Figure 1

Decade averages of geomagnetic responses to the solar wind input. Hourly values of geomagnetic (a) Dst, (b) Kp, and (c) AL indices, and (d) probability of Kp ≥4 are averaged and plotted against the modified Akasofu’s epsilon \(\epsilon ' = (4\pi /\mu _{0})\cdot \text {V}_{\textit {SW}}\cdot \text {B}_{\text {tan}}^{2}\cdot \text {sin}^{4}(\theta _{c}/2) =(4\pi /\mu _{0}) \cdot V_{\textit {SW}}\cdot (\text {B}_{\text {tan}} -\text {B}_{Z})^{2}/4\). The total energy input is estimated by multiplying square of l ₀= 7 to 10 R _E , i.e., about 3 to 5 ×10⁹ km ². Data are divided into five 10-year periods as indicated by the legend (purple lines, blue lines, dark blue lines, orange circles, and red crosses, which approximately correspond to solar cycles #20 to 24, respectively). Green pluses near the horizontal axis denote the estimated statistical errors (\(\sigma /\sqrt {(n-1)}\) where n is the number of data point and σ is the standard deviation). Representative values for each ε ^′ bin is obtained by logarithmic averaging. (e) Hourly values of geomagnetic Dst index are averaged and plotted against the solar wind proton density N _P .