Modes of Magnetospheric Response & Methods of Identification

Bob WeigelGeorge Mason University

Motivation

“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.”

From FG13 (Modes of Solar Wind Magnetosphere Energy Transfer) Description:

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

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

A few named magnetospheric modes

Storms Substorms Steady Magnetospheric Convection Sawtooth Injection Events Poleward Boundary Intensifications Pseudo-break-ups HILDCAA …

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

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

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)

ApproachesSome common data-based solar wind/magnetosphere modeling methods

a) G(t) = p0 + p1S(t)

b) G(t) = p0 + p1S(p,t)

c) dG/dt + f1(p1, G) = f2(p2,S(t))

d) G(t) = p0 + p1S(t-1)+…+pTS(t-T)

e) G(t) = p’0 +p’1S(t-1)+…+p’TS(t-T)

G(t) is an averaged measurement centered on time t and S(t) is an average solar wind measurement centered on time 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

Solution to c)

1. Integrate over all time, compute error (prediction efficiency of predicted vs actual).

2. Modify parameter(s) and goto 1.

Solution to d) and e)

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)

…

One approach is to solve d) using a “sort” variable, e.g., amplitude of G or Nsw in a given time range.

OLS – “Ordinary Least Squares”

Usually N >> T

Bargatze et al., 1985 early example of this.

d)

e)

G(t) = p0 +p1S(t-1) +p2S(t-2)+…+pTS(t-T)

G(t) = p’0 +p’1S(t-1) +p’2S(t-2)+…+p’TS(t-T)

Meaning of Impulse ResponseG(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

Outline

Mode definition and some named magnetosphere modes

Model and Mode ID using a “System ID” approach

Three examples of Mode ID using SID1. ID of MeV response modes2. Un-ID of a mode3. ID of Nsw mode

Other Mode ID approaches

Examples

1. 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 modes2. Un-ID of a mode3. ID of Nsw mode

SAMPEX MeV electron flux

L-valu

e

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]

Examples

1. ID of MeV response modes2. 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

3. ID of Nsw mode

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

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 BsIs remaining 66%

explained by • Change in reconnection

efficiency?• Conductance effects?

Weigel [2007]

~66% of variation explained when time history of Bs is included. ~75% when solar wind velocity is included

In auroral zone, result is 50% of semiannual variation is explained by solar wind (up from 0%)

Model shows new mode less significant

am(t) = p0 +p1Bs(t-1)+…+p24Bs(t-24)

am subset where Bs availableAll available am

Examples

1. ID of MeV response modes2. Un-ID of a mode3. ID of Nsw mode

Model c) gives different result than e)

Mode: Nsw and geoefficiency

Does solar wind pressure or density modify geoefficiency?

Mode: Nsw and geoefficiency

Does solar wind pressure or density modify geoefficiency?

Importance of model constraints

Many studies have looked at modifying input, S(t), in Burton equation

Most recent finding is that modifying S(t) by Pdyn

1/2 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)

Can repeat with Vsw to argue Nsw modifies response efficiency, not Pdyn.

Weigel [2010]

Burton model is constrained to this response function

Norm

aliz

ed

Dst r

esp

onse

Importance of model constraints

Time since impulse [hours]

A look ahead

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

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?