ILCT-Derived Flows are Consistent with ILCT-Derived Flows are Consistent with Induction Eqn’s Normal Component.Induction Eqn’s Normal Component.

zyxzyxz B

t

B)( v)( vvBB

Directly measuredDirectly measured Derived by ILCTDerived by ILCT

Can we extend ILCT to LOS data sets? Can we extend ILCT to LOS data sets?

0)(

zz B

t

Bu

Bvu

z

z

B

v, where

• Near disk center, we can approximate BLOS Bz.

• Use LCT to get uLCT, with LOSt to calculate uILCT that satisfies induction eqn’s normal component.

• To decompose ILCT flow, uILCT , into (vx, vy, vz), we need B at photosphere – but lack measured B!

• But we can use B from code – an educated guess for initial condition, then from current time step.

Directly measuredDirectly measured Calculated by Calculated by Boundary CodeBoundary Code

The other components can also be specified.The other components can also be specified.

Derived Derived by ILCTby ILCT

For t=0, use NLFFFFor t=0, use NLFFFextrapolation; for t>0, extrapolation; for t>0, use code’s current Buse code’s current B

at photosphere, z = 0 above photosphere, z > 0

)vv()vv(

)vv()vv(

yzyzyxyxy

xzxzxyxyx

BBz

BBxt

B

BBz

BByt

B

)vv()vv(

)vv()vv(

yzyzyxyxy

xzxzxyxyx

BBz

BBxt

B

BBz

BByt

B

Directly measuredDirectly measured Calculated by Calculated by Boundary CodeBoundary Code

Derived Derived by ILCTby ILCT

The other components can also be specified.The other components can also be specified.

For t=0, use NLFFFFor t=0, use NLFFFextrapolation; for t>0, extrapolation; for t>0, use code’s current Buse code’s current B

Extending ILCT to LOS data sets, cont’d: Extending ILCT to LOS data sets, cont’d:

• Long-duration data sets of MDI full-disk magneto- grams exist for most events in SOHO era!

• Initial B(x,y,z) can be given by combination of global PFSS model + local NLFFF consistent with X-ray/EUV observations.

• In principle, can run data-driven simulations of almost all events in SOHO era!

Induction Equation’s ComponentsInduction Equation’s Components

xzxyzxy

xzyxzyx

zyxzyxz

Bt

B

Bt

B

Bt

B

)( v)(

)( v)(

)( v)(

vvBB

vvBB

vvBB

Demoulin & Berger (Sol. Phys. 2003): Effect of Demoulin & Berger (Sol. Phys. 2003): Effect of vertical motion on apparent horizontal motion vertical motion on apparent horizontal motion UU::

Apparent horizontal motion can be either true horizontal motion, or vertical motion of a tilted field geometry.