The correlation between solar and geomagnetic activity – Part 3: An integral response model

An integral response model is proposed to describe the relationship between geomagnetic activity (aa index) and solar activity (represented by sunspot number Rz): The aa at a given time t is the integral of Rz at past times (t'≤t) multiplied by an exponential decay factor of the time differences (e−(t−t')/τ), where τ is the decay time scale (~40 months). The correlation coefficient of aa with the reconstructed series based on this model (rf=0.85) is much higher than that of aa with Rz (r0=0.61). If this model is applied to each solar cycle, the correlation coefficient will be higher (rf=0.95). This model can naturally explain some phenomena related to aa and Rz, such as (i) the significant increase in the aa index (and its baseline) over the twentieth century; (ii) the longer lag times of aa to Rz at solar cycle maxima than at minima; and (iii) the variations in the correlations related to solar and Hale cycles. These results demonstrate that aa depends not only on the present Rz but also on past values. The profile of aa can be better predicted from Rz by this model than by point-point correspondence