Phase space representation of neutron monitor count rate and atmospheric electric field in relation to solar activity in cycles 21 and 22

Heliospheric modulation of galactic cosmic rays links solar cycle activity with neutron monitor count rate on earth. A less direct relation holds between neutron monitor count rate and atmospheric electric field because different atmospheric processes, including fluctuations in the ionosphere, are involved. Although a full quantitative model is still lacking, this link is supported by solid statistical evidence. Thus, a connection between the solar cycle activity and atmospheric electric field is expected. To gain a deeper insight into these relations, sunspot area (NOAA, USA), neutron monitor count rate (Climax, Colorado, USA), and atmospheric electric field (Lisbon, Portugal) are presented here in a phase space representation. The period considered covers two solar cycles (21, 22) and extends from 1978 to 1990. Two solar maxima were observed in this dataset, one in 1979 and another in 1989, as well as one solar minimum in 1986. Two main observations of the present study were: (1) similar short-term topological features of the phase space representations of the three variables, (2) a long-term phase space radius synchronization between the solar cycle activity, neutron monitor count rate, and potential gradient (confirmed by absolute correlation values above ~0.8). Finally, the methodology proposed here can be used for obtaining the relations between other atmospheric parameters (e.g., solar radiation) and solar cycle activity.