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The diurnal variation of the global electric circuit (GEC) is simulated using the Weather Research and Forecasting model by estimating contributions of grid columns to the ionospheric potential (IP). A parameterization based on cutting off the grid columns with shallow convection and estimating the area covered by GEC generators (electrified clouds) in each column from the amount of precipitation yields the IP variation of the same shape as the classical Carnegie curve with a correlation coefficient of 0.97, although with a smaller peak‐to‐peak amplitude (18% against 34% of the mean) and maxima and minima shifted by 1–2 hr. It is shown that omission in the IP parameterization of either convective activity or the area covered by electrified clouds (estimated using the calculated precipitation) would result in poor similarity between the modeled IP variation and the classical Carnegie curve. The results of simulation show the best agreement with the Carnegie data during Northern Hemisphere winters; the shape of the simulated diurnal variation of the IP substantially changes throughout the year owing to the decrease of South America's contribution and the increase of Southern Asia's contribution in summer. The discrepancies between the results of modeling and the results of observations are probably caused by the limited ability of large‐scale models to differentiate between electrified and nonelectrified clouds. Further improvement of the parameterization of the IP in models of atmospheric dynamics requires using finer grids, which should allow computing microphysical characteristics of clouds and estimating source currents more accurately. Key Points: Large‐scale models of atmospheric dynamics can reproduce the shape of the global circuit diurnal variation but underestimate its amplitudeIt is important to take into account both convective activity and the area covered by electrified clouds (estimated from precipitation)Simulations better agree with measurements in Northern Hemisphere winters; South America and Southern Asia determine annual variation [ABSTRACT FROM AUTHOR]

Contributions of different land and ocean regions to the diurnal variation of the global electric circuit are simulated using the Weather Research and Forecasting model by estimating the ionospheric potential produced by thunderstorms and electrified shower clouds in each grid column. The model predicts that contributions from land regions have maxima at about 14:00–18:00 local time (LT), whereas contributions from oceans have maxima at about 2:00–6:00 LT, and different ocean regions show nearly the same relative diurnal variation. It is remarkable that contributions from ocean regions with many islands (Maritime Continent and Middle America) have maxima at both 14:00–18:00 and 2:00–6:00 LT. Key Points: Diurnal variation of the global electric circuit is simulated with the WRF model using a new parameterization of the ionospheric potentialModel predicts maximum contributions to the global electric circuit at 14:00–18:00 LT for continents and at 2:00–6:00 LT for oceansContributions from ocean regions with many islands (Maritime Continent and Middle America) have maxima at both 14:00–18:00 and 2:00–6:00 LT [ABSTRACT FROM AUTHOR]

Time-dependent and steady-state problems for the equations of the global atmospheric electric circuit are studied in the quasi-stationary approximation. Maxwell's equations in an anisotropic medium are written in terms of the electric potential; several types of boundary conditions (motivated by applications) are considered, including the analogues of the classical Dirichlet, Neumann and mixed conditions, as well as a non-standard condition relating the potential and normal current density at symmetric points on one of the boundary components. In each case the variational formulation of the problem is derived and is shown to be well-posed. Also, certain stabilisation theorems are proved for the solution of time-dependent problem in case the main parameters do not depend on time. [ABSTRACT FROM AUTHOR]

• The Madden-Julian Oscillation (MJO) affects the DC global electric circuit (GEC). • MJO-related patterns are seen in both simulations and electric field measurements. • On average, GEC parameters manifest sine-like variations with the phase of the MJO. • Regional contributions to the GEC reflect deep convection changes during MJO events. • Key GEC-reflected convection changes are over the Maritime Continent and Indian Ocean. The Madden–Julian Oscillation (MJO) is the most dominant component of the climate variability in the tropics on the timescale of tens of days. Occurring irregularly, the MJO consists of an eastward propagation of certain large-scale coupled structures in atmospheric circulation and deep convection. Here we investigate the effect of the MJO on the direct current global electric circuit (GEC), using both numerical simulations and the results of electric field measurements. We have reproduced the atmospheric dynamics for 1980–2020 with the help of the Weather Research and Forecasting model and meteorological reanalysis data; this allowed us to simulate 41 years of the GEC variation by parameterising contributions to the ionospheric potential (IP) in terms of precipitation and convection. Besides, we have analysed the results of surface potential gradient (PG) measurements at the Vostok station in Antarctica during 2006–2020. When averaged over many days, both the simulated IP and measured fair-weather PG show sinewave-like variations with the MJO phase, which manifest a statistically significant correlation with the MJO cycle. A more elaborate investigation involving an application of empirical orthogonal functions shows that the dynamics of contributions to the IP follows the patterns of variability of deep convection typical for the MJO. The variation of the IP on the MJO scale can largely be represented as a superposition of two basic oscillating patterns of convection, one of which is located over the Maritime Continent and its surrounding seas and the other is located over the Indian Ocean and part of South-East Asia. These oscillating patterns together describe the eastward progression of perturbations and can be naturally associated with the two components of the Real-time Multivariate MJO index, widely used to describe the MJO. Together with earlier results about links between the GEC and the El Niño—Southern Oscillation, the results concerning the MJO obtained in this study indicate that the GEC is an important part of the Earth system, which reflects climate variability on different timescales. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

It is known that the global electric circuit (GEC) intensity can be characterised by a single global index, namely the ionospheric potential (IP), made up of contributions from electrified clouds all over the globe. Using the Weather Research and Forecasting model, we have reproduced the atmospheric dynamics for 2008–2018 and simulated the variation of the GEC by parameterising regional contributions to the IP in terms of convection and precipitation. Considering that the El Niño—Southern Oscillation (ENSO) can be quantitatively characterised by sea surface temperatures (SSTs) in the Niño 3.4 region, this allowed us to identify and study in detail the effect of ENSO on regional contributions to the GEC. Our simulations have shown that contributions to the GEC from the land and oceanic parts of the Earth's surface respond oppositely to the ENSO cycle. The oceanic contribution is positively correlated with the Niño 3.4 SST, largely owing to increases in convection over the Pacific Ocean. In contrast to the oceans, the land contribution shows a negative correlation with ENSO due to decreases in convection over the Maritime Continent and South America. The observed correlations are statistically significant and are clearly seen on the decadal timescale; at the same time contributions to the IP for individual years do not always clearly reflect the corresponding Niño 3.4 SST anomalies. During the two El Niños and two La Niñas that occurred between 2008 and 2018, the oceanic contribution always changed in phase with ENSO, increasing in El Niño years and decreasing in La Niña years; on the other hand, the contribution of land showed a clear variation in antiphase with ENSO only for the 2015/16 El Niño and 2010/11 La Niña, characterised by extremely large SST anomalies, with a small and indefinite effect for the two lesser events. When summing the contributions of land and ocean, two strong effects of opposite signs nearly counterbalance each other and we obtain a much less pronounced effect of ENSO on the total IP. This effect is generally positive since land and ocean provide nearly equal contributions to the GEC during Northern Hemisphere winters and, according to our analysis, the contribution of ocean is slightly more sensitive to ENSO than that of land. • Simulations reveal land–ocean contrast in global electric circuit response to ENSO. • Contribution of oceans to the global circuit is positively correlated with ENSO cycle. • Contribution of land areas is, by contrast, negatively correlated with ENSO cycle. • When summing contributions over all Earth, there is a smaller positive effect of ENSO. • Key changes in convection are over the Pacific, Maritime Continent and South America. [ABSTRACT FROM AUTHOR]