Influence of Large-Scale Conductivity Inhomogeneities in the Atmosphere on the Global Electric Circuit

Abstract

Theoretical estimation of the influence of large-scale conductivity inhomogeneities on the global electric circuit and, in particular, on the ionospheric potential is considered. A well-posed formulation of this problem is presented, on the basis of which an approximate method is developed so as to take account of large-scale conductivity inhomogeneities. Under certain restrictions imposed on the distributions of the conductivity and the external current density, explicit approximate formulas for the ionospheric potential are derived. The approximation developed is shown to be equivalent to that of classical models of atmospheric electricity in which the atmosphere is divided into two or more columns and is replaced by a simple equivalent electric circuit. The effect of conductivity inhomogeneities located inside and outside thunderclouds is discussed and, in particular, it is demonstrated that taking account of the conductivity reduction inside thunderclouds leads to a substantial increase in the ionospheric potential. The results following from the approximate theory are compared with those obtained from direct numerical simulations. It is found that the suggested approximation qualitatively accounts for the dependence of the ionospheric potential on the parameters of the conductivity distribution, although the relative error may be significant, especially in the case of a substantial reduction in the conductivity inside thunderclouds.

Effects of conductivity perturbations in time‐dependent global electric circuit model

“…However, the reduction of conductivity inside the thundercloud can be different due to electrification processes. The effect of reduction of conductivity inside the thundercloud on ionospheric potential created from a thundercloud current dipole was recently studied by Slyunyaev et al [, Figure 5]. In our work the reduction of conductivity by a factor of 20 is used as a representative value.…”

“…A full three‐dimensional model [ Bayona et al , ], based on coupling of the continuity equation and Poisson's equation (denoted as CPM in section 2), incorporates the best horizontal resolution of 40 km. Recently, Slyunyaev et al [] compared ECM with results obtained from steady state CPM and found very good agreement under restriction that the height of the atmosphere is much smaller than the horizontal scales of the distributions of the conductivity and the external current density. Slyunyaev et al [] showed also a disagreement between ECM and CPM for horizontal scales of 5 km.…”

“…Recently, Slyunyaev et al [] compared ECM with results obtained from steady state CPM and found very good agreement under restriction that the height of the atmosphere is much smaller than the horizontal scales of the distributions of the conductivity and the external current density. Slyunyaev et al [] showed also a disagreement between ECM and CPM for horizontal scales of 5 km. As part of our present work, we present a comparison between ECM results and CPM results for horizontal scales between 5 km and hundreds of kilometers.…”

“…A thunderstorm is modeled as a current dipole at θ = 0, and conductivity perturbation is applied either in the Northern Hemisphere (same as the thunderstorm) and denoted as for 0 < θ < π /2 or in the Southern (opposite) Hemisphere and denoted as for π /2 < θ < π . The effect of high‐altitude conductivity perturbation on ionospheric potential is small [ Slyunyaev et al , ], and therefore, we exaggerate the perturbation by assuming that above the altitude 20 km are introduced instantaneously and remain constant in time. We then investigate the characteristic timescales and magnitudes of the ionospheric potential change.…”

“…If the conductivity perturbation is located outside of the source region, it can be included in the fair‐weather part of the domain, which is described by conductivity σ fw ( h , θ , φ ). The σ fw is considered as a function of horizontal coordinates θ and φ as it can be composed of several domains of sufficiently large horizontal size with horizontally independent conductivity [see Slyunyaev et al , , Figure 1].…”