > Ec VBs > 5 Dst (nT) Error: Model-Dst (nT) More errors are associated with large VBs than with large Dst

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 266 267 268 269 270 271 272 273 274 275 276 -300 -250 -200 -150 -100 -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 -100 -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.

Details of Model Errors in Simulated Real-Time Mode ACE availability was 91% (by hour) in 232 days -50 -40 -30 -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

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 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 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 = 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.

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. 1981 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

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 -80 -70 -60 -50 -40 -30 -20 -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)

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 -100 -150 -25 -20 -15 -10 -5 5 10 15 DDst

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)

Calculation of Pressure Correction -0.6 -0.4 -0.2 0.2 0.4 0.6 0.8 -12 -10 -8 -6 -4 -2 2 4 6 (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