On the Saturation (or Not) of Geomagnetic Indices

Most geomagnetic indices are associated with processes internal to the magnetosphere-ionosphere system: convection, magnetosphere-ionosphere current systems, particle pressure, ULF wave activity, etc. The saturation (or not) of various geomagnetic indices under various solar-wind driver functions (a.k.a. coupling functions) is explored by examining plots of the various indices as functions of the various driver functions. In comparing an index with a driver function, “saturation” of the index means that the trend of stronger geomagnetic activity with stronger driving weakens in going from mid-range driving to very strong driving. Issues explored are 1) whether the nature of the index matters (i.e., what the index measures and how the index measures it), 2) the relation of index saturation to cross-polar-cap potential saturation, and 3) the role of the choice of the solar-wind driver function. It is found that different geomagnetic indices exhibit different amounts of saturation. For example the SuperMAG auroral-electrojet indices SME, SML, and SMU saturate much less than do the auroral-electrojet indices AE, AL, and AU. Additionally it is found that different driver functions cause an index to show different degrees of saturation. Dividing a solar-wind driver function by the theoretical cross-polar-cap-potential correction (1+Q) often compensates for the saturation of an index, even though that index is associated with internal magnetospheric processes whereas Q is derived for solar-wind processes. There are composite geomagnetic indices E(1) that show no saturation when matched to their composite solar-wind driver functions S(1). When applied to other geomagnetic indices, the composite S(1) driver functions tend to compensate for index saturation at strong driving, but they also tend to introduce a nonlinearity at weak driving.