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From Research to Real-Time: Modeling and Forecasting the Ring Current Paul OBrien UCLA/IGPP tpoiii@igpp.ucla.edu

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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

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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 919293949596979899 -300 -200 -100 0 100 Dst (nT) March 97 Magnetic Storm 919293949596979899 0 5 10 VBs (mV/m) 919293949596979899 0 20 40 60 P sw (nPa) Pressure Effect Injection Recovery

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Measuring Dst Projection of a uniform axial field onto Earths surface Magnetic effects of a symmetric equatorial ring current

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Pressure Correction Dst is contaminated by the magnetopause currents –Dynamic pressure brings these currents closer to the Earth –The correction is usually presented as:

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Dessler-Parker-Sckopke Relation Dst is proportional to the total kinetic energy of the particles in the ring current –B 0 is the surface field of the Earth –E(t) is the energy of the field in space –E m is the quiet time energy of the field in space

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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

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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 –VB s is the most common coupling function The Dawn-Dusk component of the interplanetary electric field. B s is |B z | for Southward B z and 0 for Northward B z –Other coupling functions include v 2 B T sin 4 ( /2) P 1/3 VBs

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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 -200-150-100-50050 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 Dst (nT) Frequency 012345678910 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 VBs (mV/m) Frequency

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A Variable Decay Parameter? -300 -200 -100 0 -400 100 Feb 6Feb 7Feb 8Feb 9Feb 10Feb 11 February 1986 Great Storm Dst (nT) Total Kinetic Energy Fast Slow

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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

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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

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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 -400 Feb 6Feb 7Feb 8Feb 9Feb 10Feb 11 Dst (nT) 0.2 0.0 February 1986 Great Storm Energy Partition 0.4 0.6 0.8 1.0 H+O+H+O+ Inner Zone Fast Slow

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Phase Space & the Burton Equation Dst(t) Dst(t+ t) Recovery Main Phase Dst(t) Dst(t+ t)-Dst(t) Main Phase Recovery

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Dst Distribution (Main Phase) VBs moves & tilts trajectory

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Motion of Median Trajectory As VBs is increased, distributions slide left and tilt, but linear behavior is maintained. VBs = 0VBs = 1 mV/mVBs = 2 mV/m VBs = 3 mV/mVBs = 4 mV/mVBs = 5 mV/m

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Neural Network Verification A neural network provides good agreement in phase space The curvature outside the HTD area may not be real

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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

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Q is nearly linear in VBs The Q-VBs relationship is linear, with a cutoff below E c This is essentially the result from Burton et al. (1975)

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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 024681012 2 4 6 8 10 12 14 16 18 20 (hours) VBs (mV/m) Decay Time ( ) vs VBs ?

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Calculation of Pressure Correction So far, we have assumed that the pressure correction was not important.This is true because: But now we would like to determine the coefficients b and c. We can determine b by binning in [P 1/2 ] and removing Q(VBs) (PS Offset) - Q Best Fit ~ (7.26) [P 1/2 ] We can determine c such that Dst * decays to zero when VBs = 0

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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 n H, which results in shorter The convection electric field is related to VBs

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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 E 0 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

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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. 024681012 2 4 6 8 10 12 14 16 18 20 VBs (mV/m) (hours) Decay Time ( ) from Phase-Space Slope Points Used in Fit = 2.40e 9.74/(4.69+VBs) ?

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Small & Big Storms

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Small & Big Storm Errors More errors are associated with large VBs than with large Dst

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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 -200-150-100-500 4 6 8 10 12 14 16 18 20 Dst Range (nT) for various ranges of Dst (without specification of VBs) -200-150-100-500 4 6 8 10 12 14 16 18 20 Dst Range (nT) (hours) All VBs VBs = 0 VBs = 2 VBs = 4 for various ranges of Dst (with specification of VBs) (hours) VBs = 0 VBs = 2 VBs = 4

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Comparisons to Other Models 266267268269270271272273274275276 -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

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Details of Model Errors -50-40-30-20-1001020304050 0 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 ACE availability was 91% (by hour) in 232 days Predicting large Dst is difficult, but larger errors may be tolerated in certain applications

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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

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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

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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

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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

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