Empirical geomagne.c field modeling M. Sitnov (JHU/APL) In collabora*on with G. Stephens, A. Ukhorskiy, P. Brandt, B. Anderson, H. Korth, J. Vandegriff, and N. Tsyganenko Earth’s magnetosphere
Courtesy David Stern
- How to get its global picture?
hGp://www.bu.edu/cism/CISM_Thrusts/modelsandcoupling.html First-­‐principles modeling limita.ons: MHD Kine.c ring current models First-­‐principles approach Inner boundary condi.ons (Ionosphere) Output (B, n, v, T) Plasma model (MHD, kine.c, hybrid) Empirical approach Training output (B, database) Output (B) Model structure (divB=0, divJ=0) T≤05 and TS07D …Only Tsyganenko models? Earlier models: Mead and Fairfield [1975]; Olson and Pfitzer [1977]; Alexeev et al. [1996] Recent contribu.ons: Le et al. [2004]; Ganushkina et al. [2004]; Zaharia et al. [2005]; Yang et al. [2012] (d) -80 nT > Dst* > -100 nT
(c) -60 nT > Dst* > -80 nT
Current
Intensity
(mA/m)
100
50
Current
Intensity
(mA/m)
150
100
50
0
-50
0
-50
-100
Equatorial ring current distribu*on for different ac*vity levels [Le et al., 2004] Tsyganenko-­‐class models are freely available as open source codes TS05 model: Structure TS05 model: Input and data binning 2
α1
t1 = t1 + t1 W t1 / 1+ (W t1 /W t1c ) + t1 ( Pd /Pd 0 )
( 0)
W (t) = €
W0 +
(1)
t
∫ S(τ ) exp[r(τ − t)]dτ
0
S = aN λV β Bsγ
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€
€
( 2)
dW
= S − r(W − W 0 )
dt
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TS07 model : Spa.al structure kn = n / ρ 0
ζ = z 2 + D2
Basic idea: Magne*c field of an axisymmetric current disc [Tsyganenko, 1989] Ampereʼs equation
Solution
Finite sum
form:
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Modeling field-­‐aligned currents It is moving!
TS07D: Dynamical system approach to data mining Magnetosphere as a black box: vBz
Sym-H
Sym-­‐H index Solar wind electric field Main phase Recovery phase Burton et al. [1975]: F(vBz ,Sym − H,d ( Sym − H ) / dt) = 0
€
TS07D: Nearest neighbor method A small subset of the whole database is used to fit the model with data at the .me of interest. It consists of points that neighbor the magnetosphere at that .me in its state space. T/4=6 hours – we only consider storm scales Global parameter state space of the storm-­‐*me magnetosphere GNN(i) – nearest neighbors NN technique: April 2001 storm Sitnov et al. [2008] NN technique: April 2001 storm Sitnov et al. [2008] Nearest neighbor selec.vity NN=8000 NN algorithm provides a balance between earlier sta.s.cal models like T89, 96, 05 (NN=Ndatabase~106) and event oriented models (NN<~10). Instantaneous subsets of magne.c field data TS07D has 5 global parameters in total: <Sym-­‐H>,D<Sym-­‐H>/Dt, <vBz> plus Pdyn and .lt angle hGp://geomag_field.jhuapl.edu/model/ Hook-­‐shaped current Postmidnight current
intensification
(Brandt et al., 2002;
Ebihara and Fok, 2004)
Dayside flow-out effect
(Takahashi et al.,1990;
Ebihara and Ejiri, 1998;
Liemohn et al.1999;
Keika et al., 2004, 2005)
In TS07D tail and ring currents cons.tute the united current system and they differ only by their closure paths (through the ionosphere or the magnetopause) Ring current bifurca.on effect Nagai [1982]
TS07D captures integrated (storm-­‐scale) effects of substorms March 8-­‐11, 2008 CIR-­‐driven storm: Main phase March 8-­‐11, 2008 CIR-­‐driven storm: Recovery phase CME-­‐ and CIR-­‐driven storms compared CME-driven April 2001 storm
CIR-driven March 2008 storm
CME-­‐ and CIR-­‐driven storms compared TS07D valida.on example March 8-­‐11, 2008 magne.c storm The model accurately reconstructs the magne.c field on storm scales everywhere in the magnetosphere (note the spa.al separa.on between the spacecrar shown) TS07D valida.on: Substorm effects March 8-­‐11, 2008 magne.c storm reconstructed using TS07D model CS thinning dipolariza.on Characteris.c devia.ons of the model from THEMIS data are observed during each substorm Empirical geomagne.c field modeling: Substorms Tail current sheet thinning Kubyshkina et al. [1999, 2002, 2009, 2011] use thin current sheet module Dipolariza.on Sergeev et al., [2011] based on a new SCW module Both approaches employ classical custom-­‐tailored modules (T≤05 models) Both are missing their PRC counterparts (with Region 2-­‐sense FACs) Substorm-­‐.me magnetosphere has too many degrees of freedom to match the presently available number of observa.ons Model
TS05
TS07D
Structure
Rigid modules
Regular expansions
Data binning “Climatology”: Model Dynamical: Nearest
method
coefficients are
neighbor approach
universal functions of
the solar wind and
IMF parameters
Database
~105 points (~68%
geosynchronous)
~106 points
(weighted to provide
even distribution in
the magnetosphere)
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Adjus.ng ∂
v /∂t + ( v∇) v = ρ −1 ( j × B − ∇p)
storm .me scale €
(∂ /∂t + v∇) p = −γp∇v
equa.on of s€
tate E = −v × B + ηj
RCM equa.ons j × B = ∇p
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condi.ons €
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(∂ρ /∂t + vD∇)ηk = −ηk /τ k
j × B = ∇p
pV 5 / 3 = (2 /3)∑k ηk λk
j||nh − j||sh = Bi (B /B 2 )(∇V × ∇p)
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RUN-­‐ON-­‐REQUEST applica.on Conclusion • Modern empirical geomagne.c field modeling opens new opportuni.es in studies of the magnetosphere. • The new model, TS07D, is less dependent on assump.ons regarding the shape of magnetospheric current systems and modes of their response to solar wind driving. Therefore it allows one to infer both the geometry of the currents and their evolu.on directly from data. • This new empirical picture of the magne.c field and underlying electric currents can be used both for conven.onal applica.ons, such as par.cle tracing and mapping, and for inves.ga.on of the storm-­‐scale current morphology as well as for inges.ng addi.onal empirical informa.on into first-­‐
principles models. It looks like an elephant!
David Stern was right…