Pairs of Solar Wind-Magnetosphere Coupling Functions: Combining a Merging Term with a Pressure Term Works Best

We have investigated the behavior of 10 different characterizations of the magnetosphere, including traditional geomagnetic indices such as Kp and AE, and also using satellite based data such as global auroral power from Polar UVI, cusp latitude from DMSP, and magnetotail stretching from GOES. Multi-year data (typically a solar cycle) was studied at relatively high cadence (usually 1 hr) to provide better statistical consistency. Simple two parameters best fits to a wide variety of candidate solar wind coupling functions were considered, with no hidden variables or adjustable parameters. Previously we showed that the best performing coupling functions all were estimators of the global merging rate, with the best results from dFMP/dt =v4/3BT2/3sin8/3(tc/2). Here we investigate the best performing viscous candidates, and the best performing pairs of solar wind coupling functions, in predicting these same 10 characterizations of the magnetosphere. The top viscous functions all are closely related to the solar wind pressure, but n1/2v2 performs best, accounting for 22.3 percent of the variance, versus 14.7 for v and 12.5 for p. Altogether we considered 32 different candidate solar wind magnetosphere coupling functions, and all 32 x 32 = 1024 possible pairs of functions. Because of the large number of function pairs, some statistical fluctuations are expected. Nonetheless, certain patterns emerged. The best performing overall pair (predicting 60.6 percent of variance across all indices) was dFMP/dt coupled with n1/2v2, i.e., the best individual merging and best viscous terms make the best combination. All the top pairs consisted of one merging and one viscous term. Combining two estimators of the merging rate always has less predictive power. However any merging term, such as Bs, vBs, or EKL, when coupled with almost any pressure term, such as v, p, n1/3v2, p1/2, etc, performs reasonably well, with the merging term accounting for much the greater variance.