Table 1.

Optimized Ḟ at the center point of the WPA

Core flows	Ḟ (nT ⋅ y−1)*
	SHAWQ2K	CALS10k.2
Unrestricted flow	−396	−397
Toroidal flow	−207	−156
Poloidal flow	−338	−365
Columnar flow	−315	−322
Reduced toroidal	−103.5	−78.0
Model	−4.0	−23.3
Auroral record	∼−100

^*Assuming core flows with the given form (left column) and based on global field models at 1590 AD according to SHAWQ2k and CALS10k.2 to spherical harmonic degree 10. The “Reduced toroidal” row contains results of a calculation with a toroidal flow constrained to be one-fourth of the kinetic energy. The rates of change derived from the smoothed global models themselves, along with the rate of change inferred from the auroral records, are given in the last rows.