Modes of Magnetospheric Response & Methods of Identification

1. Modes of Magnetospheric Response & Methods of Identification Bob Weigel George Mason University

2. Motivation From FG13 (Modes of Solar Wind Magnetosphere Energy Transfer) Description: • “We are still in the process of identifying characteristic behavior that identifies various modes as separate phenomena.” • “We do not completely understand the solar wind conditions or internal state of the magnetosphere that allows a particular mode.”

3. Outline • Response Mode definition and some named magnetosphere response modes • Model and Mode ID using a “System ID” approach • Three examples of Model and Mode ID using SID • Other Mode ID approaches

4. Response Mode: Definition • A type of coupling to the solar wind (depends on different physical energy transfer process ) • Unique observational characteristics in a magnetospheric measurement (e.g., a “type” of response). Presumably explainable by solar wind energy transfer process/and magnetosphere preconditioning. Functional definition: Mode ID is used to develop better model of system

5. A few named magnetospheric modes • Storms • Substorms • Steady Magnetospheric Convection • Sawtooth Injection Events • Poleward Boundary Intensifications • Pseudo-break-ups • HILDCAA • …

6. Outline • Mode definition and some named magnetosphere modes • Model and Mode ID using a “System ID” approach • Three examples of Mode ID using SID • Other Mode ID approaches

7. Basic (data-centric) approach to Model and Mode ID

8. Basic (data-centric) approach to Model and Mode ID • Start with data and some physical guidance and derive model structure. • Does model structure reveal mode? This is referred to as “System Identification” in statistics and engineering literature (e.g, Ljung, 1999) (note implicit definition of mode here)

9. ApproachesSome common data-based solar wind/magnetosphere modeling methods G(t) is an averaged measurement centered on time t and S(t) is an average solar wind measurement centered on time t • G(t) = p0 + p1S(t) • G(t) = p0 + p1S(p,t) • dG/dt + f1(p1, G) = f2(p2,S(t)) • G(t) = p0 + p1S(t-1)+…+pTS(t-T) • G(t) = p’0 +p’1S(t-1)+…+p’TS(t-T) p represents a vector of free parameters. p’ represents free parameters that depend on another variable. Model structure is represented by p and S

10. Solution to c) • Integrate over all time, compute error (prediction efficiency of predicted vs actual). • Modify parameter(s) and goto 1.

11. Solution to d) and e) d) G(t) = p0 +p1S(t-1) +p2S(t-2)+…+pTS(t-T) OLS – “Ordinary Least Squares” Usually N >> T G(1) = po+ p1S(0)+p2S(-1)+…+pTS(1-T) G(2) = p0 +p1S(1)+p2S(0)+…+pTS(2-T) G(3) = p0 + p1S(2)+p2S(1)+…+pTS(3-T) G(N) = p0+p1S(N-1) +p2S(N-2)+…+pTS(N-T) … e) • G(t) = p’0 +p’1S(t-1) +p’2S(t-2)+…+p’TS(t-T) One approach is to solve d) using a “sort” variable, e.g., amplitude of G or Nsw in a given time range. Bargatze et al., 1985 early example of this.

12. Meaning of Impulse Response G(1) = po+p1S(0) + … G(2) = p0+p1S(1)+p2S(0) … G(3) = p0+p1S(2)+p2S(2)+p3S(0) … G(4) = p0+p1S(3)+p2S(2)+p3S(1) +p4S(0)… • If S(0) = 1 and S(t)=0 otherwise, only p0 and boxed terms are non-zero • Plot of p is usually referred to as an impulse response - shows coefficients and has a dynamical interpretation

13. Outline • Mode definition and some named magnetosphere modes • Model and Mode ID using a “System ID” approach • Three examples of Mode ID using SID • ID of MeV response modes • Un-ID of a mode • ID of Nswmode • Other Mode ID approaches

14. Examples • ID of MeV response modes • Assume a model of form d) (impulse response) • Select S(t) that gives best prediction • Model parameter and input dependence on L-shell reveal modes • Un-ID of a mode • ID of Nsw mode

15. SAMPEX MeV electron flux L-value

16. SAMPEX MeV electron flux Impulse in Vsw at t=0 Although main driver is Vsw - modes P1 and P0 have different dependence on Bz. Compare with Li et al. [2001] diffusion model? Vassiliadis et al., [2003]

17. Examples • ID of MeV response modes • Un-ID of a mode • Failure of model of form a) inspires search for new mode. • Use of form d) indicates new mode may not be needed • ID of Nsw mode

18. Missing semiannual variation • Russell and McPherron [1972]: Semiannual variation in geomagnetic activity explained by semiannual variation of effective solar wind input. • Mayaud [1973] – Problem because diurnal (UT) prediction • Cliver[2000] – Problem because of day-of-year amplitude plot (see next slide); Could be angle between Vsw and dipole • Newell et al. [2002] – Could be “UV insulation” effect • Russell et al. [2003] – Could be day-of-year variation in reconnection line length effect

19. Importance of a Model Blue only predicts about 33% of actual semiannual variation. (0% for AL) (Implied) Model of SW/M-I coupling is: 3-hour average of geomagnetic index = 3-hour average of Bs • Is remaining 66% explained by • Change in reconnection efficiency? • Conductance effects?

20. Model shows new mode less significant All available am am subset where Bs available ~66% of variation explained when time history of Bs is included. ~75% when solar wind velocity is included • am(t) = p0 +p1Bs(t-1)+…+p24Bs(t-24) In auroral zone, result is 50% of semiannual variation is explained by solar wind (up from 0%) Weigel [2007]

21. Examples • ID of MeV response modes • Un-ID of a mode • ID of Nsw mode • Model c) gives different result than e)

22. Mode: Nsw and geoefficiency • Does solar wind pressure or density modify geoefficiency?

23. Mode: Nsw and geoefficiency • Does solar wind pressure or density modify geoefficiency?

24. Importance ofmodel constraints • Many studies have looked at modifying input, S(t), in Burton equation • Most recent finding is that modifying S(t) by Pdyn1/2 gives improvement. New mode? • Others have looked at modifying t • What if you don’t constrain to Burton eqn, but constrain to be linear response? Dst(t) = p0+p1S(t-1)+p2S(t-1)+…+p48S(t-48)

25. Importance ofmodel constraints Can repeat with Vsw to argue Nswmodifies response efficiency, not Pdyn. Burton model is constrained to this response function Normalized Dst response Time since impulse [hours] Weigel [2010]

26. A look ahead

27. A few named magnetospheric modes • Storms • Substorms • Steady Magnetospheric Convection • Sawtooth Injection Events • Poleward Boundary Intensifications • Pseudo-break-ups • HILDCAA • … See McPherron et al., 1997

28. Mode ID thus far on these modes • Define constraints on magnetospheric conditions • Look for time intervals that satisfy • Quantify solar wind behavior during intervals • Ideally analysis will allow us to say: • under these solar wind conditions, this mode will occur with some probability or • this behavior implies modification of existing model necessary • How do we get here?