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

Abstract. An integral response model is proposed to describe the relationship between geomagnetic activity (aa index) and solar activity (represented by sunspot number R_z): The aa at a given time t is the integral of R_z 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 (r_f=0.85) is much higher than that of aa with R_z (r₀=0.61). If this model is applied to each solar cycle, the correlation coefficient will be higher (r_f=0.95). This model can naturally explain some phenomena related to aa and R_z, 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 R_z 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 R_z but also on past values. The profile of aa can be better predicted from R_z by this model than by point-point correspondence.